TSTP Solution File: SWC370+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC370+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 11:57:28 EDT 2022
% Result : Theorem 5.77s 3.93s
% Output : Proof 5.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC370+1 : TPTP v8.1.0. Released v2.4.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Sep 4 00:48:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 5.77/3.93 % SZS status Theorem
% 5.77/3.93 % SZS output start Proof
% 5.77/3.93 tff(segmentP_type, type, (
% 5.77/3.93 segmentP: ( $i * $i ) > $o)).
% 5.77/3.93 tff(tptp_fun_W_49_type, type, (
% 5.77/3.93 tptp_fun_W_49: $i)).
% 5.77/3.93 tff(app_type, type, (
% 5.77/3.93 app: ( $i * $i ) > $i)).
% 5.77/3.93 tff(tptp_fun_Y_51_type, type, (
% 5.77/3.93 tptp_fun_Y_51: $i)).
% 5.77/3.93 tff(nil_type, type, (
% 5.77/3.93 nil: $i)).
% 5.77/3.93 tff(tptp_fun_U_47_type, type, (
% 5.77/3.93 tptp_fun_U_47: $i)).
% 5.77/3.93 tff(tptp_fun_V_48_type, type, (
% 5.77/3.93 tptp_fun_V_48: $i)).
% 5.77/3.93 tff(cons_type, type, (
% 5.77/3.93 cons: ( $i * $i ) > $i)).
% 5.77/3.93 tff(ssList_type, type, (
% 5.77/3.93 ssList: $i > $o)).
% 5.77/3.93 tff(ssItem_type, type, (
% 5.77/3.93 ssItem: $i > $o)).
% 5.77/3.93 tff(equalelemsP_type, type, (
% 5.77/3.93 equalelemsP: $i > $o)).
% 5.77/3.93 tff(tptp_fun_X_50_type, type, (
% 5.77/3.93 tptp_fun_X_50: $i)).
% 5.77/3.93 tff(1,plain,
% 5.77/3.93 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(2,plain,
% 5.77/3.93 ((ssList(V!48) & (ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(3,plain,
% 5.77/3.93 ((ssList(W!49) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> (ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(4,plain,
% 5.77/3.93 (((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(5,plain,
% 5.77/3.93 (((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))) <=> ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(6,plain,
% 5.77/3.93 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(7,plain,
% 5.77/3.93 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(8,plain,
% 5.77/3.93 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(9,plain,
% 5.77/3.93 (((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & ((app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 5.77/3.93 inference(monotonicity,[status(thm)],[8, 7, 6, 5])).
% 5.77/3.93 tff(10,plain,
% 5.77/3.93 (((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))) <=> ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(transitivity,[status(thm)],[9, 4])).
% 5.77/3.93 tff(11,plain,
% 5.77/3.93 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(12,plain,
% 5.77/3.93 (((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))) <=> (ssList(W!49) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 5.77/3.93 inference(monotonicity,[status(thm)],[11, 10])).
% 5.77/3.93 tff(13,plain,
% 5.77/3.93 (((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))) <=> (ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.93 inference(transitivity,[status(thm)],[12, 3])).
% 5.77/3.93 tff(14,plain,
% 5.77/3.93 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 5.77/3.93 inference(rewrite,[status(thm)],[])).
% 5.77/3.93 tff(15,plain,
% 5.77/3.93 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 5.77/3.94 inference(monotonicity,[status(thm)],[14, 13])).
% 5.77/3.94 tff(16,plain,
% 5.77/3.94 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))))) <=> (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.94 inference(transitivity,[status(thm)],[15, 2])).
% 5.77/3.94 tff(17,plain,
% 5.77/3.94 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(18,plain,
% 5.77/3.94 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))),
% 5.77/3.94 inference(monotonicity,[status(thm)],[17, 16])).
% 5.77/3.94 tff(19,plain,
% 5.77/3.94 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(V!48 = X!50))) & (~(~(U!47 = W!49))) & (~(~ssList(X!50))) & ((~(~(app(W!49, Y!51) = X!50))) & (~(~equalelemsP(W!49))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49))))))),
% 5.77/3.94 inference(transitivity,[status(thm)],[18, 1])).
% 5.77/3.94 tff(20,plain,
% 5.77/3.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(21,plain,
% 5.77/3.94 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | segmentP(V, U)) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(22,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (((((~(V = X)) | (~(U = W))) | ![Y: $i] : (ssList(Y) => (((~(app(W, Y) = X)) | (~equalelemsP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W))))))) | segmentP(V, U)) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 5.77/3.94 tff(23,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[22, 21])).
% 5.77/3.94 tff(24,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[23, 20])).
% 5.77/3.94 tff(25,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[24, 20])).
