%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC188-1 : 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 : n016.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 03:08:35 PM UTC 2026
% Result : Unsatisfiable 89.97s 15.08s
% Output : CNFRefutation 74.11s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f253ERROR: Could not build tree for root c_159811ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause47) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f98,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause98) ).
fof(f99,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| nil != cons(X0,X1) ),
inference(reorient_equations,[],[f98]) ).
fof(f103,axiom,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause101) ).
fof(f119,axiom,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f121,axiom,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause118) ).
fof(f122,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f121]) ).
fof(f123,axiom,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f123]) ).
fof(f151,axiom,
! [X2,X0,X1] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause140) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause141) ).
fof(f169,axiom,
! [X2,X0,X1] :
( cons(X0,app(X1,X2)) = app(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause157) ).
fof(f173,axiom,
! [X2,X0,X1] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( X0 = X2
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(reorient_equations,[],[f173]) ).
fof(f183,axiom,
! [X2,X3,X0,X1] :
( X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause170) ).
fof(f193,axiom,
! [X2,X3,X0,X1,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause179) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f211,plain,
sk1 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(reorient_equations,[],[f210]) ).
fof(f212,negated_conjecture,
sk5 != sk6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f215,negated_conjecture,
( nil = sk4
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f216,plain,
( nil = sk4
| sk3 = cons(sk9,nil) ),
inference(reorient_equations,[],[f215]) ).
fof(f219,negated_conjecture,
( nil = sk3
| cons(sk9,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f220,plain,
( nil = sk3
| sk3 = cons(sk9,nil) ),
inference(reorient_equations,[],[f219]) ).
fof(f221,negated_conjecture,
( nil = sk3
| memberP(sk4,sk9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f225,plain,
sk3 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(definition_unfolding,[],[f211,f205]) ).
fof(f233,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f243,plain,
! [X2,X3,X0,X1] :
( ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3) ),
inference(equality_resolution,[],[f193]) ).
tcf(c_261,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_300,plain,
! [X0: $i] : ssItem(skaf44(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_324,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_327,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_339,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_354,plain,
! [X0: $i] :
( ( cons(skaf44(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_369,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_371,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_372,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_391,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f253]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_410,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cons(X2,app(X0,X1)) = app(cons(X2,X0),X1) )
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f169]) ).
tcf(c_414,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X2 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X3)
| ~ ssList(X1)
| ( cons(X0,X1) != cons(X2,X3) ) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_432,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(cnf_transformation,[],[f243]) ).
tcf(c_443,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_444,negated_conjecture,
ssItem(sk6),
inference(cnf_transformation,[],[f207]) ).
tcf(c_445,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f208]) ).
tcf(c_446,negated_conjecture,
ssList(sk8),
inference(cnf_transformation,[],[f209]) ).
tcf(c_447,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(cnf_transformation,[],[f225]) ).
tcf(c_448,negated_conjecture,
sk5 != sk6,
inference(cnf_transformation,[],[f212]) ).
tcf(c_451,negated_conjecture,
( ( sk4 = nil )
| ( cons(sk9,nil) = sk3 ) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_454,negated_conjecture,
( ( sk3 = nil )
| ( cons(sk9,nil) = sk3 ) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_455,negated_conjecture,
( memberP(sk4,sk9)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_6631,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_325]) ).
tcf(c_6632,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_325]) ).
tcf(c_6633,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_325]) ).
tcf(c_6634,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6635,definition,
iPr_def_13 = app(sk7,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6636,definition,
iPr_def_14 = cons(sk6,nil),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6637,definition,
iPr_def_15 = app(iPr_def_13,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_6638,definition,
iPr_def_16 = app(iPr_def_15,sk8),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_6639,definition,
iPr_def_17 = cons(sk9,nil),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_6640,negated_conjecture,
iPr_def_16 = sk3,
inference(demodulation,[status(thm)],[c_447,c_6636,c_6634,c_6635,c_6637,c_6638]) ).
tcf(c_6642,negated_conjecture,
( memberP(sk4,sk9)
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_455]) ).
tcf(c_6643,negated_conjecture,
( ( iPr_def_17 = sk3 )
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_454,c_6639]) ).
tcf(c_6646,negated_conjecture,
( ( iPr_def_17 = sk3 )
| ( sk4 = nil ) ),
inference(demodulation,[status(thm)],[c_451]) ).
