TSTP Solution File: SWC043+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC043+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 11:54:51 EDT 2022
% Result : Theorem 0.20s 0.55s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC043+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n019.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Sep 3 20:58:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.20/0.55 % SZS status Theorem
% 0.20/0.55 % SZS output start Proof
% 0.20/0.55 tff(tptp_fun_Y_51_type, type, (
% 0.20/0.55 tptp_fun_Y_51: $i)).
% 0.20/0.55 tff(nil_type, type, (
% 0.20/0.55 nil: $i)).
% 0.20/0.55 tff(tptp_fun_W_49_type, type, (
% 0.20/0.55 tptp_fun_W_49: $i)).
% 0.20/0.55 tff(app_type, type, (
% 0.20/0.55 app: ( $i * $i ) > $i)).
% 0.20/0.55 tff(tptp_fun_X_50_type, type, (
% 0.20/0.55 tptp_fun_X_50: $i)).
% 0.20/0.55 tff(lt_type, type, (
% 0.20/0.55 lt: ( $i * $i ) > $o)).
% 0.20/0.55 tff(cons_type, type, (
% 0.20/0.55 cons: ( $i * $i ) > $i)).
% 0.20/0.55 tff(ssList_type, type, (
% 0.20/0.55 ssList: $i > $o)).
% 0.20/0.55 tff(ssItem_type, type, (
% 0.20/0.55 ssItem: $i > $o)).
% 0.20/0.55 tff(strictorderedP_type, type, (
% 0.20/0.55 strictorderedP: $i > $o)).
% 0.20/0.55 tff(tptp_fun_V_48_type, type, (
% 0.20/0.55 tptp_fun_V_48: $i)).
% 0.20/0.55 tff(tptp_fun_U_47_type, type, (
% 0.20/0.55 tptp_fun_U_47: $i)).
% 0.20/0.55 tff(1,plain,
% 0.20/0.55 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(2,plain,
% 0.20/0.55 ((ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(3,plain,
% 0.20/0.55 ((ssList(W!49) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(4,plain,
% 0.20/0.55 (((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & (strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))) <=> ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(5,plain,
% 0.20/0.56 (((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))) <=> (strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(6,plain,
% 0.20/0.56 ((~(~ssList(X!50))) <=> ssList(X!50)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(7,plain,
% 0.20/0.56 ((~(~(nil = V!48))) <=> (nil = V!48)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(8,plain,
% 0.20/0.56 ((~(~(V!48 = X!50))) <=> (V!48 = X!50)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(9,plain,
% 0.20/0.56 ((~(~(U!47 = W!49))) <=> (U!47 = W!49)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(10,plain,
% 0.20/0.56 (((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))) <=> ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & (strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[9, 8, 7, 6, 5])).
% 0.20/0.56 tff(11,plain,
% 0.20/0.56 (((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))) <=> ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[10, 4])).
% 0.20/0.56 tff(12,plain,
% 0.20/0.56 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(13,plain,
% 0.20/0.56 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))) <=> (ssList(W!49) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[12, 11])).
% 0.20/0.56 tff(14,plain,
% 0.20/0.56 (((~(~ssList(W!49))) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))) <=> (ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[13, 3])).
% 0.20/0.56 tff(15,plain,
% 0.20/0.56 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(16,plain,
% 0.20/0.56 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))))) <=> (ssList(V!48) & (ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[15, 14])).
% 0.20/0.56 tff(17,plain,
% 0.20/0.56 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))))) <=> (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[16, 2])).
% 0.20/0.56 tff(18,plain,
% 0.20/0.56 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(19,plain,
% 0.20/0.56 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))),
% 0.20/0.56 inference(monotonicity,[status(thm)],[18, 17])).
% 0.20/0.56 tff(20,plain,
% 0.20/0.56 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~(nil = V!48))) & (~(~ssList(X!50))) & ((~(~strictorderedP(W!49))) & (~(~(app(W!49, Y!51) = X!50))) & (~(~ssList(Y!51))) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z)))))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[19, 1])).
