TSTP Solution File: SWC419+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWC419+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n014.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 11:57:52 EDT 2022
% Result : Theorem 190.77s 122.78s
% Output : Proof 191.10s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SWC419+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n014.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun Sep 4 00:53:00 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.33 Usage: tptp [options] [-file:]file
% 0.13/0.33 -h, -? prints this message.
% 0.13/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.33 -m, -model generate model.
% 0.13/0.33 -p, -proof generate proof.
% 0.13/0.33 -c, -core generate unsat core of named formulas.
% 0.13/0.33 -st, -statistics display statistics.
% 0.13/0.33 -t:timeout set timeout (in second).
% 0.13/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.33 -<param>:<value> configuration parameter and value.
% 0.13/0.33 -o:<output-file> file to place output in.
% 190.77/122.78 % SZS status Theorem
% 190.77/122.78 % SZS output start Proof
% 190.77/122.78 tff(tptp_fun_U_47_type, type, (
% 190.77/122.78 tptp_fun_U_47: $i)).
% 190.77/122.78 tff(app_type, type, (
% 190.77/122.78 app: ( $i * $i ) > $i)).
% 190.77/122.78 tff(tptp_fun_W_6_type, type, (
% 190.77/122.78 tptp_fun_W_6: ( $i * $i ) > $i)).
% 190.77/122.78 tff(tptp_fun_X3_52_type, type, (
% 190.77/122.78 tptp_fun_X3_52: $i)).
% 190.77/122.78 tff(cons_type, type, (
% 190.77/122.78 cons: ( $i * $i ) > $i)).
% 190.77/122.78 tff(nil_type, type, (
% 190.77/122.78 nil: $i)).
% 190.77/122.78 tff(tptp_fun_X2_51_type, type, (
% 190.77/122.78 tptp_fun_X2_51: $i)).
% 190.77/122.78 tff(tptp_fun_W_49_type, type, (
% 190.77/122.78 tptp_fun_W_49: $i)).
% 190.77/122.78 tff(ssList_type, type, (
% 190.77/122.78 ssList: $i > $o)).
% 190.77/122.78 tff(tptp_fun_X_50_type, type, (
% 190.77/122.78 tptp_fun_X_50: $i)).
% 190.77/122.78 tff(ssItem_type, type, (
% 190.77/122.78 ssItem: $i > $o)).
% 190.77/122.78 tff(neq_type, type, (
% 190.77/122.78 neq: ( $i * $i ) > $o)).
% 190.77/122.78 tff(tptp_fun_V_48_type, type, (
% 190.77/122.78 tptp_fun_V_48: $i)).
% 190.77/122.78 tff(rearsegP_type, type, (
% 190.77/122.78 rearsegP: ( $i * $i ) > $o)).
% 190.77/122.78 tff(1,plain,
% 190.77/122.78 ((ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.78 inference(rewrite,[status(thm)],[])).
% 190.77/122.78 tff(2,plain,
% 190.77/122.78 ((ssList(V!48) & (ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.78 inference(rewrite,[status(thm)],[])).
% 190.77/122.78 tff(3,plain,
% 190.77/122.78 ((ssList(W!49) & ((~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))) <=> (ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.78 inference(rewrite,[status(thm)],[])).
% 190.77/122.78 tff(4,plain,
% 190.77/122.78 (((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil)))) <=> ((~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(5,plain,
% 190.77/122.79 ((~(~ssList(W!49))) <=> ssList(W!49)),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(6,plain,
% 190.77/122.79 (((~(~ssList(W!49))) & ((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & ((~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))))))),
% 190.77/122.79 inference(monotonicity,[status(thm)],[5, 4])).
% 190.77/122.79 tff(7,plain,
% 190.77/122.79 (((~(~ssList(W!49))) & ((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil))))) <=> (ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.79 inference(transitivity,[status(thm)],[6, 3])).
% 190.77/122.79 tff(8,plain,
% 190.77/122.79 ((~(~ssList(V!48))) <=> ssList(V!48)),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(9,plain,
% 190.77/122.79 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & (ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))))))),
% 190.77/122.79 inference(monotonicity,[status(thm)],[8, 7])).
% 190.77/122.79 tff(10,plain,
% 190.77/122.79 (((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil)))))) <=> (ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.79 inference(transitivity,[status(thm)],[9, 2])).
% 190.77/122.79 tff(11,plain,
% 190.77/122.79 ((~(~ssList(U!47))) <=> ssList(U!47)),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(12,plain,
% 190.77/122.79 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & (ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))))))),
% 190.77/122.79 inference(monotonicity,[status(thm)],[11, 10])).
% 190.77/122.79 tff(13,plain,
% 190.77/122.79 (((~(~ssList(U!47))) & ((~(~ssList(V!48))) & ((~(~ssList(W!49))) & ((~((~(nil = W!49)) & (nil = X!50))) & (~(~(U!47 = W!49))) & (~(~(V!48 = X!50))) & (~(~ssList(X!50))) & (~(~neq(V!48, nil))) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & (((~(~ssItem(X2!51))) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))) | (~neq(X!50, nil))))))) <=> (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))))),
% 190.77/122.79 inference(transitivity,[status(thm)],[12, 1])).
