%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC079-1 : 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 : n014.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 03:07:48 PM UTC 2026
% Result : Unsatisfiable 98.10s 16.42s
% Output : CNFRefutation 98.10s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f253ERROR: Could not build tree for root c_230580ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f13,axiom,
! [X0] : ssList(skaf82(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause13) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f57,axiom,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause57) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
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(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(f96,axiom,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause96) ).
fof(f97,axiom,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause97) ).
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(f103,axiom,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
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(f112,axiom,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause109) ).
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(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(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(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(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/sandbox/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/sandbox/benchmark/Axioms/SWC001-0.ax',clause179) ).
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(f209,negated_conjecture,
! [X0,X1] :
( neq(sk2,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
! [X0] :
( ~ neq(sk4,nil)
| ~ segmentP(sk1,X0)
| ~ segmentP(sk2,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
! [X0,X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f217,plain,
! [X0,X1] :
( neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| cons(X1,nil) != X0
| ~ ssItem(X1)
| sk3 = X0
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f209,f204]) ).
fof(f218,plain,
! [X0] :
( ~ neq(sk4,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f210,f204,f205]) ).
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]) ).
fof(f233,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(f236,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]) ).
fof(f243,plain,
! [X1] :
( neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| ~ ssItem(X1)
| sk3 = cons(X1,nil)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f217]) ).
fof(f244,plain,
( neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| sk3 = cons(hd(sk4),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(equality_resolution,[],[f243]) ).
fof(f245,plain,
! [X1] :
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| hd(sk4) != X1
| ~ ssItem(X1)
| sk3 = cons(X1,nil)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f211]) ).
fof(f246,plain,
( ~ neq(sk4,nil)
| ~ neq(nil,sk4)
| ~ ssItem(hd(sk4))
| sk3 = cons(hd(sk4),nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(equality_resolution,[],[f245]) ).
tcf(c_253,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_258,plain,
! [X0: $i] : ssList(skaf82(X0)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_302,plain,
! [X0: $i] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_319,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_322,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_323,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_341,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_346,plain,
! [X0: $i] :
( ( cons(skaf44(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_349,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_354,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(skaf83(X0),skaf82(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_360,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_361,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f226]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f230]) ).
tcf(c_402,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] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_424,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,[],[f236]) ).
tcf(c_433,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_434,negated_conjecture,
ssList(sk4),
inference(cnf_transformation,[],[f203]) ).
tcf(c_435,negated_conjecture,
neq(sk4,nil),
inference(cnf_transformation,[],[f253]) ).
tcf(c_437,negated_conjecture,
( neq(sk4,nil)
| ( cons(hd(sk4),nil) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_438,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(sk4,nil)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ neq(X0,nil) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_439,negated_conjecture,
( ( cons(hd(sk4),nil) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ neq(sk4,nil)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(cnf_transformation,[],[f246]) ).
tcf(c_561,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,nil)
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0) ),
inference(global_subsumption_just,[status(thm)],[c_438,c_435,c_438]) ).
tcf(c_562,negated_conjecture,
! [X0: $i] :
( ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0)
| ~ neq(X0,nil) ),
inference(renaming,[status(thm)],[c_561]) ).
tcf(c_563,negated_conjecture,
neq(sk4,nil),
inference(global_subsumption_just,[status(thm)],[c_437,c_435]) ).
tcf(c_565,negated_conjecture,
( ( cons(hd(sk4),nil) = sk3 )
| ~ ssItem(hd(sk4))
| ~ neq(nil,sk4)
| ~ ssList(cons(hd(sk4),nil)) ),
inference(global_subsumption_just,[status(thm)],[c_439,c_435,c_439]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_389,c_330]) ).
tcf(c_3592,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_563,c_360]) ).
tcf(c_3593,plain,
( ~ ssList(sk4)
| ( sk4 != nil ) ),
inference(unflattening,[status(thm)],[c_3592]) ).
tcf(c_3594,plain,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_3593,c_434,c_3593]) ).
tcf(c_3620,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_562,c_345]) ).