tcf(c_6649,negated_conjecture,
sk5 != sk6,
inference(demodulation,[status(thm)],[c_448]) ).
tcf(c_6650,negated_conjecture,
ssList(sk8),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_6651,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_445]) ).
tcf(c_6652,negated_conjecture,
ssItem(sk6),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_6653,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_443]) ).
tcf(c_9276,plain,
( memberP(sk4,sk9)
| ( nil = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6642,c_6640]) ).
tcf(c_9287,plain,
( ( iPr_def_16 = iPr_def_17 )
| ( nil = iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_6643,c_6640]) ).
tcf(c_9786,plain,
app(nil,sk7) = sk7,
inference(superposition,[status(thm)],[c_6651,c_327]) ).
tcf(c_9872,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6635,c_338]) ).
tcf(c_9873,plain,
( ssList(iPr_def_15)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_6637,c_338]) ).
tcf(c_9890,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9872,c_6651]) ).
tcf(c_9977,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6634,c_339]) ).
tcf(c_9978,plain,
( ssList(iPr_def_14)
| ~ ssItem(sk6)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6636,c_339]) ).
tcf(c_9988,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_9978,c_6652,c_261]) ).
tcf(c_9989,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9977,c_6653,c_261]) ).
tcf(c_10000,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_9890,c_9989]) ).
tcf(c_10593,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_339,c_369]) ).
tcf(c_10606,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10593,c_261]) ).
tcf(c_10900,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6634,c_351]) ).
tcf(c_10910,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_10900,c_6653,c_261]) ).
tcf(c_12122,plain,
( ( nil = iPr_def_13 )
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ( nil != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_6637,c_371]) ).
tcf(c_12123,plain,
( ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssList(sk8)
| ( nil != iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_6638,c_371]) ).
tcf(c_12158,plain,
( ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ( nil != iPr_def_16 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12123,c_6650]) ).
tcf(c_12162,plain,
( ( nil = iPr_def_13 )
| ( nil != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12122,c_9988,c_10000]) ).
tcf(c_12196,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6635,c_372]) ).
tcf(c_12238,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_12196,c_10910,c_9989,c_6651]) ).
tcf(c_12867,plain,
nil != iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_12158,c_9873,c_10000,c_9988,c_12162,c_12158,c_12238]) ).
tcf(c_12877,plain,
iPr_def_16 = iPr_def_17,
inference(backward_subsumption_resolution,[status(thm)],[c_9287,c_12867]) ).
tcf(c_12878,plain,
memberP(sk4,sk9),
inference(backward_subsumption_resolution,[status(thm)],[c_9276,c_12867]) ).
tcf(c_13828,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(sk5)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sk5,X1)),cons(sk5,X2)))
| ~ ssList(app(app(X0,cons(sk5,X1)),cons(sk5,X2))) ),
inference(instantiation,[status(thm)],[c_432]) ).
tcf(c_13829,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ duplicatefreeP(app(app(nil,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(app(app(nil,cons(sk5,nil)),cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_13828]) ).
tcf(c_14169,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ ssList(iPr_def_15)
| ~ ssList(sk8)
| ~ ssItem(X0)
| ~ memberP(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_6638,c_393]) ).
tcf(c_14200,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ ssList(iPr_def_15)
| ~ ssItem(X0)
| ~ memberP(iPr_def_15,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14169,c_6650]) ).
tcf(c_16448,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(X0,sk7)) = app(cons(X1,X0),sk7) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6651,c_410]) ).
tcf(c_21285,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk5 )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6634,c_423]) ).
tcf(c_21299,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk5 )
| ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21285,c_6653,c_261]) ).
tcf(c_21766,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(sk5,X0)))
| ~ ssList(X1)
| ~ ssList(cons(sk5,X0)) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_21767,plain,
( ssList(app(nil,cons(sk5,nil)))
| ~ ssList(nil)
| ~ ssList(cons(sk5,nil)) ),
inference(instantiation,[status(thm)],[c_21766]) ).
tcf(c_23480,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ memberP(iPr_def_15,X0)
| ~ ssItem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_14200,c_9873,c_10000,c_9988,c_14200]) ).