% 190.77/122.79 tff(14,plain,
% 190.77/122.79 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil)))))))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(15,plain,
% 190.77/122.79 ((~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (((((((~ssList(X)) | (~(V = X))) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V)) & (app(app(X1, cons(Y, nil)), Z) = U))))) | ((~(nil = W)) & (nil = X))) | (![X2: $i] : (ssItem(X2) => ![X3: $i] : (((~ssList(X3)) | (~(app(cons(X2, nil), X3) = X))) | (~(app(X3, cons(X2, nil)) = W)))) & neq(X, nil))))))) <=> (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil)))))))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(16,axiom,(~![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ![X: $i] : (((((((~ssList(X)) | (~(V = X))) | (~(U = W))) | (~neq(V, nil))) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : ((ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V)) & (app(app(X1, cons(Y, nil)), Z) = U))))) | ((~(nil = W)) & (nil = X))) | (![X2: $i] : (ssItem(X2) => ![X3: $i] : (((~ssList(X3)) | (~(app(cons(X2, nil), X3) = X))) | (~(app(X3, cons(X2, nil)) = W)))) & neq(X, nil))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','co1')).
% 190.77/122.79 tff(17,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[16, 15])).
% 190.77/122.79 tff(18,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[17, 14])).
% 190.77/122.79 tff(19,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[18, 14])).
% 190.77/122.79 tff(20,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[19, 14])).
% 190.77/122.79 tff(21,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[20, 14])).
% 190.77/122.79 tff(22,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[21, 14])).
% 190.77/122.79 tff(23,plain,
% 190.77/122.79 (~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | ![X: $i] : (((~(nil = W)) & (nil = X)) | (~(U = W)) | (~(V = X)) | (~ssList(X)) | (~neq(V, nil)) | ?[Y: $i] : (ssItem(Y) & ?[Z: $i] : (ssList(Z) & ?[X1: $i] : (ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V) & (app(app(X1, cons(Y, nil)), Z) = U)))) | (![X2: $i] : ((~ssItem(X2)) | ![X3: $i] : ((~(app(X3, cons(X2, nil)) = W)) | (~(app(cons(X2, nil), X3) = X)) | (~ssList(X3)))) & neq(X, nil))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[22, 14])).
% 190.77/122.79 tff(24,plain,
% 190.77/122.79 (ssList(U!47) & ssList(V!48) & ssList(W!49) & (~((~(nil = W!49)) & (nil = X!50))) & (U!47 = W!49) & (V!48 = X!50) & ssList(X!50) & neq(V!48, nil) & ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) & ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[23, 13])).
% 190.77/122.79 tff(25,plain,
% 190.77/122.79 (U!47 = W!49),
% 190.77/122.79 inference(and_elim,[status(thm)],[24])).
% 190.77/122.79 tff(26,plain,
% 190.77/122.79 (W!49 = U!47),
% 190.77/122.79 inference(symmetry,[status(thm)],[25])).
% 190.77/122.79 tff(27,plain,
% 190.77/122.79 (ssList(W!49)),
% 190.77/122.79 inference(and_elim,[status(thm)],[24])).
% 190.77/122.79 tff(28,plain,
% 190.77/122.79 (^[U: $i] : refl(((~ssList(U)) | (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 190.77/122.79 inference(bind,[status(th)],[])).
% 190.77/122.79 tff(29,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(quant_intro,[status(thm)],[28])).
% 190.77/122.79 tff(30,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(31,plain,
% 190.77/122.79 (^[U: $i] : rewrite((ssList(U) => (app(U, nil) = U)) <=> ((~ssList(U)) | (app(U, nil) = U)))),
% 190.77/122.79 inference(bind,[status(th)],[])).
% 190.77/122.79 tff(32,plain,
% 190.77/122.79 (![U: $i] : (ssList(U) => (app(U, nil) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(quant_intro,[status(thm)],[31])).
% 190.77/122.79 tff(33,axiom,(![U: $i] : (ssList(U) => (app(U, nil) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax84')).
% 190.77/122.79 tff(34,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[33, 32])).
% 190.77/122.79 tff(35,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[34, 30])).
% 190.77/122.79 tff(36,plain,(
% 190.77/122.79 ![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(skolemize,[status(sab)],[35])).
% 190.77/122.79 tff(37,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(U, nil) = U))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[36, 29])).
% 190.77/122.79 tff(38,plain,
% 190.77/122.79 (((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(W!49)) | (app(W!49, nil) = W!49))) <=> ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(W!49)) | (app(W!49, nil) = W!49))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(39,plain,
% 190.77/122.79 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | ((~ssList(W!49)) | (app(W!49, nil) = W!49))),
% 190.77/122.79 inference(quant_inst,[status(thm)],[])).
% 190.77/122.79 tff(40,plain,
% 190.77/122.79 ((~![U: $i] : ((~ssList(U)) | (app(U, nil) = U))) | (~ssList(W!49)) | (app(W!49, nil) = W!49)),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[39, 38])).
% 190.77/122.79 tff(41,plain,
% 190.77/122.79 (app(W!49, nil) = W!49),
% 190.77/122.79 inference(unit_resolution,[status(thm)],[40, 37, 27])).
% 190.77/122.79 tff(42,plain,
% 190.77/122.79 (V!48 = X!50),
% 190.77/122.79 inference(and_elim,[status(thm)],[24])).
