%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC418+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 : n013.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 03:09:43 PM UTC 2026
% Result : Theorem 10.74s 2.77s
% Output : CNFRefutation 10.74s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f543ERROR: Could not build tree for root c_42662ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
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(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( neq(nil,X3)
& ? [X10] :
( neq(nil,X3)
& hd(X3) = X10
& cons(X10,nil) = X9
& ssItem(X10) )
& app(X8,X9) = X7
& tl(X3) = X8
& ssList(X9) )
& ssList(X8) )
& X2 != X7
& ssList(X7) ) )
| ( 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/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( neq(X3,nil)
& ? [X7] :
( ? [X8] :
( ? [X9] :
( neq(nil,X3)
& ? [X10] :
( neq(nil,X3)
& hd(X3) = X10
& cons(X10,nil) = X9
& ssItem(X10) )
& app(X8,X9) = X7
& tl(X3) = X8
& ssList(X9) )
& ssList(X8) )
& X2 != X7
& ssList(X7) ) )
| ( 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)
& ( ~ neq(X3,nil)
| ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ neq(nil,X3)
| ! [X10] :
( ~ neq(nil,X3)
| hd(X3) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10) )
| app(X8,X9) != X7
| tl(X3) != X8
| ~ ssList(X9) )
| ~ ssList(X8) )
| X2 = X7
| ~ ssList(X7) ) )
& ( 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)
& ( ~ neq(X3,nil)
| ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ neq(nil,X3)
| ! [X10] :
( ~ neq(nil,X3)
| hd(X3) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10) )
| app(X8,X9) != X7
| tl(X3) != X8
| ~ ssList(X9) )
| ~ ssList(X8) )
| X2 = X7
| ~ ssList(X7) ) )
& ( 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)
& ( ~ neq(sK56,nil)
| ! [X7] :
( ! [X8] :
( ! [X9] :
( ~ neq(nil,sK56)
| ! [X10] :
( ~ neq(nil,sK56)
| hd(sK56) != X10
| cons(X10,nil) != X9
| ~ ssItem(X10) )
| app(X8,X9) != X7
| tl(sK56) != X8
| ~ ssList(X9) )
| ~ ssList(X8) )
| sK55 = X7
| ~ ssList(X7) ) )
& ( 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(f497,plain,
ssList(sK54),
inference(cnf_transformation,[],[f296]) ).
fof(f502,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(f503,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f503,f505]) ).
fof(f507,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,[],[f502,f505,f504]) ).
fof(f508,plain,
ssList(sK56),
inference(definition_unfolding,[],[f497,f505]) ).
fof(f509,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f504]) ).
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,[],[f543]) ).
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,[],[f506]) ).
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,[],[f507]) ).
tcf(c_249,negated_conjecture,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(sK56,nil)
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
inference(cnf_transformation,[],[f548]) ).
tcf(c_252,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f508]) ).
tcf(c_253,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f509]) ).
tcf(c_379,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil)))
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56) ),
inference(global_subsumption_just,[status(thm)],[c_249,c_246,c_249]) ).
tcf(c_380,negated_conjecture,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ~ ssList(app(tl(sK56),cons(hd(sK56),nil))) ),
inference(renaming,[status(thm)],[c_379]) ).
tcf(c_807,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_380,c_153]) ).
tcf(c_3247,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( X1 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_807]) ).
tcf(c_3248,plain,
( ( nil = sK56 )
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(unflattening,[status(thm)],[c_3247]) ).
tcf(c_3249,plain,
( ( nil = sK56 )
| ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_3248,c_252,c_141,c_3248]) ).
tcf(c_3270,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_246]) ).
tcf(c_3271,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3270]) ).
tcf(c_3272,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3271,c_141,c_3271]) ).
tcf(c_3277,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) = sK55 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3249,c_3272]) ).
tcf(c_8899,definition,
iPr_def_10 = hd(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8900,definition,
iPr_def_11 = cons(iPr_def_10,nil),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8901,definition,
iPr_def_12 = tl(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8902,definition,
iPr_def_13 = app(iPr_def_12,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8903,plain,
( ( iPr_def_13 = sK55 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_3277,c_8902,c_8901,c_8899,c_8900]) ).
tcf(c_8904,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3272]) ).
tcf(c_8905,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_253]) ).
tcf(c_8906,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_252]) ).
tcf(c_8907,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_11832,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_8900,c_8907]) ).
tcf(c_11833,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_11832,c_8900]) ).
tcf(c_11878,plain,
! [X0: $i] :
( ~ ssList(iPr_def_12)
| ~ ssItem(iPr_def_10)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != sK55 )
| ( app(app(X0,iPr_def_11),iPr_def_12) != sK56 ) ),
inference(superposition,[status(thm)],[c_8902,c_11833]) ).
tcf(c_12228,plain,
app(sK55,nil) = sK55,
inference(superposition,[status(thm)],[c_8905,c_232]) ).
tcf(c_12290,plain,
( ssList(iPr_def_11)
| ~ ssList(nil)
| ~ ssItem(iPr_def_10) ),
inference(superposition,[status(thm)],[c_8900,c_140]) ).
tcf(c_12293,plain,
( ssList(iPr_def_11)
| ~ ssItem(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12290,c_141]) ).
tcf(c_12329,plain,
( ssItem(iPr_def_10)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8899,c_149]) ).
tcf(c_12330,plain,
ssItem(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12329,c_8904,c_8906]) ).
tcf(c_12336,plain,
! [X0: $i] :
( ~ ssList(iPr_def_12)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != sK55 )
| ( app(app(X0,iPr_def_11),iPr_def_12) != sK56 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11878,c_12330]) ).
