%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC218+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:30:33 AM UTC 2025
% Result : Theorem 11.02s 11.21s
% Output : Proof 11.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC218+1 : TPTP v9.0.0. Released v2.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n010.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 08:40:11 EDT 2025
% 0.11/0.33 % CPUTime :
% 11.02/11.21 % SZS status Theorem
% 11.02/11.21 % SZS output start Proof
% 11.02/11.21 tff(tptp_fun_U_45_type, type, (
% 11.02/11.21 tptp_fun_U_45: $i)).
% 11.02/11.21 tff(app_type, type, (
% 11.02/11.21 app: ( $i * $i ) > $i)).
% 11.02/11.21 tff(cons_type, type, (
% 11.02/11.21 cons: ( $i * $i ) > $i)).
% 11.02/11.21 tff(nil_type, type, (
% 11.02/11.21 nil: $i)).
% 11.02/11.21 tff(tptp_fun_X1_49_type, type, (
% 11.02/11.21 tptp_fun_X1_49: $i)).
% 11.02/11.21 tff(tptp_fun_Y_47_type, type, (
% 11.02/11.21 tptp_fun_Y_47: $i)).
% 11.02/11.21 tff(ssList_type, type, (
% 11.02/11.21 ssList: $i > $o)).
% 11.02/11.21 tff(frontsegP_type, type, (
% 11.02/11.21 frontsegP: ( $i * $i ) > $o)).
% 11.02/11.21 tff(tptp_fun_W_5_type, type, (
% 11.02/11.21 tptp_fun_W_5: ( $i * $i ) > $i)).
% 11.02/11.21 tff(ssItem_type, type, (
% 11.02/11.21 ssItem: $i > $o)).
% 11.02/11.21 tff(tptp_fun_Z_48_type, type, (
% 11.02/11.21 tptp_fun_Z_48: $i)).
% 11.02/11.21 tff(neq_type, type, (
% 11.02/11.21 neq: ( $i * $i ) > $o)).
% 11.02/11.21 tff(tptp_fun_V_46_type, type, (
% 11.02/11.21 tptp_fun_V_46: $i)).
% 11.02/11.21 tff(1,plain,
% 11.02/11.21 (ssList(nil) <=> ssList(nil)),
% 11.02/11.21 inference(rewrite,[status(thm)],[])).
% 11.02/11.21 tff(2,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 11.02/11.21 tff(3,plain,
% 11.02/11.21 (ssList(nil)),
% 11.02/11.21 inference(modus_ponens,[status(thm)],[2, 1])).
% 11.02/11.21 tff(4,plain,
% 11.02/11.21 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 11.02/11.21 inference(bind,[status(th)],[])).
% 11.02/11.21 tff(5,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(quant_intro,[status(thm)],[4])).
% 11.02/11.21 tff(6,plain,
% 11.02/11.21 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 11.02/11.21 inference(bind,[status(th)],[])).
% 11.02/11.21 tff(7,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(quant_intro,[status(thm)],[6])).
% 11.02/11.21 tff(8,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(transitivity,[status(thm)],[7, 5])).
% 11.02/11.21 tff(9,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(rewrite,[status(thm)],[])).
% 11.02/11.21 tff(10,plain,
% 11.02/11.21 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 11.02/11.21 inference(bind,[status(th)],[])).
% 11.02/11.21 tff(11,plain,
% 11.02/11.21 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(quant_intro,[status(thm)],[10])).
% 11.02/11.21 tff(12,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 11.02/11.21 tff(13,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(modus_ponens,[status(thm)],[12, 11])).
% 11.02/11.21 tff(14,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(modus_ponens,[status(thm)],[13, 9])).
% 11.02/11.21 tff(15,plain,(
% 11.02/11.21 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(skolemize,[status(sab)],[14])).
% 11.02/11.21 tff(16,plain,
% 11.02/11.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 11.02/11.21 inference(modus_ponens,[status(thm)],[15, 8])).
% 11.02/11.21 tff(17,plain,
% 11.02/11.21 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(18,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(19,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[18, 17])).
% 11.02/11.22 tff(20,plain,
% 11.02/11.22 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[19, 16, 3])).
% 11.02/11.22 tff(21,plain,
% 11.02/11.22 ((ssList(U!45) & (ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & ssList(U!45) & (~neq(U!45, nil)))) <=> (ssList(U!45) & ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & (~neq(U!45, nil)))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(22,plain,
% 11.02/11.22 ((ssList(V!46) & (ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45))))) & ssList(U!45) & (~neq(U!45, nil))) <=> (ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & ssList(U!45) & (~neq(U!45, nil)))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(23,plain,
% 11.02/11.22 ((ssList(Y!47) & ((app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))))) <=> (ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(24,plain,
% 11.02/11.22 ((ssList(V!46) & (ssList(Y!47) & ((app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))))) & ssList(U!45) & (~neq(U!45, nil))) <=> (ssList(V!46) & (ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45))))) & ssList(U!45) & (~neq(U!45, nil)))),
% 11.02/11.22 inference(monotonicity,[status(thm)],[23])).
% 11.02/11.22 tff(25,plain,
% 11.02/11.22 ((ssList(V!46) & (ssList(Y!47) & ((app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))))) & ssList(U!45) & (~neq(U!45, nil))) <=> (ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & ssList(U!45) & (~neq(U!45, nil)))),
% 11.02/11.22 inference(transitivity,[status(thm)],[24, 22])).
