%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM148+1 : TPTP v9.0.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:01:08 AM UTC 2025
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COM148+1 : TPTP v9.0.0. Released v6.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 12:24:53 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 tff(vsomeExp_type, type, (
% 0.20/0.42 vsomeExp: $i > $i)).
% 0.20/0.42 tff(vapp_type, type, (
% 0.20/0.42 vapp: ( $i * $i ) > $i)).
% 0.20/0.42 tff(ve2_type, type, (
% 0.20/0.42 ve2: $i)).
% 0.20/0.42 tff(vgetSomeExp_type, type, (
% 0.20/0.42 vgetSomeExp: $i > $i)).
% 0.20/0.42 tff(vreduce_type, type, (
% 0.20/0.42 vreduce: $i > $i)).
% 0.20/0.42 tff(ve1_type, type, (
% 0.20/0.42 ve1: $i)).
% 0.20/0.42 tff(vabs_type, type, (
% 0.20/0.42 vabs: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_VVe10_16_type, type, (
% 0.20/0.42 tptp_fun_VVe10_16: $i > $i)).
% 0.20/0.42 tff(tptp_fun_VVS0_17_type, type, (
% 0.20/0.42 tptp_fun_VVS0_17: $i > $i)).
% 0.20/0.42 tff(tptp_fun_VVx0_18_type, type, (
% 0.20/0.42 tptp_fun_VVx0_18: $i > $i)).
% 0.20/0.42 tff(tptp_fun_Ve2_48_type, type, (
% 0.20/0.42 tptp_fun_Ve2_48: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_Ve1_49_type, type, (
% 0.20/0.42 tptp_fun_Ve1_49: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_VT_52_type, type, (
% 0.20/0.42 tptp_fun_VT_52: $i)).
% 0.20/0.42 tff(vempty_type, type, (
% 0.20/0.42 vempty: $i)).
% 0.20/0.42 tff(varrow_type, type, (
% 0.20/0.42 varrow: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_VS_47_type, type, (
% 0.20/0.42 tptp_fun_VS_47: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(vtcheck_type, type, (
% 0.20/0.42 vtcheck: ( $i * $i * $i ) > $o)).
% 0.20/0.42 tff(tptp_fun_VT2_43_type, type, (
% 0.20/0.42 tptp_fun_VT2_43: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_Ve2_45_type, type, (
% 0.20/0.42 tptp_fun_Ve2_45: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(vbind_type, type, (
% 0.20/0.42 vbind: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_VT1_44_type, type, (
% 0.20/0.42 tptp_fun_VT1_44: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_Vx_46_type, type, (
% 0.20/0.42 tptp_fun_Vx_46: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(vsomeType_type, type, (
% 0.20/0.42 vsomeType: $i > $i)).
% 0.20/0.42 tff(vlookup_type, type, (
% 0.20/0.42 vlookup: ( $i * $i ) > $i)).
% 0.20/0.42 tff(tptp_fun_Vx_42_type, type, (
% 0.20/0.42 tptp_fun_Vx_42: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(vvar_type, type, (
% 0.20/0.42 vvar: $i > $i)).
% 0.20/0.42 tff(visValue_type, type, (
% 0.20/0.42 visValue: $i > $o)).
% 0.20/0.42 tff(visSomeExp_type, type, (
% 0.20/0.42 visSomeExp: $i > $o)).
% 0.20/0.42 tff(tptp_fun_Veout_51_type, type, (
% 0.20/0.42 tptp_fun_Veout_51: $i)).
% 0.20/0.42 tff(vsubst_type, type, (
% 0.20/0.42 vsubst: ( $i * $i * $i ) > $i)).
% 0.20/0.42 tff(vnoType_type, type, (
% 0.20/0.42 vnoType: $i)).
% 0.20/0.42 tff(tptp_fun_Veout_50_type, type, (
% 0.20/0.42 tptp_fun_Veout_50: $i)).
% 0.20/0.42 tff(1,plain,
% 0.20/0.42 ((vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = ve1) <=> (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)))),
% 0.20/0.42 inference(commutativity,[status(thm)],[])).
% 0.20/0.42 tff(2,plain,
% 0.20/0.42 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : refl((~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(3,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[2])).
% 0.20/0.42 tff(4,plain,
% 0.20/0.42 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : trans(monotonicity(rewrite(((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), trans(monotonicity(trans(monotonicity(rewrite(((VExp0 = VExp2) & (VExp1 = VExp3)) <=> (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> (~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), rewrite((~(~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), ((~((VExp0 = VExp2) & (VExp1 = VExp3))) <=> ((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> (((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), rewrite((((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))), (((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) <=> ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))), rewrite((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))) & ((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))), ((((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(5,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[4])).
% 0.20/0.42 tff(6,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.20/0.42 inference(rewrite,[status(thm)],[])).
% 0.20/0.42 tff(7,plain,
% 0.20/0.42 (^[VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : rewrite((((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))))),
% 0.20/0.42 inference(bind,[status(th)],[])).
% 0.20/0.42 tff(8,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3)))) <=> ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.20/0.42 inference(quant_intro,[status(thm)],[7])).
% 0.20/0.42 tff(9,axiom,(![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) => ((VExp0 = VExp2) & (VExp1 = VExp3))) & (((VExp0 = VExp2) & (VExp1 = VExp3)) => (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''EQ-app'')).
% 0.20/0.42 tff(10,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.20/0.42 tff(11,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.20/0.42 tff(12,plain,(
% 0.20/0.42 ![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | ((VExp0 = VExp2) & (VExp1 = VExp3))) & ((~((VExp0 = VExp2) & (VExp1 = VExp3))) | (vapp(VExp0, VExp1) = vapp(VExp2, VExp3))))),
% 0.20/0.42 inference(skolemize,[status(sab)],[11])).
% 0.20/0.42 tff(13,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.20/0.42 tff(14,plain,
% 0.20/0.42 (![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))),
% 0.20/0.42 inference(modus_ponens,[status(thm)],[13, 3])).
% 0.20/0.42 tff(15,plain,
% 0.20/0.42 ((~![VExp0: $i, VExp1: $i, VExp2: $i, VExp3: $i] : (~((~((~(vapp(VExp0, VExp1) = vapp(VExp2, VExp3))) | (~((~(VExp0 = VExp2)) | (~(VExp1 = VExp3)))))) | (~((vapp(VExp0, VExp1) = vapp(VExp2, VExp3)) | (~(VExp0 = VExp2)) | (~(VExp1 = VExp3))))))) | (~((~((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))))))),
% 0.20/0.42 inference(quant_inst,[status(thm)],[])).
% 0.20/0.42 tff(16,plain,
% 0.20/0.42 (~((~((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.20/0.42 tff(17,plain,
% 0.20/0.42 (((~((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))) | (~((vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)) | (~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))))) | ((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))),
% 0.20/0.42 inference(tautology,[status(thm)],[])).
