%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC421-1 : 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 : n005.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 03:09:49 PM UTC 2026
% Result : Unsatisfiable 70.01s 12.04s
% Output : CNFRefutation 70.01s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f245ERROR: Could not build tree for root c_125596ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f72,axiom,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause72) ).
fof(f73,axiom,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause73) ).
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(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(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(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(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(f206,negated_conjecture,
neq(sk2,nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X2,X0,X1] :
( app(app(X2,cons(X0,nil)),X1) != sk1
| app(app(X1,cons(X0,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,plain,
! [X2,X0,X1] :
( sk1 != app(app(X2,cons(X0,nil)),X1)
| sk2 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f207]) ).
fof(f210,negated_conjecture,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f214,plain,
neq(sk4,nil),
inference(definition_unfolding,[],[f206,f204]) ).
fof(f215,plain,
! [X2,X0,X1] :
( sk3 != app(app(X2,cons(X0,nil)),X1)
| sk4 != app(app(X1,cons(X0,nil)),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f208,f204,f205]) ).
fof(f233,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_316,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ 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_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_359,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f245]) ).
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_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_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,[],[f233]) ).
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,[],[f214]) ).
tcf(c_435,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != sk4 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_437,negated_conjecture,
( neq(sk3,nil)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_438,negated_conjecture,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| ~ neq(sk4,nil)
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil))) ),
inference(cnf_transformation,[],[f250]) ).
tcf(c_553,negated_conjecture,
neq(sk3,nil),
inference(global_subsumption_just,[status(thm)],[c_437,c_434,c_437]) ).
tcf(c_561,plain,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil)))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3)) ),
inference(global_subsumption_just,[status(thm)],[c_438,c_434,c_438]) ).
tcf(c_562,negated_conjecture,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ~ ssList(app(tl(sk3),cons(hd(sk3),nil))) ),
inference(renaming,[status(thm)],[c_561]) ).
tcf(c_800,plain,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ neq(nil,sk3)
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_562,c_329]) ).
tcf(c_3047,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_553,c_359]) ).
tcf(c_3048,plain,
( ~ ssList(sk3)
| ( sk3 != nil ) ),
inference(unflattening,[status(thm)],[c_3047]) ).
tcf(c_3049,plain,
sk3 != nil,
inference(global_subsumption_just,[status(thm)],[c_3048,c_432,c_3048]) ).
tcf(c_3076,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil))
| ( X1 != nil )
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_800,c_344]) ).
tcf(c_3077,plain,
( ( sk3 = nil )
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil)) ),
inference(unflattening,[status(thm)],[c_3076]) ).
tcf(c_3078,plain,
( ~ ssList(cons(hd(sk3),nil))
| ~ ssList(tl(sk3))
| ~ ssItem(hd(sk3))
| ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 ) ),
inference(global_subsumption_just,[status(thm)],[c_3077,c_432,c_252,c_3048,c_3077]) ).
tcf(c_3079,plain,
( ( app(tl(sk3),cons(hd(sk3),nil)) = sk4 )
| ~ ssItem(hd(sk3))
| ~ ssList(tl(sk3))
| ~ ssList(cons(hd(sk3),nil)) ),
inference(renaming,[status(thm)],[c_3078]) ).
tcf(c_6618,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_316]) ).
tcf(c_6619,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_316]) ).
tcf(c_6620,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_316]) ).
tcf(c_6621,definition,
iPr_def_12 = hd(sk3),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6622,definition,
iPr_def_13 = cons(iPr_def_12,nil),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6623,definition,
iPr_def_14 = tl(sk3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_6624,definition,
iPr_def_15 = app(iPr_def_14,iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_6625,plain,
( ( iPr_def_15 = sk4 )
| ~ ssItem(iPr_def_12)
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(demodulation,[status(thm)],[c_3079,c_6624,c_6623,c_6621,c_6622]) ).
tcf(c_6626,plain,
sk3 != nil,
inference(demodulation,[status(thm)],[c_3049]) ).
