TSTP Solution File: SWC373+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC373+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 : Tue Sep 20 11:57:30 EDT 2022
% Result : Theorem 2.98s 2.20s
% Output : Proof 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC373+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n009.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 : Sun Sep 4 00:25:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 2.98/2.20 % SZS status Theorem
% 2.98/2.20 % SZS output start Proof
% 2.98/2.20 tff(segmentP_type, type, (
% 2.98/2.20 segmentP: ( $i * $i ) > $o)).
% 2.98/2.20 tff(tptp_fun_W_49_type, type, (
% 2.98/2.20 tptp_fun_W_49: $i)).
% 2.98/2.20 tff(app_type, type, (
% 2.98/2.20 app: ( $i * $i ) > $i)).
% 2.98/2.20 tff(nil_type, type, (
% 2.98/2.20 nil: $i)).
% 2.98/2.20 tff(tptp_fun_W_6_type, type, (
% 2.98/2.20 tptp_fun_W_6: ( $i * $i ) > $i)).
% 2.98/2.20 tff(tptp_fun_X_50_type, type, (
% 2.98/2.20 tptp_fun_X_50: $i)).
% 2.98/2.20 tff(tptp_fun_U_47_type, type, (
% 2.98/2.20 tptp_fun_U_47: $i)).
% 2.98/2.20 tff(tptp_fun_V_48_type, type, (
% 2.98/2.20 tptp_fun_V_48: $i)).
% 2.98/2.20 tff(ssList_type, type, (
% 2.98/2.20 ssList: $i > $o)).
% 2.98/2.20 tff(rearsegP_type, type, (
% 2.98/2.20 rearsegP: ( $i * $i ) > $o)).
% 2.98/2.20 tff(1,plain,
% 2.98/2.20 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(2,plain,
% 2.98/2.20 ((ssList(V!48) & (ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(3,plain,
% 2.98/2.20 (((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(4,plain,
% 2.98/2.20 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(5,plain,
% 2.98/2.20 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 2.98/2.20 inference(monotonicity,[status(thm)],[4, 3])).
% 2.98/2.20 tff(6,plain,
% 2.98/2.20 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 2.98/2.20 inference(transitivity,[status(thm)],[5, 2])).
% 2.98/2.20 tff(7,plain,
% 2.98/2.20 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(8,plain,
% 2.98/2.20 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 2.98/2.20 inference(monotonicity,[status(thm)],[7, 6])).
% 2.98/2.20 tff(9,plain,
% 2.98/2.20 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(segmentP(V!48, U!47) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~(U!47 = W!49)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 2.98/2.20 inference(transitivity,[status(thm)],[8, 1])).
% 2.98/2.20 tff(10,plain,
% 2.98/2.20 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)))))))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(11,plain,
% 2.98/2.20 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~rearsegP(X, W))) | segmentP(V, U))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)))))))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((~(V = X)) | (~(U = W))) | (~rearsegP(X, W))) | segmentP(V, U))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','co1')).
% 2.98/2.20 tff(13,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[12, 11])).
% 2.98/2.20 tff(14,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[13, 10])).
% 2.98/2.20 tff(15,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[14, 10])).
% 2.98/2.20 tff(16,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[15, 10])).
% 2.98/2.20 tff(17,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[16, 10])).
% 2.98/2.20 tff(18,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[17, 10])).
% 2.98/2.20 tff(19,plain,
% 2.98/2.20 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | (~rearsegP(X, W)) | (~(V = X)) | (~(U = W)) | (~ssList(X))))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[18, 10])).
% 2.98/2.20 tff(20,plain,
% 2.98/2.20 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[19, 9])).
% 2.98/2.20 tff(21,plain,
% 2.98/2.20 (~(segmentP(V!48, U!47) | (~(U!47 = W!49)) | (~rearsegP(X!50, W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))),
% 2.98/2.20 inference(and_elim,[status(thm)],[20])).
% 2.98/2.20 tff(22,plain,
% 2.98/2.20 (U!47 = W!49),
% 2.98/2.20 inference(or_elim,[status(thm)],[21])).
% 2.98/2.20 tff(23,plain,
% 2.98/2.20 (W!49 = U!47),
% 2.98/2.20 inference(symmetry,[status(thm)],[22])).
