%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC091-1 : 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 03:07:51 PM UTC 2026
% Result : Unsatisfiable 78.18s 13.30s
% Output : CNFRefutation 78.18s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f240ERROR: Could not build tree for root c_190200ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f9,axiom,
ssItem(skac3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause9) ).
fof(f12,axiom,
! [X0] : ssItem(skaf83(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause12) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause13) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f56,axiom,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause56) ).
fof(f67,axiom,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause67) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(f78,axiom,
! [X0] :
( nil = X0
| ssItem(hd(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause78) ).
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(f97,axiom,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause97) ).
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(f101,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWC001-0.ax',clause104) ).
fof(f112,axiom,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause109) ).
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(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(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(f187,axiom,
! [X2,X3,X0,X1] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001-0.ax',clause173) ).
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(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
! [X0] :
( ~ totalorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f213,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f214,plain,
! [X0] :
( ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f209,f204,f205]) ).
fof(f226,plain,
! [X0,X1] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f155]) ).
fof(f229,plain,
! [X2,X0,X1] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(equality_resolution,[],[f187]) ).
fof(f232,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_252,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_253,plain,
ssItem(skac3),
inference(cnf_transformation,[],[f9]) ).
tcf(c_256,plain,
! [X0: $i] : ssItem(skaf83(X0)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_257,plain,
! [X0: $i] : ssList(skaf82(X0)),
inference(cnf_transformation,[],[f13]) ).
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_311,plain,
! [X0: $i] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_317,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
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_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_340,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f97]) ).
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_353,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_359,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f240]) ).
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_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_417,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f229]) ).
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_423,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,[],[f232]) ).
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,
neq(sk4,nil),
inference(cnf_transformation,[],[f213]) ).
tcf(c_435,negated_conjecture,
frontsegP(sk4,sk3),
inference(cnf_transformation,[],[f207]) ).
tcf(c_437,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f214]) ).
tcf(c_438,negated_conjecture,
! [X0: $i] :
( ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_794,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_3582,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ( X2 != nil )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_437,c_344]) ).
tcf(c_3583,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(unflattening,[status(thm)],[c_3582]) ).
tcf(c_3585,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3583,c_252,c_3583]) ).
tcf(c_3586,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(renaming,[status(thm)],[c_3585]) ).
tcf(c_3633,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_344]) ).
tcf(c_3634,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ ssList(sk3)
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(unflattening,[status(thm)],[c_3633]) ).
tcf(c_3636,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ frontsegP(sk4,X0)
| ~ segmentP(X0,sk3)
| ~ ssList(X0)
| ~ totalorderedP(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3634,c_432,c_3634]) ).
tcf(c_3637,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(renaming,[status(thm)],[c_3636]) ).
tcf(c_3683,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_359,c_434]) ).
tcf(c_3684,plain,
( ~ ssList(sk4)
| ( sk4 != nil ) ),
inference(unflattening,[status(thm)],[c_3683]) ).
tcf(c_3685,plain,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_3684,c_433,c_3684]) ).
tcf(c_6653,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_316]) ).
tcf(c_6654,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_316]) ).
tcf(c_6655,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_316]) ).
tcf(c_6656,plain,
sk4 != nil,
inference(demodulation,[status(thm)],[c_3685]) ).
tcf(c_6658,plain,
! [X0: $i] :
( ( X0 = sk3 )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0) ),
inference(demodulation,[status(thm)],[c_3637]) ).
tcf(c_6660,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(demodulation,[status(thm)],[c_3586]) ).
tcf(c_6662,negated_conjecture,
frontsegP(sk4,sk3),
inference(demodulation,[status(thm)],[c_435]) ).
tcf(c_6663,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_6664,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_432]) ).
tcf(c_9459,plain,
app(sk3,nil) = sk3,
inference(superposition,[status(thm)],[c_6664,c_317]) ).
tcf(c_9520,plain,
app(nil,sk3) = sk3,
inference(superposition,[status(thm)],[c_6664,c_318]) ).
tcf(c_9523,plain,
! [X0: $i] : app(nil,skaf82(X0)) = skaf82(X0),
inference(superposition,[status(thm)],[c_257,c_318]) ).
tcf(c_9958,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X0,skaf82(X1))) = skaf82(X1) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_257,c_340]) ).
tcf(c_10101,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,skaf82(X1))) = X0 )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_257,c_341]) ).
tcf(c_10244,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_321]) ).
tcf(c_10245,plain,
( ssItem(hd(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_10660,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6663,c_348]) ).
tcf(c_10692,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_10660,c_6656]) ).
