%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWC206-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 03:05:40 PM UTC 2026
% Result : Unsatisfiable 16.99s 2.77s
% Output : Proof 16.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 30
% Syntax : Number of formulae : 193 ( 125 unt; 0 def)
% Number of atoms : 381 ( 143 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 430 ( 242 ~; 188 |; 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 : 16 ( 16 usr; 10 con; 0-4 aty)
% Number of variables : 156 ( 2 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f114,axiom,
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause115) ).
fof(f114_nnf,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(nnf_transformation,[status(thm)],[f114]) ).
fof(f114_sk,plain,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
inference(skolemisation,[status(esa)],[f114_nnf]) ).
cnf(c114,plain,
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f114_sk]) ).
cnf(t138,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(t586,plain,
or(not(eq(X1,X2)),or(not(neq(X1,X2)),or(not(ssList(X2)),not(ssList(X1))))) = true,
inference(orient,[status(thm)],[t138]) ).
cnf(f195,negated_conjecture,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f195_nnf,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(nnf_transformation,[status(thm)],[f195]) ).
fof(f195_sk,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(skolemisation,[status(esa)],[f195_nnf]) ).
cnf(c195,plain,
( ~ neq(sk4,nil)
| neq(sk5,nil) ),
inference(cnf_transformation,[status(esa)],[f195_sk]) ).
cnf(t89,plain,
ifeq(neq(sk4,nil),true,neq(sk5,nil),true) = true,
inference(equality_encoding,[status(esa)],[c195]) ).
cnf(t371,plain,
ifeq(neq(sk4,nil),true,neq(sk5,nil),true) = true,
inference(orient,[status(thm)],[t89]) ).
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(t640,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(t647,plain,
sk2 = sk4,
inference(orient,[status(thm)],[t1]) ).
cnf(t9129,plain,
neq(sk4,nil) = true,
inference(step,[status(thm)],[t640,t647]) ).
cnf(t648,plain,
neq(sk4,nil) = true,
inference(rw,[status(thm)],[t9129]) ).
cnf(t8215,plain,
neq(sk4,nil) = true,
inference(orient,[status(thm)],[t648]) ).
cnf(t9133,plain,
ifeq(true,true,neq(sk5,nil),true) = true,
inference(step,[status(thm)],[t371,t8215]) ).
cnf(t69,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t222,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t69]) ).
cnf(t9134,plain,
neq(sk5,nil) = true,
inference(step,[status(thm)],[t9133,t222]) ).
cnf(t8222,plain,
neq(sk5,nil) = true,
inference(rw,[status(thm)],[t9134]) ).
cnf(t8686,plain,
neq(sk5,nil) = true,
inference(orient,[status(thm)],[t8222]) ).
cnf(t74,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t235,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t74]) ).
cnf(f99,axiom,
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause100) ).
fof(f99_nnf,plain,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
inference(nnf_transformation,[status(thm)],[f99]) ).
fof(f99_sk,plain,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
inference(skolemisation,[status(esa)],[f99_nnf]) ).
cnf(c99,plain,
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(esa)],[f99_sk]) ).
cnf(t135,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
cnf(t426,plain,
ifeq(ssList(X1),true,ifeq(ssList(X2),true,or(neq(X2,X1),eq(X2,X1)),true),true) = true,
inference(orient,[status(thm)],[t135]) ).
cnf(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(t631,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(t660,plain,
sk1 = sk3,
inference(orient,[status(thm)],[t0]) ).
cnf(t9130,plain,
neq(sk3,nil) = false,
inference(step,[status(thm)],[t631,t660]) ).
cnf(t661,plain,
neq(sk3,nil) = false,
inference(rw,[status(thm)],[t9130]) ).
cnf(t8409,plain,
neq(sk3,nil) = false,
inference(orient,[status(thm)],[t661]) ).
cnf(t8410,plain,
true = ifeq(ssList(nil),true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(cp,[status(thm)],[t426,t8409]) ).
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(t666,plain,
ssList(nil) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t9171,plain,
true = ifeq(true,true,ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),true),
inference(step,[status(thm)],[t8410,t666]) ).
cnf(t9172,plain,
true = ifeq(ssList(sk3),true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t9171,t222]) ).
