%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC248-1 : 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 : n020.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 03:09:00 PM UTC 2026
% Result : Unsatisfiable 12.46s 32.06s
% Output : CNFRefutation 12.46s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f264ERROR: Could not build tree for root c_297381ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f51,axiom,
! [X0,X1] : ssList(skaf45(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause51) ).
fof(f60,axiom,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause60) ).
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(f106,axiom,
! [X0,X1] :
( leq(X0,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ lt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause103) ).
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(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(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(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
nil != sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f213,negated_conjecture,
! [X2,X0,X1] :
( lt(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f214,plain,
! [X2,X0,X1] :
( lt(X0,sk5(X2,X1,X0))
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f213]) ).
fof(f215,negated_conjecture,
! [X2,X0,X1] :
( ~ leq(X0,sk5(X2,X1,X0))
| app(app(X1,cons(X0,nil)),X2) != sk1
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f216,plain,
! [X2,X0,X1] :
( ~ leq(X0,sk5(X2,X1,X0))
| sk1 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f215]) ).
fof(f229,plain,
nil != sk3,
inference(definition_unfolding,[],[f206,f205]) ).
fof(f233,plain,
! [X2,X0,X1] :
( lt(X0,sk5(X2,X1,X0))
| sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f214,f205]) ).
fof(f234,plain,
! [X2,X0,X1] :
( ~ leq(X0,sk5(X2,X1,X0))
| sk3 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f216,f205]) ).
fof(f252,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_260,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_303,plain,
! [X0: $i,X1: $i] : ssList(skaf45(X0,X1)),
inference(cnf_transformation,[],[f51]) ).
tcf(c_312,plain,
! [X0: $i] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_326,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_329,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_330,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_337,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_338,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_355,plain,
! [X0: $i,X1: $i] :
( leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ lt(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_356,plain,
! [X0: $i] :
( ( X0 = nil )
| ( cons(hd(X0),tl(X0)) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f107]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] :
( ( app(X1,skaf45(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_430,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,[],[f264]) ).
tcf(c_431,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,[],[f252]) ).
tcf(c_440,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_442,negated_conjecture,
sk3 != nil,
inference(cnf_transformation,[],[f229]) ).
tcf(c_446,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( lt(X1,sk5(X2,X0,X1))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f233]) ).
tcf(c_447,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ leq(X1,sk5(X2,X0,X1))
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f234]) ).
tcf(c_510,plain,
( ssList(cons(nil,nil))
| ~ ssItem(nil)
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_564,plain,
( ~ ssItem(nil)
| ~ ssList(nil)
| ~ duplicatefreeP(app(app(nil,cons(nil,nil)),cons(nil,nil)))
| ~ ssList(app(app(nil,cons(nil,nil)),cons(nil,nil))) ),
inference(instantiation,[status(thm)],[c_431]) ).
tcf(c_628,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_648,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1483,plain,
( ssList(tl(sk3))
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_329]) ).
tcf(c_1486,plain,
( ssItem(hd(sk3))
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_330]) ).
tcf(c_1872,plain,
( ( sk3 = nil )
| ( cons(hd(sk3),tl(sk3)) = sk3 )
| ~ ssList(sk3) ),
inference(instantiation,[status(thm)],[c_356]) ).
tcf(c_2136,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(X2,cons(X0,X1)))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1)) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_2137,plain,
( ssList(app(nil,cons(nil,nil)))
| ~ ssList(nil)
| ~ ssList(cons(nil,nil)) ),
inference(instantiation,[status(thm)],[c_2136]) ).
tcf(c_2248,plain,
! [X0: $i] :
( ssList(cons(hd(sk3),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk3)) ),
inference(instantiation,[status(thm)],[c_338]) ).
tcf(c_2250,plain,
! [X0: $i,X1: $i] :
( lt(hd(sk3),sk5(X1,X0,hd(sk3)))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ( app(app(X0,cons(hd(sk3),nil)),X1) != sk3 ) ),
inference(instantiation,[status(thm)],[c_446]) ).
tcf(c_2258,plain,
( ssList(cons(hd(sk3),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk3)) ),
inference(instantiation,[status(thm)],[c_2248]) ).
tcf(c_2465,plain,
sk3 = sk3,
inference(instantiation,[status(thm)],[c_628]) ).
tcf(c_7123,plain,
! [X0: $i] :
( lt(hd(sk3),sk5(skaf45(sk3,app(X0,cons(hd(sk3),nil))),X0,hd(sk3)))
| ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf45(sk3,app(X0,cons(hd(sk3),nil))))
| ( app(app(X0,cons(hd(sk3),nil)),skaf45(sk3,app(X0,cons(hd(sk3),nil)))) != sk3 ) ),
inference(instantiation,[status(thm)],[c_2250]) ).
