%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC229+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.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 03:08:57 PM UTC 2026
% Result : Theorem 16.64s 3.27s
% Output : CNFRefutation 16.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 10
% Syntax : Number of formulae : 97 ( 22 unt; 0 def)
% Number of atoms : 373 ( 111 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 462 ( 186 ~; 189 |; 60 &)
% ( 8 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn 99 !; 20 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax1) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ~ singletonP(X2) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X7,X4)
| ~ leq(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ~ singletonP(X2) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X7,X4)
| ~ leq(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| ~ segmentP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f176,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| singletonP(X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X7,X4)
& leq(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ~ neq(X3,nil)
| singletonP(X2) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ? [X7] :
( ssItem(X7)
& ~ leq(X7,X4)
& leq(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7) )
| app(app(X5,cons(X4,nil)),X6) != X0
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != X0
& segmentP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f232,plain,
! [X0] :
( ~ ssItem(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f98]) ).
fof(f237,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ singletonP(X0)
| ( cons(sK10(X0),nil) = X0
& ssItem(sK10(X0)) ) )
& ( ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) )
| singletonP(X0) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f285,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f176]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| singletonP(sK55) )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( ( ssItem(sK57(X4,X5,X6))
& ~ leq(sK57(X4,X5,X6),X4)
& leq(X4,sK57(X4,X5,X6))
& memberP(X6,sK57(X4,X5,X6))
& memberP(X5,sK57(X4,X5,X6)) )
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(X4) )
& nil != sK53
& segmentP(sK56,sK55)
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6))],[f222]) ).
fof(f298,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f232]) ).
fof(f306,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| cons(sK10(X0),nil) = X0 ),
inference(cnf_transformation,[],[f239]) ).
fof(f307,plain,
! [X0] :
( ~ ssList(X0)
| ~ singletonP(X0)
| ssItem(sK10(X0)) ),
inference(cnf_transformation,[],[f239]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f403,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f443,plain,
! [X0] :
( ~ ssList(X0)
| ~ segmentP(nil,X0)
| nil = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f444,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( ~ neq(sK56,nil)
| singletonP(sK55) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X6,X4,X5] :
( memberP(X6,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
nil != sK55,
inference(definition_unfolding,[],[f506,f508]) ).
fof(f512,plain,
! [X6,X4,X5] :
( memberP(X6,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f504,f508]) ).
fof(f515,plain,
! [X6,X4,X5] :
( ssItem(sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f501,f508]) ).
fof(f516,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f509]) ).
fof(f517,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f508]) ).
fof(f537,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_59,plain,
! [X0: $i] :
( ssItem(sK10(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f307]) ).
tcf(c_60,plain,
! [X0: $i] :
( ( cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f306]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_171,negated_conjecture,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f537]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
segmentP(sK56,sK55),
inference(cnf_transformation,[],[f507]) ).
tcf(c_247,negated_conjecture,
nil != sK55,
inference(cnf_transformation,[],[f510]) ).
tcf(c_249,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X2,sK57(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_252,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sK57(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_253,negated_conjecture,
( singletonP(sK55)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_256,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f516]) ).
tcf(c_257,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f517]) ).
tcf(c_307,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_779,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( sK55 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_544]) ).
tcf(c_780,plain,
( ( nil = sK55 )
| ( sK55 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_779]) ).
tcf(c_1173,plain,
( ( sK55 = nil )
| ~ ssList(sK55)
| ~ segmentP(nil,sK55) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_1372,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_257,c_232]) ).
tcf(c_1802,plain,
app(nil,sK55) = sK55,
inference(superposition,[status(thm)],[c_257,c_155]) ).
tcf(c_1825,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_257,c_232]) ).
tcf(c_2148,plain,
( singletonP(sK55)
| ( nil = sK56 )
| ~ ssItem(sK56)
| ~ ssItem(nil) ),
inference(superposition,[status(thm)],[c_49,c_253]) ).
tcf(c_2151,plain,
( singletonP(sK55)
| ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_253]) ).
tcf(c_2152,plain,
( singletonP(sK55)
| ( nil = sK56 ) ),
inference(global_subsumption_just,[status(thm)],[c_2148,c_256,c_141,c_2151]) ).
tcf(c_2154,plain,
( ( nil = sK56 )
| ( cons(sK10(sK55),nil) = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_2152,c_60]) ).
tcf(c_2260,plain,
( ( nil = sK56 )
| ( cons(sK10(sK55),nil) = sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_2154,c_257,c_2154]) ).
tcf(c_2269,plain,
! [X0: $i,X1: $i] :
( memberP(X1,sK57(sK10(sK55),X0,X1))
| ( nil = sK56 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK10(sK55))
| ( app(app(X0,sK55),X1) != sK55 ) ),
inference(superposition,[status(thm)],[c_2260,c_249]) ).
tcf(c_2271,plain,
! [X0: $i,X1: $i] :
( ssItem(sK57(sK10(sK55),X0,X1))
| ( nil = sK56 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK10(sK55))
| ( app(app(X0,sK55),X1) != sK55 ) ),
inference(superposition,[status(thm)],[c_2260,c_252]) ).
tcf(c_2295,plain,
! [X0: $i] :
( ssItem(sK57(sK10(sK55),nil,X0))
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK10(sK55))
| ( app(sK55,X0) != sK55 ) ),
inference(superposition,[status(thm)],[c_1802,c_2271]) ).
