%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC209-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 9.53s 1.68s
% Output : Proof 9.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 28
% Syntax : Number of formulae : 157 ( 105 unt; 0 def)
% Number of atoms : 317 ( 120 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 370 ( 210 ~; 160 |; 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 : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 140 ( 2 sgn 58 !; 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(t137,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(t580,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(orient,[status(thm)],[t137]) ).
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(t22,plain,
neq(sk2,nil) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t638,plain,
neq(sk2,nil) = true,
inference(orient,[status(thm)],[t22]) ).
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(t653,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t1]) ).
cnf(t8776,plain,
neq(sk4,nil) = true,
inference(step,[status(thm)],[t638,t653]) ).
cnf(t654,plain,
neq(sk4,nil) = true,
inference(rw,[status(thm)],[t8776]) ).
cnf(t8220,plain,
neq(sk4,nil) = true,
inference(orient,[status(thm)],[t654]) ).
cnf(t73,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t234,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t73]) ).
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(t134,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(t420,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(orient,[status(thm)],[t134]) ).
cnf(f192,negated_conjecture,
~ neq(sk1,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
~ neq(sk1,nil),
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
~ neq(sk1,nil),
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
~ neq(sk1,nil),
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(t21,plain,
neq(sk1,nil) = false,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t629,plain,
neq(sk1,nil) = false,
inference(orient,[status(thm)],[t21]) ).
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(t645,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t8775,plain,
neq(sk3,nil) = false,
inference(step,[status(thm)],[t629,t645]) ).
cnf(t646,plain,
neq(sk3,nil) = false,
inference(rw,[status(thm)],[t8775]) ).
cnf(t8213,plain,
neq(sk3,nil) = false,
inference(orient,[status(thm)],[t646]) ).
cnf(t8214,plain,
true = ifeq(ssList(nil),true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(cp,[status(thm)],[t420,t8213]) ).
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(t10,plain,
ssList(nil) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t2687,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t8805,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(step,[status(thm)],[t8214,t2687]) ).
cnf(t69,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t221,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t69]) ).
cnf(t8806,plain,
true = ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t8805,t221]) ).
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(t13,plain,
ssList(sk3) = true,
inference(equality_encoding,[status(esa)],[c187]) ).
cnf(t2859,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t8807,plain,
true = ifeq(true,true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t8806,t2859]) ).
cnf(t8808,plain,
true = or(false,eq(sk3,nil)),
inference(step,[status(thm)],[t8807,t221]) ).
cnf(t25,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t264,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t8809,plain,
true = eq(sk3,nil),
inference(step,[status(thm)],[t8808,t264]) ).
cnf(t8498,plain,
eq(sk3,nil) = true,
inference(orient,[status(thm)],[t8809]) ).
cnf(t8499,plain,
nil = ifeq(true,true,sk3,nil),
inference(cp,[status(thm)],[t234,t8498]) ).
cnf(t8810,plain,
nil = sk3,
inference(step,[status(thm)],[t8499,t221]) ).
cnf(t8505,plain,
nil = sk3,
inference(orient,[status(thm)],[t8810]) ).
cnf(t8821,plain,
neq(sk4,sk3) = true,
inference(step,[status(thm)],[t8220,t8505]) ).
cnf(t8514,plain,
neq(sk4,sk3) = true,
inference(rw,[status(thm)],[t8821]) ).
cnf(f193,negated_conjecture,
( neq(sk3,nil)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f193_nnf,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(nnf_transformation,[status(thm)],[f193]) ).
fof(f193_sk,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(skolemisation,[status(esa)],[f193_nnf]) ).
cnf(c193,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(cnf_transformation,[status(esa)],[f193_sk]) ).
cnf(t77,plain,
or(eq(nil,sk4),neq(sk3,nil)) = true,
inference(equality_encoding,[status(esa)],[c193]) ).
cnf(t592,plain,
or(eq(nil,sk4),neq(sk3,nil)) = true,
inference(orient,[status(thm)],[t77]) ).
cnf(t8777,plain,
or(eq(nil,sk4),false) = true,
inference(step,[status(thm)],[t592,t8213]) ).
cnf(t23,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t263,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t23]) ).
cnf(t8778,plain,
eq(nil,sk4) = true,
inference(step,[status(thm)],[t8777,t263]) ).
cnf(t8218,plain,
eq(nil,sk4) = true,
inference(rw,[status(thm)],[t8778]) ).
cnf(t8890,plain,
eq(sk3,sk4) = true,
inference(step,[status(thm)],[t8218,t8505]) ).
cnf(t8592,plain,
eq(sk3,sk4) = true,
inference(orient,[status(thm)],[t8890]) ).
cnf(t8593,plain,
sk4 = ifeq(true,true,sk3,sk4),
inference(cp,[status(thm)],[t234,t8592]) ).
cnf(t8891,plain,
sk4 = sk3,
inference(step,[status(thm)],[t8593,t221]) ).
cnf(t8600,plain,
sk3 = sk4,
inference(orient,[status(thm)],[t8891]) ).
cnf(t8905,plain,
neq(sk4,sk4) = true,
inference(step,[status(thm)],[t8514,t8600]) ).
cnf(t8747,plain,
neq(sk4,sk4) = true,
inference(orient,[status(thm)],[t8905]) ).
cnf(t8749,plain,
true = or(not(eq(sk4,sk4)),or(not(true),or(not(ssList(sk4)),not(ssList(sk4))))),
inference(cp,[status(thm)],[t580,t8747]) ).
cnf(t19,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t597,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t8906,plain,
true = or(not(true),or(not(true),or(not(ssList(sk4)),not(ssList(sk4))))),
inference(step,[status(thm)],[t8749,t597]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t595,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t8907,plain,
true = or(false,or(not(true),or(not(ssList(sk4)),not(ssList(sk4))))),
inference(step,[status(thm)],[t8906,t595]) ).
cnf(t8908,plain,
true = or(not(true),or(not(ssList(sk4)),not(ssList(sk4)))),
inference(step,[status(thm)],[t8907,t264]) ).
cnf(t8909,plain,
true = or(false,or(not(ssList(sk4)),not(ssList(sk4)))),
inference(step,[status(thm)],[t8908,t595]) ).
cnf(t8910,plain,
true = or(not(ssList(sk4)),not(ssList(sk4))),
inference(step,[status(thm)],[t8909,t264]) ).
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(t14,plain,
ssList(sk4) = true,
inference(equality_encoding,[status(esa)],[c188]) ).
cnf(t3043,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(t8911,plain,
true = or(not(true),not(ssList(sk4))),
inference(step,[status(thm)],[t8910,t3043]) ).
cnf(t8912,plain,
true = or(false,not(ssList(sk4))),
inference(step,[status(thm)],[t8911,t595]) ).
cnf(t8913,plain,
true = not(ssList(sk4)),
inference(step,[status(thm)],[t8912,t264]) ).
cnf(t8914,plain,
true = not(true),
inference(step,[status(thm)],[t8913,t3043]) ).
cnf(t8915,plain,
true = false,
inference(step,[status(thm)],[t8914,t595]) ).
cnf(t8753,plain,
false = true,
inference(orient,[status(thm)],[t8915]) ).
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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c10,c53,c62,c70,c97,c98,c109,c110,c113,c114,c116,c178,c184,c192]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t8753]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC209-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 16:59:36 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.53/1.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.53/1.68 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------