%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU356+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:27:41 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU356+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.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 : Fri Jun 20 06:51:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% 0.12/0.37 tff(related_type, type, (
% 0.12/0.37 related: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_D_10_type, type, (
% 0.12/0.37 tptp_fun_D_10: $i > $i)).
% 0.12/0.37 tff(tptp_fun_C_0_type, type, (
% 0.12/0.37 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_A_7_type, type, (
% 0.12/0.37 tptp_fun_A_7: $i)).
% 0.12/0.37 tff(tptp_fun_B_8_type, type, (
% 0.12/0.37 tptp_fun_B_8: $i)).
% 0.12/0.37 tff(element_type, type, (
% 0.12/0.37 element: ( $i * $i ) > $o)).
% 0.12/0.37 tff(the_carrier_type, type, (
% 0.12/0.37 the_carrier: $i > $i)).
% 0.12/0.37 tff(relstr_set_smaller_type, type, (
% 0.12/0.37 relstr_set_smaller: ( $i * $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_E_1_type, type, (
% 0.12/0.37 tptp_fun_E_1: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(ex_sup_of_relstr_set_type, type, (
% 0.12/0.37 ex_sup_of_relstr_set: ( $i * $i ) > $o)).
% 0.12/0.37 tff(tptp_fun_D_3_type, type, (
% 0.12/0.37 tptp_fun_D_3: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(tptp_fun_D_2_type, type, (
% 0.12/0.37 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 0.12/0.37 tff(rel_str_type, type, (
% 0.12/0.37 rel_str: $i > $o)).
% 0.12/0.37 tff(tptp_fun_C_9_type, type, (
% 0.12/0.37 tptp_fun_C_9: $i)).
% 0.12/0.37 tff(antisymmetric_relstr_type, type, (
% 0.12/0.37 antisymmetric_relstr: $i > $o)).
% 0.12/0.37 tff(1,plain,
% 0.12/0.37 (((antisymmetric_relstr(A!7) & rel_str(A!7)) & ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))))) <=> (antisymmetric_relstr(A!7) & rel_str(A!7) & (ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(2,plain,
% 0.12/0.37 (((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : (related(A!7, C!9, D) | (~relstr_set_smaller(A!7, B!8, D)) | (~element(D, the_carrier(A!7)))))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7)))))))) <=> ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))))),
% 0.12/0.37 inference(rewrite,[status(thm)],[])).
% 0.12/0.37 tff(3,plain,
% 0.12/0.37 (((antisymmetric_relstr(A!7) & rel_str(A!7)) & ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : (related(A!7, C!9, D) | (~relstr_set_smaller(A!7, B!8, D)) | (~element(D, the_carrier(A!7)))))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))))) <=> ((antisymmetric_relstr(A!7) & rel_str(A!7)) & ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7)))))))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[2])).
% 0.12/0.38 tff(4,plain,
% 0.12/0.38 (((antisymmetric_relstr(A!7) & rel_str(A!7)) & ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : (related(A!7, C!9, D) | (~relstr_set_smaller(A!7, B!8, D)) | (~element(D, the_carrier(A!7)))))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))))) <=> (antisymmetric_relstr(A!7) & rel_str(A!7) & (ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))))),
% 0.12/0.38 inference(transitivity,[status(thm)],[3, 1])).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 ((~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))) <=> (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(6,plain,
% 0.12/0.38 ((~![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))) <=> (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A))))))))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(7,axiom,(~![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : ((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t15_yellow_0')).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (~![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (antisymmetric_relstr(A!7) & rel_str(A!7) & (ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) & ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7)))))))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.12/0.38 tff(13,plain,
% 0.12/0.38 (rel_str(A!7)),
% 0.12/0.38 inference(and_elim,[status(thm)],[12])).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (^[A: $i] : refl(((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))) <=> ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(15,plain,
% 0.12/0.38 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[14])).
% 0.19/0.38 tff(16,plain,
% 0.19/0.38 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))) <=> ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(17,plain,
% 0.19/0.38 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[16])).
% 0.19/0.38 tff(18,plain,
% 0.19/0.38 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))),
% 0.19/0.38 inference(transitivity,[status(thm)],[17, 15])).
