%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC187-1 : 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 31.44s 15.35s
% Output : CNFRefutation 31.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 45
% Syntax : Number of formulae : 196 ( 71 unt; 4 def)
% Number of atoms : 601 ( 171 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 541 ( 265 ~; 276 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 154 ( 0 sgn 154 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause50) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause52) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause53) ).
fof(f65,axiom,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause65) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause71) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause73) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause74) ).
fof(f77,axiom,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause77) ).
fof(f83,axiom,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause84) ).
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(f96,axiom,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause96) ).
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(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(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause120) ).
fof(f126,plain,
! [X0,X1] :
( cons(X0,X1) = app(cons(X0,nil),X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f125]) ).
fof(f142,axiom,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause131) ).
fof(f143,axiom,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause132) ).
fof(f144,axiom,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause133) ).
fof(f154,axiom,
! [X2,X0,X1] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause143) ).
fof(f155,axiom,
! [X2,X0,X1] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause144) ).
fof(f162,axiom,
! [X2,X0,X1] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause150) ).
fof(f163,axiom,
! [X2,X0,X1] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause151) ).
fof(f182,axiom,
! [X0,X1] :
( app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause169) ).
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(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_4) ).
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,
ssList(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,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
sk1 = app(app(sk6,cons(sk5,nil)),sk7),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,negated_conjecture,
( nil = sk3
| ssItem(sk8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f217,negated_conjecture,
( nil = sk3
| cons(sk8,nil) = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f218,plain,
( nil = sk3
| sk3 = cons(sk8,nil) ),
inference(reorient_equations,[],[f217]) ).
fof(f222,plain,
sk3 = app(app(sk6,cons(sk5,nil)),sk7),
inference(definition_unfolding,[],[f210,f205]) ).
fof(f225,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f233,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f234,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f240,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_258,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_300,plain,
! [X0: $i,X1: $i] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_301,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_302,plain,
! [X0: $i,X1: $i] : ssList(skaf43(X0,X1)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] : ssList(skaf42(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_315,plain,
! [X0: $i] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_321,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_323,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_324,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_327,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_333,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_334,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_335,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_368,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_370,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] :
( ( app(skaf46(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_382,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_383,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( app(tl(X1),X0) = tl(app(X1,X0)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_394,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_400,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X0,X2) ) ),
inference(cnf_transformation,[],[f162]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] :
( ( app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_429,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,[],[f240]) ).
tcf(c_438,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_439,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_440,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f206]) ).
tcf(c_441,negated_conjecture,
ssList(sk6),
inference(cnf_transformation,[],[f207]) ).
tcf(c_442,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f208]) ).
tcf(c_443,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(cnf_transformation,[],[f222]) ).
tcf(c_444,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_446,negated_conjecture,
( ssItem(sk8)
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_449,negated_conjecture,
( ( sk3 = nil )
| ( cons(sk8,nil) = sk3 ) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_511,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_334]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_394,c_335]) ).
tcf(c_835,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_393,c_335]) ).
tcf(c_6554,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6555,definition,
iPr_def_13 = app(sk6,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6556,definition,
iPr_def_14 = app(iPr_def_13,sk7),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6557,definition,
iPr_def_15 = cons(sk8,nil),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_6558,negated_conjecture,
iPr_def_14 = sk3,
inference(demodulation,[status(thm)],[c_443,c_6554,c_6555,c_6556]) ).
tcf(c_6560,negated_conjecture,
( ( iPr_def_15 = sk3 )
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_449,c_6557]) ).
tcf(c_6563,negated_conjecture,
( ssItem(sk8)
| ( sk3 = nil ) ),
inference(demodulation,[status(thm)],[c_446]) ).
tcf(c_6565,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(demodulation,[status(thm)],[c_444]) ).
tcf(c_6566,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_442]) ).
tcf(c_6567,negated_conjecture,
ssList(sk6),
inference(demodulation,[status(thm)],[c_441]) ).
tcf(c_6568,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_6569,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_439]) ).
tcf(c_6570,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_438]) ).
tcf(c_6571,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_6573,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6578,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( memberP(X0,X2)
| ~ memberP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9135,plain,
ssList(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_6570,c_6558]) ).
tcf(c_9136,plain,
( ssItem(sk8)
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6563,c_6558]) ).
