%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC021-1 : 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 : n026.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 03:07:33 PM UTC 2026
% Result : Unsatisfiable 62.02s 16.96s
% Output : CNFRefutation 62.02s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f244ERROR: Could not build tree for root c_149097ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause3) ).
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(f61,axiom,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause61) ).
fof(f66,axiom,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause66) ).
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] :
( ~ frontsegP(sk1,X0)
| ~ frontsegP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ strictorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
( nil != sk1
| nil != sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f213,plain,
! [X0] :
( ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f208,f204,f205]) ).
fof(f214,plain,
( nil != sk3
| nil != sk4 ),
inference(definition_unfolding,[],[f210,f204,f205]) ).
fof(f215,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f79]) ).
fof(f217,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f83]) ).
fof(f226,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
tcf(c_247,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f3]) ).
tcf(c_252,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_253,plain,
ssItem(skac3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_300,plain,
! [X0: $i] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_305,plain,
! [X0: $i] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_310,plain,
! [X0: $i] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_318,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_321,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_322,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_323,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_327,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f217]) ).
tcf(c_328,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_348,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( hd(app(X1,X0)) = hd(X1) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f129]) ).
tcf(c_376,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_396,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_401,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_418,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_422,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,[],[f244]) ).
tcf(c_432,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_433,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_434,negated_conjecture,
frontsegP(sk4,sk3),
inference(cnf_transformation,[],[f206]) ).
tcf(c_436,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(cnf_transformation,[],[f213]) ).
tcf(c_437,negated_conjecture,
! [X0: $i] :
( ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ neq(sk3,X0)
| ~ frontsegP(sk4,X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_438,negated_conjecture,
( ( sk4 != nil )
| ( sk3 != nil ) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_499,plain,
( ( nil = nil )
| ~ ssList(nil)
| ~ frontsegP(nil,nil) ),
inference(instantiation,[status(thm)],[c_328]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_388,c_329]) ).
tcf(c_3002,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_436,c_344]) ).
tcf(c_3003,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(unflattening,[status(thm)],[c_3002]) ).
tcf(c_3005,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ frontsegP(sk3,X0)
| ~ frontsegP(sk4,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3003,c_252,c_3003]) ).
tcf(c_3006,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ frontsegP(sk4,X0)
| ~ frontsegP(sk3,X0) ),
inference(renaming,[status(thm)],[c_3005]) ).
tcf(c_3043,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ strictorderedP(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ( X2 != sk3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_437,c_344]) ).
tcf(c_3044,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(sk3)
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(unflattening,[status(thm)],[c_3043]) ).
tcf(c_3045,plain,
( ( nil = sk3 )
| ~ strictorderedP(nil)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ segmentP(nil,sk3)
| ~ frontsegP(sk4,nil) ),
inference(instantiation,[status(thm)],[c_3044]) ).
tcf(c_3046,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ strictorderedP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3044,c_432,c_3044]) ).
tcf(c_3047,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ strictorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(renaming,[status(thm)],[c_3046]) ).
tcf(c_6606,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_6610,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( segmentP(X0,X2)
| ~ segmentP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_9132,plain,
( frontsegP(sk3,sk3)
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_305]) ).
tcf(c_9133,plain,
( ( sk3 = nil )
| ~ ssList(sk3)
| ~ frontsegP(sk4,sk3)
| ~ frontsegP(sk3,sk3) ),
inference(instantiation,[status(thm)],[c_3006]) ).
tcf(c_9134,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_321]) ).
tcf(c_9135,plain,
( ssItem(hd(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_9235,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(X0,sk3)
| ~ segmentP(X1,X2)
| ( sk3 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_6610]) ).
tcf(c_9236,plain,
( segmentP(nil,sk3)
| ~ segmentP(nil,nil)
| ( nil != nil )
| ( sk3 != nil ) ),
inference(instantiation,[status(thm)],[c_9235]) ).
tcf(c_9295,plain,
( ( sk3 = nil )
| ~ ssList(sk3)
| ~ frontsegP(sk3,sk3) ),
inference(superposition,[status(thm)],[c_434,c_3006]) ).
tcf(c_9296,plain,
( ( sk3 = nil )
| ~ frontsegP(sk3,sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9295,c_432]) ).
tcf(c_9297,plain,
sk3 = nil,
inference(global_subsumption_just,[status(thm)],[c_9296,c_432,c_434,c_9132,c_9133]) ).
tcf(c_9300,plain,
frontsegP(sk4,nil),
inference(demodulation,[status(thm)],[c_434,c_9297]) ).
tcf(c_10475,negated_conjecture,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_438,c_432,c_434,c_438,c_9132,c_9133]) ).
tcf(c_10977,plain,
! [X0: $i] :
( ssList(cons(skac3,X0))
| ~ ssItem(skac3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_10978,plain,
( ssList(cons(skac3,nil))
| ~ ssItem(skac3)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_10977]) ).
