%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC031-1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:07:36 PM UTC 2026
% Result : Unsatisfiable 79.39s 15.30s
% Output : CNFRefutation 79.39s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f248ERROR: Could not build tree for root c_128707ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause4) ).
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause9) ).
fof(f11,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause11) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f56,axiom,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause56) ).
fof(f60,axiom,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
fof(f67,axiom,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause67) ).
fof(f77,axiom,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause77) ).
fof(f78,axiom,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause78) ).
fof(f79,axiom,
! [X0] :
( segmentP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause79) ).
fof(f83,axiom,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(X0)
| nil != X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause83) ).
fof(f84,axiom,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause84) ).
fof(f85,axiom,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause85) ).
fof(f86,axiom,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause86) ).
fof(f101,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause100) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(reorient_equations,[],[f101]) ).
fof(f107,axiom,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f119,axiom,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause116) ).
fof(f121,axiom,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox/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(f125,axiom,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/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(f129,axiom,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause123) ).
fof(f134,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause127) ).
fof(f135,plain,
! [X0,X1] :
( X0 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(reorient_equations,[],[f134]) ).
fof(f143,axiom,
! [X0,X1] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause132) ).
fof(f155,axiom,
! [X2,X0,X1] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause144) ).
fof(f164,axiom,
! [X2,X0,X1] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause152) ).
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/sandbox/benchmark/Axioms/SWC001-0.ax',clause157) ).
fof(f188,axiom,
! [X2,X3,X0,X1] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause174) ).
fof(f202,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
fof(f203,negated_conjecture,
ssList(sk4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ totalorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
( nil = sk1
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f212,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f215,plain,
( nil = sk3
| nil = sk4 ),
inference(definition_unfolding,[],[f209,f204,f205]) ).
fof(f218,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f212,f205,f204]) ).
fof(f219,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f79]) ).
fof(f221,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f226,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f230,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_250,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f4]) ).
tcf(c_254,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_255,plain,
ssItem(skac3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_257,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f11]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_302,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_306,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_313,plain,
! [X0: $i] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_323,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_324,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_325,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f219]) ).
tcf(c_329,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_330,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_332,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] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_350,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_362,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_366,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( hd(app(X1,X0)) = hd(X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_373,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_398,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[],[f164]) ).
tcf(c_403,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_420,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[],[f188]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_434,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_435,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_436,negated_conjecture,
frontsegP(sk4,sk3),
inference(cnf_transformation,[],[f206]) ).
tcf(c_438,negated_conjecture,
! [X0: $i] :
( ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ neq(sk3,X0)
| ~ frontsegP(sk4,X0) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_439,negated_conjecture,
( ( sk4 = nil )
| ( sk3 = nil ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_440,negated_conjecture,
( ( sk4 != nil )
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_501,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_390,c_331]) ).
tcf(c_3335,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ totalorderedP(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ( X2 != sk3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_438,c_346]) ).
tcf(c_3336,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(sk3)
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(unflattening,[status(thm)],[c_3335]) ).
tcf(c_3337,plain,
( ( nil = sk3 )
| ~ totalorderedP(nil)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(nil,sk3)
| ~ frontsegP(sk4,nil) ),
inference(instantiation,[status(thm)],[c_3336]) ).
tcf(c_3338,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ totalorderedP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3336,c_434,c_3336]) ).
tcf(c_3339,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(renaming,[status(thm)],[c_3338]) ).
tcf(c_7211,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7215,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7223,plain,
! [X0: $i,X1: $i] :
( singletonP(X0)
| ~ singletonP(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_10462,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_323]) ).
tcf(c_10463,plain,
( ssItem(hd(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_324]) ).
tcf(c_10561,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,sk3)
| ~ segmentP(X1,X2)
| ( sk3 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_7215]) ).
tcf(c_10562,plain,
( segmentP(nil,sk3)
| ~ segmentP(nil,nil)
| ( nil != nil )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_10561]) ).
tcf(c_10626,plain,
( frontsegP(nil,sk3)
| ( sk3 = nil ) ),
inference(superposition,[status(thm)],[c_439,c_436]) ).
