%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC106+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:11 AM UTC 2025
% Result : Theorem 0.87s 1.07s
% Output : Proof 0.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC106+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 08:19:22 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.87/1.07 % SZS status Theorem
% 0.87/1.07 % SZS output start Proof
% 0.87/1.07 tff(rearsegP_type, type, (
% 0.87/1.07 rearsegP: ( $i * $i ) > $o)).
% 0.87/1.07 tff(tptp_fun_U_45_type, type, (
% 0.87/1.07 tptp_fun_U_45: $i)).
% 0.87/1.07 tff(app_type, type, (
% 0.87/1.07 app: ( $i * $i ) > $i)).
% 0.87/1.07 tff(tptp_fun_Z_48_type, type, (
% 0.87/1.07 tptp_fun_Z_48: $i)).
% 0.87/1.07 tff(tptp_fun_V_46_type, type, (
% 0.87/1.07 tptp_fun_V_46: $i)).
% 0.87/1.07 tff(cons_type, type, (
% 0.87/1.07 cons: ( $i * $i ) > $i)).
% 0.87/1.07 tff(nil_type, type, (
% 0.87/1.07 nil: $i)).
% 0.87/1.07 tff(tptp_fun_Y_47_type, type, (
% 0.87/1.07 tptp_fun_Y_47: $i)).
% 0.87/1.07 tff(ssList_type, type, (
% 0.87/1.07 ssList: $i > $o)).
% 0.87/1.07 tff(ssItem_type, type, (
% 0.87/1.07 ssItem: $i > $o)).
% 0.87/1.07 tff(neq_type, type, (
% 0.87/1.07 neq: ( $i * $i ) > $o)).
% 0.87/1.07 tff(1,plain,
% 0.87/1.07 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))) <=> (ssList(U!45) & ssList(V!46) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(2,plain,
% 0.87/1.07 ((ssList(V!46) & ssList(U!45) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))) <=> (ssList(V!46) & ssList(U!45) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(3,plain,
% 0.87/1.07 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))) <=> (ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[2])).
% 0.87/1.07 tff(4,plain,
% 0.87/1.07 ((ssList(U!45) & (ssList(V!46) & ssList(U!45) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & (ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))))) <=> (ssList(U!45) & ssList(V!46) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[3, 1])).
% 0.87/1.07 tff(5,plain,
% 0.87/1.07 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V)))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(6,plain,
% 0.87/1.07 ((~![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] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ((~(cons(Y, nil) = W)) | (~(app(Z, cons(Y, nil)) = X)))))) | (neq(U, nil) & rearsegP(V, U))) & ((~neq(V, nil)) | neq(X, nil))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V)))))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 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] : (ssItem(Y) => ![Z: $i] : (ssList(Z) => ((~(cons(Y, nil) = W)) | (~(app(Z, cons(Y, nil)) = X)))))) | (neq(U, nil) & rearsegP(V, U))) & ((~neq(V, nil)) | neq(X, nil))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.87/1.07 tff(8,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.87/1.07 tff(9,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.87/1.07 tff(10,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.87/1.07 tff(11,plain,
% 0.87/1.07 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~ssList(U)) | (neq(U, nil) & rearsegP(V, U)) | (~neq(V, nil)) | ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | (~(cons(Y, nil) = U)) | (~(app(Z, cons(Y, nil)) = V))))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.87/1.07 tff(12,plain,
% 0.87/1.07 (ssList(U!45) & ssList(V!46) & (~(neq(U!45, nil) & rearsegP(V!46, U!45))) & neq(V!46, nil) & ssItem(Y!47) & (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46))))),
% 0.87/1.07 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.87/1.07 tff(13,plain,
% 0.87/1.07 (~((~ssList(Z!48)) | (~(cons(Y!47, nil) = U!45)) | (~(app(Z!48, cons(Y!47, nil)) = V!46)))),
% 0.87/1.07 inference(and_elim,[status(thm)],[12])).
% 0.87/1.07 tff(14,plain,
% 0.87/1.07 (app(Z!48, cons(Y!47, nil)) = V!46),
% 0.87/1.07 inference(or_elim,[status(thm)],[13])).
