%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC022+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 : 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 03:07:33 PM UTC 2026
% Result : Theorem 1.90s 1.70s
% Output : CNFRefutation 1.90s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f548ERROR: Could not build tree for root c_20996ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax42) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax45) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax76) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax78) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& hd(X3) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| 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)
| ~ neq(X1,nil) )
& ( ? [X5] :
( ? [X6] :
( neq(nil,X3)
& hd(X3) = X6
& cons(X6,nil) = X5
& ssItem(X6) )
& X2 != X5
& ssList(X5) )
| ? [X4] :
( frontsegP(X0,X4)
& frontsegP(X1,X4)
& neq(X4,nil)
& ssList(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f126]) ).
fof(f153,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f157,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(ennf_transformation,[],[f45]) ).
fof(f188,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(ennf_transformation,[],[f76]) ).
fof(f189,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ),
inference(flattening,[],[f188]) ).
fof(f192,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(ennf_transformation,[],[f78]) ).
fof(f193,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(flattening,[],[f192]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ! [X5] :
( ! [X6] :
( ~ neq(nil,X3)
| hd(X3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| X2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ frontsegP(X0,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& 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)
& neq(X1,nil) )
| ( ! [X5] :
( ! [X6] :
( ~ neq(nil,X3)
| hd(X3) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| X2 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ frontsegP(X0,X4)
| ~ frontsegP(X1,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f291,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ( tl(X0) = sK52(X0)
& ssList(sK52(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(X1,sK52(X0))],[f189]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ~ neq(sK56,nil)
& neq(sK54,nil) )
| ( ! [X5] :
( ! [X6] :
( ~ neq(nil,sK56)
| hd(sK56) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6) )
| sK55 = X5
| ~ ssList(X5) )
& ! [X4] :
( ~ frontsegP(sK53,X4)
| ~ frontsegP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) )
& neq(sK54,nil) ) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
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(f390,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f423,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f428,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[],[f157]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK52(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f472,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(sK52(X0)) ),
inference(cnf_transformation,[],[f291]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
! [X6,X5] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK55 = X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
! [X6,X5] :
( neq(sK54,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK55 = X5
| ~ ssList(X5) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
! [X4] :
( ~ neq(sK56,nil)
| ~ frontsegP(sK53,X4)
| ~ frontsegP(sK54,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
! [X4] :
( ~ neq(sK56,nil)
| ~ frontsegP(sK55,X4)
| ~ frontsegP(sK56,X4)
| ~ neq(X4,nil)
| ~ ssList(X4) ),
inference(definition_unfolding,[],[f502,f507,f506]) ).
fof(f512,plain,
! [X6,X5] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| sK55 = X5
| ~ ssList(X5) ),
inference(definition_unfolding,[],[f501,f507]) ).
fof(f513,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f507]) ).
fof(f514,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f542,plain,
! [X6] :
( neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| ~ ssItem(X6)
| cons(X6,nil) = sK55
| ~ ssList(cons(X6,nil)) ),
inference(equality_resolution,[],[f512]) ).
fof(f543,plain,
( neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f542]) ).
fof(f544,plain,
! [X6] :
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| hd(sK56) != X6
| ~ ssItem(X6)
| cons(X6,nil) = sK55
| ~ ssList(cons(X6,nil)) ),
inference(equality_resolution,[],[f500]) ).
fof(f545,plain,
( ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| sK55 = cons(hd(sK56),nil)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(equality_resolution,[],[f544]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f548]) ).
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_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f390]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_175,plain,
! [X0: $i] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f423]) ).
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,[],[f550]) ).
tcf(c_180,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f428]) ).
tcf(c_221,plain,
! [X0: $i] :
( ssList(sK52(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f472]) ).
tcf(c_222,plain,
! [X0: $i] :
( ( X0 = nil )
| ( tl(X0) = sK52(X0) )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f471]) ).
tcf(c_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f553]) ).
tcf(c_248,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(sK56,nil)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_249,negated_conjecture,
( neq(sK56,nil)
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(cnf_transformation,[],[f543]) ).
tcf(c_250,negated_conjecture,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(cnf_transformation,[],[f545]) ).
tcf(c_253,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f513]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f514]) ).
tcf(c_382,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0) ),
inference(global_subsumption_just,[status(thm)],[c_248,c_246,c_248]) ).
tcf(c_383,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0)
| ~ neq(X0,nil) ),
inference(renaming,[status(thm)],[c_382]) ).
tcf(c_384,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_246]) ).
tcf(c_386,plain,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_387,negated_conjecture,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(renaming,[status(thm)],[c_386]) ).
tcf(c_3237,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK55,X1)
| ~ frontsegP(sK56,X1)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_383]) ).
tcf(c_3238,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0) ),
inference(unflattening,[status(thm)],[c_3237]) ).
tcf(c_3240,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ frontsegP(sK56,X0)
| ~ frontsegP(sK55,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3238,c_141,c_3238]) ).
tcf(c_3241,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0) ),
inference(renaming,[status(thm)],[c_3240]) ).
tcf(c_3259,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( X1 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_387]) ).
tcf(c_3260,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(unflattening,[status(thm)],[c_3259]) ).
tcf(c_3261,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3260,c_253,c_141,c_3260]) ).
tcf(c_3279,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_384]) ).
tcf(c_3280,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3279]) ).
tcf(c_3281,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3280,c_141,c_3280]) ).
tcf(c_3286,plain,
( ( cons(hd(sK56),nil) = sK55 )
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3261,c_3281]) ).