tcf(c_3621,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(unflattening,[status(thm)],[c_3620]) ).
tcf(c_3623,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ segmentP(sk3,X0)
| ~ segmentP(sk4,X0)
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_3621,c_253,c_3621]) ).
tcf(c_3624,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(renaming,[status(thm)],[c_3623]) ).
tcf(c_3656,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( cons(hd(sk4),nil) = sk3 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil))
| ( X1 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_565,c_345]) ).
tcf(c_3657,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),nil) = sk3 )
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(unflattening,[status(thm)],[c_3656]) ).
tcf(c_3658,plain,
( ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) = sk3 ) ),
inference(global_subsumption_just,[status(thm)],[c_3657,c_434,c_253,c_3593,c_3657]) ).
tcf(c_3659,plain,
( ( cons(hd(sk4),nil) = sk3 )
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(renaming,[status(thm)],[c_3658]) ).
tcf(c_6611,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_317]) ).
tcf(c_6612,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_317]) ).
tcf(c_6613,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_317]) ).
tcf(c_6614,definition,
iPr_def_12 = hd(sk4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6615,definition,
iPr_def_13 = cons(iPr_def_12,nil),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6616,plain,
( ( iPr_def_13 = sk3 )
| ~ ssItem(iPr_def_12)
| ~ ssList(iPr_def_13) ),
inference(demodulation,[status(thm)],[c_3659,c_6614,c_6615]) ).
tcf(c_6617,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ ssList(X0)
| ~ segmentP(sk4,X0)
| ~ segmentP(sk3,X0) ),
inference(demodulation,[status(thm)],[c_3624]) ).
tcf(c_6618,plain,
sk4 != nil,
inference(demodulation,[status(thm)],[c_3594]) ).
tcf(c_6620,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_6621,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_9189,plain,
( ( sk3 = nil )
| ~ ssList(sk3)
| ~ segmentP(sk4,sk3) ),
inference(superposition,[status(thm)],[c_302,c_6617]) ).
tcf(c_9190,plain,
( ( sk3 = nil )
| ~ segmentP(sk4,sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9189,c_6621]) ).
tcf(c_9635,plain,
( ssItem(iPr_def_12)
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_6614,c_323]) ).
tcf(c_9636,plain,
ssItem(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9635,c_6618,c_6620]) ).
tcf(c_9644,plain,
( ( sk3 = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6616,c_9636]) ).
tcf(c_9691,plain,
( ssList(iPr_def_13)
| ~ ssItem(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6615,c_331]) ).
tcf(c_9695,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_9691,c_9636,c_253]) ).
tcf(c_9706,plain,
sk3 = iPr_def_13,
inference(backward_subsumption_resolution,[status(thm)],[c_9644,c_9695]) ).
tcf(c_9710,plain,
( ( nil = iPr_def_13 )
| ~ segmentP(sk4,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_9190,c_9706]) ).
tcf(c_10043,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_331,c_361]) ).
tcf(c_10047,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_10043,c_253]) ).
tcf(c_10372,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_10380,plain,
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ( nil != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_6615,c_343]) ).
tcf(c_10381,plain,
nil != iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_10380,c_9636,c_253]) ).
tcf(c_10382,plain,
~ segmentP(sk4,iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_9710,c_10381]) ).
tcf(c_10671,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6620,c_349]) ).
tcf(c_10705,plain,
( ( sk4 = nil )
| ( cons(iPr_def_12,tl(sk4)) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_10671,c_6614]) ).
tcf(c_10706,plain,
cons(iPr_def_12,tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_10705,c_6618]) ).
tcf(c_11001,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6620,c_365]) ).
tcf(c_11229,plain,
app(cons(iPr_def_12,nil),sk4) = cons(iPr_def_12,sk4),
inference(superposition,[status(thm)],[c_9636,c_11001]) ).
tcf(c_11230,plain,
cons(iPr_def_12,sk4) = app(iPr_def_13,sk4),
inference(light_normalisation,[status(thm)],[c_11229,c_6615]) ).
tcf(c_15407,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(sk4,X0)) = app(cons(X1,sk4),X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6620,c_402]) ).
