%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC013+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:29:55 AM UTC 2025
% Result : Theorem 0.57s 0.75s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWC013+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.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 08:00:39 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.57/0.75 % SZS status Theorem
% 0.57/0.75 % SZS output start Proof
% 0.57/0.75 tff(ssItem_type, type, (
% 0.57/0.75 ssItem: $i > $o)).
% 0.57/0.75 tff(hd_type, type, (
% 0.57/0.75 hd: $i > $i)).
% 0.57/0.75 tff(tptp_fun_V_46_type, type, (
% 0.57/0.75 tptp_fun_V_46: $i)).
% 0.57/0.75 tff(nil_type, type, (
% 0.57/0.75 nil: $i)).
% 0.57/0.75 tff(segmentP_type, type, (
% 0.57/0.75 segmentP: ( $i * $i ) > $o)).
% 0.57/0.75 tff(ssList_type, type, (
% 0.57/0.75 ssList: $i > $o)).
% 0.57/0.75 tff(neq_type, type, (
% 0.57/0.75 neq: ( $i * $i ) > $o)).
% 0.57/0.75 tff(cons_type, type, (
% 0.57/0.75 cons: ( $i * $i ) > $i)).
% 0.57/0.75 tff(tptp_fun_U_45_type, type, (
% 0.57/0.75 tptp_fun_U_45: $i)).
% 0.57/0.75 tff(1,plain,
% 0.57/0.75 ((ssList(U!45) & (~((~ssList(V!46)) | (~ssList(U!45)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil)) | (ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46)))))) <=> (ssList(U!45) & (~((~ssList(U!45)) | (~ssList(V!46)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil)) | (ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46))))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(2,plain,
% 0.57/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V)))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V))))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(3,plain,
% 0.57/0.75 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssList(Y) & (~(W = Y))) & ?[Z: $i] : (((ssItem(Z) & (cons(Z, nil) = Y)) & (hd(X) = Z)) & neq(nil, X)))) | ?[X1: $i] : ((ssList(X1) & (U = X1)) & ?[X2: $i] : (((ssItem(X2) & (cons(X2, nil) = X1)) & (hd(V) = X2)) & neq(nil, V)))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V))))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(4,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((~(V = X)) | (~(U = W))) | ((((~neq(V, nil)) | ?[Y: $i] : ((ssList(Y) & (~(W = Y))) & ?[Z: $i] : (((ssItem(Z) & (cons(Z, nil) = Y)) & (hd(X) = Z)) & neq(nil, X)))) | ?[X1: $i] : ((ssList(X1) & (U = X1)) & ?[X2: $i] : (((ssItem(X2) & (cons(X2, nil) = X1)) & (hd(V) = X2)) & neq(nil, V)))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.57/0.75 tff(5,plain,
% 0.57/0.75 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.57/0.75 tff(6,plain,
% 0.57/0.75 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[5, 2])).
% 0.57/0.75 tff(7,plain,
% 0.57/0.75 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.57/0.75 tff(8,plain,
% 0.57/0.75 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(cons(hd(V), nil)) & (~(U = cons(hd(V), nil))) & neq(nil, V) & ssItem(hd(V))) | (~neq(V, nil)) | (ssList(cons(hd(V), nil)) & (U = cons(hd(V), nil)) & neq(nil, V) & ssItem(hd(V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[7, 2])).
% 0.57/0.75 tff(9,plain,
% 0.57/0.75 (ssList(U!45) & (~((~ssList(U!45)) | (~ssList(V!46)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil)) | (ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.57/0.75 tff(10,plain,
% 0.57/0.75 (~((~ssList(U!45)) | (~ssList(V!46)) | (ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) | (~neq(V!46, nil)) | (ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46))))),
% 0.57/0.75 inference(and_elim,[status(thm)],[9])).
% 0.57/0.75 tff(11,plain,
% 0.57/0.75 (ssList(V!46)),
% 0.57/0.75 inference(or_elim,[status(thm)],[10])).
% 0.57/0.75 tff(12,plain,
% 0.57/0.75 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(13,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[12])).
% 0.57/0.75 tff(14,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(15,plain,
% 0.57/0.75 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(16,plain,
% 0.57/0.75 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[15])).
% 0.57/0.75 tff(17,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.57/0.75 tff(18,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.57/0.75 tff(19,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.57/0.75 tff(20,plain,(
% 0.57/0.75 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(skolemize,[status(sab)],[19])).
% 0.57/0.75 tff(21,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.57/0.75 tff(22,plain,
% 0.57/0.75 (((~![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)))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(23,plain,
% 0.57/0.75 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(24,plain,
% 0.57/0.75 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.57/0.75 tff(25,plain,
% 0.57/0.75 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[24, 21, 11])).
