%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC244+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n018.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 03:08:59 PM UTC 2026
% Result : Theorem 53.43s 9.28s
% Output : CNFRefutation 53.43s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f314ERROR: Could not build tree for root c_137252ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax20) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ? [X4] :
( equalelemsP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| nil = X0
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ! [X8] :
( ssItem(X8)
=> ( leq(X5,X8)
| ~ lt(X5,X8)
| ~ memberP(X7,X8)
| ~ memberP(X6,X8) ) )
& app(app(X6,cons(X5,nil)),X7) = X0
& ssList(X7) )
& ssList(X6) )
& ssItem(X5) )
| ? [X4] :
( equalelemsP(X4)
& segmentP(X4,X2)
& frontsegP(X3,X4)
& neq(X2,X4)
& ssList(X4) )
| nil = X0
| ~ equalelemsP(X2)
| ~ frontsegP(X3,X2)
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ? [X8] :
( ssItem(X8)
& ~ leq(X5,X8)
& lt(X5,X8)
& memberP(X7,X8)
& memberP(X6,X8) )
| app(app(X6,cons(X5,nil)),X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& nil != X0
& equalelemsP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ? [X8] :
( ssItem(X8)
& ~ leq(X5,X8)
& lt(X5,X8)
& memberP(X7,X8)
& memberP(X6,X8) )
| app(app(X6,cons(X5,nil)),X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,X2)
| ~ frontsegP(X3,X4)
| ~ neq(X2,X4)
| ~ ssList(X4) )
& nil != X0
& equalelemsP(X2)
& frontsegP(X3,X2)
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f103,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f104,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f103]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f117,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f120,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f163,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ( ssItem(sK4(X5,X6,X7))
& ~ leq(X5,sK4(X5,X6,X7))
& lt(X5,sK4(X5,X6,X7))
& memberP(X7,sK4(X5,X6,X7))
& memberP(X6,sK4(X5,X6,X7)) )
| app(app(X6,cons(X5,nil)),X7) != sK0
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& ! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK2)
| ~ frontsegP(sK3,X4)
| ~ neq(sK2,X4)
| ~ ssList(X4) )
& nil != sK0
& equalelemsP(sK2)
& frontsegP(sK3,sK2)
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X8,sK4(X5,X6,X7))],[f99]) ).
fof(f165,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK8(X0),sK7(X0)) = X0
& ssItem(sK8(X0))
& ssList(sK7(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X1,sK7(X0)),skolemize(X2,sK8(X0))],[f104]) ).
fof(f168,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f180,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f134]) ).
fof(f181,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ? [X3] :
( app(X1,X3) = X0
& ssList(X3) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(rectify,[],[f180]) ).
fof(f182,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ frontsegP(X0,X1)
| ( app(X1,sK11(X0,X1)) = X0
& ssList(sK11(X0,X1)) ) )
& ( ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) )
| frontsegP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X3,sK11(X0,X1))],[f181]) ).
fof(f192,plain,
ssList(sK0),
inference(cnf_transformation,[],[f163]) ).
fof(f196,plain,
! [X6,X7,X5] :
( ssItem(sK4(X5,X6,X7))
| app(app(X6,cons(X5,nil)),X7) != sK0
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f163]) ).
fof(f200,plain,
! [X6,X7,X5] :
( memberP(X6,sK4(X5,X6,X7))
| app(app(X6,cons(X5,nil)),X7) != sK0
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f163]) ).
fof(f201,plain,
! [X4] :
( ~ equalelemsP(X4)
| ~ segmentP(X4,sK2)
| ~ frontsegP(sK3,X4)
| ~ neq(sK2,X4)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f163]) ).
fof(f202,plain,
nil != sK0,
inference(cnf_transformation,[],[f163]) ).
fof(f203,plain,
equalelemsP(sK2),
inference(cnf_transformation,[],[f163]) ).