tcf(c_10836,plain,
( ( sk4 = nil )
| ( cons(skaf83(sk4),skaf82(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6663,c_353]) ).
tcf(c_10868,plain,
cons(skaf83(sk4),skaf82(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_10836,c_6656]) ).
tcf(c_11002,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6663,c_364]) ).
tcf(c_11343,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_253,c_11002]) ).
tcf(c_12754,plain,
( ( app(sk3,skaf45(sk4,sk3)) = sk4 )
| ~ ssList(sk4)
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_6662,c_376]) ).
tcf(c_12791,plain,
app(sk3,skaf45(sk4,sk3)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_12754,c_6663,c_6664]) ).
tcf(c_13783,plain,
! [X0: $i] :
( frontsegP(skaf82(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf82(X0)) ),
inference(superposition,[status(thm)],[c_9523,c_794]) ).
tcf(c_13788,plain,
! [X0: $i] : frontsegP(skaf82(X0),nil),
inference(forward_subsumption_resolution,[status(thm)],[c_13783,c_252,c_257]) ).
tcf(c_14687,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),X0) != nil ) ),
inference(instantiation,[status(thm)],[c_342]) ).
tcf(c_14689,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) != nil ) ),
inference(instantiation,[status(thm)],[c_14687]) ).
tcf(c_19613,plain,
! [X0: $i] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sk3),X0)) ),
inference(superposition,[status(thm)],[c_9520,c_417]) ).
tcf(c_19636,plain,
! [X0: $i] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(app(sk3,X0)) ),
inference(light_normalisation,[status(thm)],[c_19613,c_9520]) ).
tcf(c_19637,plain,
! [X0: $i] :
( segmentP(app(sk3,X0),sk3)
| ~ ssList(X0)
| ~ ssList(app(sk3,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19636,c_252,c_6664]) ).
tcf(c_20213,plain,
( segmentP(sk3,sk3)
| ~ ssList(nil)
| ~ ssList(app(sk3,nil)) ),
inference(superposition,[status(thm)],[c_9459,c_19637]) ).
tcf(c_20214,plain,
( segmentP(sk4,sk3)
| ~ ssList(skaf45(sk4,sk3))
| ~ ssList(app(sk3,skaf45(sk4,sk3))) ),
inference(superposition,[status(thm)],[c_12791,c_19637]) ).
tcf(c_20219,plain,
( segmentP(sk3,sk3)
| ~ ssList(nil)
| ~ ssList(sk3) ),
inference(light_normalisation,[status(thm)],[c_20213,c_9459]) ).
tcf(c_20220,plain,
segmentP(sk3,sk3),
inference(forward_subsumption_resolution,[status(thm)],[c_20219,c_252,c_6664]) ).
tcf(c_20221,plain,
( segmentP(sk4,sk3)
| ~ ssList(sk4)
| ~ ssList(skaf45(sk4,sk3)) ),
inference(light_normalisation,[status(thm)],[c_20214,c_12791]) ).
tcf(c_20222,plain,
segmentP(sk4,sk3),
inference(forward_subsumption_resolution,[status(thm)],[c_20221,c_6663,c_295]) ).
tcf(c_20254,plain,
( ( sk3 = nil )
| ~ ssList(sk3)
| ~ segmentP(sk3,sk3) ),
inference(superposition,[status(thm)],[c_20222,c_6660]) ).
tcf(c_20255,plain,
sk3 = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_20254,c_6664,c_20220]) ).
tcf(c_23542,plain,
( ( sk3 = nil )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(superposition,[status(thm)],[c_6664,c_348]) ).
tcf(c_24728,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_10692,c_422]) ).
tcf(c_27009,plain,
sk3 = nil,
inference(global_subsumption_just,[status(thm)],[c_23542,c_20255]) ).
tcf(c_32651,plain,
! [X0: $i] :
( ssList(cons(skac3,X0))
| ~ ssItem(skac3)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_32652,plain,
( ssList(cons(skac3,nil))
| ~ ssItem(skac3)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_32651]) ).
tcf(c_32685,plain,
! [X0: $i] :
( ssList(cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_32686,plain,
( ssList(cons(hd(sk4),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_32685]) ).
tcf(c_34343,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_11343,c_329]) ).
tcf(c_34365,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34343,c_6663]) ).
tcf(c_34532,plain,
ssList(cons(skac3,sk4)),
inference(global_subsumption_just,[status(thm)],[c_34365,c_253,c_252,c_32652,c_34365]) ).
tcf(c_34557,plain,
app(nil,cons(skac3,sk4)) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_34532,c_318]) ).
