%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV864-1 : TPTP v9.0.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:36:14 AM UTC 2025
% Result : Unsatisfiable 7.26s 7.42s
% Output : Proof 7.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV864-1 : TPTP v9.0.0. Released v4.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 10:58:18 EDT 2025
% 0.12/0.34 % CPUTime :
% 7.26/7.42 % SZS status Unsatisfiable
% 7.26/7.42 % SZS output start Proof
% 7.26/7.42 tff(c_Natural_Oevalc_type, type, (
% 7.26/7.42 c_Natural_Oevalc: ( $i * $i * $i ) > $o)).
% 7.26/7.42 tff(v_xb_type, type, (
% 7.26/7.42 v_xb: $i > $i)).
% 7.26/7.42 tff(c_Com_Ocom_OSemi_type, type, (
% 7.26/7.42 c_Com_Ocom_OSemi: ( $i * $i ) > $i)).
% 7.26/7.42 tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2_type, type, (
% 7.26/7.42 v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2: $i)).
% 7.26/7.42 tff(c_Com_Ocom_OSKIP_type, type, (
% 7.26/7.42 c_Com_Ocom_OSKIP: $i)).
% 7.26/7.42 tff(v_xa_type, type, (
% 7.26/7.42 v_xa: $i)).
% 7.26/7.42 tff(v_x_type, type, (
% 7.26/7.42 v_x: $i)).
% 7.26/7.42 tff(v_c_type, type, (
% 7.26/7.42 v_c: $i)).
% 7.26/7.42 tff(t_a_type, type, (
% 7.26/7.42 t_a: $i)).
% 7.26/7.42 tff(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1_type, type, (
% 7.26/7.42 v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1: $i)).
% 7.26/7.42 tff(c_Hoare__Mirabelle_Ostate__not__singleton_type, type, (
% 7.26/7.42 c_Hoare__Mirabelle_Ostate__not__singleton: $o)).
% 7.26/7.42 tff(1,assumption,(~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa)), introduced(assumption)).
% 7.26/7.42 tff(2,plain,
% 7.26/7.42 (^[V_Z_H: $i] : refl(((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H))) <=> ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H))))),
% 7.26/7.42 inference(bind,[status(th)],[])).
% 7.26/7.42 tff(3,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H))) <=> ![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))),
% 7.26/7.42 inference(quant_intro,[status(thm)],[2])).
% 7.26/7.42 tff(4,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H))) <=> ![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(5,axiom,(![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_2')).
% 7.26/7.42 tff(6,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[5, 4])).
% 7.26/7.42 tff(7,plain,(
% 7.26/7.42 ![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))),
% 7.26/7.42 inference(skolemize,[status(sab)],[6])).
% 7.26/7.42 tff(8,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[7, 3])).
% 7.26/7.42 tff(9,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))) <=> ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(10,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(11,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[10, 9])).
% 7.26/7.42 tff(12,plain,
% 7.26/7.42 (c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[11, 8, 1])).
% 7.26/7.42 tff(13,plain,
% 7.26/7.42 (^[V_Z_H: $i] : refl(((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa)) <=> ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa)))),
% 7.26/7.42 inference(bind,[status(th)],[])).
% 7.26/7.42 tff(14,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa)) <=> ![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))),
% 7.26/7.42 inference(quant_intro,[status(thm)],[13])).
% 7.26/7.42 tff(15,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa)) <=> ![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(16,axiom,(![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_3')).
% 7.26/7.42 tff(17,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[16, 15])).
% 7.26/7.42 tff(18,plain,(
% 7.26/7.42 ![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))),
% 7.26/7.42 inference(skolemize,[status(sab)],[17])).
% 7.26/7.42 tff(19,plain,
% 7.26/7.42 (![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[18, 14])).
% 7.26/7.42 tff(20,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | ((~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa))) <=> ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | (~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(21,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | ((~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(22,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | (~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[21, 20])).
% 7.26/7.42 tff(23,plain,
% 7.26/7.42 ((~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[22, 19])).
% 7.26/7.42 tff(24,plain,
% 7.26/7.42 (~(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[23, 1])).
