%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC256+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:30:42 AM UTC 2025
% Result : Theorem 0.61s 0.77s
% Output : Proof 0.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC256+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 08:47:27 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.61/0.77 % SZS status Theorem
% 0.61/0.77 % SZS output start Proof
% 0.61/0.77 tff(tptp_fun_U_45_type, type, (
% 0.61/0.77 tptp_fun_U_45: $i)).
% 0.61/0.77 tff(cons_type, type, (
% 0.61/0.77 cons: ( $i * $i ) > $i)).
% 0.61/0.77 tff(nil_type, type, (
% 0.61/0.77 nil: $i)).
% 0.61/0.77 tff(ssItem_type, type, (
% 0.61/0.77 ssItem: $i > $o)).
% 0.61/0.77 tff(singletonP_type, type, (
% 0.61/0.77 singletonP: $i > $o)).
% 0.61/0.77 tff(tptp_fun_V_4_type, type, (
% 0.61/0.77 tptp_fun_V_4: $i > $i)).
% 0.61/0.77 tff(ssList_type, type, (
% 0.61/0.77 ssList: $i > $o)).
% 0.61/0.77 tff(neq_type, type, (
% 0.61/0.77 neq: ( $i * $i ) > $o)).
% 0.61/0.77 tff(tptp_fun_V_46_type, type, (
% 0.61/0.77 tptp_fun_V_46: $i)).
% 0.61/0.77 tff(tptp_fun_Y_47_type, type, (
% 0.61/0.77 tptp_fun_Y_47: $i)).
% 0.61/0.77 tff(memberP_type, type, (
% 0.61/0.77 memberP: ( $i * $i ) > $o)).
% 0.61/0.77 tff(segmentP_type, type, (
% 0.61/0.77 segmentP: ( $i * $i ) > $o)).
% 0.61/0.77 tff(1,plain,
% 0.61/0.77 ((ssList(U!45) & (ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & (~singletonP(U!45)) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & (~singletonP(U!45)) & neq(V!46, nil))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(2,plain,
% 0.61/0.77 ((ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & (~singletonP(U!45)) & neq(V!46, nil)) <=> (ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & (~singletonP(U!45)) & neq(V!46, nil))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(3,plain,
% 0.61/0.77 ((ssList(U!45) & (ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & (~singletonP(U!45)) & neq(V!46, nil))) <=> (ssList(U!45) & (ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & ssList(U!45) & (~singletonP(U!45)) & neq(V!46, nil)))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[2])).
% 0.61/0.77 tff(4,plain,
% 0.61/0.77 ((ssList(U!45) & (ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = V!46)) | (~(nil = U!45))))) & ssList(U!45) & (~singletonP(U!45)) & neq(V!46, nil))) <=> (ssList(U!45) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & (~singletonP(U!45)) & neq(V!46, nil))),
% 0.61/0.77 inference(transitivity,[status(thm)],[3, 1])).
% 0.61/0.77 tff(5,plain,
% 0.61/0.77 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(6,plain,
% 0.61/0.77 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | singletonP(U)) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil)))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(7,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | singletonP(U)) | (![Y: $i] : (ssItem(Y) => ((~(cons(Y, nil) = W)) | (~memberP(X, Y)))) & ((~(nil = X)) | (~(nil = W)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.61/0.77 tff(8,plain,
% 0.61/0.77 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.61/0.78 tff(9,plain,
% 0.61/0.78 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.61/0.78 tff(10,plain,
% 0.61/0.78 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.61/0.78 tff(11,plain,
% 0.61/0.78 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (![Y: $i] : ((~(cons(Y, nil) = U)) | (~memberP(V, Y)) | (~ssItem(Y))) & ((~(nil = V)) | (~(nil = U)))) | (~ssList(U)) | singletonP(U) | (~neq(V, nil))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.61/0.78 tff(12,plain,
% 0.61/0.78 (ssList(U!45) & ssList(V!46) & ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))) & (~singletonP(U!45)) & neq(V!46, nil)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.61/0.78 tff(13,plain,
% 0.61/0.78 (ssList(U!45)),
% 0.61/0.78 inference(and_elim,[status(thm)],[12])).
% 0.61/0.78 tff(14,plain,
% 0.61/0.78 (^[U: $i] : refl(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(15,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[14])).
% 0.61/0.78 tff(16,plain,
% 0.61/0.78 (^[U: $i] : rewrite(((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(17,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[16])).
% 0.61/0.78 tff(18,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[17, 15])).
% 0.61/0.78 tff(19,plain,
% 0.61/0.78 (^[U: $i] : rewrite(((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U)))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(20,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U)))))) <=> ![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[19])).
% 0.61/0.78 tff(21,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(22,plain,
% 0.61/0.78 (^[U: $i] : trans(monotonicity(rewrite((singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))) <=> (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))))), rewrite((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), ((ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(23,plain,
% 0.61/0.78 (![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U)))) <=> ![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[22])).