% 0.20/0.42 tff(18,plain,
% 0.20/0.42 ((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))))),
% 0.20/0.42 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.20/0.42 tff(19,plain,
% 0.20/0.42 ((vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)) <=> (vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(20,plain,
% 0.20/0.43 ((~(vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) <=> (~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[19])).
% 0.20/0.43 tff(21,assumption,(vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)), introduced(assumption)).
% 0.20/0.43 tff(22,plain,
% 0.20/0.43 (^[VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : refl((~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(23,plain,
% 0.20/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.43 tff(24,plain,
% 0.20/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2))) <=> ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(25,axiom,(![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-abs-app'')).
% 0.20/0.43 tff(26,plain,
% 0.20/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[25, 24])).
% 0.20/0.43 tff(27,plain,(
% 0.20/0.43 ![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[26])).
% 0.20/0.43 tff(28,plain,
% 0.20/0.43 (![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.20/0.43 tff(29,plain,
% 0.20/0.43 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(30,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[29, 28, 21])).
% 0.20/0.43 tff(31,plain,(~(vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(32,plain,
% 0.20/0.43 (~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[31, 20])).
% 0.20/0.43 tff(33,plain,
% 0.20/0.43 (((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(34,plain,
% 0.20/0.43 ((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.20/0.43 tff(35,plain,
% 0.20/0.43 ((vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)) <=> (vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(commutativity,[status(thm)],[])).
% 0.20/0.43 tff(36,plain,
% 0.20/0.43 ((~(vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) <=> (~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.43 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.43 tff(37,assumption,(vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)), introduced(assumption)).
% 0.20/0.43 tff(38,plain,
% 0.20/0.43 (^[VVar0: $i, VExp0: $i, VExp1: $i] : refl((~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> (~(vvar(VVar0) = vapp(VExp0, VExp1))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(39,plain,
% 0.20/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.43 tff(40,plain,
% 0.20/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1))) <=> ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(41,axiom,(![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-var-app'')).
% 0.20/0.43 tff(42,plain,
% 0.20/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.20/0.43 tff(43,plain,(
% 0.20/0.43 ![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.20/0.43 inference(skolemize,[status(sab)],[42])).
% 0.20/0.43 tff(44,plain,
% 0.20/0.43 (![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.20/0.43 tff(45,plain,
% 0.20/0.43 ((~![VVar0: $i, VExp0: $i, VExp1: $i] : (~(vvar(VVar0) = vapp(VExp0, VExp1)))) | (~(vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)))),
% 0.20/0.43 inference(quant_inst,[status(thm)],[])).
% 0.20/0.43 tff(46,plain,
% 0.20/0.43 ($false),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[45, 44, 37])).
% 0.20/0.43 tff(47,plain,(~(vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.43 tff(48,plain,
% 0.20/0.43 (~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[47, 36])).
% 0.20/0.43 tff(49,plain,
% 0.20/0.43 (((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52)))) | (vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.43 inference(tautology,[status(thm)],[])).
% 0.20/0.43 tff(50,plain,
% 0.20/0.43 ((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52)))),
% 0.20/0.43 inference(unit_resolution,[status(thm)],[49, 48])).
% 0.20/0.43 tff(51,plain,
% 0.20/0.43 (((vtcheck(vempty, vapp(ve1, ve2), VT!52) & (~visValue(vapp(ve1, ve2)))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (vtcheck(vempty, vapp(ve1, ve2), VT!52) & (~visValue(vapp(ve1, ve2))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(52,plain,
% 0.20/0.43 ((~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(53,plain,
% 0.20/0.43 ((~![VT: $i] : ((vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2)))) => ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) <=> (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 0.20/0.43 inference(rewrite,[status(thm)],[])).
% 0.20/0.43 tff(54,axiom,(~![VT: $i] : ((vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2)))) => ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-app'')).
% 0.20/0.43 tff(55,plain,
% 0.20/0.43 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.43 tff(56,plain,
% 0.20/0.43 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.20/0.43 tff(57,plain,
% 0.20/0.43 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.43 tff(58,plain,
% 0.20/0.43 (~![VT: $i] : ((~(vtcheck(vempty, vapp(ve1, ve2), VT) & (~visValue(vapp(ve1, ve2))))) | ?[Veout: $i] : (vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[57, 52])).
% 0.20/0.43 tff(59,plain,
% 0.20/0.43 (vtcheck(vempty, vapp(ve1, ve2), VT!52) & (~visValue(vapp(ve1, ve2))) & ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.43 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.20/0.43 tff(60,plain,
% 0.20/0.43 (vtcheck(vempty, vapp(ve1, ve2), VT!52)),
% 0.20/0.43 inference(and_elim,[status(thm)],[59])).
% 0.20/0.43 tff(61,plain,
% 0.20/0.43 (^[Ve: $i, VT: $i, VC: $i] : refl(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))),
% 0.20/0.43 inference(bind,[status(th)],[])).
% 0.20/0.43 tff(62,plain,
% 0.20/0.43 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.20/0.43 inference(quant_intro,[status(thm)],[61])).
% 0.20/0.43 tff(63,plain,
% 0.20/0.43 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(rewrite(((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) <=> (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT)))))), rewrite(((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) <=> (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))))), rewrite(((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) <=> (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))))), rewrite(((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))), (((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(64,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.44 tff(65,plain,
% 0.20/0.44 (^[Ve: $i, VT: $i, VC: $i] : rewrite((((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(66,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[65])).
% 0.20/0.44 tff(67,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.44 inference(rewrite,[status(thm)],[])).
% 0.20/0.44 tff(68,plain,
% 0.20/0.44 (^[Ve: $i, VT: $i, VC: $i] : trans(monotonicity(trans(monotonicity(rewrite((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)))), quant_intro(proof_bind(^[Ve1: $i, Ve2: $i, VS: $i] : rewrite((((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)) <=> ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), rewrite(((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))), (((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS))))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))))), rewrite((vtcheck(VC, Ve, VT) => (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))), ((vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))))),
% 0.20/0.44 inference(bind,[status(th)],[])).
% 0.20/0.44 tff(69,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS)))) <=> ![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.44 tff(70,axiom,(![Ve: $i, VT: $i, VC: $i] : (vtcheck(VC, Ve, VT) => ((?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : (((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2))) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2))) | ?[Ve1: $i, Ve2: $i, VS: $i] : (((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT))) & vtcheck(VC, Ve2, VS))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''T-inv'')).
% 0.20/0.44 tff(71,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.20/0.44 tff(72,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : (?[Vx: $i] : ((Ve = vvar(Vx)) & (vlookup(Vx, VC) = vsomeType(VT))) | ?[Vx: $i, Ve2: $i, VT1: $i, VT2: $i] : ((Ve = vabs(Vx, VT1, Ve2)) & (VT = varrow(VT1, VT2)) & vtcheck(vbind(Vx, VT1, VC), Ve2, VT2)) | ?[Ve1: $i, Ve2: $i, VS: $i] : ((Ve = vapp(Ve1, Ve2)) & vtcheck(VC, Ve1, varrow(VS, VT)) & vtcheck(VC, Ve2, VS)) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.20/0.44 tff(73,plain,(
% 0.20/0.44 ![Ve: $i, VT: $i, VC: $i] : (((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))) | (~vtcheck(VC, Ve, VT)))),
% 0.20/0.44 inference(skolemize,[status(sab)],[72])).
