%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC241-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 03:05:46 PM UTC 2026
% Result : Unsatisfiable 70.52s 9.29s
% Output : Proof 70.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 29
% Syntax : Number of formulae : 184 ( 108 unt; 0 def)
% Number of atoms : 404 ( 163 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 486 ( 266 ~; 220 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-4 aty)
% Number of variables : 199 ( 2 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f102,axiom,
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause103) ).
fof(f102_nnf,plain,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
inference(nnf_transformation,[status(thm)],[f102]) ).
fof(f102_sk,plain,
! [U,V] :
( leq(U,V)
| ~ ssItem(U)
| ~ ssItem(V)
| ~ lt(U,V) ),
inference(skolemisation,[status(esa)],[f102_nnf]) ).
cnf(c102,plain,
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f102_sk]) ).
cnf(t146,plain,
ifeq(lt(X1,X2),true,ifeq(ssItem(X2),true,ifeq(ssItem(X1),true,leq(X1,X2),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c102]) ).
cnf(t3752,plain,
ifeq(lt(X1,X2),true,ifeq(ssItem(X2),true,ifeq(ssItem(X1),true,leq(X1,X2),true),true),true) = true,
inference(orient,[status(thm)],[t146]) ).
cnf(f195,negated_conjecture,
( lt(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
! [A,B,C] :
( lt(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
! [A,B,C] :
( lt(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(t208,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(app(app(X2,cons(X1,nil)),X3),sk1,lt(X1,sk5(X3,X2,X1)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(f190,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/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(t227,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t14677,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(app(app(X2,cons(X1,nil)),X3),sk3,lt(X1,sk5(X3,X2,X1)),true),true),true),true) = true,
inference(step,[status(thm)],[t208,t227]) ).
cnf(t11514,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(app(app(X2,cons(X1,nil)),X3),sk3,lt(X1,sk5(X3,X2,X1)),true),true),true),true) = true,
inference(orient,[status(thm)],[t14677]) ).
cnf(t76,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t303,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t76]) ).
cnf(f200,negated_conjecture,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_16) ).
fof(f200_nnf,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f200]) ).
fof(f200_sk,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f200_nnf]) ).
cnf(c200,plain,
( app(app(sk7,cons(sk6,nil)),sk8) = sk3
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f200_sk]) ).
cnf(t112,plain,
or(eq(nil,sk3),eq(app(app(sk7,cons(sk6,nil)),sk8),sk3)) = true,
inference(equality_encoding,[status(esa)],[c200]) ).
cnf(f191,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
nil != sk1,
inference(nnf_transformation,[status(thm)],[f191]) ).
fof(f191_sk,plain,
nil != sk1,
inference(skolemisation,[status(esa)],[f191_nnf]) ).
cnf(c191,plain,
nil != sk1,
inference(cnf_transformation,[status(esa)],[f191_sk]) ).
cnf(t20,plain,
eq(nil,sk1) = false,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t11736,plain,
eq(nil,sk3) = false,
inference(step,[status(thm)],[t20,t227]) ).
cnf(t245,plain,
eq(nil,sk3) = false,
inference(orient,[status(thm)],[t11736]) ).
cnf(t12095,plain,
or(false,eq(app(app(sk7,cons(sk6,nil)),sk8),sk3)) = true,
inference(step,[status(thm)],[t112,t245]) ).
cnf(t24,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t249,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t24]) ).
cnf(t12096,plain,
eq(app(app(sk7,cons(sk6,nil)),sk8),sk3) = true,
inference(step,[status(thm)],[t12095,t249]) ).
cnf(t1593,plain,
eq(app(app(sk7,cons(sk6,nil)),sk8),sk3) = true,
inference(orient,[status(thm)],[t12096]) ).
cnf(t1594,plain,
sk3 = ifeq(true,true,app(app(sk7,cons(sk6,nil)),sk8),sk3),
inference(cp,[status(thm)],[t303,t1593]) ).
cnf(t68,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t293,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t68]) ).
cnf(t12492,plain,
sk3 = app(app(sk7,cons(sk6,nil)),sk8),
inference(step,[status(thm)],[t1594,t293]) ).