tcf(c_40124,plain,
! [X0: $i] :
( ~ ssItem(skac3)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(app(cons(skac3,sk4),cons(skac3,X0)))
| ~ duplicatefreeP(app(app(nil,cons(skac3,sk4)),cons(skac3,X0))) ),
inference(superposition,[status(thm)],[c_34557,c_423]) ).
tcf(c_40147,plain,
! [X0: $i] :
( ~ ssItem(skac3)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0)))
| ~ ssList(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(light_normalisation,[status(thm)],[c_40124,c_34557]) ).
tcf(c_40148,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0)))
| ~ ssList(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40147,c_253,c_252,c_6663]) ).
tcf(c_40441,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,X0))
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(superposition,[status(thm)],[c_329,c_40148]) ).
tcf(c_40442,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssList(cons(skac3,X0))
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40441,c_34532]) ).
tcf(c_41913,plain,
! [X0: $i,X1: $i] : hd(cons(skaf83(X0),skaf82(X1))) = skaf83(X0),
inference(superposition,[status(thm)],[c_256,c_10101]) ).
tcf(c_43478,plain,
skaf83(sk4) = hd(sk4),
inference(superposition,[status(thm)],[c_10868,c_41913]) ).
tcf(c_43496,plain,
cons(hd(sk4),skaf82(sk4)) = sk4,
inference(demodulation,[status(thm)],[c_10868,c_43478]) ).
tcf(c_43561,plain,
ssItem(hd(sk4)),
inference(superposition,[status(thm)],[c_43478,c_256]) ).
tcf(c_89366,plain,
( totalorderedP(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4)) ),
inference(instantiation,[status(thm)],[c_311]) ).
tcf(c_108447,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(app(X1,X0))
| ~ iPr_def_11
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_329,c_6654]) ).
tcf(c_109728,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6663,c_364]) ).
tcf(c_109944,plain,
app(cons(skac3,nil),sk4) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_253,c_109728]) ).
tcf(c_109968,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(sk4)
| ~ ssList(cons(skac3,nil)) ),
inference(superposition,[status(thm)],[c_109944,c_329]) ).
tcf(c_109973,plain,
( ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_109968,c_6663]) ).
tcf(c_109985,plain,
ssList(cons(skac3,sk4)),
inference(global_subsumption_just,[status(thm)],[c_109973,c_253,c_252,c_32652,c_34365]) ).
tcf(c_109994,plain,
app(nil,cons(skac3,sk4)) = cons(skac3,sk4),
inference(superposition,[status(thm)],[c_109985,c_318]) ).
tcf(c_128255,plain,
! [X0: $i] :
( ~ ssItem(skac3)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(app(cons(skac3,sk4),cons(skac3,X0)))
| ~ duplicatefreeP(app(app(nil,cons(skac3,sk4)),cons(skac3,X0))) ),
inference(superposition,[status(thm)],[c_109994,c_423]) ).
tcf(c_128272,plain,
! [X0: $i] :
( ~ ssItem(skac3)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0)))
| ~ ssList(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(light_normalisation,[status(thm)],[c_128255,c_109994]) ).
tcf(c_128273,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0)))
| ~ ssList(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_128272,c_253,c_252,c_6663]) ).
tcf(c_135905,plain,
! [X0: $i] : tl(cons(hd(sk4),skaf82(X0))) = skaf82(X0),
inference(superposition,[status(thm)],[c_43561,c_9958]) ).
tcf(c_139309,plain,
skaf82(sk4) = tl(sk4),
inference(superposition,[status(thm)],[c_43496,c_135905]) ).
tcf(c_139403,plain,
frontsegP(tl(sk4),nil),
inference(superposition,[status(thm)],[c_139309,c_13788]) ).
tcf(c_153302,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(cons(skac3,sk4),cons(skac3,X0))) ),
inference(global_subsumption_just,[status(thm)],[c_128273,c_253,c_32651,c_40442]) ).
tcf(c_153309,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| ~ ssList(cons(skac3,sk4))
| ~ ssList(cons(skac3,X0)) ),
inference(superposition,[status(thm)],[c_108447,c_153302]) ).
tcf(c_153310,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| ~ ssList(cons(skac3,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_153309,c_109985]) ).
tcf(c_153314,plain,
( ~ iPr_def_11
| ~ ssList(nil)
| ~ ssList(cons(skac3,nil)) ),
inference(instantiation,[status(thm)],[c_153310]) ).
tcf(c_163777,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sk4,X0) ),
inference(light_normalisation,[status(thm)],[c_6658,c_27009]) ).