tcf(c_6628,negated_conjecture,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != sk4 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(demodulation,[status(thm)],[c_435]) ).
tcf(c_6629,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_6630,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_432]) ).
tcf(c_9202,plain,
( ( sk4 = iPr_def_15 )
| ~ iPr_def_10
| ~ ssList(iPr_def_14)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_6618,c_6625]) ).
tcf(c_9664,plain,
( ssList(iPr_def_14)
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_6623,c_321]) ).
tcf(c_9668,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_9664,c_6626,c_6630]) ).
tcf(c_9681,plain,
( ( sk4 = iPr_def_15 )
| ~ iPr_def_10
| ~ ssList(iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9202,c_9668]) ).
tcf(c_9682,plain,
( ( sk4 = iPr_def_15 )
| ~ ssItem(iPr_def_12)
| ~ ssList(iPr_def_13) ),
inference(backward_subsumption_resolution,[status(thm)],[c_6625,c_9668]) ).
tcf(c_9703,plain,
( ssItem(iPr_def_12)
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_6621,c_322]) ).
tcf(c_9704,plain,
ssItem(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9703,c_6626,c_6630]) ).
tcf(c_9766,plain,
( ssList(iPr_def_13)
| ~ ssItem(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6622,c_330]) ).
tcf(c_9770,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_9766,c_9704,c_252]) ).
tcf(c_9820,plain,
sk4 = iPr_def_15,
inference(global_subsumption_just,[status(thm)],[c_9681,c_9682,c_9704,c_9770]) ).
tcf(c_9826,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != iPr_def_15 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(demodulation,[status(thm)],[c_6628,c_9820]) ).
tcf(c_10832,plain,
( ( sk3 = nil )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(superposition,[status(thm)],[c_6630,c_348]) ).
tcf(c_10871,plain,
( ( sk3 = nil )
| ( cons(iPr_def_12,iPr_def_14) = sk3 ) ),
inference(light_normalisation,[status(thm)],[c_10832,c_6621,c_6623]) ).
tcf(c_10872,plain,
cons(iPr_def_12,iPr_def_14) = sk3,
inference(forward_subsumption_resolution,[status(thm)],[c_10871,c_6626]) ).
tcf(c_11166,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk3) = cons(X0,sk3) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6630,c_364]) ).
tcf(c_11388,plain,
app(cons(iPr_def_12,nil),sk3) = cons(iPr_def_12,sk3),
inference(superposition,[status(thm)],[c_9704,c_11166]) ).
tcf(c_11389,plain,
cons(iPr_def_12,sk3) = app(iPr_def_13,sk3),
inference(light_normalisation,[status(thm)],[c_11388,c_6622]) ).
tcf(c_15305,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(X0,sk3)) = app(cons(X1,X0),sk3) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6630,c_401]) ).
tcf(c_17429,plain,
! [X0: $i] :
( ( cons(X0,app(sk3,sk3)) = app(cons(X0,sk3),sk3) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6630,c_15305]) ).
tcf(c_17636,plain,
cons(iPr_def_12,app(sk3,sk3)) = app(cons(iPr_def_12,sk3),sk3),
inference(superposition,[status(thm)],[c_9704,c_17429]) ).
tcf(c_30546,plain,
( ssList(cons(iPr_def_12,sk3))
| ~ ssList(iPr_def_13)
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_11389,c_329]) ).
tcf(c_30557,plain,
ssList(cons(iPr_def_12,sk3)),
inference(forward_subsumption_resolution,[status(thm)],[c_30546,c_9770,c_6630]) ).
tcf(c_30654,plain,
app(nil,cons(iPr_def_12,sk3)) = cons(iPr_def_12,sk3),
inference(superposition,[status(thm)],[c_30557,c_318]) ).
tcf(c_34731,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ ssList(app(cons(iPr_def_12,sk3),cons(iPr_def_12,X0)))
| ~ duplicatefreeP(app(app(nil,cons(iPr_def_12,sk3)),cons(iPr_def_12,X0))) ),
inference(superposition,[status(thm)],[c_30654,c_423]) ).
