%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC330+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 : n002.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 03:09:20 PM UTC 2026
% Result : Theorem 4.91s 2.21s
% Output : CNFRefutation 4.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 11
% Syntax : Number of formulae : 113 ( 23 unt; 1 def)
% Number of atoms : 431 ( 93 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 536 ( 218 ~; 221 |; 69 &)
% ( 2 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 163 ( 0 sgn 139 !; 24 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax53) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax54) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax55) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax56) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax73) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax74) ).
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] :
( ( equalelemsP(X0)
& segmentP(X1,X0) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( equalelemsP(X0)
& segmentP(X1,X0) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X8] :
( lt(X8,X4)
& memberP(X6,X8)
& ssItem(X8) )
| ? [X7] :
( lt(X4,X7)
& memberP(X5,X7)
& ssItem(X7) )
| app(app(X5,X2),X6) != X3
| cons(X4,nil) != X2
| ~ ssList(X6) ) ) ) )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f121,plain,
! [X0] :
( ~ ssList(X0)
| ( segmentP(nil,X0)
<=> nil = X0 ) ),
inference(ennf_transformation,[],[f58]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
inference(ennf_transformation,[],[f56]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ! [X3] :
( ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ) ) ) ),
inference(flattening,[],[f123]) ).
fof(f125,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ) ) ),
inference(ennf_transformation,[],[f53]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ) ) ),
inference(flattening,[],[f128]) ).
fof(f141,plain,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f154,plain,
( ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ( ~ equalelemsP(sK4)
| ~ segmentP(sK5,sK4) )
& ( ( nil = sK6
& nil = sK7 )
| sP0(sK6,sK7) )
& sK4 = sK6
& sK5 = sK7
& ssList(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6),skolemize(X3,sK7)],[f150]) ).
fof(f166,plain,
! [X0] :
( ~ ssList(X0)
| ( ( ~ segmentP(nil,X0)
| nil = X0 )
& ( nil != X0
| segmentP(nil,X0) ) ) ),
inference(nnf_transformation,[],[f121]) ).
fof(f182,plain,
ssList(sK4),
inference(cnf_transformation,[],[f154]) ).
fof(f183,plain,
ssList(sK5),
inference(cnf_transformation,[],[f154]) ).
fof(f185,plain,
( ~ equalelemsP(sK4)
| ~ segmentP(sK5,sK4) ),
inference(cnf_transformation,[],[f154]) ).
fof(f186,plain,
( nil = sK6
| sP0(sK6,sK7) ),
inference(cnf_transformation,[],[f154]) ).
fof(f188,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f154]) ).
fof(f189,plain,
sK5 = sK7,
inference(cnf_transformation,[],[f154]) ).
fof(f204,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f108]) ).
fof(f213,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f226,plain,
! [X0] :
( ~ ssList(X0)
| nil != X0
| segmentP(nil,X0) ),
inference(cnf_transformation,[],[f166]) ).
fof(f228,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ segmentP(X0,X1)
| segmentP(app(app(X2,X0),X3),X1) ),
inference(cnf_transformation,[],[f124]) ).
fof(f229,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(X0,X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f230,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f127]) ).
fof(f231,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| segmentP(X0,X2) ),
inference(cnf_transformation,[],[f129]) ).
fof(f244,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f245,plain,
! [X0] :
( ~ ssItem(X0)
| equalelemsP(cons(X0,nil)) ),
inference(cnf_transformation,[],[f141]) ).
fof(f256,plain,
( ~ equalelemsP(sK6)
| ~ segmentP(sK7,sK6) ),
inference(definition_unfolding,[],[f185,f189,f188,f188]) ).
fof(f257,plain,
ssList(sK7),
inference(definition_unfolding,[],[f183,f189]) ).
fof(f258,plain,
ssList(sK6),
inference(definition_unfolding,[],[f182,f188]) ).
fof(f263,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f226]) ).
tcf(c_58,negated_conjecture,
( sP0(sK6,sK7)
| ( nil = sK6 ) ),
inference(cnf_transformation,[],[f186]) ).
