%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC014+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:29:56 AM UTC 2025
% Result : Theorem 0.77s 1.00s
% Output : Proof 0.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SWC014+1 : TPTP v9.0.0. Released v2.4.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.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 08:01:46 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.77/1.00 % SZS status Theorem
% 0.77/1.00 % SZS output start Proof
% 0.77/1.00 tff(ssList_type, type, (
% 0.77/1.00 ssList: $i > $o)).
% 0.77/1.00 tff(tl_type, type, (
% 0.77/1.00 tl: $i > $i)).
% 0.77/1.00 tff(tptp_fun_V_46_type, type, (
% 0.77/1.00 tptp_fun_V_46: $i)).
% 0.77/1.00 tff(tptp_fun_X2_48_type, type, (
% 0.77/1.00 tptp_fun_X2_48: $i)).
% 0.77/1.00 tff(cons_type, type, (
% 0.77/1.00 cons: ( $i * $i ) > $i)).
% 0.77/1.00 tff(tptp_fun_X1_47_type, type, (
% 0.77/1.00 tptp_fun_X1_47: $i)).
% 0.77/1.00 tff(ssItem_type, type, (
% 0.77/1.00 ssItem: $i > $o)).
% 0.77/1.00 tff(app_type, type, (
% 0.77/1.00 app: ( $i * $i ) > $i)).
% 0.77/1.00 tff(nil_type, type, (
% 0.77/1.00 nil: $i)).
% 0.77/1.00 tff(tptp_fun_U_45_type, type, (
% 0.77/1.00 tptp_fun_U_45: $i)).
% 0.77/1.00 tff(neq_type, type, (
% 0.77/1.00 neq: ( $i * $i ) > $o)).
% 0.77/1.00 tff(segmentP_type, type, (
% 0.77/1.00 segmentP: ( $i * $i ) > $o)).
% 0.77/1.00 tff(1,plain,
% 0.77/1.00 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46)))))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(2,plain,
% 0.77/1.00 ((ssList(V!46) & ssList(U!45) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46)))))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(3,plain,
% 0.77/1.00 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46))))))),
% 0.77/1.00 inference(monotonicity,[status(thm)],[2])).
% 0.77/1.00 tff(4,plain,
% 0.77/1.00 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & (ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46))))))) <=> (ssList(U!45) & ssList(V!46) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46)))))),
% 0.77/1.00 inference(transitivity,[status(thm)],[3, 1])).
% 0.77/1.00 tff(5,plain,
% 0.77/1.00 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V)))))))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(6,plain,
% 0.77/1.00 ((~![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) & (V = Y)) & ?[Z: $i] : (((ssList(Z) & (tl(V) = Z)) & (app(U, Z) = Y)) & neq(nil, V)))) | ![X1: $i] : (ssItem(X1) => ![X2: $i] : (ssList(X2) => ((~(cons(X1, nil) = W)) | (~(app(cons(X1, nil), X2) = X)))))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V)))))))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 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)) | ?[Y: $i] : ((ssList(Y) & (V = Y)) & ?[Z: $i] : (((ssList(Z) & (tl(V) = Z)) & (app(U, Z) = Y)) & neq(nil, V)))) | ![X1: $i] : (ssItem(X1) => ![X2: $i] : (ssList(X2) => ((~(cons(X1, nil) = W)) | (~(app(cons(X1, nil), X2) = X)))))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.77/1.00 tff(8,plain,
% 0.77/1.00 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V))))))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.77/1.00 tff(9,plain,
% 0.77/1.00 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V))))))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.77/1.00 tff(10,plain,
% 0.77/1.00 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V))))))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.77/1.00 tff(11,plain,
% 0.77/1.00 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (ssList(app(U, tl(V))) & (V = app(U, tl(V))) & neq(nil, V) & ssList(tl(V))) | (~neq(V, nil)) | ![X1: $i] : ((~ssItem(X1)) | ![X2: $i] : ((~ssList(X2)) | (~(cons(X1, nil) = U)) | (~(app(cons(X1, nil), X2) = V))))))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.77/1.00 tff(12,plain,
% 0.77/1.00 (ssList(U!45) & ssList(V!46) & (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) & neq(V!46, nil) & ssItem(X1!47) & (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46))))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.77/1.00 tff(13,plain,
% 0.77/1.00 (~((~ssList(X2!48)) | (~(cons(X1!47, nil) = U!45)) | (~(app(cons(X1!47, nil), X2!48) = V!46)))),
% 0.77/1.00 inference(and_elim,[status(thm)],[12])).