% 0.87/1.07 tff(15,plain,
% 0.87/1.07 (cons(Y!47, nil) = U!45),
% 0.87/1.07 inference(or_elim,[status(thm)],[13])).
% 0.87/1.07 tff(16,plain,
% 0.87/1.07 (U!45 = cons(Y!47, nil)),
% 0.87/1.07 inference(symmetry,[status(thm)],[15])).
% 0.87/1.07 tff(17,plain,
% 0.87/1.07 (app(Z!48, U!45) = app(Z!48, cons(Y!47, nil))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[16])).
% 0.87/1.07 tff(18,plain,
% 0.87/1.07 (app(Z!48, U!45) = V!46),
% 0.87/1.07 inference(transitivity,[status(thm)],[17, 14])).
% 0.87/1.07 tff(19,plain,
% 0.87/1.07 (rearsegP(app(Z!48, U!45), U!45) <=> rearsegP(V!46, U!45)),
% 0.87/1.07 inference(monotonicity,[status(thm)],[18])).
% 0.87/1.07 tff(20,plain,
% 0.87/1.07 (rearsegP(V!46, U!45) <=> rearsegP(app(Z!48, U!45), U!45)),
% 0.87/1.07 inference(symmetry,[status(thm)],[19])).
% 0.87/1.07 tff(21,plain,
% 0.87/1.07 ((~rearsegP(V!46, U!45)) <=> (~rearsegP(app(Z!48, U!45), U!45))),
% 0.87/1.07 inference(monotonicity,[status(thm)],[20])).
% 0.87/1.07 tff(22,plain,
% 0.87/1.07 (ssList(U!45)),
% 0.87/1.07 inference(and_elim,[status(thm)],[12])).
% 0.87/1.07 tff(23,plain,
% 0.87/1.07 (^[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))))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(24,plain,
% 0.87/1.07 (![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)))))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[23])).
% 0.87/1.07 tff(25,plain,
% 0.87/1.07 (^[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))))))),
% 0.87/1.07 inference(bind,[status(th)],[])).
% 0.87/1.07 tff(26,plain,
% 0.87/1.07 (![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)))))),
% 0.87/1.07 inference(quant_intro,[status(thm)],[25])).
% 0.87/1.07 tff(27,plain,
% 0.87/1.07 (![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)))))),
% 0.87/1.07 inference(transitivity,[status(thm)],[26, 24])).
% 0.87/1.07 tff(28,plain,
% 0.87/1.07 (![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)))))),
% 0.87/1.07 inference(rewrite,[status(thm)],[])).
% 0.87/1.07 tff(29,plain,
% 0.87/1.07 (^[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)))))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(30,plain,
% 0.87/1.08 (![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)))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[29])).
% 0.87/1.08 tff(31,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.87/1.08 tff(32,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.87/1.08 tff(33,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.87/1.08 tff(34,plain,(
% 0.87/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.87/1.08 inference(skolemize,[status(sab)],[33])).
% 0.87/1.08 tff(35,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[34, 27])).
% 0.87/1.08 tff(36,plain,
% 0.87/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(37,plain,
% 0.87/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V)))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(38,plain,
% 0.87/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.87/1.08 tff(39,plain,
% 0.87/1.08 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[38, 35, 22])).
% 0.87/1.08 tff(40,plain,
% 0.87/1.08 (ssList(nil) <=> ssList(nil)),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(41,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.87/1.08 tff(42,plain,
% 0.87/1.08 (ssList(nil)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.87/1.08 tff(43,plain,
% 0.87/1.08 (((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(44,plain,
% 0.87/1.08 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(45,plain,
% 0.87/1.08 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.87/1.08 tff(46,plain,
% 0.87/1.08 (~((U!45 = nil) <=> neq(U!45, nil))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[45, 42, 39])).
% 0.87/1.08 tff(47,plain,
% 0.87/1.08 ((U!45 = nil) <=> (nil = U!45)),
% 0.87/1.08 inference(commutativity,[status(thm)],[])).
% 0.87/1.08 tff(48,plain,
% 0.87/1.08 ((nil = U!45) <=> (U!45 = nil)),
% 0.87/1.08 inference(symmetry,[status(thm)],[47])).
% 0.87/1.08 tff(49,plain,
% 0.87/1.08 ((cons(Y!47, nil) = nil) <=> (U!45 = nil)),
% 0.87/1.08 inference(monotonicity,[status(thm)],[15])).
