%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC101+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:30:10 AM UTC 2025
% Result : Theorem 143.84s 144.15s
% Output : Proof 144.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC101+1 : TPTP v9.0.0. Released v2.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 08:18:10 EDT 2025
% 0.12/0.34 % CPUTime :
% 143.84/144.15 % SZS status Theorem
% 143.84/144.15 % SZS output start Proof
% 143.84/144.15 tff(tptp_fun_U_45_type, type, (
% 143.84/144.15 tptp_fun_U_45: $i)).
% 143.84/144.15 tff(nil_type, type, (
% 143.84/144.15 nil: $i)).
% 143.84/144.15 tff(neq_type, type, (
% 143.84/144.15 neq: ( $i * $i ) > $o)).
% 143.84/144.15 tff(ssList_type, type, (
% 143.84/144.15 ssList: $i > $o)).
% 143.84/144.15 tff(frontsegP_type, type, (
% 143.84/144.15 frontsegP: ( $i * $i ) > $o)).
% 143.84/144.15 tff(tptp_fun_V_46_type, type, (
% 143.84/144.15 tptp_fun_V_46: $i)).
% 143.84/144.15 tff(app_type, type, (
% 143.84/144.15 app: ( $i * $i ) > $i)).
% 143.84/144.15 tff(cons_type, type, (
% 143.84/144.15 cons: ( $i * $i ) > $i)).
% 143.84/144.15 tff(tptp_fun_Y_47_type, type, (
% 143.84/144.15 tptp_fun_Y_47: $i)).
% 143.84/144.15 tff(ssItem_type, type, (
% 143.84/144.15 ssItem: $i > $o)).
% 143.84/144.15 tff(equalelemsP_type, type, (
% 143.84/144.15 equalelemsP: $i > $o)).
% 143.84/144.15 tff(1,plain,
% 143.84/144.15 ((U!45 = nil) <=> (nil = U!45)),
% 143.84/144.15 inference(commutativity,[status(thm)],[])).
% 143.84/144.15 tff(2,plain,
% 143.84/144.15 ((ssList(U!45) & ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))) <=> (ssList(U!45) & (~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(3,plain,
% 143.84/144.15 (((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45)))) <=> ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(4,plain,
% 143.84/144.15 (((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) <=> ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(5,plain,
% 143.84/144.15 (((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45)))) <=> ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))),
% 143.84/144.15 inference(monotonicity,[status(thm)],[4])).
% 143.84/144.15 tff(6,plain,
% 143.84/144.15 (((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45)))) <=> ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))),
% 143.84/144.15 inference(transitivity,[status(thm)],[5, 3])).
% 143.84/144.15 tff(7,plain,
% 143.84/144.15 ((ssList(U!45) & ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))) <=> (ssList(U!45) & ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45)))))),
% 143.84/144.15 inference(monotonicity,[status(thm)],[6])).
% 143.84/144.15 tff(8,plain,
% 143.84/144.15 ((ssList(U!45) & ((~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & ((app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45)))))) & ssList(U!45) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))) <=> (ssList(U!45) & (~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(neq(U!45, nil) & frontsegP(V!46, U!45))))),
% 143.84/144.15 inference(transitivity,[status(thm)],[7, 2])).
% 143.84/144.15 tff(9,plain,
% 143.84/144.15 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U)))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(10,plain,
% 143.84/144.15 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ((~(nil = X)) & (nil = W))) | ((nil = V) & (nil = U))) | (neq(U, nil) & frontsegP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U)))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(11,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | ((~(nil = X)) & (nil = W))) | ((nil = V) & (nil = U))) | (neq(U, nil) & frontsegP(V, U)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 143.84/144.15 tff(12,plain,
% 143.84/144.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[11, 10])).
% 143.84/144.15 tff(13,plain,
% 143.84/144.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[12, 9])).
% 143.84/144.15 tff(14,plain,
% 143.84/144.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[13, 9])).