% 11.02/11.22 tff(26,plain,
% 11.02/11.22 ((ssList(U!45) & (ssList(V!46) & (ssList(Y!47) & ((app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))))) & ssList(U!45) & (~neq(U!45, nil)))) <=> (ssList(U!45) & (ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & ssList(U!45) & (~neq(U!45, nil))))),
% 11.02/11.22 inference(monotonicity,[status(thm)],[25])).
% 11.02/11.22 tff(27,plain,
% 11.02/11.22 ((ssList(U!45) & (ssList(V!46) & (ssList(Y!47) & ((app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))))) & ssList(U!45) & (~neq(U!45, nil)))) <=> (ssList(U!45) & ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & (~neq(U!45, nil)))),
% 11.02/11.22 inference(transitivity,[status(thm)],[26, 21])).
% 11.02/11.22 tff(28,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil)))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(29,plain,
% 11.02/11.22 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => ![Z: $i] : (ssList(Z) => ((~(app(Y, Z) = X)) | ![X1: $i] : (ssItem(X1) => (~(app(app(Y, cons(X1, nil)), Z) = W))))))) | neq(U, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(30,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) => ![Z: $i] : (ssList(Z) => ((~(app(Y, Z) = X)) | ![X1: $i] : (ssItem(X1) => (~(app(app(Y, cons(X1, nil)), Z) = W))))))) | neq(U, nil))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 11.02/11.22 tff(31,plain,
% 11.02/11.22 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[30, 29])).
% 11.02/11.22 tff(32,plain,
% 11.02/11.22 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[31, 28])).
% 11.02/11.22 tff(33,plain,
% 11.02/11.22 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[32, 28])).
% 11.02/11.22 tff(34,plain,
% 11.02/11.22 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![Y: $i] : ((~ssList(Y)) | ![Z: $i] : ((~(app(Y, Z) = V)) | (~ssList(Z)) | ![X1: $i] : ((~ssItem(X1)) | (~(app(app(Y, cons(X1, nil)), Z) = U))))) | (~ssList(U)) | neq(U, nil)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[33, 28])).
% 11.02/11.22 tff(35,plain,
% 11.02/11.22 (ssList(U!45) & ssList(V!46) & ssList(Y!47) & (app(Y!47, Z!48) = V!46) & ssList(Z!48) & (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) & (~neq(U!45, nil))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[34, 27])).
% 11.02/11.22 tff(36,plain,
% 11.02/11.22 (~((~ssItem(X1!49)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))),
% 11.02/11.22 inference(and_elim,[status(thm)],[35])).
% 11.02/11.22 tff(37,plain,
% 11.02/11.22 (ssItem(X1!49)),
% 11.02/11.22 inference(or_elim,[status(thm)],[36])).
% 11.02/11.22 tff(38,plain,
% 11.02/11.22 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X1!49)) | ssList(cons(X1!49, nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X1!49)) | ssList(cons(X1!49, nil)))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(39,plain,
% 11.02/11.22 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X1!49)) | ssList(cons(X1!49, nil)))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(40,plain,
% 11.02/11.22 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X1!49)) | ssList(cons(X1!49, nil))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[39, 38])).
% 11.02/11.22 tff(41,plain,
% 11.02/11.22 (ssList(cons(X1!49, nil))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[40, 37, 20])).
% 11.02/11.22 tff(42,plain,
% 11.02/11.22 (ssList(Y!47)),
% 11.02/11.22 inference(and_elim,[status(thm)],[35])).
% 11.02/11.22 tff(43,plain,
% 11.02/11.22 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(44,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[43])).
% 11.02/11.22 tff(45,plain,
% 11.02/11.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(46,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[45])).
% 11.02/11.22 tff(47,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(transitivity,[status(thm)],[46, 44])).
% 11.02/11.22 tff(48,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(49,plain,
% 11.02/11.22 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ssList(app(U, V))) <=> ((~ssList(V)) | ssList(app(U, V))))), (![V: $i] : (ssList(V) => ssList(app(U, V))) <=> ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(50,plain,
% 11.02/11.22 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[49])).
% 11.02/11.22 tff(51,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ssList(app(U, V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax26')).
% 11.02/11.22 tff(52,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[51, 50])).
% 11.02/11.22 tff(53,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[52, 48])).
% 11.02/11.22 tff(54,plain,(
% 11.02/11.22 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(skolemize,[status(sab)],[53])).
% 11.02/11.22 tff(55,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[54, 47])).
% 11.02/11.22 tff(56,plain,
% 11.02/11.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(57,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V))))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(58,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ssList(app(U, V))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[57, 56])).
% 11.02/11.22 tff(59,plain,
% 11.02/11.22 (![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[58, 55, 42])).
% 11.02/11.22 tff(60,plain,
% 11.02/11.22 (((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | ((~ssList(cons(X1!49, nil))) | ssList(app(Y!47, cons(X1!49, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | (~ssList(cons(X1!49, nil))) | ssList(app(Y!47, cons(X1!49, nil))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(61,plain,
% 11.02/11.22 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | ((~ssList(cons(X1!49, nil))) | ssList(app(Y!47, cons(X1!49, nil))))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(62,plain,
% 11.02/11.22 ((~![V: $i] : ((~ssList(V)) | ssList(app(Y!47, V)))) | (~ssList(cons(X1!49, nil))) | ssList(app(Y!47, cons(X1!49, nil)))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[61, 60])).