% 0.19/0.38 tff(19,plain,
% 0.19/0.38 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D))) & ![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A)))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))) <=> ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(20,plain,
% 0.19/0.38 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D))) & ![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A)))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))),
% 0.19/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.19/0.38 tff(21,plain,
% 0.19/0.38 (^[A: $i] : rewrite(((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : (related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = tptp_fun_C_0(B, A)) | (~element(D, the_carrier(A))) | ((~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & (relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : (related(A, tptp_fun_D_3(C, B, A), E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A)))))))))) <=> ((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D))) & ![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A)))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E))))))))),
% 0.19/0.38 inference(bind,[status(th)],[])).
% 0.19/0.38 tff(22,plain,
% 0.19/0.38 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : (related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = tptp_fun_C_0(B, A)) | (~element(D, the_carrier(A))) | ((~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & (relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : (related(A, tptp_fun_D_3(C, B, A), E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D))) & ![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A)))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[21])).
% 0.19/0.39 tff(23,plain,
% 0.19/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A)))))))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(24,plain,
% 0.19/0.39 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))) & ![D: $i] : (element(D, the_carrier(A)) => ((relstr_set_smaller(A, B, D) & ![E: $i] : (element(E, the_carrier(A)) => (relstr_set_smaller(A, B, E) => related(A, D, E)))) => (D = C))))) <=> (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))), (![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))) & ![D: $i] : (element(D, the_carrier(A)) => ((relstr_set_smaller(A, B, D) & ![E: $i] : (element(E, the_carrier(A)) => (relstr_set_smaller(A, B, E) => related(A, D, E)))) => (D = C))))) <=> ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))), ((rel_str(A) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))) & ![D: $i] : (element(D, the_carrier(A)) => ((relstr_set_smaller(A, B, D) & ![E: $i] : (element(E, the_carrier(A)) => (relstr_set_smaller(A, B, E) => related(A, D, E)))) => (D = C)))))) <=> (rel_str(A) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A)))))))))))), rewrite((rel_str(A) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A)))))))))) <=> ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))), ((rel_str(A) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))) & ![D: $i] : (element(D, the_carrier(A)) => ((relstr_set_smaller(A, B, D) & ![E: $i] : (element(E, the_carrier(A)) => (relstr_set_smaller(A, B, E) => related(A, D, E)))) => (D = C)))))) <=> ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))))),
% 0.19/0.39 inference(bind,[status(th)],[])).
% 0.19/0.39 tff(25,plain,
% 0.19/0.39 (![A: $i] : (rel_str(A) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))) & ![D: $i] : (element(D, the_carrier(A)) => ((relstr_set_smaller(A, B, D) & ![E: $i] : (element(E, the_carrier(A)) => (relstr_set_smaller(A, B, E) => related(A, D, E)))) => (D = C)))))) <=> ![A: $i] : ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))),
% 0.19/0.39 inference(quant_intro,[status(thm)],[24])).
% 0.19/0.39 tff(26,axiom,(![A: $i] : (rel_str(A) => ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (((element(C, the_carrier(A)) & relstr_set_smaller(A, B, C)) & ![D: $i] : (element(D, the_carrier(A)) => (relstr_set_smaller(A, B, D) => related(A, C, D)))) & ![D: $i] : (element(D, the_carrier(A)) => ((relstr_set_smaller(A, B, D) & ![E: $i] : (element(E, the_carrier(A)) => (relstr_set_smaller(A, B, E) => related(A, D, E)))) => (D = C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_yellow_0')).
% 0.19/0.39 tff(27,plain,
% 0.19/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.39 tff(28,plain,
% 0.19/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (ex_sup_of_relstr_set(A, B) <=> ?[C: $i] : (element(C, the_carrier(A)) & relstr_set_smaller(A, B, C) & ![D: $i] : (related(A, C, D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = C) | (~element(D, the_carrier(A))) | (~(relstr_set_smaller(A, B, D) & ![E: $i] : (related(A, D, E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.19/0.39 tff(29,plain,(
% 0.19/0.39 ![A: $i] : ((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : (related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)) | (~element(D, the_carrier(A)))) & ![D: $i] : ((D = tptp_fun_C_0(B, A)) | (~element(D, the_carrier(A))) | ((~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & (relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : (related(A, tptp_fun_D_3(C, B, A), E) | (~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))))))))))),
% 0.19/0.39 inference(skolemize,[status(sab)],[28])).
