TSTP Solution File: SWC046+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC046+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n027.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 11:54:53 EDT 2022
% Result : Theorem 21.95s 14.15s
% Output : Proof 22.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC046+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n027.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 21:12:36 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 21.95/14.15 % SZS status Theorem
% 21.95/14.15 % SZS output start Proof
% 21.95/14.15 tff(memberP_type, type, (
% 21.95/14.15 memberP: ( $i * $i ) > $o)).
% 21.95/14.15 tff(hd_type, type, (
% 21.95/14.15 hd: $i > $i)).
% 21.95/14.15 tff(tptp_fun_W_49_type, type, (
% 21.95/14.15 tptp_fun_W_49: $i)).
% 21.95/14.15 tff(cons_type, type, (
% 21.95/14.15 cons: ( $i * $i ) > $i)).
% 21.95/14.15 tff(tptp_fun_V_46_type, type, (
% 21.95/14.15 tptp_fun_V_46: $i > $i)).
% 21.95/14.15 tff(tptp_fun_W_44_type, type, (
% 21.95/14.15 tptp_fun_W_44: $i > $i)).
% 21.95/14.15 tff(tl_type, type, (
% 21.95/14.15 tl: $i > $i)).
% 21.95/14.15 tff(nil_type, type, (
% 21.95/14.15 nil: $i)).
% 21.95/14.15 tff(tptp_fun_U_47_type, type, (
% 21.95/14.15 tptp_fun_U_47: $i)).
% 21.95/14.15 tff(segmentP_type, type, (
% 21.95/14.15 segmentP: ( $i * $i ) > $o)).
% 21.95/14.15 tff(app_type, type, (
% 21.95/14.15 app: ( $i * $i ) > $i)).
% 21.95/14.15 tff(tptp_fun_Z_51_type, type, (
% 21.95/14.15 tptp_fun_Z_51: $i > $i)).
% 21.95/14.15 tff(tptp_fun_X_50_type, type, (
% 21.95/14.15 tptp_fun_X_50: $i)).
% 21.95/14.15 tff(ssList_type, type, (
% 21.95/14.15 ssList: $i > $o)).
% 21.95/14.15 tff(ssItem_type, type, (
% 21.95/14.15 ssItem: $i > $o)).
% 21.95/14.15 tff(tptp_fun_V_48_type, type, (
% 21.95/14.15 tptp_fun_V_48: $i)).
% 21.95/14.15 tff(tptp_fun_V_43_type, type, (
% 21.95/14.15 tptp_fun_V_43: $i > $i)).
% 21.95/14.15 tff(leq_type, type, (
% 21.95/14.15 leq: ( $i * $i ) > $o)).
% 21.95/14.15 tff(1,plain,
% 21.95/14.15 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(2,plain,
% 21.95/14.15 ((ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(3,plain,
% 21.95/14.15 ((ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(4,plain,
% 21.95/14.15 (((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y)))))) <=> ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(5,plain,
% 21.95/14.15 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(6,plain,
% 21.95/14.15 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y))))))) <=> (ssList(W!49) & ((~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.15 inference(monotonicity,[status(thm)],[5, 4])).
% 21.95/14.15 tff(7,plain,
% 21.95/14.15 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(transitivity,[status(thm)],[6, 3])).
% 21.95/14.15 tff(8,plain,
% 21.95/14.15 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(9,plain,
% 21.95/14.15 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y)))))))) <=> (ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.15 inference(monotonicity,[status(thm)],[8, 7])).
% 21.95/14.15 tff(10,plain,
% 21.95/14.15 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y)))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(transitivity,[status(thm)],[9, 2])).
% 21.95/14.15 tff(11,plain,
% 21.95/14.15 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(12,plain,
% 21.95/14.15 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.15 inference(monotonicity,[status(thm)],[11, 10])).
% 21.95/14.15 tff(13,plain,
% 21.95/14.15 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | ((~(~memberP(X!50, Y))) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & ((~(~memberP(W!49, Y))) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))) | (~memberP(X!50, Y))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))),
% 21.95/14.15 inference(transitivity,[status(thm)],[12, 1])).
% 21.95/14.15 tff(14,plain,
% 21.95/14.15 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y)))))))))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(15,plain,
% 21.95/14.15 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ?[Y: $i] : (ssItem(Y) & ((((~memberP(W, Y)) & ![Z: $i] : (ssList(Z) => (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y)))))))))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(nil = V)) | (~(V = X))) | (~(U = W))) | (nil = U)) | ?[Y: $i] : (ssItem(Y) & ((((~memberP(W, Y)) & ![Z: $i] : (ssList(Z) => (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) & memberP(X, Y)) | (memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 21.95/14.15 tff(17,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[16, 15])).
% 21.95/14.15 tff(18,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[17, 14])).
% 21.95/14.15 tff(19,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[18, 14])).
% 21.95/14.15 tff(20,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[19, 14])).
% 21.95/14.15 tff(21,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[20, 14])).
% 21.95/14.15 tff(22,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[21, 14])).
% 21.95/14.15 tff(23,plain,
% 21.95/14.15 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ?[Y: $i] : (ssItem(Y) & ((memberP(W, Y) & ((~memberP(X, Y)) | ?[Z: $i] : (ssList(Z) & segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil)))))) | ((~memberP(W, Y)) & ![Z: $i] : ((~ssList(Z)) | (~segmentP(X, app(app(cons(Y, nil), Z), cons(Y, nil))))) & memberP(X, Y))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[22, 14])).
% 21.95/14.15 tff(24,plain,
% 21.95/14.15 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & ![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[23, 13])).
% 21.95/14.15 tff(25,plain,
% 21.95/14.15 (U!47 = W!49),
% 21.95/14.15 inference(and_elim,[status(thm)],[24])).
% 21.95/14.15 tff(26,plain,
% 21.95/14.15 (W!49 = U!47),
% 21.95/14.15 inference(symmetry,[status(thm)],[25])).
% 21.95/14.15 tff(27,plain,
% 21.95/14.15 ((nil = W!49) <=> (nil = U!47)),
% 21.95/14.15 inference(monotonicity,[status(thm)],[26])).
% 21.95/14.15 tff(28,plain,
% 21.95/14.15 ((nil = U!47) <=> (nil = W!49)),
% 21.95/14.15 inference(symmetry,[status(thm)],[27])).
% 21.95/14.15 tff(29,plain,
% 21.95/14.15 ((~(nil = U!47)) <=> (~(nil = W!49))),
% 21.95/14.15 inference(monotonicity,[status(thm)],[28])).
% 21.95/14.15 tff(30,plain,
% 21.95/14.15 (~(nil = U!47)),
% 21.95/14.15 inference(and_elim,[status(thm)],[24])).
% 21.95/14.15 tff(31,plain,
% 21.95/14.15 (~(nil = W!49)),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[30, 29])).