tcf(c_7124,plain,
! [X0: $i] :
( ( app(app(X0,cons(hd(sk3),nil)),skaf45(sk3,app(X0,cons(hd(sk3),nil)))) = sk3 )
| ~ ssList(sk3)
| ~ ssList(app(X0,cons(hd(sk3),nil)))
| ~ frontsegP(sk3,app(X0,cons(hd(sk3),nil))) ),
inference(instantiation,[status(thm)],[c_384]) ).
tcf(c_7125,plain,
( lt(hd(sk3),sk5(skaf45(sk3,app(nil,cons(hd(sk3),nil))),nil,hd(sk3)))
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf45(sk3,app(nil,cons(hd(sk3),nil))))
| ( app(app(nil,cons(hd(sk3),nil)),skaf45(sk3,app(nil,cons(hd(sk3),nil)))) != sk3 ) ),
inference(instantiation,[status(thm)],[c_7123]) ).
tcf(c_7126,plain,
( ( app(app(nil,cons(hd(sk3),nil)),skaf45(sk3,app(nil,cons(hd(sk3),nil)))) = sk3 )
| ~ ssList(sk3)
| ~ ssList(app(nil,cons(hd(sk3),nil)))
| ~ frontsegP(sk3,app(nil,cons(hd(sk3),nil))) ),
inference(instantiation,[status(thm)],[c_7124]) ).
tcf(c_12621,plain,
! [X0: $i] : ssList(skaf45(sk3,app(X0,cons(hd(sk3),nil)))),
inference(instantiation,[status(thm)],[c_303]) ).
tcf(c_12622,plain,
ssList(skaf45(sk3,app(nil,cons(hd(sk3),nil)))),
inference(instantiation,[status(thm)],[c_12621]) ).
tcf(c_13689,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(hd(sk3),X0)))
| ~ ssList(X1)
| ~ ssList(cons(hd(sk3),X0)) ),
inference(instantiation,[status(thm)],[c_2136]) ).
tcf(c_13690,plain,
( ssList(app(nil,cons(hd(sk3),nil)))
| ~ ssList(nil)
| ~ ssList(cons(hd(sk3),nil)) ),
inference(instantiation,[status(thm)],[c_13689]) ).
tcf(c_55055,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(X2,cons(X0,X1)))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1)) ),
inference(instantiation,[status(thm)],[c_337]) ).
tcf(c_55162,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ~ leq(hd(sk3),sk5(X1,X0,hd(sk3)))
| ( app(app(X0,cons(hd(sk3),nil)),X1) != sk3 ) ),
inference(instantiation,[status(thm)],[c_447]) ).
tcf(c_55264,plain,
! [X0: $i,X1: $i] :
( ( sk3 = X0 )
| ( sk3 != X1 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_630]) ).
tcf(c_57303,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf45(sk3,app(X0,cons(hd(sk3),nil))))
| ~ leq(hd(sk3),sk5(skaf45(sk3,app(X0,cons(hd(sk3),nil))),X0,hd(sk3)))
| ( app(app(X0,cons(hd(sk3),nil)),skaf45(sk3,app(X0,cons(hd(sk3),nil)))) != sk3 ) ),
inference(instantiation,[status(thm)],[c_55162]) ).
tcf(c_57305,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(skaf45(sk3,app(nil,cons(hd(sk3),nil))))
| ~ leq(hd(sk3),sk5(skaf45(sk3,app(nil,cons(hd(sk3),nil))),nil,hd(sk3)))
| ( app(app(nil,cons(hd(sk3),nil)),skaf45(sk3,app(nil,cons(hd(sk3),nil)))) != sk3 ) ),
inference(instantiation,[status(thm)],[c_57303]) ).
tcf(c_57318,plain,
! [X0: $i,X1: $i] :
( leq(hd(sk3),sk5(X0,X1,hd(sk3)))
| ~ ssItem(hd(sk3))
| ~ ssItem(sk5(X0,X1,hd(sk3)))
| ~ lt(hd(sk3),sk5(X0,X1,hd(sk3))) ),
inference(instantiation,[status(thm)],[c_355]) ).
tcf(c_60156,plain,
! [X0: $i] :
( ( sk3 = X0 )
| ( sk3 != sk3 )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_55264]) ).
tcf(c_63524,plain,
! [X0: $i] :
( leq(hd(sk3),sk5(skaf45(sk3,app(X0,cons(hd(sk3),nil))),X0,hd(sk3)))
| ~ ssItem(hd(sk3))
| ~ ssItem(sk5(skaf45(sk3,app(X0,cons(hd(sk3),nil))),X0,hd(sk3)))
| ~ lt(hd(sk3),sk5(skaf45(sk3,app(X0,cons(hd(sk3),nil))),X0,hd(sk3))) ),
inference(instantiation,[status(thm)],[c_57318]) ).
