%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC099-1 : 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 : n001.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 03:07:53 PM UTC 2026
% Result : Unsatisfiable 65.05s 16.91s
% Output : CNFRefutation 65.05s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f244ERROR: Could not build tree for root c_146326ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(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(f64,axiom,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause64) ).
fof(f74,axiom,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause74) ).
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(f98,axiom,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause98) ).
fof(f99,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| nil != cons(X0,X1) ),
inference(reorient_equations,[],[f98]) ).
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(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(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] :
( ~ equalelemsP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f210,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,negated_conjecture,
( ~ frontsegP(sk2,sk1)
| ~ neq(sk1,nil)
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f216,plain,
( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil)
| nil = sk4 ),
inference(definition_unfolding,[],[f210,f204,f205,f204,f205]) ).
fof(f217,plain,
( neq(sk4,nil)
| nil != sk3 ),
inference(definition_unfolding,[],[f211,f205,f204]) ).
fof(f218,plain,
( ~ frontsegP(sk4,sk3)
| ~ neq(sk3,nil)
| nil != sk3 ),
inference(definition_unfolding,[],[f212,f205,f205,f204,f205]) ).
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(f230,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_254,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_255,plain,
ssItem(skac3),
inference(cnf_transformation,[],[f9]) ).
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_310,plain,
! [X0: $i] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_320,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
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_344,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
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_361,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f244]) ).
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_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] :
( ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ neq(sk3,X0)
| ~ frontsegP(sk4,X0) ),
inference(cnf_transformation,[],[f208]) ).
tcf(c_440,negated_conjecture,
( ( sk4 = nil )
| ~ neq(sk3,nil)
| ~ frontsegP(sk4,sk3) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_441,negated_conjecture,
( neq(sk4,nil)
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_442,negated_conjecture,
( ~ neq(sk3,nil)
| ~ frontsegP(sk4,sk3)
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_503,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_563,negated_conjecture,
( ( sk4 = nil )
| ~ neq(sk3,nil) ),
inference(global_subsumption_just,[status(thm)],[c_440,c_436,c_440]) ).
tcf(c_565,negated_conjecture,
( ~ neq(sk3,nil)
| ( sk3 != nil ) ),
inference(global_subsumption_just,[status(thm)],[c_442,c_436,c_442]) ).
tcf(c_815,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_3734,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ equalelemsP(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_3735,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(sk3)
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(unflattening,[status(thm)],[c_3734]) ).
tcf(c_3737,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ equalelemsP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3735,c_434,c_3735]) ).
tcf(c_3738,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ equalelemsP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(renaming,[status(thm)],[c_3737]) ).
tcf(c_3823,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( sk3 != nil )
| ( X1 != sk3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_346,c_565]) ).
tcf(c_3824,plain,
( ( nil = sk3 )
| ~ ssList(nil)
| ~ ssList(sk3)
| ( sk3 != nil ) ),
inference(unflattening,[status(thm)],[c_3823]) ).
tcf(c_3825,plain,
( ( nil = sk3 )
| ( sk3 != nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3824,c_434,c_254,c_3824]) ).
tcf(c_3833,plain,
! [X0: $i,X1: $i] :
( ( sk4 = nil )
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != sk3 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_346,c_563]) ).
tcf(c_3834,plain,
( ( nil = sk3 )
| ( sk4 = nil )
| ~ ssList(nil)
| ~ ssList(sk3) ),
inference(unflattening,[status(thm)],[c_3833]) ).
tcf(c_3835,plain,
( ( nil = sk3 )
| ( sk4 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3834,c_434,c_254,c_3834]) ).
tcf(c_3856,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( sk3 != nil )
| ( X0 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_361,c_441]) ).
tcf(c_3857,plain,
( ~ ssList(sk4)
| ( sk4 != nil )
| ( sk3 != nil ) ),
inference(unflattening,[status(thm)],[c_3856]) ).
tcf(c_3858,plain,
( ( sk3 != nil )
| ( sk4 != nil ) ),
inference(global_subsumption_just,[status(thm)],[c_3857,c_435,c_3857]) ).
tcf(c_3859,plain,
( ( sk4 != nil )
| ( sk3 != nil ) ),
inference(renaming,[status(thm)],[c_3858]) ).
tcf(c_7209,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_7213,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9753,plain,
( ( sk3 = nil )
| ~ ssList(sk3)
| ~ frontsegP(nil,sk3) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_9848,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,sk3)
| ~ segmentP(X1,X2)
| ( sk3 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_7213]) ).
tcf(c_9849,plain,
( segmentP(nil,sk3)
| ~ segmentP(nil,nil)
| ( nil != nil )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_9848]) ).