% 21.95/14.15 tff(32,plain,
% 21.95/14.15 (ssList(W!49)),
% 21.95/14.15 inference(and_elim,[status(thm)],[24])).
% 21.95/14.15 tff(33,plain,
% 21.95/14.15 (^[U: $i] : refl(((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U))) <=> ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U))))),
% 21.95/14.15 inference(bind,[status(th)],[])).
% 21.95/14.15 tff(34,plain,
% 21.95/14.15 (![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(quant_intro,[status(thm)],[33])).
% 21.95/14.15 tff(35,plain,
% 21.95/14.15 (![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(36,plain,
% 21.95/14.15 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => (cons(hd(U), tl(U)) = U)) <=> ((nil = U) | (cons(hd(U), tl(U)) = U))), ((ssList(U) => ((~(nil = U)) => (cons(hd(U), tl(U)) = U))) <=> (ssList(U) => ((nil = U) | (cons(hd(U), tl(U)) = U))))), rewrite((ssList(U) => ((nil = U) | (cons(hd(U), tl(U)) = U))) <=> ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => (cons(hd(U), tl(U)) = U))) <=> ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))))),
% 21.95/14.15 inference(bind,[status(th)],[])).
% 21.95/14.15 tff(37,plain,
% 21.95/14.15 (![U: $i] : (ssList(U) => ((~(nil = U)) => (cons(hd(U), tl(U)) = U))) <=> ![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(quant_intro,[status(thm)],[36])).
% 21.95/14.15 tff(38,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => (cons(hd(U), tl(U)) = U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax78')).
% 21.95/14.15 tff(39,plain,
% 21.95/14.15 (![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[38, 37])).
% 21.95/14.15 tff(40,plain,
% 21.95/14.15 (![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[39, 35])).
% 21.95/14.15 tff(41,plain,(
% 21.95/14.15 ![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(skolemize,[status(sab)],[40])).
% 21.95/14.15 tff(42,plain,
% 21.95/14.15 (![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))),
% 21.95/14.15 inference(modus_ponens,[status(thm)],[41, 34])).
% 21.95/14.15 tff(43,plain,
% 21.95/14.15 (((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | ((~ssList(W!49)) | (nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49))) <=> ((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | (~ssList(W!49)) | (nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49))),
% 21.95/14.15 inference(rewrite,[status(thm)],[])).
% 21.95/14.15 tff(44,plain,
% 21.95/14.15 (((nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49) | (~ssList(W!49))) <=> ((~ssList(W!49)) | (nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(45,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | ((nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49) | (~ssList(W!49)))) <=> ((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | ((~ssList(W!49)) | (nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49)))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[44])).
% 21.95/14.16 tff(46,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | ((nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49) | (~ssList(W!49)))) <=> ((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | (~ssList(W!49)) | (nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49))),
% 21.95/14.16 inference(transitivity,[status(thm)],[45, 43])).
% 21.95/14.16 tff(47,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | ((nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49) | (~ssList(W!49)))),
% 21.95/14.16 inference(quant_inst,[status(thm)],[])).
% 21.95/14.16 tff(48,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | (cons(hd(U), tl(U)) = U) | (~ssList(U)))) | (~ssList(W!49)) | (nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49)),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[47, 46])).
% 21.95/14.16 tff(49,plain,
% 21.95/14.16 ((nil = W!49) | (cons(hd(W!49), tl(W!49)) = W!49)),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[48, 42, 32])).
% 21.95/14.16 tff(50,plain,
% 21.95/14.16 (cons(hd(W!49), tl(W!49)) = W!49),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[49, 31])).
% 21.95/14.16 tff(51,plain,
% 21.95/14.16 (^[U: $i] : refl(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U)))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U)))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(52,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U)))))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[51])).
% 21.95/14.16 tff(53,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U))) <=> (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U)))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U)))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U)))))))), rewrite(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U)))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U)))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(54,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U)))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[53])).
% 21.95/14.16 tff(55,plain,
% 21.95/14.16 (^[U: $i] : rewrite(((nil = U) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U))) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U)))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(56,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U))) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[55])).
% 21.95/14.16 tff(57,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(58,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ?[V: $i] : (ssList(V) & (tl(U) = V))) <=> ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)))), ((ssList(U) => ((~(nil = U)) => ?[V: $i] : (ssList(V) & (tl(U) = V)))) <=> (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)))))), rewrite((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)))) <=> ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ?[V: $i] : (ssList(V) & (tl(U) = V)))) <=> ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U)))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(59,plain,
% 21.95/14.16 (![U: $i] : (ssList(U) => ((~(nil = U)) => ?[V: $i] : (ssList(V) & (tl(U) = V)))) <=> ![U: $i] : ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[58])).
% 21.95/14.16 tff(60,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ?[V: $i] : (ssList(V) & (tl(U) = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax76')).
% 21.95/14.16 tff(61,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[60, 59])).
% 21.95/14.16 tff(62,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ?[V: $i] : (ssList(V) & (tl(U) = V)) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[61, 57])).
% 21.95/14.16 tff(63,plain,(
% 21.95/14.16 ![U: $i] : ((nil = U) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U))) | (~ssList(U)))),
% 21.95/14.16 inference(skolemize,[status(sab)],[62])).
% 21.95/14.16 tff(64,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_46(U)) & (tl(U) = tptp_fun_V_46(U))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[63, 56])).
% 21.95/14.16 tff(65,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[64, 54])).
% 21.95/14.16 tff(66,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[65, 52])).
% 21.95/14.16 tff(67,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | (~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(68,plain,
% 21.95/14.16 (((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49)))))) <=> ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(69,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49)))))))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[68])).
% 21.95/14.16 tff(70,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | (~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))),
% 21.95/14.16 inference(transitivity,[status(thm)],[69, 67])).
% 21.95/14.16 tff(71,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))))),
% 21.95/14.16 inference(quant_inst,[status(thm)],[])).
% 21.95/14.16 tff(72,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_46(U))) | (~(tl(U) = tptp_fun_V_46(U))))))) | (~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49)))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[71, 70])).
% 21.95/14.16 tff(73,plain,
% 21.95/14.16 ((nil = W!49) | (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49)))))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[72, 66, 32])).
% 21.95/14.16 tff(74,plain,
% 21.95/14.16 (~((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49))))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[73, 31])).
% 21.95/14.16 tff(75,plain,
% 21.95/14.16 (((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49)))) | (tl(W!49) = tptp_fun_V_46(W!49))),
% 21.95/14.16 inference(tautology,[status(thm)],[])).
% 21.95/14.16 tff(76,plain,
% 21.95/14.16 (tl(W!49) = tptp_fun_V_46(W!49)),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[75, 74])).