% 190.77/122.79 tff(43,plain,
% 190.77/122.79 (neq(V!48, nil) <=> neq(X!50, nil)),
% 190.77/122.79 inference(monotonicity,[status(thm)],[42])).
% 190.77/122.79 tff(44,plain,
% 190.77/122.79 (neq(V!48, nil)),
% 190.77/122.79 inference(and_elim,[status(thm)],[24])).
% 190.77/122.79 tff(45,plain,
% 190.77/122.79 (neq(X!50, nil)),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[44, 43])).
% 190.77/122.79 tff(46,plain,
% 190.77/122.79 (((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))) <=> ((~neq(X!50, nil)) | (~((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(47,plain,
% 190.77/122.79 ((~neq(X!50, nil)) | (ssItem(X2!51) & (~((~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))))),
% 190.77/122.79 inference(and_elim,[status(thm)],[24])).
% 190.77/122.79 tff(48,plain,
% 190.77/122.79 ((~neq(X!50, nil)) | (~((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[47, 46])).
% 190.77/122.79 tff(49,plain,
% 190.77/122.79 (~((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52)))),
% 190.77/122.79 inference(unit_resolution,[status(thm)],[48, 45])).
% 190.77/122.79 tff(50,plain,
% 190.77/122.79 (((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))) | ssList(X3!52)),
% 190.77/122.79 inference(tautology,[status(thm)],[])).
% 190.77/122.79 tff(51,plain,
% 190.77/122.79 (ssList(X3!52)),
% 190.77/122.79 inference(unit_resolution,[status(thm)],[50, 49])).
% 190.77/122.79 tff(52,plain,
% 190.77/122.79 (^[U: $i] : refl(((~ssList(U)) | (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 190.77/122.79 inference(bind,[status(th)],[])).
% 190.77/122.79 tff(53,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(quant_intro,[status(thm)],[52])).
% 190.77/122.79 tff(54,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(55,plain,
% 190.77/122.79 (^[U: $i] : rewrite((ssList(U) => (app(nil, U) = U)) <=> ((~ssList(U)) | (app(nil, U) = U)))),
% 190.77/122.79 inference(bind,[status(th)],[])).
% 190.77/122.79 tff(56,plain,
% 190.77/122.79 (![U: $i] : (ssList(U) => (app(nil, U) = U)) <=> ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(quant_intro,[status(thm)],[55])).
% 190.77/122.79 tff(57,axiom,(![U: $i] : (ssList(U) => (app(nil, U) = U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax28')).
% 190.77/122.79 tff(58,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[57, 56])).
% 190.77/122.79 tff(59,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[58, 54])).
% 190.77/122.79 tff(60,plain,(
% 190.77/122.79 ![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(skolemize,[status(sab)],[59])).
% 190.77/122.79 tff(61,plain,
% 190.77/122.79 (![U: $i] : ((~ssList(U)) | (app(nil, U) = U))),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[60, 53])).
% 190.77/122.79 tff(62,plain,
% 190.77/122.79 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(X3!52)) | (app(nil, X3!52) = X3!52))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(X3!52)) | (app(nil, X3!52) = X3!52))),
% 190.77/122.79 inference(rewrite,[status(thm)],[])).
% 190.77/122.79 tff(63,plain,
% 190.77/122.79 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(X3!52)) | (app(nil, X3!52) = X3!52))),
% 190.77/122.79 inference(quant_inst,[status(thm)],[])).
% 190.77/122.79 tff(64,plain,
% 190.77/122.79 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(X3!52)) | (app(nil, X3!52) = X3!52)),
% 190.77/122.79 inference(modus_ponens,[status(thm)],[63, 62])).
% 190.77/122.79 tff(65,plain,
% 190.77/122.79 (app(nil, X3!52) = X3!52),
% 190.77/122.79 inference(unit_resolution,[status(thm)],[64, 61, 51])).
% 190.77/122.79 tff(66,plain,
% 190.77/122.79 (X3!52 = app(nil, X3!52)),
% 190.77/122.79 inference(symmetry,[status(thm)],[65])).
% 190.77/122.79 tff(67,plain,
% 190.77/122.79 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(68,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[67])).
% 190.77/122.80 tff(69,plain,
% 190.77/122.80 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(70,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[69])).
% 190.77/122.80 tff(71,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 190.77/122.80 inference(transitivity,[status(thm)],[70, 68])).
% 190.77/122.80 tff(72,plain,
% 190.77/122.80 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U))))))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(73,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U))))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[72])).
% 190.77/122.80 tff(74,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(75,plain,
% 190.77/122.80 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(rewrite((rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))) <=> (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), rewrite((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))), ((ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), (![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))) <=> ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), ((ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(76,plain,
% 190.77/122.80 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[75])).
% 190.77/122.80 tff(77,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax6')).
% 190.77/122.80 tff(78,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[77, 76])).
% 190.77/122.80 tff(79,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (rearsegP(U, V) <=> ?[W: $i] : (ssList(W) & (app(W, V) = U)))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[78, 74])).