cnf(t3480,plain,
app(app(sk7,cons(sk6,nil)),sk8) = sk3,
inference(orient,[status(thm)],[t12492]) ).
cnf(t11599,plain,
true = ifeq(ssItem(sk6),true,ifeq(ssList(sk7),true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),true),true),true),
inference(cp,[status(thm)],[t11514,t3480]) ).
cnf(f197,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f197_nnf,plain,
( ssItem(sk6)
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
( ssItem(sk6)
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
( ssItem(sk6)
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(t73,plain,
or(eq(nil,sk3),ssItem(sk6)) = true,
inference(equality_encoding,[status(esa)],[c197]) ).
cnf(t11739,plain,
or(false,ssItem(sk6)) = true,
inference(step,[status(thm)],[t73,t245]) ).
cnf(t11740,plain,
ssItem(sk6) = true,
inference(step,[status(thm)],[t11739,t249]) ).
cnf(t300,plain,
ssItem(sk6) = true,
inference(orient,[status(thm)],[t11740]) ).
cnf(t14678,plain,
true = ifeq(true,true,ifeq(ssList(sk7),true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),true),true),true),
inference(step,[status(thm)],[t11599,t300]) ).
cnf(t14679,plain,
true = ifeq(ssList(sk7),true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),true),true),
inference(step,[status(thm)],[t14678,t293]) ).
cnf(f198,negated_conjecture,
( ssList(sk7)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f198_nnf,plain,
( ssList(sk7)
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f198]) ).
fof(f198_sk,plain,
( ssList(sk7)
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f198_nnf]) ).
cnf(c198,plain,
( ssList(sk7)
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f198_sk]) ).
cnf(t74,plain,
or(eq(nil,sk3),ssList(sk7)) = true,
inference(equality_encoding,[status(esa)],[c198]) ).
cnf(t11741,plain,
or(false,ssList(sk7)) = true,
inference(step,[status(thm)],[t74,t245]) ).
cnf(t11742,plain,
ssList(sk7) = true,
inference(step,[status(thm)],[t11741,t249]) ).
cnf(t301,plain,
ssList(sk7) = true,
inference(orient,[status(thm)],[t11742]) ).
cnf(t14680,plain,
true = ifeq(true,true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),true),true),
inference(step,[status(thm)],[t14679,t301]) ).
cnf(t14681,plain,
true = ifeq(ssList(sk8),true,ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),true),
inference(step,[status(thm)],[t14680,t293]) ).
cnf(f199,negated_conjecture,
( ssList(sk8)
| nil = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f199_nnf,plain,
( ssList(sk8)
| nil = sk3 ),
inference(nnf_transformation,[status(thm)],[f199]) ).
fof(f199_sk,plain,
( ssList(sk8)
| nil = sk3 ),
inference(skolemisation,[status(esa)],[f199_nnf]) ).
cnf(c199,plain,
( ssList(sk8)
| nil = sk3 ),
inference(cnf_transformation,[status(esa)],[f199_sk]) ).
cnf(t75,plain,
or(eq(nil,sk3),ssList(sk8)) = true,
inference(equality_encoding,[status(esa)],[c199]) ).
cnf(t11743,plain,
or(false,ssList(sk8)) = true,
inference(step,[status(thm)],[t75,t245]) ).
cnf(t11744,plain,
ssList(sk8) = true,
inference(step,[status(thm)],[t11743,t249]) ).
cnf(t302,plain,
ssList(sk8) = true,
inference(orient,[status(thm)],[t11744]) ).
cnf(t14682,plain,
true = ifeq(true,true,ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),true),
inference(step,[status(thm)],[t14681,t302]) ).
cnf(t14683,plain,
true = ifeq(sk3,sk3,lt(sk6,sk5(sk8,sk7,sk6)),true),
inference(step,[status(thm)],[t14682,t293]) ).
cnf(t14684,plain,
true = lt(sk6,sk5(sk8,sk7,sk6)),
inference(step,[status(thm)],[t14683,t293]) ).
