%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC127+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 : n014.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 03:05:25 PM UTC 2026
% Result : Theorem 90.16s 12.26s
% Output : Proof 90.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 22
% Syntax : Number of formulae : 160 ( 101 unt; 0 def)
% Number of atoms : 437 ( 152 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 481 ( 204 ~; 157 |; 73 &)
% ( 6 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 9 con; 0-4 aty)
% Number of variables : 177 ( 2 sgn 97 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f95,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| ~ 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)
=> ( ( segmentP(V,U)
& neq(U,nil) )
| ( neq(X,nil)
& ~ singletonP(W) )
| ~ segmentP(X,W)
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f95]) ).
fof(f95_nnf,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ segmentP(V,U)
| ~ neq(U,nil) )
& ( ~ neq(X,nil)
| singletonP(W) )
& segmentP(X,W)
& 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,
( ( ~ segmentP(sk48,sk47)
| ~ neq(sk47,nil) )
& ( ~ neq(sk50,nil)
| singletonP(sk49) )
& segmentP(sk50,sk49)
& 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])],[f95_nnf]) ).
cnf(c199,plain,
( ~ segmentP(sk48,sk47)
| ~ neq(sk47,nil) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t86,plain,
or(not(neq(sk47,nil)),not(segmentP(sk48,sk47))) = true,
inference(equality_encoding,[status(esa)],[c199]) ).
cnf(t566,plain,
or(not(neq(sk47,nil)),not(segmentP(sk48,sk47))) = true,
inference(orient,[status(thm)],[t86]) ).
cnf(c194,plain,
sk48 = sk50,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t1,plain,
sk50 = sk48,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t933,plain,
sk48 = sk50,
inference(orient,[status(thm)],[t1]) ).
cnf(t68552,plain,
or(not(neq(sk47,nil)),not(segmentP(sk50,sk47))) = true,
inference(step,[status(thm)],[t566,t933]) ).
cnf(t935,plain,
or(not(neq(sk47,nil)),not(segmentP(sk50,sk47))) = true,
inference(rw,[status(thm)],[t68552]) ).
cnf(c195,plain,
sk47 = sk49,
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t0,plain,
sk49 = sk47,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t937,plain,
sk47 = sk49,
inference(orient,[status(thm)],[t0]) ).
cnf(t70752,plain,
or(not(neq(sk49,nil)),not(segmentP(sk50,sk47))) = true,
inference(step,[status(thm)],[t935,t937]) ).
cnf(t64,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)],[t64]) ).
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(c81,plain,
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(t176,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(eq(neq(X1,X2),true),eq(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t414,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(eq(neq(X1,X2),true),eq(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t176]) ).
cnf(t60,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t290,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t60]) ).
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]) ).
cnf(t111,plain,
or(not(ssList(X1)),or(not(ssItem(X2)),not(eq(cons(X2,X1),X1)))) = true,
inference(equality_encoding,[status(esa)],[c84]) ).
cnf(t584,plain,
or(not(ssList(X1)),or(not(ssItem(X2)),not(eq(cons(X2,X1),X1)))) = true,
inference(orient,[status(thm)],[t111]) ).
fof(f3,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f3_nnf,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,V] :
( ( ( cons(V,nil) != U
| ~ ssItem(V)
| singletonP(U) )
& ( ( cons(sk4(U),nil) = U
& ssItem(sk4(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f3_nnf]) ).
cnf(c10,plain,
( cons(sk4(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t98,plain,
ifeq(ssList(X1),true,ifeq(singletonP(X1),true,cons(sk4(X1),nil),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t273,plain,
ifeq(ssList(X1),true,ifeq(singletonP(X1),true,cons(sk4(X1),nil),X1),X1) = X1,
inference(orient,[status(thm)],[t98]) ).
cnf(c198,plain,
( ~ neq(sk50,nil)
| singletonP(sk49) ),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t65,plain,
ifeq(neq(sk50,nil),true,singletonP(sk49),true) = true,
inference(equality_encoding,[status(esa)],[c198]) ).
cnf(t293,plain,
ifeq(neq(sk50,nil),true,singletonP(sk49),true) = true,
inference(orient,[status(thm)],[t65]) ).
