%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC218-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 03:05:42 PM UTC 2026
% Result : Unsatisfiable 120.82s 15.69s
% Output : Proof 120.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 31
% Syntax : Number of formulae : 199 ( 135 unt; 0 def)
% Number of atoms : 403 ( 151 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 462 ( 258 ~; 204 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-4 aty)
% Number of variables : 204 ( 2 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t154,plain,
or(not(eq(cons(X1,X2),X2)),or(not(ssItem(X1)),not(ssList(X2)))) = true,
inference(equality_encoding,[status(esa)],[c98]) ).
cnf(t750,plain,
or(not(eq(cons(X1,X2),X2)),or(not(ssItem(X1)),not(ssList(X2)))) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(f126,axiom,
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause127) ).
fof(f126_nnf,plain,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
inference(nnf_transformation,[status(thm)],[f126]) ).
fof(f126_sk,plain,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
inference(skolemisation,[status(esa)],[f126_nnf]) ).
cnf(c126,plain,
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f126_sk]) ).
cnf(t200,plain,
ifeq(segmentP(X1,X2),true,ifeq(segmentP(X2,X1),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,X2,X1),X1),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c126]) ).
cnf(t276,plain,
ifeq(segmentP(X1,X2),true,ifeq(segmentP(X2,X1),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,X2,X1),X1),X1),X1) = X1,
inference(orient,[status(thm)],[t200]) ).
cnf(f172,axiom,
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause173) ).
fof(f172_nnf,plain,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
inference(nnf_transformation,[status(thm)],[f172]) ).
fof(f172_sk,plain,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
inference(skolemisation,[status(esa)],[f172_nnf]) ).
cnf(c172,plain,
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(esa)],[f172_sk]) ).
cnf(t239,plain,
ifeq(app(app(X1,X2),X3),X4,ifeq(ssList(X3),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X4),true,segmentP(X4,X2),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c172]) ).
cnf(t357,plain,
ifeq(app(app(X1,X2),X3),X4,ifeq(ssList(X3),true,ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X4),true,segmentP(X4,X2),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t239]) ).
cnf(t104,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t104]) ).
cnf(t358,plain,
true = ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(ssList(app(app(X2,X3),X1)),true,segmentP(app(app(X2,X3),X1),X3),true),true),true),true),
inference(cp,[status(thm)],[t357,t256]) ).
cnf(t66897,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,ifeq(ssList(X3),true,ifeq(ssList(app(app(X2,X3),X1)),true,segmentP(app(app(X2,X3),X1),X3),true),true),true),true) = true,
inference(orient,[status(thm)],[t358]) ).
cnf(f195,negated_conjecture,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(nnf_transformation,[status(thm)],[f195]) ).
cnf(c195,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(cnf_transformation,[status(esa)],[f195_nnf]) ).
cnf(t108,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t693,plain,
app(app(sk5,cons(sk7,nil)),sk6) = sk3,
inference(orient,[status(thm)],[t108]) ).
cnf(t109,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t269,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t109]) ).
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(t169,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(t455,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(orient,[status(thm)],[t169]) ).
cnf(f196,negated_conjecture,
~ neq(sk1,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f196_nnf,plain,
~ neq(sk1,nil),
inference(nnf_transformation,[status(thm)],[f196]) ).
fof(f196_sk,plain,
~ neq(sk1,nil),
inference(skolemisation,[status(esa)],[f196_nnf]) ).
cnf(c196,plain,
~ neq(sk1,nil),
inference(cnf_transformation,[status(esa)],[f196_sk]) ).
cnf(t33,plain,
neq(sk1,nil) = false,
inference(equality_encoding,[status(esa)],[c196]) ).
cnf(t838,plain,
neq(sk1,nil) = false,
inference(orient,[status(thm)],[t33]) ).
