TSTP Solution File: SWC205+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC205+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 11:56:07 EDT 2022
% Result : Theorem 0.73s 0.74s
% Output : Proof 0.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC205+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Sep 3 22:34:35 EDT 2022
% 0.12/0.34 % 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.
% 0.73/0.74 % SZS status Theorem
% 0.73/0.74 % SZS output start Proof
% 0.73/0.74 tff(app_type, type, (
% 0.73/0.74 app: ( $i * $i ) > $i)).
% 0.73/0.74 tff(tptp_fun_W_49_type, type, (
% 0.73/0.74 tptp_fun_W_49: $i)).
% 0.73/0.74 tff(nil_type, type, (
% 0.73/0.74 nil: $i)).
% 0.73/0.74 tff(ssList_type, type, (
% 0.73/0.74 ssList: $i > $o)).
% 0.73/0.74 tff(tptp_fun_X_50_type, type, (
% 0.73/0.74 tptp_fun_X_50: $i)).
% 0.73/0.74 tff(tptp_fun_V_48_type, type, (
% 0.73/0.74 tptp_fun_V_48: $i)).
% 0.73/0.74 tff(tptp_fun_U_47_type, type, (
% 0.73/0.74 tptp_fun_U_47: $i)).
% 0.73/0.74 tff(neq_type, type, (
% 0.73/0.74 neq: ( $i * $i ) > $o)).
% 0.73/0.74 tff(segmentP_type, type, (
% 0.73/0.74 segmentP: ( $i * $i ) > $o)).
% 0.73/0.74 tff(1,plain,
% 0.73/0.74 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(2,plain,
% 0.73/0.74 ((ssList(V!48) & (ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(3,plain,
% 0.73/0.74 (((~(~ssList(W!49))) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))) <=> (ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(4,plain,
% 0.73/0.74 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(5,plain,
% 0.73/0.74 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & (ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.73/0.74 inference(monotonicity,[status(thm)],[4, 3])).
% 0.73/0.74 tff(6,plain,
% 0.73/0.74 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))) <=> (ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.73/0.74 inference(transitivity,[status(thm)],[5, 2])).
% 0.73/0.74 tff(7,plain,
% 0.73/0.74 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(8,plain,
% 0.73/0.74 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))),
% 0.73/0.74 inference(monotonicity,[status(thm)],[7, 6])).
% 0.73/0.74 tff(9,plain,
% 0.73/0.74 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(U!47 = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))))),
% 0.73/0.74 inference(transitivity,[status(thm)],[8, 1])).
% 0.73/0.74 tff(10,plain,
% 0.73/0.74 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)))))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(11,plain,
% 0.73/0.74 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = X)) & (nil = W))) | ((~(nil = W)) & (nil = X)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X)))))))),
% 0.73/0.74 inference(rewrite,[status(thm)],[])).
% 0.73/0.74 tff(12,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => ((((((~(V = X)) | (~(U = W))) | (~neq(V, nil))) | neq(U, nil)) | ((~(nil = X)) & (nil = W))) | ((~(nil = W)) & (nil = X)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.73/0.74 tff(13,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.73/0.74 tff(14,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[13, 10])).
% 0.73/0.74 tff(15,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.73/0.74 tff(16,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.73/0.74 tff(17,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[16, 10])).
% 0.73/0.74 tff(18,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.73/0.74 tff(19,plain,
% 0.73/0.74 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (neq(U, nil) | (~neq(V, nil)) | ((~(nil = W)) & (nil = X)) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~ssList(X))))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.73/0.74 tff(20,plain,
% 0.73/0.74 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50))))),
% 0.73/0.74 inference(modus_ponens,[status(thm)],[19, 9])).
% 0.73/0.74 tff(21,plain,
% 0.73/0.74 (ssList(W!49)),
% 0.73/0.74 inference(and_elim,[status(thm)],[20])).
% 0.73/0.74 tff(22,plain,
% 0.73/0.74 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.73/0.74 inference(bind,[status(th)],[])).