% 21.95/14.16 tff(77,plain,
% 21.95/14.16 (tptp_fun_V_46(W!49) = tl(W!49)),
% 21.95/14.16 inference(symmetry,[status(thm)],[76])).
% 21.95/14.16 tff(78,plain,
% 21.95/14.16 (^[U: $i] : refl(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(79,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[78])).
% 21.95/14.16 tff(80,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) <=> (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))))), rewrite(((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))), (((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(81,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[80])).
% 21.95/14.16 tff(82,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(rewrite((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) <=> (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))), (((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) | (nil = U) | (~ssList(U))))), rewrite(((ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)) | (nil = U) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))), (((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(83,plain,
% 21.95/14.16 (![U: $i] : ((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[82])).
% 21.95/14.16 tff(84,plain,
% 21.95/14.16 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U))) <=> ![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(85,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(rewrite(((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))) <=> ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))), ((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))))), rewrite((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))), ((ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(86,plain,
% 21.95/14.16 (![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))))) <=> ![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[85])).
% 21.95/14.16 tff(87,axiom,(![U: $i] : (ssList(U) => ((nil = U) | ?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax20')).
% 21.95/14.16 tff(88,plain,
% 21.95/14.16 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[87, 86])).
% 21.95/14.16 tff(89,plain,
% 21.95/14.16 (![U: $i] : (?[V: $i] : (ssList(V) & ?[W: $i] : (ssItem(W) & (cons(W, V) = U))) | (nil = U) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[88, 84])).
% 21.95/14.16 tff(90,plain,(
% 21.95/14.16 ![U: $i] : ((ssList(tptp_fun_V_43(U)) & (ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U))) | (nil = U) | (~ssList(U)))),
% 21.95/14.16 inference(skolemize,[status(sab)],[89])).
% 21.95/14.16 tff(91,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (ssList(tptp_fun_V_43(U)) & ssItem(tptp_fun_W_44(U)) & (cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[90, 83])).
% 21.95/14.16 tff(92,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[91, 81])).
% 21.95/14.16 tff(93,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[92, 79])).
% 21.95/14.16 tff(94,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(95,plain,
% 21.95/14.16 (((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))) <=> ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(96,plain,
% 21.95/14.16 ((~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))) <=> (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(97,plain,
% 21.95/14.16 (((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))) <=> ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[96])).
% 21.95/14.16 tff(98,plain,
% 21.95/14.16 (((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))) <=> ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))),
% 21.95/14.16 inference(transitivity,[status(thm)],[97, 95])).
% 21.95/14.16 tff(99,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[98])).
% 21.95/14.16 tff(100,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))) <=> ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))),
% 21.95/14.16 inference(transitivity,[status(thm)],[99, 94])).
% 21.95/14.16 tff(101,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | ((nil = W!49) | (~ssList(W!49)) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))))),
% 21.95/14.16 inference(quant_inst,[status(thm)],[])).
% 21.95/14.16 tff(102,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | (~ssList(U)) | (~((~ssList(tptp_fun_V_43(U))) | (~ssItem(tptp_fun_W_44(U))) | (~(cons(tptp_fun_W_44(U), tptp_fun_V_43(U)) = U)))))) | (~ssList(W!49)) | (nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[101, 100])).
% 21.95/14.16 tff(103,plain,
% 21.95/14.16 ((nil = W!49) | (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[102, 93, 32])).
% 21.95/14.16 tff(104,plain,
% 21.95/14.16 (~((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[103, 31])).
% 21.95/14.16 tff(105,plain,
% 21.95/14.16 (((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))) | (cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49)),
% 21.95/14.16 inference(tautology,[status(thm)],[])).
% 21.95/14.16 tff(106,plain,
% 21.95/14.16 (cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[105, 104])).
% 21.95/14.16 tff(107,plain,
% 21.95/14.16 (hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49))) = hd(W!49)),
% 21.95/14.16 inference(monotonicity,[status(thm)],[106])).
% 21.95/14.16 tff(108,plain,
% 21.95/14.16 (((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))) | ssList(tptp_fun_V_43(W!49))),
% 21.95/14.16 inference(tautology,[status(thm)],[])).
% 21.95/14.16 tff(109,plain,
% 21.95/14.16 (ssList(tptp_fun_V_43(W!49))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[108, 104])).
% 21.95/14.16 tff(110,plain,
% 21.95/14.16 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(111,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[110])).
% 21.95/14.16 tff(112,plain,
% 21.95/14.16 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(113,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[112])).
% 21.95/14.16 tff(114,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(transitivity,[status(thm)],[113, 111])).
% 21.95/14.16 tff(115,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(116,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (hd(cons(V, U)) = V)) <=> ((~ssItem(V)) | (hd(cons(V, U)) = V)))), (![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)) <=> ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))), ((ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(117,plain,
% 21.95/14.16 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[116])).
% 21.95/14.16 tff(118,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (hd(cons(V, U)) = V)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax23')).
% 21.95/14.16 tff(119,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[118, 117])).
% 21.95/14.16 tff(120,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[119, 115])).
% 21.95/14.16 tff(121,plain,(
% 21.95/14.16 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(skolemize,[status(sab)],[120])).
% 21.95/14.16 tff(122,plain,
% 21.95/14.16 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[121, 114])).
% 21.95/14.16 tff(123,plain,
% 21.95/14.16 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V)))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(124,plain,
% 21.95/14.16 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | ((~ssList(tptp_fun_V_43(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V)))),
% 21.95/14.16 inference(quant_inst,[status(thm)],[])).
% 21.95/14.16 tff(125,plain,
% 21.95/14.16 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, U)) = V)))) | (~ssList(tptp_fun_V_43(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[124, 123])).
% 21.95/14.16 tff(126,plain,
% 21.95/14.16 (![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[125, 122, 109])).
% 21.95/14.16 tff(127,plain,
% 21.95/14.16 (((~ssList(tptp_fun_V_43(W!49))) | (~ssItem(tptp_fun_W_44(W!49))) | (~(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)) = W!49))) | ssItem(tptp_fun_W_44(W!49))),
% 21.95/14.16 inference(tautology,[status(thm)],[])).
% 21.95/14.16 tff(128,plain,
% 21.95/14.16 (ssItem(tptp_fun_W_44(W!49))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[127, 104])).
% 21.95/14.16 tff(129,plain,
% 21.95/14.16 (((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49))) = tptp_fun_W_44(W!49)))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V))) | (~ssItem(tptp_fun_W_44(W!49))) | (hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49))) = tptp_fun_W_44(W!49)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(130,plain,
% 21.95/14.16 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49))) = tptp_fun_W_44(W!49)))),
% 21.95/14.16 inference(quant_inst,[status(thm)],[])).