% 0.20/0.44 tff(74,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | ((Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve))) & (vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))) | ((Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve))) & (VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) & vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))) | ((Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve))) & vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT)) & vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.20/0.44 tff(75,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.20/0.44 tff(76,plain,
% 0.20/0.44 (![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))),
% 0.20/0.44 inference(modus_ponens,[status(thm)],[75, 62])).
% 0.20/0.44 tff(77,plain,
% 0.20/0.44 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vempty, vapp(ve1, ve2), VT!52)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(vempty, vapp(ve1, ve2), VT!52)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.45 inference(rewrite,[status(thm)],[])).
% 0.20/0.45 tff(78,plain,
% 0.20/0.45 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vempty, vapp(ve1, ve2), VT!52)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.45 inference(quant_inst,[status(thm)],[])).
% 0.20/0.45 tff(79,plain,
% 0.20/0.45 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(vempty, vapp(ve1, ve2), VT!52)) | (~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.45 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.45 tff(80,plain,
% 0.20/0.45 ((~((~(vapp(ve1, ve2) = vvar(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2))))) | (~(vlookup(tptp_fun_Vx_42(vempty, VT!52, vapp(ve1, ve2)), vempty) = vsomeType(VT!52))))) | (~((~(vapp(ve1, ve2) = vabs(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2))))) | (~(VT!52 = varrow(tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT1_44(vempty, VT!52, vapp(ve1, ve2)), vempty), tptp_fun_Ve2_45(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VT2_43(vempty, VT!52, vapp(ve1, ve2)))))) | (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[79, 76, 60])).
% 0.20/0.45 tff(81,plain,
% 0.20/0.45 (~((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[80, 50, 34])).
% 0.20/0.45 tff(82,plain,
% 0.20/0.45 (((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))) | (vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(83,plain,
% 0.20/0.45 (vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)))),
% 0.20/0.45 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.20/0.45 tff(84,plain,
% 0.20/0.45 (vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2)),
% 0.20/0.45 inference(symmetry,[status(thm)],[83])).
% 0.20/0.45 tff(85,plain,
% 0.20/0.45 ((~((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))) | (~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))))),
% 0.20/0.45 inference(tautology,[status(thm)],[])).
% 0.20/0.45 tff(86,plain,
% 0.20/0.45 ((~((~(vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))) = vapp(ve1, ve2))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.20/0.46 tff(87,plain,
% 0.20/0.46 (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[86, 18])).
% 0.20/0.46 tff(88,plain,
% 0.20/0.46 (((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))) | (tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(89,plain,
% 0.20/0.46 (tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.20/0.46 tff(90,assumption,(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))), introduced(assumption)).
% 0.20/0.46 tff(91,plain,
% 0.20/0.46 (vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))) = tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))),
% 0.20/0.46 inference(symmetry,[status(thm)],[90])).
% 0.20/0.46 tff(92,plain,
% 0.20/0.46 (vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))) = ve1),
% 0.20/0.46 inference(transitivity,[status(thm)],[91, 89])).
% 0.20/0.46 tff(93,plain,
% 0.20/0.46 (vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2) = vapp(ve1, ve2)),
% 0.20/0.46 inference(monotonicity,[status(thm)],[92])).
% 0.20/0.46 tff(94,plain,
% 0.20/0.46 (vapp(ve1, ve2) = vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)),
% 0.20/0.46 inference(symmetry,[status(thm)],[93])).
% 0.20/0.46 tff(95,plain,
% 0.20/0.46 (vreduce(vapp(ve1, ve2)) = vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.46 tff(96,plain,
% 0.20/0.46 (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vreduce(vapp(ve1, ve2))),
% 0.20/0.46 inference(symmetry,[status(thm)],[95])).
% 0.20/0.46 tff(97,plain,
% 0.20/0.46 ((vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) <=> (vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.46 tff(98,plain,
% 0.20/0.46 ((vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) <=> (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.46 inference(symmetry,[status(thm)],[97])).
% 0.20/0.46 tff(99,plain,
% 0.20/0.46 ((~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) <=> (~(vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[98])).
% 0.20/0.46 tff(100,assumption,(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))), introduced(assumption)).
% 0.20/0.46 tff(101,plain,
% 0.20/0.46 (^[Veout: $i] : refl((~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))) <=> (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(102,plain,
% 0.20/0.46 (![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout))) <=> ![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[101])).
% 0.20/0.46 tff(103,plain,
% 0.20/0.46 (![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.46 inference(and_elim,[status(thm)],[59])).
% 0.20/0.46 tff(104,plain,
% 0.20/0.46 (![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.20/0.46 tff(105,plain,
% 0.20/0.46 ((~![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(106,plain,
% 0.20/0.46 ($false),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[105, 104, 100])).
% 0.20/0.46 tff(107,plain,(~(vreduce(vapp(ve1, ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.46 tff(108,plain,
% 0.20/0.46 (~(vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[107, 99])).
% 0.20/0.46 tff(109,plain,
% 0.20/0.46 ((vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) <=> (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2)))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[96])).
% 0.20/0.47 tff(110,plain,
% 0.20/0.47 ((vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) <=> (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2)))))),
% 0.20/0.47 inference(symmetry,[status(thm)],[109])).
% 0.20/0.47 tff(111,plain,
% 0.20/0.47 ((~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2)))))) <=> (~(vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[110])).
% 0.20/0.47 tff(112,assumption,(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))), introduced(assumption)).
% 0.20/0.47 tff(113,plain,
% 0.20/0.47 ((~![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(114,plain,
% 0.20/0.47 ($false),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[113, 104, 112])).
% 0.20/0.47 tff(115,plain,(~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.47 tff(116,plain,
% 0.20/0.47 (~(vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.20/0.47 tff(117,plain,
% 0.20/0.47 (^[Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : refl(((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2)))) <=> ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(118,plain,
% 0.20/0.47 (![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2)))) <=> ![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[117])).
% 0.20/0.47 tff(119,plain,
% 0.20/0.47 (![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2)))) <=> ![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(120,plain,
% 0.20/0.47 (![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2)))) <=> ![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.47 tff(121,plain,
% 0.20/0.47 (![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)))) <=> ![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.47 tff(122,plain,
% 0.20/0.47 (![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)))) <=> ![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[121, 120])).