% 5.77/3.94 tff(26,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[25, 20])).
% 5.77/3.94 tff(27,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[26, 20])).
% 5.77/3.94 tff(28,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[27, 20])).
% 5.77/3.94 tff(29,plain,
% 5.77/3.94 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(V, U) | ((~(nil = X)) & (nil = W)) | (~(V = X)) | (~(U = W)) | (~ssList(X)) | ![Y: $i] : ((~(app(W, Y) = X)) | (~equalelemsP(W)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssList(X2) & (app(X2, cons(Z, nil)) = W)))))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[28, 20])).
% 5.77/3.94 tff(30,plain,
% 5.77/3.94 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~segmentP(V!48, U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (V!48 = X!50) & (U!47 = W!49) & ssList(X!50) & (app(W!49, Y!51) = X!50) & equalelemsP(W!49) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : (~(ssList(X2) & (app(X2, cons(Z, nil)) = W!49)))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[29, 19])).
% 5.77/3.94 tff(31,plain,
% 5.77/3.94 (U!47 = W!49),
% 5.77/3.94 inference(and_elim,[status(thm)],[30])).
% 5.77/3.94 tff(32,plain,
% 5.77/3.94 (W!49 = U!47),
% 5.77/3.94 inference(symmetry,[status(thm)],[31])).
% 5.77/3.94 tff(33,plain,
% 5.77/3.94 (V!48 = X!50),
% 5.77/3.94 inference(and_elim,[status(thm)],[30])).
% 5.77/3.94 tff(34,plain,
% 5.77/3.94 (X!50 = V!48),
% 5.77/3.94 inference(symmetry,[status(thm)],[33])).
% 5.77/3.94 tff(35,plain,
% 5.77/3.94 (app(W!49, Y!51) = X!50),
% 5.77/3.94 inference(and_elim,[status(thm)],[30])).
% 5.77/3.94 tff(36,plain,
% 5.77/3.94 (ssList(W!49)),
% 5.77/3.94 inference(and_elim,[status(thm)],[30])).
% 5.77/3.94 tff(37,plain,
% 5.77/3.94 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 5.77/3.94 inference(bind,[status(th)],[])).
% 5.77/3.94 tff(38,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(quant_intro,[status(thm)],[37])).
% 5.77/3.94 tff(39,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(40,plain,
% 5.77/3.94 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 5.77/3.94 inference(bind,[status(th)],[])).
% 5.77/3.94 tff(41,plain,
% 5.77/3.94 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(quant_intro,[status(thm)],[40])).
% 5.77/3.94 tff(42,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 5.77/3.94 tff(43,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[42, 41])).
% 5.77/3.94 tff(44,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[43, 39])).
% 5.77/3.94 tff(45,plain,(
% 5.77/3.94 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(skolemize,[status(sab)],[44])).
% 5.77/3.94 tff(46,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[45, 38])).
% 5.77/3.94 tff(47,plain,
% 5.77/3.94 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(48,plain,
% 5.77/3.94 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(W!49)) | (app(nil, W!49) = W!49))),
% 5.77/3.94 inference(quant_inst,[status(thm)],[])).
% 5.77/3.94 tff(49,plain,
% 5.77/3.94 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(W!49)) | (app(nil, W!49) = W!49)),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[48, 47])).
% 5.77/3.94 tff(50,plain,
% 5.77/3.94 (app(nil, W!49) = W!49),
% 5.77/3.94 inference(unit_resolution,[status(thm)],[49, 46, 36])).
% 5.77/3.94 tff(51,plain,
% 5.77/3.94 (app(app(nil, W!49), Y!51) = app(W!49, Y!51)),
% 5.77/3.94 inference(monotonicity,[status(thm)],[50])).
% 5.77/3.94 tff(52,plain,
% 5.77/3.94 (app(app(nil, W!49), Y!51) = V!48),
% 5.77/3.94 inference(transitivity,[status(thm)],[51, 35, 34])).
% 5.77/3.94 tff(53,plain,
% 5.77/3.94 (segmentP(app(app(nil, W!49), Y!51), W!49) <=> segmentP(V!48, U!47)),
% 5.77/3.94 inference(monotonicity,[status(thm)],[52, 32])).
% 5.77/3.94 tff(54,plain,
% 5.77/3.94 (segmentP(V!48, U!47) <=> segmentP(app(app(nil, W!49), Y!51), W!49)),
% 5.77/3.94 inference(symmetry,[status(thm)],[53])).
% 5.77/3.94 tff(55,plain,
% 5.77/3.94 ((~segmentP(V!48, U!47)) <=> (~segmentP(app(app(nil, W!49), Y!51), W!49))),
% 5.77/3.94 inference(monotonicity,[status(thm)],[54])).
