%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC224+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 : n007.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 03:08:56 PM UTC 2026
% Result : Theorem 105.64s 17.44s
% Output : CNFRefutation 105.64s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f552ERROR: Could not build tree for root c_334931ERROR: 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(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(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax58) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssList(X8)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X8
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(X2,X8) != X3 ) )
| ? [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
| 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)
=> ( ( nil = X2
& nil != X3 )
| ! [X8] :
( ssList(X8)
=> ( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X8
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(X2,X8) != X3 ) )
| ? [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
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f101,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f123,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(ennf_transformation,[],[f20]) ).
fof(f124,plain,
! [X0] :
( ~ ssList(X0)
| ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ),
inference(flattening,[],[f123]) ).
fof(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
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(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(X11,cons(X9,nil)) != X2
| ~ ssList(X11) )
| app(cons(X9,nil),X10) != X8
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& ! [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
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( nil != X2
| nil = X3 )
& ? [X8] :
( ssList(X8)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(X11,cons(X9,nil)) != X2
| ~ ssList(X11) )
| app(cons(X9,nil),X10) != X8
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(X2)
& app(X2,X8) = X3 )
& ! [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
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f240,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,[],[f101]) ).
fof(f241,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,[],[f240]) ).
fof(f242,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))],[f241]) ).
fof(f274,plain,
! [X0] :
( ~ ssList(X0)
| ( cons(sK50(X0),sK49(X0)) = X0
& ssItem(sK50(X0))
& ssList(sK49(X0)) )
| nil = X0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49,sK50]),skolemize(X1,sK49(X0)),skolemize(X2,sK50(X0))],[f124]) ).
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)
& ( nil != sK55
| nil = sK56 )
& ssList(sK58)
& ! [X9] :
( ! [X10] :
( ! [X11] :
( app(X11,cons(X9,nil)) != sK55
| ~ ssList(X11) )
| app(cons(X9,nil),X10) != sK58
| ~ ssList(X10) )
| ~ ssItem(X9) )
& equalelemsP(sK55)
& sK56 = app(sK55,sK58)
& ! [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
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57(X4,X5,X6)),skolemize(X8,sK58)],[f222]) ).
fof(f309,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| app(X1,sK11(X0,X1)) = X0 ),
inference(cnf_transformation,[],[f242]) ).
fof(f310,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ssList(sK11(X0,X1)) ),
inference(cnf_transformation,[],[f242]) ).
fof(f311,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f242]) ).
fof(f388,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f393,plain,
! [X0] :
( ~ ssList(X0)
| cons(sK50(X0),sK49(X0)) = X0
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f394,plain,
! [X0] :
( ~ ssList(X0)
| ssItem(sK50(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f395,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK49(X0))
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f401,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
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(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f505,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(f509,plain,
! [X6,X4,X5] :
( memberP(X5,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK53
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
nil != sK53,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
nil != sK55,
inference(definition_unfolding,[],[f510,f511]) ).
fof(f514,plain,
! [X6,X4,X5] :
( memberP(X5,sK57(X4,X5,X6))
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f509,f511]) ).
fof(f518,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,[],[f505,f511]) ).
fof(f520,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f511]) ).
fof(f524,plain,
! [X2,X1] :
( ~ ssList(app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X2)
| frontsegP(app(X1,X2),X1) ),
inference(equality_resolution,[],[f311]) ).
fof(f540,plain,
( ~ ssList(nil)
| segmentP(nil,nil) ),
inference(equality_resolution,[],[f444]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f524]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( ssList(sK11(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ( app(X1,sK11(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f309]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f388]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_145,plain,
! [X0: $i] :
( ssList(sK49(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_146,plain,
! [X0: $i] :
( ssItem(sK50(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f394]) ).
tcf(c_147,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(sK50(X0),sK49(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_177,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f552]) ).
tcf(c_195,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f540]) ).
tcf(c_196,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[],[f443]) ).
tcf(c_246,negated_conjecture,
nil != sK55,
inference(cnf_transformation,[],[f513]) ).
tcf(c_247,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X0,sK57(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_251,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,[],[f518]) ).
tcf(c_260,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f520]) ).
tcf(c_310,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ segmentP(nil,nil) ),
inference(instantiation,[status(thm)],[c_196]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_61,c_153,c_61]) ).
tcf(c_9097,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_260]) ).
tcf(c_9103,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(demodulation,[status(thm)],[c_251]) ).