tcf(c_8923,definition,
iPr_def_10 = hd(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8924,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8926,plain,
( ( iPr_def_11 = sK55 )
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3286,c_8923,c_8924]) ).
tcf(c_8927,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3281]) ).
tcf(c_8928,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(sK55,X0)
| ~ frontsegP(sK56,X0) ),
inference(demodulation,[status(thm)],[c_3241]) ).
tcf(c_8929,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8930,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_11842,plain,
( ( nil = sK55 )
| ~ ssList(sK55)
| ~ frontsegP(sK56,sK55) ),
inference(superposition,[status(thm)],[c_175,c_8928]) ).
tcf(c_11845,plain,
( ( nil = sK55 )
| ~ frontsegP(sK56,sK55) ),
inference(forward_subsumption_resolution,[status(thm)],[c_11842,c_8929]) ).
tcf(c_12267,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8924,c_140]) ).
tcf(c_12270,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12267,c_141]) ).
tcf(c_12306,plain,
( ssItem(iPr_def_10)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8923,c_149]) ).
tcf(c_12307,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12306,c_8927,c_8930]) ).
tcf(c_12312,plain,
( ( sK55 = iPr_def_11 )
| ~ ssList(iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8926,c_12307]) ).
tcf(c_12318,plain,
sK55 = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_12312,c_12270,c_12307,c_12312]) ).
tcf(c_12324,plain,
( ( nil = iPr_def_11 )
| ~ frontsegP(sK56,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_11845,c_12318]) ).
tcf(c_13330,plain,
( ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ( nil != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_8924,c_142]) ).
tcf(c_13331,plain,
nil != iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_13330,c_141,c_12307]) ).
tcf(c_13332,plain,
~ frontsegP(sK56,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_12324,c_13331]) ).
tcf(c_14564,plain,
( ( nil = sK56 )
| ( tl(sK56) = sK52(sK56) ) ),
inference(superposition,[status(thm)],[c_8930,c_222]) ).
tcf(c_14568,plain,
tl(sK56) = sK52(sK56),
inference(forward_subsumption_resolution,[status(thm)],[c_14564,c_8927]) ).
tcf(c_14888,plain,
( ssList(tl(sK56))
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_14568,c_221]) ).
tcf(c_14889,plain,
ssList(tl(sK56)),
inference(forward_subsumption_resolution,[status(thm)],[c_14888,c_8927,c_8930]) ).
tcf(c_15995,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8930,c_224]) ).
tcf(c_16000,plain,
( ( nil = sK56 )
| ( cons(iPr_def_10,tl(sK56)) = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_15995,c_8923]) ).
tcf(c_16001,plain,
cons(iPr_def_10,tl(sK56)) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_16000,c_8927]) ).
tcf(c_20305,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(superposition,[status(thm)],[c_8924,c_177]) ).
tcf(c_20315,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20305,c_141,c_12307]) ).
tcf(c_20984,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_10,X0),iPr_def_11)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_20315,c_180,c_20315]) ).
tcf(c_20992,plain,
( frontsegP(sK56,iPr_def_11)
| ~ ssList(tl(sK56)) ),
inference(superposition,[status(thm)],[c_16001,c_20984]) ).
tcf(c_20996,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_20992,c_13332,c_14889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC022+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n018.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 15:59:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 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
% 0.12/0.40
% 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...
% 1.90/1.70 % SZS status Started for theBenchmark.p
% 1.90/1.70 % SZS status Theorem for theBenchmark.p
% 1.90/1.70
% 1.90/1.70 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.90/1.70
% 1.90/1.70 % ------ iProver source info
% 1.90/1.70
% 1.90/1.70 % git: date: 2026-07-19 20:42:38 +0200
% 1.90/1.70 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.90/1.70 % git: non_committed_changes: false
% 1.90/1.70
% 1.90/1.70 % ------ Parsing...
% 1.90/1.70 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.90/1.70
% 1.90/1.70 % ------ 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: 5 0s sf_e pe_s pe_e %
% 1.90/1.70
% 1.90/1.70 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.90/1.70
% 1.90/1.70 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.90/1.70 % ------ Proving...
% 1.90/1.70 % ------ Problem Properties
% 1.90/1.70
% 1.90/1.70 %
% 1.90/1.70 % clauses 188
% 1.90/1.70 % conjectures 2
% 1.90/1.70 % EPR 55
% 1.90/1.70 % Horn 120
% 1.90/1.70 % unary 21
% 1.90/1.70 % binary 41
% 1.90/1.70 % lits 632
% 1.90/1.70 % lits eq 83
% 1.90/1.70 % fd_pure 0
% 1.90/1.70 % fd_pseudo 0
% 1.90/1.70 % fd_cond 22
% 1.90/1.70 % fd_pseudo_cond 14
% 1.90/1.70 % AC symbols 0
% 1.90/1.70
% 1.90/1.70 % ------ Schedule dynamic 5 is on
% 1.90/1.70
% 1.90/1.70 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.90/1.70
% 1.90/1.70
% 1.90/1.70 % ------
% 1.90/1.70 % Current options:
% 1.90/1.70 % ------
% 1.90/1.70
% 1.90/1.70
% 1.90/1.70 %
% 1.90/1.70
% 1.90/1.70 % ------ Proving...
% 1.90/1.70 %
% 1.90/1.70
% 1.90/1.70 % SZS status Theorem for theBenchmark.p
% 1.90/1.70
% 1.90/1.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.90/1.71
% 1.90/1.71
%------------------------------------------------------------------------------