fof(f204,plain,
frontsegP(sK3,sK2),
inference(cnf_transformation,[],[f163]) ).
fof(f205,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f163]) ).
fof(f213,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK8(X0),sK7(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f214,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK8(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f215,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK7(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f165]) ).
fof(f219,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f227,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f228,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f117]) ).
fof(f230,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f168]) ).
fof(f233,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f234,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f255,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f182]) ).
fof(f256,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f182]) ).
fof(f257,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
fof(f262,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f139]) ).
fof(f289,plain,
nil != sK2,
inference(definition_unfolding,[],[f202,f205]) ).
fof(f290,plain,
! [X6,X7,X5] :
( memberP(X6,sK4(X5,X6,X7))
| app(app(X6,cons(X5,nil)),X7) != sK2
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(definition_unfolding,[],[f200,f205]) ).
fof(f294,plain,
! [X6,X7,X5] :
( ssItem(sK4(X5,X6,X7))
| app(app(X6,cons(X5,nil)),X7) != sK2
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(definition_unfolding,[],[f196,f205]) ).
fof(f296,plain,
ssList(sK2),
inference(definition_unfolding,[],[f192,f205]) ).
fof(f305,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f257]) ).
tcf(c_49,negated_conjecture,
frontsegP(sK3,sK2),
inference(cnf_transformation,[],[f204]) ).
tcf(c_50,negated_conjecture,
equalelemsP(sK2),
inference(cnf_transformation,[],[f203]) ).
tcf(c_51,negated_conjecture,
sK2 != nil,
inference(cnf_transformation,[],[f289]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ equalelemsP(X0)
| ~ segmentP(X0,sK2)
| ~ neq(sK2,X0)
| ~ frontsegP(sK3,X0) ),
inference(cnf_transformation,[],[f201]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X0,sK4(X1,X0,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f290]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ssItem(sK4(X1,X0,X2))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X0,cons(X1,nil)),X2) != sK2 ) ),
inference(cnf_transformation,[],[f294]) ).
tcf(c_61,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f296]) ).
tcf(c_68,plain,
! [X0: $i] :
( ssList(sK7(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_69,plain,
! [X0: $i] :
( ssItem(sK8(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_70,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK8(X0),sK7(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_82,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_88,plain,
ssList(nil),
inference(cnf_transformation,[],[f233]) ).
tcf(c_89,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f314]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f305]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ssList(sK11(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK11(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_117,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f262]) ).
tcf(c_320,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_110,c_83]) ).
tcf(c_1526,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| ~ segmentP(X0,sK2)
| ~ frontsegP(sK3,X0)
| ( X2 != sK2 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_84]) ).
tcf(c_1527,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ equalelemsP(X0)
| ~ segmentP(X0,sK2)
| ~ frontsegP(sK3,X0) ),
inference(unflattening,[status(thm)],[c_1526]) ).
tcf(c_1529,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ frontsegP(sK3,X0)
| ~ segmentP(X0,sK2)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1527,c_61,c_1527]) ).
tcf(c_1530,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ ssList(X0)
| ~ equalelemsP(X0)
| ~ segmentP(X0,sK2)
| ~ frontsegP(sK3,X0) ),
inference(renaming,[status(thm)],[c_1529]) ).
tcf(c_3718,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_5335,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(nil,sK7(X0)) = sK7(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_68,c_82]) ).
tcf(c_5820,plain,
( ( sK2 = nil )
| ( cons(sK8(sK2),sK7(sK2)) = sK2 ) ),
inference(superposition,[status(thm)],[c_61,c_70]) ).
tcf(c_5832,plain,
cons(sK8(sK2),sK7(sK2)) = sK2,
inference(forward_subsumption_resolution,[status(thm)],[c_5820,c_51]) ).
tcf(c_5954,plain,
( ( sK2 = nil )
| ( app(nil,sK7(sK2)) = sK7(sK2) ) ),
inference(superposition,[status(thm)],[c_61,c_5335]) ).