% 0.20/0.47 tff(123,plain,
% 0.20/0.47 (^[Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : trans(monotonicity(trans(monotonicity(rewrite(((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))) <=> ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))), ((((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) <=> (((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))))), rewrite((((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) <=> ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))))), ((((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))) <=> ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)))))), (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => (((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))))))), rewrite(((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))))) <=> ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2))))), (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => (((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))) <=> ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(124,plain,
% 0.20/0.47 (![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => (((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))) <=> ![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[123])).
% 0.20/0.47 tff(125,plain,
% 0.20/0.47 (![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => (((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red))))))) <=> ![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[124, 122])).
% 0.20/0.47 tff(126,axiom,(![Ve2: $i, VExp0: $i, RESULT: $i, Vx: $i, VS: $i, Ve1: $i, Ve2red: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => (((Ve2red = vreduce(Ve2)) & visSomeExp(Ve2red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(Ve2red)))))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','reduce2')).
% 0.20/0.47 tff(127,plain,
% 0.20/0.47 (![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.20/0.48 tff(128,plain,
% 0.20/0.48 (![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[127, 119])).
% 0.20/0.48 tff(129,plain,(
% 0.20/0.48 ![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[128])).
% 0.20/0.48 tff(130,plain,
% 0.20/0.48 (![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[129, 118])).
% 0.20/0.48 tff(131,plain,
% 0.20/0.48 (((~![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))) | ((vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) | (~visSomeExp(vreduce(ve2))))) <=> ((~![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) | (~visSomeExp(vreduce(ve2))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(132,plain,
% 0.20/0.48 ((~![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))) | ((vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) | (~visSomeExp(vreduce(ve2))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(133,plain,
% 0.20/0.48 ((~![Ve2: $i, Vx: $i, VS: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vapp(vabs(Vx, VS, Ve1), vgetSomeExp(vreduce(Ve2))))) | (~visSomeExp(vreduce(Ve2))))) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) | (~visSomeExp(vreduce(ve2)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[132, 131])).
% 0.20/0.48 tff(134,plain,
% 0.20/0.48 ((vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), vgetSomeExp(vreduce(ve2))))) | (~visSomeExp(vreduce(ve2)))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[133, 130])).
% 0.20/0.48 tff(135,plain,
% 0.20/0.48 (~visSomeExp(vreduce(ve2))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[134, 116])).
% 0.20/0.48 tff(136,plain,
% 0.20/0.48 (^[VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : refl(((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(137,plain,
% 0.20/0.48 (![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[136])).
% 0.20/0.48 tff(138,plain,
% 0.20/0.48 (![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(139,plain,
% 0.20/0.48 (^[VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : rewrite(((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~visValue(Ve2)) | visSomeExp(vreduce(Ve2))) <=> ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(140,plain,
% 0.20/0.48 (![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~visValue(Ve2)) | visSomeExp(vreduce(Ve2))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[139])).
% 0.20/0.48 tff(141,plain,
% 0.20/0.48 (![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~visValue(Ve2)) | visSomeExp(vreduce(Ve2))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~visValue(Ve2)) | visSomeExp(vreduce(Ve2)))),
% 0.20/0.48 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.48 tff(142,plain,
% 0.20/0.48 (![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)))) <=> ![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~visValue(Ve2)) | visSomeExp(vreduce(Ve2)))),
% 0.20/0.48 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.48 tff(143,plain,
% 0.20/0.48 (![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~visValue(Ve2)) | visSomeExp(vreduce(Ve2)))),
% 0.20/0.48 inference(transitivity,[status(thm)],[142, 141])).
% 0.20/0.48 tff(144,plain,
% 0.20/0.48 (![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[143, 140])).
% 0.20/0.48 tff(145,plain,
% 0.20/0.48 (^[VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : trans(monotonicity(trans(monotonicity(rewrite((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) <=> ((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))), rewrite(((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))) <=> ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))), (((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) <=> (((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))))), rewrite((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) <=> ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))))), (((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))) <=> ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2)))))), (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))) <=> ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))))))), rewrite(((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))))) <=> ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2))))), (((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))) <=> ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(146,plain,
% 0.20/0.48 (![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))) <=> ![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))) | (~(RESULT = vreduce(VExp0))) | (~((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red)) & visValue(Ve2))) | (~(VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[145])).
% 0.20/0.48 tff(147,plain,
% 0.20/0.48 (![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1)))))) <=> ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[146, 144])).
% 0.20/0.48 tff(148,axiom,(![VS: $i, Ve2red: $i, VExp0: $i, RESULT: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((VExp0 = vapp(vabs(Vx, VS, Ve1), Ve2)) => ((((Ve2red = vreduce(Ve2)) & (~visSomeExp(Ve2red))) & visValue(Ve2)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vsubst(Vx, Ve2, Ve1))))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','reduce3')).
% 0.20/0.48 tff(149,plain,
% 0.20/0.48 (![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.48 tff(150,plain,
% 0.20/0.48 (![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[149, 138])).
% 0.20/0.48 tff(151,plain,(
% 0.20/0.48 ![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[150])).
% 0.20/0.48 tff(152,plain,
% 0.20/0.48 (![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[151, 137])).
% 0.20/0.48 tff(153,plain,
% 0.20/0.48 (((~![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ((~visValue(ve2)) | visSomeExp(vreduce(ve2)) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))) <=> ((~![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | (~visValue(ve2)) | visSomeExp(vreduce(ve2)) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(154,plain,
% 0.20/0.48 ((~![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | ((~visValue(ve2)) | visSomeExp(vreduce(ve2)) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(155,plain,
% 0.20/0.48 ((~![VS: $i, Vx: $i, Ve2: $i, Ve1: $i] : ((~visValue(Ve2)) | visSomeExp(vreduce(Ve2)) | (vreduce(vapp(vabs(Vx, VS, Ve1), Ve2)) = vsomeExp(vsubst(Vx, Ve2, Ve1))))) | (~visValue(ve2)) | visSomeExp(vreduce(ve2)) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.48 tff(156,plain,
% 0.20/0.48 ((~visValue(ve2)) | visSomeExp(vreduce(ve2)) | (vreduce(vapp(vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))), ve2)) = vsomeExp(vsubst(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), ve2, tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[155, 152])).
% 0.20/0.48 tff(157,plain,
% 0.20/0.48 (~visValue(ve2)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[156, 135, 108])).
% 0.20/0.48 tff(158,plain,
% 0.20/0.48 (((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = ve1)) | (~(tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2))) | (tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2)),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(159,plain,
% 0.20/0.48 (tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)) = ve2),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[158, 87])).
% 0.20/0.48 tff(160,plain,
% 0.20/0.48 (ve2 = tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))),
% 0.20/0.48 inference(symmetry,[status(thm)],[159])).
% 0.20/0.48 tff(161,plain,
% 0.20/0.48 (vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))) <=> vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[160])).
% 0.20/0.48 tff(162,plain,
% 0.20/0.48 (vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))) <=> vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))),
% 0.20/0.48 inference(symmetry,[status(thm)],[161])).