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(t896,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t67992,plain,
neq(sk3,nil) = false,
inference(step,[status(thm)],[t838,t896]) ).
cnf(t898,plain,
neq(sk3,nil) = false,
inference(rw,[status(thm)],[t67992]) ).
cnf(t9282,plain,
neq(sk3,nil) = false,
inference(orient,[status(thm)],[t898]) ).
cnf(t9283,plain,
true = ifeq(ssList(nil),true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(cp,[status(thm)],[t455,t9282]) ).
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(t3162,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t68032,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(step,[status(thm)],[t9283,t3162]) ).
cnf(t68033,plain,
true = ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t68032,t256]) ).
cnf(f185,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_1) ).
fof(f185_nnf,plain,
ssList(sk1),
inference(nnf_transformation,[status(thm)],[f185]) ).
cnf(c185,plain,
ssList(sk1),
inference(cnf_transformation,[status(esa)],[f185_nnf]) ).
cnf(t12,plain,
ssList(sk1) = true,
inference(equality_encoding,[status(esa)],[c185]) ).
cnf(t68001,plain,
ssList(sk3) = true,
inference(step,[status(thm)],[t12,t896]) ).
cnf(t3505,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t68001]) ).
cnf(t68034,plain,
true = ifeq(true,true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t68033,t3505]) ).
cnf(t68035,plain,
true = or(false,eq(sk3,nil)),
inference(step,[status(thm)],[t68034,t256]) ).
cnf(t36,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t299,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t36]) ).
cnf(t68036,plain,
true = eq(sk3,nil),
inference(step,[status(thm)],[t68035,t299]) ).
cnf(t9773,plain,
eq(sk3,nil) = true,
inference(orient,[status(thm)],[t68036]) ).
cnf(t9774,plain,
nil = ifeq(true,true,sk3,nil),
inference(cp,[status(thm)],[t269,t9773]) ).
cnf(t68037,plain,
nil = sk3,
inference(step,[status(thm)],[t9774,t256]) ).
cnf(t9780,plain,
nil = sk3,
inference(orient,[status(thm)],[t68037]) ).
cnf(t68089,plain,
app(app(sk5,cons(sk7,sk3)),sk6) = sk3,
inference(step,[status(thm)],[t693,t9780]) ).
cnf(t9829,plain,
app(app(sk5,cons(sk7,sk3)),sk6) = sk3,
inference(rw,[status(thm)],[t68089]) ).
cnf(t11965,plain,
app(app(sk5,cons(sk7,sk3)),sk6) = sk3,
inference(orient,[status(thm)],[t9829]) ).
cnf(t67506,plain,
true = ifeq(ssList(sk6),true,ifeq(ssList(sk5),true,ifeq(ssList(cons(sk7,sk3)),true,ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),true),true),true),
inference(cp,[status(thm)],[t66897,t11965]) ).
cnf(f192,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
ssList(sk6),
inference(nnf_transformation,[status(thm)],[f192]) ).
cnf(c192,plain,
ssList(sk6),
inference(cnf_transformation,[status(esa)],[f192_nnf]) ).
cnf(t17,plain,
ssList(sk6) = true,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t3687,plain,
ssList(sk6) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(t71846,plain,
true = ifeq(true,true,ifeq(ssList(sk5),true,ifeq(ssList(cons(sk7,sk3)),true,ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),true),true),true),
inference(step,[status(thm)],[t67506,t3687]) ).
cnf(t71847,plain,
true = ifeq(ssList(sk5),true,ifeq(ssList(cons(sk7,sk3)),true,ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),true),true),
inference(step,[status(thm)],[t71846,t256]) ).
cnf(f191,negated_conjecture,
ssList(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
ssList(sk5),
inference(nnf_transformation,[status(thm)],[f191]) ).
cnf(c191,plain,
ssList(sk5),
inference(cnf_transformation,[status(esa)],[f191_nnf]) ).
cnf(t16,plain,
ssList(sk5) = true,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t3871,plain,
ssList(sk5) = true,
inference(orient,[status(thm)],[t16]) ).