% 0.73/0.74 tff(23,plain,
% 0.73/0.74 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[22])).
% 0.73/0.75 tff(24,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(25,plain,
% 0.73/0.75 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(26,plain,
% 0.73/0.75 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[25])).
% 0.73/0.75 tff(27,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 0.73/0.75 tff(28,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.73/0.75 tff(29,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.73/0.75 tff(30,plain,(
% 0.73/0.75 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(skolemize,[status(sab)],[29])).
% 0.73/0.75 tff(31,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.73/0.75 tff(32,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(33,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(34,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49)),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.73/0.75 tff(35,plain,
% 0.73/0.75 (app(nil, W!49) = W!49),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[34, 31, 21])).
% 0.73/0.75 tff(36,plain,
% 0.73/0.75 ((nil = app(nil, W!49)) <=> (nil = W!49)),
% 0.73/0.75 inference(monotonicity,[status(thm)],[35])).
% 0.73/0.75 tff(37,plain,
% 0.73/0.75 ((nil = W!49) <=> (nil = app(nil, W!49))),
% 0.73/0.75 inference(symmetry,[status(thm)],[36])).
% 0.73/0.75 tff(38,plain,
% 0.73/0.75 ((W!49 = nil) <=> (nil = W!49)),
% 0.73/0.75 inference(commutativity,[status(thm)],[])).
% 0.73/0.75 tff(39,plain,
% 0.73/0.75 ((W!49 = nil) <=> (nil = app(nil, W!49))),
% 0.73/0.75 inference(transitivity,[status(thm)],[38, 37])).
% 0.73/0.75 tff(40,plain,
% 0.73/0.75 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(41,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[40])).
% 0.73/0.75 tff(42,plain,
% 0.73/0.75 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(43,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[42])).
% 0.73/0.75 tff(44,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[43, 41])).
% 0.73/0.75 tff(45,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(46,plain,
% 0.73/0.75 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), (![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))) <=> ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(47,plain,
% 0.73/0.75 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[46])).
% 0.73/0.75 tff(48,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (neq(U, V) <=> (~(U = V)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax15')).
% 0.73/0.75 tff(49,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.73/0.75 tff(50,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.73/0.75 tff(51,plain,(
% 0.73/0.75 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(skolemize,[status(sab)],[50])).
% 0.73/0.75 tff(52,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.73/0.75 tff(53,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(54,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V)))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(55,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.73/0.75 tff(56,plain,
% 0.73/0.75 (![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[55, 52, 21])).
% 0.73/0.75 tff(57,plain,
% 0.73/0.75 (ssList(nil) <=> ssList(nil)),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(58,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 0.73/0.75 tff(59,plain,
% 0.73/0.75 (ssList(nil)),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.73/0.75 tff(60,plain,
% 0.73/0.75 (((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(61,plain,
% 0.73/0.75 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | ((~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(62,plain,
% 0.73/0.75 ((~![V: $i] : ((~ssList(V)) | (neq(W!49, V) <=> (~(W!49 = V))))) | (~ssList(nil)) | (neq(W!49, nil) <=> (~(W!49 = nil)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.73/0.75 tff(63,plain,
% 0.73/0.75 (neq(W!49, nil) <=> (~(W!49 = nil))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[62, 59, 56])).
% 0.73/0.75 tff(64,plain,
% 0.73/0.75 (~(neq(U!47, nil) | (~neq(V!48, nil)) | (~(U!47 = W!49)) | ((~(nil = W!49)) & (nil = X!50)) | ((~(nil = X!50)) & (nil = W!49)) | (~(V!48 = X!50)) | (~ssList(X!50)))),
% 0.73/0.75 inference(and_elim,[status(thm)],[20])).
% 0.73/0.75 tff(65,plain,
% 0.73/0.75 (U!47 = W!49),
% 0.73/0.75 inference(or_elim,[status(thm)],[64])).