% 0.87/1.08 tff(50,plain,
% 0.87/1.08 ((cons(Y!47, nil) = nil) <=> (nil = U!45)),
% 0.87/1.08 inference(transitivity,[status(thm)],[49, 47])).
% 0.87/1.08 tff(51,plain,
% 0.87/1.08 ((cons(Y!47, nil) = nil) <=> (U!45 = nil)),
% 0.87/1.08 inference(transitivity,[status(thm)],[50, 48])).
% 0.87/1.08 tff(52,plain,
% 0.87/1.08 ((~(cons(Y!47, nil) = nil)) <=> (~(U!45 = nil))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[51])).
% 0.87/1.08 tff(53,plain,
% 0.87/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(54,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[53])).
% 0.87/1.08 tff(55,plain,
% 0.87/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(56,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[55])).
% 0.87/1.08 tff(57,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[56, 54])).
% 0.87/1.08 tff(58,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(59,plain,
% 0.87/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (~(cons(V, U) = U))) <=> ((~ssItem(V)) | (~(cons(V, U) = U))))), (![V: $i] : (ssItem(V) => (~(cons(V, U) = U))) <=> ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(60,plain,
% 0.87/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[59])).
% 0.87/1.08 tff(61,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 0.87/1.08 tff(62,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.87/1.08 tff(63,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[62, 58])).
% 0.87/1.08 tff(64,plain,(
% 0.87/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(skolemize,[status(sab)],[63])).
% 0.87/1.08 tff(65,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[64, 57])).
% 0.87/1.08 tff(66,plain,
% 0.87/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(67,plain,
% 0.87/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(68,plain,
% 0.87/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.87/1.08 tff(69,plain,
% 0.87/1.08 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[68, 42, 65])).
% 0.87/1.08 tff(70,plain,
% 0.87/1.08 (ssItem(Y!47)),
% 0.87/1.08 inference(and_elim,[status(thm)],[12])).
% 0.87/1.08 tff(71,plain,
% 0.87/1.08 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(72,plain,
% 0.87/1.08 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil)))),
% 0.87/1.08 inference(quant_inst,[status(thm)],[])).
% 0.87/1.08 tff(73,plain,
% 0.87/1.08 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(Y!47)) | (~(cons(Y!47, nil) = nil))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.87/1.08 tff(74,plain,
% 0.87/1.08 (~(cons(Y!47, nil) = nil)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[73, 70, 69])).
% 0.87/1.08 tff(75,plain,
% 0.87/1.08 (~(U!45 = nil)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[74, 52])).
% 0.87/1.08 tff(76,plain,
% 0.87/1.08 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 0.87/1.08 inference(tautology,[status(thm)],[])).
% 0.87/1.08 tff(77,plain,
% 0.87/1.08 (neq(U!45, nil)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[76, 75, 46])).
% 0.87/1.08 tff(78,plain,
% 0.87/1.08 ((~(~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))) <=> ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(79,plain,
% 0.87/1.08 ((neq(U!45, nil) & rearsegP(V!46, U!45)) <=> (~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(80,plain,
% 0.87/1.08 ((~(neq(U!45, nil) & rearsegP(V!46, U!45))) <=> (~(~((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))))),
% 0.87/1.08 inference(monotonicity,[status(thm)],[79])).
% 0.87/1.08 tff(81,plain,
% 0.87/1.08 ((~(neq(U!45, nil) & rearsegP(V!46, U!45))) <=> ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45)))),
% 0.87/1.08 inference(transitivity,[status(thm)],[80, 78])).
% 0.87/1.08 tff(82,plain,
% 0.87/1.08 (~(neq(U!45, nil) & rearsegP(V!46, U!45))),
% 0.87/1.08 inference(and_elim,[status(thm)],[12])).
% 0.87/1.08 tff(83,plain,
% 0.87/1.08 ((~neq(U!45, nil)) | (~rearsegP(V!46, U!45))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[82, 81])).
% 0.87/1.08 tff(84,plain,
% 0.87/1.08 (~rearsegP(V!46, U!45)),
% 0.87/1.08 inference(unit_resolution,[status(thm)],[83, 77])).