cnf(t71848,plain,
true = ifeq(true,true,ifeq(ssList(cons(sk7,sk3)),true,ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),true),true),
inference(step,[status(thm)],[t71847,t3871]) ).
cnf(t71849,plain,
true = ifeq(ssList(cons(sk7,sk3)),true,ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),true),
inference(step,[status(thm)],[t71848,t256]) ).
cnf(f85,axiom,
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause86) ).
fof(f85_nnf,plain,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
inference(nnf_transformation,[status(thm)],[f85]) ).
fof(f85_sk,plain,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
inference(skolemisation,[status(esa)],[f85_nnf]) ).
cnf(c85,plain,
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(esa)],[f85_sk]) ).
cnf(t151,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ssList(cons(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c85]) ).
cnf(t416,plain,
ifeq(ssItem(X1),true,ifeq(ssList(X2),true,ssList(cons(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t151]) ).
cnf(f194,negated_conjecture,
ssItem(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f194_nnf,plain,
ssItem(sk7),
inference(nnf_transformation,[status(thm)],[f194]) ).
cnf(c194,plain,
ssItem(sk7),
inference(cnf_transformation,[status(esa)],[f194_nnf]) ).
cnf(t8,plain,
ssItem(sk7) = true,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t1030,plain,
ssItem(sk7) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t1042,plain,
true = ifeq(true,true,ifeq(ssList(X1),true,ssList(cons(sk7,X1)),true),true),
inference(cp,[status(thm)],[t416,t1030]) ).
cnf(t70019,plain,
true = ifeq(ssList(X1),true,ssList(cons(sk7,X1)),true),
inference(step,[status(thm)],[t1042,t256]) ).
cnf(t17149,plain,
ifeq(ssList(X1),true,ssList(cons(sk7,X1)),true) = true,
inference(orient,[status(thm)],[t70019]) ).
cnf(t17180,plain,
true = ifeq(true,true,ssList(cons(sk7,sk3)),true),
inference(cp,[status(thm)],[t17149,t3505]) ).
cnf(t70023,plain,
true = ssList(cons(sk7,sk3)),
inference(step,[status(thm)],[t17180,t256]) ).
cnf(t17723,plain,
ssList(cons(sk7,sk3)) = true,
inference(orient,[status(thm)],[t70023]) ).
cnf(t71850,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),true),
inference(step,[status(thm)],[t71849,t17723]) ).
cnf(t71851,plain,
true = ifeq(ssList(sk3),true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),
inference(step,[status(thm)],[t71850,t256]) ).
cnf(t71852,plain,
true = ifeq(true,true,segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),true),
inference(step,[status(thm)],[t71851,t3505]) ).
cnf(t71853,plain,
true = segmentP(app(app(sk5,cons(sk7,sk3)),sk6),cons(sk7,sk3)),
inference(step,[status(thm)],[t71852,t256]) ).
cnf(t71854,plain,
true = segmentP(sk3,cons(sk7,sk3)),
inference(step,[status(thm)],[t71853,t11965]) ).
cnf(t67800,plain,
segmentP(sk3,cons(sk7,sk3)) = true,
inference(orient,[status(thm)],[t71854]) ).
cnf(t67801,plain,
sk3 = ifeq(true,true,ifeq(segmentP(cons(sk7,sk3),sk3),true,ifeq(ssList(sk3),true,ifeq(ssList(cons(sk7,sk3)),true,cons(sk7,sk3),sk3),sk3),sk3),sk3),
inference(cp,[status(thm)],[t276,t67800]) ).
cnf(t71855,plain,
sk3 = ifeq(segmentP(cons(sk7,sk3),sk3),true,ifeq(ssList(sk3),true,ifeq(ssList(cons(sk7,sk3)),true,cons(sk7,sk3),sk3),sk3),sk3),
inference(step,[status(thm)],[t67801,t256]) ).
cnf(f55,axiom,
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause56) ).
fof(f55_nnf,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(t122,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t581,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(orient,[status(thm)],[t122]) ).
