%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC421+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 : n012.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 03:09:49 PM UTC 2026
% Result : Theorem 18.48s 3.19s
% Output : CNFRefutation 18.48s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f544ERROR: Could not build tree for root c_44195ERROR: 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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ? [X7] :
( ? [X8] :
( ? [X9] :
( neq(nil,X2)
& ? [X10] :
( neq(nil,X2)
& hd(X2) = X10
& cons(X10,nil) = X9
& ssItem(X10) )
& app(X8,X9) = X7
& tl(X2) = X8
& ssList(X9) )
& ssList(X8) )
& X3 != X7
& ssList(X7) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(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)
=> ( ( ( ? [X7] :
( ? [X8] :
( ? [X9] :
( neq(nil,X2)
& ? [X10] :
( neq(nil,X2)
& hd(X2) = X10
& cons(X10,nil) = X9
& ssItem(X10) )
& app(X8,X9) = X7
& tl(X2) = X8
& ssList(X9) )
& ssList(X8) )
& X3 != X7
& ssList(X7) )
| ~ neq(X2,nil) )
& neq(X3,nil) )
| ( nil = X3
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X6,cons(X4,nil)),X5) = X0
& app(app(X5,cons(X4,nil)),X6) = X1
& ssList(X6) )
& ssList(X5) )
& ssItem(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(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(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f129]) ).
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(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(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ neq(nil,X2)
| ! [X10] :
( ~ neq(nil,X2)
| hd(X2) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10) )
| app(X8,X9) != X7
| tl(X2) != X8
| ~ ssList(X9) )
| ~ ssList(X8) )
| X3 = X7
| ~ ssList(X7) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(X6,cons(X4,nil)),X5) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(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)
& ( ( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ neq(nil,X2)
| ! [X10] :
( ~ neq(nil,X2)
| hd(X2) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10) )
| app(X8,X9) != X7
| tl(X2) != X8
| ~ ssList(X9) )
| ~ ssList(X8) )
| X3 = X7
| ~ ssList(X7) )
& neq(X2,nil) )
| ~ neq(X3,nil) )
& ( nil != X3
| nil = X2 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(X6,cons(X4,nil)),X5) != X0
| app(app(X5,cons(X4,nil)),X6) != X1
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(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(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ neq(nil,sK55)
| ! [X10] :
( ~ neq(nil,sK55)
| hd(sK55) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10) )
| app(X8,X9) != X7
| tl(sK55) != X8
| ~ ssList(X9) )
| ~ ssList(X8) )
| sK56 = X7
| ~ ssList(X7) )
& neq(sK55,nil) )
| ~ neq(sK56,nil) )
& ( nil != sK56
| nil = sK55 )
& ! [X4] :
( ! [X5] :
( ! [X6] :
( app(app(X6,cons(X4,nil)),X5) != sK53
| app(app(X5,cons(X4,nil)),X6) != sK54
| ~ ssList(X6) )
| ~ ssList(X5) )
| ~ ssItem(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(f397,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f399,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
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(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f193]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK53
| app(app(X5,cons(X4,nil)),X6) != sK54
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f508,plain,
! [X6,X4,X5] :
( app(app(X6,cons(X4,nil)),X5) != sK55
| app(app(X5,cons(X4,nil)),X6) != sK56
| ~ ssList(X6)
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f503,f506,f505]) ).
fof(f510,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f505]) ).
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,[],[f544]) ).
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_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f399]) ).
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_224,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f474]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f507]) ).
tcf(c_247,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X2,cons(X1,nil)),X0) != sK56 )
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_249,negated_conjecture,
( neq(sK55,nil)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f501]) ).
tcf(c_250,negated_conjecture,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(sK56,nil)
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(cnf_transformation,[],[f549]) ).
tcf(c_254,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f510]) ).
tcf(c_368,negated_conjecture,
neq(sK55,nil),
inference(global_subsumption_just,[status(thm)],[c_249,c_246,c_249]) ).
tcf(c_382,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil)))
| ~ ssList(cons(hd(sK55),nil))
| ~ neq(nil,sK55) ),
inference(global_subsumption_just,[status(thm)],[c_250,c_246,c_250]) ).
tcf(c_383,negated_conjecture,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil))
| ~ ssList(app(tl(sK55),cons(hd(sK55),nil))) ),
inference(renaming,[status(thm)],[c_382]) ).