tcf(c_17583,plain,
! [X0: $i] :
( ( cons(X0,app(sk4,sk4)) = app(cons(X0,sk4),sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6620,c_15407]) ).
tcf(c_17886,plain,
cons(iPr_def_12,app(sk4,sk4)) = app(cons(iPr_def_12,sk4),sk4),
inference(superposition,[status(thm)],[c_9636,c_17583]) ).
tcf(c_27372,plain,
( ssList(cons(iPr_def_12,sk4))
| ~ ssList(iPr_def_13)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_11230,c_330]) ).
tcf(c_27391,plain,
ssList(cons(iPr_def_12,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_27372,c_9695,c_6620]) ).
tcf(c_27533,plain,
app(nil,cons(iPr_def_12,sk4)) = cons(iPr_def_12,sk4),
inference(superposition,[status(thm)],[c_27391,c_319]) ).
tcf(c_29156,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ ssList(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0)))
| ~ duplicatefreeP(app(app(nil,cons(iPr_def_12,sk4)),cons(iPr_def_12,X0))) ),
inference(superposition,[status(thm)],[c_27533,c_424]) ).
tcf(c_29184,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(sk4)
| ~ ssList(X0)
| ~ duplicatefreeP(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0)))
| ~ ssList(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0))) ),
inference(light_normalisation,[status(thm)],[c_29156,c_27533]) ).
tcf(c_29185,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0)))
| ~ ssList(app(cons(iPr_def_12,sk4),cons(iPr_def_12,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_29184,c_9636,c_253,c_6620]) ).
tcf(c_29308,plain,
( ~ ssList(tl(sk4))
| ~ ssList(app(cons(iPr_def_12,sk4),sk4))
| ~ duplicatefreeP(app(cons(iPr_def_12,sk4),cons(iPr_def_12,tl(sk4)))) ),
inference(superposition,[status(thm)],[c_10706,c_29185]) ).
tcf(c_29316,plain,
( ~ ssList(tl(sk4))
| ~ duplicatefreeP(cons(iPr_def_12,app(sk4,sk4)))
| ~ ssList(cons(iPr_def_12,app(sk4,sk4))) ),
inference(light_normalisation,[status(thm)],[c_29308,c_10706,c_17886]) ).
tcf(c_92893,plain,
( ssList(cons(iPr_def_12,app(sk4,sk4)))
| ~ ssList(sk4)
| ~ ssList(cons(iPr_def_12,sk4)) ),
inference(superposition,[status(thm)],[c_17886,c_330]) ).
tcf(c_92933,plain,
ssList(cons(iPr_def_12,app(sk4,sk4))),
inference(forward_subsumption_resolution,[status(thm)],[c_92893,c_6620,c_27391]) ).
tcf(c_93301,plain,
( duplicatefreeP(cons(iPr_def_12,app(sk4,sk4)))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_92933,c_6612]) ).
tcf(c_93785,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_93301,c_434,c_3593,c_10372,c_29316,c_92933,c_93301]) ).
tcf(c_93787,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6613,c_93785]) ).
tcf(c_93805,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_6611,c_93787]) ).
tcf(c_93927,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_365,c_93805]) ).
tcf(c_93937,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_342,c_93805]) ).
tcf(c_93938,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_341,c_93805]) ).
tcf(c_155775,plain,
iPr_def_13 = sk3,
inference(global_subsumption_just,[status(thm)],[c_6616,c_6616,c_9636,c_9695]) ).
tcf(c_155778,plain,
ssList(iPr_def_13),
inference(demodulation,[status(thm)],[c_6621,c_155775]) ).
tcf(c_155906,plain,
app(nil,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_155778,c_319]) ).
tcf(c_156314,plain,
! [X0: $i] : singletonP(cons(X0,nil)),
inference(global_subsumption_just,[status(thm)],[c_361,c_434,c_3593,c_6611,c_6613,c_10047,c_10372,c_29316,c_92933,c_93301]) ).
tcf(c_156316,plain,
singletonP(iPr_def_13),
inference(superposition,[status(thm)],[c_6615,c_156314]) ).