tcf(c_2296,plain,
( ssItem(sK57(sK10(sK55),nil,nil))
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK10(sK55))
| ( app(sK55,nil) != sK55 ) ),
inference(instantiation,[status(thm)],[c_2295]) ).
tcf(c_2297,plain,
! [X0: $i] :
( memberP(X0,sK57(sK10(sK55),nil,X0))
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK10(sK55))
| ( app(sK55,X0) != sK55 ) ),
inference(superposition,[status(thm)],[c_1802,c_2269]) ).
tcf(c_2298,plain,
( memberP(nil,sK57(sK10(sK55),nil,nil))
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK10(sK55))
| ( app(sK55,nil) != sK55 ) ),
inference(instantiation,[status(thm)],[c_2297]) ).
tcf(c_4216,plain,
! [X0: $i] :
( memberP(X0,sK57(sK10(sK55),nil,X0))
| ( nil = sK56 )
| ( app(sK55,X0) != sK55 )
| ~ ssItem(sK10(sK55))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2297,c_141,c_2297]) ).
tcf(c_4217,plain,
! [X0: $i] :
( memberP(X0,sK57(sK10(sK55),nil,X0))
| ( nil = sK56 )
| ~ ssList(X0)
| ~ ssItem(sK10(sK55))
| ( app(sK55,X0) != sK55 ) ),
inference(renaming,[status(thm)],[c_4216]) ).
tcf(c_4218,plain,
( memberP(nil,sK57(sK10(sK55),nil,nil))
| ( nil = sK56 )
| ~ ssList(nil)
| ~ ssItem(sK10(sK55)) ),
inference(superposition,[status(thm)],[c_1825,c_4217]) ).
tcf(c_4219,plain,
( memberP(nil,sK57(sK10(sK55),nil,nil))
| ( nil = sK56 )
| ~ ssItem(sK10(sK55)) ),
inference(global_subsumption_just,[status(thm)],[c_4218,c_141,c_1372,c_2298]) ).
tcf(c_4221,plain,
( ( nil = sK56 )
| ~ ssItem(sK10(sK55))
| ~ ssItem(sK57(sK10(sK55),nil,nil)) ),
inference(superposition,[status(thm)],[c_4219,c_171]) ).
tcf(c_4243,plain,
( ( nil = sK56 )
| ~ ssItem(sK10(sK55)) ),
inference(global_subsumption_just,[status(thm)],[c_4221,c_141,c_1372,c_2296,c_4221]) ).
tcf(c_4245,plain,
( ( nil = sK56 )
| ~ singletonP(sK55)
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_59,c_4243]) ).
tcf(c_4246,plain,
nil = sK56,
inference(global_subsumption_just,[status(thm)],[c_4245,c_257,c_2152,c_4245]) ).
tcf(c_4264,plain,
segmentP(nil,sK55),
inference(superposition,[status(thm)],[c_4246,c_246]) ).
tcf(c_4266,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4264,c_1173,c_780,c_307,c_195,c_247,c_141,c_257]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC229+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 17:06:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 16.64/3.27 % SZS status Started for theBenchmark.p
% 16.64/3.27 % SZS status Theorem for theBenchmark.p
% 16.64/3.27
% 16.64/3.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 16.64/3.27
% 16.64/3.27 % ------ iProver source info
% 16.64/3.27
% 16.64/3.27 % git: date: 2026-07-19 20:42:38 +0200
% 16.64/3.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 16.64/3.27 % git: non_committed_changes: false
% 16.64/3.27
% 16.64/3.27 % ------ Parsing...
% 16.64/3.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 16.64/3.27
% 16.64/3.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e %
% 16.64/3.27
% 16.64/3.27 % ------ Preprocessing...%
% 16.64/3.27
% 16.64/3.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 16.64/3.27 % ------ Proving...
% 16.64/3.27 % ------ Problem Properties
% 16.64/3.27
% 16.64/3.27 %
% 16.64/3.27 % clauses 203
% 16.64/3.27 % conjectures 22
% 16.64/3.27 % EPR 67
% 16.64/3.27 % Horn 133
% 16.64/3.27 % unary 20
% 16.64/3.27 % binary 49
% 16.64/3.27 % lits 682
% 16.64/3.27 % lits eq 86
% 16.64/3.27 % fd_pure 0
% 16.64/3.27 % fd_pseudo 0
% 16.64/3.27 % fd_cond 21
% 16.64/3.27 % fd_pseudo_cond 16
% 16.64/3.27 % AC symbols 0
% 16.64/3.27
% 16.64/3.27 % ------ Input Options Time Limit: Unbounded
% 16.64/3.27
% 16.64/3.27
% 16.64/3.27 % ------
% 16.64/3.27 % Current options:
% 16.64/3.27 % ------
% 16.64/3.27
% 16.64/3.27
% 16.64/3.27 %
% 16.64/3.27
% 16.64/3.27 % ------ Proving...
% 16.64/3.27 %
% 16.64/3.27
% 16.64/3.27 % SZS status Theorem for theBenchmark.p
% 16.64/3.27
% 16.64/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 16.64/3.27
% 16.64/3.27
%------------------------------------------------------------------------------