% 143.84/144.15 tff(15,plain,
% 143.84/144.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((nil = V) & (nil = U)) | ((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~(app(U, Y) = V)) | (~equalelemsP(U)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = U))))) | (~ssList(U)) | (neq(U, nil) & frontsegP(V, U))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[14, 9])).
% 143.84/144.15 tff(16,plain,
% 143.84/144.15 (ssList(U!45) & (~((nil = V!46) & (nil = U!45))) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (app(U!45, Y!47) = V!46) & equalelemsP(U!45) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = U!45))))) & (~(neq(U!45, nil) & frontsegP(V!46, U!45)))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[15, 8])).
% 143.84/144.15 tff(17,plain,
% 143.84/144.15 (ssList(U!45)),
% 143.84/144.15 inference(and_elim,[status(thm)],[16])).
% 143.84/144.15 tff(18,plain,
% 143.84/144.15 (^[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))))))),
% 143.84/144.15 inference(bind,[status(th)],[])).
% 143.84/144.15 tff(19,plain,
% 143.84/144.15 (![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)))))),
% 143.84/144.15 inference(quant_intro,[status(thm)],[18])).
% 143.84/144.15 tff(20,plain,
% 143.84/144.15 (^[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))))))),
% 143.84/144.15 inference(bind,[status(th)],[])).
% 143.84/144.15 tff(21,plain,
% 143.84/144.15 (![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)))))),
% 143.84/144.15 inference(quant_intro,[status(thm)],[20])).
% 143.84/144.15 tff(22,plain,
% 143.84/144.15 (![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)))))),
% 143.84/144.15 inference(transitivity,[status(thm)],[21, 19])).
% 143.84/144.15 tff(23,plain,
% 143.84/144.15 (![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)))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(24,plain,
% 143.84/144.15 (^[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)))))))),
% 143.84/144.15 inference(bind,[status(th)],[])).
% 143.84/144.15 tff(25,plain,
% 143.84/144.15 (![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)))))),
% 143.84/144.15 inference(quant_intro,[status(thm)],[24])).
% 143.84/144.15 tff(26,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 143.84/144.15 tff(27,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[26, 25])).
% 143.84/144.15 tff(28,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[27, 23])).
% 143.84/144.15 tff(29,plain,(
% 143.84/144.15 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 143.84/144.15 inference(skolemize,[status(sab)],[28])).
% 143.84/144.15 tff(30,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[29, 22])).
% 143.84/144.15 tff(31,plain,
% 143.84/144.15 (((~![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)))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(32,plain,
% 143.84/144.15 ((~![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)))))),
% 143.84/144.15 inference(quant_inst,[status(thm)],[])).
% 143.84/144.15 tff(33,plain,
% 143.84/144.15 ((~![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))))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[32, 31])).
% 143.84/144.15 tff(34,plain,
% 143.84/144.15 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 143.84/144.15 inference(unit_resolution,[status(thm)],[33, 30, 17])).
% 143.84/144.15 tff(35,plain,
% 143.84/144.15 (ssList(nil) <=> ssList(nil)),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(36,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 143.84/144.15 tff(37,plain,
% 143.84/144.15 (ssList(nil)),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[36, 35])).
% 143.84/144.15 tff(38,plain,
% 143.84/144.15 (((~![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))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(39,plain,
% 143.84/144.15 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 143.84/144.15 inference(quant_inst,[status(thm)],[])).
% 143.84/144.15 tff(40,plain,
% 143.84/144.15 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 143.84/144.15 inference(modus_ponens,[status(thm)],[39, 38])).
% 143.84/144.15 tff(41,plain,
% 143.84/144.15 (~((U!45 = nil) <=> neq(U!45, nil))),
% 143.84/144.15 inference(unit_resolution,[status(thm)],[40, 37, 34])).
% 143.84/144.15 tff(42,plain,
% 143.84/144.15 (app(U!45, Y!47) = V!46),
% 143.84/144.15 inference(and_elim,[status(thm)],[16])).
% 143.84/144.15 tff(43,plain,
% 143.84/144.15 (frontsegP(app(U!45, Y!47), U!45) <=> frontsegP(V!46, U!45)),
% 143.84/144.15 inference(monotonicity,[status(thm)],[42])).