tcf(c_11011,plain,
! [X0: $i] :
( ssList(cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_11012,plain,
( ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_11011]) ).
tcf(c_11079,plain,
! [X0: $i,X1: $i] :
( ( cons(X0,X1) = sk3 )
| ~ strictorderedP(cons(X0,X1))
| ~ ssList(cons(X0,X1))
| ~ segmentP(cons(X0,X1),sk3)
| ~ frontsegP(sk4,cons(X0,X1)) ),
inference(instantiation,[status(thm)],[c_3047]) ).
tcf(c_12041,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_433,c_364]) ).
tcf(c_12326,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_253,c_12041]) ).
tcf(c_13174,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_12326,c_329]) ).
tcf(c_13179,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13174,c_433]) ).
tcf(c_13950,plain,
! [X0: $i] :
( ssList(app(sk4,X0))
| ~ ssList(sk4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_329]) ).
tcf(c_25987,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = sk3 )
| ~ strictorderedP(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_11079]) ).
tcf(c_25988,plain,
( ( cons(hd(sk4),nil) = sk3 )
| ~ strictorderedP(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_25987]) ).
tcf(c_31909,plain,
( ssList(app(sk4,sk4))
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_13950]) ).
tcf(c_33626,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_33627,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_33626]) ).
tcf(c_44074,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_433,c_348]) ).
tcf(c_44106,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_44074,c_10475]) ).
tcf(c_44177,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_433,c_364]) ).
tcf(c_44303,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_253,c_44177]) ).
tcf(c_44360,plain,
! [X0: $i] :
( ( X0 = nil )
| ( hd(app(X0,sk4)) = hd(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_433,c_367]) ).
tcf(c_44404,plain,
( ( sk4 = nil )
| ( hd(app(sk4,sk4)) = hd(sk4) ) ),
inference(superposition,[status(thm)],[c_433,c_44360]) ).
tcf(c_44436,plain,
hd(app(sk4,sk4)) = hd(sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_44404,c_10475]) ).
tcf(c_44437,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil )
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_44436,c_322]) ).
tcf(c_44503,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_44303,c_329]) ).
tcf(c_44508,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_44503,c_433]) ).
tcf(c_44512,plain,
ssList(cons(skac3,sk4)),
inference(global_subsumption_just,[status(thm)],[c_44508,c_253,c_252,c_10978,c_13179]) ).
tcf(c_45515,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_44106,c_422]) ).
tcf(c_45568,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(sk4,X0)) = app(cons(X1,sk4),X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_433,c_401]) ).
tcf(c_46838,plain,
! [X0: $i] :
( ( cons(X0,app(sk4,sk4)) = app(cons(X0,sk4),sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_433,c_45568]) ).
tcf(c_46875,plain,
cons(skac3,app(sk4,sk4)) = app(cons(skac3,sk4),sk4),
inference(superposition,[status(thm)],[c_253,c_46838]) ).
tcf(c_50472,plain,
( frontsegP(cons(skac3,app(sk4,sk4)),cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,sk4)) ),
inference(superposition,[status(thm)],[c_46875,c_795]) ).
tcf(c_50488,plain,
frontsegP(cons(skac3,app(sk4,sk4)),cons(skac3,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_50472,c_433,c_44512]) ).
tcf(c_50564,plain,
( frontsegP(app(sk4,sk4),sk4)
| ~ ssItem(skac3)
| ~ ssList(sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_50488,c_418]) ).
tcf(c_50565,plain,
( frontsegP(app(sk4,sk4),sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50564,c_253,c_433]) ).
tcf(c_50570,plain,
frontsegP(app(sk4,sk4),sk4),
inference(global_subsumption_just,[status(thm)],[c_50565,c_433,c_31909,c_50565]) ).
tcf(c_50573,plain,
( ( app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4) )
| ~ ssList(sk4)
| ~ ssList(app(sk4,sk4)) ),
inference(superposition,[status(thm)],[c_50570,c_376]) ).
tcf(c_50576,plain,
( ( app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4) )
| ~ ssList(app(sk4,sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_50573,c_433]) ).
tcf(c_52737,plain,
app(sk4,skaf45(app(sk4,sk4),sk4)) = app(sk4,sk4),
inference(global_subsumption_just,[status(thm)],[c_50576,c_433,c_31909,c_50576]) ).
tcf(c_52740,plain,
( ssList(app(sk4,sk4))
| ~ ssList(sk4)
| ~ ssList(skaf45(app(sk4,sk4),sk4)) ),
inference(superposition,[status(thm)],[c_52737,c_329]) ).
tcf(c_52746,plain,
( ( sk4 = nil )
| ~ ssList(sk4)
| ~ ssList(skaf45(app(sk4,sk4),sk4))
| ( app(sk4,sk4) != nil ) ),
inference(superposition,[status(thm)],[c_52737,c_362]) ).