% 2.98/2.20 tff(24,plain,
% 2.98/2.20 (V!48 = X!50),
% 2.98/2.20 inference(or_elim,[status(thm)],[21])).
% 2.98/2.20 tff(25,plain,
% 2.98/2.20 (X!50 = V!48),
% 2.98/2.20 inference(symmetry,[status(thm)],[24])).
% 2.98/2.20 tff(26,plain,
% 2.98/2.20 (ssList(X!50)),
% 2.98/2.20 inference(or_elim,[status(thm)],[21])).
% 2.98/2.20 tff(27,plain,
% 2.98/2.20 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 2.98/2.20 inference(bind,[status(th)],[])).
% 2.98/2.20 tff(28,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(quant_intro,[status(thm)],[27])).
% 2.98/2.20 tff(29,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(30,plain,
% 2.98/2.20 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 2.98/2.20 inference(bind,[status(th)],[])).
% 2.98/2.20 tff(31,plain,
% 2.98/2.20 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(quant_intro,[status(thm)],[30])).
% 2.98/2.20 tff(32,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax84')).
% 2.98/2.20 tff(33,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.98/2.20 tff(34,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[33, 29])).
% 2.98/2.20 tff(35,plain,(
% 2.98/2.20 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(skolemize,[status(sab)],[34])).
% 2.98/2.20 tff(36,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[35, 28])).
% 2.98/2.20 tff(37,plain,
% 2.98/2.20 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 2.98/2.20 inference(rewrite,[status(thm)],[])).
% 2.98/2.20 tff(38,plain,
% 2.98/2.20 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(X!50)) | (app(X!50, nil) = X!50))),
% 2.98/2.20 inference(quant_inst,[status(thm)],[])).
% 2.98/2.20 tff(39,plain,
% 2.98/2.20 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(X!50)) | (app(X!50, nil) = X!50)),
% 2.98/2.20 inference(modus_ponens,[status(thm)],[38, 37])).
% 2.98/2.20 tff(40,plain,
% 2.98/2.20 (app(X!50, nil) = X!50),
% 2.98/2.20 inference(unit_resolution,[status(thm)],[39, 36, 26])).
% 2.98/2.20 tff(41,plain,
% 2.98/2.20 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 2.98/2.20 inference(bind,[status(th)],[])).
% 2.98/2.20 tff(42,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 2.98/2.20 inference(quant_intro,[status(thm)],[41])).
% 2.98/2.20 tff(43,plain,
% 2.98/2.20 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 2.98/2.20 inference(bind,[status(th)],[])).
% 2.98/2.20 tff(44,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 2.98/2.20 inference(quant_intro,[status(thm)],[43])).
% 2.98/2.20 tff(45,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 2.98/2.20 inference(transitivity,[status(thm)],[44, 42])).
% 2.98/2.20 tff(46,plain,
% 2.98/2.20 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 2.98/2.20 inference(bind,[status(th)],[])).
% 2.98/2.20 tff(47,plain,
% 2.98/2.20 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 2.98/2.21 inference(quant_intro,[status(thm)],[46])).
% 2.98/2.21 tff(48,plain,
% 2.98/2.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 2.98/2.21 inference(rewrite,[status(thm)],[])).
% 2.98/2.21 tff(49,plain,
% 2.98/2.21 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))) <=> (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), rewrite((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), (![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))))),
% 2.98/2.21 inference(bind,[status(th)],[])).
% 2.98/2.21 tff(50,plain,
% 2.98/2.21 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 2.98/2.21 inference(quant_intro,[status(thm)],[49])).
% 2.98/2.21 tff(51,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax6')).
% 2.98/2.21 tff(52,plain,
% 2.98/2.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 2.98/2.21 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.98/2.21 tff(53,plain,
% 2.98/2.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 2.98/2.21 inference(modus_ponens,[status(thm)],[52, 48])).
% 2.98/2.21 tff(54,plain,(
% 2.98/2.21 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U)))))))),
% 2.98/2.21 inference(skolemize,[status(sab)],[53])).
% 2.98/2.21 tff(55,plain,
% 2.98/2.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 2.98/2.21 inference(modus_ponens,[status(thm)],[54, 47])).
% 2.98/2.21 tff(56,plain,
% 2.98/2.21 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 2.98/2.21 inference(modus_ponens,[status(thm)],[55, 45])).
