%------------------------------------------------------------------------------
% 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 : n011.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 : Unsatisfiable 20.91s 3.24s
% Output : Proof 20.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 29
% Syntax : Number of formulae : 160 ( 100 unt; 0 def)
% Number of atoms : 352 ( 135 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 446 ( 254 ~; 192 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 11 con; 0-4 aty)
% Number of variables : 162 ( 2 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f114,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f114_nnf,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t138,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t616,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(orient,[status(thm)],[t138]) ).
cnf(f191,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
neq(sk2,nil),
inference(nnf_transformation,[status(thm)],[f191]) ).
cnf(c191,plain,
neq(sk2,nil),
inference(cnf_transformation,[status(esa)],[f191_nnf]) ).
cnf(t25,plain,
neq(sk2,nil) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t674,plain,
neq(sk2,nil) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f189,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
sk2 = sk4,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
sk2 = sk4,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(t1,plain,
sk4 = sk2,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t700,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t1]) ).
cnf(t9814,plain,
neq(sk4,nil) = true,
inference(step,[status(thm)],[t674,t700]) ).
cnf(t701,plain,
neq(sk4,nil) = true,
inference(rw,[status(thm)],[t9814]) ).
cnf(t8947,plain,
neq(sk4,nil) = true,
inference(orient,[status(thm)],[t701]) ).
cnf(t78,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t239,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t78]) ).
cnf(f99,axiom,
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f99_nnf,plain,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f99_nnf]) ).
cnf(c99,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(t135,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
cnf(t428,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(orient,[status(thm)],[t135]) ).
cnf(f198,negated_conjecture,
~ neq(sk1,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f198_nnf,plain,
~ neq(sk1,nil),
inference(nnf_transformation,[status(thm)],[f198]) ).
fof(f198_sk,plain,
~ neq(sk1,nil),
inference(skolemisation,[status(esa)],[f198_nnf]) ).
cnf(c198,plain,
~ neq(sk1,nil),
inference(cnf_transformation,[status(esa)],[f198_sk]) ).
cnf(t24,plain,
neq(sk1,nil) = false,
inference(equality_encoding,[status(esa)],[c198]) ).
cnf(t663,plain,
neq(sk1,nil) = false,
inference(orient,[status(thm)],[t24]) ).
cnf(f190,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f190_nnf,plain,
sk1 = sk3,
inference(nnf_transformation,[status(thm)],[f190]) ).
cnf(c190,plain,
sk1 = sk3,
inference(cnf_transformation,[status(esa)],[f190_nnf]) ).
cnf(t0,plain,
sk3 = sk1,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t672,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t9813,plain,
neq(sk3,nil) = false,
inference(step,[status(thm)],[t663,t672]) ).
cnf(t673,plain,
neq(sk3,nil) = false,
inference(rw,[status(thm)],[t9813]) ).
cnf(t8942,plain,
neq(sk3,nil) = false,
inference(orient,[status(thm)],[t673]) ).
cnf(t8943,plain,
true = ifeq(ssList(nil),true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(cp,[status(thm)],[t428,t8942]) ).
cnf(f7,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause8) ).
fof(f7_nnf,plain,
ssList(nil),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
ssList(nil),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t11,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t2793,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t9855,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(step,[status(thm)],[t8943,t2793]) ).
cnf(t73,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t226,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t73]) ).
cnf(t9856,plain,
true = ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t9855,t226]) ).
cnf(f187,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f187_nnf,plain,
ssList(sk3),
inference(nnf_transformation,[status(thm)],[f187]) ).
cnf(c187,plain,
ssList(sk3),
inference(cnf_transformation,[status(esa)],[f187_nnf]) ).
cnf(t14,plain,
ssList(sk3) = true,
inference(equality_encoding,[status(esa)],[c187]) ).
cnf(t2973,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t9857,plain,
true = ifeq(true,true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t9856,t2973]) ).
cnf(t9858,plain,
true = or(false,eq(sk3,nil)),
inference(step,[status(thm)],[t9857,t226]) ).
cnf(t28,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t269,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t28]) ).
cnf(t9859,plain,
true = eq(sk3,nil),
inference(step,[status(thm)],[t9858,t269]) ).
cnf(t9518,plain,
eq(sk3,nil) = true,
inference(orient,[status(thm)],[t9859]) ).
cnf(t9519,plain,
nil = ifeq(true,true,sk3,nil),
inference(cp,[status(thm)],[t239,t9518]) ).
cnf(t9860,plain,
nil = sk3,
inference(step,[status(thm)],[t9519,t226]) ).
cnf(t9525,plain,
nil = sk3,
inference(orient,[status(thm)],[t9860]) ).
cnf(t9881,plain,
neq(sk4,sk3) = true,
inference(step,[status(thm)],[t8947,t9525]) ).