% 11.02/11.22 tff(63,plain,
% 11.02/11.22 (ssList(app(Y!47, cons(X1!49, nil)))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[62, 59, 41])).
% 11.02/11.22 tff(64,plain,
% 11.02/11.22 (ssList(U!45)),
% 11.02/11.22 inference(and_elim,[status(thm)],[35])).
% 11.02/11.22 tff(65,plain,
% 11.02/11.22 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(66,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[65])).
% 11.02/11.22 tff(67,plain,
% 11.02/11.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(68,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[67])).
% 11.02/11.22 tff(69,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 11.02/11.22 inference(transitivity,[status(thm)],[68, 66])).
% 11.02/11.22 tff(70,plain,
% 11.02/11.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U))))))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(71,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[70])).
% 11.02/11.22 tff(72,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(73,plain,
% 11.02/11.22 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))) <=> (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), rewrite((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))), ((ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), (![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))) <=> ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(74,plain,
% 11.02/11.22 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[73])).
% 11.02/11.22 tff(75,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax5')).
% 11.02/11.22 tff(76,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[75, 74])).
% 11.02/11.22 tff(77,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (frontsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(V, W) = U)))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[76, 72])).
% 11.02/11.22 tff(78,plain,(
% 11.02/11.22 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~frontsegP(U, V)) | (ssList(tptp_fun_W_5(V, U)) & (app(V, tptp_fun_W_5(V, U)) = U))) & (frontsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(V, W) = U)))))))),
% 11.02/11.22 inference(skolemize,[status(sab)],[77])).
% 11.02/11.22 tff(79,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[78, 71])).
% 11.02/11.22 tff(80,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[79, 69])).
% 11.02/11.22 tff(81,plain,
% 11.02/11.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(82,plain,
% 11.02/11.22 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(83,plain,
% 11.02/11.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))))),
% 11.02/11.22 inference(monotonicity,[status(thm)],[82])).
% 11.02/11.22 tff(84,plain,
% 11.02/11.22 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45))))))))))),
% 11.02/11.22 inference(transitivity,[status(thm)],[83, 81])).
% 11.02/11.22 tff(85,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))) | (~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45)))))))))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(86,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~frontsegP(U, V)) | (~((~ssList(tptp_fun_W_5(V, U))) | (~(app(V, tptp_fun_W_5(V, U)) = U)))))) | (~(frontsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U)))))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[85, 84])).
% 11.02/11.22 tff(87,plain,
% 11.02/11.22 (![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[86, 80, 64])).
% 11.02/11.22 tff(88,plain,
% 11.02/11.22 (((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | ((~ssList(app(Y!47, cons(X1!49, nil)))) | (~((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | (~((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | (~((~ssList(tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45))) | (~(app(app(Y!47, cons(X1!49, nil)), tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45)) = U!45)))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | (~((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | (~((~ssList(tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45))) | (~(app(app(Y!47, cons(X1!49, nil)), tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45)) = U!45)))))))))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(89,plain,
% 11.02/11.22 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | ((~ssList(app(Y!47, cons(X1!49, nil)))) | (~((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | (~((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | (~((~ssList(tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45))) | (~(app(app(Y!47, cons(X1!49, nil)), tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45)) = U!45)))))))))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(90,plain,
% 11.02/11.22 ((~![V: $i] : ((~ssList(V)) | (~((~(frontsegP(U!45, V) | ![W: $i] : ((~ssList(W)) | (~(app(V, W) = U!45))))) | (~((~frontsegP(U!45, V)) | (~((~ssList(tptp_fun_W_5(V, U!45))) | (~(app(V, tptp_fun_W_5(V, U!45)) = U!45)))))))))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | (~((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | (~((~ssList(tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45))) | (~(app(app(Y!47, cons(X1!49, nil)), tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45)) = U!45))))))))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[89, 88])).
% 11.02/11.22 tff(91,plain,
% 11.02/11.22 (~((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | (~((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | (~((~ssList(tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45))) | (~(app(app(Y!47, cons(X1!49, nil)), tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45)) = U!45)))))))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[90, 87, 63])).
% 11.02/11.22 tff(92,plain,
% 11.02/11.22 (((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | (~((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | (~((~ssList(tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45))) | (~(app(app(Y!47, cons(X1!49, nil)), tptp_fun_W_5(app(Y!47, cons(X1!49, nil)), U!45)) = U!45))))))) | (frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))),
% 11.02/11.22 inference(tautology,[status(thm)],[])).
% 11.02/11.22 tff(93,plain,
% 11.02/11.22 (frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[92, 91])).
% 11.02/11.22 tff(94,plain,
% 11.02/11.22 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(95,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[94])).
% 11.02/11.22 tff(96,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(97,plain,
% 11.02/11.22 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, nil)) <=> ((~ssList(U)) | frontsegP(U, nil)))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(98,plain,
% 11.02/11.22 (![U: $i] : (ssList(U) => frontsegP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[97])).
