%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWC124+1 : TPTP v9.0.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:30:14 AM UTC 2025
% Result : Theorem 9.46s 9.64s
% Output : Proof 9.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC124+1 : TPTP v9.0.0. Released v2.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 08:24:53 EDT 2025
% 0.12/0.34 % CPUTime :
% 9.46/9.64 % SZS status Theorem
% 9.46/9.64 % SZS output start Proof
% 9.46/9.64 tff(segmentP_type, type, (
% 9.46/9.64 segmentP: ( $i * $i ) > $o)).
% 9.46/9.64 tff(tptp_fun_U_45_type, type, (
% 9.46/9.64 tptp_fun_U_45: $i)).
% 9.46/9.64 tff(app_type, type, (
% 9.46/9.64 app: ( $i * $i ) > $i)).
% 9.46/9.64 tff(tptp_fun_Y_47_type, type, (
% 9.46/9.64 tptp_fun_Y_47: $i)).
% 9.46/9.64 tff(nil_type, type, (
% 9.46/9.64 nil: $i)).
% 9.46/9.64 tff(tptp_fun_V_46_type, type, (
% 9.46/9.64 tptp_fun_V_46: $i)).
% 9.46/9.64 tff(neq_type, type, (
% 9.46/9.64 neq: ( $i * $i ) > $o)).
% 9.46/9.64 tff(leq_type, type, (
% 9.46/9.64 leq: ( $i * $i ) > $o)).
% 9.46/9.64 tff(cons_type, type, (
% 9.46/9.64 cons: ( $i * $i ) > $i)).
% 9.46/9.64 tff(ssList_type, type, (
% 9.46/9.64 ssList: $i > $o)).
% 9.46/9.64 tff(ssItem_type, type, (
% 9.46/9.64 ssItem: $i > $o)).
% 9.46/9.64 tff(totalorderedP_type, type, (
% 9.46/9.64 totalorderedP: $i > $o)).
% 9.46/9.64 tff(1,plain,
% 9.46/9.64 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(2,plain,
% 9.46/9.64 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(3,plain,
% 9.46/9.64 ((totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) <=> (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(4,plain,
% 9.46/9.64 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 9.46/9.64 inference(monotonicity,[status(thm)],[3])).
% 9.46/9.64 tff(5,plain,
% 9.46/9.64 (((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)) <=> ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 9.46/9.64 inference(transitivity,[status(thm)],[4, 2])).
% 9.46/9.64 tff(6,plain,
% 9.46/9.64 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))) <=> (ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)))),
% 9.46/9.64 inference(monotonicity,[status(thm)],[5])).
% 9.46/9.64 tff(7,plain,
% 9.46/9.64 ((ssList(U!45) & ((~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & (totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z))))))) & ssList(U!45) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))) <=> (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil))),
% 9.46/9.64 inference(transitivity,[status(thm)],[6, 1])).
% 9.46/9.64 tff(8,plain,
% 9.46/9.64 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)))))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(9,plain,
% 9.46/9.64 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~totalorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & leq(X2, Z)))))))) | ((~(nil = X)) & (nil = W))) | (neq(U, nil) & segmentP(V, U)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil)))))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(10,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~totalorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & leq(X2, Z)))))))) | ((~(nil = X)) & (nil = W))) | (neq(U, nil) & segmentP(V, U)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 9.46/9.64 tff(11,plain,
% 9.46/9.64 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[10, 9])).
% 9.46/9.64 tff(12,plain,
% 9.46/9.64 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[11, 8])).
% 9.46/9.64 tff(13,plain,
% 9.46/9.64 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[12, 8])).
% 9.46/9.64 tff(14,plain,
% 9.46/9.64 (~![U: $i] : ((~ssList(U)) | ![V: $i] : (((~(nil = V)) & (nil = U)) | (~ssList(V)) | ![Y: $i] : ((~totalorderedP(U)) | (~(app(U, Y) = V)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = U) & leq(X2, Z)))))) | (~ssList(U)) | (neq(U, nil) & segmentP(V, U)) | (~neq(V, nil))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[13, 8])).