% 0.73/0.75 tff(66,plain,
% 0.73/0.75 (W!49 = U!47),
% 0.73/0.75 inference(symmetry,[status(thm)],[65])).
% 0.73/0.75 tff(67,plain,
% 0.73/0.75 (neq(W!49, nil) <=> neq(U!47, nil)),
% 0.73/0.75 inference(monotonicity,[status(thm)],[66])).
% 0.73/0.75 tff(68,plain,
% 0.73/0.75 (neq(U!47, nil) <=> neq(W!49, nil)),
% 0.73/0.75 inference(symmetry,[status(thm)],[67])).
% 0.73/0.75 tff(69,plain,
% 0.73/0.75 ((~neq(U!47, nil)) <=> (~neq(W!49, nil))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[68])).
% 0.73/0.75 tff(70,plain,
% 0.73/0.75 (~neq(U!47, nil)),
% 0.73/0.75 inference(or_elim,[status(thm)],[64])).
% 0.73/0.75 tff(71,plain,
% 0.73/0.75 (~neq(W!49, nil)),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.73/0.75 tff(72,plain,
% 0.73/0.75 ((~(neq(W!49, nil) <=> (~(W!49 = nil)))) | neq(W!49, nil) | (W!49 = nil)),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(73,plain,
% 0.73/0.75 (W!49 = nil),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[72, 71, 63])).
% 0.73/0.75 tff(74,plain,
% 0.73/0.75 (nil = app(nil, W!49)),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[73, 39])).
% 0.73/0.75 tff(75,plain,
% 0.73/0.75 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(76,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[75])).
% 0.73/0.75 tff(77,plain,
% 0.73/0.75 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(78,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[77])).
% 0.73/0.75 tff(79,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[78, 76])).
% 0.73/0.75 tff(80,plain,
% 0.73/0.75 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(81,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[80])).
% 0.73/0.75 tff(82,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(83,plain,
% 0.73/0.75 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(84,plain,
% 0.73/0.75 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[83])).
% 0.73/0.75 tff(85,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 0.73/0.75 tff(86,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.73/0.75 tff(87,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.73/0.75 tff(88,plain,(
% 0.73/0.75 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.73/0.75 inference(skolemize,[status(sab)],[87])).
% 0.73/0.75 tff(89,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.73/0.75 tff(90,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.73/0.75 tff(91,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(92,plain,
% 0.73/0.75 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil))))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(93,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))))),
% 0.73/0.75 inference(monotonicity,[status(thm)],[92])).
% 0.73/0.75 tff(94,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V))))),
% 0.73/0.75 inference(transitivity,[status(thm)],[93, 91])).
% 0.73/0.75 tff(95,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (~((~(nil = V)) | (~(nil = nil)))))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(96,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.73/0.75 tff(97,plain,
% 0.73/0.75 (![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[96, 59, 90])).
% 0.73/0.75 tff(98,plain,
% 0.73/0.75 (((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | ((~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | (~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(99,plain,
% 0.73/0.75 ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | ((~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49)))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(100,plain,
% 0.73/0.75 ((~![V: $i] : ((~ssList(V)) | ((nil = app(nil, V)) <=> (nil = V)))) | (~ssList(W!49)) | ((nil = app(nil, W!49)) <=> (nil = W!49))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.73/0.75 tff(101,plain,
% 0.73/0.75 ((nil = app(nil, W!49)) <=> (nil = W!49)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[100, 21, 97])).
% 0.73/0.75 tff(102,plain,
% 0.73/0.75 (ssList(X!50)),
% 0.73/0.75 inference(or_elim,[status(thm)],[64])).
% 0.73/0.75 tff(103,plain,
% 0.73/0.75 (^[U: $i] : refl(((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(104,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[103])).
% 0.73/0.75 tff(105,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(106,plain,
% 0.73/0.75 (^[U: $i] : rewrite((ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(107,plain,
% 0.73/0.75 (![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U))) <=> ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[106])).
% 0.73/0.75 tff(108,axiom,(![U: $i] : (ssList(U) => (segmentP(nil, U) <=> (nil = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax58')).