% 0.20/0.48 tff(163,plain,
% 0.20/0.48 (((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))) | vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[163, 81])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 (vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[164, 162])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (^[VT: $i] : refl((visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT))) <=> (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT))) <=> ![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[166])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (^[VT: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) <=> (~(visValue(ve2) | (~vtcheck(vempty, ve2, VT))))), ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) <=> (~(~(visValue(ve2) | (~vtcheck(vempty, ve2, VT))))))), rewrite((~(~(visValue(ve2) | (~vtcheck(vempty, ve2, VT))))) <=> (visValue(ve2) | (~vtcheck(vempty, ve2, VT)))), ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) <=> (visValue(ve2) | (~vtcheck(vempty, ve2, VT))))), (((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!51))) <=> ((visValue(ve2) | (~vtcheck(vempty, ve2, VT))) | (vreduce(ve2) = vsomeExp(Veout!51))))), rewrite(((visValue(ve2) | (~vtcheck(vempty, ve2, VT))) | (vreduce(ve2) = vsomeExp(Veout!51))) <=> (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))), (((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!51))) <=> (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!51))) <=> ![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (^[VT: $i] : rewrite(((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) => ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))) <=> ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 (![VT: $i] : ((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) => ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.49 tff(173,axiom,(![VT: $i] : ((vtcheck(vempty, ve2, VT) & (~visValue(ve2))) => ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-app-IH2'')).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.49 tff(175,plain,
% 0.20/0.49 (![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | ?[Veout: $i] : (vreduce(ve2) = vsomeExp(Veout)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[174, 170])).
% 0.20/0.49 tff(176,plain,(
% 0.20/0.49 ![VT: $i] : ((~(vtcheck(vempty, ve2, VT) & (~visValue(ve2)))) | (vreduce(ve2) = vsomeExp(Veout!51)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[175])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[177, 167])).
% 0.20/0.49 tff(179,plain,
% 0.20/0.49 (((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))) | (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))) <=> ((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))) | visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(180,plain,
% 0.20/0.49 ((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))) | (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(181,plain,
% 0.20/0.49 ((~![VT: $i] : (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, VT)))) | visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.20/0.49 tff(182,plain,
% 0.20/0.49 (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51)) | (~vtcheck(vempty, ve2, tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[181, 178])).
% 0.20/0.49 tff(183,plain,
% 0.20/0.49 (visValue(ve2) | (vreduce(ve2) = vsomeExp(Veout!51))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[182, 165])).
% 0.20/0.49 tff(184,plain,
% 0.20/0.49 (vreduce(ve2) = vsomeExp(Veout!51)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[183, 157])).
% 0.20/0.49 tff(185,plain,
% 0.20/0.49 (vsomeExp(Veout!51) = vreduce(ve2)),
% 0.20/0.49 inference(symmetry,[status(thm)],[184])).
% 0.20/0.49 tff(186,plain,
% 0.20/0.49 (visSomeExp(vsomeExp(Veout!51)) <=> visSomeExp(vreduce(ve2))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[185])).
% 0.20/0.49 tff(187,plain,
% 0.20/0.49 (visSomeExp(vreduce(ve2)) <=> visSomeExp(vsomeExp(Veout!51))),
% 0.20/0.49 inference(symmetry,[status(thm)],[186])).
% 0.20/0.49 tff(188,plain,
% 0.20/0.49 ((~visSomeExp(vreduce(ve2))) <=> (~visSomeExp(vsomeExp(Veout!51)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.49 tff(189,plain,
% 0.20/0.49 (~visSomeExp(vsomeExp(Veout!51))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[135, 188])).
% 0.20/0.49 tff(190,plain,
% 0.20/0.49 (^[Ve: $i] : refl(visSomeExp(vsomeExp(Ve)) <=> visSomeExp(vsomeExp(Ve)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(191,plain,
% 0.20/0.49 (![Ve: $i] : visSomeExp(vsomeExp(Ve)) <=> ![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[190])).
% 0.20/0.49 tff(192,plain,
% 0.20/0.49 (![Ve: $i] : visSomeExp(vsomeExp(Ve)) <=> ![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(193,plain,
% 0.20/0.49 (![Ve: $i, VOptExp0: $i] : visSomeExp(vsomeExp(Ve)) <=> ![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.49 tff(194,plain,
% 0.20/0.49 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))) <=> ![Ve: $i, VOptExp0: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.49 tff(195,plain,
% 0.20/0.49 (![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))) <=> ![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(transitivity,[status(thm)],[194, 193])).
% 0.20/0.49 tff(196,plain,
% 0.20/0.49 (^[Ve: $i, VOptExp0: $i] : rewrite(((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0)) <=> (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(197,plain,
% 0.20/0.49 (![Ve: $i, VOptExp0: $i] : ((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0)) <=> ![Ve: $i, VOptExp0: $i] : (visSomeExp(VOptExp0) | (~(VOptExp0 = vsomeExp(Ve))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[196])).
% 0.20/0.49 tff(198,plain,
% 0.20/0.49 (![Ve: $i, VOptExp0: $i] : ((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0)) <=> ![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(transitivity,[status(thm)],[197, 195])).
% 0.20/0.49 tff(199,axiom,(![Ve: $i, VOptExp0: $i] : ((VOptExp0 = vsomeExp(Ve)) => visSomeExp(VOptExp0))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isSomeExp1')).
% 0.20/0.49 tff(200,plain,
% 0.20/0.49 (![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.49 tff(201,plain,
% 0.20/0.49 (![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[200, 192])).
% 0.20/0.49 tff(202,plain,(
% 0.20/0.49 ![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(skolemize,[status(sab)],[201])).
% 0.20/0.49 tff(203,plain,
% 0.20/0.49 (![Ve: $i] : visSomeExp(vsomeExp(Ve))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[202, 191])).
% 0.20/0.49 tff(204,plain,
% 0.20/0.49 ((~![Ve: $i] : visSomeExp(vsomeExp(Ve))) | visSomeExp(vsomeExp(Veout!51))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(205,plain,
% 0.20/0.49 (visSomeExp(vsomeExp(Veout!51))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.20/0.49 tff(206,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[205, 189])).
% 0.20/0.49 tff(207,plain,(~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(208,plain,
% 0.20/0.49 (((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(209,plain,
% 0.20/0.49 ((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.20/0.49 tff(210,assumption,(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))), introduced(assumption)).
% 0.20/0.49 tff(211,plain,
% 0.20/0.49 (^[Vx: $i] : refl((vlookup(Vx, vempty) = vnoType) <=> (vlookup(Vx, vempty) = vnoType))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(212,plain,
% 0.20/0.49 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.49 tff(213,plain,
% 0.20/0.49 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(214,plain,
% 0.20/0.49 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (vlookup(Vx, vempty) = vnoType) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.49 tff(215,plain,
% 0.20/0.49 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty)))) <=> ![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.49 tff(216,plain,
% 0.20/0.49 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty)))) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(transitivity,[status(thm)],[215, 214])).