% 11.02/11.22 tff(99,axiom,(![U: $i] : (ssList(U) => frontsegP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax45')).
% 11.02/11.22 tff(100,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[99, 98])).
% 11.02/11.22 tff(101,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[100, 96])).
% 11.02/11.22 tff(102,plain,(
% 11.02/11.22 ![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(skolemize,[status(sab)],[101])).
% 11.02/11.22 tff(103,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | frontsegP(U, nil))),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[102, 95])).
% 11.02/11.22 tff(104,plain,
% 11.02/11.22 (((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(app(Y!47, cons(X1!49, nil)))) | frontsegP(app(Y!47, cons(X1!49, nil)), nil))) <=> ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | frontsegP(app(Y!47, cons(X1!49, nil)), nil))),
% 11.02/11.22 inference(rewrite,[status(thm)],[])).
% 11.02/11.22 tff(105,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | ((~ssList(app(Y!47, cons(X1!49, nil)))) | frontsegP(app(Y!47, cons(X1!49, nil)), nil))),
% 11.02/11.22 inference(quant_inst,[status(thm)],[])).
% 11.02/11.22 tff(106,plain,
% 11.02/11.22 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | frontsegP(app(Y!47, cons(X1!49, nil)), nil)),
% 11.02/11.22 inference(modus_ponens,[status(thm)],[105, 104])).
% 11.02/11.22 tff(107,plain,
% 11.02/11.22 (frontsegP(app(Y!47, cons(X1!49, nil)), nil)),
% 11.02/11.22 inference(unit_resolution,[status(thm)],[106, 103, 63])).
% 11.02/11.22 tff(108,plain,
% 11.02/11.22 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(109,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[108])).
% 11.02/11.22 tff(110,plain,
% 11.02/11.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 11.02/11.22 inference(bind,[status(th)],[])).
% 11.02/11.22 tff(111,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 11.02/11.22 inference(quant_intro,[status(thm)],[110])).
% 11.02/11.22 tff(112,plain,
% 11.02/11.22 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 11.02/11.22 inference(transitivity,[status(thm)],[111, 109])).
% 11.02/11.22 tff(113,plain,
% 11.02/11.22 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V)))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(114,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[113])).
% 11.02/11.23 tff(115,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(116,plain,
% 11.02/11.23 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(117,plain,
% 11.02/11.23 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[116])).
% 11.02/11.23 tff(118,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 11.02/11.23 tff(119,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[118, 117])).
% 11.02/11.23 tff(120,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[119, 115])).
% 11.02/11.23 tff(121,plain,(
% 11.02/11.23 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 11.02/11.23 inference(skolemize,[status(sab)],[120])).
% 11.02/11.23 tff(122,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[121, 114])).
% 11.02/11.23 tff(123,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[122, 112])).
% 11.02/11.23 tff(124,plain,
% 11.02/11.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V))))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(125,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | ((~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V))))))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(126,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = U))) <=> (nil = app(U, V))))))) | (~ssList(Y!47)) | ![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[125, 124])).
% 11.02/11.23 tff(127,plain,
% 11.02/11.23 (![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[126, 123, 42])).
% 11.02/11.23 tff(128,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | ((~ssList(cons(X1!49, nil))) | (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | (~ssList(cons(X1!49, nil))) | (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil))))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(129,plain,
% 11.02/11.23 (((~ssList(cons(X1!49, nil))) | (~(((~(nil = cons(X1!49, nil))) | (~(nil = Y!47))) <=> (nil = app(Y!47, cons(X1!49, nil)))))) <=> ((~ssList(cons(X1!49, nil))) | (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil))))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(130,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | ((~ssList(cons(X1!49, nil))) | (~(((~(nil = cons(X1!49, nil))) | (~(nil = Y!47))) <=> (nil = app(Y!47, cons(X1!49, nil))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | ((~ssList(cons(X1!49, nil))) | (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil)))))))),
% 11.02/11.23 inference(monotonicity,[status(thm)],[129])).
% 11.02/11.23 tff(131,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | ((~ssList(cons(X1!49, nil))) | (~(((~(nil = cons(X1!49, nil))) | (~(nil = Y!47))) <=> (nil = app(Y!47, cons(X1!49, nil))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | (~ssList(cons(X1!49, nil))) | (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil))))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[130, 128])).
% 11.02/11.23 tff(132,plain,
% 11.02/11.23 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | ((~ssList(cons(X1!49, nil))) | (~(((~(nil = cons(X1!49, nil))) | (~(nil = Y!47))) <=> (nil = app(Y!47, cons(X1!49, nil))))))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(133,plain,
% 11.02/11.23 ((~![V: $i] : ((~ssList(V)) | (~(((~(nil = V)) | (~(nil = Y!47))) <=> (nil = app(Y!47, V)))))) | (~ssList(cons(X1!49, nil))) | (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[132, 131])).
% 11.02/11.23 tff(134,plain,
% 11.02/11.23 (~(((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil))))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[133, 127, 41])).
% 11.02/11.23 tff(135,plain,
% 11.02/11.23 ((nil = cons(X1!49, nil)) <=> (cons(X1!49, nil) = nil)),
% 11.02/11.23 inference(commutativity,[status(thm)],[])).