tcf(c_812,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ neq(nil,sK55)
| ~ ssList(cons(hd(sK55),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_383,c_153]) ).
tcf(c_3252,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil))
| ( X1 != sK55 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_812]) ).
tcf(c_3253,plain,
( ( nil = sK55 )
| ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(sK55)
| ~ ssList(nil)
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil)) ),
inference(unflattening,[status(thm)],[c_3252]) ).
tcf(c_3254,plain,
( ( nil = sK55 )
| ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3253,c_254,c_141,c_3253]) ).
tcf(c_3284,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK55 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_368]) ).
tcf(c_3285,plain,
( ~ ssList(nil)
| ( nil != sK55 ) ),
inference(unflattening,[status(thm)],[c_3284]) ).
tcf(c_3286,plain,
nil != sK55,
inference(global_subsumption_just,[status(thm)],[c_3285,c_141,c_3285]) ).
tcf(c_3291,plain,
( ( app(tl(sK55),cons(hd(sK55),nil)) = sK56 )
| ~ ssList(tl(sK55))
| ~ ssItem(hd(sK55))
| ~ ssList(cons(hd(sK55),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3254,c_3286]) ).
tcf(c_8917,definition,
iPr_def_10 = hd(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8918,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8919,definition,
iPr_def_12 = tl(sK55),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8920,definition,
iPr_def_13 = app(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8921,plain,
( ( iPr_def_13 = sK56 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3291,c_8920,c_8919,c_8917,c_8918]) ).
tcf(c_8922,plain,
nil != sK55,
inference(demodulation,[status(thm)],[c_3286]) ).
tcf(c_8924,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_8926,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ( app(app(X2,cons(X1,nil)),X0) != sK56 )
| ( app(app(X0,cons(X1,nil)),X2) != sK55 ) ),
inference(demodulation,[status(thm)],[c_247]) ).
tcf(c_11851,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(iPr_def_10)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_11),X0) != sK55 )
| ( app(app(X0,cons(iPr_def_10,nil)),X1) != sK56 ) ),
inference(superposition,[status(thm)],[c_8918,c_8926]) ).
tcf(c_11852,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(iPr_def_10)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_11),X0) != sK55 )
| ( app(app(X0,iPr_def_11),X1) != sK56 ) ),
inference(light_normalisation,[status(thm)],[c_11851,c_8918]) ).
tcf(c_12331,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8918,c_140]) ).
tcf(c_12334,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12331,c_141]) ).
tcf(c_12368,plain,
( ( sK56 = iPr_def_13 )
| ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8921,c_12334]) ).
tcf(c_12378,plain,
( ssItem(iPr_def_10)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8917,c_149]) ).
tcf(c_12379,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12378,c_8922,c_8924]) ).
tcf(c_12380,plain,
ssList(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_12334,c_12379]) ).
tcf(c_12387,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_11),X0) != sK55 )
| ( app(app(X0,iPr_def_11),X1) != sK56 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11852,c_12379]) ).
tcf(c_12402,plain,
app(nil,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_12380,c_155]) ).
tcf(c_12424,plain,
( ssList(iPr_def_12)
| ( nil = sK55 )
| ~ ssList(sK55) ),
inference(superposition,[status(thm)],[c_8919,c_151]) ).
tcf(c_12427,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12424,c_8922,c_8924]) ).
tcf(c_12449,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(superposition,[status(thm)],[c_8920,c_153]) ).
tcf(c_12457,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12449,c_12380]) ).
tcf(c_12490,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_12457,c_12427,c_12457]) ).
tcf(c_12492,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_12490,c_232]) ).
tcf(c_12530,plain,
sK56 = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_12368,c_12368,c_12379,c_12427]) ).
tcf(c_12532,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_11),X0) != sK55 )
| ( app(app(X0,iPr_def_11),X1) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_12387,c_12530]) ).
tcf(c_12774,plain,
! [X0: $i] :
( ~ ssList(nil)
| ~ ssList(X0)
| ( app(iPr_def_11,X0) != sK55 )
| ( app(app(X0,iPr_def_11),nil) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_12402,c_12532]) ).
tcf(c_12775,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(iPr_def_11,X0) != sK55 )
| ( app(app(X0,iPr_def_11),nil) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12774,c_141]) ).