% 0.61/0.78 tff(24,axiom,(![U: $i] : (ssList(U) => (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax4')).
% 0.61/0.78 tff(25,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.61/0.78 tff(26,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (singletonP(U) <=> ?[V: $i] : (ssItem(V) & (cons(V, nil) = U))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.61/0.78 tff(27,plain,(
% 0.61/0.78 ![U: $i] : ((~ssList(U)) | (((~singletonP(U)) | (ssItem(tptp_fun_V_4(U)) & (cons(tptp_fun_V_4(U), nil) = U))) & (singletonP(U) | ![V: $i] : (~(ssItem(V) & (cons(V, nil) = U))))))),
% 0.61/0.78 inference(skolemize,[status(sab)],[26])).
% 0.61/0.78 tff(28,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.61/0.78 tff(29,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.61/0.78 tff(30,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(31,plain,
% 0.61/0.78 (((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))))))) <=> ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(32,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[31])).
% 0.61/0.78 tff(33,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))) <=> ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[32, 30])).
% 0.61/0.78 tff(34,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | ((~ssList(U!45)) | (~((~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))) | (~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(35,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | (~((~((~singletonP(U)) | (~((~ssItem(tptp_fun_V_4(U))) | (~(cons(tptp_fun_V_4(U), nil) = U)))))) | (~(singletonP(U) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U))))))))) | (~ssList(U!45)) | (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.61/0.78 tff(36,plain,
% 0.61/0.78 (~((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45)))))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[35, 29, 13])).
% 0.61/0.78 tff(37,plain,
% 0.61/0.78 (((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | (~((~singletonP(U!45)) | (~((~ssItem(tptp_fun_V_4(U!45))) | (~(cons(tptp_fun_V_4(U!45), nil) = U!45))))))) | (singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(38,plain,
% 0.61/0.78 (singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.61/0.78 tff(39,plain,
% 0.61/0.78 (~singletonP(U!45)),
% 0.61/0.78 inference(and_elim,[status(thm)],[12])).
% 0.61/0.78 tff(40,plain,
% 0.61/0.78 ((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(41,plain,
% 0.61/0.78 ((~(singletonP(U!45) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45))))) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[40, 39])).
% 0.61/0.78 tff(42,plain,
% 0.61/0.78 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.61/0.78 tff(43,plain,
% 0.61/0.78 (ssList(V!46)),
% 0.61/0.78 inference(and_elim,[status(thm)],[12])).
% 0.61/0.78 tff(44,plain,
% 0.61/0.78 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(45,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[44])).
% 0.61/0.78 tff(46,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(47,plain,
% 0.61/0.78 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(48,plain,
% 0.61/0.78 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[47])).
% 0.61/0.78 tff(49,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.61/0.78 tff(50,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.61/0.78 tff(51,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[50, 46])).
% 0.61/0.78 tff(52,plain,(
% 0.61/0.78 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(skolemize,[status(sab)],[51])).
% 0.61/0.78 tff(53,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[52, 45])).
% 0.61/0.78 tff(54,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(55,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(56,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.61/0.78 tff(57,plain,
% 0.61/0.78 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[56, 53, 43])).
% 0.61/0.78 tff(58,plain,
% 0.61/0.78 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(59,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[58])).
% 0.61/0.78 tff(60,plain,
% 0.61/0.78 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(61,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[60])).
% 0.61/0.78 tff(62,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[61, 59])).
% 0.61/0.78 tff(63,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(64,plain,
% 0.61/0.78 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(trans(rewrite((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V)))), rewrite((~((U = V) <=> neq(U, V))) <=> (~((U = V) <=> neq(U, V)))), ((neq(U, V) <=> (~(U = V))) <=> (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> (ssList(V) => (~((U = V) <=> neq(U, V)))))), rewrite((ssList(V) => (~((U = V) <=> neq(U, V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))), ((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(65,plain,
% 0.61/0.78 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[64])).
% 0.61/0.78 tff(66,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.61/0.78 tff(67,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.61/0.78 tff(68,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[67, 63])).
% 0.61/0.78 tff(69,plain,(
% 0.61/0.78 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(skolemize,[status(sab)],[68])).
% 0.61/0.78 tff(70,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.61/0.78 tff(71,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(72,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(73,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.61/0.78 tff(74,plain,
% 0.61/0.78 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[73, 70, 43])).
% 0.61/0.78 tff(75,plain,
% 0.61/0.78 (ssList(nil) <=> ssList(nil)),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(76,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.61/0.78 tff(77,plain,
% 0.61/0.78 (ssList(nil)),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.61/0.78 tff(78,plain,
% 0.61/0.78 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(79,plain,
% 0.61/0.78 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(80,plain,
% 0.61/0.78 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.61/0.78 tff(81,plain,
% 0.61/0.78 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[80, 77, 74])).
% 0.61/0.78 tff(82,plain,
% 0.61/0.78 (neq(V!46, nil)),
% 0.61/0.78 inference(and_elim,[status(thm)],[12])).