% 0.19/0.39 tff(30,plain,
% 0.19/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (((~ex_sup_of_relstr_set(A, B)) | (element(tptp_fun_C_0(B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_C_0(B, A)) & ![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D))) & ![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A)))))))) & (ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | ((~(tptp_fun_D_3(C, B, A) = C)) & element(tptp_fun_D_3(C, B, A), the_carrier(A)) & relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A)) & ![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.19/0.39 tff(31,plain,
% 0.19/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.19/0.39 tff(32,plain,
% 0.19/0.39 (![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))),
% 0.19/0.39 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.19/0.39 tff(33,plain,
% 0.19/0.39 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | ((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | (~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7)))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(34,plain,
% 0.19/0.39 (((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B, A!7), D) | (~relstr_set_smaller(A!7, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (D = tptp_fun_C_0(B, A!7)) | (~relstr_set_smaller(A!7, B, D)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~(related(A!7, C, tptp_fun_D_2(C, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | (~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))))) | (~((~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))))))))))) <=> ((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7)))))))))))),
% 0.19/0.39 inference(rewrite,[status(thm)],[])).
% 0.19/0.39 tff(35,plain,
% 0.19/0.39 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | ((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B, A!7), D) | (~relstr_set_smaller(A!7, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (D = tptp_fun_C_0(B, A!7)) | (~relstr_set_smaller(A!7, B, D)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~(related(A!7, C, tptp_fun_D_2(C, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | (~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))))) | (~((~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | ((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))))),
% 0.19/0.40 inference(monotonicity,[status(thm)],[34])).
% 0.19/0.40 tff(36,plain,
% 0.19/0.40 (((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | ((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B, A!7), D) | (~relstr_set_smaller(A!7, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (D = tptp_fun_C_0(B, A!7)) | (~relstr_set_smaller(A!7, B, D)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~(related(A!7, C, tptp_fun_D_2(C, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | (~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))))) | (~((~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E)))))))))))) <=> ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | (~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7)))))))))))),
% 0.19/0.40 inference(transitivity,[status(thm)],[35, 33])).
% 0.19/0.40 tff(37,plain,
% 0.19/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | ((~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B, A!7), D) | (~relstr_set_smaller(A!7, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (D = tptp_fun_C_0(B, A!7)) | (~relstr_set_smaller(A!7, B, D)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~(related(A!7, C, tptp_fun_D_2(C, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | (~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))))) | (~((~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E)))))))))))),
% 0.19/0.40 inference(quant_inst,[status(thm)],[])).
% 0.19/0.40 tff(38,plain,
% 0.19/0.40 ((~![A: $i] : ((~rel_str(A)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A, B)) | (~((~element(tptp_fun_C_0(B, A), the_carrier(A))) | (~relstr_set_smaller(A, B, tptp_fun_C_0(B, A))) | (~![D: $i] : ((~element(D, the_carrier(A))) | related(A, tptp_fun_C_0(B, A), D) | (~relstr_set_smaller(A, B, D)))) | (~![D: $i] : ((~element(D, the_carrier(A))) | (D = tptp_fun_C_0(B, A)) | (~relstr_set_smaller(A, B, D)) | (~(related(A, D, tptp_fun_E_1(D, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_E_1(D, B, A))) | (~element(tptp_fun_E_1(D, B, A), the_carrier(A))))))))))) | (~(ex_sup_of_relstr_set(A, B) | ![C: $i] : ((~element(C, the_carrier(A))) | (~relstr_set_smaller(A, B, C)) | (~(related(A, C, tptp_fun_D_2(C, B, A)) | (~relstr_set_smaller(A, B, tptp_fun_D_2(C, B, A))) | (~element(tptp_fun_D_2(C, B, A), the_carrier(A))))) | (~((~element(tptp_fun_D_3(C, B, A), the_carrier(A))) | (tptp_fun_D_3(C, B, A) = C) | (~relstr_set_smaller(A, B, tptp_fun_D_3(C, B, A))) | (~![E: $i] : ((~relstr_set_smaller(A, B, E)) | (~element(E, the_carrier(A))) | related(A, tptp_fun_D_3(C, B, A), E)))))))))))) | (~rel_str(A!7)) | ![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))),
% 0.19/0.40 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.19/0.40 tff(39,plain,
% 0.19/0.40 (![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))),
% 0.19/0.40 inference(unit_resolution,[status(thm)],[38, 32, 13])).