% 190.77/122.80 tff(80,plain,(
% 190.77/122.80 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (((~rearsegP(U, V)) | (ssList(tptp_fun_W_6(V, U)) & (app(tptp_fun_W_6(V, U), V) = U))) & (rearsegP(U, V) | ![W: $i] : (~(ssList(W) & (app(W, V) = U)))))))),
% 190.77/122.80 inference(skolemize,[status(sab)],[79])).
% 190.77/122.80 tff(81,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[80, 73])).
% 190.77/122.80 tff(82,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[81, 71])).
% 190.77/122.80 tff(83,plain,
% 190.77/122.80 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(X3!52)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52)))))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(X3!52)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52)))))))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(84,plain,
% 190.77/122.80 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | ((~ssList(X3!52)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52)))))))))),
% 190.77/122.80 inference(quant_inst,[status(thm)],[])).
% 190.77/122.80 tff(85,plain,
% 190.77/122.80 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(U, V)) | (~((~ssList(tptp_fun_W_6(V, U))) | (~(app(tptp_fun_W_6(V, U), V) = U)))))) | (~(rearsegP(U, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = U)))))))))) | (~ssList(X3!52)) | ![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52))))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[84, 83])).
% 190.77/122.80 tff(86,plain,
% 190.77/122.80 (![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52))))))))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[85, 82, 51])).
% 190.77/122.80 tff(87,plain,
% 190.77/122.80 (((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52))))))))) | ((~ssList(X3!52)) | (~((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~(rearsegP(X3!52, X3!52) | ![W: $i] : ((~ssList(W)) | (~(app(W, X3!52) = X3!52))))))))) <=> ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52))))))))) | (~ssList(X3!52)) | (~((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~(rearsegP(X3!52, X3!52) | ![W: $i] : ((~ssList(W)) | (~(app(W, X3!52) = X3!52))))))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(88,plain,
% 190.77/122.80 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52))))))))) | ((~ssList(X3!52)) | (~((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~(rearsegP(X3!52, X3!52) | ![W: $i] : ((~ssList(W)) | (~(app(W, X3!52) = X3!52))))))))),
% 190.77/122.80 inference(quant_inst,[status(thm)],[])).
% 190.77/122.80 tff(89,plain,
% 190.77/122.80 ((~![V: $i] : ((~ssList(V)) | (~((~((~rearsegP(X3!52, V)) | (~((~ssList(tptp_fun_W_6(V, X3!52))) | (~(app(tptp_fun_W_6(V, X3!52), V) = X3!52)))))) | (~(rearsegP(X3!52, V) | ![W: $i] : ((~ssList(W)) | (~(app(W, V) = X3!52))))))))) | (~ssList(X3!52)) | (~((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~(rearsegP(X3!52, X3!52) | ![W: $i] : ((~ssList(W)) | (~(app(W, X3!52) = X3!52)))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[88, 87])).
% 190.77/122.80 tff(90,plain,
% 190.77/122.80 (~((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~(rearsegP(X3!52, X3!52) | ![W: $i] : ((~ssList(W)) | (~(app(W, X3!52) = X3!52))))))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[89, 51, 86])).
% 190.77/122.80 tff(91,plain,
% 190.77/122.80 (((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~(rearsegP(X3!52, X3!52) | ![W: $i] : ((~ssList(W)) | (~(app(W, X3!52) = X3!52)))))) | ((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))),
% 190.77/122.80 inference(tautology,[status(thm)],[])).
% 190.77/122.80 tff(92,plain,
% 190.77/122.80 ((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52))))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[91, 90])).
% 190.77/122.80 tff(93,plain,
% 190.77/122.80 (^[U: $i] : refl(((~ssList(U)) | rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(94,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[93])).
% 190.77/122.80 tff(95,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(96,plain,
% 190.77/122.80 (^[U: $i] : rewrite((ssList(U) => rearsegP(U, U)) <=> ((~ssList(U)) | rearsegP(U, U)))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(97,plain,
% 190.77/122.80 (![U: $i] : (ssList(U) => rearsegP(U, U)) <=> ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[96])).
% 190.77/122.80 tff(98,axiom,(![U: $i] : (ssList(U) => rearsegP(U, U))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax49')).
% 190.77/122.80 tff(99,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[98, 97])).
% 190.77/122.80 tff(100,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[99, 95])).
% 190.77/122.80 tff(101,plain,(
% 190.77/122.80 ![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(skolemize,[status(sab)],[100])).
% 190.77/122.80 tff(102,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | rearsegP(U, U))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[101, 94])).
% 190.77/122.80 tff(103,plain,
% 190.77/122.80 (((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(X3!52)) | rearsegP(X3!52, X3!52))) <=> ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(X3!52)) | rearsegP(X3!52, X3!52))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(104,plain,
% 190.77/122.80 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | ((~ssList(X3!52)) | rearsegP(X3!52, X3!52))),
% 190.77/122.80 inference(quant_inst,[status(thm)],[])).
% 190.77/122.80 tff(105,plain,
% 190.77/122.80 ((~![U: $i] : ((~ssList(U)) | rearsegP(U, U))) | (~ssList(X3!52)) | rearsegP(X3!52, X3!52)),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[104, 103])).
% 190.77/122.80 tff(106,plain,
% 190.77/122.80 (rearsegP(X3!52, X3!52)),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[105, 102, 51])).