tcf(c_63525,plain,
( leq(hd(sk3),sk5(skaf45(sk3,app(nil,cons(hd(sk3),nil))),nil,hd(sk3)))
| ~ ssItem(hd(sk3))
| ~ ssItem(sk5(skaf45(sk3,app(nil,cons(hd(sk3),nil))),nil,hd(sk3)))
| ~ lt(hd(sk3),sk5(skaf45(sk3,app(nil,cons(hd(sk3),nil))),nil,hd(sk3))) ),
inference(instantiation,[status(thm)],[c_63524]) ).
tcf(c_70671,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,cons(hd(sk3),X0)))
| ~ ssList(X1)
| ~ ssList(cons(hd(sk3),X0)) ),
inference(instantiation,[status(thm)],[c_55055]) ).
tcf(c_87598,plain,
( ( sk3 = cons(hd(sk3),tl(sk3)) )
| ( sk3 != sk3 )
| ( cons(hd(sk3),tl(sk3)) != sk3 ) ),
inference(instantiation,[status(thm)],[c_60156]) ).
tcf(c_130410,plain,
! [X0: $i,X1: $i,X2: $i] :
( ssList(app(app(X0,cons(hd(sk3),X1)),cons(hd(sk3),X2)))
| ~ ssList(cons(hd(sk3),X2))
| ~ ssList(app(X0,cons(hd(sk3),X1))) ),
inference(instantiation,[status(thm)],[c_70671]) ).
tcf(c_130411,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ~ duplicatefreeP(app(app(X0,cons(hd(sk3),X1)),cons(hd(sk3),X2)))
| ~ ssList(app(app(X0,cons(hd(sk3),X1)),cons(hd(sk3),X2))) ),
inference(instantiation,[status(thm)],[c_431]) ).
tcf(c_130412,plain,
( ssList(app(app(nil,cons(hd(sk3),nil)),cons(hd(sk3),nil)))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(app(nil,cons(hd(sk3),nil))) ),
inference(instantiation,[status(thm)],[c_130410]) ).
tcf(c_130413,plain,
( ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ duplicatefreeP(app(app(nil,cons(hd(sk3),nil)),cons(hd(sk3),nil)))
| ~ ssList(app(app(nil,cons(hd(sk3),nil)),cons(hd(sk3),nil))) ),
inference(instantiation,[status(thm)],[c_130411]) ).
tcf(c_140261,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(cons(X1,X3))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(instantiation,[status(thm)],[c_55055]) ).
tcf(c_140262,plain,
( ssList(app(app(nil,cons(nil,nil)),cons(nil,nil)))
| ~ ssList(cons(nil,nil))
| ~ ssList(app(nil,cons(nil,nil))) ),
inference(instantiation,[status(thm)],[c_140261]) ).
tcf(c_151335,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ssItem(X4)
| duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(instantiation,[status(thm)],[c_324]) ).
tcf(c_157457,plain,
! [X0: $i,X1: $i,X2: $i] :
( frontsegP(sk3,X0)
| ~ frontsegP(X2,X1)
| ( sk3 != X2 )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_648]) ).
tcf(c_164841,plain,
! [X0: $i] :
( ( app(nil,cons(X0,nil)) = cons(X0,nil) )
| ~ ssList(cons(X0,nil)) ),
inference(instantiation,[status(thm)],[c_326]) ).
tcf(c_211060,plain,
! [X0: $i] :
( frontsegP(cons(hd(sk3),tl(sk3)),cons(hd(sk3),X0))
| ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ frontsegP(tl(sk3),X0) ),
inference(instantiation,[status(thm)],[c_430]) ).
tcf(c_211062,plain,
( frontsegP(cons(hd(sk3),tl(sk3)),cons(hd(sk3),nil))
| ~ ssList(nil)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ frontsegP(tl(sk3),nil) ),
inference(instantiation,[status(thm)],[c_211060]) ).
tcf(c_212173,plain,
( frontsegP(tl(sk3),nil)
| ~ ssList(tl(sk3)) ),
inference(instantiation,[status(thm)],[c_312]) ).
tcf(c_217747,plain,
( ( app(nil,cons(hd(sk3),nil)) = cons(hd(sk3),nil) )
| ~ ssList(cons(hd(sk3),nil)) ),
inference(instantiation,[status(thm)],[c_164841]) ).
tcf(c_230684,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk3,X0)
| ~ frontsegP(cons(hd(sk3),tl(sk3)),X1)
| ( sk3 != cons(hd(sk3),tl(sk3)) )
| ( X0 != X1 ) ),
inference(instantiation,[status(thm)],[c_157457]) ).