% 0.19/0.40 tff(40,plain,
% 0.19/0.40 (((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))))))) <=> ((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(41,plain,
% 0.19/0.41 ((~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7)))))))))) <=> (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))))))),
% 0.19/0.41 inference(rewrite,[status(thm)],[])).
% 0.19/0.41 tff(42,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))))))))))) <=> ((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))))))),
% 0.19/0.41 inference(monotonicity,[status(thm)],[41])).
% 0.19/0.41 tff(43,plain,
% 0.19/0.41 (((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))))))))))) <=> ((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))))))),
% 0.19/0.42 inference(transitivity,[status(thm)],[42, 40])).
% 0.19/0.42 tff(44,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))))))))))),
% 0.19/0.42 inference(quant_inst,[status(thm)],[])).
% 0.19/0.42 tff(45,plain,
% 0.19/0.42 ((~![B: $i] : (~((~((~ex_sup_of_relstr_set(A!7, B)) | (~((~element(tptp_fun_C_0(B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_C_0(B, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | related(A!7, tptp_fun_C_0(B, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, D)) | (D = tptp_fun_C_0(B, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B, A!7)) | (~relstr_set_smaller(A!7, B, tptp_fun_E_1(D, B, A!7))) | (~element(tptp_fun_E_1(D, B, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, C)) | (~((~element(tptp_fun_D_2(C, B, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_2(C, B, A!7))) | related(A!7, C, tptp_fun_D_2(C, B, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B, A!7), E))) | (~relstr_set_smaller(A!7, B, tptp_fun_D_3(C, B, A!7))) | (tptp_fun_D_3(C, B, A!7) = C) | (~element(tptp_fun_D_3(C, B, A!7), the_carrier(A!7))))))))))) | (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.19/0.42 tff(46,plain,
% 0.19/0.42 (~((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))))),
% 0.19/0.42 inference(unit_resolution,[status(thm)],[45, 39])).
% 0.19/0.42 tff(47,plain,
% 0.19/0.42 (((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))))) | ((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(48,plain,
% 0.19/0.43 ((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7)))))))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.43 tff(49,assumption,(~ex_sup_of_relstr_set(A!7, B!8)), introduced(assumption)).
% 0.19/0.43 tff(50,plain,
% 0.19/0.43 ((ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))))) <=> (ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(51,plain,
% 0.19/0.43 ((ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))))) <=> (ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(52,plain,
% 0.19/0.43 ((element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) <=> (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(53,plain,
% 0.19/0.43 ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) <=> (ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))))))),
% 0.19/0.43 inference(monotonicity,[status(thm)],[52])).
% 0.19/0.43 tff(54,plain,
% 0.19/0.43 ((ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) <=> (ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))))))),
% 0.19/0.43 inference(transitivity,[status(thm)],[53, 51])).
% 0.19/0.43 tff(55,plain,
% 0.19/0.43 (ex_sup_of_relstr_set(A!7, B!8) | (element(C!9, the_carrier(A!7)) & relstr_set_smaller(A!7, B!8, C!9) & ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))),
% 0.19/0.43 inference(and_elim,[status(thm)],[12])).
% 0.19/0.43 tff(56,plain,
% 0.19/0.43 (ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.19/0.43 tff(57,plain,
% 0.19/0.43 (ex_sup_of_relstr_set(A!7, B!8) | (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[56, 50])).
% 0.19/0.43 tff(58,plain,
% 0.19/0.43 (~((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[57, 49])).
% 0.19/0.43 tff(59,plain,
% 0.19/0.43 (((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) | ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(60,plain,
% 0.19/0.43 (![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[59, 58])).
% 0.19/0.43 tff(61,plain,
% 0.19/0.43 (((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) | relstr_set_smaller(A!7, B!8, C!9)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(62,plain,
% 0.19/0.43 (relstr_set_smaller(A!7, B!8, C!9)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[61, 58])).
% 0.19/0.43 tff(63,plain,
% 0.19/0.43 (((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))) | element(C!9, the_carrier(A!7))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(64,plain,
% 0.19/0.43 (element(C!9, the_carrier(A!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[63, 58])).