% 11.02/11.23 tff(136,plain,
% 11.02/11.23 ((cons(X1!49, nil) = nil) <=> (nil = cons(X1!49, nil))),
% 11.02/11.23 inference(symmetry,[status(thm)],[135])).
% 11.02/11.23 tff(137,plain,
% 11.02/11.23 ((~(cons(X1!49, nil) = nil)) <=> (~(nil = cons(X1!49, nil)))),
% 11.02/11.23 inference(monotonicity,[status(thm)],[136])).
% 11.02/11.23 tff(138,plain,
% 11.02/11.23 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(139,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[138])).
% 11.02/11.23 tff(140,plain,
% 11.02/11.23 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(141,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[140])).
% 11.02/11.23 tff(142,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[141, 139])).
% 11.02/11.23 tff(143,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(144,plain,
% 11.02/11.23 (^[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))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(145,plain,
% 11.02/11.23 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[144])).
% 11.02/11.23 tff(146,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (~(cons(V, U) = U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax18')).
% 11.02/11.23 tff(147,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[146, 145])).
% 11.02/11.23 tff(148,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[147, 143])).
% 11.02/11.23 tff(149,plain,(
% 11.02/11.23 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(skolemize,[status(sab)],[148])).
% 11.02/11.23 tff(150,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[149, 142])).
% 11.02/11.23 tff(151,plain,
% 11.02/11.23 (((~![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))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(152,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil))))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(153,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, U) = U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[152, 151])).
% 11.02/11.23 tff(154,plain,
% 11.02/11.23 (![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[153, 3, 150])).
% 11.02/11.23 tff(155,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(X1!49)) | (~(cons(X1!49, nil) = nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(X1!49)) | (~(cons(X1!49, nil) = nil)))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(156,plain,
% 11.02/11.23 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | ((~ssItem(X1!49)) | (~(cons(X1!49, nil) = nil)))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(157,plain,
% 11.02/11.23 ((~![V: $i] : ((~ssItem(V)) | (~(cons(V, nil) = nil)))) | (~ssItem(X1!49)) | (~(cons(X1!49, nil) = nil))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[156, 155])).
% 11.02/11.23 tff(158,plain,
% 11.02/11.23 (~(cons(X1!49, nil) = nil)),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[157, 37, 154])).
% 11.02/11.23 tff(159,plain,
% 11.02/11.23 (~(nil = cons(X1!49, nil))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[158, 137])).
% 11.02/11.23 tff(160,plain,
% 11.02/11.23 (((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) | (nil = cons(X1!49, nil))),
% 11.02/11.23 inference(tautology,[status(thm)],[])).
% 11.02/11.23 tff(161,plain,
% 11.02/11.23 ((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[160, 159])).
% 11.02/11.23 tff(162,plain,
% 11.02/11.23 ((((~(nil = Y!47)) | (~(nil = cons(X1!49, nil)))) <=> (nil = app(Y!47, cons(X1!49, nil)))) | (~((~(nil = Y!47)) | (~(nil = cons(X1!49, nil))))) | (~(nil = app(Y!47, cons(X1!49, nil))))),
% 11.02/11.23 inference(tautology,[status(thm)],[])).
% 11.02/11.23 tff(163,plain,
% 11.02/11.23 (~(nil = app(Y!47, cons(X1!49, nil)))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[162, 161, 134])).
% 11.02/11.23 tff(164,plain,
% 11.02/11.23 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(165,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[164])).
% 11.02/11.23 tff(166,plain,
% 11.02/11.23 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(167,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[166])).
% 11.02/11.23 tff(168,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[167, 165])).
% 11.02/11.23 tff(169,plain,
% 11.02/11.23 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U)))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(170,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[169])).
% 11.02/11.23 tff(171,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(172,plain,
% 11.02/11.23 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((frontsegP(U, V) & frontsegP(V, U)) => (U = V)) <=> ((~(frontsegP(U, V) & frontsegP(V, U))) | (U = V))), ((ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))) <=> (ssList(V) => ((~(frontsegP(U, V) & frontsegP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(frontsegP(U, V) & frontsegP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))), ((ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))))), (![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(173,plain,
% 11.02/11.23 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[172])).
% 11.02/11.23 tff(174,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((frontsegP(U, V) & frontsegP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax41')).
% 11.02/11.23 tff(175,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[174, 173])).
% 11.02/11.23 tff(176,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[175, 171])).
% 11.02/11.23 tff(177,plain,(
% 11.02/11.23 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(frontsegP(U, V) & frontsegP(V, U)))))),
% 11.02/11.23 inference(skolemize,[status(sab)],[176])).
% 11.02/11.23 tff(178,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[177, 170])).
% 11.02/11.23 tff(179,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[178, 168])).
% 11.02/11.23 tff(180,plain,
% 11.02/11.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | (~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(181,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil))))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(182,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~frontsegP(U, V)) | (~frontsegP(V, U))))) | (~ssList(nil)) | ![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[181, 180])).
% 11.02/11.23 tff(183,plain,
% 11.02/11.23 (![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[182, 3, 179])).
