%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:05:41 PM UTC 2026
% Result : Theorem 60.14s 18.30s
% Output : Proof 60.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 18
% Syntax : Number of formulae : 133 ( 78 unt; 0 def)
% Number of atoms : 446 ( 156 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 534 ( 221 ~; 172 |; 92 &)
% ( 5 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 11 con; 0-4 aty)
% Number of variables : 196 ( 2 sgn 108 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f14_nnf,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [U,V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c80,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t182,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(neq(X1,X2),true,ifeq(X1,X2,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(t398,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(neq(X1,X2),true,ifeq(X1,X2,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t182]) ).
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = W
& ssList(X6) )
& app(cons(X4,nil),X5) = Z
& ssList(X5) )
& ssItem(X4) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X1,nil),X3) = W
& ssList(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(app(Y,W),Z) != X ) ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f95_neg,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| neq(U,nil)
| ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( ? [X4] :
( ? [X5] :
( ? [X6] :
( app(X6,cons(X4,nil)) = W
& ssList(X6) )
& app(cons(X4,nil),X5) = Z
& ssList(X5) )
& ssItem(X4) )
| ? [X1] :
( ? [X2] :
( ? [X3] :
( app(cons(X1,nil),X3) = W
& ssList(X3) )
& app(X2,cons(X1,nil)) = Y
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(app(Y,W),Z) != X ) ) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ neq(U,nil)
& ? [Y] :
( ? [Z] :
( ! [X4] :
( ! [X5] :
( ! [X6] :
( app(X6,cons(X4,nil)) != W
| ~ ssList(X6) )
| app(cons(X4,nil),X5) != Z
| ~ ssList(X5) )
| ~ ssItem(X4) )
& ! [X1] :
( ! [X2] :
( ! [X3] :
( app(cons(X1,nil),X3) != W
| ~ ssList(X3) )
| app(X2,cons(X1,nil)) != Y
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(app(Y,W),Z) = X
& ssList(Z) )
& ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(nnf_transformation,[status(thm)],[f95_neg]) ).
fof(f95_sk,plain,
! [X1,X2,X3,X4,X5,X6] :
( ( nil != sk49
| nil = sk50 )
& ~ neq(sk47,nil)
& ( app(X6,cons(X4,nil)) != sk49
| ~ ssList(X6)
| app(cons(X4,nil),X5) != sk52
| ~ ssList(X5)
| ~ ssItem(X4) )
& ( app(cons(X1,nil),X3) != sk49
| ~ ssList(X3)
| app(X2,cons(X1,nil)) != sk51
| ~ ssList(X2)
| ~ ssItem(X1) )
& equalelemsP(sk49)
& app(app(sk51,sk49),sk52) = sk50
& ssList(sk52)
& ssList(sk51)
& neq(sk48,nil)
& sk47 = sk49
& sk48 = sk50
& ssList(sk50)
& ssList(sk49)
& ssList(sk48)
& ssList(sk47) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk47,sk48,sk49,sk50,sk51,sk52])],[f95_nnf]) ).
cnf(c196,plain,
neq(sk48,nil),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t33,plain,
neq(sk48,nil) = true,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t936,plain,
neq(sk48,nil) = true,
inference(orient,[status(thm)],[t33]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t1,plain,
sk50 = sk48,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t949,plain,
sk48 = sk50,
inference(orient,[status(thm)],[t1]) ).
cnf(t3412,plain,
neq(sk50,nil) = true,
inference(step,[status(thm)],[t936,t949]) ).
cnf(t950,plain,
neq(sk50,nil) = true,
inference(rw,[status(thm)],[t3412]) ).
cnf(t2678,plain,
neq(sk50,nil) = true,
inference(orient,[status(thm)],[t950]) ).
cnf(t62,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t257,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t62]) ).
cnf(c81,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t159,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X1,X2),eq(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t420,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X1,X2),eq(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t159]) ).
cnf(c203,plain,
~ neq(sk47,nil),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t32,plain,
neq(sk47,nil) = false,
inference(equality_encoding,[status(esa)],[c203]) ).
cnf(t734,plain,
neq(sk47,nil) = false,
inference(orient,[status(thm)],[t32]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t0,plain,
sk49 = sk47,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t943,plain,
sk47 = sk49,
inference(orient,[status(thm)],[t0]) ).
cnf(t3409,plain,
neq(sk49,nil) = false,
inference(step,[status(thm)],[t734,t943]) ).
cnf(t947,plain,
neq(sk49,nil) = false,
inference(rw,[status(thm)],[t3409]) ).
cnf(t2647,plain,
neq(sk49,nil) = false,
inference(orient,[status(thm)],[t947]) ).