tcf(c_34759,plain,
! [X0: $i] :
( ~ ssItem(iPr_def_12)
| ~ ssList(nil)
| ~ ssList(sk3)
| ~ ssList(X0)
| ~ duplicatefreeP(app(cons(iPr_def_12,sk3),cons(iPr_def_12,X0)))
| ~ ssList(app(cons(iPr_def_12,sk3),cons(iPr_def_12,X0))) ),
inference(light_normalisation,[status(thm)],[c_34731,c_30654]) ).
tcf(c_34760,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(cons(iPr_def_12,sk3),cons(iPr_def_12,X0)))
| ~ ssList(app(cons(iPr_def_12,sk3),cons(iPr_def_12,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34759,c_9704,c_252,c_6630]) ).
tcf(c_34874,plain,
( ~ ssList(iPr_def_14)
| ~ ssList(app(cons(iPr_def_12,sk3),sk3))
| ~ duplicatefreeP(app(cons(iPr_def_12,sk3),cons(iPr_def_12,iPr_def_14))) ),
inference(superposition,[status(thm)],[c_10872,c_34760]) ).
tcf(c_34876,plain,
( ~ ssList(iPr_def_14)
| ~ duplicatefreeP(cons(iPr_def_12,app(sk3,sk3)))
| ~ ssList(cons(iPr_def_12,app(sk3,sk3))) ),
inference(light_normalisation,[status(thm)],[c_34874,c_10872,c_17636]) ).
tcf(c_34877,plain,
( ~ duplicatefreeP(cons(iPr_def_12,app(sk3,sk3)))
| ~ ssList(cons(iPr_def_12,app(sk3,sk3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_34876,c_9668]) ).
tcf(c_121255,plain,
( ssList(cons(iPr_def_12,app(sk3,sk3)))
| ~ ssList(sk3)
| ~ ssList(cons(iPr_def_12,sk3)) ),
inference(superposition,[status(thm)],[c_17636,c_329]) ).
tcf(c_121302,plain,
ssList(cons(iPr_def_12,app(sk3,sk3))),
inference(forward_subsumption_resolution,[status(thm)],[c_121255,c_6630,c_30557]) ).
tcf(c_122207,plain,
( duplicatefreeP(cons(iPr_def_12,app(sk3,sk3)))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_121302,c_6619]) ).
tcf(c_123023,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_122207,c_34877,c_121302,c_122207]) ).
tcf(c_123025,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6620,c_123023]) ).
tcf(c_123045,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_6618,c_123025]) ).
tcf(c_123167,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != iPr_def_15 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_9826,c_123045]) ).
tcf(c_123203,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_364,c_123045]) ).
tcf(c_123215,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_330,c_123045]) ).
tcf(c_123894,plain,
iPr_def_15 = sk4,
inference(global_subsumption_just,[status(thm)],[c_6625,c_6625,c_9668,c_9704,c_9770]) ).
tcf(c_123897,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != iPr_def_15 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(demodulation,[status(thm)],[c_6628,c_123894]) ).
tcf(c_123898,plain,
ssList(iPr_def_15),
inference(demodulation,[status(thm)],[c_6629,c_123894]) ).
tcf(c_123904,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( app(app(X0,cons(X1,nil)),X2) != sk3 )
| ( app(app(X2,cons(X1,nil)),X0) != iPr_def_15 )
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(global_subsumption_just,[status(thm)],[c_123897,c_123167]) ).
tcf(c_123905,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(X2)
| ~ ssList(X0)
| ( app(app(X2,cons(X1,nil)),X0) != iPr_def_15 )
| ( app(app(X0,cons(X1,nil)),X2) != sk3 ) ),
inference(renaming,[status(thm)],[c_123904]) ).