% 21.95/14.16 tff(131,plain,
% 21.95/14.16 ((~![V: $i] : ((~ssItem(V)) | (hd(cons(V, tptp_fun_V_43(W!49))) = V))) | (~ssItem(tptp_fun_W_44(W!49))) | (hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49))) = tptp_fun_W_44(W!49))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[130, 129])).
% 21.95/14.16 tff(132,plain,
% 21.95/14.16 (hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49))) = tptp_fun_W_44(W!49)),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[131, 128, 126])).
% 21.95/14.16 tff(133,plain,
% 21.95/14.16 (tptp_fun_W_44(W!49) = hd(cons(tptp_fun_W_44(W!49), tptp_fun_V_43(W!49)))),
% 21.95/14.16 inference(symmetry,[status(thm)],[132])).
% 21.95/14.16 tff(134,plain,
% 21.95/14.16 (tptp_fun_W_44(W!49) = hd(W!49)),
% 21.95/14.16 inference(transitivity,[status(thm)],[133, 107])).
% 21.95/14.16 tff(135,plain,
% 21.95/14.16 (cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)) = cons(hd(W!49), tl(W!49))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[134, 77])).
% 21.95/14.16 tff(136,plain,
% 21.95/14.16 (cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)) = W!49),
% 21.95/14.16 inference(transitivity,[status(thm)],[135, 50])).
% 21.95/14.16 tff(137,plain,
% 21.95/14.16 (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> memberP(W!49, hd(W!49))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[136])).
% 21.95/14.16 tff(138,plain,
% 21.95/14.16 (memberP(W!49, hd(W!49)) <=> memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49))),
% 21.95/14.16 inference(symmetry,[status(thm)],[137])).
% 21.95/14.16 tff(139,plain,
% 21.95/14.16 ((~memberP(W!49, hd(W!49))) <=> (~memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[138])).
% 21.95/14.16 tff(140,plain,
% 21.95/14.16 (^[U: $i] : refl(((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(141,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[140])).
% 21.95/14.16 tff(142,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(143,plain,
% 21.95/14.16 (^[U: $i] : trans(monotonicity(rewrite(((~(nil = U)) => ssItem(hd(U))) <=> ((nil = U) | ssItem(hd(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> (ssList(U) => ((nil = U) | ssItem(hd(U)))))), rewrite((ssList(U) => ((nil = U) | ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))), ((ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ((nil = U) | ssItem(hd(U)) | (~ssList(U)))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(144,plain,
% 21.95/14.16 (![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U)))) <=> ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[143])).
% 21.95/14.16 tff(145,axiom,(![U: $i] : (ssList(U) => ((~(nil = U)) => ssItem(hd(U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax22')).
% 21.95/14.16 tff(146,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[145, 144])).
% 21.95/14.16 tff(147,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[146, 142])).
% 21.95/14.16 tff(148,plain,(
% 21.95/14.16 ![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(skolemize,[status(sab)],[147])).
% 21.95/14.16 tff(149,plain,
% 21.95/14.16 (![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[148, 141])).
% 21.95/14.16 tff(150,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(W!49)) | (nil = W!49) | ssItem(hd(W!49)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(W!49)) | (nil = W!49) | ssItem(hd(W!49)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(151,plain,
% 21.95/14.16 (((nil = W!49) | ssItem(hd(W!49)) | (~ssList(W!49))) <=> ((~ssList(W!49)) | (nil = W!49) | ssItem(hd(W!49)))),
% 21.95/14.16 inference(rewrite,[status(thm)],[])).
% 21.95/14.16 tff(152,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = W!49) | ssItem(hd(W!49)) | (~ssList(W!49)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((~ssList(W!49)) | (nil = W!49) | ssItem(hd(W!49))))),
% 21.95/14.16 inference(monotonicity,[status(thm)],[151])).
% 21.95/14.16 tff(153,plain,
% 21.95/14.16 (((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = W!49) | ssItem(hd(W!49)) | (~ssList(W!49)))) <=> ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(W!49)) | (nil = W!49) | ssItem(hd(W!49)))),
% 21.95/14.16 inference(transitivity,[status(thm)],[152, 150])).
% 21.95/14.16 tff(154,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | ((nil = W!49) | ssItem(hd(W!49)) | (~ssList(W!49)))),
% 21.95/14.16 inference(quant_inst,[status(thm)],[])).
% 21.95/14.16 tff(155,plain,
% 21.95/14.16 ((~![U: $i] : ((nil = U) | ssItem(hd(U)) | (~ssList(U)))) | (~ssList(W!49)) | (nil = W!49) | ssItem(hd(W!49))),
% 21.95/14.16 inference(modus_ponens,[status(thm)],[154, 153])).
% 21.95/14.16 tff(156,plain,
% 21.95/14.16 ((nil = W!49) | ssItem(hd(W!49))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[155, 149, 32])).
% 21.95/14.16 tff(157,plain,
% 21.95/14.16 (ssItem(hd(W!49))),
% 21.95/14.16 inference(unit_resolution,[status(thm)],[156, 31])).
% 21.95/14.16 tff(158,plain,
% 21.95/14.16 (^[Y: $i] : rewrite(((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))))))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(159,plain,
% 21.95/14.16 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[158])).
% 21.95/14.16 tff(160,plain,
% 21.95/14.16 (^[Y: $i] : refl(((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(161,plain,
% 21.95/14.16 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[160])).
% 21.95/14.16 tff(162,plain,
% 21.95/14.16 (^[Y: $i] : rewrite(((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))))),
% 21.95/14.16 inference(bind,[status(th)],[])).
% 21.95/14.16 tff(163,plain,
% 21.95/14.16 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.16 inference(quant_intro,[status(thm)],[162])).
% 21.95/14.16 tff(164,plain,
% 21.95/14.16 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.16 inference(transitivity,[status(thm)],[163, 161])).
% 21.95/14.16 tff(165,plain,
% 21.95/14.16 (^[Y: $i] : rewrite(((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))) <=> ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(166,plain,
% 21.95/14.17 (![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil))))))))) <=> ![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[165])).
% 21.95/14.17 tff(167,plain,
% 21.95/14.17 (![Y: $i] : ((~ssItem(Y)) | (((~memberP(W!49, Y)) | (memberP(X!50, Y) & ![Z: $i] : (~(ssList(Z) & segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil))))))) & (memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))),
% 21.95/14.17 inference(and_elim,[status(thm)],[24])).
% 21.95/14.17 tff(168,plain,
% 21.95/14.17 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[167, 166])).
% 21.95/14.17 tff(169,plain,
% 21.95/14.17 (![Y: $i] : ((~ssItem(Y)) | (~((~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))) | (~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[168, 164])).
% 21.95/14.17 tff(170,plain,
% 21.95/14.17 (![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[169, 159])).