tcf(c_9107,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X0,sK57(X1,X0,X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_9108,negated_conjecture,
nil != sK55,
inference(demodulation,[status(thm)],[c_246]) ).
tcf(c_9109,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_9111,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_14135,plain,
! [X0: $i] :
( ( nil = sK55 )
| ( sK55 != X0 )
| ( nil != X0 ) ),
inference(instantiation,[status(thm)],[c_9111]) ).
tcf(c_14136,plain,
( ( nil = sK55 )
| ( sK55 != nil )
| ( nil != nil ) ),
inference(instantiation,[status(thm)],[c_14135]) ).
tcf(c_14722,plain,
( ssItem(sK50(sK55))
| ( sK55 = nil )
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_146]) ).
tcf(c_14723,plain,
( ssList(sK49(sK55))
| ( sK55 = nil )
| ~ ssList(sK55) ),
inference(instantiation,[status(thm)],[c_145]) ).
tcf(c_15527,plain,
( ( nil = sK55 )
| ( cons(sK50(sK55),sK49(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_9097,c_147]) ).
tcf(c_15534,plain,
cons(sK50(sK55),sK49(sK55)) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_15527,c_9108]) ).
tcf(c_20246,plain,
! [X0: $i] :
( frontsegP(sK55,cons(sK50(sK55),X0))
| ~ ssList(X0)
| ~ ssList(sK49(sK55))
| ~ ssItem(sK50(sK55))
| ~ frontsegP(sK49(sK55),X0) ),
inference(superposition,[status(thm)],[c_15534,c_177]) ).
tcf(c_20328,plain,
( frontsegP(sK55,cons(sK50(sK55),nil))
| ~ ssList(nil)
| ~ ssList(sK49(sK55))
| ~ ssItem(sK50(sK55))
| ~ frontsegP(sK49(sK55),nil) ),
inference(instantiation,[status(thm)],[c_20246]) ).
tcf(c_23494,plain,
! [X0: $i] :
( ssList(cons(sK50(sK55),X0))
| ~ ssList(X0)
| ~ ssItem(sK50(sK55)) ),
inference(instantiation,[status(thm)],[c_140]) ).
tcf(c_23509,plain,
( ssList(cons(sK50(sK55),nil))
| ~ ssList(nil)
| ~ ssItem(sK50(sK55)) ),
inference(instantiation,[status(thm)],[c_23494]) ).
tcf(c_26025,plain,
sK55 = sK55,
inference(instantiation,[status(thm)],[c_9109]) ).
tcf(c_31824,plain,
! [X0: $i,X1: $i] :
( ssItem(sK57(X1,X0,sK11(sK55,app(X0,cons(X1,nil)))))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(sK11(sK55,app(X0,cons(X1,nil))))
| ( app(app(X0,cons(X1,nil)),sK11(sK55,app(X0,cons(X1,nil)))) != sK55 ) ),
inference(instantiation,[status(thm)],[c_9103]) ).
tcf(c_38450,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(X0,nil)))
| ~ ssList(X1)
| ~ ssList(cons(X0,nil)) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_38859,plain,
! [X0: $i] :
( ssItem(sK57(sK50(sK55),X0,sK11(sK55,app(X0,cons(sK50(sK55),nil)))))
| ~ ssList(X0)
| ~ ssItem(sK50(sK55))
| ~ ssList(sK11(sK55,app(X0,cons(sK50(sK55),nil))))
| ( app(app(X0,cons(sK50(sK55),nil)),sK11(sK55,app(X0,cons(sK50(sK55),nil)))) != sK55 ) ),
inference(instantiation,[status(thm)],[c_31824]) ).
tcf(c_38860,plain,
( ssItem(sK57(sK50(sK55),nil,sK11(sK55,app(nil,cons(sK50(sK55),nil)))))
| ~ ssList(nil)
| ~ ssItem(sK50(sK55))
| ~ ssList(sK11(sK55,app(nil,cons(sK50(sK55),nil))))
| ( app(app(nil,cons(sK50(sK55),nil)),sK11(sK55,app(nil,cons(sK50(sK55),nil)))) != sK55 ) ),
inference(instantiation,[status(thm)],[c_38859]) ).