tcf(c_5966,plain,
app(nil,sK7(sK2)) = sK7(sK2),
inference(forward_subsumption_resolution,[status(thm)],[c_5954,c_51]) ).
tcf(c_6029,plain,
( frontsegP(sK7(sK2),nil)
| ~ ssList(nil)
| ~ ssList(sK7(sK2)) ),
inference(superposition,[status(thm)],[c_5966,c_320]) ).
tcf(c_6031,plain,
( frontsegP(sK7(sK2),nil)
| ~ ssList(sK7(sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6029,c_88]) ).
tcf(c_6124,plain,
( ssList(sK7(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_68]) ).
tcf(c_6125,plain,
( segmentP(sK2,sK2)
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_117]) ).
tcf(c_6126,plain,
( ( sK2 = sK2 )
| ~ ssList(sK2)
| ~ equalelemsP(sK2)
| ~ segmentP(sK2,sK2)
| ~ frontsegP(sK3,sK2) ),
inference(instantiation,[status(thm)],[c_1530]) ).
tcf(c_6127,plain,
( ssItem(sK8(sK2))
| ( sK2 = nil )
| ~ ssList(sK2) ),
inference(instantiation,[status(thm)],[c_69]) ).
tcf(c_7064,plain,
! [X0: $i] :
( ssList(cons(sK8(sK2),X0))
| ~ ssList(X0)
| ~ ssItem(sK8(sK2)) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_7068,plain,
! [X0: $i,X1: $i] :
( memberP(X0,sK4(sK8(sK2),X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK8(sK2))
| ( app(app(X0,cons(sK8(sK2),nil)),X1) != sK2 ) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_7069,plain,
! [X0: $i,X1: $i] :
( ssItem(sK4(sK8(sK2),X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK8(sK2))
| ( app(app(X0,cons(sK8(sK2),nil)),X1) != sK2 ) ),
inference(instantiation,[status(thm)],[c_57]) ).
tcf(c_7074,plain,
( ssList(cons(sK8(sK2),nil))
| ~ ssList(nil)
| ~ ssItem(sK8(sK2)) ),
inference(instantiation,[status(thm)],[c_7064]) ).
tcf(c_7117,plain,
! [X0: $i] :
( frontsegP(sK2,cons(sK8(sK2),X0))
| ~ ssList(X0)
| ~ ssItem(sK8(sK2))
| ~ ssList(sK7(sK2))
| ~ frontsegP(sK7(sK2),X0) ),
inference(superposition,[status(thm)],[c_5832,c_103]) ).
tcf(c_7172,plain,
( frontsegP(sK2,cons(sK8(sK2),nil))
| ~ ssList(nil)
| ~ ssItem(sK8(sK2))
| ~ ssList(sK7(sK2))
| ~ frontsegP(sK7(sK2),nil) ),
inference(instantiation,[status(thm)],[c_7117]) ).
tcf(c_13116,plain,
! [X0: $i] :
( ( app(app(X0,cons(sK8(sK2),nil)),sK11(sK2,app(X0,cons(sK8(sK2),nil)))) = sK2 )
| ~ ssList(sK2)
| ~ ssList(app(X0,cons(sK8(sK2),nil)))
| ~ frontsegP(sK2,app(X0,cons(sK8(sK2),nil))) ),
inference(instantiation,[status(thm)],[c_112]) ).
tcf(c_13118,plain,
( ( app(app(nil,cons(sK8(sK2),nil)),sK11(sK2,app(nil,cons(sK8(sK2),nil)))) = sK2 )
| ~ ssList(sK2)
| ~ ssList(app(nil,cons(sK8(sK2),nil)))
| ~ frontsegP(sK2,app(nil,cons(sK8(sK2),nil))) ),
inference(instantiation,[status(thm)],[c_13116]) ).