tcf(c_156317,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_341,c_93938]) ).
tcf(c_156325,plain,
! [X0: $i,X1: $i] : tl(cons(X0,skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_258,c_156317]) ).
tcf(c_156364,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_342,c_93937]) ).
tcf(c_156370,plain,
! [X0: $i] : hd(cons(X0,sk4)) = X0,
inference(superposition,[status(thm)],[c_6620,c_156364]) ).
tcf(c_156479,plain,
( ( cons(skaf44(iPr_def_13),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_156316,c_346]) ).
tcf(c_156480,plain,
cons(skaf44(iPr_def_13),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_156479,c_155778]) ).
tcf(c_156577,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6620,c_349]) ).
tcf(c_156612,plain,
( ( sk4 = nil )
| ( cons(iPr_def_12,tl(sk4)) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_156577,c_6614]) ).
tcf(c_156613,plain,
cons(iPr_def_12,tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_156612,c_6618]) ).
tcf(c_156705,plain,
( ( sk4 = nil )
| ( cons(skaf83(sk4),skaf82(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6620,c_354]) ).
tcf(c_156740,plain,
cons(skaf83(sk4),skaf82(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_156705,c_6618]) ).
tcf(c_156885,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_365,c_93927]) ).
tcf(c_156891,plain,
! [X0: $i] : app(cons(X0,nil),sk4) = cons(X0,sk4),
inference(superposition,[status(thm)],[c_6620,c_156885]) ).
tcf(c_156893,plain,
! [X0: $i,X1: $i] : app(cons(X0,nil),skaf82(X1)) = cons(X0,skaf82(X1)),
inference(superposition,[status(thm)],[c_258,c_156885]) ).
tcf(c_157110,plain,
cons(iPr_def_12,sk4) = app(iPr_def_13,sk4),
inference(superposition,[status(thm)],[c_6615,c_156891]) ).
tcf(c_157111,plain,
cons(skaf44(iPr_def_13),sk4) = app(iPr_def_13,sk4),
inference(superposition,[status(thm)],[c_156480,c_156891]) ).
tcf(c_157192,plain,
cons(skaf44(iPr_def_13),sk4) = cons(iPr_def_12,sk4),
inference(light_normalisation,[status(thm)],[c_157111,c_157110]) ).
tcf(c_157201,plain,
hd(cons(iPr_def_12,sk4)) = skaf44(iPr_def_13),
inference(superposition,[status(thm)],[c_157192,c_156370]) ).
tcf(c_157639,plain,
skaf44(iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_157201,c_156370]) ).
tcf(c_157643,plain,
cons(iPr_def_12,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_156480,c_157639]) ).
tcf(c_158956,plain,
skaf82(sk4) = tl(sk4),
inference(superposition,[status(thm)],[c_156740,c_156325]) ).
tcf(c_166504,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,iPr_def_13),X0)) ),
inference(superposition,[status(thm)],[c_155906,c_418]) ).
tcf(c_166530,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(light_normalisation,[status(thm)],[c_166504,c_155906]) ).
tcf(c_166531,plain,
! [X0: $i] :
( segmentP(app(iPr_def_13,X0),iPr_def_13)
| ~ ssList(X0)
| ~ ssList(app(iPr_def_13,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_166530,c_155778,c_253]) ).
tcf(c_226066,plain,
! [X0: $i] : cons(iPr_def_12,skaf82(X0)) = app(iPr_def_13,skaf82(X0)),
inference(superposition,[status(thm)],[c_157643,c_156893]) ).
tcf(c_230004,plain,
! [X0: $i] :
( frontsegP(cons(iPr_def_12,skaf82(X0)),iPr_def_13)
| ~ ssList(iPr_def_13)
| ~ ssList(skaf82(X0)) ),
inference(superposition,[status(thm)],[c_226066,c_797]) ).
tcf(c_230018,plain,
! [X0: $i] : frontsegP(cons(iPr_def_12,skaf82(X0)),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_230004,c_155778,c_258]) ).
