%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 03:05:09 PM UTC 2026
% Result : Unsatisfiable 22.74s 8.34s
% Output : Proof 22.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 25
% Syntax : Number of formulae : 172 ( 108 unt; 0 def)
% Number of atoms : 348 ( 144 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 398 ( 222 ~; 176 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 142 ( 2 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t154,plain,
ifeq(X1,X2,ifeq(neq(X1,X2),true,ifeq(ssList(X2),true,ifeq(ssList(X1),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t283,plain,
ifeq(X1,X2,ifeq(neq(X1,X2),true,ifeq(ssList(X2),true,ifeq(ssList(X1),true,false,true),true),true),true) = true,
inference(orient,[status(thm)],[t154]) ).
cnf(f198,negated_conjecture,
( nil = sk3
| neq(sk5,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_14) ).
fof(f198_nnf,plain,
( nil = sk3
| neq(sk5,nil) ),
inference(nnf_transformation,[status(thm)],[f198]) ).
fof(f198_sk,plain,
( nil = sk3
| neq(sk5,nil) ),
inference(skolemisation,[status(esa)],[f198_nnf]) ).
cnf(c198,plain,
( nil = sk3
| neq(sk5,nil) ),
inference(cnf_transformation,[status(esa)],[f198_sk]) ).
cnf(t77,plain,
or(neq(sk5,nil),eq(nil,sk3)) = true,
inference(equality_encoding,[status(esa)],[c198]) ).
cnf(f189,negated_conjecture,
nil = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f189_nnf,plain,
nil = sk2,
inference(nnf_transformation,[status(thm)],[f189]) ).
cnf(c189,plain,
nil = sk2,
inference(cnf_transformation,[status(esa)],[f189_nnf]) ).
cnf(t0,plain,
sk2 = nil,
inference(equality_encoding,[status(esa)],[c189]) ).
cnf(t581,plain,
nil = sk2,
inference(orient,[status(thm)],[t0]) ).
cnf(t9707,plain,
or(neq(sk5,sk2),eq(nil,sk3)) = true,
inference(step,[status(thm)],[t77,t581]) ).
cnf(t9708,plain,
or(neq(sk5,sk2),eq(sk2,sk3)) = true,
inference(step,[status(thm)],[t9707,t581]) ).
cnf(t642,plain,
or(neq(sk5,sk2),eq(sk2,sk3)) = true,
inference(orient,[status(thm)],[t9708]) ).
cnf(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f190_nnf,plain,
sk2 = sk4,
inference(nnf_transformation,[status(thm)],[f190]) ).
cnf(c190,plain,
sk2 = sk4,
inference(cnf_transformation,[status(esa)],[f190_nnf]) ).
cnf(t2,plain,
sk4 = sk2,
inference(equality_encoding,[status(esa)],[c190]) ).
cnf(t678,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t2]) ).
cnf(t9718,plain,
or(neq(sk5,sk4),eq(sk2,sk3)) = true,
inference(step,[status(thm)],[t642,t678]) ).
cnf(t9719,plain,
or(neq(sk5,sk4),eq(sk4,sk3)) = true,
inference(step,[status(thm)],[t9718,t678]) ).
cnf(t684,plain,
or(neq(sk5,sk4),eq(sk4,sk3)) = true,
inference(rw,[status(thm)],[t9719]) ).
cnf(f192,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f192_nnf,plain,
nil != sk1,
inference(nnf_transformation,[status(thm)],[f192]) ).
fof(f192_sk,plain,
nil != sk1,
inference(skolemisation,[status(esa)],[f192_nnf]) ).
cnf(c192,plain,
nil != sk1,
inference(cnf_transformation,[status(esa)],[f192_sk]) ).
cnf(t21,plain,
eq(nil,sk1) = false,
inference(equality_encoding,[status(esa)],[c192]) ).
cnf(t9711,plain,
eq(sk2,sk1) = false,
inference(step,[status(thm)],[t21,t581]) ).
cnf(t656,plain,
eq(sk2,sk1) = false,
inference(orient,[status(thm)],[t9711]) ).
cnf(t9716,plain,
eq(sk4,sk1) = false,
inference(step,[status(thm)],[t656,t678]) ).
cnf(t682,plain,
eq(sk4,sk1) = false,
inference(rw,[status(thm)],[t9716]) ).
cnf(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f191_nnf,plain,
sk1 = sk3,
inference(nnf_transformation,[status(thm)],[f191]) ).
cnf(c191,plain,
sk1 = sk3,
inference(cnf_transformation,[status(esa)],[f191_nnf]) ).
cnf(t1,plain,
sk3 = sk1,
inference(equality_encoding,[status(esa)],[c191]) ).
cnf(t689,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t1]) ).