tcf(c_10649,plain,
! [X0: $i,X1: $i] :
( singletonP(X0)
| ~ singletonP(cons(X1,nil))
| ( X0 != cons(X1,nil) ) ),
inference(instantiation,[status(thm)],[c_7223]) ).
tcf(c_11224,plain,
( ( sk3 = nil )
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_10626,c_330]) ).
tcf(c_11225,plain,
sk3 = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_11224,c_434]) ).
tcf(c_11234,plain,
frontsegP(sk4,nil),
inference(demodulation,[status(thm)],[c_436,c_11225]) ).
tcf(c_11704,plain,
! [X0: $i,X1: $i] :
( ( X1 = cons(X0,nil) )
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ segmentP(X1,cons(X0,nil))
| ~ segmentP(cons(X0,nil),X1) ),
inference(instantiation,[status(thm)],[c_373]) ).
tcf(c_11752,negated_conjecture,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_440,c_440,c_11225]) ).
tcf(c_13326,plain,
! [X0: $i] :
( segmentP(cons(X0,nil),nil)
| ~ ssList(cons(X0,nil)) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_13367,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_435,c_366]) ).
tcf(c_13616,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_255,c_13367]) ).
tcf(c_13879,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,X1) = sk3 )
| ~ totalorderedP(cons(X0,X1))
| ~ ssList(cons(X0,X1))
| ~ segmentP(cons(X0,X1),sk3)
| ~ frontsegP(sk4,cons(X0,X1)) ),
inference(instantiation,[status(thm)],[c_3339]) ).
tcf(c_14343,plain,
! [X0: $i] :
( ssList(app(sk4,X0))
| ~ ssList(sk4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_331]) ).
tcf(c_14498,plain,
! [X0: $i] :
( ssList(cons(skac3,X0))
| ~ ssItem(skac3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_332]) ).
tcf(c_14499,plain,
( ssList(cons(skac3,nil))
| ~ ssItem(skac3)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_14498]) ).
tcf(c_14532,plain,
! [X0: $i] :
( ssList(cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_332]) ).
tcf(c_14533,plain,
( ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_14532]) ).
tcf(c_14541,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_13616,c_331]) ).
tcf(c_14546,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14541,c_435]) ).
tcf(c_22442,plain,
! [X0: $i] :
( ( X0 = cons(hd(sk4),nil) )
| ~ ssList(X0)
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(X0,cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),X0) ),
inference(instantiation,[status(thm)],[c_11704]) ).
tcf(c_22449,plain,
( singletonP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_362]) ).
tcf(c_22454,plain,
( segmentP(cons(hd(sk4),nil),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_13326]) ).
tcf(c_22458,plain,
( ( nil = cons(hd(sk4),nil) )
| ~ ssList(nil)
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(nil,cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),nil) ),
inference(instantiation,[status(thm)],[c_22442]) ).
tcf(c_29254,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = sk3 )
| ~ totalorderedP(cons(hd(sk4),X0))
| ~ ssList(cons(hd(sk4),X0))
| ~ segmentP(cons(hd(sk4),X0),sk3)
| ~ frontsegP(sk4,cons(hd(sk4),X0)) ),
inference(instantiation,[status(thm)],[c_13879]) ).
tcf(c_29255,plain,
( ( cons(hd(sk4),nil) = sk3 )
| ~ totalorderedP(cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),sk3)
| ~ frontsegP(sk4,cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_29254]) ).
tcf(c_32742,plain,
( ssList(app(sk4,sk4))
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_14343]) ).
tcf(c_40415,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X1,cons(hd(sk4),nil))
| ~ segmentP(X2,X0)
| ( X1 != X2 )
| ( cons(hd(sk4),nil) != X0 ) ),
inference(instantiation,[status(thm)],[c_7215]) ).
tcf(c_40416,plain,
( segmentP(nil,cons(hd(sk4),nil))
| ~ segmentP(nil,nil)
| ( nil != nil )
| ( cons(hd(sk4),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_40415]) ).
tcf(c_41552,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_435,c_350]) ).
tcf(c_41584,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_41552,c_11752]) ).