% 0.77/1.00 tff(14,plain,
% 0.77/1.00 (ssList(X2!48)),
% 0.77/1.00 inference(or_elim,[status(thm)],[13])).
% 0.77/1.00 tff(15,plain,
% 0.77/1.00 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(16,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[15])).
% 0.77/1.00 tff(17,plain,
% 0.77/1.00 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(18,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[17])).
% 0.77/1.00 tff(19,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(transitivity,[status(thm)],[18, 16])).
% 0.77/1.00 tff(20,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(21,plain,
% 0.77/1.00 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (tl(cons(V, U)) = U)) <=> ((~ssItem(V)) | (tl(cons(V, U)) = U)))), (![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)) <=> ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(22,plain,
% 0.77/1.00 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[21])).
% 0.77/1.00 tff(23,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (tl(cons(V, U)) = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax25')).
% 0.77/1.00 tff(24,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.77/1.00 tff(25,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.77/1.00 tff(26,plain,(
% 0.77/1.00 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(skolemize,[status(sab)],[25])).
% 0.77/1.00 tff(27,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.77/1.00 tff(28,plain,
% 0.77/1.00 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48)))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(29,plain,
% 0.77/1.00 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | ((~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48)))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(30,plain,
% 0.77/1.00 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, U)) = U)))) | (~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48))),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.77/1.00 tff(31,plain,
% 0.77/1.00 (![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48))),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 0.77/1.00 tff(32,plain,
% 0.77/1.00 (ssItem(X1!47)),
% 0.77/1.00 inference(and_elim,[status(thm)],[12])).
% 0.77/1.00 tff(33,plain,
% 0.77/1.00 (((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48))) | ((~ssItem(X1!47)) | (tl(cons(X1!47, X2!48)) = X2!48))) <=> ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48))) | (~ssItem(X1!47)) | (tl(cons(X1!47, X2!48)) = X2!48))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(34,plain,
% 0.77/1.00 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48))) | ((~ssItem(X1!47)) | (tl(cons(X1!47, X2!48)) = X2!48))),
% 0.77/1.00 inference(quant_inst,[status(thm)],[])).
% 0.77/1.00 tff(35,plain,
% 0.77/1.00 ((~![V: $i] : ((~ssItem(V)) | (tl(cons(V, X2!48)) = X2!48))) | (~ssItem(X1!47)) | (tl(cons(X1!47, X2!48)) = X2!48)),
% 0.77/1.00 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.77/1.00 tff(36,plain,
% 0.77/1.00 (tl(cons(X1!47, X2!48)) = X2!48),
% 0.77/1.00 inference(unit_resolution,[status(thm)],[35, 32, 31])).
% 0.77/1.00 tff(37,plain,
% 0.77/1.00 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(38,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[37])).
% 0.77/1.00 tff(39,plain,
% 0.77/1.00 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(40,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.00 inference(quant_intro,[status(thm)],[39])).
% 0.77/1.00 tff(41,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.00 inference(transitivity,[status(thm)],[40, 38])).
% 0.77/1.00 tff(42,plain,
% 0.77/1.00 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.00 inference(rewrite,[status(thm)],[])).
% 0.77/1.00 tff(43,plain,
% 0.77/1.00 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 0.77/1.00 inference(bind,[status(th)],[])).
% 0.77/1.00 tff(44,plain,
% 0.77/1.00 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[43])).