tcf(c_59,negated_conjecture,
( ~ equalelemsP(sK6)
| ~ segmentP(sK7,sK6) ),
inference(cnf_transformation,[],[f256]) ).
tcf(c_61,negated_conjecture,
ssList(sK7),
inference(cnf_transformation,[],[f257]) ).
tcf(c_62,negated_conjecture,
ssList(sK6),
inference(cnf_transformation,[],[f258]) ).
tcf(c_76,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_85,plain,
ssList(nil),
inference(cnf_transformation,[],[f213]) ).
tcf(c_97,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f263]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f228]) ).
tcf(c_101,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f229]) ).
tcf(c_102,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_116,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f244]) ).
tcf(c_117,plain,
! [X0: $i] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_129,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_101]) ).
tcf(c_166,plain,
segmentP(nil,nil),
inference(global_subsumption_just,[status(thm)],[c_97,c_85,c_129]) ).
tcf(c_1362,plain,
( ~ segmentP(sK7,sK6)
| ( nil != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_116]) ).
tcf(c_3211,plain,
app(sK7,nil) = sK7,
inference(superposition,[status(thm)],[c_61,c_76]) ).
tcf(c_3212,plain,
app(sK6,nil) = sK6,
inference(superposition,[status(thm)],[c_62,c_76]) ).
tcf(c_4436,plain,
! [X0: $i] :
( segmentP(sK7,sK6)
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssList(X0)
| ~ segmentP(sK7,X0)
| ~ segmentP(X0,sK6) ),
inference(instantiation,[status(thm)],[c_103]) ).
tcf(c_4439,plain,
( segmentP(sK7,sK6)
| ~ ssList(sK6)
| ~ ssList(sK7)
| ~ ssList(nil)
| ~ segmentP(sK7,nil)
| ~ segmentP(nil,sK6) ),
inference(instantiation,[status(thm)],[c_4436]) ).
tcf(c_8972,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK6,X1),X0)
| ~ ssList(sK6)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(superposition,[status(thm)],[c_3212,c_100]) ).
tcf(c_8973,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK7,X1),X0)
| ~ ssList(sK7)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(superposition,[status(thm)],[c_3211,c_100]) ).
tcf(c_9030,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK7,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8973,c_61,c_85]) ).
tcf(c_9035,plain,
! [X0: $i,X1: $i] :
( segmentP(app(sK6,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8972,c_62,c_85]) ).
tcf(c_12620,plain,
! [X0: $i] :
( segmentP(sK7,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(superposition,[status(thm)],[c_3211,c_9030]) ).
tcf(c_12624,plain,
! [X0: $i] :
( segmentP(sK7,X0)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12620,c_85]) ).
tcf(c_12646,plain,
( segmentP(sK7,nil)
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_12624]) ).
tcf(c_12657,plain,
! [X0: $i] :
( segmentP(sK6,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(superposition,[status(thm)],[c_3212,c_9035]) ).
tcf(c_12661,plain,
! [X0: $i] :
( segmentP(sK6,X0)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12657,c_85]) ).
tcf(c_12949,plain,
( segmentP(sK6,nil)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_166,c_12661]) ).
tcf(c_12952,plain,
segmentP(sK6,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_12949,c_85]) ).
tcf(c_13698,plain,
( ( nil = sK6 )
| ~ ssList(sK6)
| ~ ssList(nil)
| ~ segmentP(nil,sK6) ),
inference(superposition,[status(thm)],[c_12952,c_102]) ).
tcf(c_13699,plain,
( ( nil = sK6 )
| ~ segmentP(nil,sK6) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13698,c_62,c_85]) ).
fof(f149,definition,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f150,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ~ equalelemsP(X0)
| ~ segmentP(X1,X0) )
& ( ( nil = X2
& nil = X3 )
| sP0(X2,X3) )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(definition_folding,[],[f98,f149]) ).