% 143.84/144.15 tff(44,plain,
% 143.84/144.15 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 143.84/144.15 inference(bind,[status(th)],[])).
% 143.84/144.15 tff(45,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.15 inference(quant_intro,[status(thm)],[44])).
% 143.84/144.15 tff(46,plain,
% 143.84/144.15 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))),
% 143.84/144.15 inference(bind,[status(th)],[])).
% 143.84/144.15 tff(47,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.15 inference(quant_intro,[status(thm)],[46])).
% 143.84/144.15 tff(48,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.15 inference(transitivity,[status(thm)],[47, 45])).
% 143.84/144.15 tff(49,plain,
% 143.84/144.15 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.15 inference(rewrite,[status(thm)],[])).
% 143.84/144.15 tff(50,plain,
% 143.84/144.15 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite((frontsegP(U, V) => frontsegP(app(U, W), V)) <=> ((~frontsegP(U, V)) | frontsegP(app(U, W), V))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))))), rewrite((ssList(W) => ((~frontsegP(U, V)) | frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))), ((ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), (![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))) <=> ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> (ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), rewrite((ssList(V) => ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))), ((ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))))),
% 143.84/144.16 inference(bind,[status(th)],[])).
% 143.84/144.16 tff(51,plain,
% 143.84/144.16 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.16 inference(quant_intro,[status(thm)],[50])).
% 143.84/144.16 tff(52,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => (frontsegP(U, V) => frontsegP(app(U, W), V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax43')).
% 143.84/144.16 tff(53,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[52, 51])).
% 143.84/144.16 tff(54,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[53, 49])).
% 143.84/144.16 tff(55,plain,(
% 143.84/144.16 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.16 inference(skolemize,[status(sab)],[54])).
% 143.84/144.16 tff(56,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[55, 48])).
% 143.84/144.16 tff(57,plain,
% 143.84/144.16 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(58,plain,
% 143.84/144.16 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(59,plain,
% 143.84/144.16 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))))),
% 143.84/144.16 inference(monotonicity,[status(thm)],[58])).
% 143.84/144.16 tff(60,plain,
% 143.84/144.16 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V)))))),
% 143.84/144.16 inference(transitivity,[status(thm)],[59, 57])).
% 143.84/144.16 tff(61,plain,
% 143.84/144.16 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U!45, W), V) | (~ssList(W)) | (~frontsegP(U!45, V)))))),
% 143.84/144.16 inference(quant_inst,[status(thm)],[])).
% 143.84/144.16 tff(62,plain,
% 143.84/144.16 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(app(U, W), V) | (~ssList(W)) | (~frontsegP(U, V)))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[61, 60])).
% 143.84/144.16 tff(63,plain,
% 143.84/144.16 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))),
% 143.84/144.16 inference(unit_resolution,[status(thm)],[62, 56, 17])).
% 143.84/144.16 tff(64,plain,
% 143.84/144.16 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(65,plain,
% 143.84/144.16 (((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45)))) <=> ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(66,plain,
% 143.84/144.16 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))))),
% 143.84/144.16 inference(monotonicity,[status(thm)],[65])).
% 143.84/144.16 tff(67,plain,
% 143.84/144.16 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45)))),
% 143.84/144.16 inference(transitivity,[status(thm)],[66, 64])).
% 143.84/144.16 tff(68,plain,
% 143.84/144.16 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), U!45) | (~frontsegP(U!45, U!45))))),
% 143.84/144.16 inference(quant_inst,[status(thm)],[])).
% 143.84/144.16 tff(69,plain,
% 143.84/144.16 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | frontsegP(app(U!45, W), V) | (~frontsegP(U!45, V))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[68, 67])).
% 143.84/144.16 tff(70,plain,
% 143.84/144.16 (![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))),
% 143.84/144.16 inference(unit_resolution,[status(thm)],[69, 17, 63])).
% 143.84/144.16 tff(71,plain,
% 143.84/144.16 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 143.84/144.16 inference(bind,[status(th)],[])).