tcf(c_163797,plain,
! [X0: $i] : ssItem(X0),
inference(global_subsumption_just,[status(thm)],[c_6653,c_253,c_252,c_6653,c_6655,c_32652,c_153314]) ).
tcf(c_163807,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ totalorderedP(X0)
| ~ ssList(X0)
| ~ frontsegP(sk4,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_163777,c_300]) ).
tcf(c_164491,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6663,c_348]) ).
tcf(c_164523,plain,
cons(hd(sk4),tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_164491,c_6656]) ).
tcf(c_168667,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_422,c_163797]) ).
tcf(c_168680,plain,
! [X0: $i] :
( frontsegP(sk4,cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ ssList(tl(sk4))
| ~ frontsegP(tl(sk4),X0) ),
inference(superposition,[status(thm)],[c_164523,c_168667]) ).
tcf(c_190158,plain,
! [X0: $i] :
( frontsegP(sk4,cons(hd(sk4),X0))
| ~ ssList(X0)
| ~ frontsegP(tl(sk4),X0) ),
inference(global_subsumption_just,[status(thm)],[c_168680,c_433,c_3684,c_10244,c_10245,c_24728]) ).
tcf(c_190168,plain,
! [X0: $i] :
( ( cons(hd(sk4),X0) = nil )
| ~ ssList(X0)
| ~ frontsegP(tl(sk4),X0)
| ~ totalorderedP(cons(hd(sk4),X0))
| ~ ssList(cons(hd(sk4),X0)) ),
inference(superposition,[status(thm)],[c_190158,c_163807]) ).
tcf(c_190199,plain,
( ( cons(hd(sk4),nil) = nil )
| ~ ssList(nil)
| ~ frontsegP(tl(sk4),nil)
| ~ totalorderedP(cons(hd(sk4),nil))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(instantiation,[status(thm)],[c_190168]) ).
tcf(c_190200,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_190199,c_139403,c_89366,c_32686,c_14689,c_10245,c_3684,c_252,c_433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC091-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 16:25:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 78.18/13.30 % SZS status Started for theBenchmark.p
% 78.18/13.30 % SZS status Unsatisfiable for theBenchmark.p
% 78.18/13.30
% 78.18/13.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 78.18/13.30
% 78.18/13.30 % ------ iProver source info
% 78.18/13.30
% 78.18/13.30 % git: date: 2026-07-19 20:42:38 +0200
% 78.18/13.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 78.18/13.30 % git: non_committed_changes: false
% 78.18/13.30
% 78.18/13.30 % ------ Parsing...% successful
% 78.18/13.30
% 78.18/13.30
% 78.18/13.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 78.18/13.30
% 78.18/13.30 % ------ 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 %
% 78.18/13.30
% 78.18/13.30 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 78.18/13.30
% 78.18/13.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 78.18/13.30 % ------ Proving...
% 78.18/13.30 % ------ Problem Properties
% 78.18/13.30
% 78.18/13.30 %
% 78.18/13.30 % clauses 186
% 78.18/13.30 % conjectures 4
% 78.18/13.30 % EPR 61
% 78.18/13.30 % Horn 158
% 78.18/13.30 % unary 63
% 78.18/13.30 % binary 22
% 78.18/13.30 % lits 560
% 78.18/13.30 % lits eq 73
% 78.18/13.30 % fd_pure 0
% 78.18/13.30 % fd_pseudo 0
% 78.18/13.30 % fd_cond 17
% 78.18/13.30 % fd_pseudo_cond 14
% 78.18/13.30 % AC symbols 0
% 78.18/13.30
% 78.18/13.30 % ------ Schedule dynamic 5 is on
% 78.18/13.30
% 78.18/13.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 78.18/13.30
% 78.18/13.30
% 78.18/13.30 % ------
% 78.18/13.30 % Current options:
% 78.18/13.30 % ------
% 78.18/13.30
% 78.18/13.30
% 78.18/13.30 %
% 78.18/13.30
% 78.18/13.30 % ------ Proving...
% 78.18/13.30 % Proof_search_loop: time out after: 5697 full_loop iterations
% 78.18/13.30
% 78.18/13.30 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 78.18/13.30
% 78.18/13.30
% 78.18/13.30 % ------
% 78.18/13.30 % Current options:
% 78.18/13.30 % ------
% 78.18/13.30
% 78.18/13.30
% 78.18/13.30 %
% 78.18/13.30
% 78.18/13.30 % ------ Proving...
% 78.18/13.30 %
% 78.18/13.30
% 78.18/13.30 % SZS status Unsatisfiable for theBenchmark.p
% 78.18/13.30
% 78.18/13.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 78.18/13.30
% 78.18/13.30
%------------------------------------------------------------------------------