cnf(t68082,plain,
ifeq(ssList(X1),true,segmentP(X1,sk3),true) = true,
inference(step,[status(thm)],[t581,t9780]) ).
cnf(t9823,plain,
ifeq(ssList(X1),true,segmentP(X1,sk3),true) = true,
inference(rw,[status(thm)],[t68082]) ).
cnf(t12984,plain,
ifeq(ssList(X1),true,segmentP(X1,sk3),true) = true,
inference(orient,[status(thm)],[t9823]) ).
cnf(t17727,plain,
true = ifeq(true,true,segmentP(cons(sk7,sk3),sk3),true),
inference(cp,[status(thm)],[t12984,t17723]) ).
cnf(t70055,plain,
true = segmentP(cons(sk7,sk3),sk3),
inference(step,[status(thm)],[t17727,t256]) ).
cnf(t21853,plain,
segmentP(cons(sk7,sk3),sk3) = true,
inference(orient,[status(thm)],[t70055]) ).
cnf(t71856,plain,
sk3 = ifeq(true,true,ifeq(ssList(sk3),true,ifeq(ssList(cons(sk7,sk3)),true,cons(sk7,sk3),sk3),sk3),sk3),
inference(step,[status(thm)],[t71855,t21853]) ).
cnf(t71857,plain,
sk3 = ifeq(ssList(sk3),true,ifeq(ssList(cons(sk7,sk3)),true,cons(sk7,sk3),sk3),sk3),
inference(step,[status(thm)],[t71856,t256]) ).
cnf(t71858,plain,
sk3 = ifeq(true,true,ifeq(ssList(cons(sk7,sk3)),true,cons(sk7,sk3),sk3),sk3),
inference(step,[status(thm)],[t71857,t3505]) ).
cnf(t71859,plain,
sk3 = ifeq(ssList(cons(sk7,sk3)),true,cons(sk7,sk3),sk3),
inference(step,[status(thm)],[t71858,t256]) ).
cnf(t71860,plain,
sk3 = ifeq(true,true,cons(sk7,sk3),sk3),
inference(step,[status(thm)],[t71859,t17723]) ).
cnf(t71861,plain,
sk3 = cons(sk7,sk3),
inference(step,[status(thm)],[t71860,t256]) ).
cnf(t67809,plain,
cons(sk7,sk3) = sk3,
inference(orient,[status(thm)],[t71861]) ).
cnf(t67812,plain,
true = or(not(eq(sk3,sk3)),or(not(ssItem(sk7)),not(ssList(sk3)))),
inference(cp,[status(thm)],[t750,t67809]) ).
cnf(t25,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t768,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(t71880,plain,
true = or(not(true),or(not(ssItem(sk7)),not(ssList(sk3)))),
inference(step,[status(thm)],[t67812,t768]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t766,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t71881,plain,
true = or(false,or(not(ssItem(sk7)),not(ssList(sk3)))),
inference(step,[status(thm)],[t71880,t766]) ).
cnf(t71882,plain,
true = or(not(ssItem(sk7)),not(ssList(sk3))),
inference(step,[status(thm)],[t71881,t299]) ).
cnf(t71883,plain,
true = or(not(true),not(ssList(sk3))),
inference(step,[status(thm)],[t71882,t1030]) ).
cnf(t71884,plain,
true = or(false,not(ssList(sk3))),
inference(step,[status(thm)],[t71883,t766]) ).
cnf(t71885,plain,
true = not(ssList(sk3)),
inference(step,[status(thm)],[t71884,t299]) ).
cnf(t71886,plain,
true = not(true),
inference(step,[status(thm)],[t71885,t3505]) ).
cnf(t71887,plain,
true = false,
inference(step,[status(thm)],[t71886,t766]) ).
cnf(t67863,plain,
false = true,
inference(orient,[status(thm)],[t71887]) ).
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(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(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(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,c196]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t67863]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC218-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 17:04:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 120.82/15.69 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 120.82/15.69 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------