cnf(t9732,plain,
eq(sk4,sk3) = false,
inference(step,[status(thm)],[t682,t689]) ).
cnf(t6556,plain,
eq(sk4,sk3) = false,
inference(orient,[status(thm)],[t9732]) ).
cnf(t9967,plain,
or(neq(sk5,sk4),false) = true,
inference(step,[status(thm)],[t684,t6556]) ).
cnf(t23,plain,
or(X1,false) = X1,
introduced(definition) ).
cnf(t267,plain,
or(X1,false) = X1,
inference(orient,[status(thm)],[t23]) ).
cnf(t9968,plain,
neq(sk5,sk4) = true,
inference(step,[status(thm)],[t9967,t267]) ).
cnf(t8261,plain,
neq(sk5,sk4) = true,
inference(orient,[status(thm)],[t9968]) ).
cnf(t8265,plain,
true = ifeq(sk5,sk4,ifeq(true,true,ifeq(ssList(sk4),true,ifeq(ssList(sk5),true,false,true),true),true),true),
inference(cp,[status(thm)],[t283,t8261]) ).
cnf(t69,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t225,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t69]) ).
cnf(t9978,plain,
true = ifeq(sk5,sk4,ifeq(ssList(sk4),true,ifeq(ssList(sk5),true,false,true),true),true),
inference(step,[status(thm)],[t8265,t225]) ).
cnf(f7,axiom,
ssList(nil),
file('/export/starexec/sandbox/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(t9713,plain,
nil = sk4,
inference(step,[status(thm)],[t581,t678]) ).
cnf(t679,plain,
nil = sk4,
inference(orient,[status(thm)],[t9713]) ).
cnf(t9727,plain,
ssList(sk4) = true,
inference(step,[status(thm)],[t11,t679]) ).
cnf(t705,plain,
ssList(sk4) = true,
inference(orient,[status(thm)],[t9727]) ).
cnf(t9979,plain,
true = ifeq(sk5,sk4,ifeq(true,true,ifeq(ssList(sk5),true,false,true),true),true),
inference(step,[status(thm)],[t9978,t705]) ).
cnf(t9980,plain,
true = ifeq(sk5,sk4,ifeq(ssList(sk5),true,false,true),true),
inference(step,[status(thm)],[t9979,t225]) ).
cnf(f194,negated_conjecture,
( nil = sk3
| ssList(sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f194_nnf,plain,
( nil = sk3
| ssList(sk5) ),
inference(nnf_transformation,[status(thm)],[f194]) ).
fof(f194_sk,plain,
( nil = sk3
| ssList(sk5) ),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
( nil = sk3
| ssList(sk5) ),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(t74,plain,
or(ssList(sk5),eq(nil,sk3)) = true,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t9710,plain,
or(ssList(sk5),eq(sk2,sk3)) = true,
inference(step,[status(thm)],[t74,t581]) ).
cnf(t644,plain,
or(ssList(sk5),eq(sk2,sk3)) = true,
inference(orient,[status(thm)],[t9710]) ).
cnf(t9717,plain,
or(ssList(sk5),eq(sk4,sk3)) = true,
inference(step,[status(thm)],[t644,t678]) ).
cnf(t683,plain,
or(ssList(sk5),eq(sk4,sk3)) = true,
inference(rw,[status(thm)],[t9717]) ).
cnf(t9875,plain,
or(ssList(sk5),false) = true,
inference(step,[status(thm)],[t683,t6556]) ).
cnf(t9876,plain,
ssList(sk5) = true,
inference(step,[status(thm)],[t9875,t267]) ).
cnf(t7706,plain,
ssList(sk5) = true,
inference(orient,[status(thm)],[t9876]) ).
cnf(t9981,plain,
true = ifeq(sk5,sk4,ifeq(true,true,false,true),true),
inference(step,[status(thm)],[t9980,t7706]) ).
cnf(t9982,plain,
true = ifeq(sk5,sk4,false,true),
inference(step,[status(thm)],[t9981,t225]) ).
cnf(t8381,plain,
ifeq(sk5,sk4,false,true) = true,
inference(orient,[status(thm)],[t9982]) ).
cnf(f126,axiom,
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/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(t169,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(t244,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)],[t169]) ).
cnf(f55,axiom,
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/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(t92,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t550,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(orient,[status(thm)],[t92]) ).
cnf(t9643,plain,
ifeq(ssList(X1),true,segmentP(X1,sk2),true) = true,
inference(step,[status(thm)],[t550,t581]) ).
cnf(t584,plain,
ifeq(ssList(X1),true,segmentP(X1,sk2),true) = true,
inference(rw,[status(thm)],[t9643]) ).
cnf(t10375,plain,
ifeq(ssList(X1),true,segmentP(X1,sk4),true) = true,
inference(step,[status(thm)],[t584,t678]) ).