tcf(c_9919,plain,
( frontsegP(nil,sk3)
| ( sk3 = nil ) ),
inference(superposition,[status(thm)],[c_3835,c_436]) ).
tcf(c_9930,plain,
sk3 = nil,
inference(global_subsumption_just,[status(thm)],[c_9919,c_434,c_9753,c_9919]) ).
tcf(c_10100,plain,
( ssItem(hd(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_324]) ).
tcf(c_10101,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_323]) ).
tcf(c_10461,plain,
! [X0: $i] :
( ssList(cons(skac3,X0))
| ~ ssItem(skac3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_332]) ).
tcf(c_10462,plain,
( ssList(cons(skac3,nil))
| ~ ssItem(skac3)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_10461]) ).
tcf(c_11268,plain,
sk4 != nil,
inference(backward_subsumption_resolution,[status(thm)],[c_3859,c_9930]) ).
tcf(c_11782,plain,
! [X0: $i] :
( ssList(cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_332]) ).
tcf(c_11783,plain,
( ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_11782]) ).
tcf(c_12718,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_435,c_366]) ).
tcf(c_13099,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_255,c_12718]) ).
tcf(c_14001,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_13099,c_331]) ).
tcf(c_14006,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_14001,c_435]) ).
tcf(c_20916,plain,
! [X0: $i] :
( ssList(app(sk4,X0))
| ~ ssList(sk4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_331]) ).
tcf(c_40081,plain,
( ssList(app(sk4,sk4))
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_20916]) ).
tcf(c_41035,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_435,c_350]) ).
tcf(c_41067,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_41035,c_11268]) ).
tcf(c_41143,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_435,c_366]) ).
tcf(c_41267,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_255,c_41143]) ).
tcf(c_41315,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk4)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_435,c_369]) ).
tcf(c_41379,plain,
( ( sk4 = nil )
| ( hd(app(sk4,sk4)) = hd(sk4) ) ),
inference(superposition,[status(thm)],[c_435,c_41315]) ).
tcf(c_41411,plain,
hd(app(sk4,sk4)) = hd(sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_41379,c_11268]) ).
tcf(c_41412,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil )
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_41411,c_324]) ).
tcf(c_41415,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_41267,c_331]) ).
tcf(c_41420,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_41415,c_435]) ).
tcf(c_41424,plain,
ssList(cons(skac3,sk4)),
inference(global_subsumption_just,[status(thm)],[c_41420,c_255,c_254,c_10462,c_14006]) ).
tcf(c_42468,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_41067,c_424]) ).
tcf(c_42696,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_43752,plain,
! [X0: $i] :
( ( cons(X0,app(sk4,sk4)) = app(cons(X0,sk4),sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_435,c_42696]) ).
tcf(c_43789,plain,
cons(skac3,app(sk4,sk4)) = app(cons(skac3,sk4),sk4),
inference(superposition,[status(thm)],[c_255,c_43752]) ).
tcf(c_48721,plain,
( frontsegP(cons(skac3,app(sk4,sk4)),cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,sk4)) ),
inference(superposition,[status(thm)],[c_43789,c_815]) ).
tcf(c_48737,plain,
frontsegP(cons(skac3,app(sk4,sk4)),cons(skac3,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_48721,c_435,c_41424]) ).
tcf(c_49945,plain,
( frontsegP(app(sk4,sk4),sk4)
| ~ ssItem(skac3)
| ~ ssList(sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_48737,c_420]) ).
tcf(c_49946,plain,
( frontsegP(app(sk4,sk4),sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_49945,c_255,c_435]) ).
tcf(c_51483,plain,
frontsegP(app(sk4,sk4),sk4),
inference(global_subsumption_just,[status(thm)],[c_49946,c_435,c_40081,c_49946]) ).
tcf(c_51486,plain,
( ( app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4) )
| ~ ssList(sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_51483,c_378]) ).
tcf(c_51489,plain,
( ( app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4) )
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_51486,c_435]) ).
tcf(c_65221,plain,
app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4),
inference(global_subsumption_just,[status(thm)],[c_51489,c_435,c_40081,c_51489]) ).
tcf(c_65224,plain,
( ssList(app(sk4,sk4))
| ~ ssList(sk4)
| ~ ssList(skaf45(app(sk4,sk4),sk4)) ),
inference(superposition,[status(thm)],[c_65221,c_331]) ).
tcf(c_65230,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(skaf45(app(sk4,sk4),sk4))
| ( app(sk4,sk4) != nil ) ),
inference(superposition,[status(thm)],[c_65221,c_364]) ).
tcf(c_65245,plain,
ssList(app(sk4,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_65224,c_435,c_297]) ).
tcf(c_65250,plain,
app(sk4,sk4) != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_65230,c_11268,c_435,c_297]) ).
tcf(c_65299,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_41412,c_65245]) ).