% 143.84/144.16 tff(72,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(quant_intro,[status(thm)],[71])).
% 143.84/144.16 tff(73,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(74,plain,
% 143.84/144.16 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 143.84/144.16 inference(bind,[status(th)],[])).
% 143.84/144.16 tff(75,plain,
% 143.84/144.16 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(quant_intro,[status(thm)],[74])).
% 143.84/144.16 tff(76,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax42')).
% 143.84/144.16 tff(77,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[76, 75])).
% 143.84/144.16 tff(78,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[77, 73])).
% 143.84/144.16 tff(79,plain,(
% 143.84/144.16 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(skolemize,[status(sab)],[78])).
% 143.84/144.16 tff(80,plain,
% 143.84/144.16 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[79, 72])).
% 143.84/144.16 tff(81,plain,
% 143.84/144.16 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(82,plain,
% 143.84/144.16 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))),
% 143.84/144.16 inference(quant_inst,[status(thm)],[])).
% 143.84/144.16 tff(83,plain,
% 143.84/144.16 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45)),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[82, 81])).
% 143.84/144.16 tff(84,plain,
% 143.84/144.16 (frontsegP(U!45, U!45)),
% 143.84/144.16 inference(unit_resolution,[status(thm)],[83, 80, 17])).
% 143.84/144.16 tff(85,plain,
% 143.84/144.16 (ssList(Y!47)),
% 143.84/144.16 inference(and_elim,[status(thm)],[16])).
% 143.84/144.16 tff(86,plain,
% 143.84/144.16 (((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(Y!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Y!47), U!45))) <=> ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~ssList(Y!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Y!47), U!45))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(87,plain,
% 143.84/144.16 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | ((~ssList(Y!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Y!47), U!45))),
% 143.84/144.16 inference(quant_inst,[status(thm)],[])).
% 143.84/144.16 tff(88,plain,
% 143.84/144.16 ((~![W: $i] : ((~ssList(W)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, W), U!45))) | (~ssList(Y!47)) | (~frontsegP(U!45, U!45)) | frontsegP(app(U!45, Y!47), U!45)),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[87, 86])).
% 143.84/144.16 tff(89,plain,
% 143.84/144.16 (frontsegP(app(U!45, Y!47), U!45)),
% 143.84/144.16 inference(unit_resolution,[status(thm)],[88, 85, 84, 70])).
% 143.84/144.16 tff(90,plain,
% 143.84/144.16 (frontsegP(V!46, U!45)),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[89, 43])).
% 143.84/144.16 tff(91,plain,
% 143.84/144.16 ((~(~((~neq(U!45, nil)) | (~frontsegP(V!46, U!45))))) <=> ((~neq(U!45, nil)) | (~frontsegP(V!46, U!45)))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(92,plain,
% 143.84/144.16 ((neq(U!45, nil) & frontsegP(V!46, U!45)) <=> (~((~neq(U!45, nil)) | (~frontsegP(V!46, U!45))))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(93,plain,
% 143.84/144.16 ((~(neq(U!45, nil) & frontsegP(V!46, U!45))) <=> (~(~((~neq(U!45, nil)) | (~frontsegP(V!46, U!45)))))),
% 143.84/144.16 inference(monotonicity,[status(thm)],[92])).
% 143.84/144.16 tff(94,plain,
% 143.84/144.16 ((~(neq(U!45, nil) & frontsegP(V!46, U!45))) <=> ((~neq(U!45, nil)) | (~frontsegP(V!46, U!45)))),
% 143.84/144.16 inference(transitivity,[status(thm)],[93, 91])).
% 143.84/144.16 tff(95,plain,
% 143.84/144.16 (~(neq(U!45, nil) & frontsegP(V!46, U!45))),
% 143.84/144.16 inference(and_elim,[status(thm)],[16])).
% 143.84/144.16 tff(96,plain,
% 143.84/144.16 ((~neq(U!45, nil)) | (~frontsegP(V!46, U!45))),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[95, 94])).