tcf(c_15966,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(sK8(sK2),X0)))
| ~ ssList(X1)
| ~ ssList(cons(sK8(sK2),X0)) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_15967,plain,
( ssList(app(nil,cons(sK8(sK2),nil)))
| ~ ssList(nil)
| ~ ssList(cons(sK8(sK2),nil)) ),
inference(instantiation,[status(thm)],[c_15966]) ).
tcf(c_29261,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(sK2,app(X0,cons(sK8(sK2),nil)))
| ~ frontsegP(X2,X1)
| ( sK2 != X2 )
| ( app(X0,cons(sK8(sK2),nil)) != X1 ) ),
inference(instantiation,[status(thm)],[c_3718]) ).
tcf(c_30595,plain,
! [X0: $i] :
( ssList(sK11(sK2,app(X0,cons(sK8(sK2),nil))))
| ~ ssList(sK2)
| ~ ssList(app(X0,cons(sK8(sK2),nil)))
| ~ frontsegP(sK2,app(X0,cons(sK8(sK2),nil))) ),
inference(instantiation,[status(thm)],[c_111]) ).
tcf(c_30596,plain,
( ssList(sK11(sK2,app(nil,cons(sK8(sK2),nil))))
| ~ ssList(sK2)
| ~ ssList(app(nil,cons(sK8(sK2),nil)))
| ~ frontsegP(sK2,app(nil,cons(sK8(sK2),nil))) ),
inference(instantiation,[status(thm)],[c_30595]) ).
tcf(c_63374,plain,
! [X0: $i,X1: $i] :
( frontsegP(sK2,app(X0,cons(sK8(sK2),nil)))
| ~ frontsegP(sK2,X1)
| ( sK2 != sK2 )
| ( app(X0,cons(sK8(sK2),nil)) != X1 ) ),
inference(instantiation,[status(thm)],[c_29261]) ).
tcf(c_63537,plain,
! [X0: $i,X1: $i] :
( ( app(nil,cons(X0,X1)) = cons(X0,X1) )
| ~ ssList(cons(X0,X1)) ),
inference(instantiation,[status(thm)],[c_82]) ).
tcf(c_82159,plain,
( frontsegP(sK2,app(nil,cons(sK8(sK2),nil)))
| ~ frontsegP(sK2,cons(sK8(sK2),nil))
| ( sK2 != sK2 )
| ( app(nil,cons(sK8(sK2),nil)) != cons(sK8(sK2),nil) ) ),
inference(instantiation,[status(thm)],[c_63374]) ).
tcf(c_82160,plain,
( ( app(nil,cons(sK8(sK2),nil)) = cons(sK8(sK2),nil) )
| ~ ssList(cons(sK8(sK2),nil)) ),
inference(instantiation,[status(thm)],[c_63537]) ).
tcf(c_130049,plain,
! [X0: $i] :
( memberP(X0,sK4(sK8(sK2),X0,sK11(sK2,app(X0,cons(sK8(sK2),nil)))))
| ~ ssList(X0)
| ~ ssItem(sK8(sK2))
| ~ ssList(sK11(sK2,app(X0,cons(sK8(sK2),nil))))
| ( app(app(X0,cons(sK8(sK2),nil)),sK11(sK2,app(X0,cons(sK8(sK2),nil)))) != sK2 ) ),
inference(instantiation,[status(thm)],[c_7068]) ).
tcf(c_130051,plain,
! [X0: $i] :
( ssItem(sK4(sK8(sK2),X0,sK11(sK2,app(X0,cons(sK8(sK2),nil)))))
| ~ ssList(X0)
| ~ ssItem(sK8(sK2))
| ~ ssList(sK11(sK2,app(X0,cons(sK8(sK2),nil))))
| ( app(app(X0,cons(sK8(sK2),nil)),sK11(sK2,app(X0,cons(sK8(sK2),nil)))) != sK2 ) ),
inference(instantiation,[status(thm)],[c_7069]) ).