fof(f151,plain,
! [X2,X3] :
( ~ sP0(X2,X3)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ! [X8] :
( ~ lt(X8,X4)
| ~ memberP(X6,X8)
| ~ ssItem(X8) )
& ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,X2),X6) = X3
& cons(X4,nil) = X2
& ssList(X6) ) ) ) ),
inference(nnf_transformation,[],[f149]) ).
fof(f152,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ? [X2] :
( ssItem(X2)
& ? [X3] :
( ssList(X3)
& ? [X4] :
( ! [X6] :
( ~ lt(X6,X2)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(X2,X5)
| ~ memberP(X3,X5)
| ~ ssItem(X5) )
& app(app(X3,X0),X4) = X1
& cons(X2,nil) = X0
& ssList(X4) ) ) ) ),
inference(rectify,[],[f151]) ).
fof(f153,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ( ssItem(sK1(X0,X1))
& ssList(sK2(X0,X1))
& ! [X6] :
( ~ lt(X6,sK1(X0,X1))
| ~ memberP(sK3(X0,X1),X6)
| ~ ssItem(X6) )
& ! [X5] :
( ~ lt(sK1(X0,X1),X5)
| ~ memberP(sK2(X0,X1),X5)
| ~ ssItem(X5) )
& app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1
& cons(sK1(X0,X1),nil) = X0
& ssList(sK3(X0,X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X2,sK1(X0,X1)),skolemize(X3,sK2(X0,X1)),skolemize(X4,sK3(X0,X1))],[f152]) ).
fof(f175,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssItem(sK1(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK2(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f153]) ).
fof(f180,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| cons(sK1(X0,X1),nil) = X0 ),
inference(cnf_transformation,[],[f153]) ).
fof(f181,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| ssList(sK3(X0,X1)) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f181]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( cons(sK1(X0,X1),nil) = X0 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f180]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f179]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_1186,plain,
! [X0: $i,X1: $i] :
( ssItem(sK1(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).
tcf(c_1187,plain,
( ssItem(sK1(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1186]) ).
tcf(c_1202,plain,
! [X0: $i,X1: $i] :
( ssList(sK2(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_58]) ).
tcf(c_1203,plain,
( ssList(sK2(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1202]) ).
tcf(c_1278,plain,
! [X0: $i,X1: $i] :
( ( nil = sK6 )
| ( app(app(sK2(X0,X1),X0),sK3(X0,X1)) = X1 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_58]) ).
tcf(c_1279,plain,
( ( nil = sK6 )
| ( app(app(sK2(sK6,sK7),sK6),sK3(sK6,sK7)) = sK7 ) ),
inference(unflattening,[status(thm)],[c_1278]) ).
tcf(c_1294,plain,
! [X0: $i,X1: $i] :
( ( nil = sK6 )
| ( cons(sK1(X0,X1),nil) = X0 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_58]) ).
tcf(c_1295,plain,
( ( nil = sK6 )
| ( cons(sK1(sK6,sK7),nil) = sK6 ) ),
inference(unflattening,[status(thm)],[c_1294]) ).
tcf(c_1310,plain,
! [X0: $i,X1: $i] :
( ssList(sK3(X0,X1))
| ( nil = sK6 )
| ( X1 != sK7 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_58]) ).
tcf(c_1311,plain,
( ssList(sK3(sK6,sK7))
| ( nil = sK6 ) ),
inference(unflattening,[status(thm)],[c_1310]) ).
tcf(c_3081,plain,
( equalelemsP(sK6)
| ( nil = sK6 )
| ~ ssItem(sK1(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1295,c_117]) ).
tcf(c_3136,plain,
( equalelemsP(sK6)
| ( nil = sK6 ) ),
inference(global_subsumption_just,[status(thm)],[c_3081,c_1187,c_3081]) ).
tcf(c_4962,negated_conjecture,
~ segmentP(sK7,sK6),
inference(global_subsumption_just,[status(thm)],[c_59,c_59,c_1362,c_3136]) ).
tcf(c_8956,plain,
! [X0: $i] :
( segmentP(sK7,X0)
| ( nil = sK6 )
| ~ ssList(sK6)
| ~ ssList(X0)
| ~ segmentP(sK6,X0)
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7)) ),
inference(superposition,[status(thm)],[c_1279,c_100]) ).