% 0.19/0.43 tff(65,assumption,(~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))), introduced(assumption)).
% 0.19/0.43 tff(66,plain,
% 0.19/0.43 (((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))) | ![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(67,plain,
% 0.19/0.43 (![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[66, 65])).
% 0.19/0.43 tff(68,assumption,(relstr_set_smaller(A!7, B!8, C!9)), introduced(assumption)).
% 0.19/0.43 tff(69,assumption,(element(C!9, the_carrier(A!7))), introduced(assumption)).
% 0.19/0.43 tff(70,plain,
% 0.19/0.43 (((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | ((~relstr_set_smaller(A!7, B!8, C!9)) | (~element(C!9, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9))) <=> ((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~element(C!9, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(71,plain,
% 0.19/0.43 ((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | ((~relstr_set_smaller(A!7, B!8, C!9)) | (~element(C!9, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(72,plain,
% 0.19/0.43 ((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~element(C!9, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9)),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[71, 70])).
% 0.19/0.43 tff(73,plain,
% 0.19/0.43 (related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[72, 69, 68, 67])).
% 0.19/0.43 tff(74,plain,
% 0.19/0.43 (((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))) | element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(75,plain,
% 0.19/0.43 (element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[74, 65])).
% 0.19/0.43 tff(76,plain,
% 0.19/0.43 (((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))) | relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(77,plain,
% 0.19/0.43 (relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[76, 65])).
% 0.19/0.43 tff(78,assumption,(![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))), introduced(assumption)).
% 0.19/0.43 tff(79,plain,
% 0.19/0.43 (((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | ((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(80,plain,
% 0.19/0.43 ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | ((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(81,plain,
% 0.19/0.43 ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.19/0.43 tff(82,plain,
% 0.19/0.43 (related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[81, 78, 77, 75])).
% 0.19/0.43 tff(83,plain,
% 0.19/0.43 (^[A: $i] : refl(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(84,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))),
% 0.19/0.43 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.43 tff(85,plain,
% 0.19/0.43 (^[A: $i] : rewrite(((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))))),
% 0.19/0.43 inference(bind,[status(th)],[])).
% 0.19/0.43 tff(86,plain,
% 0.19/0.43 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.44 tff(87,plain,
% 0.19/0.44 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))),
% 0.19/0.44 inference(transitivity,[status(thm)],[86, 84])).
% 0.19/0.44 tff(88,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((antisymmetric_relstr(A) & rel_str(A)) <=> (~((~antisymmetric_relstr(A)) | (~rel_str(A))))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> (~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))))), rewrite((~(~((~antisymmetric_relstr(A)) | (~rel_str(A))))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A)))), ((~(antisymmetric_relstr(A) & rel_str(A))) <=> ((~antisymmetric_relstr(A)) | (~rel_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))), (![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))) <=> (((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))))), rewrite((((~antisymmetric_relstr(A)) | (~rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))), (((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))) <=> ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(89,plain,
% 0.19/0.44 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))) <=> ![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.44 tff(90,plain,
% 0.19/0.44 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(91,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((related(A, B, C) & related(A, C, B)) => (B = C)) <=> ((~(related(A, B, C) & related(A, C, B))) | (B = C))), ((element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C))) <=> (element(C, the_carrier(A)) => ((~(related(A, B, C) & related(A, C, B))) | (B = C))))), rewrite((element(C, the_carrier(A)) => ((~(related(A, B, C) & related(A, C, B))) | (B = C))) <=> ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))), ((element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C))) <=> ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))), (![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C))) <=> ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C)))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C)))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C))))) <=> ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))))), rewrite(((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A)))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))), (((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C))))) <=> ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(92,plain,
% 0.19/0.44 (![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C))))) <=> ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.44 tff(93,axiom,(![A: $i] : ((antisymmetric_relstr(A) & rel_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => ((related(A, B, C) & related(A, C, B)) => (B = C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t25_orders_2')).
% 0.19/0.44 tff(94,plain,
% 0.19/0.44 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.19/0.44 tff(95,plain,
% 0.19/0.44 (![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[94, 90])).