% 190.77/122.80 tff(107,plain,
% 190.77/122.80 ((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52))))),
% 190.77/122.80 inference(tautology,[status(thm)],[])).
% 190.77/122.80 tff(108,plain,
% 190.77/122.80 ((~((~rearsegP(X3!52, X3!52)) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))))) | (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52))))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[107, 106])).
% 190.77/122.80 tff(109,plain,
% 190.77/122.80 (~((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[108, 92])).
% 190.77/122.80 tff(110,plain,
% 190.77/122.80 (((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52))) | (app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52)),
% 190.77/122.80 inference(tautology,[status(thm)],[])).
% 190.77/122.80 tff(111,plain,
% 190.77/122.80 (app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[110, 109])).
% 190.77/122.80 tff(112,plain,
% 190.77/122.80 (app(tptp_fun_W_6(X3!52, X3!52), X3!52) = app(nil, X3!52)),
% 190.77/122.80 inference(transitivity,[status(thm)],[111, 66])).
% 190.77/122.80 tff(113,plain,
% 190.77/122.80 (((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = X3!52))) | ssList(tptp_fun_W_6(X3!52, X3!52))),
% 190.77/122.80 inference(tautology,[status(thm)],[])).
% 190.77/122.80 tff(114,plain,
% 190.77/122.80 (ssList(tptp_fun_W_6(X3!52, X3!52))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[113, 109])).
% 190.77/122.80 tff(115,plain,
% 190.77/122.80 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(116,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[115])).
% 190.77/122.80 tff(117,plain,
% 190.77/122.80 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(118,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[117])).
% 190.77/122.80 tff(119,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(transitivity,[status(thm)],[118, 116])).
% 190.77/122.80 tff(120,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(121,plain,
% 190.77/122.80 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : trans(monotonicity(quant_intro(proof_bind(^[W: $i] : trans(monotonicity(rewrite(((app(W, V) = app(U, V)) => (W = U)) <=> ((~(app(W, V) = app(U, V))) | (W = U))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> (ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))))), rewrite((ssList(W) => ((~(app(W, V) = app(U, V))) | (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))), ((ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), (![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))) <=> ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> (ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), rewrite((ssList(V) => ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))), ((ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), (![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))) <=> ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> (ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))))), rewrite((ssList(U) => ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V)))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))), ((ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(122,plain,
% 190.77/122.80 (![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U))))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[121])).
% 190.77/122.80 tff(123,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssList(V) => ![W: $i] : (ssList(W) => ((app(W, V) = app(U, V)) => (W = U)))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax79')).
% 190.77/122.80 tff(124,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[123, 122])).
% 190.77/122.80 tff(125,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[124, 120])).
% 190.77/122.80 tff(126,plain,(
% 190.77/122.80 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(skolemize,[status(sab)],[125])).
% 190.77/122.80 tff(127,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[126, 119])).
% 190.77/122.80 tff(128,plain,
% 190.77/122.80 (ssList(nil) <=> ssList(nil)),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(129,axiom,(ssList(nil)), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax17')).
% 190.77/122.80 tff(130,plain,
% 190.77/122.80 (ssList(nil)),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[129, 128])).
% 190.77/122.80 tff(131,plain,
% 190.77/122.80 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(132,plain,
% 190.77/122.80 (((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V)))))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(133,plain,
% 190.77/122.80 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))))),
% 190.77/122.80 inference(monotonicity,[status(thm)],[132])).
% 190.77/122.80 tff(134,plain,
% 190.77/122.80 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V))))))),
% 190.77/122.80 inference(transitivity,[status(thm)],[133, 131])).
% 190.77/122.80 tff(135,plain,
% 190.77/122.80 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | ((~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = nil) | (~ssList(W)) | (~(app(W, V) = app(nil, V))))))),
% 190.77/122.80 inference(quant_inst,[status(thm)],[])).
% 190.77/122.80 tff(136,plain,
% 190.77/122.80 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((W = U) | (~ssList(W)) | (~(app(W, V) = app(U, V))))))) | (~ssList(nil)) | ![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[135, 134])).
% 190.77/122.80 tff(137,plain,
% 190.77/122.80 (![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[136, 130, 127])).
% 190.77/122.80 tff(138,plain,
% 190.77/122.80 (((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(X3!52)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52)))))) <=> ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(X3!52)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52)))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(139,plain,
% 190.77/122.80 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | ((~ssList(X3!52)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52)))))),
% 190.77/122.80 inference(quant_inst,[status(thm)],[])).
% 190.77/122.80 tff(140,plain,
% 190.77/122.80 ((~![V: $i] : ((~ssList(V)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, V) = app(nil, V)))))) | (~ssList(X3!52)) | ![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52))))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[139, 138])).
% 190.77/122.80 tff(141,plain,
% 190.77/122.80 (![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52))))),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[140, 51, 137])).
% 190.77/122.80 tff(142,plain,
% 190.77/122.80 (((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52))))) | ((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (tptp_fun_W_6(X3!52, X3!52) = nil) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = app(nil, X3!52))))) <=> ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52))))) | (~ssList(tptp_fun_W_6(X3!52, X3!52))) | (tptp_fun_W_6(X3!52, X3!52) = nil) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = app(nil, X3!52))))),
% 190.77/122.80 inference(rewrite,[status(thm)],[])).