tcf(c_65305,plain,
ssItem(hd(sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_65299,c_65250]) ).
tcf(c_65329,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_42468,c_65305]) ).
tcf(c_65344,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),nil) ),
inference(instantiation,[status(thm)],[c_65329]) ).
tcf(c_75768,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_344]) ).
tcf(c_75769,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_75768]) ).
tcf(c_77330,plain,
! [X0: $i,X1: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != X1 )
| ( cons(hd(sk4),X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_7209]) ).
tcf(c_80618,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),X0) != sk3 ) ),
inference(instantiation,[status(thm)],[c_77330]) ).
tcf(c_80619,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = sk3 )
| ~ equalelemsP(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_3738]) ).
tcf(c_80620,plain,
( ( cons(hd(sk4),nil) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),nil) != sk3 ) ),
inference(instantiation,[status(thm)],[c_80618]) ).
tcf(c_80621,plain,
( ( cons(hd(sk4),nil) = sk3 )
| ~ equalelemsP(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_80619]) ).
tcf(c_82908,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_82911,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_82908]) ).
tcf(c_87455,plain,
! [X0: $i] :
( segmentP(cons(hd(sk4),X0),nil)
| ~ ssList(cons(hd(sk4),X0)) ),
inference(instantiation,[status(thm)],[c_302]) ).
tcf(c_87456,plain,
( segmentP(cons(hd(sk4),nil),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_87455]) ).
tcf(c_120691,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(nil,tl(X0)) = tl(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_323,c_320]) ).
tcf(c_120778,plain,
( ( sk4 = nil )
| ( app(nil,tl(sk4)) = tl(sk4) ) ),
inference(superposition,[status(thm)],[c_435,c_120691]) ).
tcf(c_120810,plain,
app(nil,tl(sk4)) = tl(sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_120778,c_11268]) ).
tcf(c_120868,plain,
( frontsegP(tl(sk4),nil)
| ~ ssList(nil)
| ~ ssList(tl(sk4)) ),
inference(superposition,[status(thm)],[c_120810,c_815]) ).
tcf(c_120870,plain,
( frontsegP(tl(sk4),nil)
| ~ ssList(tl(sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_120868,c_254]) ).
tcf(c_146325,plain,
( equalelemsP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_146326,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_146325,c_120870,c_87456,c_82911,c_80621,c_80620,c_75769,c_65344,c_11783,c_10100,c_10101,c_9930,c_9849,c_3859,c_3825,c_503,c_325,c_329,c_254,c_434,c_435]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC099-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 16:28:39 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 65.05/16.91 % SZS status Started for theBenchmark.p
% 65.05/16.91 % SZS status Unsatisfiable for theBenchmark.p
% 65.05/16.91
% 65.05/16.91 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 65.05/16.91
% 65.05/16.91 % ------ iProver source info
% 65.05/16.91
% 65.05/16.91 % git: date: 2026-07-19 20:42:38 +0200
% 65.05/16.91 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 65.05/16.91 % git: non_committed_changes: false
% 65.05/16.91
% 65.05/16.91 % ------ Parsing...% successful
% 65.05/16.91
% 65.05/16.91
% 65.05/16.91 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 65.05/16.91
% 65.05/16.91 % ------ 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 %
% 65.05/16.91
% 65.05/16.91 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 65.05/16.91
% 65.05/16.91 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 65.05/16.91 % ------ Proving...
% 65.05/16.91 % ------ Problem Properties
% 65.05/16.91
% 65.05/16.91 %
% 65.05/16.91 % clauses 187
% 65.05/16.91 % conjectures 4
% 65.05/16.91 % EPR 62
% 65.05/16.91 % Horn 158
% 65.05/16.91 % unary 62
% 65.05/16.91 % binary 26
% 65.05/16.91 % lits 560
% 65.05/16.91 % lits eq 80
% 65.05/16.91 % fd_pure 0
% 65.05/16.91 % fd_pseudo 0
% 65.05/16.91 % fd_cond 16
% 65.05/16.91 % fd_pseudo_cond 14
% 65.05/16.91 % AC symbols 0
% 65.05/16.91
% 65.05/16.91 % ------ Input Options Time Limit: Unbounded
% 65.05/16.91
% 65.05/16.91
% 65.05/16.91 % ------
% 65.05/16.91 % Current options:
% 65.05/16.91 % ------
% 65.05/16.91
% 65.05/16.91
% 65.05/16.91 %
% 65.05/16.91
% 65.05/16.91 % ------ Proving...
% 65.05/16.91 %
% 65.05/16.91
% 65.05/16.91 % SZS status Unsatisfiable for theBenchmark.p
% 65.05/16.91
% 65.05/16.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 65.05/16.91
% 65.05/16.91
%------------------------------------------------------------------------------