cnf(t9451,plain,
ifeq(ssList(X1),true,segmentP(X1,sk4),true) = true,
inference(orient,[status(thm)],[t10375]) ).
cnf(t9452,plain,
true = ifeq(true,true,segmentP(sk5,sk4),true),
inference(cp,[status(thm)],[t9451,t7706]) ).
cnf(t10376,plain,
true = segmentP(sk5,sk4),
inference(step,[status(thm)],[t9452,t225]) ).
cnf(t9488,plain,
segmentP(sk5,sk4) = true,
inference(orient,[status(thm)],[t10376]) ).
cnf(t9489,plain,
sk5 = ifeq(true,true,ifeq(segmentP(sk4,sk5),true,ifeq(ssList(sk5),true,ifeq(ssList(sk4),true,sk4,sk5),sk5),sk5),sk5),
inference(cp,[status(thm)],[t244,t9488]) ).
cnf(t10381,plain,
sk5 = ifeq(segmentP(sk4,sk5),true,ifeq(ssList(sk5),true,ifeq(ssList(sk4),true,sk4,sk5),sk5),sk5),
inference(step,[status(thm)],[t9489,t225]) ).
cnf(f199,negated_conjecture,
( nil = sk3
| segmentP(sk4,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_15) ).
fof(f199_nnf,plain,
( nil = sk3
| segmentP(sk4,sk5) ),
inference(nnf_transformation,[status(thm)],[f199]) ).
fof(f199_sk,plain,
( nil = sk3
| segmentP(sk4,sk5) ),
inference(skolemisation,[status(esa)],[f199_nnf]) ).
cnf(c199,plain,
( nil = sk3
| segmentP(sk4,sk5) ),
inference(cnf_transformation,[status(esa)],[f199_sk]) ).
cnf(t81,plain,
or(segmentP(sk4,sk5),eq(nil,sk3)) = true,
inference(equality_encoding,[status(esa)],[c199]) ).
cnf(t9702,plain,
or(segmentP(sk4,sk5),eq(sk2,sk3)) = true,
inference(step,[status(thm)],[t81,t581]) ).
cnf(t638,plain,
or(segmentP(sk4,sk5),eq(sk2,sk3)) = true,
inference(orient,[status(thm)],[t9702]) ).
cnf(t9721,plain,
or(segmentP(sk4,sk5),eq(sk4,sk3)) = true,
inference(step,[status(thm)],[t638,t678]) ).
cnf(t686,plain,
or(segmentP(sk4,sk5),eq(sk4,sk3)) = true,
inference(rw,[status(thm)],[t9721]) ).
cnf(t9985,plain,
or(segmentP(sk4,sk5),false) = true,
inference(step,[status(thm)],[t686,t6556]) ).
cnf(t9986,plain,
segmentP(sk4,sk5) = true,
inference(step,[status(thm)],[t9985,t267]) ).
cnf(t8392,plain,
segmentP(sk4,sk5) = true,
inference(orient,[status(thm)],[t9986]) ).
cnf(t10382,plain,
sk5 = ifeq(true,true,ifeq(ssList(sk5),true,ifeq(ssList(sk4),true,sk4,sk5),sk5),sk5),
inference(step,[status(thm)],[t10381,t8392]) ).
cnf(t10383,plain,
sk5 = ifeq(ssList(sk5),true,ifeq(ssList(sk4),true,sk4,sk5),sk5),
inference(step,[status(thm)],[t10382,t225]) ).
cnf(t10384,plain,
sk5 = ifeq(true,true,ifeq(ssList(sk4),true,sk4,sk5),sk5),
inference(step,[status(thm)],[t10383,t7706]) ).
cnf(t10385,plain,
sk5 = ifeq(ssList(sk4),true,sk4,sk5),
inference(step,[status(thm)],[t10384,t225]) ).
cnf(t10386,plain,
sk5 = ifeq(true,true,sk4,sk5),
inference(step,[status(thm)],[t10385,t705]) ).
cnf(t10387,plain,
sk5 = sk4,
inference(step,[status(thm)],[t10386,t225]) ).
cnf(t9499,plain,
sk4 = sk5,
inference(orient,[status(thm)],[t10387]) ).
cnf(t10395,plain,
ifeq(sk5,sk5,false,true) = true,
inference(step,[status(thm)],[t8381,t9499]) ).
cnf(t10396,plain,
false = true,
inference(step,[status(thm)],[t10395,t225]) ).
cnf(t9506,plain,
false = true,
inference(rw,[status(thm)],[t10396]) ).
cnf(t9582,plain,
false = true,
inference(orient,[status(thm)],[t9506]) ).
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(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,c192]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t9582]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n019.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 16:02:56 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.74/8.34 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.74/8.34 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------