cnf(t11601,plain,
lt(sk6,sk5(sk8,sk7,sk6)) = true,
inference(orient,[status(thm)],[t14684]) ).
cnf(t11606,plain,
true = ifeq(true,true,ifeq(ssItem(sk5(sk8,sk7,sk6)),true,ifeq(ssItem(sk6),true,leq(sk6,sk5(sk8,sk7,sk6)),true),true),true),
inference(cp,[status(thm)],[t3752,t11601]) ).
cnf(t14685,plain,
true = ifeq(ssItem(sk5(sk8,sk7,sk6)),true,ifeq(ssItem(sk6),true,leq(sk6,sk5(sk8,sk7,sk6)),true),true),
inference(step,[status(thm)],[t11606,t293]) ).
cnf(f192,negated_conjecture,
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
! [A,B,C] :
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
! [A,B,C] :
( ssItem(sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
( ssItem(sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(t203,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(app(app(X2,cons(X1,nil)),X3),sk1,ssItem(sk5(X3,X2,X1)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t14429,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(app(app(X2,cons(X1,nil)),X3),sk3,ssItem(sk5(X3,X2,X1)),true),true),true),true) = true,
inference(step,[status(thm)],[t203,t227]) ).
cnf(t10684,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(app(app(X2,cons(X1,nil)),X3),sk3,ssItem(sk5(X3,X2,X1)),true),true),true),true) = true,
inference(orient,[status(thm)],[t14429]) ).
cnf(t10769,plain,
true = ifeq(ssItem(sk6),true,ifeq(ssList(sk7),true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),true),true),true),
inference(cp,[status(thm)],[t10684,t3480]) ).
cnf(t14430,plain,
true = ifeq(true,true,ifeq(ssList(sk7),true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),true),true),true),
inference(step,[status(thm)],[t10769,t300]) ).
cnf(t14431,plain,
true = ifeq(ssList(sk7),true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),true),true),
inference(step,[status(thm)],[t14430,t293]) ).
cnf(t14432,plain,
true = ifeq(true,true,ifeq(ssList(sk8),true,ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),true),true),
inference(step,[status(thm)],[t14431,t301]) ).
cnf(t14433,plain,
true = ifeq(ssList(sk8),true,ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),true),
inference(step,[status(thm)],[t14432,t293]) ).
cnf(t14434,plain,
true = ifeq(true,true,ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),true),
inference(step,[status(thm)],[t14433,t302]) ).
cnf(t14435,plain,
true = ifeq(sk3,sk3,ssItem(sk5(sk8,sk7,sk6)),true),
inference(step,[status(thm)],[t14434,t293]) ).
cnf(t14436,plain,
true = ssItem(sk5(sk8,sk7,sk6)),
inference(step,[status(thm)],[t14435,t293]) ).
cnf(t10770,plain,
ssItem(sk5(sk8,sk7,sk6)) = true,
inference(orient,[status(thm)],[t14436]) ).
cnf(t14686,plain,
true = ifeq(true,true,ifeq(ssItem(sk6),true,leq(sk6,sk5(sk8,sk7,sk6)),true),true),
inference(step,[status(thm)],[t14685,t10770]) ).
cnf(t14687,plain,
true = ifeq(ssItem(sk6),true,leq(sk6,sk5(sk8,sk7,sk6)),true),
inference(step,[status(thm)],[t14686,t293]) ).
cnf(t14688,plain,
true = ifeq(true,true,leq(sk6,sk5(sk8,sk7,sk6)),true),
inference(step,[status(thm)],[t14687,t300]) ).
cnf(t14689,plain,
true = leq(sk6,sk5(sk8,sk7,sk6)),
inference(step,[status(thm)],[t14688,t293]) ).
cnf(t71,plain,
ifeq(not(X1),true,X1,false) = false,
introduced(definition) ).
cnf(t296,plain,
ifeq(not(X1),true,X1,false) = false,
inference(orient,[status(thm)],[t71]) ).