tcf(c_57423,plain,
! [X0: $i] :
( ssList(sK11(sK55,app(X0,cons(sK50(sK55),nil))))
| ~ ssList(sK55)
| ~ ssList(app(X0,cons(sK50(sK55),nil)))
| ~ frontsegP(sK55,app(X0,cons(sK50(sK55),nil))) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_57424,plain,
( ssList(sK11(sK55,app(nil,cons(sK50(sK55),nil))))
| ~ ssList(sK55)
| ~ ssList(app(nil,cons(sK50(sK55),nil)))
| ~ frontsegP(sK55,app(nil,cons(sK50(sK55),nil))) ),
inference(instantiation,[status(thm)],[c_57423]) ).
tcf(c_77939,plain,
! [X0: $i] :
( ssList(app(X0,cons(sK50(sK55),nil)))
| ~ ssList(X0)
| ~ ssList(cons(sK50(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_38450]) ).
tcf(c_77944,plain,
( ssList(app(nil,cons(sK50(sK55),nil)))
| ~ ssList(nil)
| ~ ssList(cons(sK50(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_77939]) ).
tcf(c_102458,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(nil,sK49(X0)) = sK49(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_145,c_155]) ).
tcf(c_106035,plain,
( ( nil = sK55 )
| ( app(nil,sK49(sK55)) = sK49(sK55) ) ),
inference(superposition,[status(thm)],[c_9097,c_102458]) ).
tcf(c_106041,plain,
app(nil,sK49(sK55)) = sK49(sK55),
inference(forward_subsumption_resolution,[status(thm)],[c_106035,c_9108]) ).
tcf(c_107049,plain,
( frontsegP(sK49(sK55),nil)
| ~ ssList(nil)
| ~ ssList(sK49(sK55)) ),
inference(superposition,[status(thm)],[c_106041,c_389]) ).
tcf(c_107052,plain,
( frontsegP(sK49(sK55),nil)
| ~ ssList(sK49(sK55)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_107049,c_141]) ).
tcf(c_194341,plain,
! [X0: $i] :
( ( app(app(X0,cons(sK50(sK55),nil)),sK11(sK55,app(X0,cons(sK50(sK55),nil)))) = sK55 )
| ~ ssList(sK55)
| ~ ssList(app(X0,cons(sK50(sK55),nil)))
| ~ frontsegP(sK55,app(X0,cons(sK50(sK55),nil))) ),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_194343,plain,
( ( app(app(nil,cons(sK50(sK55),nil)),sK11(sK55,app(nil,cons(sK50(sK55),nil)))) = sK55 )
| ~ ssList(sK55)
| ~ ssList(app(nil,cons(sK50(sK55),nil)))
| ~ frontsegP(sK55,app(nil,cons(sK50(sK55),nil))) ),
inference(instantiation,[status(thm)],[c_194341]) ).
tcf(c_197148,plain,
! [X0: $i,X1: $i] :
( memberP(X0,sK57(X1,X0,sK11(sK55,app(X0,cons(X1,nil)))))
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(sK11(sK55,app(X0,cons(X1,nil))))
| ( app(app(X0,cons(X1,nil)),sK11(sK55,app(X0,cons(X1,nil)))) != sK55 ) ),
inference(instantiation,[status(thm)],[c_9107]) ).
tcf(c_198982,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(sK55,app(X0,cons(X1,nil)))
| ~ frontsegP(X3,X2)
| ( sK55 != X3 )
| ( app(X0,cons(X1,nil)) != X2 ) ),
inference(instantiation,[status(thm)],[c_9118]) ).
tcf(c_200423,plain,
! [X0: $i] :
( ( app(nil,cons(X0,nil)) = cons(X0,nil) )
| ~ ssList(cons(X0,nil)) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_207137,plain,
! [X0: $i] :
( memberP(X0,sK57(sK50(sK55),X0,sK11(sK55,app(X0,cons(sK50(sK55),nil)))))
| ~ ssList(X0)
| ~ ssItem(sK50(sK55))
| ~ ssList(sK11(sK55,app(X0,cons(sK50(sK55),nil))))
| ( app(app(X0,cons(sK50(sK55),nil)),sK11(sK55,app(X0,cons(sK50(sK55),nil)))) != sK55 ) ),
inference(instantiation,[status(thm)],[c_197148]) ).
tcf(c_207142,plain,
( memberP(nil,sK57(sK50(sK55),nil,sK11(sK55,app(nil,cons(sK50(sK55),nil)))))
| ~ ssList(nil)
| ~ ssItem(sK50(sK55))
| ~ ssList(sK11(sK55,app(nil,cons(sK50(sK55),nil))))
| ( app(app(nil,cons(sK50(sK55),nil)),sK11(sK55,app(nil,cons(sK50(sK55),nil)))) != sK55 ) ),
inference(instantiation,[status(thm)],[c_207137]) ).