% 190.77/122.80 tff(143,plain,
% 190.77/122.80 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52))))) | ((~ssList(tptp_fun_W_6(X3!52, X3!52))) | (tptp_fun_W_6(X3!52, X3!52) = nil) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = app(nil, X3!52))))),
% 190.77/122.80 inference(quant_inst,[status(thm)],[])).
% 190.77/122.80 tff(144,plain,
% 190.77/122.80 ((~![W: $i] : ((~ssList(W)) | (W = nil) | (~(app(W, X3!52) = app(nil, X3!52))))) | (~ssList(tptp_fun_W_6(X3!52, X3!52))) | (tptp_fun_W_6(X3!52, X3!52) = nil) | (~(app(tptp_fun_W_6(X3!52, X3!52), X3!52) = app(nil, X3!52)))),
% 190.77/122.80 inference(modus_ponens,[status(thm)],[143, 142])).
% 190.77/122.80 tff(145,plain,
% 190.77/122.80 (tptp_fun_W_6(X3!52, X3!52) = nil),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[144, 141, 114, 112])).
% 190.77/122.80 tff(146,plain,
% 190.77/122.80 (((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))) | (app(X3!52, cons(X2!51, nil)) = W!49)),
% 190.77/122.80 inference(tautology,[status(thm)],[])).
% 190.77/122.80 tff(147,plain,
% 190.77/122.80 (app(X3!52, cons(X2!51, nil)) = W!49),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[146, 49])).
% 190.77/122.80 tff(148,plain,
% 190.77/122.80 (app(app(X3!52, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = app(W!49, nil)),
% 190.77/122.80 inference(monotonicity,[status(thm)],[147, 145])).
% 190.77/122.80 tff(149,plain,
% 190.77/122.80 (app(app(X3!52, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47),
% 190.77/122.80 inference(transitivity,[status(thm)],[148, 41, 26])).
% 190.77/122.80 tff(150,plain,
% 190.77/122.80 (X!50 = V!48),
% 190.77/122.80 inference(symmetry,[status(thm)],[42])).
% 190.77/122.80 tff(151,plain,
% 190.77/122.80 (((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))) | (app(cons(X2!51, nil), X3!52) = X!50)),
% 190.77/122.80 inference(tautology,[status(thm)],[])).
% 190.77/122.80 tff(152,plain,
% 190.77/122.80 (app(cons(X2!51, nil), X3!52) = X!50),
% 190.77/122.80 inference(unit_resolution,[status(thm)],[151, 49])).
% 190.77/122.80 tff(153,plain,
% 190.77/122.80 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 190.77/122.80 inference(bind,[status(th)],[])).
% 190.77/122.80 tff(154,plain,
% 190.77/122.80 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.80 inference(quant_intro,[status(thm)],[153])).
% 190.77/122.80 tff(155,plain,
% 190.77/122.80 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(156,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[155])).
% 190.77/122.81 tff(157,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(transitivity,[status(thm)],[156, 154])).
% 190.77/122.81 tff(158,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(159,plain,
% 190.77/122.81 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), (![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))) <=> ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(160,plain,
% 190.77/122.81 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[159])).
% 190.77/122.81 tff(161,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => (cons(V, U) = app(cons(V, nil), U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax81')).
% 190.77/122.81 tff(162,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[161, 160])).
% 190.77/122.81 tff(163,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[162, 158])).
% 190.77/122.81 tff(164,plain,(
% 190.77/122.81 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(skolemize,[status(sab)],[163])).
% 190.77/122.81 tff(165,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[164, 157])).
% 190.77/122.81 tff(166,plain,
% 190.77/122.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(167,plain,
% 190.77/122.81 (((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) <=> ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(168,plain,
% 190.77/122.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))))),
% 190.77/122.81 inference(monotonicity,[status(thm)],[167])).
% 190.77/122.81 tff(169,plain,
% 190.77/122.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 190.77/122.81 inference(transitivity,[status(thm)],[168, 166])).
% 190.77/122.81 tff(170,plain,
% 190.77/122.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil))))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(171,plain,
% 190.77/122.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | (cons(V, U) = app(cons(V, nil), U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[170, 169])).
% 190.77/122.81 tff(172,plain,
% 190.77/122.81 (![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[171, 130, 165])).
% 190.77/122.81 tff(173,plain,
% 190.77/122.81 (((~ssItem(X2!51)) | (~(app(X3!52, cons(X2!51, nil)) = W!49)) | (~(app(cons(X2!51, nil), X3!52) = X!50)) | (~ssList(X3!52))) | ssItem(X2!51)),
% 190.77/122.81 inference(tautology,[status(thm)],[])).
% 190.77/122.81 tff(174,plain,
% 190.77/122.81 (ssItem(X2!51)),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[173, 49])).
% 190.77/122.81 tff(175,plain,
% 190.77/122.81 (((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(X2!51)) | (cons(X2!51, nil) = app(cons(X2!51, nil), nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(X2!51)) | (cons(X2!51, nil) = app(cons(X2!51, nil), nil)))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(176,plain,
% 190.77/122.81 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | ((~ssItem(X2!51)) | (cons(X2!51, nil) = app(cons(X2!51, nil), nil)))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(177,plain,
% 190.77/122.81 ((~![V: $i] : ((~ssItem(V)) | (cons(V, nil) = app(cons(V, nil), nil)))) | (~ssItem(X2!51)) | (cons(X2!51, nil) = app(cons(X2!51, nil), nil))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[176, 175])).