tcf(c_23481,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_15,X0) ),
inference(renaming,[status(thm)],[c_23480]) ).
tcf(c_30427,plain,
( singletonP(iPr_def_12)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_6634,c_10606]) ).
tcf(c_30433,plain,
singletonP(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_30427,c_6653]) ).
tcf(c_30441,plain,
( ( cons(skaf44(iPr_def_12),nil) = iPr_def_12 )
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_30433,c_354]) ).
tcf(c_30442,plain,
cons(skaf44(iPr_def_12),nil) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_30441,c_9989]) ).
tcf(c_33295,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(app(app(X0,cons(sk5,X1)),cons(X2,X3)))
| ~ ssList(cons(X2,X3))
| ~ ssList(app(X0,cons(sk5,X1))) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_33486,plain,
! [X0: $i] :
( ssList(cons(sk5,X0))
| ~ ssItem(sk5)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_339]) ).
tcf(c_33487,plain,
( ssList(cons(sk5,nil))
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_33486]) ).
tcf(c_36945,plain,
( ( skaf44(iPr_def_12) = sk5 )
| ~ ssList(nil)
| ~ ssItem(skaf44(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_30442,c_21299]) ).
tcf(c_36979,plain,
skaf44(iPr_def_12) = sk5,
inference(forward_subsumption_resolution,[status(thm)],[c_36945,c_261,c_300]) ).
tcf(c_37122,plain,
cons(sk5,nil) = iPr_def_12,
inference(demodulation,[status(thm)],[c_30442,c_36979]) ).
tcf(c_54001,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,cons(sk5,X1)),cons(sk5,X2)))
| ~ ssList(cons(sk5,X2))
| ~ ssList(app(X0,cons(sk5,X1))) ),
inference(instantiation,[status(thm)],[c_33295]) ).
tcf(c_54002,plain,
( ssList(app(app(nil,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(nil,cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_54001]) ).
tcf(c_64749,plain,
! [X0: $i] :
( ( cons(sk5,app(X0,sk7)) = app(cons(sk5,X0),sk7) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6653,c_16448]) ).
tcf(c_64926,plain,
cons(sk5,app(nil,sk7)) = app(cons(sk5,nil),sk7),
inference(superposition,[status(thm)],[c_261,c_64749]) ).
tcf(c_64995,plain,
cons(sk5,sk7) = app(iPr_def_12,sk7),
inference(light_normalisation,[status(thm)],[c_64926,c_9786,c_37122]) ).
tcf(c_69323,plain,
( ssList(cons(sk5,sk7))
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_64995,c_338]) ).
tcf(c_69339,plain,
ssList(cons(sk5,sk7)),
inference(forward_subsumption_resolution,[status(thm)],[c_69323,c_9989,c_6651]) ).
tcf(c_69467,plain,
( duplicatefreeP(cons(sk5,sk7))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_69339,c_6632]) ).
tcf(c_69903,plain,
! [X0: $i,X1: $i,X2: $i] :
( duplicatefreeP(app(app(X0,cons(sk5,X1)),cons(sk5,X2)))
| ~ iPr_def_11
| ~ ssList(app(app(X0,cons(sk5,X1)),cons(sk5,X2))) ),
inference(instantiation,[status(thm)],[c_6632]) ).
tcf(c_69904,plain,
( duplicatefreeP(app(app(nil,cons(sk5,nil)),cons(sk5,nil)))
| ~ iPr_def_11
| ~ ssList(app(app(nil,cons(sk5,nil)),cons(sk5,nil))) ),
inference(instantiation,[status(thm)],[c_69903]) ).
tcf(c_70409,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_69467,c_443,c_261,c_13829,c_21767,c_33487,c_54002,c_69904]) ).
tcf(c_70411,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6633,c_70409]) ).
tcf(c_70412,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_6631,c_70411]) ).
tcf(c_70426,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ memberP(iPr_def_15,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_23481,c_70412]) ).
tcf(c_70458,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_391,c_70412]) ).
tcf(c_70459,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_414,c_70412]) ).
tcf(c_70469,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_394,c_70412]) ).
tcf(c_70470,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[c_393,c_70412]) ).
tcf(c_70491,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_339,c_70412]) ).