% 9.46/9.64 tff(15,plain,
% 9.46/9.64 (ssList(U!45) & (~((~(nil = V!46)) & (nil = U!45))) & ssList(V!46) & totalorderedP(U!45) & (app(U!45, Y!47) = V!46) & ssList(Y!47) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!47)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = U!45) & leq(X2, Z)))))) & (~(neq(U!45, nil) & segmentP(V!46, U!45))) & neq(V!46, nil)),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[14, 7])).
% 9.46/9.64 tff(16,plain,
% 9.46/9.64 (app(U!45, Y!47) = V!46),
% 9.46/9.64 inference(and_elim,[status(thm)],[15])).
% 9.46/9.64 tff(17,plain,
% 9.46/9.64 (ssList(U!45)),
% 9.46/9.64 inference(and_elim,[status(thm)],[15])).
% 9.46/9.64 tff(18,plain,
% 9.46/9.64 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 9.46/9.64 inference(bind,[status(th)],[])).
% 9.46/9.64 tff(19,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(quant_intro,[status(thm)],[18])).
% 9.46/9.64 tff(20,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(21,plain,
% 9.46/9.64 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 9.46/9.64 inference(bind,[status(th)],[])).
% 9.46/9.64 tff(22,plain,
% 9.46/9.64 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(quant_intro,[status(thm)],[21])).
% 9.46/9.64 tff(23,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax28')).
% 9.46/9.64 tff(24,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[23, 22])).
% 9.46/9.64 tff(25,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[24, 20])).
% 9.46/9.64 tff(26,plain,(
% 9.46/9.64 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(skolemize,[status(sab)],[25])).
% 9.46/9.64 tff(27,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[26, 19])).
% 9.46/9.64 tff(28,plain,
% 9.46/9.64 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(29,plain,
% 9.46/9.64 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(U!45)) | (app(nil, U!45) = U!45))),
% 9.46/9.64 inference(quant_inst,[status(thm)],[])).
% 9.46/9.64 tff(30,plain,
% 9.46/9.64 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(U!45)) | (app(nil, U!45) = U!45)),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[29, 28])).
% 9.46/9.64 tff(31,plain,
% 9.46/9.64 (app(nil, U!45) = U!45),
% 9.46/9.64 inference(unit_resolution,[status(thm)],[30, 27, 17])).
% 9.46/9.64 tff(32,plain,
% 9.46/9.64 (app(app(nil, U!45), Y!47) = app(U!45, Y!47)),
% 9.46/9.64 inference(monotonicity,[status(thm)],[31])).
% 9.46/9.64 tff(33,plain,
% 9.46/9.64 (app(app(nil, U!45), Y!47) = V!46),
% 9.46/9.64 inference(transitivity,[status(thm)],[32, 16])).
% 9.46/9.64 tff(34,plain,
% 9.46/9.64 (segmentP(app(app(nil, U!45), Y!47), U!45) <=> segmentP(V!46, U!45)),
% 9.46/9.64 inference(monotonicity,[status(thm)],[33])).
% 9.46/9.64 tff(35,plain,
% 9.46/9.64 (segmentP(V!46, U!45) <=> segmentP(app(app(nil, U!45), Y!47), U!45)),
% 9.46/9.64 inference(symmetry,[status(thm)],[34])).
% 9.46/9.64 tff(36,plain,
% 9.46/9.64 ((~segmentP(V!46, U!45)) <=> (~segmentP(app(app(nil, U!45), Y!47), U!45))),
% 9.46/9.64 inference(monotonicity,[status(thm)],[35])).
% 9.46/9.64 tff(37,plain,
% 9.46/9.64 (^[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))))))),
% 9.46/9.64 inference(bind,[status(th)],[])).
% 9.46/9.64 tff(38,plain,
% 9.46/9.64 (![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)))))),
% 9.46/9.64 inference(quant_intro,[status(thm)],[37])).
% 9.46/9.64 tff(39,plain,
% 9.46/9.64 (^[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))))))),
% 9.46/9.64 inference(bind,[status(th)],[])).