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(t1022,plain,
ssList(sk3) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(t9173,plain,
true = ifeq(true,true,or(false,eq(sk3,nil)),true),
inference(step,[status(thm)],[t9172,t1022]) ).
cnf(t9174,plain,
true = or(false,eq(sk3,nil)),
inference(step,[status(thm)],[t9173,t222]) ).
cnf(t25,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t265,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t25]) ).
cnf(t9175,plain,
true = eq(sk3,nil),
inference(step,[status(thm)],[t9174,t265]) ).
cnf(t8904,plain,
eq(sk3,nil) = true,
inference(orient,[status(thm)],[t9175]) ).
cnf(t8905,plain,
nil = ifeq(true,true,sk3,nil),
inference(cp,[status(thm)],[t235,t8904]) ).
cnf(t9176,plain,
nil = sk3,
inference(step,[status(thm)],[t8905,t222]) ).
cnf(t8911,plain,
nil = sk3,
inference(orient,[status(thm)],[t9176]) ).
cnf(t9182,plain,
neq(sk5,sk3) = true,
inference(step,[status(thm)],[t8686,t8911]) ).
cnf(t8917,plain,
neq(sk5,sk3) = true,
inference(rw,[status(thm)],[t9182]) ).
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(t166,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(t242,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)],[t166]) ).
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(t86,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t552,plain,
ifeq(ssList(X1),true,segmentP(X1,nil),true) = true,
inference(orient,[status(thm)],[t86]) ).
cnf(f194,negated_conjecture,
( ~ neq(sk4,nil)
| ssList(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f194_nnf,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(nnf_transformation,[status(thm)],[f194]) ).
fof(f194_sk,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(skolemisation,[status(esa)],[f194_nnf]) ).
cnf(c194,plain,
( ~ neq(sk4,nil)
| ssList(sk5) ),
inference(cnf_transformation,[status(esa)],[f194_sk]) ).
cnf(t76,plain,
ifeq(neq(sk4,nil),true,ssList(sk5),true) = true,
inference(equality_encoding,[status(esa)],[c194]) ).
cnf(t372,plain,
ifeq(neq(sk4,nil),true,ssList(sk5),true) = true,
inference(orient,[status(thm)],[t76]) ).
cnf(t9131,plain,
ifeq(true,true,ssList(sk5),true) = true,
inference(step,[status(thm)],[t372,t8215]) ).
cnf(t9132,plain,
ssList(sk5) = true,
inference(step,[status(thm)],[t9131,t222]) ).
cnf(t8221,plain,
ssList(sk5) = true,
inference(rw,[status(thm)],[t9132]) ).
cnf(t8225,plain,
ssList(sk5) = true,
inference(orient,[status(thm)],[t8221]) ).
cnf(t8228,plain,
true = ifeq(true,true,segmentP(sk5,nil),true),
inference(cp,[status(thm)],[t552,t8225]) ).
cnf(t9165,plain,
true = segmentP(sk5,nil),
inference(step,[status(thm)],[t8228,t222]) ).
cnf(t8726,plain,
segmentP(sk5,nil) = true,
inference(orient,[status(thm)],[t9165]) ).
cnf(t9180,plain,
segmentP(sk5,sk3) = true,
inference(step,[status(thm)],[t8726,t8911]) ).
cnf(t8915,plain,
segmentP(sk5,sk3) = true,
inference(rw,[status(thm)],[t9180]) ).
cnf(t9053,plain,
segmentP(sk5,sk3) = true,
inference(orient,[status(thm)],[t8915]) ).
cnf(t9054,plain,
sk5 = ifeq(true,true,ifeq(segmentP(sk3,sk5),true,ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,sk3,sk5),sk5),sk5),sk5),
inference(cp,[status(thm)],[t242,t9053]) ).
cnf(t9263,plain,
sk5 = ifeq(segmentP(sk3,sk5),true,ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,sk3,sk5),sk5),sk5),
inference(step,[status(thm)],[t9054,t222]) ).
cnf(f197,negated_conjecture,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f197_nnf,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(nnf_transformation,[status(thm)],[f197]) ).
fof(f197_sk,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(skolemisation,[status(esa)],[f197_nnf]) ).
cnf(c197,plain,
( ~ neq(sk4,nil)
| segmentP(sk3,sk5) ),
inference(cnf_transformation,[status(esa)],[f197_sk]) ).