% 0.61/0.78 tff(83,plain,
% 0.61/0.78 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(84,plain,
% 0.61/0.78 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[83, 82])).
% 0.61/0.78 tff(85,plain,
% 0.61/0.78 (~(V!46 = nil)),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[84, 81])).
% 0.61/0.78 tff(86,plain,
% 0.61/0.78 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(87,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[86])).
% 0.61/0.78 tff(88,plain,
% 0.61/0.78 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(89,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[88])).
% 0.61/0.78 tff(90,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[89, 87])).
% 0.61/0.78 tff(91,plain,
% 0.61/0.78 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(92,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[91])).
% 0.61/0.78 tff(93,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(94,plain,
% 0.61/0.78 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(95,plain,
% 0.61/0.78 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[94])).
% 0.61/0.78 tff(96,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.61/0.78 tff(97,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.61/0.78 tff(98,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.61/0.78 tff(99,plain,(
% 0.61/0.78 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.61/0.78 inference(skolemize,[status(sab)],[98])).
% 0.61/0.78 tff(100,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.61/0.78 tff(101,plain,
% 0.61/0.78 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.61/0.78 tff(102,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(103,plain,
% 0.61/0.78 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(104,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[103])).
% 0.61/0.78 tff(105,plain,
% 0.61/0.78 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[104, 102])).
% 0.61/0.78 tff(106,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(107,plain,
% 0.61/0.78 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.61/0.78 tff(108,plain,
% 0.61/0.78 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[107, 101, 43])).
% 0.61/0.79 tff(109,plain,
% 0.61/0.79 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(110,plain,
% 0.61/0.79 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[109])).
% 0.61/0.79 tff(111,plain,
% 0.61/0.79 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(112,plain,
% 0.61/0.79 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(113,plain,
% 0.61/0.79 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[112])).
% 0.61/0.79 tff(114,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.61/0.79 tff(115,plain,
% 0.61/0.79 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.61/0.79 tff(116,plain,
% 0.61/0.79 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.61/0.79 tff(117,plain,(
% 0.61/0.79 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(skolemize,[status(sab)],[116])).
% 0.61/0.79 tff(118,plain,
% 0.61/0.79 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.61/0.79 tff(119,plain,
% 0.61/0.79 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(120,plain,
% 0.61/0.79 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(121,plain,
% 0.61/0.79 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.61/0.79 tff(122,plain,
% 0.61/0.79 (segmentP(V!46, nil)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[121, 118, 43])).
% 0.61/0.79 tff(123,plain,
% 0.61/0.79 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(124,plain,
% 0.61/0.79 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(125,plain,
% 0.61/0.79 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[124])).
% 0.61/0.79 tff(126,plain,
% 0.61/0.79 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[125, 123])).
% 0.61/0.79 tff(127,plain,
% 0.61/0.79 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(128,plain,
% 0.61/0.79 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.61/0.79 tff(129,plain,
% 0.61/0.79 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[128, 77, 122, 108])).
% 0.61/0.79 tff(130,plain,
% 0.61/0.79 (~segmentP(nil, V!46)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[129, 85])).
% 0.61/0.79 tff(131,plain,
% 0.61/0.79 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(132,plain,
% 0.61/0.79 (~(nil = V!46)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[131, 130, 57])).
% 0.61/0.79 tff(133,plain,
% 0.61/0.79 (((~(nil = U!45)) | (~(nil = V!46))) | (nil = V!46)),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(134,plain,
% 0.61/0.79 ((~(nil = U!45)) | (~(nil = V!46))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[133, 132])).
% 0.61/0.79 tff(135,plain,
% 0.61/0.79 ((~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))) | (~((~(nil = U!45)) | (~(nil = V!46))))),
% 0.61/0.79 inference(and_elim,[status(thm)],[12])).
% 0.61/0.79 tff(136,plain,
% 0.61/0.79 (~((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47)))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.61/0.79 tff(137,plain,
% 0.61/0.79 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | ssItem(Y!47)),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(138,plain,
% 0.61/0.79 (ssItem(Y!47)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.61/0.79 tff(139,plain,
% 0.61/0.79 (((~(cons(Y!47, nil) = U!45)) | (~memberP(V!46, Y!47)) | (~ssItem(Y!47))) | (cons(Y!47, nil) = U!45)),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(140,plain,
% 0.61/0.79 (cons(Y!47, nil) = U!45),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[139, 136])).
% 0.61/0.79 tff(141,plain,
% 0.61/0.79 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = U!45)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = U!45)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(142,plain,
% 0.61/0.79 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = U!45)))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(143,plain,
% 0.61/0.79 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = U!45)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = U!45))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.61/0.79 tff(144,plain,
% 0.61/0.79 ($false),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[143, 140, 138, 42])).
% 0.61/0.79 % SZS output end Proof
% 0.61/0.80 % E exiting
%------------------------------------------------------------------------------