% 0.20/0.57 tff(21,plain,
% 0.20/0.57 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z)))))))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(22,plain,
% 0.20/0.57 ((~![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] : (ssList(Y) => (((~(app(W, Y) = X)) | (~strictorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & lt(X2, Z)))))))) | ((~(nil = X)) & (nil = W)))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z)))))))))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(23,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] : (ssList(Y) => (((~(app(W, Y) = X)) | (~strictorderedP(W))) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : ((ssList(X1) & (app(cons(Z, nil), X1) = Y)) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : ((ssList(X3) & (app(X3, cons(X2, nil)) = W)) & lt(X2, Z)))))))) | ((~(nil = X)) & (nil = W)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 0.20/0.57 tff(24,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.20/0.57 tff(25,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[24, 21])).
% 0.20/0.57 tff(26,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.57 tff(27,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[26, 21])).
% 0.20/0.57 tff(28,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[27, 21])).
% 0.20/0.57 tff(29,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.20/0.57 tff(30,plain,
% 0.20/0.57 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : ((nil = U) | ((~(nil = X)) & (nil = W)) | (~(U = W)) | (~(V = X)) | (~(nil = V)) | (~ssList(X)) | ![Y: $i] : ((~strictorderedP(W)) | (~(app(W, Y) = X)) | (~ssList(Y)) | ?[Z: $i] : (ssItem(Z) & ?[X1: $i] : (ssList(X1) & (app(cons(Z, nil), X1) = Y) & ?[X2: $i] : (ssItem(X2) & ?[X3: $i] : (ssList(X3) & (app(X3, cons(X2, nil)) = W) & lt(X2, Z))))))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.20/0.57 tff(31,plain,
% 0.20/0.57 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~(nil = U!47)) & (~((~(nil = X!50)) & (nil = W!49))) & (U!47 = W!49) & (V!48 = X!50) & (nil = V!48) & ssList(X!50) & strictorderedP(W!49) & (app(W!49, Y!51) = X!50) & ssList(Y!51) & ![Z: $i] : ((~ssItem(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(cons(Z, nil), X1) = Y!51)) | ![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : (~(ssList(X3) & (app(X3, cons(X2, nil)) = W!49) & lt(X2, Z))))))),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.20/0.57 tff(32,plain,
% 0.20/0.57 (app(W!49, Y!51) = X!50),
% 0.20/0.57 inference(and_elim,[status(thm)],[31])).
% 0.20/0.57 tff(33,plain,
% 0.20/0.57 (X!50 = app(W!49, Y!51)),
% 0.20/0.57 inference(symmetry,[status(thm)],[32])).
% 0.20/0.57 tff(34,plain,
% 0.20/0.57 (V!48 = X!50),
% 0.20/0.57 inference(and_elim,[status(thm)],[31])).
% 0.20/0.57 tff(35,plain,
% 0.20/0.57 (nil = V!48),
% 0.20/0.57 inference(and_elim,[status(thm)],[31])).
% 0.20/0.57 tff(36,plain,
% 0.20/0.57 (nil = app(W!49, Y!51)),
% 0.20/0.57 inference(transitivity,[status(thm)],[35, 34, 33])).
% 0.20/0.57 tff(37,plain,
% 0.20/0.57 (U!47 = W!49),
% 0.20/0.57 inference(and_elim,[status(thm)],[31])).
% 0.20/0.57 tff(38,plain,
% 0.20/0.57 ((nil = U!47) <=> (nil = W!49)),
% 0.20/0.57 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.57 tff(39,plain,
% 0.20/0.57 ((~(nil = U!47)) <=> (~(nil = W!49))),
% 0.20/0.57 inference(monotonicity,[status(thm)],[38])).
% 0.20/0.57 tff(40,plain,
% 0.20/0.57 (~(nil = U!47)),
% 0.20/0.57 inference(and_elim,[status(thm)],[31])).
% 0.20/0.57 tff(41,plain,
% 0.20/0.57 (~(nil = W!49)),
% 0.20/0.57 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.57 tff(42,plain,
% 0.20/0.57 (((~(nil = W!49)) | (~(nil = Y!51))) | (nil = W!49)),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(43,plain,
% 0.20/0.57 ((~(nil = W!49)) | (~(nil = Y!51))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.20/0.57 tff(44,plain,
% 0.20/0.57 ((~((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51)))))) | (~(nil = app(W!49, Y!51))) | (~((~(nil = W!49)) | (~(nil = Y!51))))),
% 0.20/0.57 inference(tautology,[status(thm)],[])).