% 9.46/9.64 tff(40,plain,
% 9.46/9.64 (![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)))))),
% 9.46/9.64 inference(quant_intro,[status(thm)],[39])).
% 9.46/9.64 tff(41,plain,
% 9.46/9.64 (![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)))))),
% 9.46/9.64 inference(transitivity,[status(thm)],[40, 38])).
% 9.46/9.64 tff(42,plain,
% 9.46/9.64 (![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)))))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(43,plain,
% 9.46/9.64 (^[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)))))))),
% 9.46/9.64 inference(bind,[status(th)],[])).
% 9.46/9.64 tff(44,plain,
% 9.46/9.64 (![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)))))),
% 9.46/9.64 inference(quant_intro,[status(thm)],[43])).
% 9.46/9.64 tff(45,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax15')).
% 9.46/9.64 tff(46,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[45, 44])).
% 9.46/9.64 tff(47,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[46, 42])).
% 9.46/9.64 tff(48,plain,(
% 9.46/9.64 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 9.46/9.64 inference(skolemize,[status(sab)],[47])).
% 9.46/9.64 tff(49,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[48, 41])).
% 9.46/9.64 tff(50,plain,
% 9.46/9.64 (((~![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)))))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(51,plain,
% 9.46/9.64 ((~![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)))))),
% 9.46/9.64 inference(quant_inst,[status(thm)],[])).
% 9.46/9.64 tff(52,plain,
% 9.46/9.64 ((~![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))))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[51, 50])).
% 9.46/9.64 tff(53,plain,
% 9.46/9.64 (![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))),
% 9.46/9.64 inference(unit_resolution,[status(thm)],[52, 49, 17])).
% 9.46/9.64 tff(54,plain,
% 9.46/9.64 (ssList(nil) <=> ssList(nil)),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(55,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 9.46/9.64 tff(56,plain,
% 9.46/9.64 (ssList(nil)),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[55, 54])).
% 9.46/9.64 tff(57,plain,
% 9.46/9.64 (((~![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))))),
% 9.46/9.64 inference(rewrite,[status(thm)],[])).
% 9.46/9.64 tff(58,plain,
% 9.46/9.64 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | ((~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil))))),
% 9.46/9.64 inference(quant_inst,[status(thm)],[])).
% 9.46/9.64 tff(59,plain,
% 9.46/9.64 ((~![V: $i] : ((~ssList(V)) | (~((U!45 = V) <=> neq(U!45, V))))) | (~ssList(nil)) | (~((U!45 = nil) <=> neq(U!45, nil)))),
% 9.46/9.64 inference(modus_ponens,[status(thm)],[58, 57])).
% 9.46/9.64 tff(60,plain,
% 9.46/9.64 (~((U!45 = nil) <=> neq(U!45, nil))),
% 9.46/9.64 inference(unit_resolution,[status(thm)],[59, 56, 53])).
% 9.46/9.64 tff(61,plain,
% 9.46/9.64 ((U!45 = nil) <=> (nil = U!45)),
% 9.46/9.64 inference(commutativity,[status(thm)],[])).
% 9.46/9.64 tff(62,plain,
% 9.46/9.64 ((nil = U!45) <=> (U!45 = nil)),
% 9.46/9.64 inference(symmetry,[status(thm)],[61])).
% 9.46/9.64 tff(63,plain,
% 9.46/9.64 ((~(nil = U!45)) <=> (~(U!45 = nil))),
% 9.46/9.64 inference(monotonicity,[status(thm)],[62])).
% 9.46/9.64 tff(64,plain,
% 9.46/9.64 (ssList(V!46)),
% 9.46/9.64 inference(and_elim,[status(thm)],[15])).
% 9.46/9.64 tff(65,plain,
% 9.46/9.64 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 9.46/9.64 inference(bind,[status(th)],[])).
% 9.46/9.64 tff(66,plain,
% 9.46/9.64 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[65])).
% 9.46/9.65 tff(67,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(68,plain,
% 9.46/9.65 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(69,plain,
% 9.46/9.65 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[68])).
% 9.46/9.65 tff(70,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax58')).