% 0.19/0.44 tff(96,plain,(
% 0.19/0.44 ![A: $i] : ((~(antisymmetric_relstr(A) & rel_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~(related(A, B, C) & related(A, C, B))) | (~element(C, the_carrier(A))))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[95])).
% 0.19/0.44 tff(97,plain,
% 0.19/0.44 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.19/0.44 tff(98,plain,
% 0.19/0.44 (![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[97, 87])).
% 0.19/0.44 tff(99,plain,
% 0.19/0.44 (antisymmetric_relstr(A!7)),
% 0.19/0.44 inference(and_elim,[status(thm)],[12])).
% 0.19/0.44 tff(100,plain,
% 0.19/0.44 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | (![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))) | (~antisymmetric_relstr(A!7)) | (~rel_str(A!7)))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))) | (~antisymmetric_relstr(A!7)) | (~rel_str(A!7)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(101,plain,
% 0.19/0.44 (((~rel_str(A!7)) | (~antisymmetric_relstr(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) <=> (![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))) | (~antisymmetric_relstr(A!7)) | (~rel_str(A!7)))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(102,plain,
% 0.19/0.44 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | ((~rel_str(A!7)) | (~antisymmetric_relstr(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | (![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))) | (~antisymmetric_relstr(A!7)) | (~rel_str(A!7))))),
% 0.19/0.44 inference(monotonicity,[status(thm)],[101])).
% 0.19/0.44 tff(103,plain,
% 0.19/0.44 (((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | ((~rel_str(A!7)) | (~antisymmetric_relstr(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))))) <=> ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))) | (~antisymmetric_relstr(A!7)) | (~rel_str(A!7)))),
% 0.19/0.44 inference(transitivity,[status(thm)],[102, 100])).
% 0.19/0.44 tff(104,plain,
% 0.19/0.44 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | ((~rel_str(A!7)) | (~antisymmetric_relstr(A!7)) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))))),
% 0.19/0.44 inference(quant_inst,[status(thm)],[])).
% 0.19/0.44 tff(105,plain,
% 0.19/0.44 ((~![A: $i] : ((~rel_str(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A))) | (~related(A, B, C)) | (~related(A, C, B)))))) | ![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B)))) | (~antisymmetric_relstr(A!7)) | (~rel_str(A!7))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.19/0.44 tff(106,plain,
% 0.19/0.44 (![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))),
% 0.19/0.44 inference(unit_resolution,[status(thm)],[105, 99, 13, 98])).
% 0.19/0.44 tff(107,plain,
% 0.19/0.44 (((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | (~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(108,plain,
% 0.19/0.44 (((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((C!9 = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))) <=> ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(109,plain,
% 0.19/0.44 (((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((C!9 = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[108])).
% 0.19/0.45 tff(110,plain,
% 0.19/0.45 (((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((C!9 = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | (~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[109, 107])).
% 0.19/0.45 tff(111,plain,
% 0.19/0.45 ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | ((~element(C!9, the_carrier(A!7))) | ![C: $i] : ((C!9 = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9))))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(112,plain,
% 0.19/0.45 ((~![B: $i] : ((~element(B, the_carrier(A!7))) | ![C: $i] : ((B = C) | (~element(C, the_carrier(A!7))) | (~related(A!7, B, C)) | (~related(A!7, C, B))))) | (~element(C!9, the_carrier(A!7))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.19/0.45 tff(113,plain,
% 0.19/0.45 (![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[112, 69, 106])).
% 0.19/0.45 tff(114,plain,
% 0.19/0.45 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))) | ((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (C!9 = tptp_fun_D_3(C!9, B!8, A!7)) | (~related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))) | (~related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (C!9 = tptp_fun_D_3(C!9, B!8, A!7)) | (~related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))) | (~related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(115,plain,
% 0.19/0.45 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))) | ((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (C!9 = tptp_fun_D_3(C!9, B!8, A!7)) | (~related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))) | (~related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(116,plain,
% 0.19/0.45 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (C!9 = C) | (~related(A!7, C!9, C)) | (~related(A!7, C, C!9)))) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (C!9 = tptp_fun_D_3(C!9, B!8, A!7)) | (~related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))) | (~related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.45 tff(117,plain,
% 0.19/0.45 ((C!9 = tptp_fun_D_3(C!9, B!8, A!7)) | (~related(A!7, C!9, tptp_fun_D_3(C!9, B!8, A!7))) | (~related(A!7, tptp_fun_D_3(C!9, B!8, A!7), C!9))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[116, 113, 75])).