cnf(c196,plain,
neq(sk48,nil),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t29,plain,
neq(sk48,nil) = true,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t908,plain,
neq(sk48,nil) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t68551,plain,
neq(sk50,nil) = true,
inference(step,[status(thm)],[t908,t933]) ).
cnf(t934,plain,
neq(sk50,nil) = true,
inference(rw,[status(thm)],[t68551]) ).
cnf(t2168,plain,
neq(sk50,nil) = true,
inference(orient,[status(thm)],[t934]) ).
cnf(t68561,plain,
ifeq(true,true,singletonP(sk49),true) = true,
inference(step,[status(thm)],[t293,t2168]) ).
cnf(t58,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t58]) ).
cnf(t68562,plain,
singletonP(sk49) = true,
inference(step,[status(thm)],[t68561,t256]) ).
cnf(t2174,plain,
singletonP(sk49) = true,
inference(rw,[status(thm)],[t68562]) ).
cnf(t2175,plain,
singletonP(sk49) = true,
inference(orient,[status(thm)],[t2174]) ).
cnf(t2178,plain,
sk49 = ifeq(ssList(sk49),true,ifeq(true,true,cons(sk4(sk49),nil),sk49),sk49),
inference(cp,[status(thm)],[t273,t2175]) ).
cnf(c190,plain,
ssList(sk47),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t11,plain,
ssList(sk47) = true,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t68559,plain,
ssList(sk49) = true,
inference(step,[status(thm)],[t11,t937]) ).
cnf(t1369,plain,
ssList(sk49) = true,
inference(orient,[status(thm)],[t68559]) ).
cnf(t68600,plain,
sk49 = ifeq(true,true,ifeq(true,true,cons(sk4(sk49),nil),sk49),sk49),
inference(step,[status(thm)],[t2178,t1369]) ).
cnf(t68601,plain,
sk49 = ifeq(true,true,cons(sk4(sk49),nil),sk49),
inference(step,[status(thm)],[t68600,t256]) ).
cnf(t68602,plain,
sk49 = cons(sk4(sk49),nil),
inference(step,[status(thm)],[t68601,t256]) ).
cnf(t2792,plain,
cons(sk4(sk49),nil) = sk49,
inference(orient,[status(thm)],[t68602]) ).
cnf(t2807,plain,
true = or(not(ssList(nil)),or(not(ssItem(sk4(sk49))),not(eq(sk49,nil)))),
inference(cp,[status(thm)],[t584,t2792]) ).
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(t10,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(t1180,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t68705,plain,
true = or(not(true),or(not(ssItem(sk4(sk49))),not(eq(sk49,nil)))),
inference(step,[status(thm)],[t2807,t1180]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t653,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t68706,plain,
true = or(false,or(not(ssItem(sk4(sk49))),not(eq(sk49,nil)))),
inference(step,[status(thm)],[t68705,t653]) ).
cnf(t32,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t289,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t32]) ).
cnf(t68707,plain,
true = or(not(ssItem(sk4(sk49))),not(eq(sk49,nil))),
inference(step,[status(thm)],[t68706,t289]) ).
cnf(c9,plain,
( ssItem(sk4(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t96,plain,
ifeq(ssList(X1),true,ifeq(singletonP(X1),true,ssItem(sk4(X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t371,plain,
ifeq(ssList(X1),true,ifeq(singletonP(X1),true,ssItem(sk4(X1)),true),true) = true,
inference(orient,[status(thm)],[t96]) ).
cnf(t2177,plain,
true = ifeq(ssList(sk49),true,ifeq(true,true,ssItem(sk4(sk49)),true),true),
inference(cp,[status(thm)],[t371,t2175]) ).
cnf(t68575,plain,
true = ifeq(true,true,ifeq(true,true,ssItem(sk4(sk49)),true),true),
inference(step,[status(thm)],[t2177,t1369]) ).
cnf(t68576,plain,
true = ifeq(true,true,ssItem(sk4(sk49)),true),
inference(step,[status(thm)],[t68575,t256]) ).
cnf(t68577,plain,
true = ssItem(sk4(sk49)),
inference(step,[status(thm)],[t68576,t256]) ).