% 11.02/11.23 tff(184,plain,
% 11.02/11.23 (((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | ((nil = app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, app(Y!47, cons(X1!49, nil)))) | (~frontsegP(app(Y!47, cons(X1!49, nil)), nil)))) <=> ((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | (nil = app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, app(Y!47, cons(X1!49, nil)))) | (~frontsegP(app(Y!47, cons(X1!49, nil)), nil)))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(185,plain,
% 11.02/11.23 ((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | ((nil = app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, app(Y!47, cons(X1!49, nil)))) | (~frontsegP(app(Y!47, cons(X1!49, nil)), nil)))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(186,plain,
% 11.02/11.23 ((~![V: $i] : ((nil = V) | (~ssList(V)) | (~frontsegP(nil, V)) | (~frontsegP(V, nil)))) | (nil = app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, app(Y!47, cons(X1!49, nil)))) | (~frontsegP(app(Y!47, cons(X1!49, nil)), nil))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[185, 184])).
% 11.02/11.23 tff(187,plain,
% 11.02/11.23 ((nil = app(Y!47, cons(X1!49, nil))) | (~frontsegP(nil, app(Y!47, cons(X1!49, nil)))) | (~frontsegP(app(Y!47, cons(X1!49, nil)), nil))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[186, 183, 63])).
% 11.02/11.23 tff(188,plain,
% 11.02/11.23 (~frontsegP(nil, app(Y!47, cons(X1!49, nil)))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[187, 163, 107])).
% 11.02/11.23 tff(189,plain,
% 11.02/11.23 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(190,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[189])).
% 11.02/11.23 tff(191,plain,
% 11.02/11.23 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(192,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[191])).
% 11.02/11.23 tff(193,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[192, 190])).
% 11.02/11.23 tff(194,plain,
% 11.02/11.23 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(195,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[194])).
% 11.02/11.23 tff(196,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(197,plain,
% 11.02/11.23 (^[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(V, W)) => frontsegP(U, W)) <=> ((~(frontsegP(U, V) & frontsegP(V, W))) | frontsegP(U, W))), ((ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W))) <=> (ssList(W) => ((~(frontsegP(U, V) & frontsegP(V, W))) | frontsegP(U, W))))), rewrite((ssList(W) => ((~(frontsegP(U, V) & frontsegP(V, W))) | frontsegP(U, W))) <=> (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))), ((ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W))) <=> (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))), (![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W))) <=> ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W)))) <=> (ssList(V) => ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))), rewrite((ssList(V) => ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W)))) <=> ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(198,plain,
% 11.02/11.23 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[197])).
% 11.02/11.23 tff(199,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((frontsegP(U, V) & frontsegP(V, W)) => frontsegP(U, W)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax40')).
% 11.02/11.23 tff(200,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[199, 198])).
% 11.02/11.23 tff(201,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[200, 196])).
% 11.02/11.23 tff(202,plain,(
% 11.02/11.23 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~(frontsegP(U, V) & frontsegP(V, W))))))),
% 11.02/11.23 inference(skolemize,[status(sab)],[201])).
% 11.02/11.23 tff(203,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[202, 195])).
% 11.02/11.23 tff(204,plain,
% 11.02/11.23 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[203, 193])).
% 11.02/11.23 tff(205,plain,
% 11.02/11.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V)))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(206,plain,
% 11.02/11.23 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, V)) | (~frontsegP(V, W))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V)))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(207,plain,
% 11.02/11.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, V)) | (~frontsegP(V, W)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))))),
% 11.02/11.23 inference(monotonicity,[status(thm)],[206])).
% 11.02/11.23 tff(208,plain,
% 11.02/11.23 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, V)) | (~frontsegP(V, W)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V)))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[207, 205])).
% 11.02/11.23 tff(209,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, V)) | (~frontsegP(V, W)))))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(210,plain,
% 11.02/11.23 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(U, W) | (~ssList(W)) | (~frontsegP(U, V)) | (~frontsegP(V, W)))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[209, 208])).
% 11.02/11.23 tff(211,plain,
% 11.02/11.23 (![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[210, 3, 204])).
% 11.02/11.23 tff(212,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | ((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | (~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(213,plain,
% 11.02/11.23 (((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(U!45, W)) | (~frontsegP(nil, U!45)))) <=> ((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(214,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | ((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(U!45, W)) | (~frontsegP(nil, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | ((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))))),
% 11.02/11.23 inference(monotonicity,[status(thm)],[213])).
% 11.02/11.23 tff(215,plain,
% 11.02/11.23 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | ((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(U!45, W)) | (~frontsegP(nil, U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | (~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[214, 212])).
% 11.02/11.23 tff(216,plain,
% 11.02/11.23 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | ((~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(U!45, W)) | (~frontsegP(nil, U!45))))),
% 11.02/11.23 inference(quant_inst,[status(thm)],[])).
% 11.02/11.23 tff(217,plain,
% 11.02/11.23 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(V, W)) | (~frontsegP(nil, V))))) | (~ssList(U!45)) | ![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))),
% 11.02/11.23 inference(modus_ponens,[status(thm)],[216, 215])).
% 11.02/11.23 tff(218,plain,
% 11.02/11.23 (![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))),
% 11.02/11.23 inference(unit_resolution,[status(thm)],[217, 64, 211])).
% 11.02/11.23 tff(219,plain,
% 11.02/11.23 (^[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))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(220,plain,
% 11.02/11.23 (![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)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[219])).