% 0.20/0.49 tff(217,plain,
% 0.20/0.49 (^[Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : trans(monotonicity(rewrite(((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType)) <=> ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vnoType))), ((((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> (((VVar0 = Vx) & (VCtx0 = vempty)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vnoType))))), rewrite((((VVar0 = Vx) & (VCtx0 = vempty)) => ((~(RESULT = vlookup(VVar0, VCtx0))) | (RESULT = vnoType))) <=> ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty))))), ((((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(218,plain,
% 0.20/0.49 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> ![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : ((RESULT = vnoType) | (~(RESULT = vlookup(VVar0, VCtx0))) | (~((VVar0 = Vx) & (VCtx0 = vempty))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[217])).
% 0.20/0.49 tff(219,plain,
% 0.20/0.49 (![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType))) <=> ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(transitivity,[status(thm)],[218, 216])).
% 0.20/0.49 tff(220,axiom,(![Vx: $i, VVar0: $i, VCtx0: $i, RESULT: $i] : (((VVar0 = Vx) & (VCtx0 = vempty)) => ((RESULT = vlookup(VVar0, VCtx0)) => (RESULT = vnoType)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','lookup0')).
% 0.20/0.49 tff(221,plain,
% 0.20/0.49 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.49 tff(222,plain,
% 0.20/0.49 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[221, 213])).
% 0.20/0.49 tff(223,plain,(
% 0.20/0.49 ![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(skolemize,[status(sab)],[222])).
% 0.20/0.49 tff(224,plain,
% 0.20/0.49 (![Vx: $i] : (vlookup(Vx, vempty) = vnoType)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[223, 212])).
% 0.20/0.49 tff(225,plain,
% 0.20/0.49 ((~![Vx: $i] : (vlookup(Vx, vempty) = vnoType)) | (vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vnoType)),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(226,plain,
% 0.20/0.49 (vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vnoType),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.20/0.49 tff(227,plain,
% 0.20/0.49 (vnoType = vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty)),
% 0.20/0.49 inference(symmetry,[status(thm)],[226])).
% 0.20/0.49 tff(228,plain,
% 0.20/0.49 (vnoType = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))),
% 0.20/0.49 inference(transitivity,[status(thm)],[227, 210])).
% 0.20/0.49 tff(229,plain,
% 0.20/0.49 (^[VTyp0: $i] : refl((~(vnoType = vsomeType(VTyp0))) <=> (~(vnoType = vsomeType(VTyp0))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(230,plain,
% 0.20/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[229])).
% 0.20/0.49 tff(231,plain,
% 0.20/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0))) <=> ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(232,axiom,(![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-noType-someType'')).
% 0.20/0.49 tff(233,plain,
% 0.20/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.49 tff(234,plain,(
% 0.20/0.49 ![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[233])).
% 0.20/0.49 tff(235,plain,
% 0.20/0.49 (![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.20/0.49 tff(236,plain,
% 0.20/0.49 ((~![VTyp0: $i] : (~(vnoType = vsomeType(VTyp0)))) | (~(vnoType = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(237,plain,
% 0.20/0.49 (~(vnoType = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.20/0.49 tff(238,plain,
% 0.20/0.49 ($false),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[237, 228])).
% 0.20/0.49 tff(239,plain,(~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.49 tff(240,plain,
% 0.20/0.49 (((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))))) | (vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(241,plain,
% 0.20/0.49 ((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[240, 239])).
% 0.20/0.49 tff(242,plain,
% 0.20/0.49 (((~(vapp(ve1, ve2) = vapp(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, VT!52, vapp(ve1, ve2)), tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2))))) | vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(243,plain,
% 0.20/0.49 (vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[242, 81])).
% 0.20/0.49 tff(244,plain,
% 0.20/0.49 (((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))))) <=> ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(245,plain,
% 0.20/0.50 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | ((~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(246,plain,
% 0.20/0.50 ((~![Ve: $i, VT: $i, VC: $i] : ((~vtcheck(VC, Ve, VT)) | (~((~(Ve = vvar(tptp_fun_Vx_42(VC, VT, Ve)))) | (~(vlookup(tptp_fun_Vx_42(VC, VT, Ve), VC) = vsomeType(VT))))) | (~((~(Ve = vabs(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_Ve2_45(VC, VT, Ve)))) | (~(VT = varrow(tptp_fun_VT1_44(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve)))) | (~vtcheck(vbind(tptp_fun_Vx_46(VC, VT, Ve), tptp_fun_VT1_44(VC, VT, Ve), VC), tptp_fun_Ve2_45(VC, VT, Ve), tptp_fun_VT2_43(VC, VT, Ve))))) | (~((~(Ve = vapp(tptp_fun_Ve1_49(VC, VT, Ve), tptp_fun_Ve2_48(VC, VT, Ve)))) | (~vtcheck(VC, tptp_fun_Ve1_49(VC, VT, Ve), varrow(tptp_fun_VS_47(VC, VT, Ve), VT))) | (~vtcheck(VC, tptp_fun_Ve2_48(VC, VT, Ve), tptp_fun_VS_47(VC, VT, Ve))))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.20/0.50 tff(247,plain,
% 0.20/0.50 ((~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vvar(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(vlookup(tptp_fun_Vx_42(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty) = vsomeType(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[246, 76, 243])).
% 0.20/0.50 tff(248,plain,
% 0.20/0.50 ((~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vabs(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~(varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52) = varrow(tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vbind(tptp_fun_Vx_46(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT1_44(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), vempty), tptp_fun_Ve2_45(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VT2_43(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))) | (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[247, 241])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (~((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[248, 209])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~vtcheck(vempty, tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))) | (~vtcheck(vempty, tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_VS_47(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.51 inference(tautology,[status(thm)],[])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 (tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[250, 249])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 (vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))) = tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))),
% 0.20/0.51 inference(symmetry,[status(thm)],[251])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 (vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))) = ve1),
% 0.20/0.51 inference(transitivity,[status(thm)],[252, 89])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 ((vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))) <=> (vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = ve1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[253])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 ((vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))) <=> (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[254, 1])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 ((~(vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) <=> (~(ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[255])).
% 0.20/0.51 tff(257,assumption,(vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))), introduced(assumption)).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 ((~![VVar0: $i, VTyp0: $i, VExp0: $i, VExp1: $i, VExp2: $i] : (~(vabs(VVar0, VTyp0, VExp0) = vapp(VExp1, VExp2)))) | (~(vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[258, 28, 257])).
% 0.20/0.51 tff(260,plain,(~(vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (~(ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[260, 256])).
% 0.20/0.51 tff(262,assumption,(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))), introduced(assumption)).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))) = tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))),
% 0.20/0.51 inference(symmetry,[status(thm)],[262])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 (vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))) = ve1),
% 0.20/0.51 inference(transitivity,[status(thm)],[263, 89])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 (visValue(vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))) <=> visValue(ve1)),
% 0.20/0.51 inference(monotonicity,[status(thm)],[264])).