% 7.26/7.42 tff(25,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = c_Com_Ocom_OSemi(t_a, v_xa)) <=> (c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.42 inference(commutativity,[status(thm)],[])).
% 7.26/7.42 tff(26,assumption,(c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))), introduced(assumption)).
% 7.26/7.42 tff(27,assumption,(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa), introduced(assumption)).
% 7.26/7.42 tff(28,plain,
% 7.26/7.42 (v_xa = v_xb(c_Com_Ocom_OSemi(t_a, v_xa))),
% 7.26/7.42 inference(symmetry,[status(thm)],[27])).
% 7.26/7.42 tff(29,plain,
% 7.26/7.42 (c_Natural_Oevalc(v_c, v_x, v_xa) <=> c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[28])).
% 7.26/7.42 tff(30,plain,
% 7.26/7.42 (c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa))) <=> c_Natural_Oevalc(v_c, v_x, v_xa)),
% 7.26/7.42 inference(symmetry,[status(thm)],[29])).
% 7.26/7.42 tff(31,plain,
% 7.26/7.42 (c_Natural_Oevalc(v_c, v_x, v_xa)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[26, 30])).
% 7.26/7.42 tff(32,plain,
% 7.26/7.42 ((~c_Natural_Oevalc(v_c, v_x, v_xa)) <=> (~c_Natural_Oevalc(v_c, v_x, v_xa))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(33,axiom,(~c_Natural_Oevalc(v_c, v_x, v_xa)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_1')).
% 7.26/7.42 tff(34,plain,
% 7.26/7.42 (~c_Natural_Oevalc(v_c, v_x, v_xa)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[33, 32])).
% 7.26/7.42 tff(35,plain,
% 7.26/7.42 ($false),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[34, 31])).
% 7.26/7.42 tff(36,plain,((~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa)) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))), inference(lemma,lemma(discharge,[]))).
% 7.26/7.42 tff(37,plain,
% 7.26/7.42 (~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[36, 26])).
% 7.26/7.42 tff(38,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | ((~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa))) <=> ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | (~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(39,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | ((~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(40,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | (~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[39, 38])).
% 7.26/7.42 tff(41,plain,
% 7.26/7.42 ((~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[40, 19])).
% 7.26/7.42 tff(42,plain,
% 7.26/7.42 (~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[41, 37])).
% 7.26/7.42 tff(43,assumption,(c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))), introduced(assumption)).
% 7.26/7.42 tff(44,assumption,(~(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))), introduced(assumption)).
% 7.26/7.42 tff(45,plain,
% 7.26/7.42 (^[V_c: $i, V_u: $i, V_t: $i, V_s: $i] : refl(((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) <=> ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)))),
% 7.26/7.42 inference(bind,[status(th)],[])).
% 7.26/7.42 tff(46,plain,
% 7.26/7.42 (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) <=> ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(quant_intro,[status(thm)],[45])).
% 7.26/7.42 tff(47,plain,
% 7.26/7.42 (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) <=> ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(48,plain,
% 7.26/7.42 (^[V_c: $i, V_u: $i, V_t: $i, V_s: $i] : trans(monotonicity(rewrite(((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) <=> ((~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))), ((((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> (((~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_t))))), rewrite((((~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))), ((((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))))),
% 7.26/7.42 inference(bind,[status(th)],[])).
% 7.26/7.42 tff(49,plain,
% 7.26/7.42 (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : (((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t))) <=> ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(quant_intro,[status(thm)],[48])).
% 7.26/7.42 tff(50,axiom,(![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : (((V_u = V_t) | (~c_Natural_Oevalc(V_c, V_s, V_u))) | (~c_Natural_Oevalc(V_c, V_s, V_t)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_com__det_0')).
% 7.26/7.42 tff(51,plain,
% 7.26/7.42 (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[50, 49])).
% 7.26/7.42 tff(52,plain,
% 7.26/7.42 (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[51, 47])).
% 7.26/7.42 tff(53,plain,(
% 7.26/7.42 ![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(skolemize,[status(sab)],[52])).