cnf(t90,plain,
ifeq(neq(sk4,nil),true,segmentP(sk3,sk5),true) = true,
inference(equality_encoding,[status(esa)],[c197]) ).
cnf(t370,plain,
ifeq(neq(sk4,nil),true,segmentP(sk3,sk5),true) = true,
inference(orient,[status(thm)],[t90]) ).
cnf(t9135,plain,
ifeq(true,true,segmentP(sk3,sk5),true) = true,
inference(step,[status(thm)],[t370,t8215]) ).
cnf(t9136,plain,
segmentP(sk3,sk5) = true,
inference(step,[status(thm)],[t9135,t222]) ).
cnf(t8223,plain,
segmentP(sk3,sk5) = true,
inference(rw,[status(thm)],[t9136]) ).
cnf(t8692,plain,
segmentP(sk3,sk5) = true,
inference(orient,[status(thm)],[t8223]) ).
cnf(t9264,plain,
sk5 = ifeq(true,true,ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,sk3,sk5),sk5),sk5),
inference(step,[status(thm)],[t9263,t8692]) ).
cnf(t9265,plain,
sk5 = ifeq(ssList(sk5),true,ifeq(ssList(sk3),true,sk3,sk5),sk5),
inference(step,[status(thm)],[t9264,t222]) ).
cnf(t9266,plain,
sk5 = ifeq(true,true,ifeq(ssList(sk3),true,sk3,sk5),sk5),
inference(step,[status(thm)],[t9265,t8225]) ).
cnf(t9267,plain,
sk5 = ifeq(ssList(sk3),true,sk3,sk5),
inference(step,[status(thm)],[t9266,t222]) ).
cnf(t9268,plain,
sk5 = ifeq(true,true,sk3,sk5),
inference(step,[status(thm)],[t9267,t1022]) ).
cnf(t9269,plain,
sk5 = sk3,
inference(step,[status(thm)],[t9268,t222]) ).
cnf(t9062,plain,
sk3 = sk5,
inference(orient,[status(thm)],[t9269]) ).
cnf(t9284,plain,
neq(sk5,sk5) = true,
inference(step,[status(thm)],[t8917,t9062]) ).
cnf(t9101,plain,
neq(sk5,sk5) = true,
inference(orient,[status(thm)],[t9284]) ).
cnf(t9103,plain,
true = or(not(eq(sk5,sk5)),or(not(true),or(not(ssList(sk5)),not(ssList(sk5))))),
inference(cp,[status(thm)],[t586,t9101]) ).
cnf(t19,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t599,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t19]) ).
cnf(t9285,plain,
true = or(not(true),or(not(true),or(not(ssList(sk5)),not(ssList(sk5))))),
inference(step,[status(thm)],[t9103,t599]) ).
cnf(t6,plain,
not(true) = false,
introduced(definition) ).
cnf(t597,plain,
not(true) = false,
inference(orient,[status(thm)],[t6]) ).
cnf(t9286,plain,
true = or(false,or(not(true),or(not(ssList(sk5)),not(ssList(sk5))))),
inference(step,[status(thm)],[t9285,t597]) ).
cnf(t9287,plain,
true = or(not(true),or(not(ssList(sk5)),not(ssList(sk5)))),
inference(step,[status(thm)],[t9286,t265]) ).
cnf(t9288,plain,
true = or(false,or(not(ssList(sk5)),not(ssList(sk5)))),
inference(step,[status(thm)],[t9287,t597]) ).
cnf(t9289,plain,
true = or(not(ssList(sk5)),not(ssList(sk5))),
inference(step,[status(thm)],[t9288,t265]) ).
cnf(t9290,plain,
true = or(not(true),not(ssList(sk5))),
inference(step,[status(thm)],[t9289,t8225]) ).
cnf(t9291,plain,
true = or(false,not(ssList(sk5))),
inference(step,[status(thm)],[t9290,t597]) ).
cnf(t9292,plain,
true = not(ssList(sk5)),
inference(step,[status(thm)],[t9291,t265]) ).
cnf(t9293,plain,
true = not(true),
inference(step,[status(thm)],[t9292,t8225]) ).
cnf(t9294,plain,
true = false,
inference(step,[status(thm)],[t9293,t597]) ).
cnf(t9107,plain,
false = true,
inference(orient,[status(thm)],[t9294]) ).
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,t9107]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC206-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 16:54:01 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 16.99/2.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.99/2.77 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------