% 21.95/14.17 tff(171,plain,
% 21.95/14.17 (((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))) | ((~ssItem(hd(W!49))) | (~((~(memberP(W!49, hd(W!49)) | (~memberP(X!50, hd(W!49))) | (~((~ssList(tptp_fun_Z_51(hd(W!49)))) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), tptp_fun_Z_51(hd(W!49))), cons(hd(W!49), nil)))))))) | (~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil)))))))))))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))) | (~ssItem(hd(W!49))) | (~((~(memberP(W!49, hd(W!49)) | (~memberP(X!50, hd(W!49))) | (~((~ssList(tptp_fun_Z_51(hd(W!49)))) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), tptp_fun_Z_51(hd(W!49))), cons(hd(W!49), nil)))))))) | (~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil)))))))))))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(172,plain,
% 21.95/14.17 ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))) | ((~ssItem(hd(W!49))) | (~((~(memberP(W!49, hd(W!49)) | (~memberP(X!50, hd(W!49))) | (~((~ssList(tptp_fun_Z_51(hd(W!49)))) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), tptp_fun_Z_51(hd(W!49))), cons(hd(W!49), nil)))))))) | (~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil)))))))))))))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(173,plain,
% 21.95/14.17 ((~![Y: $i] : ((~ssItem(Y)) | (~((~(memberP(W!49, Y) | (~memberP(X!50, Y)) | (~((~ssList(tptp_fun_Z_51(Y))) | (~segmentP(X!50, app(app(cons(Y, nil), tptp_fun_Z_51(Y)), cons(Y, nil)))))))) | (~((~memberP(W!49, Y)) | (~((~memberP(X!50, Y)) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(Y, nil), Z), cons(Y, nil)))))))))))))) | (~ssItem(hd(W!49))) | (~((~(memberP(W!49, hd(W!49)) | (~memberP(X!50, hd(W!49))) | (~((~ssList(tptp_fun_Z_51(hd(W!49)))) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), tptp_fun_Z_51(hd(W!49))), cons(hd(W!49), nil)))))))) | (~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil))))))))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[172, 171])).
% 21.95/14.17 tff(174,plain,
% 21.95/14.17 (~((~(memberP(W!49, hd(W!49)) | (~memberP(X!50, hd(W!49))) | (~((~ssList(tptp_fun_Z_51(hd(W!49)))) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), tptp_fun_Z_51(hd(W!49))), cons(hd(W!49), nil)))))))) | (~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil)))))))))))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[173, 170, 157])).
% 21.95/14.17 tff(175,plain,
% 21.95/14.17 (((~(memberP(W!49, hd(W!49)) | (~memberP(X!50, hd(W!49))) | (~((~ssList(tptp_fun_Z_51(hd(W!49)))) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), tptp_fun_Z_51(hd(W!49))), cons(hd(W!49), nil)))))))) | (~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil))))))))))) | ((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil)))))))))),
% 21.95/14.17 inference(tautology,[status(thm)],[])).
% 21.95/14.17 tff(176,plain,
% 21.95/14.17 ((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil))))))))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[175, 174])).
% 21.95/14.17 tff(177,plain,
% 21.95/14.17 (V!48 = X!50),
% 21.95/14.17 inference(and_elim,[status(thm)],[24])).
% 21.95/14.17 tff(178,plain,
% 21.95/14.17 (nil = V!48),
% 21.95/14.17 inference(and_elim,[status(thm)],[24])).
% 21.95/14.17 tff(179,plain,
% 21.95/14.17 (nil = X!50),
% 21.95/14.17 inference(transitivity,[status(thm)],[178, 177])).
% 21.95/14.17 tff(180,plain,
% 21.95/14.17 (memberP(nil, hd(W!49)) <=> memberP(X!50, hd(W!49))),
% 21.95/14.17 inference(monotonicity,[status(thm)],[179])).
% 21.95/14.17 tff(181,plain,
% 21.95/14.17 ((~memberP(nil, hd(W!49))) <=> (~memberP(X!50, hd(W!49)))),
% 21.95/14.17 inference(monotonicity,[status(thm)],[180])).
% 21.95/14.17 tff(182,plain,
% 21.95/14.17 (^[U: $i] : refl(((~ssItem(U)) | (~memberP(nil, U))) <=> ((~ssItem(U)) | (~memberP(nil, U))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(183,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U))) <=> ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[182])).
% 21.95/14.17 tff(184,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U))) <=> ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(185,plain,
% 21.95/14.17 (^[U: $i] : rewrite((ssItem(U) => (~memberP(nil, U))) <=> ((~ssItem(U)) | (~memberP(nil, U))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(186,plain,
% 21.95/14.17 (![U: $i] : (ssItem(U) => (~memberP(nil, U))) <=> ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[185])).
% 21.95/14.17 tff(187,axiom,(![U: $i] : (ssItem(U) => (~memberP(nil, U)))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax38')).
% 21.95/14.17 tff(188,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[187, 186])).
% 21.95/14.17 tff(189,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[188, 184])).
% 21.95/14.17 tff(190,plain,(
% 21.95/14.17 ![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(skolemize,[status(sab)],[189])).
% 21.95/14.17 tff(191,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[190, 183])).
% 21.95/14.17 tff(192,plain,
% 21.95/14.17 (((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | ((~ssItem(hd(W!49))) | (~memberP(nil, hd(W!49))))) <=> ((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | (~ssItem(hd(W!49))) | (~memberP(nil, hd(W!49))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(193,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | ((~ssItem(hd(W!49))) | (~memberP(nil, hd(W!49))))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(194,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssItem(U)) | (~memberP(nil, U)))) | (~ssItem(hd(W!49))) | (~memberP(nil, hd(W!49)))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[193, 192])).
% 21.95/14.17 tff(195,plain,
% 21.95/14.17 (~memberP(nil, hd(W!49))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[194, 191, 157])).
% 21.95/14.17 tff(196,plain,
% 21.95/14.17 (~memberP(X!50, hd(W!49))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[195, 181])).
% 21.95/14.17 tff(197,plain,
% 21.95/14.17 (((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil))))))) | memberP(X!50, hd(W!49))),
% 21.95/14.17 inference(tautology,[status(thm)],[])).
% 21.95/14.17 tff(198,plain,
% 21.95/14.17 ((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil))))))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[197, 196])).
% 21.95/14.17 tff(199,plain,
% 21.95/14.17 ((~((~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil)))))))))) | (~memberP(W!49, hd(W!49))) | (~((~memberP(X!50, hd(W!49))) | (~![Z: $i] : ((~ssList(Z)) | (~segmentP(X!50, app(app(cons(hd(W!49), nil), Z), cons(hd(W!49), nil))))))))),
% 21.95/14.17 inference(tautology,[status(thm)],[])).
% 21.95/14.17 tff(200,plain,
% 21.95/14.17 (~memberP(W!49, hd(W!49))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[199, 198, 176])).