% 0.77/1.01 tff(45,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 0.77/1.01 tff(46,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.77/1.01 tff(47,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.77/1.01 tff(48,plain,(
% 0.77/1.01 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.01 inference(skolemize,[status(sab)],[47])).
% 0.77/1.01 tff(49,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[48, 41])).
% 0.77/1.01 tff(50,plain,
% 0.77/1.01 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(51,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48))))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(52,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(X2!48)) | ![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.77/1.01 tff(53,plain,
% 0.77/1.01 (![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48)))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[52, 49, 14])).
% 0.77/1.01 tff(54,plain,
% 0.77/1.01 (((~![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48)))) | ((~ssItem(X1!47)) | (cons(X1!47, X2!48) = app(cons(X1!47, nil), X2!48)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48)))) | (~ssItem(X1!47)) | (cons(X1!47, X2!48) = app(cons(X1!47, nil), X2!48)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(55,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48)))) | ((~ssItem(X1!47)) | (cons(X1!47, X2!48) = app(cons(X1!47, nil), X2!48)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(56,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssItem(V)) | (cons(V, X2!48) = app(cons(V, nil), X2!48)))) | (~ssItem(X1!47)) | (cons(X1!47, X2!48) = app(cons(X1!47, nil), X2!48))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.77/1.01 tff(57,plain,
% 0.77/1.01 (cons(X1!47, X2!48) = app(cons(X1!47, nil), X2!48)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[56, 32, 53])).
% 0.77/1.01 tff(58,plain,
% 0.77/1.01 (app(cons(X1!47, nil), X2!48) = cons(X1!47, X2!48)),
% 0.77/1.01 inference(symmetry,[status(thm)],[57])).
% 0.77/1.01 tff(59,plain,
% 0.77/1.01 (app(cons(X1!47, nil), X2!48) = V!46),
% 0.77/1.01 inference(or_elim,[status(thm)],[13])).
% 0.77/1.01 tff(60,plain,
% 0.77/1.01 (V!46 = app(cons(X1!47, nil), X2!48)),
% 0.77/1.01 inference(symmetry,[status(thm)],[59])).
% 0.77/1.01 tff(61,plain,
% 0.77/1.01 (V!46 = cons(X1!47, X2!48)),
% 0.77/1.01 inference(transitivity,[status(thm)],[60, 58])).
% 0.77/1.01 tff(62,plain,
% 0.77/1.01 (tl(V!46) = tl(cons(X1!47, X2!48))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[61])).
% 0.77/1.01 tff(63,plain,
% 0.77/1.01 (tl(V!46) = X2!48),
% 0.77/1.01 inference(transitivity,[status(thm)],[62, 36])).
% 0.77/1.01 tff(64,plain,
% 0.77/1.01 (ssList(tl(V!46)) <=> ssList(X2!48)),
% 0.77/1.01 inference(monotonicity,[status(thm)],[63])).
% 0.77/1.01 tff(65,plain,
% 0.77/1.01 (ssList(X2!48) <=> ssList(tl(V!46))),
% 0.77/1.01 inference(symmetry,[status(thm)],[64])).
% 0.77/1.01 tff(66,plain,
% 0.77/1.01 (ssList(tl(V!46))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[14, 65])).
% 0.77/1.01 tff(67,plain,
% 0.77/1.01 (ssList(nil) <=> ssList(nil)),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(68,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.77/1.01 tff(69,plain,
% 0.77/1.01 (ssList(nil)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.77/1.01 tff(70,plain,
% 0.77/1.01 (^[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))))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(71,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[70])).
% 0.77/1.01 tff(72,plain,
% 0.77/1.01 (^[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))))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(73,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[72])).
% 0.77/1.01 tff(74,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(transitivity,[status(thm)],[73, 71])).
% 0.77/1.01 tff(75,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(76,plain,
% 0.77/1.01 (^[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)))))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(77,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[76])).