% 5.77/3.94 tff(56,plain,
% 5.77/3.94 (~segmentP(V!48, U!47)),
% 5.77/3.94 inference(and_elim,[status(thm)],[30])).
% 5.77/3.94 tff(57,plain,
% 5.77/3.94 (~segmentP(app(app(nil, W!49), Y!51), W!49)),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[56, 55])).
% 5.77/3.94 tff(58,plain,
% 5.77/3.94 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 5.77/3.94 inference(bind,[status(th)],[])).
% 5.77/3.94 tff(59,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(quant_intro,[status(thm)],[58])).
% 5.77/3.94 tff(60,plain,
% 5.77/3.94 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))),
% 5.77/3.94 inference(bind,[status(th)],[])).
% 5.77/3.94 tff(61,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(quant_intro,[status(thm)],[60])).
% 5.77/3.94 tff(62,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(transitivity,[status(thm)],[61, 59])).
% 5.77/3.94 tff(63,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(64,plain,
% 5.77/3.94 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(quant_intro(proof_bind(^[X: $i] : trans(monotonicity(rewrite((segmentP(U, V) => segmentP(app(app(W, U), X), V)) <=> ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))))), rewrite((ssList(X) => ((~segmentP(U, V)) | segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))), ((ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), (![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))) <=> ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> (ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), rewrite((ssList(W) => ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))), ((ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), (![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))) <=> ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> (ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))))),
% 5.77/3.94 inference(bind,[status(th)],[])).
% 5.77/3.94 tff(65,plain,
% 5.77/3.94 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(quant_intro,[status(thm)],[64])).
% 5.77/3.94 tff(66,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (ssList(X) => (segmentP(U, V) => segmentP(app(app(W, U), X), V))))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax56')).
% 5.77/3.94 tff(67,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[66, 65])).
% 5.77/3.94 tff(68,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[67, 63])).
% 5.77/3.94 tff(69,plain,(
% 5.77/3.94 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(skolemize,[status(sab)],[68])).
% 5.77/3.94 tff(70,plain,
% 5.77/3.94 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[69, 62])).
% 5.77/3.94 tff(71,plain,
% 5.77/3.94 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(72,plain,
% 5.77/3.94 (((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V)))))) <=> ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(73,plain,
% 5.77/3.94 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))))),
% 5.77/3.94 inference(monotonicity,[status(thm)],[72])).
% 5.77/3.94 tff(74,plain,
% 5.77/3.94 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V))))))),
% 5.77/3.94 inference(transitivity,[status(thm)],[73, 71])).
% 5.77/3.94 tff(75,plain,
% 5.77/3.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, W!49), X), V) | (~ssList(X)) | (~segmentP(W!49, V))))))),
% 5.77/3.94 inference(quant_inst,[status(thm)],[])).
% 5.77/3.94 tff(76,plain,
% 5.77/3.94 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (segmentP(app(app(W, U), X), V) | (~ssList(X)) | (~segmentP(U, V))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[75, 74])).
% 5.77/3.94 tff(77,plain,
% 5.77/3.94 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))),
% 5.77/3.94 inference(unit_resolution,[status(thm)],[76, 70, 36])).
% 5.77/3.94 tff(78,plain,
% 5.77/3.94 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(79,plain,
% 5.77/3.94 (((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49))))) <=> ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(80,plain,
% 5.77/3.94 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))))),
% 5.77/3.94 inference(monotonicity,[status(thm)],[79])).
% 5.77/3.94 tff(81,plain,
% 5.77/3.94 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49))))),
% 5.77/3.94 inference(transitivity,[status(thm)],[80, 78])).
% 5.77/3.94 tff(82,plain,
% 5.77/3.94 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | ((~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), W!49) | (~segmentP(W!49, W!49)))))),
% 5.77/3.94 inference(quant_inst,[status(thm)],[])).
% 5.77/3.94 tff(83,plain,
% 5.77/3.94 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | segmentP(app(app(W, W!49), X), V) | (~segmentP(W!49, V)))))) | (~ssList(W!49)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[82, 81])).
% 5.77/3.94 tff(84,plain,
% 5.77/3.94 (![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))),
% 5.77/3.94 inference(unit_resolution,[status(thm)],[83, 36, 77])).
% 5.77/3.94 tff(85,plain,
% 5.77/3.94 (ssList(nil) <=> ssList(nil)),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(86,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 5.77/3.94 tff(87,plain,
% 5.77/3.94 (ssList(nil)),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[86, 85])).
% 5.77/3.94 tff(88,plain,
% 5.77/3.94 (((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49)))) <=> ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49)))),
% 5.77/3.94 inference(rewrite,[status(thm)],[])).