% 21.95/14.17 tff(201,plain,
% 21.95/14.17 (~memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[200, 139])).
% 21.95/14.17 tff(202,plain,
% 21.95/14.17 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(203,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[202])).
% 21.95/14.17 tff(204,plain,
% 21.95/14.17 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(205,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[204])).
% 21.95/14.17 tff(206,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(transitivity,[status(thm)],[205, 203])).
% 21.95/14.17 tff(207,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(208,plain,
% 21.95/14.17 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : rewrite((ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))) <=> ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))), (![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))) <=> ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))), ((ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> (ssItem(V) => ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), rewrite((ssItem(V) => ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))), ((ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))), (![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))) <=> ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> (ssItem(U) => ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))))), rewrite((ssItem(U) => ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(209,plain,
% 21.95/14.17 (![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U)))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[208])).
% 21.95/14.17 tff(210,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => ![W: $i] : (ssList(W) => (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax37')).
% 21.95/14.17 tff(211,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[210, 209])).
% 21.95/14.17 tff(212,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[211, 207])).
% 21.95/14.17 tff(213,plain,(
% 21.95/14.17 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(skolemize,[status(sab)],[212])).
% 21.95/14.17 tff(214,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[213, 206])).
% 21.95/14.17 tff(215,plain,
% 21.95/14.17 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49)))))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | (~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49)))))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(216,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49)))))))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(217,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), U) <=> ((U = V) | memberP(W, U))))))) | (~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49))))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[216, 215])).
% 21.95/14.17 tff(218,plain,
% 21.95/14.17 (![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49))))))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[217, 214, 157])).
% 21.95/14.17 tff(219,plain,
% 21.95/14.17 (((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49))))))) | ((~ssItem(tptp_fun_W_44(W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49))))))) <=> ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49))))))) | (~ssItem(tptp_fun_W_44(W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49))))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(220,plain,
% 21.95/14.17 ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49))))))) | ((~ssItem(tptp_fun_W_44(W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49))))))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(221,plain,
% 21.95/14.17 ((~![V: $i] : ((~ssItem(V)) | ![W: $i] : ((~ssList(W)) | (memberP(cons(V, W), hd(W!49)) <=> ((hd(W!49) = V) | memberP(W, hd(W!49))))))) | (~ssItem(tptp_fun_W_44(W!49))) | ![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49)))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[220, 219])).
% 21.95/14.17 tff(222,plain,
% 21.95/14.17 (![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49)))))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[221, 128, 218])).
% 21.95/14.17 tff(223,plain,
% 21.95/14.17 (((~ssList(tptp_fun_V_46(W!49))) | (~(tl(W!49) = tptp_fun_V_46(W!49)))) | ssList(tptp_fun_V_46(W!49))),
% 21.95/14.17 inference(tautology,[status(thm)],[])).
% 21.95/14.17 tff(224,plain,
% 21.95/14.17 (ssList(tptp_fun_V_46(W!49))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[223, 74])).
% 21.95/14.17 tff(225,plain,
% 21.95/14.17 (((~![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49)))))) | ((~ssList(tptp_fun_V_46(W!49))) | (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49)))))) <=> ((~![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49)))))) | (~ssList(tptp_fun_V_46(W!49))) | (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49)))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(226,plain,
% 21.95/14.17 ((~![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49)))))) | ((~ssList(tptp_fun_V_46(W!49))) | (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49)))))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(227,plain,
% 21.95/14.17 ((~![W: $i] : ((~ssList(W)) | (memberP(cons(tptp_fun_W_44(W!49), W), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(W, hd(W!49)))))) | (~ssList(tptp_fun_V_46(W!49))) | (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[226, 225])).
% 21.95/14.17 tff(228,plain,
% 21.95/14.17 (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49)))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[227, 224, 222])).
% 21.95/14.17 tff(229,plain,
% 21.95/14.17 (leq(hd(W!49), tptp_fun_W_44(W!49)) <=> leq(hd(W!49), hd(W!49))),
% 21.95/14.17 inference(monotonicity,[status(thm)],[134])).
% 21.95/14.17 tff(230,plain,
% 21.95/14.17 (leq(hd(W!49), hd(W!49)) <=> leq(hd(W!49), tptp_fun_W_44(W!49))),
% 21.95/14.17 inference(symmetry,[status(thm)],[229])).
% 21.95/14.17 tff(231,plain,
% 21.95/14.17 (^[U: $i] : refl(((~ssItem(U)) | leq(U, U)) <=> ((~ssItem(U)) | leq(U, U)))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(232,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | leq(U, U)) <=> ![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[231])).
% 21.95/14.17 tff(233,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | leq(U, U)) <=> ![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(234,plain,
% 21.95/14.17 (^[U: $i] : rewrite((ssItem(U) => leq(U, U)) <=> ((~ssItem(U)) | leq(U, U)))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(235,plain,
% 21.95/14.17 (![U: $i] : (ssItem(U) => leq(U, U)) <=> ![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[234])).
% 21.95/14.17 tff(236,axiom,(![U: $i] : (ssItem(U) => leq(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax31')).
% 21.95/14.17 tff(237,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[236, 235])).
% 21.95/14.17 tff(238,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[237, 233])).
% 21.95/14.17 tff(239,plain,(
% 21.95/14.17 ![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(skolemize,[status(sab)],[238])).
% 21.95/14.17 tff(240,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | leq(U, U))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[239, 232])).
% 21.95/14.17 tff(241,plain,
% 21.95/14.17 (((~![U: $i] : ((~ssItem(U)) | leq(U, U))) | ((~ssItem(hd(W!49))) | leq(hd(W!49), hd(W!49)))) <=> ((~![U: $i] : ((~ssItem(U)) | leq(U, U))) | (~ssItem(hd(W!49))) | leq(hd(W!49), hd(W!49)))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(242,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssItem(U)) | leq(U, U))) | ((~ssItem(hd(W!49))) | leq(hd(W!49), hd(W!49)))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(243,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssItem(U)) | leq(U, U))) | (~ssItem(hd(W!49))) | leq(hd(W!49), hd(W!49))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[242, 241])).
% 21.95/14.17 tff(244,plain,
% 21.95/14.17 (leq(hd(W!49), hd(W!49))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[243, 240, 157])).
% 21.95/14.17 tff(245,plain,
% 21.95/14.17 (leq(hd(W!49), tptp_fun_W_44(W!49))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[244, 230])).
% 21.95/14.17 tff(246,plain,
% 21.95/14.17 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(247,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[246])).
% 21.95/14.17 tff(248,plain,
% 21.95/14.17 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(249,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[248])).
% 21.95/14.17 tff(250,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(transitivity,[status(thm)],[249, 247])).