tcf(c_99878,plain,
! [X0: $i] : ~ memberP(nil,X0),
inference(global_subsumption_just,[status(thm)],[c_324,c_443,c_261,c_324,c_6631,c_6633,c_13829,c_21767,c_33487,c_54002,c_69904]) ).
tcf(c_125969,negated_conjecture,
memberP(sk4,sk9),
inference(global_subsumption_just,[status(thm)],[c_6642,c_12878]) ).
tcf(c_126001,plain,
( ( iPr_def_16 = iPr_def_17 )
| ( sk4 = nil ) ),
inference(light_normalisation,[status(thm)],[c_6646,c_6640]) ).
tcf(c_126008,plain,
( memberP(nil,sk9)
| ( iPr_def_16 = iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_126001,c_125969]) ).
tcf(c_126032,plain,
iPr_def_16 = iPr_def_17,
inference(global_subsumption_just,[status(thm)],[c_126008,c_12877]) ).
tcf(c_126070,plain,
cons(sk9,nil) = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_6639,c_126032]) ).
tcf(c_126203,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6635,c_338]) ).
tcf(c_126221,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_126203,c_6651]) ).
tcf(c_126230,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_339,c_70491]) ).
tcf(c_126236,plain,
( ssList(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6634,c_126230]) ).
tcf(c_126237,plain,
( ssList(iPr_def_14)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6636,c_126230]) ).
tcf(c_126241,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_126237,c_261]) ).
tcf(c_126242,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_126236,c_261]) ).
tcf(c_126257,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_126221,c_10000]) ).
tcf(c_126366,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_391,c_70458]) ).
tcf(c_126372,plain,
( memberP(iPr_def_12,sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6634,c_126366]) ).
tcf(c_126373,plain,
( memberP(iPr_def_14,sk6)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6636,c_126366]) ).
tcf(c_126376,plain,
memberP(iPr_def_14,sk6),
inference(forward_subsumption_resolution,[status(thm)],[c_126373,c_261]) ).
tcf(c_126377,plain,
memberP(iPr_def_12,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_126372,c_261]) ).
tcf(c_129628,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ memberP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(global_subsumption_just,[status(thm)],[c_393,c_70470]) ).
tcf(c_129629,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,X2),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_129628]) ).
tcf(c_129640,plain,
! [X0: $i] :
( memberP(iPr_def_15,X0)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ memberP(iPr_def_13,X0) ),
inference(superposition,[status(thm)],[c_6637,c_129629]) ).
tcf(c_129641,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ ssList(iPr_def_15)
| ~ ssList(sk8)
| ~ memberP(iPr_def_15,X0) ),
inference(superposition,[status(thm)],[c_6638,c_129629]) ).
tcf(c_129703,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ ssList(iPr_def_15)
| ~ memberP(iPr_def_15,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129641,c_6650]) ).
tcf(c_129707,plain,
! [X0: $i] :
( memberP(iPr_def_15,X0)
| ~ memberP(iPr_def_13,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129640,c_126241,c_126257]) ).
tcf(c_129735,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ memberP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(global_subsumption_just,[status(thm)],[c_394,c_70469]) ).
tcf(c_129736,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(renaming,[status(thm)],[c_129735]) ).
tcf(c_129746,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_6635,c_129736]) ).
tcf(c_129747,plain,
! [X0: $i] :
( memberP(iPr_def_15,X0)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ memberP(iPr_def_14,X0) ),
inference(superposition,[status(thm)],[c_6637,c_129736]) ).
tcf(c_129814,plain,
! [X0: $i] :
( memberP(iPr_def_15,X0)
| ~ memberP(iPr_def_14,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129747,c_126241,c_126257]) ).
tcf(c_129817,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129746,c_126242,c_6651]) ).
tcf(c_129869,plain,
memberP(iPr_def_13,sk5),
inference(superposition,[status(thm)],[c_126377,c_129817]) ).
tcf(c_132373,plain,
! [X0: $i] :
( memberP(iPr_def_16,X0)
| ~ memberP(iPr_def_15,X0) ),
inference(global_subsumption_just,[status(thm)],[c_129703,c_70426]) ).
tcf(c_134012,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(global_subsumption_just,[status(thm)],[c_414,c_70459]) ).
tcf(c_134026,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sk9 )
| ~ ssList(nil)
| ~ memberP(iPr_def_16,X0) ),
inference(superposition,[status(thm)],[c_126070,c_134012]) ).