% 9.46/9.65 tff(71,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[70, 69])).
% 9.46/9.65 tff(72,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[71, 67])).
% 9.46/9.65 tff(73,plain,(
% 9.46/9.65 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(skolemize,[status(sab)],[72])).
% 9.46/9.65 tff(74,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[73, 66])).
% 9.46/9.65 tff(75,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(76,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46)))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(77,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(V!46)) | (segmentP(nil, V!46) <=> (nil = V!46))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[76, 75])).
% 9.46/9.65 tff(78,plain,
% 9.46/9.65 (segmentP(nil, V!46) <=> (nil = V!46)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[77, 74, 64])).
% 9.46/9.65 tff(79,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(80,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V)))))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(81,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((U = V) <=> neq(U, V)))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[80, 79])).
% 9.46/9.65 tff(82,plain,
% 9.46/9.65 (![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[81, 49, 64])).
% 9.46/9.65 tff(83,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(84,plain,
% 9.46/9.65 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | ((~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil))))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(85,plain,
% 9.46/9.65 ((~![V: $i] : ((~ssList(V)) | (~((V!46 = V) <=> neq(V!46, V))))) | (~ssList(nil)) | (~((V!46 = nil) <=> neq(V!46, nil)))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[84, 83])).
% 9.46/9.65 tff(86,plain,
% 9.46/9.65 (~((V!46 = nil) <=> neq(V!46, nil))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[85, 56, 82])).
% 9.46/9.65 tff(87,plain,
% 9.46/9.65 (neq(V!46, nil)),
% 9.46/9.65 inference(and_elim,[status(thm)],[15])).
% 9.46/9.65 tff(88,plain,
% 9.46/9.65 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil)) | (~neq(V!46, nil))),
% 9.46/9.65 inference(tautology,[status(thm)],[])).
% 9.46/9.65 tff(89,plain,
% 9.46/9.65 (((V!46 = nil) <=> neq(V!46, nil)) | (~(V!46 = nil))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[88, 87])).
% 9.46/9.65 tff(90,plain,
% 9.46/9.65 (~(V!46 = nil)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[89, 86])).
% 9.46/9.65 tff(91,plain,
% 9.46/9.65 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(92,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[91])).
% 9.46/9.65 tff(93,plain,
% 9.46/9.65 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(94,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[93])).
% 9.46/9.65 tff(95,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.46/9.65 inference(transitivity,[status(thm)],[94, 92])).
% 9.46/9.65 tff(96,plain,
% 9.46/9.65 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U)))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(97,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[96])).
% 9.46/9.65 tff(98,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(99,plain,
% 9.46/9.65 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((segmentP(U, V) & segmentP(V, U)) => (U = V)) <=> ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> (ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))))), rewrite((ssList(V) => ((~(segmentP(U, V) & segmentP(V, U))) | (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))), ((ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), (![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> (ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))))), rewrite((ssList(U) => ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U))))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(100,plain,
% 9.46/9.65 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[99])).
% 9.46/9.65 tff(101,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax54')).
% 9.46/9.65 tff(102,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[101, 100])).
% 9.46/9.65 tff(103,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[102, 98])).
% 9.46/9.65 tff(104,plain,(
% 9.46/9.65 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 9.46/9.65 inference(skolemize,[status(sab)],[103])).
% 9.46/9.65 tff(105,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[104, 97])).
% 9.46/9.65 tff(106,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[105, 95])).
% 9.46/9.65 tff(107,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(108,plain,
% 9.46/9.65 (((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) <=> ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(109,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))))),
% 9.46/9.65 inference(monotonicity,[status(thm)],[108])).
% 9.46/9.65 tff(110,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 9.46/9.65 inference(transitivity,[status(thm)],[109, 107])).
% 9.46/9.65 tff(111,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(V!46)) | ![V: $i] : ((V!46 = V) | (~ssList(V)) | (~segmentP(V!46, V)) | (~segmentP(V, V!46))))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(112,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(V!46)) | ![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[111, 110])).
% 9.46/9.65 tff(113,plain,
% 9.46/9.65 (![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[112, 106, 64])).