% 0.73/0.75 tff(109,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.73/0.75 tff(110,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.73/0.75 tff(111,plain,(
% 0.73/0.75 ![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(skolemize,[status(sab)],[110])).
% 0.73/0.75 tff(112,plain,
% 0.73/0.75 (![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.73/0.75 tff(113,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))) <=> ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(114,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | ((~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50)))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(115,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | (segmentP(nil, U) <=> (nil = U)))) | (~ssList(X!50)) | (segmentP(nil, X!50) <=> (nil = X!50))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.73/0.75 tff(116,plain,
% 0.73/0.75 (segmentP(nil, X!50) <=> (nil = X!50)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[115, 112, 102])).
% 0.73/0.75 tff(117,plain,
% 0.73/0.75 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(118,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V)))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(119,plain,
% 0.73/0.75 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (neq(U, V) <=> (~(U = V)))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.73/0.75 tff(120,plain,
% 0.73/0.75 (![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[119, 52, 102])).
% 0.73/0.75 tff(121,plain,
% 0.73/0.75 (((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))) <=> ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.73/0.75 inference(rewrite,[status(thm)],[])).
% 0.73/0.75 tff(122,plain,
% 0.73/0.75 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | ((~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil))))),
% 0.73/0.75 inference(quant_inst,[status(thm)],[])).
% 0.73/0.75 tff(123,plain,
% 0.73/0.75 ((~![V: $i] : ((~ssList(V)) | (neq(X!50, V) <=> (~(X!50 = V))))) | (~ssList(nil)) | (neq(X!50, nil) <=> (~(X!50 = nil)))),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.73/0.75 tff(124,plain,
% 0.73/0.75 (neq(X!50, nil) <=> (~(X!50 = nil))),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[123, 59, 120])).
% 0.73/0.75 tff(125,plain,
% 0.73/0.75 (V!48 = X!50),
% 0.73/0.75 inference(or_elim,[status(thm)],[64])).
% 0.73/0.75 tff(126,plain,
% 0.73/0.75 (X!50 = V!48),
% 0.73/0.75 inference(symmetry,[status(thm)],[125])).
% 0.73/0.75 tff(127,plain,
% 0.73/0.75 (neq(X!50, nil) <=> neq(V!48, nil)),
% 0.73/0.75 inference(monotonicity,[status(thm)],[126])).
% 0.73/0.75 tff(128,plain,
% 0.73/0.75 (neq(V!48, nil) <=> neq(X!50, nil)),
% 0.73/0.75 inference(symmetry,[status(thm)],[127])).
% 0.73/0.75 tff(129,plain,
% 0.73/0.75 (neq(V!48, nil)),
% 0.73/0.75 inference(or_elim,[status(thm)],[64])).
% 0.73/0.75 tff(130,plain,
% 0.73/0.75 (neq(X!50, nil)),
% 0.73/0.75 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.73/0.75 tff(131,plain,
% 0.73/0.75 ((~(neq(X!50, nil) <=> (~(X!50 = nil)))) | (~neq(X!50, nil)) | (~(X!50 = nil))),
% 0.73/0.75 inference(tautology,[status(thm)],[])).
% 0.73/0.75 tff(132,plain,
% 0.73/0.75 (~(X!50 = nil)),
% 0.73/0.75 inference(unit_resolution,[status(thm)],[131, 130, 124])).
% 0.73/0.75 tff(133,plain,
% 0.73/0.75 (^[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)))))),
% 0.73/0.75 inference(bind,[status(th)],[])).
% 0.73/0.75 tff(134,plain,
% 0.73/0.75 (![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))))),
% 0.73/0.75 inference(quant_intro,[status(thm)],[133])).
% 0.73/0.75 tff(135,plain,
% 0.73/0.75 (^[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)))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(136,plain,
% 0.73/0.76 (![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))))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[135])).