tcf(c_9158,plain,
( ( iPr_def_14 = iPr_def_15 )
| ( nil = iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_6560,c_6558]) ).
tcf(c_9470,plain,
( duplicatefreeP(iPr_def_15)
| ~ ssItem(sk8) ),
inference(superposition,[status(thm)],[c_6557,c_315]) ).
tcf(c_9602,plain,
( duplicatefreeP(iPr_def_15)
| ( nil = iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9136,c_9470]) ).
tcf(c_9696,plain,
app(nil,sk4) = sk4,
inference(superposition,[status(thm)],[c_6569,c_324]) ).
tcf(c_9783,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6555,c_335]) ).
tcf(c_9797,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9783,c_6567]) ).
tcf(c_9884,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6554,c_336]) ).
tcf(c_9893,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9884,c_6568,c_258]) ).
tcf(c_9904,plain,
ssList(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_9797,c_9893]) ).
tcf(c_9936,plain,
app(iPr_def_13,nil) = iPr_def_13,
inference(superposition,[status(thm)],[c_9904,c_323]) ).
tcf(c_10248,plain,
( frontsegP(iPr_def_13,sk6)
| ~ ssList(iPr_def_12)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_6555,c_834]) ).
tcf(c_10296,plain,
frontsegP(iPr_def_13,sk6),
inference(forward_subsumption_resolution,[status(thm)],[c_10248,c_9893,c_6567]) ).
tcf(c_10332,plain,
( ~ ssItem(sk5)
| ~ memberP(nil,sk5) ),
inference(instantiation,[status(thm)],[c_321]) ).
tcf(c_10373,plain,
( rearsegP(iPr_def_14,sk7)
| ~ ssList(iPr_def_13)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6556,c_835]) ).
tcf(c_10419,plain,
rearsegP(iPr_def_14,sk7),
inference(forward_subsumption_resolution,[status(thm)],[c_10373,c_9904,c_6566]) ).
tcf(c_10549,plain,
! [X0: $i] :
( ( tl(cons(X0,sk4)) = sk4 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6569,c_346]) ).
tcf(c_10989,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_6554,c_348]) ).
tcf(c_10996,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_10989,c_6568,c_258]) ).
tcf(c_11930,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6569,c_370]) ).
tcf(c_12331,plain,
( ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6556,c_368]) ).
tcf(c_12370,plain,
( ( nil = iPr_def_13 )
| ( nil != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12331,c_9904,c_6566]) ).
tcf(c_12385,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6555,c_369]) ).
tcf(c_12428,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_12385,c_10996,c_9893,c_6567]) ).
tcf(c_12542,plain,
nil != iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_12370,c_12370,c_12428]) ).
tcf(c_12550,plain,
duplicatefreeP(iPr_def_15),
inference(backward_subsumption_resolution,[status(thm)],[c_9602,c_12542]) ).
tcf(c_12552,plain,
iPr_def_14 = iPr_def_15,
inference(backward_subsumption_resolution,[status(thm)],[c_9158,c_12542]) ).
tcf(c_12554,plain,
ssItem(sk8),
inference(backward_subsumption_resolution,[status(thm)],[c_9136,c_12542]) ).
tcf(c_12557,plain,
cons(sk8,nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_6557,c_12552]) ).
tcf(c_13038,plain,
! [X0: $i] :
( ( app(skaf42(X0,sk5),cons(sk5,skaf43(sk5,X0))) = X0 )
| ~ ssItem(sk5)
| ~ ssList(X0)
| ~ memberP(X0,sk5) ),
inference(instantiation,[status(thm)],[c_419]) ).
tcf(c_13627,plain,
( ( app(skaf46(iPr_def_14,sk7),sk7) = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_10419,c_381]) ).
tcf(c_13663,plain,
app(skaf46(iPr_def_14,sk7),sk7) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_13627,c_9135,c_6566]) ).
tcf(c_13763,plain,
duplicatefreeP(iPr_def_14),
inference(light_normalisation,[status(thm)],[c_12550,c_12552]) ).
tcf(c_13820,plain,
( ( app(sk6,skaf45(iPr_def_13,sk6)) = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_10296,c_382]) ).
tcf(c_13847,plain,
app(sk6,skaf45(iPr_def_13,sk6)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_13820,c_9904,c_6567]) ).
tcf(c_14271,plain,
app(cons(sk8,nil),sk4) = cons(sk8,sk4),
inference(superposition,[status(thm)],[c_12554,c_11930]) ).