cnf(f196,negated_conjecture,
( ~ leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
! [A,B,C] :
( ~ leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
! [A,B,C] :
( ~ leq(A,sk5(C,B,A))
| app(app(B,cons(A,nil)),C) != sk1
| ~ ssList(C)
| ~ ssList(B)
| ~ ssItem(A) ),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(t204,plain,
or(not(ssItem(X1)),or(not(ssList(X2)),or(not(ssList(X3)),or(not(eq(app(app(X2,cons(X1,nil)),X3),sk1)),not(leq(X1,sk5(X3,X2,X1))))))) = true,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t14446,plain,
or(not(ssItem(X1)),or(not(ssList(X2)),or(not(ssList(X3)),or(not(eq(app(app(X2,cons(X1,nil)),X3),sk3)),not(leq(X1,sk5(X3,X2,X1))))))) = true,
inference(step,[status(thm)],[t204,t227]) ).
cnf(t10892,plain,
or(not(ssItem(X1)),or(not(ssList(X2)),or(not(ssList(X3)),or(not(eq(app(app(X2,cons(X1,nil)),X3),sk3)),not(leq(X1,sk5(X3,X2,X1))))))) = true,
inference(orient,[status(thm)],[t14446]) ).
cnf(t10977,plain,
true = or(not(ssItem(sk6)),or(not(ssList(sk7)),or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6))))))),
inference(cp,[status(thm)],[t10892,t3480]) ).
cnf(t14448,plain,
true = or(not(true),or(not(ssList(sk7)),or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6))))))),
inference(step,[status(thm)],[t10977,t300]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t233,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t14449,plain,
true = or(false,or(not(ssList(sk7)),or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6))))))),
inference(step,[status(thm)],[t14448,t233]) ).
cnf(t14450,plain,
true = or(not(ssList(sk7)),or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6)))))),
inference(step,[status(thm)],[t14449,t249]) ).
cnf(t14451,plain,
true = or(not(true),or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6)))))),
inference(step,[status(thm)],[t14450,t301]) ).
cnf(t14452,plain,
true = or(false,or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6)))))),
inference(step,[status(thm)],[t14451,t233]) ).
cnf(t14453,plain,
true = or(not(ssList(sk8)),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6))))),
inference(step,[status(thm)],[t14452,t249]) ).
cnf(t14454,plain,
true = or(not(true),or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6))))),
inference(step,[status(thm)],[t14453,t302]) ).
cnf(t14455,plain,
true = or(false,or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6))))),
inference(step,[status(thm)],[t14454,t233]) ).
cnf(t14456,plain,
true = or(not(eq(sk3,sk3)),not(leq(sk6,sk5(sk8,sk7,sk6)))),
inference(step,[status(thm)],[t14455,t249]) ).
cnf(t19,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t244,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t14457,plain,
true = or(not(true),not(leq(sk6,sk5(sk8,sk7,sk6)))),
inference(step,[status(thm)],[t14456,t244]) ).
cnf(t14458,plain,
true = or(false,not(leq(sk6,sk5(sk8,sk7,sk6)))),
inference(step,[status(thm)],[t14457,t233]) ).
cnf(t14459,plain,
true = not(leq(sk6,sk5(sk8,sk7,sk6))),
inference(step,[status(thm)],[t14458,t249]) ).
cnf(t10984,plain,
not(leq(sk6,sk5(sk8,sk7,sk6))) = true,
inference(orient,[status(thm)],[t14459]) ).
cnf(t10985,plain,
false = ifeq(true,true,leq(sk6,sk5(sk8,sk7,sk6)),false),
inference(cp,[status(thm)],[t296,t10984]) ).
cnf(t14460,plain,
false = leq(sk6,sk5(sk8,sk7,sk6)),
inference(step,[status(thm)],[t10985,t293]) ).
cnf(t10986,plain,
leq(sk6,sk5(sk8,sk7,sk6)) = false,
inference(orient,[status(thm)],[t14460]) ).
cnf(t14690,plain,
true = false,
inference(step,[status(thm)],[t14689,t10986]) ).
cnf(t11614,plain,
false = true,
inference(orient,[status(thm)],[t14690]) ).
cnf(f10,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f114,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/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(f116,axiom,
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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,c191,c196]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t11614]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC241-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/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 17:10:07 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 70.52/9.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 70.52/9.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------