cnf(t9544,plain,
neq(sk4,sk3) = true,
inference(rw,[status(thm)],[t9881]) ).
cnf(f199,negated_conjecture,
( nil != sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f199_nnf,plain,
( nil != sk3
| nil = sk4 ),
inference(nnf_transformation,[status(thm)],[f199]) ).
fof(f199_sk,plain,
( nil != sk3
| nil = sk4 ),
inference(skolemisation,[status(esa)],[f199_nnf]) ).
cnf(c199,plain,
( nil != sk3
| nil = sk4 ),
inference(cnf_transformation,[status(esa)],[f199_sk]) ).
cnf(t74,plain,
ifeq(nil,sk3,nil,sk4) = sk4,
inference(equality_encoding,[status(esa)],[c199]) ).
cnf(t339,plain,
ifeq(nil,sk3,nil,sk4) = sk4,
inference(orient,[status(thm)],[t74]) ).
cnf(t9890,plain,
ifeq(sk3,sk3,nil,sk4) = sk4,
inference(step,[status(thm)],[t339,t9525]) ).
cnf(t9891,plain,
nil = sk4,
inference(step,[status(thm)],[t9890,t226]) ).
cnf(t9892,plain,
sk3 = sk4,
inference(step,[status(thm)],[t9891,t9525]) ).
cnf(t9553,plain,
sk3 = sk4,
inference(rw,[status(thm)],[t9892]) ).
cnf(t9601,plain,
sk3 = sk4,
inference(orient,[status(thm)],[t9553]) ).
cnf(t9983,plain,
neq(sk4,sk4) = true,
inference(step,[status(thm)],[t9544,t9601]) ).
cnf(t9785,plain,
neq(sk4,sk4) = true,
inference(orient,[status(thm)],[t9983]) ).
cnf(t9787,plain,
true = or(not(eq(sk4,sk4)),or(not(true),or(not(ssList(sk4)),not(ssList(sk4))))),
inference(cp,[status(thm)],[t616,t9785]) ).
cnf(t22,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t631,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t9984,plain,
true = or(not(true),or(not(true),or(not(ssList(sk4)),not(ssList(sk4))))),
inference(step,[status(thm)],[t9787,t631]) ).
cnf(t7,plain,
not(true) = false,
introduced(definition) ).
cnf(t629,plain,
not(true) = false,
inference(orient,[status(thm)],[t7]) ).
cnf(t9985,plain,
true = or(false,or(not(true),or(not(ssList(sk4)),not(ssList(sk4))))),
inference(step,[status(thm)],[t9984,t629]) ).
cnf(t9986,plain,
true = or(not(true),or(not(ssList(sk4)),not(ssList(sk4)))),
inference(step,[status(thm)],[t9985,t269]) ).
cnf(t9987,plain,
true = or(false,or(not(ssList(sk4)),not(ssList(sk4)))),
inference(step,[status(thm)],[t9986,t629]) ).
cnf(t9988,plain,
true = or(not(ssList(sk4)),not(ssList(sk4))),
inference(step,[status(thm)],[t9987,t269]) ).
cnf(f188,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
fof(f188_nnf,plain,
ssList(sk4),
inference(nnf_transformation,[status(thm)],[f188]) ).
cnf(c188,plain,
ssList(sk4),
inference(cnf_transformation,[status(esa)],[f188_nnf]) ).
cnf(t15,plain,
ssList(sk4) = true,
inference(equality_encoding,[status(esa)],[c188]) ).
cnf(t3164,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t9989,plain,
true = or(not(true),not(ssList(sk4))),
inference(step,[status(thm)],[t9988,t3164]) ).
cnf(t9990,plain,
true = or(false,not(ssList(sk4))),
inference(step,[status(thm)],[t9989,t629]) ).
cnf(t9991,plain,
true = not(ssList(sk4)),
inference(step,[status(thm)],[t9990,t269]) ).
cnf(t9992,plain,
true = not(true),
inference(step,[status(thm)],[t9991,t3164]) ).
cnf(t9993,plain,
true = false,
inference(step,[status(thm)],[t9992,t629]) ).
cnf(t9791,plain,
false = true,
inference(orient,[status(thm)],[t9993]) ).
cnf(f10,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause11) ).
fof(f10_nnf,plain,
~ singletonP(nil),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ singletonP(nil),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f53,axiom,
skac3 != skac2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause54) ).
fof(f53_nnf,plain,
skac3 != skac2,
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
skac3 != skac2,
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
skac3 != skac2,
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(f62,axiom,
( ~ ssItem(U)
| ~ lt(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause63) ).
fof(f62_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(nnf_transformation,[status(thm)],[f62]) ).