% 0.19/0.45 tff(118,plain,
% 0.19/0.45 (C!9 = tptp_fun_D_3(C!9, B!8, A!7)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[117, 82, 73])).
% 0.19/0.45 tff(119,plain,
% 0.19/0.45 (tptp_fun_D_3(C!9, B!8, A!7) = C!9),
% 0.19/0.45 inference(symmetry,[status(thm)],[118])).
% 0.19/0.45 tff(120,plain,
% 0.19/0.45 (((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))) | (~(tptp_fun_D_3(C!9, B!8, A!7) = C!9))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(121,plain,
% 0.19/0.45 (~(tptp_fun_D_3(C!9, B!8, A!7) = C!9)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[120, 65])).
% 0.19/0.45 tff(122,plain,
% 0.19/0.45 ($false),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[121, 119])).
% 0.19/0.45 tff(123,plain,(((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))) | (~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D)))), inference(lemma,lemma(discharge,[]))).
% 0.19/0.45 tff(124,plain,
% 0.19/0.45 ((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[123, 64, 62, 60])).
% 0.19/0.45 tff(125,plain,
% 0.19/0.45 (((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))))) | (ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(126,plain,
% 0.19/0.45 (ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[125, 46])).
% 0.19/0.45 tff(127,plain,
% 0.19/0.45 ((~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))) | ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(128,plain,
% 0.19/0.45 ((~(ex_sup_of_relstr_set(A!7, B!8) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E)))))))) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[127, 49])).
% 0.19/0.45 tff(129,plain,
% 0.19/0.45 (![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[128, 126])).
% 0.19/0.45 tff(130,plain,
% 0.19/0.45 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | (~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(131,plain,
% 0.19/0.46 (((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))))) <=> ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(132,plain,
% 0.19/0.46 ((~((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))))) <=> (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(133,plain,
% 0.19/0.46 (((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E)))))) <=> ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[132])).
% 0.19/0.46 tff(134,plain,
% 0.19/0.46 (((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E)))))) <=> ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[133, 131])).
% 0.19/0.46 tff(135,plain,
% 0.19/0.46 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[134])).
% 0.19/0.46 tff(136,plain,
% 0.19/0.46 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | (~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[135, 130])).
% 0.19/0.46 tff(137,plain,
% 0.19/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | ((~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(138,plain,
% 0.19/0.46 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~((~element(tptp_fun_D_2(C, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C, B!8, A!7))) | related(A!7, C, tptp_fun_D_2(C, B!8, A!7)))) | (~((~element(tptp_fun_D_3(C, B!8, A!7), the_carrier(A!7))) | (tptp_fun_D_3(C, B!8, A!7) = C) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C, B!8, A!7))) | (~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C, B!8, A!7), E))))))) | (~element(C!9, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C!9)) | (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.19/0.46 tff(139,plain,
% 0.19/0.46 ((~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) | (~((~![E: $i] : ((~relstr_set_smaller(A!7, B!8, E)) | (~element(E, the_carrier(A!7))) | related(A!7, tptp_fun_D_3(C!9, B!8, A!7), E))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_3(C!9, B!8, A!7))) | (tptp_fun_D_3(C!9, B!8, A!7) = C!9) | (~element(tptp_fun_D_3(C!9, B!8, A!7), the_carrier(A!7)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[138, 64, 62, 129])).
% 0.19/0.46 tff(140,plain,
% 0.19/0.46 (~((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[139, 124])).
% 0.19/0.46 tff(141,plain,
% 0.19/0.46 (((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7))) | (~related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(142,plain,
% 0.19/0.46 (~related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.19/0.46 tff(143,plain,
% 0.19/0.46 (((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7))) | relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(144,plain,
% 0.19/0.46 (relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[143, 140])).
% 0.19/0.46 tff(145,plain,
% 0.19/0.46 (((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7))) | element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(146,plain,
% 0.19/0.46 (element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[145, 140])).