% 21.95/14.17 tff(251,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(252,plain,
% 21.95/14.17 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((~(nil = U)) => (hd(app(U, V)) = hd(U))) <=> ((nil = U) | (hd(app(U, V)) = hd(U)))), ((ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U)))) <=> (ssList(V) => ((nil = U) | (hd(app(U, V)) = hd(U)))))), rewrite((ssList(V) => ((nil = U) | (hd(app(U, V)) = hd(U)))) <=> ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))), ((ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U)))) <=> ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))))), (![V: $i] : (ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U)))) <=> ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U))))) <=> (ssList(U) => ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))))), rewrite((ssList(U) => ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V)))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U))))) <=> ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(253,plain,
% 21.95/14.17 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[252])).
% 21.95/14.17 tff(254,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((~(nil = U)) => (hd(app(U, V)) = hd(U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax85')).
% 21.95/14.17 tff(255,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[254, 253])).
% 21.95/14.17 tff(256,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[255, 251])).
% 21.95/14.17 tff(257,plain,(
% 21.95/14.17 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(skolemize,[status(sab)],[256])).
% 21.95/14.17 tff(258,plain,
% 21.95/14.17 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[257, 250])).
% 21.95/14.17 tff(259,plain,
% 21.95/14.17 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(260,plain,
% 21.95/14.17 (((~ssList(W!49)) | ![V: $i] : ((nil = W!49) | (hd(app(W!49, V)) = hd(W!49)) | (~ssList(V)))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(261,plain,
% 21.95/14.17 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | ((~ssList(W!49)) | ![V: $i] : ((nil = W!49) | (hd(app(W!49, V)) = hd(W!49)) | (~ssList(V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))))),
% 21.95/14.17 inference(monotonicity,[status(thm)],[260])).
% 21.95/14.17 tff(262,plain,
% 21.95/14.17 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | ((~ssList(W!49)) | ![V: $i] : ((nil = W!49) | (hd(app(W!49, V)) = hd(W!49)) | (~ssList(V))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49))))),
% 21.95/14.17 inference(transitivity,[status(thm)],[261, 259])).
% 21.95/14.17 tff(263,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | ((~ssList(W!49)) | ![V: $i] : ((nil = W!49) | (hd(app(W!49, V)) = hd(W!49)) | (~ssList(V))))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(264,plain,
% 21.95/14.17 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((nil = U) | (hd(app(U, V)) = hd(U)) | (~ssList(V))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[263, 262])).
% 21.95/14.17 tff(265,plain,
% 21.95/14.17 (![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[264, 258, 32])).
% 21.95/14.17 tff(266,plain,
% 21.95/14.17 (((~![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))) | ((~ssList(W!49)) | (nil = W!49) | (hd(app(W!49, W!49)) = hd(W!49)))) <=> ((~![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))) | (~ssList(W!49)) | (nil = W!49) | (hd(app(W!49, W!49)) = hd(W!49)))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(267,plain,
% 21.95/14.17 ((~![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))) | ((~ssList(W!49)) | (nil = W!49) | (hd(app(W!49, W!49)) = hd(W!49)))),
% 21.95/14.17 inference(quant_inst,[status(thm)],[])).
% 21.95/14.17 tff(268,plain,
% 21.95/14.17 ((~![V: $i] : ((~ssList(V)) | (nil = W!49) | (hd(app(W!49, V)) = hd(W!49)))) | (~ssList(W!49)) | (nil = W!49) | (hd(app(W!49, W!49)) = hd(W!49))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[267, 266])).
% 21.95/14.17 tff(269,plain,
% 21.95/14.17 (hd(app(W!49, W!49)) = hd(W!49)),
% 21.95/14.17 inference(unit_resolution,[status(thm)],[268, 32, 265, 31])).
% 21.95/14.17 tff(270,plain,
% 21.95/14.17 (hd(W!49) = hd(app(W!49, W!49))),
% 21.95/14.17 inference(symmetry,[status(thm)],[269])).
% 21.95/14.17 tff(271,plain,
% 21.95/14.17 (leq(tptp_fun_W_44(W!49), hd(W!49)) <=> leq(tptp_fun_W_44(W!49), hd(app(W!49, W!49)))),
% 21.95/14.17 inference(monotonicity,[status(thm)],[270])).
% 21.95/14.17 tff(272,plain,
% 21.95/14.17 (leq(tptp_fun_W_44(W!49), hd(app(W!49, W!49))) <=> leq(tptp_fun_W_44(W!49), hd(W!49))),
% 21.95/14.17 inference(symmetry,[status(thm)],[271])).
% 21.95/14.17 tff(273,plain,
% 21.95/14.17 (leq(tptp_fun_W_44(W!49), hd(app(W!49, W!49))) <=> leq(hd(W!49), hd(W!49))),
% 21.95/14.17 inference(monotonicity,[status(thm)],[134, 269])).
% 21.95/14.17 tff(274,plain,
% 21.95/14.17 (leq(hd(W!49), hd(W!49)) <=> leq(tptp_fun_W_44(W!49), hd(app(W!49, W!49)))),
% 21.95/14.17 inference(symmetry,[status(thm)],[273])).
% 21.95/14.17 tff(275,plain,
% 21.95/14.17 (leq(hd(W!49), hd(W!49)) <=> leq(tptp_fun_W_44(W!49), hd(W!49))),
% 21.95/14.17 inference(transitivity,[status(thm)],[274, 272])).
% 21.95/14.17 tff(276,plain,
% 21.95/14.17 (leq(tptp_fun_W_44(W!49), hd(W!49))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[244, 275])).
% 21.95/14.17 tff(277,plain,
% 21.95/14.17 (^[U: $i] : refl(((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))) <=> ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(278,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[277])).
% 21.95/14.17 tff(279,plain,
% 21.95/14.17 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))) <=> ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(280,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[279])).
% 21.95/14.17 tff(281,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))),
% 21.95/14.17 inference(transitivity,[status(thm)],[280, 278])).
% 21.95/14.17 tff(282,plain,
% 21.95/14.17 (^[U: $i] : rewrite(((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))) <=> ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U)))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(283,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[282])).
% 21.95/14.17 tff(284,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))),
% 21.95/14.17 inference(rewrite,[status(thm)],[])).
% 21.95/14.17 tff(285,plain,
% 21.95/14.17 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite(((leq(U, V) & leq(V, U)) => (U = V)) <=> ((~(leq(U, V) & leq(V, U))) | (U = V))), ((ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V))) <=> (ssItem(V) => ((~(leq(U, V) & leq(V, U))) | (U = V))))), rewrite((ssItem(V) => ((~(leq(U, V) & leq(V, U))) | (U = V))) <=> ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))), ((ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V))) <=> ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))))), (![V: $i] : (ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V))) <=> ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V)))) <=> (ssItem(U) => ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))))), rewrite((ssItem(U) => ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U))))) <=> ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))), ((ssItem(U) => ![V: $i] : (ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V)))) <=> ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))))),
% 21.95/14.17 inference(bind,[status(th)],[])).