% 190.77/122.81 tff(178,plain,
% 190.77/122.81 (cons(X2!51, nil) = app(cons(X2!51, nil), nil)),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[177, 174, 172])).
% 190.77/122.81 tff(179,plain,
% 190.77/122.81 (app(cons(X2!51, nil), nil) = cons(X2!51, nil)),
% 190.77/122.81 inference(symmetry,[status(thm)],[178])).
% 190.77/122.81 tff(180,plain,
% 190.77/122.81 (ssList(app(cons(X2!51, nil), nil)) <=> ssList(cons(X2!51, nil))),
% 190.77/122.81 inference(monotonicity,[status(thm)],[179])).
% 190.77/122.81 tff(181,plain,
% 190.77/122.81 (ssList(cons(X2!51, nil)) <=> ssList(app(cons(X2!51, nil), nil))),
% 190.77/122.81 inference(symmetry,[status(thm)],[180])).
% 190.77/122.81 tff(182,plain,
% 190.77/122.81 (^[U: $i] : refl(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(183,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[182])).
% 190.77/122.81 tff(184,plain,
% 190.77/122.81 (^[U: $i] : rewrite(((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(185,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[184])).
% 190.77/122.81 tff(186,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(transitivity,[status(thm)],[185, 183])).
% 190.77/122.81 tff(187,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(188,plain,
% 190.77/122.81 (^[U: $i] : trans(monotonicity(quant_intro(proof_bind(^[V: $i] : rewrite((ssItem(V) => ssList(cons(V, U))) <=> ((~ssItem(V)) | ssList(cons(V, U))))), (![V: $i] : (ssItem(V) => ssList(cons(V, U))) <=> ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> (ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))))), rewrite((ssList(U) => ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))), ((ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(189,plain,
% 190.77/122.81 (![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U)))) <=> ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[188])).
% 190.77/122.81 tff(190,axiom,(![U: $i] : (ssList(U) => ![V: $i] : (ssItem(V) => ssList(cons(V, U))))), file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax','ax16')).
% 190.77/122.81 tff(191,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[190, 189])).
% 190.77/122.81 tff(192,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[191, 187])).
% 190.77/122.81 tff(193,plain,(
% 190.77/122.81 ![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(skolemize,[status(sab)],[192])).
% 190.77/122.81 tff(194,plain,
% 190.77/122.81 (![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[193, 186])).
% 190.77/122.81 tff(195,plain,
% 190.77/122.81 (((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))) <=> ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(196,plain,
% 190.77/122.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | ((~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil))))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(197,plain,
% 190.77/122.81 ((~![U: $i] : ((~ssList(U)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, U))))) | (~ssList(nil)) | ![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[196, 195])).
% 190.77/122.81 tff(198,plain,
% 190.77/122.81 (![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[197, 194, 130])).
% 190.77/122.81 tff(199,plain,
% 190.77/122.81 (((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X2!51)) | ssList(cons(X2!51, nil)))) <=> ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X2!51)) | ssList(cons(X2!51, nil)))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(200,plain,
% 190.77/122.81 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | ((~ssItem(X2!51)) | ssList(cons(X2!51, nil)))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(201,plain,
% 190.77/122.81 ((~![V: $i] : ((~ssItem(V)) | ssList(cons(V, nil)))) | (~ssItem(X2!51)) | ssList(cons(X2!51, nil))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[200, 199])).
% 190.77/122.81 tff(202,plain,
% 190.77/122.81 (ssList(cons(X2!51, nil))),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[201, 174, 198])).
% 190.77/122.81 tff(203,plain,
% 190.77/122.81 (ssList(app(cons(X2!51, nil), nil))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[202, 181])).
% 190.77/122.81 tff(204,plain,
% 190.77/122.81 (((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(app(cons(X2!51, nil), nil))) | (app(nil, app(cons(X2!51, nil), nil)) = app(cons(X2!51, nil), nil)))) <=> ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(app(cons(X2!51, nil), nil))) | (app(nil, app(cons(X2!51, nil), nil)) = app(cons(X2!51, nil), nil)))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(205,plain,
% 190.77/122.81 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | ((~ssList(app(cons(X2!51, nil), nil))) | (app(nil, app(cons(X2!51, nil), nil)) = app(cons(X2!51, nil), nil)))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(206,plain,
% 190.77/122.81 ((~![U: $i] : ((~ssList(U)) | (app(nil, U) = U))) | (~ssList(app(cons(X2!51, nil), nil))) | (app(nil, app(cons(X2!51, nil), nil)) = app(cons(X2!51, nil), nil))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[205, 204])).
% 190.77/122.81 tff(207,plain,
% 190.77/122.81 ((~ssList(app(cons(X2!51, nil), nil))) | (app(nil, app(cons(X2!51, nil), nil)) = app(cons(X2!51, nil), nil))),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[206, 61])).
% 190.77/122.81 tff(208,plain,
% 190.77/122.81 (app(nil, app(cons(X2!51, nil), nil)) = app(cons(X2!51, nil), nil)),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[207, 203])).