fof(f62_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ lt(U,U) ),
inference(skolemisation,[status(esa)],[f62_nnf]) ).
cnf(c62,plain,
( ~ ssItem(X0)
| ~ lt(X0,X0) ),
inference(cnf_transformation,[status(esa)],[f62_sk]) ).
cnf(f70,axiom,
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause71) ).
fof(f70_nnf,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(nnf_transformation,[status(thm)],[f70]) ).
fof(f70_sk,plain,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
inference(skolemisation,[status(esa)],[f70_nnf]) ).
cnf(c70,plain,
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(esa)],[f70_sk]) ).
cnf(f97,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause98) ).
fof(f97_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(nnf_transformation,[status(thm)],[f97]) ).
fof(f97_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
inference(skolemisation,[status(esa)],[f97_nnf]) ).
cnf(c97,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(esa)],[f97_sk]) ).
cnf(f98,axiom,
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause99) ).
fof(f98_nnf,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(nnf_transformation,[status(thm)],[f98]) ).
fof(f98_sk,plain,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != V ),
inference(skolemisation,[status(esa)],[f98_nnf]) ).
cnf(c98,plain,
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f98_sk]) ).
cnf(f109,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause110) ).
fof(f109_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(nnf_transformation,[status(thm)],[f109]) ).
fof(f109_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ gt(V,U)
| ~ gt(U,V) ),
inference(skolemisation,[status(esa)],[f109_nnf]) ).
cnf(c109,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ gt(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f109_sk]) ).
cnf(f110,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause111) ).
fof(f110_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f110]) ).
fof(f110_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f110_nnf]) ).
cnf(c110,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f110_sk]) ).
cnf(f113,axiom,
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause114) ).
fof(f113_nnf,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(nnf_transformation,[status(thm)],[f113]) ).
fof(f113_sk,plain,
! [U,V] :
( ~ ssItem(V)
| ~ ssItem(U)
| ~ lt(V,U)
| ~ lt(U,V) ),
inference(skolemisation,[status(esa)],[f113_nnf]) ).
cnf(c113,plain,
( ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X1,X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f113_sk]) ).
cnf(f116,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause117) ).
fof(f116_nnf,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f116]) ).
fof(f116_sk,plain,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f116_nnf]) ).
cnf(c116,plain,
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f116_sk]) ).
cnf(f178,axiom,
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause179) ).
fof(f178_nnf,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(nnf_transformation,[status(thm)],[f178]) ).
fof(f178_sk,plain,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
inference(skolemisation,[status(esa)],[f178_nnf]) ).
cnf(c178,plain,
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(esa)],[f178_sk]) ).
cnf(f184,axiom,
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause185) ).
fof(f184_nnf,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(nnf_transformation,[status(thm)],[f184]) ).
fof(f184_sk,plain,
! [U,V,W,X,Y,Z] :
( ~ ssList(Z)
| ~ cyclefreeP(Z)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(X)
| ~ ssList(Y)
| app(app(W,cons(U,X)),cons(V,Y)) != Z
| ~ leq(V,U)
| ~ leq(U,V) ),
inference(skolemisation,[status(esa)],[f184_nnf]) ).
cnf(c184,plain,
( ~ ssList(X5)
| ~ cyclefreeP(X5)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X4)
| app(app(X2,cons(X0,X3)),cons(X1,X4)) != X5
| ~ leq(X1,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f184_sk]) ).
cnf(f196,negated_conjecture,
( app(cons(A,nil),C) != sk3
| ~ ssList(C)
| app(B,cons(A,nil)) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
! [A,B,C] :
( app(cons(A,nil),C) != sk3
| ~ ssList(C)
| app(B,cons(A,nil)) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
! [A,B,C] :
( app(cons(A,nil),C) != sk3
| ~ ssList(C)
| app(B,cons(A,nil)) != sk5
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( app(cons(X0,nil),X2) != sk3
| ~ ssList(X2)
| app(X1,cons(X0,nil)) != sk5
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(f197,negated_conjecture,
( app(C,cons(A,nil)) != sk3
| ~ ssList(C)
| app(cons(A,nil),B) != sk6
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f197_nnf,plain,
! [A,B,C] :
( app(C,cons(A,nil)) != sk3
| ~ ssList(C)
| app(cons(A,nil),B) != sk6
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
! [A,B,C] :
( app(C,cons(A,nil)) != sk3
| ~ ssList(C)
| app(cons(A,nil),B) != sk6
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
( app(X2,cons(X0,nil)) != sk3
| ~ ssList(X2)
| app(cons(X0,nil),X1) != sk6
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c53,c62,c70,c97,c98,c109,c110,c113,c114,c116,c178,c184,c196,c197,c198]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t9791]) ).
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
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 17:01:28 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 20.91/3.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.91/3.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------