tcf(c_239836,plain,
! [X0: $i,X1: $i] :
( frontsegP(sk3,app(X0,cons(hd(sk3),nil)))
| ~ frontsegP(cons(hd(sk3),tl(sk3)),X1)
| ( sk3 != cons(hd(sk3),tl(sk3)) )
| ( app(X0,cons(hd(sk3),nil)) != X1 ) ),
inference(instantiation,[status(thm)],[c_230684]) ).
tcf(c_244666,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ssItem(sk5(skaf45(sk3,app(X4,cons(hd(sk3),nil))),X4,hd(sk3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(instantiation,[status(thm)],[c_151335]) ).
tcf(c_244667,plain,
( duplicatefreeP(app(app(nil,cons(nil,nil)),cons(nil,nil)))
| ssItem(sk5(skaf45(sk3,app(nil,cons(hd(sk3),nil))),nil,hd(sk3)))
| ~ ssList(app(app(nil,cons(nil,nil)),cons(nil,nil))) ),
inference(instantiation,[status(thm)],[c_244666]) ).
tcf(c_261036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(X3)
| duplicatefreeP(app(app(X0,cons(hd(sk3),X1)),cons(hd(sk3),X2)))
| ~ ssList(app(app(X0,cons(hd(sk3),X1)),cons(hd(sk3),X2))) ),
inference(instantiation,[status(thm)],[c_151335]) ).
tcf(c_261037,plain,
( ssItem(nil)
| duplicatefreeP(app(app(nil,cons(hd(sk3),nil)),cons(hd(sk3),nil)))
| ~ ssList(app(app(nil,cons(hd(sk3),nil)),cons(hd(sk3),nil))) ),
inference(instantiation,[status(thm)],[c_261036]) ).
tcf(c_297380,plain,
( frontsegP(sk3,app(nil,cons(hd(sk3),nil)))
| ~ frontsegP(cons(hd(sk3),tl(sk3)),cons(hd(sk3),nil))
| ( sk3 != cons(hd(sk3),tl(sk3)) )
| ( app(nil,cons(hd(sk3),nil)) != cons(hd(sk3),nil) ) ),
inference(instantiation,[status(thm)],[c_239836]) ).
tcf(c_297381,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_297380,c_261037,c_244667,c_217747,c_212173,c_211062,c_140262,c_130413,c_130412,c_87598,c_63525,c_57305,c_13690,c_12622,c_7126,c_7125,c_2465,c_2258,c_2137,c_1872,c_1486,c_1483,c_564,c_510,c_442,c_260,c_440]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC248-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n020.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 17:14:04 UTC 2026
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 12.46/32.06 % SZS status Started for theBenchmark.p
% 12.46/32.06 % SZS status Unsatisfiable for theBenchmark.p
% 12.46/32.06
% 12.46/32.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 12.46/32.06
% 12.46/32.06 % ------ iProver source info
% 12.46/32.06
% 12.46/32.06 % git: date: 2026-07-19 20:42:38 +0200
% 12.46/32.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 12.46/32.06 % git: non_committed_changes: false
% 12.46/32.06
% 12.46/32.06 % ------ Parsing...% successful
% 12.46/32.06
% 12.46/32.06
% 12.46/32.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 12.46/32.06
% 12.46/32.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 1 0s sf_e %
% 12.46/32.06
% 12.46/32.06 % ------ Preprocessing...%
% 12.46/32.06
% 12.46/32.06 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 12.46/32.06 % ------ Proving...
% 12.46/32.06 % ------ Problem Properties
% 12.46/32.06
% 12.46/32.06 %
% 12.46/32.06 % clauses 193
% 12.46/32.06 % conjectures 14
% 12.46/32.06 % EPR 60
% 12.46/32.06 % Horn 163
% 12.46/32.06 % unary 65
% 12.46/32.06 % binary 21
% 12.46/32.06 % lits 597
% 12.46/32.06 % lits eq 82
% 12.46/32.06 % fd_pure 0
% 12.46/32.06 % fd_pseudo 0
% 12.46/32.06 % fd_cond 15
% 12.46/32.06 % fd_pseudo_cond 16
% 12.46/32.06 % AC symbols 0
% 12.46/32.06
% 12.46/32.06 % ------ Input Options Time Limit: Unbounded
% 12.46/32.06
% 12.46/32.06
% 12.46/32.06 % ------
% 12.46/32.06 % Current options:
% 12.46/32.06 % ------
% 12.46/32.06
% 12.46/32.06
% 12.46/32.06 %
% 12.46/32.06
% 12.46/32.06 % ------ Proving...
% 12.46/32.06 %
% 12.46/32.06
% 12.46/32.06 % SZS status Unsatisfiable for theBenchmark.p
% 12.46/32.06
% 12.46/32.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 12.46/32.06
% 12.46/32.06
%------------------------------------------------------------------------------