% 0.73/0.76 tff(137,plain,
% 0.73/0.76 (![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))))),
% 0.73/0.76 inference(transitivity,[status(thm)],[136, 134])).
% 0.73/0.76 tff(138,plain,
% 0.73/0.76 (^[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)))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(139,plain,
% 0.73/0.76 (![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))))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[138])).
% 0.73/0.76 tff(140,plain,
% 0.73/0.76 (![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)))))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(141,plain,
% 0.73/0.76 (^[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)))))))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(142,plain,
% 0.73/0.76 (![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)))))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[141])).
% 0.73/0.76 tff(143,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((segmentP(U, V) & segmentP(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax54')).
% 0.73/0.76 tff(144,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[143, 142])).
% 0.73/0.76 tff(145,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.73/0.76 tff(146,plain,(
% 0.73/0.76 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~(segmentP(U, V) & segmentP(V, U)))))),
% 0.73/0.76 inference(skolemize,[status(sab)],[145])).
% 0.73/0.76 tff(147,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[146, 139])).
% 0.73/0.76 tff(148,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[147, 137])).
% 0.73/0.76 tff(149,plain,
% 0.73/0.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(150,plain,
% 0.73/0.76 (((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) <=> ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(151,plain,
% 0.73/0.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))))),
% 0.73/0.76 inference(monotonicity,[status(thm)],[150])).
% 0.73/0.76 tff(152,plain,
% 0.73/0.76 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 0.73/0.76 inference(transitivity,[status(thm)],[151, 149])).
% 0.73/0.76 tff(153,plain,
% 0.73/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | ((~ssList(X!50)) | ![V: $i] : ((X!50 = V) | (~ssList(V)) | (~segmentP(X!50, V)) | (~segmentP(V, X!50))))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(154,plain,
% 0.73/0.76 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((U = V) | (~ssList(V)) | (~segmentP(U, V)) | (~segmentP(V, U))))) | (~ssList(X!50)) | ![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.73/0.76 tff(155,plain,
% 0.73/0.76 (![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[154, 148, 102])).
% 0.73/0.76 tff(156,plain,
% 0.73/0.76 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(157,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[156])).
% 0.73/0.76 tff(158,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(159,plain,
% 0.73/0.76 (^[U: $i] : rewrite((ssList(U) => segmentP(U, nil)) <=> ((~ssList(U)) | segmentP(U, nil)))),
% 0.73/0.76 inference(bind,[status(th)],[])).
% 0.73/0.76 tff(160,plain,
% 0.73/0.76 (![U: $i] : (ssList(U) => segmentP(U, nil)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(quant_intro,[status(thm)],[159])).
% 0.73/0.76 tff(161,axiom,(![U: $i] : (ssList(U) => segmentP(U, nil))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax57')).
% 0.73/0.76 tff(162,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.73/0.76 tff(163,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[162, 158])).
% 0.73/0.76 tff(164,plain,(
% 0.73/0.76 ![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(skolemize,[status(sab)],[163])).
% 0.73/0.76 tff(165,plain,
% 0.73/0.76 (![U: $i] : ((~ssList(U)) | segmentP(U, nil))),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[164, 157])).
% 0.73/0.76 tff(166,plain,
% 0.73/0.76 (((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(167,plain,
% 0.73/0.76 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | ((~ssList(X!50)) | segmentP(X!50, nil))),
% 0.73/0.76 inference(quant_inst,[status(thm)],[])).
% 0.73/0.76 tff(168,plain,
% 0.73/0.76 ((~![U: $i] : ((~ssList(U)) | segmentP(U, nil))) | (~ssList(X!50)) | segmentP(X!50, nil)),
% 0.73/0.76 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.73/0.76 tff(169,plain,
% 0.73/0.76 (segmentP(X!50, nil)),
% 0.73/0.76 inference(unit_resolution,[status(thm)],[168, 165, 102])).
% 0.73/0.76 tff(170,plain,
% 0.73/0.76 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(171,plain,
% 0.73/0.76 (((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50))) <=> ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 0.73/0.76 inference(rewrite,[status(thm)],[])).