% 0.57/0.75 tff(26,plain,
% 0.57/0.75 (^[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))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(27,plain,
% 0.57/0.75 (![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)))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[26])).
% 0.57/0.75 tff(28,plain,
% 0.57/0.75 (^[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))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(29,plain,
% 0.57/0.75 (![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)))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[28])).
% 0.57/0.75 tff(30,plain,
% 0.57/0.75 (![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)))))),
% 0.57/0.75 inference(transitivity,[status(thm)],[29, 27])).
% 0.57/0.75 tff(31,plain,
% 0.57/0.75 (![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)))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(32,plain,
% 0.57/0.75 (^[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)))))))),
% 0.57/0.75 inference(bind,[status(th)],[])).
% 0.57/0.75 tff(33,plain,
% 0.57/0.75 (![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)))))),
% 0.57/0.75 inference(quant_intro,[status(thm)],[32])).
% 0.57/0.75 tff(34,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.57/0.75 tff(35,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.57/0.75 tff(36,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[35, 31])).
% 0.57/0.75 tff(37,plain,(
% 0.57/0.75 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.75 inference(skolemize,[status(sab)],[36])).
% 0.57/0.75 tff(38,plain,
% 0.57/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[37, 30])).
% 0.57/0.75 tff(39,plain,
% 0.57/0.75 (((~![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)))))),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(40,plain,
% 0.57/0.75 ((~![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)))))),
% 0.57/0.75 inference(quant_inst,[status(thm)],[])).
% 0.57/0.75 tff(41,plain,
% 0.57/0.75 ((~![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))))),
% 0.57/0.75 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.57/0.75 tff(42,plain,
% 0.57/0.75 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.57/0.75 inference(unit_resolution,[status(thm)],[41, 38, 11])).
% 0.57/0.75 tff(43,plain,
% 0.57/0.75 (ssList(nil) <=> ssList(nil)),
% 0.57/0.75 inference(rewrite,[status(thm)],[])).
% 0.57/0.75 tff(44,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.57/0.76 tff(45,plain,
% 0.57/0.76 (ssList(nil)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.57/0.76 tff(46,plain,
% 0.57/0.76 (((~![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))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(47,plain,
% 0.57/0.76 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(48,plain,
% 0.57/0.76 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.57/0.76 tff(49,plain,
% 0.57/0.76 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[48, 45, 42])).
% 0.57/0.76 tff(50,plain,
% 0.57/0.76 (neq(V!46, nil)),
% 0.57/0.76 inference(or_elim,[status(thm)],[10])).
% 0.57/0.76 tff(51,plain,
% 0.57/0.76 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.57/0.76 inference(tautology,[status(thm)],[])).
% 0.57/0.76 tff(52,plain,
% 0.57/0.76 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.57/0.76 tff(53,plain,
% 0.57/0.76 (~(V!46 = nil)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[52, 49])).
% 0.57/0.76 tff(54,plain,
% 0.57/0.76 (^[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)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(55,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[54])).
% 0.57/0.76 tff(56,plain,
% 0.57/0.76 (^[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)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(57,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[56])).
% 0.57/0.76 tff(58,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[57, 55])).
% 0.57/0.76 tff(59,plain,
% 0.57/0.76 (^[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)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(60,plain,
% 0.57/0.76 (![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))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[59])).
% 0.57/0.76 tff(61,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(62,plain,
% 0.57/0.76 (^[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)))))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(63,plain,
% 0.57/0.76 (![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)))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[62])).
% 0.57/0.76 tff(64,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')).
% 0.57/0.76 tff(65,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.57/0.76 tff(66,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[65, 61])).
% 0.57/0.76 tff(67,plain,(
% 0.57/0.76 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.57/0.76 inference(skolemize,[status(sab)],[66])).
% 0.57/0.76 tff(68,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[67, 60])).
% 0.57/0.76 tff(69,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[68, 58])).
% 0.57/0.76 tff(70,plain,
% 0.57/0.76 (((~![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))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(71,plain,
% 0.57/0.76 (((~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))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(72,plain,
% 0.57/0.76 (((~![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)))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[71])).
% 0.57/0.76 tff(73,plain,
% 0.57/0.76 (((~![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))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[72, 70])).
% 0.57/0.76 tff(74,plain,
% 0.57/0.76 ((~![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))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(75,plain,
% 0.57/0.76 ((~![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)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.57/0.76 tff(76,plain,
% 0.57/0.76 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[75, 69, 11])).
% 0.57/0.76 tff(77,plain,
% 0.57/0.76 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(78,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[77])).