% 2.98/2.21 tff(57,plain,
% 2.98/2.21 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50)))))))))),
% 2.98/2.21 inference(rewrite,[status(thm)],[])).
% 2.98/2.21 tff(58,plain,
% 2.98/2.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50)))))))))),
% 2.98/2.21 inference(quant_inst,[status(thm)],[])).
% 2.98/2.21 tff(59,plain,
% 2.98/2.21 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))),
% 2.98/2.21 inference(modus_ponens,[status(thm)],[58, 57])).
% 2.98/2.21 tff(60,plain,
% 2.98/2.21 (![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))),
% 2.98/2.21 inference(unit_resolution,[status(thm)],[59, 56, 26])).
% 2.98/2.21 tff(61,plain,
% 2.98/2.21 (ssList(W!49)),
% 2.98/2.21 inference(and_elim,[status(thm)],[20])).
% 2.98/2.21 tff(62,plain,
% 2.98/2.21 (((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | ((~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | (~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))))),
% 2.98/2.21 inference(rewrite,[status(thm)],[])).
% 2.98/2.21 tff(63,plain,
% 2.98/2.21 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | ((~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))))),
% 2.98/2.21 inference(quant_inst,[status(thm)],[])).
% 2.98/2.21 tff(64,plain,
% 2.98/2.21 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X!50, V)) | (~((~ssList(tptp_fun_W_6(V, X!50))) | (~(app(tptp_fun_W_6(V, X!50), V) = X!50)))))) | (~(rearsegP(X!50, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X!50))))))))) | (~ssList(W!49)) | (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50)))))))),
% 2.98/2.21 inference(modus_ponens,[status(thm)],[63, 62])).
% 2.98/2.21 tff(65,plain,
% 2.98/2.21 (~((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50))))))),
% 2.98/2.21 inference(unit_resolution,[status(thm)],[64, 61, 60])).
% 2.98/2.21 tff(66,plain,
% 2.98/2.21 (((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~(rearsegP(X!50, W!49) | ![W: $i] : ((~ssList(W)) | (~(app(W, W!49) = X!50)))))) | ((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))),
% 2.98/2.21 inference(tautology,[status(thm)],[])).
% 2.98/2.21 tff(67,plain,
% 2.98/2.21 ((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))))),
% 2.98/2.21 inference(unit_resolution,[status(thm)],[66, 65])).
% 2.98/2.21 tff(68,plain,
% 2.98/2.21 (rearsegP(X!50, W!49)),
% 2.98/2.21 inference(or_elim,[status(thm)],[21])).
% 2.98/2.21 tff(69,plain,
% 2.98/2.21 ((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))))),
% 2.98/2.21 inference(tautology,[status(thm)],[])).
% 2.98/2.21 tff(70,plain,
% 2.98/2.21 ((~((~rearsegP(X!50, W!49)) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))))) | (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))))),
% 2.98/2.21 inference(unit_resolution,[status(thm)],[69, 68])).
% 2.98/2.21 tff(71,plain,
% 3.07/2.21 (~((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)))),
% 3.07/2.21 inference(unit_resolution,[status(thm)],[70, 67])).
% 3.07/2.21 tff(72,plain,
% 3.07/2.21 (((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))) | (app(tptp_fun_W_6(W!49, X!50), W!49) = X!50)),
% 3.07/2.21 inference(tautology,[status(thm)],[])).
% 3.07/2.21 tff(73,plain,
% 3.07/2.21 (app(tptp_fun_W_6(W!49, X!50), W!49) = X!50),
% 3.07/2.21 inference(unit_resolution,[status(thm)],[72, 71])).
% 3.07/2.21 tff(74,plain,
% 3.07/2.21 (app(app(tptp_fun_W_6(W!49, X!50), W!49), nil) = app(X!50, nil)),
% 3.07/2.21 inference(monotonicity,[status(thm)],[73])).
% 3.07/2.21 tff(75,plain,
% 3.07/2.21 (app(app(tptp_fun_W_6(W!49, X!50), W!49), nil) = V!48),
% 3.07/2.21 inference(transitivity,[status(thm)],[74, 40, 25])).
% 3.07/2.21 tff(76,plain,
% 3.07/2.21 (segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49) <=> segmentP(V!48, U!47)),
% 3.07/2.21 inference(monotonicity,[status(thm)],[75, 23])).