% 7.26/7.42 tff(54,plain,
% 7.26/7.42 (![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[53, 46])).
% 7.26/7.42 tff(55,plain,
% 7.26/7.42 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(56,plain,
% 7.26/7.42 (((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) <=> ((v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(57,plain,
% 7.26/7.42 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[56])).
% 7.26/7.42 tff(58,plain,
% 7.26/7.42 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))))),
% 7.26/7.42 inference(transitivity,[status(thm)],[57, 55])).
% 7.26/7.42 tff(59,plain,
% 7.26/7.42 ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(60,plain,
% 7.26/7.42 ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[59, 58])).
% 7.26/7.42 tff(61,plain,
% 7.26/7.42 ($false),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[60, 54, 26, 44, 43])).
% 7.26/7.42 tff(62,plain,((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))), inference(lemma,lemma(discharge,[]))).
% 7.26/7.42 tff(63,plain,
% 7.26/7.42 (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[62, 42, 26])).
% 7.26/7.42 tff(64,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))) <=> ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(65,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(66,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_xb(c_Com_Ocom_OSemi(t_a, v_xa)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[65, 64])).
% 7.26/7.42 tff(67,plain,
% 7.26/7.42 ($false),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[66, 8, 37, 63])).
% 7.26/7.42 tff(68,plain,(~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))), inference(lemma,lemma(discharge,[]))).
% 7.26/7.42 tff(69,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((c_Com_Ocom_OSemi(t_a, v_xa) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))) <=> ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (c_Com_Ocom_OSemi(t_a, v_xa) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(70,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((c_Com_Ocom_OSemi(t_a, v_xa) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa))))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(71,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (c_Com_Ocom_OSemi(t_a, v_xa) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[70, 69])).
% 7.26/7.42 tff(72,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(t_a, v_xa) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(t_a, v_xa)))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[71, 8])).
% 7.26/7.42 tff(73,plain,
% 7.26/7.42 (c_Com_Ocom_OSemi(t_a, v_xa) = v_xa),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[72, 68])).
% 7.26/7.42 tff(74,plain,
% 7.26/7.42 (v_xa = c_Com_Ocom_OSemi(t_a, v_xa)),
% 7.26/7.42 inference(symmetry,[status(thm)],[73])).
% 7.26/7.42 tff(75,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) <=> (c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = c_Com_Ocom_OSemi(t_a, v_xa))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[74])).
% 7.26/7.42 tff(76,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) <=> (c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.42 inference(transitivity,[status(thm)],[75, 25])).
% 7.26/7.42 tff(77,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) <=> (c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa)),
% 7.26/7.42 inference(symmetry,[status(thm)],[76])).
% 7.26/7.42 tff(78,plain,
% 7.26/7.42 ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) <=> (~(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[77])).
% 7.26/7.42 tff(79,plain,
% 7.26/7.42 ((v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) <=> (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2) = v_xa)),
% 7.26/7.42 inference(commutativity,[status(thm)],[])).
% 7.26/7.42 tff(80,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2) = v_xa) <=> (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(symmetry,[status(thm)],[79])).
% 7.26/7.42 tff(81,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) <=> (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[73])).
% 7.26/7.42 tff(82,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) <=> (c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2) = v_xa)),
% 7.26/7.42 inference(transitivity,[status(thm)],[81, 79])).
% 7.26/7.42 tff(83,plain,
% 7.26/7.42 ((c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) <=> (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(transitivity,[status(thm)],[82, 80])).
% 7.26/7.42 tff(84,plain,
% 7.26/7.42 ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) <=> (~(v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[83])).
% 7.26/7.42 tff(85,assumption,(c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))), introduced(assumption)).
% 7.26/7.42 tff(86,assumption,(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa), introduced(assumption)).
% 7.26/7.42 tff(87,plain,
% 7.26/7.42 (c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)) <=> c_Natural_Oevalc(v_c, v_x, v_xa)),
% 7.26/7.42 inference(monotonicity,[status(thm)],[86])).