cnf(t2581,plain,
ssItem(sk4(sk49)) = true,
inference(orient,[status(thm)],[t68577]) ).
cnf(t68708,plain,
true = or(not(true),not(eq(sk49,nil))),
inference(step,[status(thm)],[t68707,t2581]) ).
cnf(t68709,plain,
true = or(false,not(eq(sk49,nil))),
inference(step,[status(thm)],[t68708,t653]) ).
cnf(t68710,plain,
true = not(eq(sk49,nil)),
inference(step,[status(thm)],[t68709,t289]) ).
cnf(t6736,plain,
not(eq(sk49,nil)) = true,
inference(orient,[status(thm)],[t68710]) ).
cnf(t6737,plain,
false = ifeq(true,true,eq(sk49,nil),false),
inference(cp,[status(thm)],[t290,t6736]) ).
cnf(t68711,plain,
false = eq(sk49,nil),
inference(step,[status(thm)],[t6737,t256]) ).
cnf(t6738,plain,
eq(sk49,nil) = false,
inference(orient,[status(thm)],[t68711]) ).
cnf(t6740,plain,
true = ifeq(ssList(sk49),true,ifeq(ssList(nil),true,or(eq(neq(sk49,nil),true),false),true),true),
inference(cp,[status(thm)],[t414,t6738]) ).
cnf(t68850,plain,
true = ifeq(true,true,ifeq(ssList(nil),true,or(eq(neq(sk49,nil),true),false),true),true),
inference(step,[status(thm)],[t6740,t1369]) ).
cnf(t68851,plain,
true = ifeq(ssList(nil),true,or(eq(neq(sk49,nil),true),false),true),
inference(step,[status(thm)],[t68850,t256]) ).
cnf(t68852,plain,
true = ifeq(true,true,or(eq(neq(sk49,nil),true),false),true),
inference(step,[status(thm)],[t68851,t1180]) ).
cnf(t68853,plain,
true = or(eq(neq(sk49,nil),true),false),
inference(step,[status(thm)],[t68852,t256]) ).
cnf(t30,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t288,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t30]) ).
cnf(t68854,plain,
true = eq(neq(sk49,nil),true),
inference(step,[status(thm)],[t68853,t288]) ).
cnf(t7552,plain,
eq(neq(sk49,nil),true) = true,
inference(orient,[status(thm)],[t68854]) ).
cnf(t7553,plain,
true = ifeq(true,true,neq(sk49,nil),true),
inference(cp,[status(thm)],[t257,t7552]) ).
cnf(t68855,plain,
true = neq(sk49,nil),
inference(step,[status(thm)],[t7553,t256]) ).
cnf(t7565,plain,
neq(sk49,nil) = true,
inference(orient,[status(thm)],[t68855]) ).
cnf(t70753,plain,
or(not(true),not(segmentP(sk50,sk47))) = true,
inference(step,[status(thm)],[t70752,t7565]) ).
cnf(t70754,plain,
or(false,not(segmentP(sk50,sk47))) = true,
inference(step,[status(thm)],[t70753,t653]) ).
cnf(t70755,plain,
not(segmentP(sk50,sk47)) = true,
inference(step,[status(thm)],[t70754,t289]) ).
cnf(t70756,plain,
not(segmentP(sk50,sk49)) = true,
inference(step,[status(thm)],[t70755,t937]) ).
cnf(c197,plain,
segmentP(sk50,sk49),
inference(cnf_transformation,[status(esa)],[f95_sk]) ).
cnf(t38,plain,
segmentP(sk50,sk49) = true,
inference(equality_encoding,[status(esa)],[c197]) ).
cnf(t767,plain,
segmentP(sk50,sk49) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t70757,plain,
not(true) = true,
inference(step,[status(thm)],[t70756,t767]) ).
cnf(t70758,plain,
false = true,
inference(step,[status(thm)],[t70757,t653]) ).
cnf(t68486,plain,
false = true,
inference(orient,[status(thm)],[t70758]) ).
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]) ).
cnf(c80,plain,
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f14_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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c4,c22,c65,c80,c84,c90,c103,c113,c114,c182,c185,c188,c199]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t68486]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC127+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 16:32:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 90.16/12.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 90.16/12.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------