% 3.07/2.21 tff(77,plain,
% 3.07/2.21 (segmentP(V!48, U!47) <=> segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 3.07/2.21 inference(symmetry,[status(thm)],[76])).
% 3.07/2.21 tff(78,plain,
% 3.07/2.21 ((~segmentP(V!48, U!47)) <=> (~segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))),
% 3.07/2.21 inference(monotonicity,[status(thm)],[77])).
% 3.07/2.21 tff(79,plain,
% 3.07/2.21 (~segmentP(V!48, U!47)),
% 3.07/2.21 inference(or_elim,[status(thm)],[21])).
% 3.07/2.21 tff(80,plain,
% 3.07/2.21 (~segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[79, 78])).
% 3.07/2.21 tff(81,plain,
% 3.07/2.21 (((~ssList(tptp_fun_W_6(W!49, X!50))) | (~(app(tptp_fun_W_6(W!49, X!50), W!49) = X!50))) | ssList(tptp_fun_W_6(W!49, X!50))),
% 3.07/2.21 inference(tautology,[status(thm)],[])).
% 3.07/2.21 tff(82,plain,
% 3.07/2.21 (ssList(tptp_fun_W_6(W!49, X!50))),
% 3.07/2.21 inference(unit_resolution,[status(thm)],[81, 71])).
% 3.07/2.21 tff(83,plain,
% 3.07/2.21 (^[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)))))))),
% 3.07/2.21 inference(bind,[status(th)],[])).
% 3.07/2.21 tff(84,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(quant_intro,[status(thm)],[83])).
% 3.07/2.21 tff(85,plain,
% 3.07/2.21 (^[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)))))))),
% 3.07/2.21 inference(bind,[status(th)],[])).
% 3.07/2.21 tff(86,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(quant_intro,[status(thm)],[85])).
% 3.07/2.21 tff(87,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(transitivity,[status(thm)],[86, 84])).
% 3.07/2.21 tff(88,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(89,plain,
% 3.07/2.21 (^[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))))))))),
% 3.07/2.21 inference(bind,[status(th)],[])).
% 3.07/2.21 tff(90,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(quant_intro,[status(thm)],[89])).
% 3.07/2.21 tff(91,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')).
% 3.07/2.21 tff(92,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[91, 90])).
% 3.07/2.21 tff(93,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[92, 88])).
% 3.07/2.21 tff(94,plain,(
% 3.07/2.21 ![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))))))),
% 3.07/2.21 inference(skolemize,[status(sab)],[93])).
% 3.07/2.21 tff(95,plain,
% 3.07/2.21 (![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))))))),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[94, 87])).
% 3.07/2.21 tff(96,plain,
% 3.07/2.21 (((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, 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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(97,plain,
% 3.07/2.21 (((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V)))))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(98,plain,
% 3.07/2.21 (((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, 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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))))),
% 3.07/2.21 inference(monotonicity,[status(thm)],[97])).
% 3.07/2.21 tff(99,plain,
% 3.07/2.21 (((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, 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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 3.07/2.21 inference(transitivity,[status(thm)],[98, 96])).
% 3.07/2.21 tff(100,plain,
% 3.07/2.21 ((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))),
% 3.07/2.21 inference(quant_inst,[status(thm)],[])).
% 3.07/2.21 tff(101,plain,
% 3.07/2.21 ((~![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(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[100, 99])).
% 3.07/2.21 tff(102,plain,
% 3.07/2.21 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 3.07/2.21 inference(unit_resolution,[status(thm)],[101, 95, 61])).
% 3.07/2.21 tff(103,plain,
% 3.07/2.21 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(104,plain,
% 3.07/2.21 (((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49))))) <=> ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(105,plain,
% 3.07/2.21 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))))),
% 3.07/2.21 inference(monotonicity,[status(thm)],[104])).
% 3.07/2.21 tff(106,plain,
% 3.07/2.21 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 3.07/2.21 inference(transitivity,[status(thm)],[105, 103])).
% 3.07/2.21 tff(107,plain,
% 3.07/2.21 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))),
% 3.07/2.21 inference(quant_inst,[status(thm)],[])).
% 3.07/2.21 tff(108,plain,
% 3.07/2.21 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[107, 106])).
% 3.07/2.21 tff(109,plain,
% 3.07/2.21 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 3.07/2.21 inference(unit_resolution,[status(thm)],[108, 61, 102])).