% 0.20/0.51 tff(266,plain,
% 0.20/0.51 (visValue(ve1) <=> visValue(vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.51 inference(symmetry,[status(thm)],[265])).
% 0.20/0.51 tff(267,assumption,(visValue(ve1)), introduced(assumption)).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 (visValue(vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[267, 266])).
% 0.20/0.51 tff(269,plain,
% 0.20/0.51 (^[Ve1: $i, Ve2: $i] : refl((~visValue(vapp(Ve1, Ve2))) <=> (~visValue(vapp(Ve1, Ve2))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(270,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2))) <=> ![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[269])).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2))) <=> ![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(272,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i, VExp0: $i] : (~visValue(vapp(Ve1, Ve2))) <=> ![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.51 tff(273,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))) <=> ![Ve1: $i, Ve2: $i, VExp0: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.51 tff(274,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))) <=> ![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[273, 272])).
% 0.20/0.51 tff(275,plain,
% 0.20/0.51 (^[Ve1: $i, Ve2: $i, VExp0: $i] : rewrite(((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0))) <=> ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(276,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0))) <=> ![Ve1: $i, Ve2: $i, VExp0: $i] : ((~visValue(VExp0)) | (~(VExp0 = vapp(Ve1, Ve2))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[275])).
% 0.20/0.51 tff(277,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i, VExp0: $i] : ((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0))) <=> ![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(transitivity,[status(thm)],[276, 274])).
% 0.20/0.51 tff(278,axiom,(![Ve1: $i, Ve2: $i, VExp0: $i] : ((VExp0 = vapp(Ve1, Ve2)) => (~visValue(VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','isValue2')).
% 0.20/0.51 tff(279,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.20/0.51 tff(280,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[279, 271])).
% 0.20/0.51 tff(281,plain,(
% 0.20/0.51 ![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[280])).
% 0.20/0.51 tff(282,plain,
% 0.20/0.51 (![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[281, 270])).
% 0.20/0.51 tff(283,plain,
% 0.20/0.51 ((~![Ve1: $i, Ve2: $i] : (~visValue(vapp(Ve1, Ve2)))) | (~visValue(vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(284,plain,
% 0.20/0.51 (~visValue(vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[283, 282])).
% 0.20/0.51 tff(285,plain,
% 0.20/0.51 ($false),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[284, 268])).
% 0.20/0.51 tff(286,plain,((~(tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)) = vapp(tptp_fun_Ve1_49(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))), tptp_fun_Ve2_48(vempty, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52), tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)))))) | (~visValue(ve1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.51 tff(287,plain,
% 0.20/0.51 (~visValue(ve1)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[286, 251])).
% 0.20/0.51 tff(288,plain,
% 0.20/0.51 (ve1 = tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2))),
% 0.20/0.51 inference(symmetry,[status(thm)],[89])).
% 0.20/0.51 tff(289,plain,
% 0.20/0.51 (vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)) <=> vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[288])).
% 0.20/0.51 tff(290,plain,
% 0.20/0.51 (vtcheck(vempty, tptp_fun_Ve1_49(vempty, VT!52, vapp(ve1, ve2)), varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)) <=> vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))),
% 0.20/0.51 inference(symmetry,[status(thm)],[289])).
% 0.20/0.51 tff(291,plain,
% 0.20/0.51 (vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[243, 290])).
% 0.20/0.51 tff(292,plain,
% 0.20/0.51 (^[VT: $i] : refl((visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT))) <=> (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(293,plain,
% 0.20/0.51 (![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT))) <=> ![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[292])).
% 0.20/0.51 tff(294,plain,
% 0.20/0.51 (^[VT: $i] : trans(monotonicity(trans(monotonicity(rewrite((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) <=> (~(visValue(ve1) | (~vtcheck(vempty, ve1, VT))))), ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) <=> (~(~(visValue(ve1) | (~vtcheck(vempty, ve1, VT))))))), rewrite((~(~(visValue(ve1) | (~vtcheck(vempty, ve1, VT))))) <=> (visValue(ve1) | (~vtcheck(vempty, ve1, VT)))), ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) <=> (visValue(ve1) | (~vtcheck(vempty, ve1, VT))))), (((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!50))) <=> ((visValue(ve1) | (~vtcheck(vempty, ve1, VT))) | (vreduce(ve1) = vsomeExp(Veout!50))))), rewrite(((visValue(ve1) | (~vtcheck(vempty, ve1, VT))) | (vreduce(ve1) = vsomeExp(Veout!50))) <=> (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))), (((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!50))) <=> (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(295,plain,
% 0.20/0.51 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!50))) <=> ![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[294])).
% 0.20/0.51 tff(296,plain,
% 0.20/0.51 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(297,plain,
% 0.20/0.51 (^[VT: $i] : rewrite(((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) => ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))) <=> ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(298,plain,
% 0.20/0.51 (![VT: $i] : ((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) => ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout))) <=> ![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[297])).
% 0.20/0.51 tff(299,axiom,(![VT: $i] : ((vtcheck(vempty, ve1, VT) & (~visValue(ve1))) => ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Progress-T-app-IH1'')).
% 0.20/0.51 tff(300,plain,
% 0.20/0.51 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.20/0.51 tff(301,plain,
% 0.20/0.51 (![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | ?[Veout: $i] : (vreduce(ve1) = vsomeExp(Veout)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.20/0.51 tff(302,plain,(
% 0.20/0.51 ![VT: $i] : ((~(vtcheck(vempty, ve1, VT) & (~visValue(ve1)))) | (vreduce(ve1) = vsomeExp(Veout!50)))),
% 0.20/0.51 inference(skolemize,[status(sab)],[301])).
% 0.20/0.51 tff(303,plain,
% 0.20/0.51 (![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[302, 295])).
% 0.20/0.51 tff(304,plain,
% 0.20/0.51 (![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[303, 293])).
% 0.20/0.51 tff(305,plain,
% 0.20/0.51 (((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))) | (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))))) <=> ((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))) | visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(306,plain,
% 0.20/0.51 ((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))) | (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(307,plain,
% 0.20/0.51 ((~![VT: $i] : (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, VT)))) | visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.20/0.52 tff(308,plain,
% 0.20/0.52 (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50)) | (~vtcheck(vempty, ve1, varrow(tptp_fun_VS_47(vempty, VT!52, vapp(ve1, ve2)), VT!52)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[307, 304])).
% 0.20/0.52 tff(309,plain,
% 0.20/0.52 (visValue(ve1) | (vreduce(ve1) = vsomeExp(Veout!50))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[308, 291])).
% 0.20/0.52 tff(310,plain,
% 0.20/0.52 (vreduce(ve1) = vsomeExp(Veout!50)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[309, 287])).
% 0.20/0.52 tff(311,assumption,(vreduce(ve1) = vsomeExp(Veout!50)), introduced(assumption)).