% 9.46/9.65 tff(114,plain,
% 9.46/9.65 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(115,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[114])).
% 9.46/9.65 tff(116,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(117,plain,
% 9.46/9.65 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(118,plain,
% 9.46/9.65 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[117])).
% 9.46/9.65 tff(119,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax57')).
% 9.46/9.65 tff(120,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[119, 118])).
% 9.46/9.65 tff(121,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[120, 116])).
% 9.46/9.65 tff(122,plain,(
% 9.46/9.65 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(skolemize,[status(sab)],[121])).
% 9.46/9.65 tff(123,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[122, 115])).
% 9.46/9.65 tff(124,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(125,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(V!46)) | segmentP(V!46, nil))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(126,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(V!46)) | segmentP(V!46, nil)),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[125, 124])).
% 9.46/9.65 tff(127,plain,
% 9.46/9.65 (segmentP(V!46, nil)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[126, 123, 64])).
% 9.46/9.65 tff(128,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(129,plain,
% 9.46/9.65 (((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46))) <=> ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(130,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))))),
% 9.46/9.65 inference(monotonicity,[status(thm)],[129])).
% 9.46/9.65 tff(131,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))) <=> ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil)))),
% 9.46/9.65 inference(transitivity,[status(thm)],[130, 128])).
% 9.46/9.65 tff(132,plain,
% 9.46/9.65 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | ((~ssList(nil)) | (V!46 = nil) | (~segmentP(V!46, nil)) | (~segmentP(nil, V!46)))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(133,plain,
% 9.46/9.65 ((~![V: $i] : ((~ssList(V)) | (V!46 = V) | (~segmentP(V!46, V)) | (~segmentP(V, V!46)))) | (~ssList(nil)) | (~segmentP(nil, V!46)) | (V!46 = nil) | (~segmentP(V!46, nil))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[132, 131])).
% 9.46/9.65 tff(134,plain,
% 9.46/9.65 ((~segmentP(nil, V!46)) | (V!46 = nil)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[133, 56, 127, 113])).
% 9.46/9.65 tff(135,plain,
% 9.46/9.65 (~segmentP(nil, V!46)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[134, 90])).
% 9.46/9.65 tff(136,plain,
% 9.46/9.65 ((~(segmentP(nil, V!46) <=> (nil = V!46))) | segmentP(nil, V!46) | (~(nil = V!46))),
% 9.46/9.65 inference(tautology,[status(thm)],[])).
% 9.46/9.65 tff(137,plain,
% 9.46/9.65 (~(nil = V!46)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[136, 135, 78])).
% 9.46/9.65 tff(138,plain,
% 9.46/9.65 ((~(~((nil = V!46) | (~(nil = U!45))))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(139,plain,
% 9.46/9.65 (((~(nil = V!46)) & (nil = U!45)) <=> (~((nil = V!46) | (~(nil = U!45))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(140,plain,
% 9.46/9.65 ((~((~(nil = V!46)) & (nil = U!45))) <=> (~(~((nil = V!46) | (~(nil = U!45)))))),
% 9.46/9.65 inference(monotonicity,[status(thm)],[139])).
% 9.46/9.65 tff(141,plain,
% 9.46/9.65 ((~((~(nil = V!46)) & (nil = U!45))) <=> ((nil = V!46) | (~(nil = U!45)))),
% 9.46/9.65 inference(transitivity,[status(thm)],[140, 138])).
% 9.46/9.65 tff(142,plain,
% 9.46/9.65 (~((~(nil = V!46)) & (nil = U!45))),
% 9.46/9.65 inference(and_elim,[status(thm)],[15])).
% 9.46/9.65 tff(143,plain,
% 9.46/9.65 ((nil = V!46) | (~(nil = U!45))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[142, 141])).
% 9.46/9.65 tff(144,plain,
% 9.46/9.65 (~(nil = U!45)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[143, 137])).
% 9.46/9.65 tff(145,plain,
% 9.46/9.65 (~(U!45 = nil)),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[144, 63])).