% 11.02/11.23 tff(221,plain,
% 11.02/11.23 (^[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))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(222,plain,
% 11.02/11.23 (![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)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[221])).
% 11.02/11.23 tff(223,plain,
% 11.02/11.23 (![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)))))),
% 11.02/11.23 inference(transitivity,[status(thm)],[222, 220])).
% 11.02/11.23 tff(224,plain,
% 11.02/11.23 (![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)))))),
% 11.02/11.23 inference(rewrite,[status(thm)],[])).
% 11.02/11.23 tff(225,plain,
% 11.02/11.23 (^[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)))))))),
% 11.02/11.23 inference(bind,[status(th)],[])).
% 11.02/11.23 tff(226,plain,
% 11.02/11.23 (![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)))))),
% 11.02/11.23 inference(quant_intro,[status(thm)],[225])).
% 11.02/11.23 tff(227,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 11.02/11.24 tff(228,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[227, 226])).
% 11.02/11.24 tff(229,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[228, 224])).
% 11.02/11.24 tff(230,plain,(
% 11.02/11.24 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 11.02/11.24 inference(skolemize,[status(sab)],[229])).
% 11.02/11.24 tff(231,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[230, 223])).
% 11.02/11.24 tff(232,plain,
% 11.02/11.24 (((~![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)))))),
% 11.02/11.24 inference(rewrite,[status(thm)],[])).
% 11.02/11.24 tff(233,plain,
% 11.02/11.24 ((~![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)))))),
% 11.02/11.24 inference(quant_inst,[status(thm)],[])).
% 11.02/11.24 tff(234,plain,
% 11.02/11.24 ((~![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))))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[233, 232])).
% 11.02/11.24 tff(235,plain,
% 11.02/11.24 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 11.02/11.24 inference(unit_resolution,[status(thm)],[234, 231, 64])).
% 11.02/11.24 tff(236,plain,
% 11.02/11.24 (((~![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))))),
% 11.02/11.24 inference(rewrite,[status(thm)],[])).
% 11.02/11.24 tff(237,plain,
% 11.02/11.24 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 11.02/11.24 inference(quant_inst,[status(thm)],[])).
% 11.02/11.24 tff(238,plain,
% 11.02/11.24 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[237, 236])).
% 11.02/11.24 tff(239,plain,
% 11.02/11.24 (~((U!45 = nil) <=> neq(U!45, nil))),
% 11.02/11.24 inference(unit_resolution,[status(thm)],[238, 3, 235])).
% 11.02/11.24 tff(240,plain,
% 11.02/11.24 (~neq(U!45, nil)),
% 11.02/11.24 inference(and_elim,[status(thm)],[35])).
% 11.02/11.24 tff(241,plain,
% 11.02/11.24 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 11.02/11.24 inference(tautology,[status(thm)],[])).
% 11.02/11.24 tff(242,plain,
% 11.02/11.24 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil)),
% 11.02/11.24 inference(unit_resolution,[status(thm)],[241, 240])).
% 11.02/11.24 tff(243,plain,
% 11.02/11.24 (U!45 = nil),
% 11.02/11.24 inference(unit_resolution,[status(thm)],[242, 239])).
% 11.02/11.24 tff(244,plain,
% 11.02/11.24 (nil = U!45),
% 11.02/11.24 inference(symmetry,[status(thm)],[243])).
% 11.02/11.24 tff(245,plain,
% 11.02/11.24 (frontsegP(nil, U!45) <=> frontsegP(U!45, U!45)),
% 11.02/11.24 inference(monotonicity,[status(thm)],[244])).
% 11.02/11.24 tff(246,plain,
% 11.02/11.24 (frontsegP(U!45, U!45) <=> frontsegP(nil, U!45)),
% 11.02/11.24 inference(symmetry,[status(thm)],[245])).
% 11.02/11.24 tff(247,plain,
% 11.02/11.24 (^[U: $i] : refl(((~ssList(U)) | frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 11.02/11.24 inference(bind,[status(th)],[])).
% 11.02/11.24 tff(248,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(quant_intro,[status(thm)],[247])).
% 11.02/11.24 tff(249,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(rewrite,[status(thm)],[])).
% 11.02/11.24 tff(250,plain,
% 11.02/11.24 (^[U: $i] : rewrite((ssList(U) => frontsegP(U, U)) <=> ((~ssList(U)) | frontsegP(U, U)))),
% 11.02/11.24 inference(bind,[status(th)],[])).
% 11.02/11.24 tff(251,plain,
% 11.02/11.24 (![U: $i] : (ssList(U) => frontsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(quant_intro,[status(thm)],[250])).
% 11.02/11.24 tff(252,axiom,(![U: $i] : (ssList(U) => frontsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax42')).
% 11.02/11.24 tff(253,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[252, 251])).
% 11.02/11.24 tff(254,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[253, 249])).
% 11.02/11.24 tff(255,plain,(
% 11.02/11.24 ![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(skolemize,[status(sab)],[254])).
% 11.02/11.24 tff(256,plain,
% 11.02/11.24 (![U: $i] : ((~ssList(U)) | frontsegP(U, U))),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[255, 248])).
% 11.02/11.24 tff(257,plain,
% 11.02/11.24 (((~![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))),
% 11.02/11.24 inference(rewrite,[status(thm)],[])).