% 7.26/7.42 tff(88,plain,
% 7.26/7.42 (c_Natural_Oevalc(v_c, v_x, v_xa) <=> c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))),
% 7.26/7.42 inference(symmetry,[status(thm)],[87])).
% 7.26/7.42 tff(89,plain,
% 7.26/7.42 ((~c_Natural_Oevalc(v_c, v_x, v_xa)) <=> (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[88])).
% 7.26/7.42 tff(90,plain,
% 7.26/7.42 (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[34, 89])).
% 7.26/7.42 tff(91,plain,
% 7.26/7.42 ($false),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[85, 90])).
% 7.26/7.42 tff(92,plain,((~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa)) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))), inference(lemma,lemma(discharge,[]))).
% 7.26/7.42 tff(93,plain,
% 7.26/7.42 (~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[92, 85])).
% 7.26/7.42 tff(94,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | ((~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa))) <=> ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | (~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(95,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | ((~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(96,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((~(V_Z_H = v_xb(V_Z_H))) | (V_Z_H = v_xa))) | (~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[95, 94])).
% 7.26/7.42 tff(97,plain,
% 7.26/7.42 ((~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[96, 19])).
% 7.26/7.42 tff(98,plain,
% 7.26/7.42 (~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[97, 93])).
% 7.26/7.42 tff(99,assumption,(c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))), introduced(assumption)).
% 7.26/7.42 tff(100,assumption,(~(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))), introduced(assumption)).
% 7.26/7.42 tff(101,plain,
% 7.26/7.42 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(102,plain,
% 7.26/7.42 (((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) <=> ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(103,plain,
% 7.26/7.42 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[102])).
% 7.26/7.42 tff(104,plain,
% 7.26/7.42 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))))),
% 7.26/7.42 inference(transitivity,[status(thm)],[103, 101])).
% 7.26/7.42 tff(105,plain,
% 7.26/7.42 ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(106,plain,
% 7.26/7.42 ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[105, 104])).
% 7.26/7.42 tff(107,plain,
% 7.26/7.42 ($false),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[106, 54, 85, 100, 99])).
% 7.26/7.42 tff(108,plain,((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))), inference(lemma,lemma(discharge,[]))).
% 7.26/7.42 tff(109,plain,
% 7.26/7.42 (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[108, 98, 85])).
% 7.26/7.42 tff(110,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))) <=> ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(111,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(112,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[111, 110])).
% 7.26/7.42 tff(113,plain,
% 7.26/7.42 ($false),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[112, 8, 93, 109])).
% 7.26/7.42 tff(114,plain,(~c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))), inference(lemma,lemma(discharge,[]))).
% 7.26/7.42 tff(115,plain,
% 7.26/7.42 (((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))) <=> ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(116,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1)))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(117,plain,
% 7.26/7.42 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[116, 115])).
% 7.26/7.42 tff(118,plain,
% 7.26/7.42 ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[117, 8])).
% 7.26/7.42 tff(119,plain,
% 7.26/7.42 (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_xa),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[118, 114])).
% 7.26/7.42 tff(120,plain,
% 7.26/7.42 (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1),
% 7.26/7.42 inference(symmetry,[status(thm)],[119])).
% 7.26/7.42 tff(121,plain,
% 7.26/7.42 ((v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2) <=> (v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)),
% 7.26/7.42 inference(monotonicity,[status(thm)],[120])).
% 7.26/7.42 tff(122,plain,
% 7.26/7.42 ((v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2) <=> (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)),
% 7.26/7.42 inference(symmetry,[status(thm)],[121])).
% 7.26/7.42 tff(123,plain,
% 7.26/7.42 ((~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) <=> (~(v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(monotonicity,[status(thm)],[122])).
% 7.26/7.42 tff(124,plain,
% 7.26/7.42 (c_Hoare__Mirabelle_Ostate__not__singleton <=> c_Hoare__Mirabelle_Ostate__not__singleton),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(125,axiom,(c_Hoare__Mirabelle_Ostate__not__singleton), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_conjecture_0')).