tcf(c_134036,plain,
! [X0: $i] :
( ( X0 = sk9 )
| ~ memberP(iPr_def_16,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_134026,c_99878,c_261]) ).
tcf(c_149781,plain,
memberP(iPr_def_15,sk5),
inference(superposition,[status(thm)],[c_129869,c_129707]) ).
tcf(c_149786,plain,
memberP(iPr_def_15,sk6),
inference(superposition,[status(thm)],[c_126376,c_129814]) ).
tcf(c_149792,plain,
memberP(iPr_def_16,sk5),
inference(superposition,[status(thm)],[c_149781,c_132373]) ).
tcf(c_149795,plain,
memberP(iPr_def_16,sk6),
inference(superposition,[status(thm)],[c_149786,c_132373]) ).
tcf(c_159765,plain,
sk6 = sk9,
inference(superposition,[status(thm)],[c_149795,c_134036]) ).
tcf(c_159766,plain,
sk5 = sk9,
inference(superposition,[status(thm)],[c_149792,c_134036]) ).
tcf(c_159810,plain,
sk5 != sk9,
inference(demodulation,[status(thm)],[c_6649,c_159765]) ).
tcf(c_159811,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_159810,c_159766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC188-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.41 % Computer : n016.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Thu Sep 24 16:57:59 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/0.46 Running first-order theorem proving
% 0.15/0.46 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
% 0.15/0.48
% 0.15/0.48 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.48
% 0.15/0.48 % Detected problem language: tptp
% 0.15/0.50 % Proving...
% 89.97/15.08 % SZS status Started for theBenchmark.p
% 89.97/15.08 % SZS status Unsatisfiable for theBenchmark.p
% 89.97/15.08
% 89.97/15.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 89.97/15.08
% 89.97/15.08 % ------ iProver source info
% 89.97/15.08
% 89.97/15.08 % git: date: 2026-07-19 20:42:38 +0200
% 89.97/15.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 89.97/15.08 % git: non_committed_changes: false
% 89.97/15.08
% 89.97/15.08 % ------ Parsing...% successful
% 89.97/15.08
% 89.97/15.08
% 89.97/15.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 89.97/15.08
% 89.97/15.08 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 89.97/15.08
% 89.97/15.08 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 89.97/15.08
% 89.97/15.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 89.97/15.08 % ------ Proving...
% 89.97/15.08 % ------ Problem Properties
% 89.97/15.08
% 89.97/15.08 %
% 89.97/15.08 % clauses 199
% 89.97/15.08 % conjectures 16
% 89.97/15.08 % EPR 68
% 89.97/15.08 % Horn 163
% 89.97/15.08 % unary 72
% 89.97/15.08 % binary 27
% 89.97/15.08 % lits 577
% 89.97/15.08 % lits eq 89
% 89.97/15.08 % fd_pure 0
% 89.97/15.08 % fd_pseudo 0
% 89.97/15.08 % fd_cond 17
% 89.97/15.08 % fd_pseudo_cond 14
% 89.97/15.08 % AC symbols 0
% 89.97/15.08
% 89.97/15.08 % ------ Schedule dynamic 5 is on
% 89.97/15.08
% 89.97/15.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 89.97/15.08
% 89.97/15.08
% 89.97/15.08 % ------
% 89.97/15.08 % Current options:
% 89.97/15.08 % ------
% 89.97/15.08
% 89.97/15.08
% 89.97/15.08 %
% 89.97/15.08
% 89.97/15.08 % ------ Proving...
% 89.97/15.08 % Proof_search_loop: time out after: 6621 full_loop iterations
% 89.97/15.08
% 89.97/15.08 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 89.97/15.08
% 89.97/15.08
% 89.97/15.08 % ------
% 89.97/15.08 % Current options:
% 89.97/15.08 % ------
% 89.97/15.08
% 89.97/15.08
% 89.97/15.08 %
% 89.97/15.08
% 89.97/15.08 % ------ Proving...
% 89.97/15.08 %
% 89.97/15.08
% 89.97/15.08 % SZS status Unsatisfiable for theBenchmark.p
% 89.97/15.08
% 89.97/15.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 74.11/15.08
% 74.11/15.08
%------------------------------------------------------------------------------