tcf(c_52761,plain,
ssList(app(sk4,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_52740,c_433,c_295]) ).
tcf(c_52766,plain,
app(sk4,sk4) != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_52746,c_10475,c_433,c_295]) ).
tcf(c_52817,plain,
( ssItem(hd(sk4))
| ( app(sk4,sk4) = nil ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_44437,c_52761]) ).
tcf(c_52823,plain,
ssItem(hd(sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_52817,c_52766]) ).
tcf(c_52852,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_45515,c_52823]) ).
tcf(c_52865,plain,
( frontsegP(sk4,cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),nil) ),
inference(instantiation,[status(thm)],[c_52852]) ).
tcf(c_87084,plain,
! [X0: $i,X1: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != X1 )
| ( cons(hd(sk4),X0) != X1 ) ),
inference(instantiation,[status(thm)],[c_6606]) ).
tcf(c_94346,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),X0) != sk3 ) ),
inference(instantiation,[status(thm)],[c_87084]) ).
tcf(c_94348,plain,
( ( cons(hd(sk4),nil) = nil )
| ( nil != sk3 )
| ( cons(hd(sk4),nil) != sk3 ) ),
inference(instantiation,[status(thm)],[c_94346]) ).
tcf(c_94889,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_396]) ).
tcf(c_94892,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_94889]) ).
tcf(c_110253,plain,
( segmentP(cons(hd(sk4),nil),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_300]) ).
tcf(c_121212,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(nil,tl(X0)) = tl(X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_321,c_318]) ).
tcf(c_121291,plain,
( ( sk4 = nil )
| ( app(nil,tl(sk4)) = tl(sk4) ) ),
inference(superposition,[status(thm)],[c_433,c_121212]) ).
tcf(c_121323,plain,
app(nil,tl(sk4)) = tl(sk4),
inference(forward_subsumption_resolution,[status(thm)],[c_121291,c_10475]) ).
tcf(c_121378,plain,
( frontsegP(tl(sk4),nil)
| ~ ssList(nil)
| ~ ssList(tl(sk4)) ),
inference(superposition,[status(thm)],[c_121323,c_795]) ).
tcf(c_121380,plain,
( frontsegP(tl(sk4),nil)
| ~ ssList(tl(sk4)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121378,c_252]) ).
tcf(c_149096,plain,
( strictorderedP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_310]) ).
tcf(c_149097,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_149096,c_121380,c_110253,c_94892,c_94348,c_52865,c_33627,c_25988,c_11012,c_9300,c_9236,c_9135,c_9134,c_9133,c_9132,c_3045,c_499,c_438,c_323,c_327,c_434,c_247,c_252,c_432,c_433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC021-1 : 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 : n026.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 16:00:25 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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...
% 62.02/16.96 % SZS status Started for theBenchmark.p
% 62.02/16.96 % SZS status Unsatisfiable for theBenchmark.p
% 62.02/16.96
% 62.02/16.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 62.02/16.96
% 62.02/16.96 % ------ iProver source info
% 62.02/16.96
% 62.02/16.96 % git: date: 2026-07-19 20:42:38 +0200
% 62.02/16.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 62.02/16.96 % git: non_committed_changes: false
% 62.02/16.96
% 62.02/16.96 % ------ Parsing...% successful
% 62.02/16.96
% 62.02/16.96
% 62.02/16.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 62.02/16.96
% 62.02/16.96 % ------ 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 %
% 62.02/16.96
% 62.02/16.96 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 62.02/16.96
% 62.02/16.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 62.02/16.96 % ------ Proving...
% 62.02/16.96 % ------ Problem Properties
% 62.02/16.96
% 62.02/16.96 %
% 62.02/16.96 % clauses 184
% 62.02/16.96 % conjectures 5
% 62.02/16.96 % EPR 59
% 62.02/16.96 % Horn 156
% 62.02/16.96 % unary 62
% 62.02/16.96 % binary 22
% 62.02/16.96 % lits 556
% 62.02/16.96 % lits eq 73
% 62.02/16.96 % fd_pure 0
% 62.02/16.96 % fd_pseudo 0
% 62.02/16.96 % fd_cond 17
% 62.02/16.96 % fd_pseudo_cond 14
% 62.02/16.96 % AC symbols 0
% 62.02/16.96
% 62.02/16.96 % ------ Input Options Time Limit: Unbounded
% 62.02/16.96
% 62.02/16.96
% 62.02/16.96 % ------
% 62.02/16.96 % Current options:
% 62.02/16.96 % ------
% 62.02/16.96
% 62.02/16.96
% 62.02/16.96 %
% 62.02/16.96
% 62.02/16.96 % ------ Proving...
% 62.02/16.96 %
% 62.02/16.96
% 62.02/16.96 % SZS status Unsatisfiable for theBenchmark.p
% 62.02/16.96
% 62.02/16.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 62.02/16.96
% 62.02/16.96
%------------------------------------------------------------------------------