% 7.26/7.42 tff(126,plain,
% 7.26/7.42 (c_Hoare__Mirabelle_Ostate__not__singleton),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 7.26/7.42 tff(127,plain,
% 7.26/7.42 (((~c_Hoare__Mirabelle_Ostate__not__singleton) | (~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) <=> ((~c_Hoare__Mirabelle_Ostate__not__singleton) | (~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(128,plain,
% 7.26/7.42 (((~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) | (~c_Hoare__Mirabelle_Ostate__not__singleton)) <=> ((~c_Hoare__Mirabelle_Ostate__not__singleton) | (~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(129,axiom,((~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) | (~c_Hoare__Mirabelle_Ostate__not__singleton)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_state__not__singleton__def_0')).
% 7.26/7.42 tff(130,plain,
% 7.26/7.42 ((~c_Hoare__Mirabelle_Ostate__not__singleton) | (~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[129, 128])).
% 7.26/7.42 tff(131,plain,
% 7.26/7.42 ((~c_Hoare__Mirabelle_Ostate__not__singleton) | (~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[130, 127])).
% 7.26/7.42 tff(132,plain,
% 7.26/7.42 (~(v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__1 = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[131, 126])).
% 7.26/7.42 tff(133,plain,
% 7.26/7.42 (~(v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[132, 123])).
% 7.26/7.42 tff(134,plain,
% 7.26/7.42 (^[V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : refl(((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)) <=> ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)))),
% 7.26/7.42 inference(bind,[status(th)],[])).
% 7.26/7.42 tff(135,plain,
% 7.26/7.42 (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)) <=> ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 7.26/7.42 inference(quant_intro,[status(thm)],[134])).
% 7.26/7.42 tff(136,plain,
% 7.26/7.42 (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H)) <=> ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(137,axiom,(![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cls_com_Osimps_I3_J_1')).
% 7.26/7.42 tff(138,plain,
% 7.26/7.42 (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[137, 136])).
% 7.26/7.42 tff(139,plain,(
% 7.26/7.42 ![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 7.26/7.42 inference(skolemize,[status(sab)],[138])).
% 7.26/7.42 tff(140,plain,
% 7.26/7.42 (![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[139, 135])).
% 7.26/7.42 tff(141,plain,
% 7.26/7.42 (((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) | (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) <=> ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) | (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.42 tff(142,plain,
% 7.26/7.42 ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) | (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(quant_inst,[status(thm)],[])).
% 7.26/7.42 tff(143,plain,
% 7.26/7.42 ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) | (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[142, 141])).
% 7.26/7.42 tff(144,plain,
% 7.26/7.42 ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) | (v_xa = v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[143, 140])).
% 7.26/7.42 tff(145,plain,
% 7.26/7.42 (~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(unit_resolution,[status(thm)],[144, 133])).
% 7.26/7.42 tff(146,plain,
% 7.26/7.42 (~(v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.42 inference(modus_ponens,[status(thm)],[145, 84])).
% 7.26/7.42 tff(147,plain,
% 7.26/7.42 (((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) | (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) <=> ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) | (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.42 inference(rewrite,[status(thm)],[])).
% 7.26/7.43 tff(148,plain,
% 7.26/7.43 ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | ((~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) | (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.43 inference(quant_inst,[status(thm)],[])).
% 7.26/7.43 tff(149,plain,
% 7.26/7.43 ((~![V_com1: $i, V_com1_H: $i, V_com2_H: $i, V_com2: $i] : ((~(c_Com_Ocom_OSemi(V_com1, V_com2) = c_Com_Ocom_OSemi(V_com1_H, V_com2_H))) | (V_com2 = V_com2_H))) | (~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) | (v_xa = c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))),
% 7.26/7.43 inference(modus_ponens,[status(thm)],[148, 147])).
% 7.26/7.43 tff(150,plain,
% 7.26/7.43 (~(c_Com_Ocom_OSemi(t_a, v_xa) = c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))),
% 7.26/7.43 inference(unit_resolution,[status(thm)],[149, 140, 146])).
% 7.26/7.43 tff(151,plain,
% 7.26/7.43 (~(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa)),
% 7.26/7.43 inference(modus_ponens,[status(thm)],[150, 78])).