tcf(c_14277,plain,
tl(cons(sk8,sk4)) = sk4,
inference(superposition,[status(thm)],[c_12554,c_10549]) ).
tcf(c_14278,plain,
cons(sk8,sk4) = app(iPr_def_14,sk4),
inference(light_normalisation,[status(thm)],[c_14271,c_12557]) ).
tcf(c_15170,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(tl(X0),sk4) = tl(app(X0,sk4)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6569,c_383]) ).
tcf(c_15172,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(tl(X0),sk7) = tl(app(X0,sk7)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6566,c_383]) ).
tcf(c_16909,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ ssList(iPr_def_12)
| ~ ssList(sk6)
| ~ ssList(X0)
| ( app(sk6,X0) != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6555,c_400]) ).
tcf(c_17008,plain,
! [X0: $i] :
( ( X0 = iPr_def_12 )
| ~ ssList(X0)
| ( app(sk6,X0) != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16909,c_9893,c_6567]) ).
tcf(c_17143,plain,
( ( app(skaf42(sk6,sk5),cons(sk5,skaf43(sk5,sk6))) = sk6 )
| ~ ssItem(sk5)
| ~ ssList(sk6)
| ~ memberP(sk6,sk5) ),
inference(instantiation,[status(thm)],[c_13038]) ).
tcf(c_17332,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk7)
| ~ ssList(X0)
| ( app(X0,sk7) != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_6556,c_401]) ).
tcf(c_17357,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ( app(X0,sk4) != sk4 ) ),
inference(superposition,[status(thm)],[c_9696,c_401]) ).
tcf(c_17402,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ( app(X0,sk4) != sk4 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17357,c_258,c_6569]) ).
tcf(c_17426,plain,
! [X0: $i] :
( ( X0 = iPr_def_13 )
| ~ ssList(X0)
| ( app(X0,sk7) != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_17332,c_9904,c_6566]) ).
tcf(c_19808,plain,
( memberP(sk6,sk5)
| ( app(skaf42(sk7,sk5),cons(sk5,skaf43(sk5,sk7))) = sk7 )
| ~ ssItem(sk5)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_6565,c_419]) ).
tcf(c_19821,plain,
( memberP(sk6,sk5)
| ( app(skaf42(sk7,sk5),cons(sk5,skaf43(sk5,sk7))) = sk7 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19808,c_6568,c_6566]) ).
tcf(c_21886,plain,
! [X0: $i,X1: $i] :
( memberP(X0,X1)
| ~ memberP(sk7,sk5)
| ( X1 != sk5 )
| ( X0 != sk7 ) ),
inference(instantiation,[status(thm)],[c_6578]) ).
tcf(c_21913,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,cons(sk5,X1)),iPr_def_12))
| ~ duplicatefreeP(app(app(X0,cons(sk5,X1)),cons(sk5,nil))) ),
inference(superposition,[status(thm)],[c_6554,c_429]) ).
tcf(c_21920,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sk5,X1)),iPr_def_12))
| ~ ssList(app(app(X0,cons(sk5,X1)),iPr_def_12)) ),
inference(light_normalisation,[status(thm)],[c_21913,c_6554]) ).
tcf(c_21921,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sk5,X1)),iPr_def_12))
| ~ ssList(app(app(X0,cons(sk5,X1)),iPr_def_12)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_21920,c_6568,c_258]) ).
tcf(c_26849,plain,
( ( skaf45(iPr_def_13,sk6) = iPr_def_12 )
| ~ ssList(skaf45(iPr_def_13,sk6)) ),
inference(superposition,[status(thm)],[c_13847,c_17008]) ).
tcf(c_26851,plain,
skaf45(iPr_def_13,sk6) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_26849,c_301]) ).
tcf(c_26858,plain,
app(sk6,iPr_def_12) = iPr_def_13,
inference(demodulation,[status(thm)],[c_13847,c_26851]) ).
tcf(c_27130,plain,
( ( skaf46(iPr_def_14,sk7) = iPr_def_13 )
| ~ ssList(skaf46(iPr_def_14,sk7)) ),
inference(superposition,[status(thm)],[c_13663,c_17426]) ).
tcf(c_27131,plain,
skaf46(iPr_def_14,sk7) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_27130,c_300]) ).
tcf(c_27135,plain,
app(iPr_def_13,sk7) = iPr_def_14,
inference(demodulation,[status(thm)],[c_13663,c_27131]) ).