% 0.77/1.01 tff(78,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.77/1.01 tff(79,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.77/1.01 tff(80,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.77/1.01 tff(81,plain,(
% 0.77/1.01 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.77/1.01 inference(skolemize,[status(sab)],[80])).
% 0.77/1.01 tff(82,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.77/1.01 tff(83,plain,
% 0.77/1.01 (((~![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)))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(84,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V)))))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(85,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.77/1.01 tff(86,plain,
% 0.77/1.01 (![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[85, 82, 69])).
% 0.77/1.01 tff(87,plain,
% 0.77/1.01 (ssList(V!46)),
% 0.77/1.01 inference(and_elim,[status(thm)],[12])).
% 0.77/1.01 tff(88,plain,
% 0.77/1.01 (((~![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))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(89,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | ((~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46))))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(90,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssList(V)) | (~((nil = V) <=> neq(nil, V))))) | (~ssList(V!46)) | (~((nil = V!46) <=> neq(nil, V!46)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.77/1.01 tff(91,plain,
% 0.77/1.01 (~((nil = V!46) <=> neq(nil, V!46))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[90, 87, 86])).
% 0.77/1.01 tff(92,plain,
% 0.77/1.01 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(93,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[92])).
% 0.77/1.01 tff(94,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(95,plain,
% 0.77/1.01 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(96,plain,
% 0.77/1.01 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[95])).
% 0.77/1.01 tff(97,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.77/1.01 tff(98,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.77/1.01 tff(99,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[98, 94])).
% 0.77/1.01 tff(100,plain,(
% 0.77/1.01 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(skolemize,[status(sab)],[99])).
% 0.77/1.01 tff(101,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[100, 93])).
% 0.77/1.01 tff(102,plain,
% 0.77/1.01 (((~![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)))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(103,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(104,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.77/1.01 tff(105,plain,
% 0.77/1.01 (segmentP(nil, V!46) <=> (nil = V!46)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[104, 101, 87])).
% 0.77/1.01 tff(106,plain,
% 0.77/1.01 (((~![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)))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(107,plain,
% 0.77/1.01 ((~![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)))))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(108,plain,
% 0.77/1.01 ((~![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))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.77/1.01 tff(109,plain,
% 0.77/1.01 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[108, 82, 87])).
% 0.77/1.01 tff(110,plain,
% 0.77/1.01 (((~![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))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(111,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(112,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[111, 110])).
% 0.77/1.01 tff(113,plain,
% 0.77/1.01 (~((V!46 = nil) <=> neq(V!46, nil))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[112, 69, 109])).
% 0.77/1.01 tff(114,plain,
% 0.77/1.01 (neq(V!46, nil)),
% 0.77/1.01 inference(and_elim,[status(thm)],[12])).
% 0.77/1.01 tff(115,plain,
% 0.77/1.01 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 0.77/1.01 inference(tautology,[status(thm)],[])).
% 0.77/1.01 tff(116,plain,
% 0.77/1.01 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.77/1.01 tff(117,plain,
% 0.77/1.01 (~(V!46 = nil)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[116, 113])).
% 0.77/1.01 tff(118,plain,
% 0.77/1.01 (^[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)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(119,plain,
% 0.77/1.01 (![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))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[118])).
% 0.77/1.01 tff(120,plain,
% 0.77/1.01 (^[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)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(121,plain,
% 0.77/1.01 (![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))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[120])).
% 0.77/1.01 tff(122,plain,
% 0.77/1.01 (![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))))),
% 0.77/1.01 inference(transitivity,[status(thm)],[121, 119])).
% 0.77/1.01 tff(123,plain,
% 0.77/1.01 (^[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)))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(124,plain,
% 0.77/1.01 (![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))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[123])).
% 0.77/1.01 tff(125,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(126,plain,
% 0.77/1.01 (^[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)))))))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(127,plain,
% 0.77/1.01 (![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)))))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[126])).
% 0.77/1.01 tff(128,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')).
% 0.77/1.01 tff(129,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.77/1.01 tff(130,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[129, 125])).