tcf(c_12797,plain,
( ~ ssList(iPr_def_12)
| ( app(iPr_def_13,nil) != iPr_def_13 )
| ( app(iPr_def_11,iPr_def_12) != sK55 ) ),
inference(superposition,[status(thm)],[c_8920,c_12775]) ).
tcf(c_12803,plain,
( ~ ssList(iPr_def_12)
| ( app(iPr_def_11,iPr_def_12) != sK55 ) ),
inference(ground_joinability,[status(thm)],[c_12797,c_12492]) ).
tcf(c_12804,plain,
app(iPr_def_11,iPr_def_12) != sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_12803,c_12427]) ).
tcf(c_15368,plain,
( ( nil = sK55 )
| ( cons(hd(sK55),tl(sK55)) = sK55 ) ),
inference(superposition,[status(thm)],[c_8924,c_224]) ).
tcf(c_15378,plain,
( ( nil = sK55 )
| ( cons(iPr_def_10,iPr_def_12) = sK55 ) ),
inference(light_normalisation,[status(thm)],[c_15368,c_8917,c_8919]) ).
tcf(c_15379,plain,
cons(iPr_def_10,iPr_def_12) = sK55,
inference(forward_subsumption_resolution,[status(thm)],[c_15378,c_8922]) ).
tcf(c_15572,plain,
! [X0: $i] :
( ( app(cons(iPr_def_10,nil),X0) = cons(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12379,c_227]) ).
tcf(c_15575,plain,
! [X0: $i] :
( ( cons(iPr_def_10,X0) = app(iPr_def_11,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_15572,c_8918]) ).
tcf(c_44187,plain,
cons(iPr_def_10,iPr_def_12) = app(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_12427,c_15575]) ).
tcf(c_44194,plain,
app(iPr_def_11,iPr_def_12) = sK55,
inference(light_normalisation,[status(thm)],[c_44187,c_15379]) ).
tcf(c_44195,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_44194,c_12804]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC421+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/0.33 % Computer : n012.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Thu Sep 24 18:09:35 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.34 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 Running first-order theorem proving
% 0.10/0.37 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
% 0.10/0.38
% 0.10/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.38
% 0.10/0.38 % Detected problem language: tptp
% 0.10/0.39 % Proving...
% 18.48/3.19 % SZS status Started for theBenchmark.p
% 18.48/3.19 % SZS status Theorem for theBenchmark.p
% 18.48/3.19
% 18.48/3.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.48/3.19
% 18.48/3.19 % ------ iProver source info
% 18.48/3.19
% 18.48/3.19 % git: date: 2026-07-19 20:42:38 +0200
% 18.48/3.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.48/3.19 % git: non_committed_changes: false
% 18.48/3.19
% 18.48/3.19 % ------ Parsing...
% 18.48/3.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.48/3.19
% 18.48/3.19 % ------ 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 %
% 18.48/3.19
% 18.48/3.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.48/3.19
% 18.48/3.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.48/3.19 % ------ Proving...
% 18.48/3.19 % ------ Problem Properties
% 18.48/3.19
% 18.48/3.19 %
% 18.48/3.19 % clauses 190
% 18.48/3.19 % conjectures 3
% 18.48/3.19 % EPR 54
% 18.48/3.19 % Horn 122
% 18.48/3.19 % unary 24
% 18.48/3.19 % binary 40
% 18.48/3.19 % lits 635
% 18.48/3.19 % lits eq 87
% 18.48/3.19 % fd_pure 0
% 18.48/3.19 % fd_pseudo 0
% 18.48/3.19 % fd_cond 21
% 18.48/3.19 % fd_pseudo_cond 14
% 18.48/3.19 % AC symbols 0
% 18.48/3.19
% 18.48/3.19 % ------ Schedule dynamic 5 is on
% 18.48/3.19
% 18.48/3.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.48/3.19
% 18.48/3.19
% 18.48/3.19 % ------
% 18.48/3.19 % Current options:
% 18.48/3.19 % ------
% 18.48/3.19
% 18.48/3.19
% 18.48/3.19 %
% 18.48/3.19
% 18.48/3.19 % ------ Proving...
% 18.48/3.19 %
% 18.48/3.19
% 18.48/3.19 % SZS status Theorem for theBenchmark.p
% 18.48/3.19
% 18.48/3.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.48/3.19
% 18.48/3.19
%------------------------------------------------------------------------------