tcf(c_230479,plain,
frontsegP(cons(iPr_def_12,tl(sk4)),iPr_def_13),
inference(superposition,[status(thm)],[c_158956,c_230018]) ).
tcf(c_230485,plain,
frontsegP(sk4,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_230479,c_156613]) ).
tcf(c_230494,plain,
( ( app(iPr_def_13,skaf45(sk4,iPr_def_13)) = sk4 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_230485,c_377]) ).
tcf(c_230499,plain,
app(iPr_def_13,skaf45(sk4,iPr_def_13)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_230494,c_155778,c_6620]) ).
tcf(c_230541,plain,
( segmentP(sk4,iPr_def_13)
| ~ ssList(skaf45(sk4,iPr_def_13))
| ~ ssList(app(iPr_def_13,skaf45(sk4,iPr_def_13))) ),
inference(superposition,[status(thm)],[c_230499,c_166531]) ).
tcf(c_230544,plain,
( segmentP(sk4,iPr_def_13)
| ~ ssList(sk4)
| ~ ssList(skaf45(sk4,iPr_def_13)) ),
inference(light_normalisation,[status(thm)],[c_230541,c_230499]) ).
tcf(c_230545,plain,
segmentP(sk4,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_230544,c_6620,c_296]) ).
tcf(c_230580,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_230545,c_10382]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC079-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n014.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 16:16:34 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...
% 98.10/16.42 % SZS status Started for theBenchmark.p
% 98.10/16.42 % SZS status Unsatisfiable for theBenchmark.p
% 98.10/16.42
% 98.10/16.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 98.10/16.42
% 98.10/16.42 % ------ iProver source info
% 98.10/16.42
% 98.10/16.42 % git: date: 2026-07-19 20:42:38 +0200
% 98.10/16.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 98.10/16.42 % git: non_committed_changes: false
% 98.10/16.42
% 98.10/16.42 % ------ Parsing...% successful
% 98.10/16.42
% 98.10/16.42
% 98.10/16.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 98.10/16.42
% 98.10/16.42 % ------ 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 %
% 98.10/16.42
% 98.10/16.42 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 98.10/16.42
% 98.10/16.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 98.10/16.42 % ------ Proving...
% 98.10/16.42 % ------ Problem Properties
% 98.10/16.42
% 98.10/16.42 %
% 98.10/16.42 % clauses 185
% 98.10/16.42 % conjectures 2
% 98.10/16.42 % EPR 58
% 98.10/16.42 % Horn 157
% 98.10/16.42 % unary 63
% 98.10/16.42 % binary 22
% 98.10/16.42 % lits 555
% 98.10/16.42 % lits eq 74
% 98.10/16.42 % fd_pure 0
% 98.10/16.42 % fd_pseudo 0
% 98.10/16.42 % fd_cond 16
% 98.10/16.42 % fd_pseudo_cond 14
% 98.10/16.42 % AC symbols 0
% 98.10/16.42
% 98.10/16.42 % ------ Schedule dynamic 5 is on
% 98.10/16.42
% 98.10/16.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 98.10/16.42
% 98.10/16.42
% 98.10/16.42 % ------
% 98.10/16.42 % Current options:
% 98.10/16.42 % ------
% 98.10/16.42
% 98.10/16.42
% 98.10/16.42 %
% 98.10/16.42
% 98.10/16.42 % ------ Proving...
% 98.10/16.42 % Proof_search_loop: time out after: 6230 full_loop iterations
% 98.10/16.42
% 98.10/16.42 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 98.10/16.42
% 98.10/16.42
% 98.10/16.42 % ------
% 98.10/16.42 % Current options:
% 98.10/16.42 % ------
% 98.10/16.42
% 98.10/16.42
% 98.10/16.42 %
% 98.10/16.42
% 98.10/16.42 % ------ Proving...
% 98.10/16.42 %
% 98.10/16.42
% 98.10/16.42 % SZS status Unsatisfiable for theBenchmark.p
% 98.10/16.42
% 98.10/16.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 98.10/16.43
% 98.10/16.43
%------------------------------------------------------------------------------