% 0.77/1.01 tff(131,plain,(
% 0.77/1.01 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.77/1.01 inference(skolemize,[status(sab)],[130])).
% 0.77/1.01 tff(132,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[131, 124])).
% 0.77/1.01 tff(133,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[132, 122])).
% 0.77/1.01 tff(134,plain,
% 0.77/1.01 (((~![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))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(135,plain,
% 0.77/1.01 (((~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))))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(136,plain,
% 0.77/1.01 (((~![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)))))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[135])).
% 0.77/1.01 tff(137,plain,
% 0.77/1.01 (((~![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))))),
% 0.77/1.01 inference(transitivity,[status(thm)],[136, 134])).
% 0.77/1.01 tff(138,plain,
% 0.77/1.01 ((~![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))))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(139,plain,
% 0.77/1.01 ((~![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)))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.77/1.01 tff(140,plain,
% 0.77/1.01 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[139, 133, 87])).
% 0.77/1.01 tff(141,plain,
% 0.77/1.01 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(142,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[141])).
% 0.77/1.01 tff(143,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(144,plain,
% 0.77/1.01 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.77/1.01 inference(bind,[status(th)],[])).
% 0.77/1.01 tff(145,plain,
% 0.77/1.01 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(quant_intro,[status(thm)],[144])).
% 0.77/1.01 tff(146,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.77/1.01 tff(147,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.77/1.01 tff(148,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.77/1.01 tff(149,plain,(
% 0.77/1.01 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(skolemize,[status(sab)],[148])).
% 0.77/1.01 tff(150,plain,
% 0.77/1.01 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.77/1.01 tff(151,plain,
% 0.77/1.01 (((~![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))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(152,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(153,plain,
% 0.77/1.01 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.77/1.01 tff(154,plain,
% 0.77/1.01 (segmentP(V!46, nil)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[153, 150, 87])).
% 0.77/1.01 tff(155,plain,
% 0.77/1.01 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (~segmentP(V!46, nil)) | (V!46 = nil))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (~segmentP(V!46, nil)) | (V!46 = nil))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(156,plain,
% 0.77/1.01 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (~segmentP(V!46, nil)) | (V!46 = nil))),
% 0.77/1.01 inference(rewrite,[status(thm)],[])).
% 0.77/1.01 tff(157,plain,
% 0.77/1.01 (((~![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)) | (~segmentP(V!46, nil)) | (V!46 = nil)))),
% 0.77/1.01 inference(monotonicity,[status(thm)],[156])).
% 0.77/1.01 tff(158,plain,
% 0.77/1.01 (((~![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)) | (~segmentP(V!46, nil)) | (V!46 = nil))),
% 0.77/1.01 inference(transitivity,[status(thm)],[157, 155])).
% 0.77/1.01 tff(159,plain,
% 0.77/1.01 ((~![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)))),
% 0.77/1.01 inference(quant_inst,[status(thm)],[])).
% 0.77/1.01 tff(160,plain,
% 0.77/1.01 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (~segmentP(V!46, nil)) | (V!46 = nil)),
% 0.77/1.01 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.77/1.01 tff(161,plain,
% 0.77/1.01 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[160, 69, 154, 140])).
% 0.77/1.01 tff(162,plain,
% 0.77/1.01 (~segmentP(nil, V!46)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[161, 117])).
% 0.77/1.01 tff(163,plain,
% 0.77/1.01 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 0.77/1.01 inference(tautology,[status(thm)],[])).
% 0.77/1.01 tff(164,plain,
% 0.77/1.01 (~(nil = V!46)),
% 0.77/1.01 inference(unit_resolution,[status(thm)],[163, 162, 105])).
% 0.77/1.01 tff(165,plain,
% 0.77/1.01 (((nil = V!46) <=> neq(nil, V!46)) | (nil = V!46) | neq(nil, V!46)),
% 0.77/1.02 inference(tautology,[status(thm)],[])).