tcf(c_9138,plain,
! [X0: $i] :
( segmentP(sK7,X0)
| ( nil = sK6 )
| ~ ssList(X0)
| ~ segmentP(sK6,X0)
| ~ ssList(sK2(sK6,sK7))
| ~ ssList(sK3(sK6,sK7)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_8956,c_62]) ).
tcf(c_13712,plain,
~ segmentP(nil,sK6),
inference(global_subsumption_just,[status(thm)],[c_13699,c_62,c_61,c_85,c_129,c_4439,c_4962,c_12646]) ).
tcf(c_30403,plain,
! [X0: $i] :
( segmentP(sK7,X0)
| ( nil = sK6 )
| ~ ssList(X0)
| ~ segmentP(sK6,X0) ),
inference(global_subsumption_just,[status(thm)],[c_9138,c_1203,c_1311,c_9138]) ).
tcf(c_30414,plain,
( segmentP(sK7,sK6)
| ( nil = sK6 )
| ~ ssList(sK6) ),
inference(superposition,[status(thm)],[c_101,c_30403]) ).
tcf(c_30417,plain,
( segmentP(sK7,sK6)
| ( nil = sK6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_30414,c_62]) ).
tcf(c_30420,plain,
nil = sK6,
inference(global_subsumption_just,[status(thm)],[c_30417,c_59,c_1362,c_3136,c_30417]) ).
tcf(c_30579,plain,
~ segmentP(nil,nil),
inference(demodulation,[status(thm)],[c_13712,c_30420]) ).
tcf(c_30693,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_30579,c_166]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC330+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.38 % Computer : n002.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Thu Sep 24 17:42:19 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.42 Running first-order theorem proving
% 0.08/0.42 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
% 0.08/0.43
% 0.08/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.43
% 0.08/0.43 % Detected problem language: tptp
% 0.08/0.44 % Proving...
% 4.91/2.21 % SZS status Started for theBenchmark.p
% 4.91/2.21 % SZS status Theorem for theBenchmark.p
% 4.91/2.21
% 4.91/2.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.91/2.21
% 4.91/2.21 % ------ iProver source info
% 4.91/2.21
% 4.91/2.21 % git: date: 2026-07-19 20:42:38 +0200
% 4.91/2.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.91/2.21 % git: non_committed_changes: false
% 4.91/2.21
% 4.91/2.21 % ------ Parsing...
% 4.91/2.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.91/2.21
% 4.91/2.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e %
% 4.91/2.21
% 4.91/2.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.91/2.21
% 4.91/2.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.91/2.21 % ------ Proving...
% 4.91/2.21 % ------ Problem Properties
% 4.91/2.21
% 4.91/2.21 %
% 4.91/2.21 % clauses 80
% 4.91/2.21 % conjectures 3
% 4.91/2.21 % EPR 24
% 4.91/2.21 % Horn 59
% 4.91/2.21 % unary 9
% 4.91/2.21 % binary 19
% 4.91/2.21 % lits 270
% 4.91/2.21 % lits eq 53
% 4.91/2.21 % fd_pure 0
% 4.91/2.21 % fd_pseudo 0
% 4.91/2.21 % fd_cond 5
% 4.91/2.21 % fd_pseudo_cond 9
% 4.91/2.21 % AC symbols 0
% 4.91/2.21
% 4.91/2.21 % ------ Schedule dynamic 5 is on
% 4.91/2.21
% 4.91/2.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.91/2.21
% 4.91/2.21
% 4.91/2.21 % ------
% 4.91/2.21 % Current options:
% 4.91/2.21 % ------
% 4.91/2.21
% 4.91/2.21
% 4.91/2.21 %
% 4.91/2.21
% 4.91/2.21 % ------ Proving...
% 4.91/2.21 %
% 4.91/2.21
% 4.91/2.21 % SZS status Theorem for theBenchmark.p
% 4.91/2.21
% 4.91/2.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.91/2.21
%------------------------------------------------------------------------------