tcf(c_27428,plain,
sk5 = sk5,
inference(instantiation,[status(thm)],[c_6571]) ).
tcf(c_28064,plain,
( ( app(skaf42(sk7,sk5),cons(sk5,skaf43(sk5,sk7))) = sk7 )
| ( app(skaf42(sk6,sk5),cons(sk5,skaf43(sk5,sk6))) = sk6 )
| ~ ssItem(sk5)
| ~ ssList(sk6) ),
inference(superposition,[status(thm)],[c_19821,c_419]) ).
tcf(c_28067,plain,
( ( app(skaf42(sk7,sk5),cons(sk5,skaf43(sk5,sk7))) = sk7 )
| ( app(skaf42(sk6,sk5),cons(sk5,skaf43(sk5,sk6))) = sk6 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_28064,c_6568,c_6567]) ).
tcf(c_28113,plain,
! [X0: $i,X1: $i] :
( ( X0 = sk7 )
| ( sk7 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6573]) ).
tcf(c_28114,plain,
( ( nil = sk7 )
| ( nil != nil )
| ( sk7 != nil ) ),
inference(instantiation,[status(thm)],[c_28113]) ).
tcf(c_29390,plain,
( ( nil = iPr_def_14 )
| ( app(tl(iPr_def_14),sk4) = tl(app(iPr_def_14,sk4)) ) ),
inference(superposition,[status(thm)],[c_9135,c_15170]) ).
tcf(c_29396,plain,
( ( nil = iPr_def_14 )
| ( app(tl(iPr_def_14),sk4) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_29390,c_14277,c_14278]) ).
tcf(c_29397,plain,
app(tl(iPr_def_14),sk4) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_29396,c_12542]) ).
tcf(c_30284,plain,
( ( nil = iPr_def_13 )
| ( app(tl(iPr_def_13),sk7) = tl(app(iPr_def_13,sk7)) ) ),
inference(superposition,[status(thm)],[c_9904,c_15172]) ).
tcf(c_30288,plain,
( ( nil = iPr_def_13 )
| ( app(tl(iPr_def_13),sk7) = tl(iPr_def_14) ) ),
inference(light_normalisation,[status(thm)],[c_30284,c_27135]) ).
tcf(c_30289,plain,
app(tl(iPr_def_13),sk7) = tl(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_30288,c_12428]) ).
tcf(c_33792,plain,
( ( tl(iPr_def_14) = nil )
| ~ ssList(tl(iPr_def_14)) ),
inference(superposition,[status(thm)],[c_29397,c_17402]) ).
tcf(c_44120,plain,
! [X0: $i] :
( memberP(X0,sk5)
| ~ memberP(sk7,sk5)
| ( sk5 != sk5 )
| ( X0 != sk7 ) ),
inference(instantiation,[status(thm)],[c_21886]) ).
tcf(c_44121,plain,
( memberP(nil,sk5)
| ~ memberP(sk7,sk5)
| ( nil != sk7 )
| ( sk5 != sk5 ) ),
inference(instantiation,[status(thm)],[c_44120]) ).
tcf(c_56096,plain,
( ssList(tl(iPr_def_14))
| ~ ssList(sk7)
| ~ ssList(tl(iPr_def_13)) ),
inference(superposition,[status(thm)],[c_30289,c_335]) ).
tcf(c_56100,plain,
( ( sk7 = nil )
| ~ ssList(sk7)
| ~ ssList(tl(iPr_def_13))
| ( tl(iPr_def_14) != nil ) ),
inference(superposition,[status(thm)],[c_30289,c_369]) ).
tcf(c_56112,plain,
( ssList(tl(iPr_def_14))
| ~ ssList(tl(iPr_def_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56096,c_6566]) ).
tcf(c_56130,plain,
( ( sk7 = nil )
| ~ ssList(tl(iPr_def_13))
| ( tl(iPr_def_14) != nil ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_56100,c_6566]) ).
tcf(c_56180,plain,
( ssList(tl(iPr_def_14))
| ( nil = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_327,c_56112]) ).
tcf(c_56181,plain,
ssList(tl(iPr_def_14)),
inference(forward_subsumption_resolution,[status(thm)],[c_56180,c_12428,c_9904]) ).
tcf(c_57456,plain,
( ( sk7 = nil )
| ~ ssList(tl(iPr_def_13)) ),
inference(global_subsumption_just,[status(thm)],[c_56130,c_33792,c_56130,c_56181]) ).