% 0.57/0.76 tff(79,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(80,plain,
% 0.57/0.76 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(81,plain,
% 0.57/0.76 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[80])).
% 0.57/0.76 tff(82,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.57/0.76 tff(83,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.57/0.76 tff(84,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[83, 79])).
% 0.57/0.76 tff(85,plain,(
% 0.57/0.76 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(skolemize,[status(sab)],[84])).
% 0.57/0.76 tff(86,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[85, 78])).
% 0.57/0.76 tff(87,plain,
% 0.57/0.76 (((~![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))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(88,plain,
% 0.57/0.76 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(89,plain,
% 0.57/0.76 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.57/0.76 tff(90,plain,
% 0.57/0.76 (segmentP(V!46, nil)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[89, 86, 11])).
% 0.57/0.76 tff(91,plain,
% 0.57/0.76 (((~![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)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(92,plain,
% 0.57/0.76 (((~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)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(93,plain,
% 0.57/0.76 (((~![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))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[92])).
% 0.57/0.76 tff(94,plain,
% 0.57/0.76 (((~![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)))),
% 0.57/0.76 inference(transitivity,[status(thm)],[93, 91])).
% 0.57/0.76 tff(95,plain,
% 0.57/0.76 ((~![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)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(96,plain,
% 0.57/0.76 ((~![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))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.57/0.76 tff(97,plain,
% 0.57/0.76 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[96, 45, 90, 76])).
% 0.57/0.76 tff(98,plain,
% 0.57/0.76 (~segmentP(nil, V!46)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[97, 53])).
% 0.57/0.76 tff(99,plain,
% 0.57/0.76 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.57/0.76 inference(tautology,[status(thm)],[])).
% 0.57/0.76 tff(100,plain,
% 0.57/0.76 (~(nil = V!46)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[99, 98, 25])).
% 0.57/0.76 tff(101,plain,
% 0.57/0.76 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(102,plain,
% 0.57/0.76 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[101])).
% 0.57/0.76 tff(103,plain,
% 0.57/0.76 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(104,plain,
% 0.57/0.76 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssItem(hd(U))) <=> ((nil = U) | ssItem(hd(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> (ssList(U) => ((nil = U) | ssItem(hd(U)))))), rewrite((ssList(U) => ((nil = U) | ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(105,plain,
% 0.57/0.76 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[104])).
% 0.57/0.76 tff(106,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax22')).
% 0.57/0.76 tff(107,plain,
% 0.57/0.76 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[106, 105])).
% 0.57/0.76 tff(108,plain,
% 0.57/0.76 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.57/0.76 tff(109,plain,(
% 0.57/0.76 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(skolemize,[status(sab)],[108])).
% 0.57/0.76 tff(110,plain,
% 0.57/0.76 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[109, 102])).
% 0.57/0.76 tff(111,plain,
% 0.57/0.76 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(112,plain,
% 0.57/0.76 (((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46))) <=> ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(113,plain,
% 0.57/0.76 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46)))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[112])).
% 0.57/0.76 tff(114,plain,
% 0.57/0.76 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46))),
% 0.57/0.76 inference(transitivity,[status(thm)],[113, 111])).
% 0.57/0.76 tff(115,plain,
% 0.57/0.76 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = V!46) | ssItem(hd(V!46)) | (~ssList(V!46)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(116,plain,
% 0.57/0.76 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(V!46)) | ssItem(hd(V!46)) | (nil = V!46)),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.57/0.76 tff(117,plain,
% 0.57/0.76 (ssItem(hd(V!46)) | (nil = V!46)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[116, 110, 11])).
% 0.57/0.76 tff(118,plain,
% 0.57/0.76 (ssItem(hd(V!46))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[117, 100])).
% 0.57/0.76 tff(119,plain,
% 0.57/0.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(120,plain,
% 0.57/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(121,plain,
% 0.57/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.57/0.76 tff(122,plain,
% 0.57/0.76 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[121, 38, 45])).
% 0.57/0.76 tff(123,plain,
% 0.57/0.76 (((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(124,plain,
% 0.57/0.76 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(125,plain,
% 0.57/0.76 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.57/0.76 tff(126,plain,
% 0.57/0.76 (~((nil = V!46) <=> neq(nil, V!46))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[125, 11, 122])).
% 0.57/0.76 tff(127,plain,
% 0.57/0.76 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 0.57/0.76 inference(tautology,[status(thm)],[])).
% 0.57/0.76 tff(128,plain,
% 0.57/0.76 (neq(nil, V!46)),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[127, 100, 126])).
% 0.57/0.76 tff(129,plain,
% 0.57/0.76 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(130,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[129])).
% 0.57/0.76 tff(131,plain,
% 0.57/0.76 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(132,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[131])).