% 21.95/14.17 tff(286,plain,
% 21.95/14.17 (![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V)))) <=> ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))),
% 21.95/14.17 inference(quant_intro,[status(thm)],[285])).
% 21.95/14.17 tff(287,axiom,(![U: $i] : (ssItem(U) => ![V: $i] : (ssItem(V) => ((leq(U, V) & leq(V, U)) => (U = V))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax29')).
% 21.95/14.17 tff(288,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[287, 286])).
% 21.95/14.17 tff(289,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))),
% 21.95/14.17 inference(modus_ponens,[status(thm)],[288, 284])).
% 21.95/14.17 tff(290,plain,(
% 21.95/14.17 ![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~(leq(U, V) & leq(V, U)))))),
% 21.95/14.17 inference(skolemize,[status(sab)],[289])).
% 21.95/14.17 tff(291,plain,
% 21.95/14.17 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))),
% 21.95/14.18 inference(modus_ponens,[status(thm)],[290, 283])).
% 21.95/14.18 tff(292,plain,
% 21.95/14.18 (![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))),
% 21.95/14.18 inference(modus_ponens,[status(thm)],[291, 281])).
% 21.95/14.18 tff(293,plain,
% 21.95/14.18 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | (~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))),
% 21.95/14.18 inference(rewrite,[status(thm)],[])).
% 21.95/14.18 tff(294,plain,
% 21.95/14.18 (((~ssItem(hd(W!49))) | ![V: $i] : ((hd(W!49) = V) | (~ssItem(V)) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) <=> ((~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))),
% 21.95/14.18 inference(rewrite,[status(thm)],[])).
% 21.95/14.18 tff(295,plain,
% 21.95/14.18 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((hd(W!49) = V) | (~ssItem(V)) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))))),
% 21.95/14.18 inference(monotonicity,[status(thm)],[294])).
% 21.95/14.18 tff(296,plain,
% 21.95/14.18 (((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((hd(W!49) = V) | (~ssItem(V)) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))) <=> ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | (~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))),
% 21.95/14.18 inference(transitivity,[status(thm)],[295, 293])).
% 21.95/14.18 tff(297,plain,
% 21.95/14.18 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | ((~ssItem(hd(W!49))) | ![V: $i] : ((hd(W!49) = V) | (~ssItem(V)) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49)))))),
% 21.95/14.18 inference(quant_inst,[status(thm)],[])).
% 21.95/14.18 tff(298,plain,
% 21.95/14.18 ((~![U: $i] : ((~ssItem(U)) | ![V: $i] : ((U = V) | (~ssItem(V)) | (~leq(U, V)) | (~leq(V, U))))) | (~ssItem(hd(W!49))) | ![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))),
% 21.95/14.18 inference(modus_ponens,[status(thm)],[297, 296])).
% 21.95/14.18 tff(299,plain,
% 21.95/14.18 (![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))),
% 21.95/14.18 inference(unit_resolution,[status(thm)],[298, 292, 157])).
% 21.95/14.18 tff(300,plain,
% 21.95/14.18 (((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49))))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | (~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49))))),
% 21.95/14.18 inference(rewrite,[status(thm)],[])).
% 21.95/14.18 tff(301,plain,
% 21.95/14.18 (((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(hd(W!49), tptp_fun_W_44(W!49))) | (~leq(tptp_fun_W_44(W!49), hd(W!49)))) <=> ((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49))))),
% 21.95/14.18 inference(rewrite,[status(thm)],[])).
% 21.95/14.18 tff(302,plain,
% 21.95/14.18 (((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(hd(W!49), tptp_fun_W_44(W!49))) | (~leq(tptp_fun_W_44(W!49), hd(W!49))))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49)))))),
% 22.09/14.20 inference(monotonicity,[status(thm)],[301])).
% 22.09/14.20 tff(303,plain,
% 22.09/14.20 (((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(hd(W!49), tptp_fun_W_44(W!49))) | (~leq(tptp_fun_W_44(W!49), hd(W!49))))) <=> ((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | (~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49))))),
% 22.09/14.20 inference(transitivity,[status(thm)],[302, 300])).
% 22.09/14.20 tff(304,plain,
% 22.09/14.20 ((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | ((~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(hd(W!49), tptp_fun_W_44(W!49))) | (~leq(tptp_fun_W_44(W!49), hd(W!49))))),
% 22.09/14.20 inference(quant_inst,[status(thm)],[])).
% 22.09/14.20 tff(305,plain,
% 22.09/14.20 ((~![V: $i] : ((~ssItem(V)) | (hd(W!49) = V) | (~leq(hd(W!49), V)) | (~leq(V, hd(W!49))))) | (~ssItem(tptp_fun_W_44(W!49))) | (hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49)))),
% 22.09/14.20 inference(modus_ponens,[status(thm)],[304, 303])).
% 22.09/14.20 tff(306,plain,
% 22.09/14.20 ((hd(W!49) = tptp_fun_W_44(W!49)) | (~leq(tptp_fun_W_44(W!49), hd(W!49))) | (~leq(hd(W!49), tptp_fun_W_44(W!49)))),
% 22.09/14.20 inference(unit_resolution,[status(thm)],[305, 128, 299])).
% 22.09/14.20 tff(307,plain,
% 22.09/14.20 (hd(W!49) = tptp_fun_W_44(W!49)),
% 22.09/14.20 inference(unit_resolution,[status(thm)],[306, 276, 245])).
% 22.09/14.20 tff(308,plain,
% 22.09/14.20 (((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49))) | (~(hd(W!49) = tptp_fun_W_44(W!49)))),
% 22.09/14.20 inference(tautology,[status(thm)],[])).
% 22.09/14.20 tff(309,plain,
% 22.09/14.20 ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49))),
% 22.09/14.20 inference(unit_resolution,[status(thm)],[308, 307])).
% 22.09/14.20 tff(310,plain,
% 22.09/14.20 ((~(memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) <=> ((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49))))) | memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49)) | (~((hd(W!49) = tptp_fun_W_44(W!49)) | memberP(tptp_fun_V_46(W!49), hd(W!49))))),
% 22.09/14.20 inference(tautology,[status(thm)],[])).
% 22.09/14.20 tff(311,plain,
% 22.09/14.20 (memberP(cons(tptp_fun_W_44(W!49), tptp_fun_V_46(W!49)), hd(W!49))),
% 22.09/14.20 inference(unit_resolution,[status(thm)],[310, 309, 228])).
% 22.09/14.20 tff(312,plain,
% 22.09/14.20 ($false),
% 22.09/14.20 inference(unit_resolution,[status(thm)],[311, 201])).
% 22.09/14.20 % SZS output end Proof
%------------------------------------------------------------------------------