tcf(c_41655,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_435,c_366]) ).
tcf(c_41775,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_255,c_41655]) ).
tcf(c_41831,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk4)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_435,c_369]) ).
tcf(c_41880,plain,
( ( sk4 = nil )
| ( hd(app(sk4,sk4)) = hd(sk4) ) ),
inference(superposition,[status(thm)],[c_435,c_41831]) ).
tcf(c_41912,plain,
hd(app(sk4,sk4)) = hd(sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_41880,c_11752]) ).
tcf(c_41913,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil )
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_41912,c_324]) ).
tcf(c_41978,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_41775,c_331]) ).
tcf(c_41983,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41978,c_435]) ).
tcf(c_41987,plain,
ssList(cons(skac3,sk4)),
inference(global_subsumption_just,[status(thm)],[c_41983,c_255,c_254,c_14499,c_14546]) ).
tcf(c_43047,plain,
! [X0: $i] :
( frontsegP(sk4,cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),X0) ),
inference(superposition,[status(thm)],[c_41584,c_424]) ).
tcf(c_43100,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(sk4,X0)) = app(cons(X1,sk4),X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_435,c_403]) ).
tcf(c_44326,plain,
! [X0: $i] :
( ( cons(X0,app(sk4,sk4)) = app(cons(X0,sk4),sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_435,c_43100]) ).
tcf(c_44363,plain,
cons(skac3,app(sk4,sk4)) = app(cons(skac3,sk4),sk4),
inference(superposition,[status(thm)],[c_255,c_44326]) ).
tcf(c_49292,plain,
( frontsegP(cons(skac3,app(sk4,sk4)),cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,sk4)) ),
inference(superposition,[status(thm)],[c_44363,c_1137]) ).
tcf(c_49304,plain,
frontsegP(cons(skac3,app(sk4,sk4)),cons(skac3,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_49292,c_435,c_41987]) ).
tcf(c_50133,plain,
( frontsegP(app(sk4,sk4),sk4)
| ~ ssItem(skac3)
| ~ ssList(sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_49304,c_420]) ).
tcf(c_50134,plain,
( frontsegP(app(sk4,sk4),sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50133,c_255,c_435]) ).
tcf(c_50687,plain,
frontsegP(app(sk4,sk4),sk4),
inference(global_subsumption_just,[status(thm)],[c_50134,c_435,c_32742,c_50134]) ).
tcf(c_50690,plain,
( ( app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4) )
| ~ ssList(sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_50687,c_378]) ).
tcf(c_50693,plain,
( ( app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4) )
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50690,c_435]) ).
tcf(c_51905,plain,
app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4),
inference(global_subsumption_just,[status(thm)],[c_50693,c_435,c_32742,c_50693]) ).
tcf(c_51908,plain,
( ssList(app(sk4,sk4))
| ~ ssList(sk4)
| ~ ssList(skaf45(app(sk4,sk4),sk4)) ),
inference(superposition,[status(thm)],[c_51905,c_331]) ).
tcf(c_51914,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(skaf45(app(sk4,sk4),sk4))
| ( app(sk4,sk4) != nil ) ),
inference(superposition,[status(thm)],[c_51905,c_364]) ).
tcf(c_51927,plain,
ssList(app(sk4,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_51908,c_435,c_297]) ).
tcf(c_51932,plain,
app(sk4,sk4) != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_51914,c_11752,c_435,c_297]) ).
tcf(c_51979,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_41913,c_51927]) ).
tcf(c_51985,plain,
ssItem(hd(sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_51979,c_51932]) ).
tcf(c_52014,plain,
! [X0: $i] :
( frontsegP(sk4,cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_43047,c_51985]) ).
tcf(c_52030,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),nil) ),
inference(instantiation,[status(thm)],[c_52014]) ).
tcf(c_52254,plain,
( frontsegP(tl(sk4),nil)
| ~ ssList(tl(sk4)) ),
inference(instantiation,[status(thm)],[c_306]) ).
tcf(c_101374,plain,
! [X0: $i] :
( singletonP(X0)
| ~ singletonP(cons(hd(sk4),nil))
| ( X0 != cons(hd(sk4),nil) ) ),
inference(instantiation,[status(thm)],[c_10649]) ).