% 0.57/0.76 tff(133,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(transitivity,[status(thm)],[132, 130])).
% 0.57/0.76 tff(134,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(135,plain,
% 0.57/0.76 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 0.57/0.76 inference(bind,[status(th)],[])).
% 0.57/0.76 tff(136,plain,
% 0.57/0.76 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(quant_intro,[status(thm)],[135])).
% 0.57/0.76 tff(137,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 0.57/0.76 tff(138,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.57/0.76 tff(139,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[138, 134])).
% 0.57/0.76 tff(140,plain,(
% 0.57/0.76 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(skolemize,[status(sab)],[139])).
% 0.57/0.76 tff(141,plain,
% 0.57/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[140, 133])).
% 0.57/0.76 tff(142,plain,
% 0.57/0.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(143,plain,
% 0.57/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(144,plain,
% 0.57/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.57/0.76 tff(145,plain,
% 0.57/0.76 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[144, 141, 45])).
% 0.57/0.76 tff(146,plain,
% 0.57/0.76 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(147,plain,
% 0.57/0.76 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil)))),
% 0.57/0.76 inference(quant_inst,[status(thm)],[])).
% 0.57/0.76 tff(148,plain,
% 0.57/0.76 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(hd(V!46))) | ssList(cons(hd(V!46), nil))),
% 0.57/0.76 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.57/0.76 tff(149,plain,
% 0.57/0.76 (ssList(cons(hd(V!46), nil))),
% 0.57/0.76 inference(unit_resolution,[status(thm)],[148, 118, 145])).
% 0.57/0.76 tff(150,plain,
% 0.57/0.76 ((~(~((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))))) <=> ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(151,plain,
% 0.57/0.76 ((ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46))) <=> (~((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))))),
% 0.57/0.76 inference(rewrite,[status(thm)],[])).
% 0.57/0.76 tff(152,plain,
% 0.57/0.76 ((~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))) <=> (~(~((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))))),
% 0.57/0.76 inference(monotonicity,[status(thm)],[151])).
% 0.57/0.76 tff(153,plain,
% 0.57/0.76 ((~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))) <=> ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))),
% 0.57/0.77 inference(transitivity,[status(thm)],[152, 150])).
% 0.57/0.77 tff(154,plain,
% 0.57/0.77 (~(ssList(cons(hd(V!46), nil)) & (~(U!45 = cons(hd(V!46), nil))) & neq(nil, V!46) & ssItem(hd(V!46)))),
% 0.57/0.77 inference(or_elim,[status(thm)],[10])).
% 0.57/0.77 tff(155,plain,
% 0.57/0.77 ((U!45 = cons(hd(V!46), nil)) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.57/0.77 tff(156,plain,
% 0.57/0.77 (U!45 = cons(hd(V!46), nil)),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[155, 149, 128, 118])).
% 0.57/0.77 tff(157,plain,
% 0.57/0.77 ((~(~((~(U!45 = cons(hd(V!46), nil))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))))) <=> ((~(U!45 = cons(hd(V!46), nil))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(158,plain,
% 0.57/0.77 ((ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46))) <=> (~((~(U!45 = cons(hd(V!46), nil))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))))),
% 0.57/0.77 inference(rewrite,[status(thm)],[])).
% 0.57/0.77 tff(159,plain,
% 0.57/0.77 ((~(ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46)))) <=> (~(~((~(U!45 = cons(hd(V!46), nil))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))))),
% 0.57/0.77 inference(monotonicity,[status(thm)],[158])).
% 0.57/0.77 tff(160,plain,
% 0.57/0.77 ((~(ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46)))) <=> ((~(U!45 = cons(hd(V!46), nil))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46))))),
% 0.57/0.77 inference(transitivity,[status(thm)],[159, 157])).
% 0.57/0.77 tff(161,plain,
% 0.57/0.77 (~(ssList(cons(hd(V!46), nil)) & (U!45 = cons(hd(V!46), nil)) & neq(nil, V!46) & ssItem(hd(V!46)))),
% 0.57/0.77 inference(or_elim,[status(thm)],[10])).
% 0.57/0.77 tff(162,plain,
% 0.57/0.77 ((~(U!45 = cons(hd(V!46), nil))) | (~ssList(cons(hd(V!46), nil))) | (~neq(nil, V!46)) | (~ssItem(hd(V!46)))),
% 0.57/0.77 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.57/0.77 tff(163,plain,
% 0.57/0.77 ($false),
% 0.57/0.77 inference(unit_resolution,[status(thm)],[162, 156, 149, 128, 118])).
% 0.57/0.77 % SZS output end Proof
% 0.57/0.77 % E exiting
%------------------------------------------------------------------------------