% 0.87/1.08 tff(85,plain,
% 0.87/1.08 (~rearsegP(app(Z!48, U!45), U!45)),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[84, 21])).
% 0.87/1.08 tff(86,plain,
% 0.87/1.08 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(87,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[86])).
% 0.87/1.08 tff(88,plain,
% 0.87/1.08 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(89,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[88])).
% 0.87/1.08 tff(90,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(transitivity,[status(thm)],[89, 87])).
% 0.87/1.08 tff(91,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(rewrite,[status(thm)],[])).
% 0.87/1.08 tff(92,plain,
% 0.87/1.08 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((rearsegP(U, V) => rearsegP(app(W, U), V)) <=> ((~rearsegP(U, V)) | rearsegP(app(W, U), V))), ((ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V))) <=> (ssList(W) => ((~rearsegP(U, V)) | rearsegP(app(W, U), V))))), rewrite((ssList(W) => ((~rearsegP(U, V)) | rearsegP(app(W, U), V))) <=> (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))), ((ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V))) <=> (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))), (![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V))) <=> ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V)))) <=> (ssList(V) => ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))), rewrite((ssList(V) => ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))) <=> ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V)))) <=> ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))))),
% 0.87/1.08 inference(bind,[status(th)],[])).
% 0.87/1.08 tff(93,plain,
% 0.87/1.08 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(quant_intro,[status(thm)],[92])).
% 0.87/1.08 tff(94,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (rearsegP(U, V) => rearsegP(app(W, U), V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax50')).
% 0.87/1.08 tff(95,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.87/1.08 tff(96,plain,
% 0.87/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.87/1.08 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.87/1.08 tff(97,plain,(
% 0.87/1.08 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.94/1.08 inference(skolemize,[status(sab)],[96])).
% 0.94/1.08 tff(98,plain,
% 0.94/1.08 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.94/1.08 tff(99,plain,
% 0.94/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V)))))),
% 0.94/1.08 inference(rewrite,[status(thm)],[])).
% 0.94/1.08 tff(100,plain,
% 0.94/1.08 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U!45), V) | (~ssList(W)) | (~rearsegP(U!45, V))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V)))))),
% 0.94/1.08 inference(rewrite,[status(thm)],[])).
% 0.94/1.08 tff(101,plain,
% 0.94/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U!45), V) | (~ssList(W)) | (~rearsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))))),
% 0.94/1.08 inference(monotonicity,[status(thm)],[100])).
% 0.94/1.08 tff(102,plain,
% 0.94/1.08 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U!45), V) | (~ssList(W)) | (~rearsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V)))))),
% 0.94/1.08 inference(transitivity,[status(thm)],[101, 99])).
% 0.94/1.08 tff(103,plain,
% 0.94/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U!45), V) | (~ssList(W)) | (~rearsegP(U!45, V)))))),
% 0.94/1.08 inference(quant_inst,[status(thm)],[])).
% 0.94/1.08 tff(104,plain,
% 0.94/1.08 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (rearsegP(app(W, U), V) | (~ssList(W)) | (~rearsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.94/1.08 tff(105,plain,
% 0.94/1.08 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))),
% 0.94/1.08 inference(unit_resolution,[status(thm)],[104, 98, 22])).
% 0.94/1.08 tff(106,plain,
% 0.94/1.08 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45)))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45)))),
% 0.94/1.08 inference(rewrite,[status(thm)],[])).
% 0.94/1.08 tff(107,plain,
% 0.94/1.08 (((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), U!45) | (~rearsegP(U!45, U!45)))) <=> ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45)))),
% 0.94/1.08 inference(rewrite,[status(thm)],[])).
% 0.94/1.08 tff(108,plain,
% 0.94/1.08 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), U!45) | (~rearsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))))),
% 0.94/1.08 inference(monotonicity,[status(thm)],[107])).
% 0.94/1.08 tff(109,plain,
% 0.94/1.08 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), U!45) | (~rearsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45)))),
% 0.94/1.08 inference(transitivity,[status(thm)],[108, 106])).
% 0.94/1.08 tff(110,plain,
% 0.94/1.08 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), U!45) | (~rearsegP(U!45, U!45))))),
% 0.94/1.08 inference(quant_inst,[status(thm)],[])).