% 0.20/0.57 tff(45,plain,
% 0.20/0.57 (~((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51)))))),
% 0.20/0.57 inference(unit_resolution,[status(thm)],[44, 43, 36])).
% 0.20/0.57 tff(46,plain,
% 0.20/0.57 (ssList(W!49)),
% 0.20/0.57 inference(and_elim,[status(thm)],[31])).
% 0.20/0.57 tff(47,plain,
% 0.20/0.57 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(48,plain,
% 0.20/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[47])).
% 0.20/0.57 tff(49,plain,
% 0.20/0.57 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(50,plain,
% 0.20/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.57 tff(51,plain,
% 0.20/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.20/0.57 inference(transitivity,[status(thm)],[50, 48])).
% 0.20/0.57 tff(52,plain,
% 0.20/0.57 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U))))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(53,plain,
% 0.20/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.20/0.57 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.57 tff(54,plain,
% 0.20/0.57 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.57 inference(rewrite,[status(thm)],[])).
% 0.20/0.57 tff(55,plain,
% 0.20/0.57 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), (![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))) <=> ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))))),
% 0.20/0.57 inference(bind,[status(th)],[])).
% 0.20/0.57 tff(56,plain,
% 0.20/0.57 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.58 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.58 tff(57,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax83')).
% 0.20/0.58 tff(58,plain,
% 0.20/0.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.20/0.58 tff(59,plain,
% 0.20/0.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.20/0.58 tff(60,plain,(
% 0.20/0.58 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> ((nil = V) & (nil = U)))))),
% 0.20/0.58 inference(skolemize,[status(sab)],[59])).
% 0.20/0.58 tff(61,plain,
% 0.20/0.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.20/0.58 tff(62,plain,
% 0.20/0.58 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.20/0.58 tff(63,plain,
% 0.20/0.58 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49)))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49)))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(64,plain,
% 0.20/0.58 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | ((~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49)))))))),
% 0.20/0.58 inference(quant_inst,[status(thm)],[])).
% 0.20/0.58 tff(65,plain,
% 0.20/0.58 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ((nil = app(U, V)) <=> (~((~(nil = V)) | (~(nil = U)))))))) | (~ssList(W!49)) | ![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))),
% 0.20/0.58 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.58 tff(66,plain,
% 0.20/0.58 (![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))),
% 0.20/0.58 inference(unit_resolution,[status(thm)],[65, 62, 46])).
% 0.20/0.58 tff(67,plain,
% 0.20/0.58 (ssList(Y!51)),
% 0.20/0.58 inference(and_elim,[status(thm)],[31])).
% 0.20/0.58 tff(68,plain,
% 0.20/0.58 (((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | (~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(69,plain,
% 0.20/0.58 (((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = Y!51)) | (~(nil = W!49)))))) <=> ((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51))))))),
% 0.20/0.58 inference(rewrite,[status(thm)],[])).
% 0.20/0.58 tff(70,plain,
% 0.20/0.58 (((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = Y!51)) | (~(nil = W!49))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51)))))))),
% 0.20/0.58 inference(monotonicity,[status(thm)],[69])).
% 0.20/0.58 tff(71,plain,
% 0.20/0.58 (((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = Y!51)) | (~(nil = W!49))))))) <=> ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | (~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51))))))),
% 0.20/0.59 inference(transitivity,[status(thm)],[70, 68])).
% 0.20/0.59 tff(72,plain,
% 0.20/0.59 ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | ((~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = Y!51)) | (~(nil = W!49))))))),
% 0.20/0.59 inference(quant_inst,[status(thm)],[])).
% 0.20/0.59 tff(73,plain,
% 0.20/0.59 ((~![V: $i] : ((~ssList(V)) | ((nil = app(W!49, V)) <=> (~((~(nil = V)) | (~(nil = W!49))))))) | (~ssList(Y!51)) | ((nil = app(W!49, Y!51)) <=> (~((~(nil = W!49)) | (~(nil = Y!51)))))),
% 0.20/0.59 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.59 tff(74,plain,
% 0.20/0.59 ($false),
% 0.20/0.59 inference(unit_resolution,[status(thm)],[73, 67, 66, 45])).
% 0.20/0.59 % SZS output end Proof
%------------------------------------------------------------------------------