% 5.77/3.94 tff(89,plain,
% 5.77/3.94 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | ((~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49)))),
% 5.77/3.94 inference(quant_inst,[status(thm)],[])).
% 5.77/3.94 tff(90,plain,
% 5.77/3.94 ((~![W: $i] : ((~ssList(W)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(W, W!49), X), W!49)))) | (~ssList(nil)) | ![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))),
% 5.77/3.94 inference(modus_ponens,[status(thm)],[89, 88])).
% 5.77/3.94 tff(91,plain,
% 5.77/3.94 (![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))),
% 5.77/3.94 inference(unit_resolution,[status(thm)],[90, 87, 84])).
% 5.77/3.96 tff(92,plain,
% 5.77/3.96 (^[U: $i] : refl(((~ssList(U)) | segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 5.77/3.96 inference(bind,[status(th)],[])).
% 5.77/3.96 tff(93,plain,
% 5.77/3.96 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(quant_intro,[status(thm)],[92])).
% 5.77/3.96 tff(94,plain,
% 5.77/3.96 (![U: $i] : ((~ssList(U)) | segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(rewrite,[status(thm)],[])).
% 5.77/3.96 tff(95,plain,
% 5.77/3.96 (^[U: $i] : rewrite((ssList(U) => segmentP(U, U)) <=> ((~ssList(U)) | segmentP(U, U)))),
% 5.77/3.96 inference(bind,[status(th)],[])).
% 5.77/3.96 tff(96,plain,
% 5.77/3.96 (![U: $i] : (ssList(U) => segmentP(U, U)) <=> ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(quant_intro,[status(thm)],[95])).
% 5.77/3.96 tff(97,axiom,(![U: $i] : (ssList(U) => segmentP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax55')).
% 5.77/3.96 tff(98,plain,
% 5.77/3.96 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(modus_ponens,[status(thm)],[97, 96])).
% 5.77/3.96 tff(99,plain,
% 5.77/3.96 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(modus_ponens,[status(thm)],[98, 94])).
% 5.77/3.96 tff(100,plain,(
% 5.77/3.96 ![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(skolemize,[status(sab)],[99])).
% 5.77/3.96 tff(101,plain,
% 5.77/3.96 (![U: $i] : ((~ssList(U)) | segmentP(U, U))),
% 5.77/3.96 inference(modus_ponens,[status(thm)],[100, 93])).
% 5.77/3.96 tff(102,plain,
% 5.77/3.96 (((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))) <=> ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49))),
% 5.77/3.96 inference(rewrite,[status(thm)],[])).
% 5.77/3.96 tff(103,plain,
% 5.77/3.96 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | ((~ssList(W!49)) | segmentP(W!49, W!49))),
% 5.77/3.96 inference(quant_inst,[status(thm)],[])).
% 5.77/3.96 tff(104,plain,
% 5.77/3.96 ((~![U: $i] : ((~ssList(U)) | segmentP(U, U))) | (~ssList(W!49)) | segmentP(W!49, W!49)),
% 5.77/3.96 inference(modus_ponens,[status(thm)],[103, 102])).
% 5.77/3.96 tff(105,plain,
% 5.77/3.96 (segmentP(W!49, W!49)),
% 5.77/3.96 inference(unit_resolution,[status(thm)],[104, 101, 36])).
% 5.77/3.96 tff(106,plain,
% 5.77/3.96 (ssList(Y!51)),
% 5.77/3.96 inference(and_elim,[status(thm)],[30])).
% 5.77/3.96 tff(107,plain,
% 5.77/3.96 (((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | ((~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Y!51), W!49))) <=> ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | (~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Y!51), W!49))),
% 5.77/3.96 inference(rewrite,[status(thm)],[])).
% 5.77/3.96 tff(108,plain,
% 5.77/3.96 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | ((~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Y!51), W!49))),
% 5.77/3.96 inference(quant_inst,[status(thm)],[])).
% 5.77/3.96 tff(109,plain,
% 5.77/3.96 ((~![X: $i] : ((~ssList(X)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), X), W!49))) | (~ssList(Y!51)) | (~segmentP(W!49, W!49)) | segmentP(app(app(nil, W!49), Y!51), W!49)),
% 5.77/3.96 inference(modus_ponens,[status(thm)],[108, 107])).
% 5.77/3.96 tff(110,plain,
% 5.77/3.96 (segmentP(app(app(nil, W!49), Y!51), W!49)),
% 5.77/3.96 inference(unit_resolution,[status(thm)],[109, 106, 105, 91])).
% 5.77/3.96 tff(111,plain,
% 5.77/3.96 ($false),
% 5.77/3.96 inference(unit_resolution,[status(thm)],[110, 57])).
% 5.77/3.96 % SZS output end Proof
%------------------------------------------------------------------------------