cnf(t2648,plain,
true = ifeq(ssList(sk49),true,ifeq(ssList(nil),true,or(false,eq(sk49,nil)),true),true),
inference(cp,[status(thm)],[t420,t2647]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t12,plain,
ssList(sk47) = true,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t3413,plain,
ssList(sk49) = true,
inference(step,[status(thm)],[t12,t943]) ).
cnf(t1148,plain,
ssList(sk49) = true,
inference(orient,[status(thm)],[t3413]) ).
cnf(t3443,plain,
true = ifeq(true,true,ifeq(ssList(nil),true,or(false,eq(sk49,nil)),true),true),
inference(step,[status(thm)],[t2648,t1148]) ).
cnf(t55,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t55]) ).
cnf(t3444,plain,
true = ifeq(ssList(nil),true,or(false,eq(sk49,nil)),true),
inference(step,[status(thm)],[t3443,t256]) ).
fof(f16,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f16_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c83,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(t11,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(t951,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t3445,plain,
true = ifeq(true,true,or(false,eq(sk49,nil)),true),
inference(step,[status(thm)],[t3444,t951]) ).
cnf(t3446,plain,
true = or(false,eq(sk49,nil)),
inference(step,[status(thm)],[t3445,t256]) ).
cnf(t36,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t289,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t36]) ).
cnf(t3447,plain,
true = eq(sk49,nil),
inference(step,[status(thm)],[t3446,t289]) ).
cnf(t3069,plain,
eq(sk49,nil) = true,
inference(orient,[status(thm)],[t3447]) ).
cnf(t3070,plain,
nil = ifeq(true,true,sk49,nil),
inference(cp,[status(thm)],[t257,t3069]) ).
cnf(t3448,plain,
nil = sk49,
inference(step,[status(thm)],[t3070,t256]) ).
cnf(t3078,plain,
nil = sk49,
inference(orient,[status(thm)],[t3448]) ).
cnf(t3465,plain,
neq(sk50,sk49) = true,
inference(step,[status(thm)],[t2678,t3078]) ).
cnf(t3095,plain,
neq(sk50,sk49) = true,
inference(rw,[status(thm)],[t3465]) ).
cnf(c204,plain,
( nil != sk49
| nil = sk50 ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t56,plain,
ifeq(nil,sk49,nil,sk50) = sk50,
inference(equality_encoding,[status(esa)],[c204]) ).
cnf(t290,plain,
ifeq(nil,sk49,nil,sk50) = sk50,
inference(orient,[status(thm)],[t56]) ).
cnf(t3478,plain,
ifeq(sk49,sk49,nil,sk50) = sk50,
inference(step,[status(thm)],[t290,t3078]) ).
cnf(t3479,plain,
nil = sk50,
inference(step,[status(thm)],[t3478,t256]) ).
cnf(t3480,plain,
sk49 = sk50,
inference(step,[status(thm)],[t3479,t3078]) ).
cnf(t3106,plain,
sk49 = sk50,
inference(rw,[status(thm)],[t3480]) ).
cnf(t3172,plain,
sk49 = sk50,
inference(orient,[status(thm)],[t3106]) ).
cnf(t3591,plain,
neq(sk50,sk50) = true,
inference(step,[status(thm)],[t3095,t3172]) ).
cnf(t3378,plain,
neq(sk50,sk50) = true,
inference(orient,[status(thm)],[t3591]) ).
cnf(t3379,plain,
true = ifeq(ssList(sk50),true,ifeq(ssList(sk50),true,ifeq(true,true,ifeq(sk50,sk50,false,true),true),true),true),
inference(cp,[status(thm)],[t398,t3378]) ).
cnf(c191,plain,
ssList(sk48),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t13,plain,
ssList(sk48) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t3414,plain,
ssList(sk50) = true,
inference(step,[status(thm)],[t13,t949]) ).
cnf(t1386,plain,
ssList(sk50) = true,
inference(orient,[status(thm)],[t3414]) ).
cnf(t3592,plain,
true = ifeq(true,true,ifeq(ssList(sk50),true,ifeq(true,true,ifeq(sk50,sk50,false,true),true),true),true),
inference(step,[status(thm)],[t3379,t1386]) ).
cnf(t3593,plain,
true = ifeq(ssList(sk50),true,ifeq(true,true,ifeq(sk50,sk50,false,true),true),true),
inference(step,[status(thm)],[t3592,t256]) ).
cnf(t3594,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(sk50,sk50,false,true),true),true),
inference(step,[status(thm)],[t3593,t1386]) ).
cnf(t3595,plain,
true = ifeq(true,true,ifeq(sk50,sk50,false,true),true),
inference(step,[status(thm)],[t3594,t256]) ).
cnf(t3596,plain,
true = ifeq(sk50,sk50,false,true),
inference(step,[status(thm)],[t3595,t256]) ).