% 3.07/2.21 tff(110,plain,
% 3.07/2.21 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49)))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49)))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(111,plain,
% 3.07/2.21 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49)))),
% 3.07/2.21 inference(quant_inst,[status(thm)],[])).
% 3.07/2.21 tff(112,plain,
% 3.07/2.21 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(tptp_fun_W_6(W!49, X!50))) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))),
% 3.07/2.21 inference(modus_ponens,[status(thm)],[111, 110])).
% 3.07/2.21 tff(113,plain,
% 3.07/2.21 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))),
% 3.07/2.21 inference(unit_resolution,[status(thm)],[112, 109, 82])).
% 3.07/2.21 tff(114,plain,
% 3.07/2.21 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 3.07/2.21 inference(bind,[status(th)],[])).
% 3.07/2.21 tff(115,plain,
% 3.07/2.21 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.21 inference(quant_intro,[status(thm)],[114])).
% 3.07/2.21 tff(116,plain,
% 3.07/2.21 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.21 inference(rewrite,[status(thm)],[])).
% 3.07/2.21 tff(117,plain,
% 3.07/2.21 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 3.07/2.21 inference(bind,[status(th)],[])).
% 3.07/2.21 tff(118,plain,
% 3.07/2.21 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.22 inference(quant_intro,[status(thm)],[117])).
% 3.07/2.22 tff(119,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax55')).
% 3.07/2.22 tff(120,plain,
% 3.07/2.22 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.22 inference(modus_ponens,[status(thm)],[119, 118])).
% 3.07/2.22 tff(121,plain,
% 3.07/2.22 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.22 inference(modus_ponens,[status(thm)],[120, 116])).
% 3.07/2.22 tff(122,plain,(
% 3.07/2.22 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.22 inference(skolemize,[status(sab)],[121])).
% 3.07/2.22 tff(123,plain,
% 3.07/2.22 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 3.07/2.22 inference(modus_ponens,[status(thm)],[122, 115])).
% 3.07/2.22 tff(124,plain,
% 3.07/2.22 (((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49))),
% 3.07/2.22 inference(rewrite,[status(thm)],[])).
% 3.07/2.22 tff(125,plain,
% 3.07/2.22 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 3.07/2.22 inference(quant_inst,[status(thm)],[])).
% 3.07/2.22 tff(126,plain,
% 3.07/2.22 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 3.07/2.22 inference(modus_ponens,[status(thm)],[125, 124])).
% 3.07/2.22 tff(127,plain,
% 3.07/2.22 (segmentP(W!49, W!49)),
% 3.07/2.22 inference(unit_resolution,[status(thm)],[126, 123, 61])).
% 3.07/2.22 tff(128,plain,
% 3.07/2.22 (ssList(nil) <=> ssList(nil)),
% 3.07/2.22 inference(rewrite,[status(thm)],[])).
% 3.07/2.22 tff(129,axiom,(ssList(nil)), file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax','ax17')).
% 3.07/2.22 tff(130,plain,
% 3.07/2.22 (ssList(nil)),
% 3.07/2.22 inference(modus_ponens,[status(thm)],[129, 128])).
% 3.07/2.22 tff(131,plain,
% 3.07/2.22 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | ((~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | (~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))),
% 3.07/2.22 inference(rewrite,[status(thm)],[])).
% 3.07/2.22 tff(132,plain,
% 3.07/2.22 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | ((~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49))),
% 3.07/2.22 inference(quant_inst,[status(thm)],[])).
% 3.07/2.22 tff(133,plain,
% 3.07/2.22 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), X), W!49))) | (~ssList(nil)) | (~segmentP(W!49, W!49)) | segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 3.07/2.22 inference(modus_ponens,[status(thm)],[132, 131])).
% 3.07/2.22 tff(134,plain,
% 3.07/2.22 (segmentP(app(app(tptp_fun_W_6(W!49, X!50), W!49), nil), W!49)),
% 3.07/2.22 inference(unit_resolution,[status(thm)],[133, 130, 127, 113])).
% 3.07/2.22 tff(135,plain,
% 3.07/2.22 ($false),
% 3.07/2.22 inference(unit_resolution,[status(thm)],[134, 80])).
% 3.07/2.22 % SZS output end Proof
%------------------------------------------------------------------------------