tcf(c_12338,plain,
( ( sK55 = iPr_def_13 )
| ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_11) ),
inference(backward_subsumption_resolution,[status(thm)],[c_8903,c_12330]) ).
tcf(c_12355,plain,
( ( sK55 = iPr_def_13 )
| ~ ssList(iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_12338,c_12293,c_12330,c_12338]) ).
tcf(c_12385,plain,
ssList(iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_12293,c_12293,c_12330]) ).
tcf(c_12388,plain,
app(nil,iPr_def_11) = iPr_def_11,
inference(superposition,[status(thm)],[c_12385,c_155]) ).
tcf(c_12406,plain,
( ssList(iPr_def_12)
| ( nil = sK56 )
| ~ ssList(sK56) ),
inference(superposition,[status(thm)],[c_8901,c_151]) ).
tcf(c_12409,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12406,c_8904,c_8906]) ).
tcf(c_12416,plain,
sK55 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_12355,c_12409]) ).
tcf(c_12417,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(iPr_def_13,X0) != sK55 )
| ( app(app(X0,iPr_def_11),iPr_def_12) != sK56 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_12336,c_12409]) ).
tcf(c_12420,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_12228,c_12416]) ).
tcf(c_12515,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(iPr_def_13,X0) != iPr_def_13 )
| ( app(app(X0,iPr_def_11),iPr_def_12) != sK56 ) ),
inference(light_normalisation,[status(thm)],[c_12417,c_12416]) ).
tcf(c_12526,plain,
( ~ ssList(nil)
| ( app(iPr_def_13,nil) != iPr_def_13 )
| ( app(iPr_def_11,iPr_def_12) != sK56 ) ),
inference(superposition,[status(thm)],[c_12388,c_12515]) ).
tcf(c_12527,plain,
( ~ ssList(nil)
| ( app(iPr_def_11,iPr_def_12) != sK56 ) ),
inference(ground_joinability,[status(thm)],[c_12526,c_12420]) ).
tcf(c_12528,plain,
app(iPr_def_11,iPr_def_12) != sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_12527,c_141]) ).
tcf(c_15407,plain,
( ( nil = sK56 )
| ( cons(hd(sK56),tl(sK56)) = sK56 ) ),
inference(superposition,[status(thm)],[c_8906,c_224]) ).
tcf(c_15418,plain,
( ( nil = sK56 )
| ( cons(iPr_def_10,iPr_def_12) = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_15407,c_8899,c_8901]) ).
tcf(c_15419,plain,
cons(iPr_def_10,iPr_def_12) = sK56,
inference(forward_subsumption_resolution,[status(thm)],[c_15418,c_8904]) ).
tcf(c_16074,plain,
! [X0: $i] :
( ( app(cons(iPr_def_10,nil),X0) = cons(iPr_def_10,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12330,c_227]) ).
tcf(c_16077,plain,
! [X0: $i] :
( ( cons(iPr_def_10,X0) = app(iPr_def_11,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_16074,c_8900]) ).
tcf(c_42654,plain,
cons(iPr_def_10,iPr_def_12) = app(iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_12409,c_16077]) ).
tcf(c_42661,plain,
app(iPr_def_11,iPr_def_12) = sK56,
inference(light_normalisation,[status(thm)],[c_42654,c_15419]) ).
tcf(c_42662,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_42661,c_12528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC418+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 18:08:36 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.36 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...
% 10.74/2.77 % SZS status Started for theBenchmark.p
% 10.74/2.77 % SZS status Theorem for theBenchmark.p
% 10.74/2.77
% 10.74/2.77 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 10.74/2.77
% 10.74/2.77 % ------ iProver source info
% 10.74/2.77
% 10.74/2.77 % git: date: 2026-07-19 20:42:38 +0200
% 10.74/2.77 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 10.74/2.77 % git: non_committed_changes: false
% 10.74/2.77
% 10.74/2.77 % ------ Parsing...
% 10.74/2.77 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 10.74/2.77
% 10.74/2.77 % ------ 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 %
% 10.74/2.77
% 10.74/2.77 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 10.74/2.77
% 10.74/2.77 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 10.74/2.77 % ------ Proving...
% 10.74/2.77 % ------ Problem Properties
% 10.74/2.77
% 10.74/2.77 %
% 10.74/2.77 % clauses 189
% 10.74/2.77 % conjectures 3
% 10.74/2.77 % EPR 53
% 10.74/2.77 % Horn 121
% 10.74/2.77 % unary 23
% 10.74/2.77 % binary 40
% 10.74/2.77 % lits 634
% 10.74/2.77 % lits eq 86
% 10.74/2.77 % fd_pure 0
% 10.74/2.77 % fd_pseudo 0
% 10.74/2.77 % fd_cond 21
% 10.74/2.77 % fd_pseudo_cond 14
% 10.74/2.77 % AC symbols 0
% 10.74/2.77
% 10.74/2.77 % ------ Schedule dynamic 5 is on
% 10.74/2.77
% 10.74/2.77 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 10.74/2.77
% 10.74/2.77
% 10.74/2.77 % ------
% 10.74/2.77 % Current options:
% 10.74/2.77 % ------
% 10.74/2.77
% 10.74/2.77
% 10.74/2.77 %
% 10.74/2.77
% 10.74/2.77 % ------ Proving...
% 10.74/2.77 %
% 10.74/2.77
% 10.74/2.77 % SZS status Theorem for theBenchmark.p
% 10.74/2.77
% 10.74/2.77 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 10.74/2.77
% 10.74/2.77
%------------------------------------------------------------------------------