% 0.77/1.02 tff(166,plain,
% 0.77/1.02 (neq(nil, V!46)),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[165, 164, 91])).
% 0.77/1.02 tff(167,plain,
% 0.77/1.02 (cons(X1!47, nil) = U!45),
% 0.77/1.02 inference(or_elim,[status(thm)],[13])).
% 0.77/1.02 tff(168,plain,
% 0.77/1.02 (U!45 = cons(X1!47, nil)),
% 0.77/1.02 inference(symmetry,[status(thm)],[167])).
% 0.77/1.02 tff(169,plain,
% 0.77/1.02 (app(U!45, tl(V!46)) = app(cons(X1!47, nil), X2!48)),
% 0.77/1.02 inference(monotonicity,[status(thm)],[168, 63])).
% 0.77/1.02 tff(170,plain,
% 0.77/1.02 (app(cons(X1!47, nil), X2!48) = app(U!45, tl(V!46))),
% 0.77/1.02 inference(symmetry,[status(thm)],[169])).
% 0.77/1.02 tff(171,plain,
% 0.77/1.02 (V!46 = app(U!45, tl(V!46))),
% 0.77/1.02 inference(transitivity,[status(thm)],[60, 170])).
% 0.77/1.02 tff(172,plain,
% 0.77/1.02 (app(U!45, tl(V!46)) = V!46),
% 0.77/1.02 inference(transitivity,[status(thm)],[169, 59])).
% 0.77/1.02 tff(173,plain,
% 0.77/1.02 (ssList(app(U!45, tl(V!46))) <=> ssList(V!46)),
% 0.77/1.02 inference(monotonicity,[status(thm)],[172])).
% 0.77/1.02 tff(174,plain,
% 0.77/1.02 (ssList(V!46) <=> ssList(app(U!45, tl(V!46)))),
% 0.77/1.02 inference(symmetry,[status(thm)],[173])).
% 0.77/1.02 tff(175,plain,
% 0.77/1.02 (ssList(app(U!45, tl(V!46)))),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[87, 174])).
% 0.77/1.02 tff(176,plain,
% 0.77/1.02 ((~(~((~ssList(app(U!45, tl(V!46)))) | (~(V!46 = app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))))) <=> ((~ssList(app(U!45, tl(V!46)))) | (~(V!46 = app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46))))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(177,plain,
% 0.77/1.02 ((ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46))) <=> (~((~ssList(app(U!45, tl(V!46)))) | (~(V!46 = app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))))),
% 0.77/1.02 inference(rewrite,[status(thm)],[])).
% 0.77/1.02 tff(178,plain,
% 0.77/1.02 ((~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) <=> (~(~((~ssList(app(U!45, tl(V!46)))) | (~(V!46 = app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46))))))),
% 0.77/1.02 inference(monotonicity,[status(thm)],[177])).
% 0.77/1.02 tff(179,plain,
% 0.77/1.02 ((~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))) <=> ((~ssList(app(U!45, tl(V!46)))) | (~(V!46 = app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46))))),
% 0.77/1.02 inference(transitivity,[status(thm)],[178, 176])).
% 0.77/1.02 tff(180,plain,
% 0.77/1.02 (~(ssList(app(U!45, tl(V!46))) & (V!46 = app(U!45, tl(V!46))) & neq(nil, V!46) & ssList(tl(V!46)))),
% 0.77/1.02 inference(and_elim,[status(thm)],[12])).
% 0.77/1.02 tff(181,plain,
% 0.77/1.02 ((~ssList(app(U!45, tl(V!46)))) | (~(V!46 = app(U!45, tl(V!46)))) | (~neq(nil, V!46)) | (~ssList(tl(V!46)))),
% 0.77/1.02 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.77/1.02 tff(182,plain,
% 0.77/1.02 ($false),
% 0.77/1.02 inference(unit_resolution,[status(thm)],[181, 175, 171, 166, 66])).
% 0.77/1.02 % SZS output end Proof
% 0.77/1.02 % E exiting
%------------------------------------------------------------------------------