% 0.73/0.76 tff(172,plain,
% 0.73/0.76 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))))),
% 0.73/0.76 inference(monotonicity,[status(thm)],[171])).
% 0.73/0.76 tff(173,plain,
% 0.73/0.76 (((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))) <=> ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil)))),
% 0.82/0.77 inference(transitivity,[status(thm)],[172, 170])).
% 0.82/0.77 tff(174,plain,
% 0.82/0.77 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | ((~ssList(nil)) | (X!50 = nil) | (~segmentP(X!50, nil)) | (~segmentP(nil, X!50)))),
% 0.82/0.77 inference(quant_inst,[status(thm)],[])).
% 0.82/0.77 tff(175,plain,
% 0.82/0.77 ((~![V: $i] : ((~ssList(V)) | (X!50 = V) | (~segmentP(X!50, V)) | (~segmentP(V, X!50)))) | (~ssList(nil)) | (~segmentP(nil, X!50)) | (X!50 = nil) | (~segmentP(X!50, nil))),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.82/0.77 tff(176,plain,
% 0.82/0.77 ((~segmentP(nil, X!50)) | (X!50 = nil)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[175, 59, 169, 155])).
% 0.82/0.77 tff(177,plain,
% 0.82/0.77 (~segmentP(nil, X!50)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[176, 132])).
% 0.82/0.77 tff(178,plain,
% 0.82/0.77 ((~(segmentP(nil, X!50) <=> (nil = X!50))) | segmentP(nil, X!50) | (~(nil = X!50))),
% 0.82/0.77 inference(tautology,[status(thm)],[])).
% 0.82/0.77 tff(179,plain,
% 0.82/0.77 (~(nil = X!50)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[178, 177, 116])).
% 0.82/0.77 tff(180,plain,
% 0.82/0.77 ((~(~((~(nil = W!49)) | (nil = X!50)))) <=> ((~(nil = W!49)) | (nil = X!50))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(181,plain,
% 0.82/0.77 (((~(nil = X!50)) & (nil = W!49)) <=> (~((~(nil = W!49)) | (nil = X!50)))),
% 0.82/0.77 inference(rewrite,[status(thm)],[])).
% 0.82/0.77 tff(182,plain,
% 0.82/0.77 ((~((~(nil = X!50)) & (nil = W!49))) <=> (~(~((~(nil = W!49)) | (nil = X!50))))),
% 0.82/0.77 inference(monotonicity,[status(thm)],[181])).
% 0.82/0.77 tff(183,plain,
% 0.82/0.77 ((~((~(nil = X!50)) & (nil = W!49))) <=> ((~(nil = W!49)) | (nil = X!50))),
% 0.82/0.77 inference(transitivity,[status(thm)],[182, 180])).
% 0.82/0.77 tff(184,plain,
% 0.82/0.77 (~((~(nil = X!50)) & (nil = W!49))),
% 0.82/0.77 inference(or_elim,[status(thm)],[64])).
% 0.82/0.77 tff(185,plain,
% 0.82/0.77 ((~(nil = W!49)) | (nil = X!50)),
% 0.82/0.77 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.82/0.77 tff(186,plain,
% 0.82/0.77 (~(nil = W!49)),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[185, 179])).
% 0.82/0.77 tff(187,plain,
% 0.82/0.77 ((~((nil = app(nil, W!49)) <=> (nil = W!49))) | (~(nil = app(nil, W!49))) | (nil = W!49)),
% 0.82/0.77 inference(tautology,[status(thm)],[])).
% 0.82/0.77 tff(188,plain,
% 0.82/0.77 (~(nil = app(nil, W!49))),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[187, 186, 101])).
% 0.82/0.77 tff(189,plain,
% 0.82/0.77 ($false),
% 0.82/0.77 inference(unit_resolution,[status(thm)],[188, 74])).
% 0.82/0.77 % SZS output end Proof
%------------------------------------------------------------------------------