% 143.84/144.16 tff(97,plain,
% 143.84/144.16 (~neq(U!45, nil)),
% 143.84/144.16 inference(unit_resolution,[status(thm)],[96, 90])).
% 143.84/144.16 tff(98,plain,
% 143.84/144.16 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 143.84/144.16 inference(tautology,[status(thm)],[])).
% 143.84/144.16 tff(99,plain,
% 143.84/144.16 (U!45 = nil),
% 143.84/144.16 inference(unit_resolution,[status(thm)],[98, 97, 41])).
% 143.84/144.16 tff(100,plain,
% 143.84/144.16 (nil = U!45),
% 143.84/144.16 inference(modus_ponens,[status(thm)],[99, 1])).
% 143.84/144.16 tff(101,plain,
% 143.84/144.16 ((~(~((~(nil = V!46)) | (~(nil = U!45))))) <=> ((~(nil = V!46)) | (~(nil = U!45)))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(102,plain,
% 143.84/144.16 (((nil = V!46) & (nil = U!45)) <=> (~((~(nil = V!46)) | (~(nil = U!45))))),
% 143.84/144.16 inference(rewrite,[status(thm)],[])).
% 143.84/144.16 tff(103,plain,
% 143.84/144.16 ((~((nil = V!46) & (nil = U!45))) <=> (~(~((~(nil = V!46)) | (~(nil = U!45)))))),
% 143.84/144.16 inference(monotonicity,[status(thm)],[102])).
% 143.84/144.16 tff(104,plain,
% 143.84/144.16 ((~((nil = V!46) & (nil = U!45))) <=> ((~(nil = V!46)) | (~(nil = U!45)))),
% 143.84/144.16 inference(transitivity,[status(thm)],[103, 101])).
% 144.08/144.41 tff(105,plain,
% 144.08/144.41 (~((nil = V!46) & (nil = U!45))),
% 144.08/144.41 inference(and_elim,[status(thm)],[16])).
% 144.08/144.41 tff(106,plain,
% 144.08/144.41 ((~(nil = V!46)) | (~(nil = U!45))),
% 144.08/144.41 inference(modus_ponens,[status(thm)],[105, 104])).
% 144.08/144.41 tff(107,plain,
% 144.08/144.41 (~(nil = V!46)),
% 144.08/144.41 inference(unit_resolution,[status(thm)],[106, 100])).
% 144.08/144.41 tff(108,plain,
% 144.08/144.41 ((~(~((nil = V!46) | (~(nil = U!45))))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 144.08/144.41 inference(rewrite,[status(thm)],[])).
% 144.08/144.41 tff(109,plain,
% 144.08/144.41 (((~(nil = V!46)) & (nil = U!45)) <=> (~((nil = V!46) | (~(nil = U!45))))),
% 144.08/144.41 inference(rewrite,[status(thm)],[])).
% 144.08/144.41 tff(110,plain,
% 144.08/144.41 ((~((~(nil = V!46)) & (nil = U!45))) <=> (~(~((nil = V!46) | (~(nil = U!45)))))),
% 144.08/144.41 inference(monotonicity,[status(thm)],[109])).
% 144.08/144.41 tff(111,plain,
% 144.08/144.41 ((~((~(nil = V!46)) & (nil = U!45))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 144.08/144.41 inference(transitivity,[status(thm)],[110, 108])).
% 144.08/144.41 tff(112,plain,
% 144.08/144.41 (~((~(nil = V!46)) & (nil = U!45))),
% 144.08/144.41 inference(and_elim,[status(thm)],[16])).
% 144.08/144.41 tff(113,plain,
% 144.08/144.41 ((nil = V!46) | (~(nil = U!45))),
% 144.08/144.41 inference(modus_ponens,[status(thm)],[112, 111])).
% 144.08/144.41 tff(114,plain,
% 144.08/144.41 ($false),
% 144.08/144.41 inference(unit_resolution,[status(thm)],[113, 107, 100])).
% 144.08/144.41 % SZS output end Proof
% 144.08/144.41 % E exiting
%------------------------------------------------------------------------------