tcf(c_57462,plain,
( ( nil = iPr_def_13 )
| ( sk7 = nil )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_327,c_57456]) ).
tcf(c_57463,plain,
sk7 = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_57462,c_12428,c_9904]) ).
tcf(c_57642,plain,
app(iPr_def_13,nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_6556,c_57463]) ).
tcf(c_57646,plain,
iPr_def_13 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_57642,c_9936]) ).
tcf(c_57660,plain,
ssList(tl(iPr_def_13)),
inference(demodulation,[status(thm)],[c_56181,c_57646]) ).
tcf(c_57716,plain,
duplicatefreeP(iPr_def_13),
inference(demodulation,[status(thm)],[c_13763,c_57646]) ).
tcf(c_86649,plain,
app(skaf42(sk6,sk5),cons(sk5,skaf43(sk5,sk6))) = sk6,
inference(global_subsumption_just,[status(thm)],[c_28067,c_441,c_440,c_258,c_444,c_333,c_511,c_10332,c_17143,c_27428,c_28114,c_44121,c_57456,c_57660]) ).
tcf(c_86664,plain,
( ~ ssList(skaf42(sk6,sk5))
| ~ ssList(skaf43(sk5,sk6))
| ~ ssList(app(sk6,iPr_def_12))
| ~ duplicatefreeP(app(app(skaf42(sk6,sk5),cons(sk5,skaf43(sk5,sk6))),iPr_def_12)) ),
inference(superposition,[status(thm)],[c_86649,c_21921]) ).
tcf(c_86681,plain,
( ~ duplicatefreeP(iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(skaf42(sk6,sk5))
| ~ ssList(skaf43(sk5,sk6)) ),
inference(light_normalisation,[status(thm)],[c_86664,c_26858,c_86649]) ).
tcf(c_86682,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_86681,c_57716,c_9904,c_303,c_302]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC187-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.39 % Computer : n016.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Thu Sep 24 16:56:55 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 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
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.44 % Detected problem language: tptp
% 0.15/10.46 % Proving...
% 31.44/15.35 % SZS status Started for theBenchmark.p
% 31.44/15.35 % SZS status Unsatisfiable for theBenchmark.p
% 31.44/15.35
% 31.44/15.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 31.44/15.35
% 31.44/15.35 % ------ iProver source info
% 31.44/15.35
% 31.44/15.35 % git: date: 2026-07-19 20:42:38 +0200
% 31.44/15.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 31.44/15.35 % git: non_committed_changes: false
% 31.44/15.35
% 31.44/15.35 % ------ Parsing...% successful
% 31.44/15.35
% 31.44/15.35
% 31.44/15.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 31.44/15.35
% 31.44/15.35 % ------ 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 %
% 31.44/15.35
% 31.44/15.35 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 31.44/15.35
% 31.44/15.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 31.44/15.35 % ------ Proving...
% 31.44/15.35 % ------ Problem Properties
% 31.44/15.35
% 31.44/15.35 %
% 31.44/15.35 % clauses 194
% 31.44/15.35 % conjectures 13
% 31.44/15.35 % EPR 65
% 31.44/15.35 % Horn 159
% 31.44/15.35 % unary 68
% 31.44/15.35 % binary 28
% 31.44/15.35 % lits 565
% 31.44/15.35 % lits eq 82
% 31.44/15.35 % fd_pure 0
% 31.44/15.35 % fd_pseudo 0
% 31.44/15.35 % fd_cond 15
% 31.44/15.35 % fd_pseudo_cond 14
% 31.44/15.35 % AC symbols 0
% 31.44/15.35
% 31.44/15.35 % ------ Schedule dynamic 5 is on
% 31.44/15.35
% 31.44/15.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 31.44/15.35
% 31.44/15.35
% 31.44/15.35 % ------
% 31.44/15.35 % Current options:
% 31.44/15.35 % ------
% 31.44/15.35
% 31.44/15.35
% 31.44/15.35 %
% 31.44/15.35
% 31.44/15.35 % ------ Proving...
% 31.44/15.35 %
% 31.44/15.35
% 31.44/15.35 % SZS status Unsatisfiable for theBenchmark.p
% 31.44/15.35
% 31.44/15.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 31.44/15.35
% 31.44/15.35
%------------------------------------------------------------------------------