% 9.46/9.65 tff(146,plain,
% 9.46/9.65 (((U!45 = nil) <=> neq(U!45, nil)) | (U!45 = nil) | neq(U!45, nil)),
% 9.46/9.65 inference(tautology,[status(thm)],[])).
% 9.46/9.65 tff(147,plain,
% 9.46/9.65 (neq(U!45, nil)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[146, 145, 60])).
% 9.46/9.65 tff(148,plain,
% 9.46/9.65 ((~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(149,plain,
% 9.46/9.65 ((neq(U!45, nil) & segmentP(V!46, U!45)) <=> (~((~neq(U!45, nil)) | (~segmentP(V!46, U!45))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(150,plain,
% 9.46/9.65 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> (~(~((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))))),
% 9.46/9.65 inference(monotonicity,[status(thm)],[149])).
% 9.46/9.65 tff(151,plain,
% 9.46/9.65 ((~(neq(U!45, nil) & segmentP(V!46, U!45))) <=> ((~neq(U!45, nil)) | (~segmentP(V!46, U!45)))),
% 9.46/9.65 inference(transitivity,[status(thm)],[150, 148])).
% 9.46/9.65 tff(152,plain,
% 9.46/9.65 (~(neq(U!45, nil) & segmentP(V!46, U!45))),
% 9.46/9.65 inference(and_elim,[status(thm)],[15])).
% 9.46/9.65 tff(153,plain,
% 9.46/9.65 ((~neq(U!45, nil)) | (~segmentP(V!46, U!45))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[152, 151])).
% 9.46/9.65 tff(154,plain,
% 9.46/9.65 (~segmentP(V!46, U!45)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[153, 147])).
% 9.46/9.65 tff(155,plain,
% 9.46/9.65 (~segmentP(app(app(nil, U!45), Y!47), U!45)),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[154, 36])).
% 9.46/9.65 tff(156,plain,
% 9.46/9.65 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(157,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[156])).
% 9.46/9.65 tff(158,plain,
% 9.46/9.65 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(159,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[158])).
% 9.46/9.65 tff(160,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(transitivity,[status(thm)],[159, 157])).
% 9.46/9.65 tff(161,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(162,plain,
% 9.46/9.65 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((segmentP(U, V) => segmentP(app(app(W, U), X), V)) <=> ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))))), rewrite((ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), (![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> (ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), rewrite((ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), (![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(163,plain,
% 9.46/9.65 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[162])).
% 9.46/9.65 tff(164,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax56')).
% 9.46/9.65 tff(165,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[164, 163])).
% 9.46/9.65 tff(166,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[165, 161])).
% 9.46/9.65 tff(167,plain,(
% 9.46/9.65 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(skolemize,[status(sab)],[166])).
% 9.46/9.65 tff(168,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[167, 160])).
% 9.46/9.65 tff(169,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V))))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(170,plain,
% 9.46/9.65 (((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U!45), X), V) | (~ssList(X)) | (~segmentP(U!45, V)))))) <=> ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V))))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(171,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U!45), X), V) | (~ssList(X)) | (~segmentP(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))))),
% 9.46/9.65 inference(monotonicity,[status(thm)],[170])).
% 9.46/9.65 tff(172,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U!45), X), V) | (~ssList(X)) | (~segmentP(U!45, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V))))))),
% 9.46/9.65 inference(transitivity,[status(thm)],[171, 169])).
% 9.46/9.65 tff(173,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U!45), X), V) | (~ssList(X)) | (~segmentP(U!45, V))))))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(174,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(U!45)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[173, 172])).
% 9.46/9.65 tff(175,plain,
% 9.46/9.65 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[174, 168, 17])).
% 9.46/9.65 tff(176,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(177,plain,
% 9.46/9.65 (((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), U!45) | (~segmentP(U!45, U!45))))) <=> ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45))))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(178,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), U!45) | (~segmentP(U!45, U!45)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))))),
% 9.46/9.65 inference(monotonicity,[status(thm)],[177])).
% 9.46/9.65 tff(179,plain,
% 9.46/9.65 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), U!45) | (~segmentP(U!45, U!45)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45))))),
% 9.46/9.65 inference(transitivity,[status(thm)],[178, 176])).