tcf(c_224314,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(sK55,app(X0,cons(X1,nil)))
| ~ frontsegP(sK55,X2)
| ( sK55 != sK55 )
| ( app(X0,cons(X1,nil)) != X2 ) ),
inference(instantiation,[status(thm)],[c_198982]) ).
tcf(c_229452,plain,
( ( app(nil,cons(sK50(sK55),nil)) = cons(sK50(sK55),nil) )
| ~ ssList(cons(sK50(sK55),nil)) ),
inference(instantiation,[status(thm)],[c_200423]) ).
tcf(c_310075,plain,
( frontsegP(sK55,app(nil,cons(sK50(sK55),nil)))
| ~ frontsegP(sK55,cons(sK50(sK55),nil))
| ( sK55 != sK55 )
| ( app(nil,cons(sK50(sK55),nil)) != cons(sK50(sK55),nil) ) ),
inference(instantiation,[status(thm)],[c_224314]) ).
tcf(c_334930,plain,
( ~ ssItem(sK57(sK50(sK55),nil,sK11(sK55,app(nil,cons(sK50(sK55),nil)))))
| ~ memberP(nil,sK57(sK50(sK55),nil,sK11(sK55,app(nil,cons(sK50(sK55),nil))))) ),
inference(instantiation,[status(thm)],[c_171]) ).
tcf(c_334931,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_334930,c_310075,c_229452,c_207142,c_194343,c_107052,c_77944,c_57424,c_38860,c_26025,c_23509,c_20328,c_14722,c_14723,c_14136,c_310,c_195,c_246,c_141,c_260]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC224+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.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 17:02:22 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 105.64/17.44 % SZS status Started for theBenchmark.p
% 105.64/17.44 % SZS status Theorem for theBenchmark.p
% 105.64/17.44
% 105.64/17.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 105.64/17.44
% 105.64/17.44 % ------ iProver source info
% 105.64/17.44
% 105.64/17.44 % git: date: 2026-07-19 20:42:38 +0200
% 105.64/17.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 105.64/17.44 % git: non_committed_changes: false
% 105.64/17.44
% 105.64/17.44 % ------ Parsing...
% 105.64/17.44 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 105.64/17.44
% 105.64/17.44 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 105.64/17.44
% 105.64/17.44 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 105.64/17.44
% 105.64/17.44 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 105.64/17.44 % ------ Proving...
% 105.64/17.44 % ------ Problem Properties
% 105.64/17.44
% 105.64/17.44 %
% 105.64/17.44 % clauses 193
% 105.64/17.44 % conjectures 12
% 105.64/17.44 % EPR 55
% 105.64/17.44 % Horn 125
% 105.64/17.44 % unary 23
% 105.64/17.44 % binary 40
% 105.64/17.44 % lits 655
% 105.64/17.44 % lits eq 88
% 105.64/17.44 % fd_pure 0
% 105.64/17.44 % fd_pseudo 0
% 105.64/17.44 % fd_cond 21
% 105.64/17.44 % fd_pseudo_cond 14
% 105.64/17.44 % AC symbols 0
% 105.64/17.44
% 105.64/17.44 % ------ Schedule dynamic 5 is on
% 105.64/17.44
% 105.64/17.44 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 105.64/17.44
% 105.64/17.44
% 105.64/17.44 % ------
% 105.64/17.44 % Current options:
% 105.64/17.44 % ------
% 105.64/17.44
% 105.64/17.44
% 105.64/17.44 %
% 105.64/17.44
% 105.64/17.44 % ------ Proving...
% 105.64/17.44 % Proof_search_loop: time out after: 7070 full_loop iterations
% 105.64/17.44
% 105.64/17.44 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 105.64/17.44
% 105.64/17.44
% 105.64/17.44 % ------
% 105.64/17.44 % Current options:
% 105.64/17.44 % ------
% 105.64/17.44
% 105.64/17.44
% 105.64/17.44 %
% 105.64/17.44
% 105.64/17.44 % ------ Proving...
% 105.64/17.44 %
% 105.64/17.44
% 105.64/17.44 % SZS status Theorem for theBenchmark.p
% 105.64/17.44
% 105.64/17.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 105.64/17.44
% 105.64/17.44
%------------------------------------------------------------------------------