tcf(c_101375,plain,
( singletonP(nil)
| ~ singletonP(cons(hd(sk4),nil))
| ( nil != cons(hd(sk4),nil) ) ),
inference(instantiation,[status(thm)],[c_101374]) ).
tcf(c_104845,plain,
! [X0: $i,X1: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != X1 )
| ( cons(hd(sk4),X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_7211]) ).
tcf(c_112292,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),X0) != sk3 ) ),
inference(instantiation,[status(thm)],[c_104845]) ).
tcf(c_112294,plain,
( ( cons(hd(sk4),nil) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),nil) != sk3 ) ),
inference(instantiation,[status(thm)],[c_112292]) ).
tcf(c_119397,plain,
! [X0: $i,X1: $i] :
( segmentP(cons(hd(sk4),X0),sk3)
| ~ ssList(sk3)
| ~ ssList(X1)
| ~ segmentP(X1,sk3)
| ~ ssList(cons(hd(sk4),X0))
| ~ segmentP(cons(hd(sk4),X0),X1) ),
inference(instantiation,[status(thm)],[c_398]) ).
tcf(c_119400,plain,
( segmentP(cons(hd(sk4),nil),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(nil,sk3)
| ~ ssList(cons(hd(sk4),nil))
| ~ segmentP(cons(hd(sk4),nil),nil) ),
inference(instantiation,[status(thm)],[c_119397]) ).
tcf(c_128706,plain,
( totalorderedP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_313]) ).
tcf(c_128707,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_128706,c_119400,c_112294,c_101375,c_52254,c_52030,c_40416,c_29255,c_22458,c_22449,c_22454,c_14533,c_11234,c_11225,c_10562,c_10463,c_10462,c_3337,c_501,c_440,c_325,c_329,c_257,c_250,c_254,c_434,c_435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC031-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Thu Sep 24 16:00:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 79.39/15.30 % SZS status Started for theBenchmark.p
% 79.39/15.30 % SZS status Unsatisfiable for theBenchmark.p
% 79.39/15.30
% 79.39/15.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 79.39/15.30
% 79.39/15.30 % ------ iProver source info
% 79.39/15.30
% 79.39/15.30 % git: date: 2026-07-19 20:42:38 +0200
% 79.39/15.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 79.39/15.30 % git: non_committed_changes: false
% 79.39/15.30
% 79.39/15.30 % ------ Parsing...% successful
% 79.39/15.30
% 79.39/15.30
% 79.39/15.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 79.39/15.30
% 79.39/15.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 79.39/15.30
% 79.39/15.30 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 79.39/15.30
% 79.39/15.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 79.39/15.30 % ------ Proving...
% 79.39/15.30 % ------ Problem Properties
% 79.39/15.30
% 79.39/15.30 %
% 79.39/15.30 % clauses 184
% 79.39/15.30 % conjectures 6
% 79.39/15.30 % EPR 59
% 79.39/15.30 % Horn 155
% 79.39/15.30 % unary 62
% 79.39/15.30 % binary 23
% 79.39/15.30 % lits 554
% 79.39/15.30 % lits eq 74
% 79.39/15.30 % fd_pure 0
% 79.39/15.30 % fd_pseudo 0
% 79.39/15.30 % fd_cond 16
% 79.39/15.30 % fd_pseudo_cond 14
% 79.39/15.30 % AC symbols 0
% 79.39/15.30
% 79.39/15.30 % ------ Input Options Time Limit: Unbounded
% 79.39/15.30
% 79.39/15.30
% 79.39/15.30 % ------
% 79.39/15.30 % Current options:
% 79.39/15.30 % ------
% 79.39/15.30
% 79.39/15.30
% 79.39/15.30 %
% 79.39/15.30
% 79.39/15.30 % ------ Proving...
% 79.39/15.30 %
% 79.39/15.30
% 79.39/15.30 % SZS status Unsatisfiable for theBenchmark.p
% 79.39/15.30
% 79.39/15.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 79.39/15.30
% 79.39/15.30
%------------------------------------------------------------------------------