% 11.02/11.24 tff(258,plain,
% 11.02/11.24 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | ((~ssList(U!45)) | frontsegP(U!45, U!45))),
% 11.02/11.24 inference(quant_inst,[status(thm)],[])).
% 11.02/11.24 tff(259,plain,
% 11.02/11.24 ((~![U: $i] : ((~ssList(U)) | frontsegP(U, U))) | (~ssList(U!45)) | frontsegP(U!45, U!45)),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[258, 257])).
% 11.02/11.24 tff(260,plain,
% 11.02/11.24 (frontsegP(U!45, U!45)),
% 11.02/11.24 inference(unit_resolution,[status(thm)],[259, 256, 64])).
% 11.02/11.24 tff(261,plain,
% 11.02/11.24 (frontsegP(nil, U!45)),
% 11.02/11.24 inference(modus_ponens,[status(thm)],[260, 246])).
% 11.02/11.24 tff(262,plain,
% 11.02/11.24 (((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | ((~frontsegP(nil, U!45)) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil))))) <=> ((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | (~frontsegP(nil, U!45)) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil))))),
% 11.02/11.24 inference(rewrite,[status(thm)],[])).
% 11.02/11.24 tff(263,plain,
% 11.02/11.24 ((frontsegP(nil, app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil))))) <=> ((~frontsegP(nil, U!45)) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil))))),
% 11.02/11.24 inference(rewrite,[status(thm)],[])).
% 11.02/11.24 tff(264,plain,
% 11.02/11.24 (((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | (frontsegP(nil, app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))))) <=> ((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | ((~frontsegP(nil, U!45)) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil)))))),
% 11.02/11.24 inference(monotonicity,[status(thm)],[263])).
% 11.02/11.24 tff(265,plain,
% 11.02/11.24 (((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | (frontsegP(nil, app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))))) <=> ((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | (~frontsegP(nil, U!45)) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil))))),
% 11.02/11.24 inference(transitivity,[status(thm)],[264, 262])).
% 11.02/11.24 tff(266,plain,
% 11.02/11.24 ((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | (frontsegP(nil, app(Y!47, cons(X1!49, nil))) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))))),
% 11.02/11.24 inference(quant_inst,[status(thm)],[])).
% 11.02/11.24 tff(267,plain,
% 11.02/11.24 ((~![W: $i] : (frontsegP(nil, W) | (~ssList(W)) | (~frontsegP(nil, U!45)) | (~frontsegP(U!45, W)))) | (~frontsegP(nil, U!45)) | (~ssList(app(Y!47, cons(X1!49, nil)))) | (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil)))),
% 11.09/11.27 inference(modus_ponens,[status(thm)],[266, 265])).
% 11.09/11.27 tff(268,plain,
% 11.09/11.27 ((~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))) | frontsegP(nil, app(Y!47, cons(X1!49, nil)))),
% 11.09/11.27 inference(unit_resolution,[status(thm)],[267, 261, 218, 63])).
% 11.09/11.27 tff(269,plain,
% 11.09/11.27 (~frontsegP(U!45, app(Y!47, cons(X1!49, nil)))),
% 11.09/11.27 inference(unit_resolution,[status(thm)],[268, 188])).
% 11.09/11.27 tff(270,plain,
% 11.09/11.27 ((~(frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45))))) | frontsegP(U!45, app(Y!47, cons(X1!49, nil))) | ![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))),
% 11.09/11.27 inference(tautology,[status(thm)],[])).
% 11.09/11.27 tff(271,plain,
% 11.09/11.27 (![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))),
% 11.09/11.27 inference(unit_resolution,[status(thm)],[270, 269, 93])).
% 11.09/11.27 tff(272,plain,
% 11.09/11.27 (app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45),
% 11.09/11.27 inference(or_elim,[status(thm)],[36])).
% 11.09/11.27 tff(273,plain,
% 11.09/11.27 (ssList(Z!48)),
% 11.09/11.27 inference(and_elim,[status(thm)],[35])).
% 11.09/11.27 tff(274,plain,
% 11.09/11.27 (((~![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))) | ((~ssList(Z!48)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))) <=> ((~![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))) | (~ssList(Z!48)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))),
% 11.09/11.27 inference(rewrite,[status(thm)],[])).
% 11.09/11.27 tff(275,plain,
% 11.09/11.27 ((~![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))) | ((~ssList(Z!48)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45)))),
% 11.09/11.27 inference(quant_inst,[status(thm)],[])).
% 11.09/11.27 tff(276,plain,
% 11.09/11.27 ((~![W: $i] : ((~ssList(W)) | (~(app(app(Y!47, cons(X1!49, nil)), W) = U!45)))) | (~ssList(Z!48)) | (~(app(app(Y!47, cons(X1!49, nil)), Z!48) = U!45))),
% 11.09/11.27 inference(modus_ponens,[status(thm)],[275, 274])).
% 11.09/11.27 tff(277,plain,
% 11.09/11.27 ($false),
% 11.09/11.27 inference(unit_resolution,[status(thm)],[276, 273, 272, 271])).
% 11.09/11.27 % SZS output end Proof
% 11.09/11.27 % E exiting
%------------------------------------------------------------------------------