% 0.94/1.08 tff(111,plain,
% 0.94/1.08 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | rearsegP(app(W, U!45), V) | (~rearsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.94/1.08 tff(112,plain,
% 0.94/1.08 (![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))),
% 0.94/1.08 inference(unit_resolution,[status(thm)],[111, 22, 105])).
% 0.94/1.08 tff(113,plain,
% 0.94/1.08 (^[U: $i] : refl(((~ssList(U)) | rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 0.94/1.08 inference(bind,[status(th)],[])).
% 0.94/1.08 tff(114,plain,
% 0.94/1.08 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(quant_intro,[status(thm)],[113])).
% 0.94/1.08 tff(115,plain,
% 0.94/1.08 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(rewrite,[status(thm)],[])).
% 0.94/1.08 tff(116,plain,
% 0.94/1.08 (^[U: $i] : rewrite((ssList(U) => rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 0.94/1.08 inference(bind,[status(th)],[])).
% 0.94/1.08 tff(117,plain,
% 0.94/1.08 (![U: $i] : (ssList(U) => rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(quant_intro,[status(thm)],[116])).
% 0.94/1.08 tff(118,axiom,(![U: $i] : (ssList(U) => rearsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax49')).
% 0.94/1.08 tff(119,plain,
% 0.94/1.08 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.94/1.08 tff(120,plain,
% 0.94/1.08 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.94/1.08 tff(121,plain,(
% 0.94/1.08 ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(skolemize,[status(sab)],[120])).
% 0.94/1.08 tff(122,plain,
% 0.94/1.08 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.94/1.08 tff(123,plain,
% 0.94/1.08 (((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(U!45)) | rearsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(U!45)) | rearsegP(U!45, U!45))),
% 0.94/1.08 inference(rewrite,[status(thm)],[])).
% 0.94/1.08 tff(124,plain,
% 0.94/1.08 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(U!45)) | rearsegP(U!45, U!45))),
% 0.94/1.08 inference(quant_inst,[status(thm)],[])).
% 0.94/1.08 tff(125,plain,
% 0.94/1.08 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(U!45)) | rearsegP(U!45, U!45)),
% 0.94/1.08 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.94/1.08 tff(126,plain,
% 0.94/1.08 (rearsegP(U!45, U!45)),
% 0.94/1.08 inference(unit_resolution,[status(thm)],[125, 122, 22])).
% 0.94/1.08 tff(127,plain,
% 0.94/1.08 (ssList(Z!48)),
% 0.94/1.08 inference(or_elim,[status(thm)],[13])).
% 0.94/1.08 tff(128,plain,
% 0.94/1.08 (((~![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))) | ((~ssList(Z!48)) | (~rearsegP(U!45, U!45)) | rearsegP(app(Z!48, U!45), U!45))) <=> ((~![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))) | (~ssList(Z!48)) | (~rearsegP(U!45, U!45)) | rearsegP(app(Z!48, U!45), U!45))),
% 0.94/1.09 inference(rewrite,[status(thm)],[])).
% 0.94/1.09 tff(129,plain,
% 0.94/1.09 ((~![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))) | ((~ssList(Z!48)) | (~rearsegP(U!45, U!45)) | rearsegP(app(Z!48, U!45), U!45))),
% 0.94/1.09 inference(quant_inst,[status(thm)],[])).
% 0.94/1.09 tff(130,plain,
% 0.94/1.09 ((~![W: $i] : ((~ssList(W)) | (~rearsegP(U!45, U!45)) | rearsegP(app(W, U!45), U!45))) | (~ssList(Z!48)) | (~rearsegP(U!45, U!45)) | rearsegP(app(Z!48, U!45), U!45)),
% 0.94/1.09 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.94/1.09 tff(131,plain,
% 0.94/1.09 (rearsegP(app(Z!48, U!45), U!45)),
% 0.94/1.09 inference(unit_resolution,[status(thm)],[130, 127, 126, 112])).
% 0.94/1.09 tff(132,plain,
% 0.94/1.09 ($false),
% 0.94/1.09 inference(unit_resolution,[status(thm)],[131, 85])).
% 0.94/1.09 % SZS output end Proof
% 0.94/1.09 % E exiting
%------------------------------------------------------------------------------