cnf(t3597,plain,
true = false,
inference(step,[status(thm)],[t3596,t256]) ).
cnf(t3384,plain,
false = true,
inference(orient,[status(thm)],[t3597]) ).
fof(f0,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
fof(f0_nnf,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f1,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f1_nnf,plain,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( sk0 != sk1
& ssItem(sk1)
& ssItem(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f1_nnf]) ).
cnf(c4,plain,
sk0 != sk1,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(W,V)
& leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f7_nnf,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [U,V,W,X,Y,Z] :
( ( ( ( leq(sk10(U),sk9(U))
& leq(sk9(U),sk10(U))
& app(app(sk11(U),cons(sk9(U),sk12(U))),cons(sk10(U),sk13(U))) = U
& ssList(sk13(U))
& ssList(sk12(U))
& ssList(sk11(U))
& ssItem(sk10(U))
& ssItem(sk9(U)) )
| cyclefreeP(U) )
& ( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z)
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10,sk11,sk12,sk13])],[f7_nnf]) ).
cnf(c22,plain,
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f12_nnf,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( V = W
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [U,V,W,X,Y,Z] :
( ( ( ( sk34(U) = sk35(U)
& app(app(sk36(U),cons(sk34(U),sk37(U))),cons(sk35(U),sk38(U))) = U
& ssList(sk38(U))
& ssList(sk37(U))
& ssList(sk36(U))
& ssItem(sk35(U))
& ssItem(sk34(U)) )
| duplicatefreeP(U) )
& ( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z)
| ~ ssList(Y)
| ~ ssList(X)
| ~ ssItem(W)
| ~ ssItem(V)
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk34,sk35,sk36,sk37,sk38])],[f12_nnf]) ).
cnf(c65,plain,
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f17,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f17_nnf,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [U,V] :
( cons(V,U) != U
| ~ ssItem(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c84,plain,
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f20_nnf,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [U,V] :
( nil != cons(V,U)
| ~ ssItem(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c90,plain,
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
fof(f32,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
=> ~ lt(V,U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f32_nnf,plain,
! [U] :
( ! [V] :
( ~ lt(V,U)
| ~ lt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [U,V] :
( ~ lt(V,U)
| ~ lt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c103,plain,
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f37_nnf,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c113,plain,
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f38,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f38_nnf,plain,
~ singletonP(nil),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
~ singletonP(nil),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c114,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
fof(f89,axiom,
! [U] :
( ssItem(U)
=> ~ lt(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
fof(f89_nnf,plain,
! [U] :
( ~ lt(U,U)
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f89]) ).
fof(f89_sk,plain,
! [U] :
( ~ lt(U,U)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f89_nnf]) ).
cnf(c182,plain,
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f89_sk]) ).
fof(f92,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( lt(U,V)
<=> ( leq(U,V)
& U != V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f92_nnf,plain,
! [U] :
( ! [V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f92]) ).
fof(f92_sk,plain,
! [U,V] :
( ( ( ~ leq(U,V)
| U = V
| lt(U,V) )
& ( ( leq(U,V)
& U != V )
| ~ lt(U,V) ) )
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f92_nnf]) ).
cnf(c185,plain,
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f92_sk]) ).
fof(f93,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( gt(U,V)
=> ~ gt(V,U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
fof(f93_nnf,plain,
! [U] :
( ! [V] :
( ~ gt(V,U)
| ~ gt(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f93]) ).
fof(f93_sk,plain,
! [U,V] :
( ~ gt(V,U)
| ~ gt(U,V)
| ~ ssItem(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f93_nnf]) ).
cnf(c188,plain,
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f93_sk]) ).
cnf(c201,plain,
( app(cons(X6,nil),X8) != sk49
| ~ ssList(X8)
| app(X7,cons(X6,nil)) != sk51
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(c202,plain,
( app(X11,cons(X9,nil)) != sk49
| ~ ssList(X11)
| app(cons(X9,nil),X10) != sk52
| ~ ssList(X10)
| ~ ssItem(X9) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c4,c22,c65,c80,c84,c90,c103,c113,c114,c182,c185,c188,c201,c202,c203]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3384]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.59 % Computer : n020.cluster.edu
% 0.09/10.59 % Model : x86_64 x86_64
% 0.09/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.59 % Memory : 8046.5625MB
% 0.09/10.59 % OS : Linux 6.8.0-71-generic
% 0.09/10.59 % CPULimit : 300
% 0.09/10.59 % WCLimit : 300
% 0.09/10.59 % DateTime : Thu Sep 24 17:02:15 UTC 2026
% 0.09/10.59 % CPUTime :
% 0.09/10.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 60.14/18.30 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 60.14/18.30 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------