% 0.20/0.52 tff(312,plain,
% 0.20/0.52 (vsomeExp(Veout!50) = vreduce(ve1)),
% 0.20/0.52 inference(symmetry,[status(thm)],[311])).
% 0.20/0.52 tff(313,plain,
% 0.20/0.52 (visSomeExp(vsomeExp(Veout!50)) <=> visSomeExp(vreduce(ve1))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[312])).
% 0.20/0.52 tff(314,plain,
% 0.20/0.52 (visSomeExp(vreduce(ve1)) <=> visSomeExp(vsomeExp(Veout!50))),
% 0.20/0.52 inference(symmetry,[status(thm)],[313])).
% 0.20/0.52 tff(315,plain,
% 0.20/0.52 ((~visSomeExp(vreduce(ve1))) <=> (~visSomeExp(vsomeExp(Veout!50)))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[314])).
% 0.20/0.52 tff(316,assumption,(~visSomeExp(vreduce(ve1))), introduced(assumption)).
% 0.20/0.52 tff(317,plain,
% 0.20/0.52 (~visSomeExp(vsomeExp(Veout!50))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.20/0.52 tff(318,plain,
% 0.20/0.52 ((~![Ve: $i] : visSomeExp(vsomeExp(Ve))) | visSomeExp(vsomeExp(Veout!50))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(319,plain,
% 0.20/0.52 (visSomeExp(vsomeExp(Veout!50))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[318, 203])).
% 0.20/0.52 tff(320,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[319, 317])).
% 0.20/0.52 tff(321,plain,((~(vreduce(ve1) = vsomeExp(Veout!50))) | visSomeExp(vreduce(ve1))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.52 tff(322,plain,
% 0.20/0.52 (visSomeExp(vreduce(ve1))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[321, 310])).
% 0.20/0.52 tff(323,plain,
% 0.20/0.52 (^[Ve1: $i, Ve2: $i] : refl(((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1)))) <=> ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(324,plain,
% 0.20/0.52 (![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1)))) <=> ![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[323])).
% 0.20/0.52 tff(325,plain,
% 0.20/0.52 (![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))) <=> ![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(326,plain,
% 0.20/0.52 (^[Ve1: $i, Ve2: $i] : trans(monotonicity(rewrite((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) <=> (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))), (((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1)))) <=> ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1)))))), rewrite(((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1)))) <=> ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))), (((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1)))) <=> ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(327,plain,
% 0.20/0.52 (![Ve1: $i, Ve2: $i] : ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1)))) <=> ![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[326])).
% 0.20/0.52 tff(328,plain,
% 0.20/0.52 (![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1)))) <=> ![Ve1: $i, Ve2: $i] : ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1))))),
% 0.20/0.52 inference(elim_unused_vars,[status(thm)],[])).
% 0.20/0.52 tff(329,plain,
% 0.20/0.52 (![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))) | (~((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))) <=> ![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1))))),
% 0.20/0.52 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.20/0.52 tff(330,plain,
% 0.20/0.52 (![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))) | (~((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))) <=> ![Ve1: $i, Ve2: $i] : ((~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~visSomeExp(vreduce(Ve1))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[329, 328])).
% 0.20/0.52 tff(331,plain,
% 0.20/0.52 (![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))) | (~((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))) <=> ![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[330, 327])).
% 0.20/0.52 tff(332,plain,
% 0.20/0.52 (^[Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : trans(monotonicity(rewrite(((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) <=> ((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))), trans(monotonicity(rewrite(((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))) <=> ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))), ((((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) <=> (((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))))), rewrite((((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) <=> ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))))), ((((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))) <=> ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)))))), ((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => (((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))) <=> (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))))))), rewrite((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))))) <=> ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))) | (~((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))))), ((((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => (((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))) <=> ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))) | (~((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(333,plain,
% 0.20/0.52 (![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => (((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))) <=> ![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : ((RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))) | (~(RESULT = vreduce(VExp0))) | (~((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red))) | (~((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10))))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[332])).
% 0.20/0.52 tff(334,plain,
% 0.20/0.52 (![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => (((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2)))))) <=> ![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[333, 331])).
% 0.20/0.52 tff(335,axiom,(![Ve1: $i, VExp0: $i, RESULT: $i, Ve1red: $i, Ve2: $i] : (((VExp0 = vapp(Ve1, Ve2)) & ![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))) => (((Ve1red = vreduce(Ve1)) & visSomeExp(Ve1red)) => ((RESULT = vreduce(VExp0)) => (RESULT = vsomeExp(vapp(vgetSomeExp(Ve1red), Ve2))))))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','reduce5')).
% 0.20/0.52 tff(336,plain,
% 0.20/0.52 (![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.20/0.52 tff(337,plain,
% 0.20/0.52 (![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (~![VVx0: $i, VVS0: $i, VVe10: $i] : (~(Ve1 = vabs(VVx0, VVS0, VVe10)))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[336, 325])).
% 0.20/0.52 tff(338,plain,(
% 0.20/0.52 ![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[337])).
% 0.20/0.52 tff(339,plain,
% 0.20/0.52 (![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[338, 324])).
% 0.20/0.52 tff(340,plain,
% 0.20/0.52 (((~![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))) | ((~visSomeExp(vreduce(ve1))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))) | (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1))))) <=> ((~![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))) | (~visSomeExp(vreduce(ve1))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))) | (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(341,plain,
% 0.20/0.52 ((~![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))) | ((~visSomeExp(vreduce(ve1))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))) | (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(342,plain,
% 0.20/0.52 ((~![Ve1: $i, Ve2: $i] : ((~visSomeExp(vreduce(Ve1))) | (vreduce(vapp(Ve1, Ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(Ve1)), Ve2))) | (Ve1 = vabs(tptp_fun_VVx0_18(Ve1), tptp_fun_VVS0_17(Ve1), tptp_fun_VVe10_16(Ve1))))) | (~visSomeExp(vreduce(ve1))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))) | (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.20/0.52 tff(343,plain,
% 0.20/0.52 ((~visSomeExp(vreduce(ve1))) | (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))) | (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[342, 339])).
% 0.20/0.52 tff(344,plain,
% 0.20/0.52 ((vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))) | (ve1 = vabs(tptp_fun_VVx0_18(ve1), tptp_fun_VVS0_17(ve1), tptp_fun_VVe10_16(ve1)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[343, 322])).
% 0.20/0.52 tff(345,plain,
% 0.20/0.52 (vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[344, 261])).
% 0.20/0.52 tff(346,plain,
% 0.20/0.52 ((~![Veout: $i] : (~(vreduce(vapp(ve1, ve2)) = vsomeExp(Veout)))) | (~(vreduce(vapp(ve1, ve2)) = vsomeExp(vapp(vgetSomeExp(vreduce(ve1)), ve2))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(347,plain,
% 0.20/0.52 ($false),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[346, 104, 345])).
% 0.20/0.52 % SZS output end Proof
% 0.20/0.53 % E exiting
%------------------------------------------------------------------------------