tcf(c_130053,plain,
( ssItem(sK4(sK8(sK2),nil,sK11(sK2,app(nil,cons(sK8(sK2),nil)))))
| ~ ssList(nil)
| ~ ssItem(sK8(sK2))
| ~ ssList(sK11(sK2,app(nil,cons(sK8(sK2),nil))))
| ( app(app(nil,cons(sK8(sK2),nil)),sK11(sK2,app(nil,cons(sK8(sK2),nil)))) != sK2 ) ),
inference(instantiation,[status(thm)],[c_130051]) ).
tcf(c_130055,plain,
( memberP(nil,sK4(sK8(sK2),nil,sK11(sK2,app(nil,cons(sK8(sK2),nil)))))
| ~ ssList(nil)
| ~ ssItem(sK8(sK2))
| ~ ssList(sK11(sK2,app(nil,cons(sK8(sK2),nil))))
| ( app(app(nil,cons(sK8(sK2),nil)),sK11(sK2,app(nil,cons(sK8(sK2),nil)))) != sK2 ) ),
inference(instantiation,[status(thm)],[c_130049]) ).
tcf(c_137251,plain,
( ~ ssItem(sK4(sK8(sK2),nil,sK11(sK2,app(nil,cons(sK8(sK2),nil)))))
| ~ memberP(nil,sK4(sK8(sK2),nil,sK11(sK2,app(nil,cons(sK8(sK2),nil))))) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_137252,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_137251,c_130055,c_130053,c_82160,c_82159,c_30596,c_15967,c_13118,c_7172,c_7074,c_6127,c_6126,c_6125,c_6124,c_6031,c_51,c_49,c_88,c_50,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC244+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 17:13:19 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 53.43/9.28 % SZS status Started for theBenchmark.p
% 53.43/9.28 % SZS status Theorem for theBenchmark.p
% 53.43/9.28
% 53.43/9.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 53.43/9.28
% 53.43/9.28 % ------ iProver source info
% 53.43/9.28
% 53.43/9.28 % git: date: 2026-07-19 20:42:38 +0200
% 53.43/9.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 53.43/9.28 % git: non_committed_changes: false
% 53.43/9.28
% 53.43/9.28 % ------ Parsing...
% 53.43/9.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 53.43/9.28
% 53.43/9.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 53.43/9.28
% 53.43/9.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 53.43/9.28
% 53.43/9.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 53.43/9.28 % ------ Proving...
% 53.43/9.28 % ------ Problem Properties
% 53.43/9.28
% 53.43/9.28 %
% 53.43/9.28 % clauses 87
% 53.43/9.28 % conjectures 10
% 53.43/9.28 % EPR 33
% 53.43/9.28 % Horn 76
% 53.43/9.28 % unary 13
% 53.43/9.28 % binary 10
% 53.43/9.28 % lits 317
% 53.43/9.28 % lits eq 46
% 53.43/9.28 % fd_pure 0
% 53.43/9.28 % fd_pseudo 0
% 53.43/9.28 % fd_cond 7
% 53.43/9.28 % fd_pseudo_cond 11
% 53.43/9.28 % AC symbols 0
% 53.43/9.28
% 53.43/9.28 % ------ Schedule dynamic 5 is on
% 53.43/9.28
% 53.43/9.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 53.43/9.28
% 53.43/9.28
% 53.43/9.28 % ------
% 53.43/9.28 % Current options:
% 53.43/9.28 % ------
% 53.43/9.28
% 53.43/9.28
% 53.43/9.28 %
% 53.43/9.28
% 53.43/9.28 % ------ Proving...
% 53.43/9.28 %
% 53.43/9.28
% 53.43/9.28 % SZS status Theorem for theBenchmark.p
% 53.43/9.28
% 53.43/9.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 53.43/9.28
% 53.43/9.28
%------------------------------------------------------------------------------