% 190.77/122.81 tff(209,plain,
% 190.77/122.81 (app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)) = app(nil, app(cons(X2!51, nil), nil))),
% 190.77/122.81 inference(monotonicity,[status(thm)],[145, 178])).
% 190.77/122.81 tff(210,plain,
% 190.77/122.81 (app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)) = cons(X2!51, nil)),
% 190.77/122.81 inference(transitivity,[status(thm)],[209, 208, 179])).
% 190.77/122.81 tff(211,plain,
% 190.77/122.81 (app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X3!52) = app(cons(X2!51, nil), X3!52)),
% 190.77/122.81 inference(monotonicity,[status(thm)],[210])).
% 190.77/122.81 tff(212,plain,
% 190.77/122.81 (app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X3!52) = V!48),
% 190.77/122.81 inference(transitivity,[status(thm)],[211, 152, 150])).
% 190.77/122.81 tff(213,plain,
% 190.77/122.81 (^[Y: $i] : refl(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(214,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[213])).
% 190.77/122.81 tff(215,plain,
% 190.77/122.81 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(216,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[215])).
% 190.77/122.81 tff(217,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(transitivity,[status(thm)],[216, 214])).
% 190.77/122.81 tff(218,plain,
% 190.77/122.81 (^[Y: $i] : rewrite(((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47))))))),
% 190.77/122.81 inference(bind,[status(th)],[])).
% 190.77/122.81 tff(219,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47))))) <=> ![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(quant_intro,[status(thm)],[218])).
% 190.77/122.81 tff(220,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : (~(ssList(X1) & (app(app(Z, cons(Y, nil)), X1) = V!48) & (app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(and_elim,[status(thm)],[24])).
% 190.77/122.81 tff(221,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[220, 219])).
% 190.77/122.81 tff(222,plain,
% 190.77/122.81 (![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[221, 217])).
% 190.77/122.81 tff(223,plain,
% 190.77/122.81 (((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))) | ((~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47)))))) <=> ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))) | (~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(224,plain,
% 190.77/122.81 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))) | ((~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47)))))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(225,plain,
% 190.77/122.81 ((~![Y: $i] : ((~ssItem(Y)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(Y, nil)), X1) = V!48)) | (~(app(app(X1, cons(Y, nil)), Z) = U!47)))))) | (~ssItem(X2!51)) | ![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47))))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[224, 223])).
% 190.77/122.81 tff(226,plain,
% 190.77/122.81 (![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47))))),
% 190.77/122.81 inference(unit_resolution,[status(thm)],[225, 222, 174])).
% 190.77/122.81 tff(227,plain,
% 190.77/122.81 (((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47))))) | ((~ssList(tptp_fun_W_6(X3!52, X3!52))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47))))) <=> ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47))))) | (~ssList(tptp_fun_W_6(X3!52, X3!52))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47))))),
% 190.77/122.81 inference(rewrite,[status(thm)],[])).
% 190.77/122.81 tff(228,plain,
% 190.77/122.81 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47))))) | ((~ssList(tptp_fun_W_6(X3!52, X3!52))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47))))),
% 190.77/122.81 inference(quant_inst,[status(thm)],[])).
% 190.77/122.81 tff(229,plain,
% 190.77/122.81 ((~![Z: $i] : ((~ssList(Z)) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(Z, cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), Z) = U!47))))) | (~ssList(tptp_fun_W_6(X3!52, X3!52))) | ![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))),
% 190.77/122.81 inference(modus_ponens,[status(thm)],[228, 227])).
% 190.77/122.81 tff(230,plain,
% 190.77/122.81 (![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))),
% 191.10/123.01 inference(unit_resolution,[status(thm)],[229, 226, 114])).
% 191.10/123.01 tff(231,plain,
% 191.10/123.01 (((~![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))) | ((~ssList(X3!52)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X3!52) = V!48)) | (~(app(app(X3!52, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))) <=> ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))) | (~ssList(X3!52)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X3!52) = V!48)) | (~(app(app(X3!52, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))),
% 191.10/123.01 inference(rewrite,[status(thm)],[])).
% 191.10/123.01 tff(232,plain,
% 191.10/123.01 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))) | ((~ssList(X3!52)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X3!52) = V!48)) | (~(app(app(X3!52, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))),
% 191.10/123.01 inference(quant_inst,[status(thm)],[])).
% 191.10/123.01 tff(233,plain,
% 191.10/123.01 ((~![X1: $i] : ((~ssList(X1)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X1) = V!48)) | (~(app(app(X1, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47)))) | (~ssList(X3!52)) | (~(app(app(tptp_fun_W_6(X3!52, X3!52), cons(X2!51, nil)), X3!52) = V!48)) | (~(app(app(X3!52, cons(X2!51, nil)), tptp_fun_W_6(X3!52, X3!52)) = U!47))),
% 191.10/123.01 inference(modus_ponens,[status(thm)],[232, 231])).
% 191.10/123.01 tff(234,plain,
% 191.10/123.01 ($false),
% 191.10/123.01 inference(unit_resolution,[status(thm)],[233, 51, 230, 212, 149])).
% 191.10/123.01 % SZS output end Proof
%------------------------------------------------------------------------------