% 9.46/9.65 tff(180,plain,
% 9.46/9.65 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | ((~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), U!45) | (~segmentP(U!45, U!45)))))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(181,plain,
% 9.46/9.65 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, U!45), X), V) | (~segmentP(U!45, V)))))) | (~ssList(U!45)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[180, 179])).
% 9.46/9.65 tff(182,plain,
% 9.46/9.65 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[181, 17, 175])).
% 9.46/9.65 tff(183,plain,
% 9.46/9.65 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45)))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45)))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(184,plain,
% 9.46/9.65 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45)))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(185,plain,
% 9.46/9.65 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(W, U!45), X), U!45)))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[184, 183])).
% 9.46/9.65 tff(186,plain,
% 9.46/9.65 (![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45))),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[185, 56, 182])).
% 9.46/9.65 tff(187,plain,
% 9.46/9.65 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(188,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[187])).
% 9.46/9.65 tff(189,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(190,plain,
% 9.46/9.65 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 9.46/9.65 inference(bind,[status(th)],[])).
% 9.46/9.65 tff(191,plain,
% 9.46/9.65 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(quant_intro,[status(thm)],[190])).
% 9.46/9.65 tff(192,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax55')).
% 9.46/9.65 tff(193,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[192, 191])).
% 9.46/9.65 tff(194,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[193, 189])).
% 9.46/9.65 tff(195,plain,(
% 9.46/9.65 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(skolemize,[status(sab)],[194])).
% 9.46/9.65 tff(196,plain,
% 9.46/9.65 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[195, 188])).
% 9.46/9.65 tff(197,plain,
% 9.46/9.65 (((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(U!45)) | segmentP(U!45, U!45))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(U!45)) | segmentP(U!45, U!45))),
% 9.46/9.65 inference(rewrite,[status(thm)],[])).
% 9.46/9.65 tff(198,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(U!45)) | segmentP(U!45, U!45))),
% 9.46/9.65 inference(quant_inst,[status(thm)],[])).
% 9.46/9.65 tff(199,plain,
% 9.46/9.65 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(U!45)) | segmentP(U!45, U!45)),
% 9.46/9.65 inference(modus_ponens,[status(thm)],[198, 197])).
% 9.46/9.65 tff(200,plain,
% 9.46/9.65 (segmentP(U!45, U!45)),
% 9.46/9.65 inference(unit_resolution,[status(thm)],[199, 196, 17])).
% 9.46/9.65 tff(201,plain,
% 9.46/9.65 (ssList(Y!47)),
% 9.46/9.65 inference(and_elim,[status(thm)],[15])).
% 9.46/9.65 tff(202,plain,
% 9.46/9.65 (((~![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45))) | ((~ssList(Y!47)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), Y!47), U!45))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45))) | (~ssList(Y!47)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), Y!47), U!45))),
% 9.46/9.69 inference(rewrite,[status(thm)],[])).
% 9.46/9.69 tff(203,plain,
% 9.46/9.69 ((~![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45))) | ((~ssList(Y!47)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), Y!47), U!45))),
% 9.46/9.69 inference(quant_inst,[status(thm)],[])).
% 9.46/9.69 tff(204,plain,
% 9.46/9.69 ((~![X: $i] : ((~ssList(X)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), X), U!45))) | (~ssList(Y!47)) | (~segmentP(U!45, U!45)) | segmentP(app(app(nil, U!45), Y!47), U!45)),
% 9.46/9.69 inference(modus_ponens,[status(thm)],[203, 202])).
% 9.46/9.69 tff(205,plain,
% 9.46/9.69 (segmentP(app(app(nil, U!45), Y!47), U!45)),
% 9.46/9.69 inference(unit_resolution,[status(thm)],[204, 201, 200, 186])).
% 9.46/9.69 tff(206,plain,
% 9.46/9.69 ($false),
% 9.46/9.69 inference(unit_resolution,[status(thm)],[205, 155])).
% 9.46/9.69 % SZS output end Proof
% 9.46/9.69 % E exiting
%------------------------------------------------------------------------------