% 0.19/0.46 tff(147,plain,
% 0.19/0.46 (((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | ((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | (~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(148,plain,
% 0.19/0.46 ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | ((~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7)))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(149,plain,
% 0.19/0.46 ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, C!9, D))) | (~element(tptp_fun_D_2(C!9, B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_2(C!9, B!8, A!7))) | related(A!7, C!9, tptp_fun_D_2(C!9, B!8, A!7))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.46 tff(150,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[149, 60, 146, 144, 142])).
% 0.19/0.46 tff(151,plain,(ex_sup_of_relstr_set(A!7, B!8)), inference(lemma,lemma(discharge,[]))).
% 0.19/0.46 tff(152,plain,
% 0.19/0.46 ((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7)))))))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 ((~((~ex_sup_of_relstr_set(A!7, B!8)) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))))) | (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7)))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.19/0.47 tff(154,plain,
% 0.19/0.47 (~((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7))))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[153, 48])).
% 0.19/0.47 tff(155,plain,
% 0.19/0.47 (((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7)))))))) | relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(156,plain,
% 0.19/0.47 (relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.19/0.47 tff(157,plain,
% 0.19/0.47 (((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7)))))))) | element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(158,plain,
% 0.19/0.47 (element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.19/0.47 tff(159,plain,
% 0.19/0.47 (((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) <=> ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7)))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(160,plain,
% 0.19/0.47 ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))),
% 0.19/0.47 inference(and_elim,[status(thm)],[12])).
% 0.19/0.47 tff(161,plain,
% 0.19/0.47 ((~ex_sup_of_relstr_set(A!7, B!8)) | ![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.19/0.47 tff(162,plain,
% 0.19/0.47 (![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[161, 151])).
% 0.19/0.47 tff(163,plain,
% 0.19/0.47 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | ((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | (~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(164,plain,
% 0.19/0.47 (((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~(related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7)))))) <=> ((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(165,plain,
% 0.19/0.47 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | ((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~(related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | ((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[164])).
% 0.19/0.47 tff(166,plain,
% 0.19/0.47 (((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | ((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~(related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | (~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[165, 163])).
% 0.19/0.47 tff(167,plain,
% 0.19/0.47 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | ((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~(related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(168,plain,
% 0.19/0.47 ((~![C: $i] : ((~element(C, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, C)) | (~(related(A!7, C, tptp_fun_D_10(C)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(C))) | (~element(tptp_fun_D_10(C), the_carrier(A!7))))))) | (~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.19/0.47 tff(169,plain,
% 0.19/0.47 (~((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[168, 162, 158, 156])).
% 0.19/0.47 tff(170,plain,
% 0.19/0.47 (((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(171,plain,
% 0.19/0.47 (~related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[170, 169])).
% 0.19/0.47 tff(172,plain,
% 0.19/0.47 (((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(173,plain,
% 0.19/0.47 (element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[172, 169])).
% 0.19/0.47 tff(174,plain,
% 0.19/0.47 (((~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(175,plain,
% 0.19/0.47 (relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[174, 169])).
% 0.19/0.47 tff(176,plain,
% 0.19/0.47 (((~element(tptp_fun_C_0(B!8, A!7), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_C_0(B!8, A!7))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | (D = tptp_fun_C_0(B!8, A!7)) | (~(related(A!7, D, tptp_fun_E_1(D, B!8, A!7)) | (~relstr_set_smaller(A!7, B!8, tptp_fun_E_1(D, B!8, A!7))) | (~element(tptp_fun_E_1(D, B!8, A!7), the_carrier(A!7)))))))) | ![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(177,plain,
% 0.19/0.47 (![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[176, 154])).
% 0.19/0.47 tff(178,plain,
% 0.19/0.47 (((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | ((~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))) <=> ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(179,plain,
% 0.19/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | ((~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(180,plain,
% 0.19/0.47 ((~![D: $i] : ((~element(D, the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, D)) | related(A!7, tptp_fun_C_0(B!8, A!7), D))) | (~element(tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)), the_carrier(A!7))) | (~relstr_set_smaller(A!7, B!8, tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))) | related(A!7, tptp_fun_C_0(B!8, A!7), tptp_fun_D_10(tptp_fun_C_0(B!8, A!7)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.47 tff(181,plain,
% 0.19/0.47 ($false),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[180, 177, 175, 173, 171])).
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47 % E exiting
%------------------------------------------------------------------------------