% 7.26/7.43 tff(152,plain,
% 7.26/7.43 (((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) <=> ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))),
% 7.26/7.43 inference(rewrite,[status(thm)],[])).
% 7.26/7.43 tff(153,plain,
% 7.26/7.43 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | ((c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))),
% 7.26/7.43 inference(quant_inst,[status(thm)],[])).
% 7.26/7.43 tff(154,plain,
% 7.26/7.43 ((~![V_Z_H: $i] : ((V_Z_H = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(V_Z_H)))) | (c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))),
% 7.26/7.43 inference(modus_ponens,[status(thm)],[153, 152])).
% 7.26/7.43 tff(155,plain,
% 7.26/7.43 ((c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)) = v_xa) | c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))),
% 7.26/7.43 inference(unit_resolution,[status(thm)],[154, 8])).
% 7.26/7.43 tff(156,plain,
% 7.26/7.43 (c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))),
% 7.26/7.43 inference(unit_resolution,[status(thm)],[155, 151])).
% 7.26/7.43 tff(157,plain,
% 7.26/7.43 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))))),
% 7.27/7.43 inference(rewrite,[status(thm)],[])).
% 7.27/7.43 tff(158,plain,
% 7.27/7.43 (((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) <=> ((~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))))),
% 7.27/7.43 inference(rewrite,[status(thm)],[])).
% 7.27/7.43 tff(159,plain,
% 7.27/7.43 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))))),
% 7.27/7.43 inference(monotonicity,[status(thm)],[158])).
% 7.27/7.43 tff(160,plain,
% 7.27/7.43 (((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))) <=> ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))))),
% 7.27/7.43 inference(transitivity,[status(thm)],[159, 157])).
% 7.27/7.43 tff(161,plain,
% 7.27/7.43 ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | ((~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))),
% 7.27/7.43 inference(quant_inst,[status(thm)],[])).
% 7.27/7.43 tff(162,plain,
% 7.27/7.43 ((~![V_c: $i, V_u: $i, V_t: $i, V_s: $i] : ((~c_Natural_Oevalc(V_c, V_s, V_t)) | (~c_Natural_Oevalc(V_c, V_s, V_u)) | (V_u = V_t))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))) | (~c_Natural_Oevalc(v_c, v_x, v_xb(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))))),
% 7.27/7.43 inference(modus_ponens,[status(thm)],[161, 160])).
% 7.27/7.43 tff(163,plain,
% 7.27/7.43 ($false),
% 7.27/7.43 inference(unit_resolution,[status(thm)],[162, 54, 156, 24, 12])).
% 7.27/7.43 tff(164,plain,(v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))) = v_xa), inference(lemma,lemma(discharge,[]))).
% 7.27/7.43 tff(165,plain,
% 7.27/7.43 (c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))) <=> c_Natural_Oevalc(v_c, v_x, v_xa)),
% 7.27/7.43 inference(monotonicity,[status(thm)],[164])).
% 7.27/7.43 tff(166,plain,
% 7.27/7.43 (c_Natural_Oevalc(v_c, v_x, v_xa) <=> c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))),
% 7.27/7.43 inference(symmetry,[status(thm)],[165])).
% 7.27/7.43 tff(167,plain,
% 7.27/7.43 ((~c_Natural_Oevalc(v_c, v_x, v_xa)) <=> (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2)))))),
% 7.27/7.43 inference(monotonicity,[status(thm)],[166])).
% 7.27/7.43 tff(168,plain,
% 7.27/7.43 (~c_Natural_Oevalc(v_c, v_x, v_xb(c_Com_Ocom_OSemi(v_xa, c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP, v_sko__Hoare__Mirabelle__Xstate__not__singleton__def__2))))),
% 7.27/7.43 inference(modus_ponens,[status(thm)],[34, 167])).
% 7.27/7.43 tff(169,plain,
% 7.27/7.43 ($false),
% 7.27/7.43 inference(unit_resolution,[status(thm)],[156, 168])).
% 7.27/7.43 % SZS output end Proof
% 7.27/7.44 % E exiting
%------------------------------------------------------------------------------