tcf(c_123912,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_13),X0) != sk3 )
| ( app(app(X0,cons(iPr_def_12,nil)),X1) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_6622,c_123905]) ).
tcf(c_123913,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssList(X0)
| ( app(app(X1,iPr_def_13),X0) != sk3 )
| ( app(app(X0,iPr_def_13),X1) != iPr_def_15 ) ),
inference(light_normalisation,[status(thm)],[c_123912,c_6622]) ).
tcf(c_124025,plain,
app(iPr_def_15,nil) = iPr_def_15,
inference(superposition,[status(thm)],[c_123898,c_317]) ).
tcf(c_124078,plain,
( ssList(iPr_def_14)
| ( sk3 = nil )
| ~ ssList(sk3) ),
inference(superposition,[status(thm)],[c_6623,c_321]) ).
tcf(c_124081,plain,
ssList(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_124078,c_6626,c_6630]) ).
tcf(c_124127,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_330,c_123215]) ).
tcf(c_124133,plain,
( ssList(iPr_def_13)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6622,c_124127]) ).
tcf(c_124136,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_124133,c_252]) ).
tcf(c_124163,plain,
app(nil,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_124136,c_318]) ).
tcf(c_124167,plain,
! [X0: $i] :
( ~ ssList(nil)
| ~ ssList(X0)
| ( app(iPr_def_13,X0) != sk3 )
| ( app(app(X0,iPr_def_13),nil) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_124163,c_123913]) ).
tcf(c_124172,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( app(iPr_def_13,X0) != sk3 )
| ( app(app(X0,iPr_def_13),nil) != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_124167,c_252]) ).
tcf(c_124188,plain,
( ~ ssList(iPr_def_14)
| ( app(iPr_def_15,nil) != iPr_def_15 )
| ( app(iPr_def_13,iPr_def_14) != sk3 ) ),
inference(superposition,[status(thm)],[c_6624,c_124172]) ).
tcf(c_124194,plain,
( ~ ssList(iPr_def_14)
| ( app(iPr_def_13,iPr_def_14) != sk3 ) ),
inference(ground_joinability,[status(thm)],[c_124188,c_124025]) ).
tcf(c_124195,plain,
app(iPr_def_13,iPr_def_14) != sk3,
inference(forward_subsumption_resolution,[status(thm)],[c_124194,c_124081]) ).
tcf(c_124876,plain,
( ( sk3 = nil )
| ( cons(hd(sk3),tl(sk3)) = sk3 ) ),
inference(superposition,[status(thm)],[c_6630,c_348]) ).
tcf(c_124916,plain,
( ( sk3 = nil )
| ( cons(iPr_def_12,iPr_def_14) = sk3 ) ),
inference(light_normalisation,[status(thm)],[c_124876,c_6621,c_6623]) ).
tcf(c_124917,plain,
cons(iPr_def_12,iPr_def_14) = sk3,
inference(forward_subsumption_resolution,[status(thm)],[c_124916,c_6626]) ).
tcf(c_125167,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_364,c_123203]) ).
tcf(c_125206,plain,
! [X0: $i] : app(cons(X0,nil),iPr_def_14) = cons(X0,iPr_def_14),
inference(superposition,[status(thm)],[c_124081,c_125167]) ).
tcf(c_125589,plain,
cons(iPr_def_12,iPr_def_14) = app(iPr_def_13,iPr_def_14),
inference(superposition,[status(thm)],[c_6622,c_125206]) ).
tcf(c_125595,plain,
app(iPr_def_13,iPr_def_14) = sk3,
inference(light_normalisation,[status(thm)],[c_125589,c_124917]) ).
tcf(c_125596,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_125595,c_124195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC421-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.40 % Computer : n005.cluster.edu
% 0.16/0.40 % Model : x86_64 x86_64
% 0.16/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.40 % Memory : 8046.5625MB
% 0.16/0.40 % OS : Linux 6.8.0-71-generic
% 0.16/0.40 % CPULimit : 300
% 0.16/0.40 % WCLimit : 300
% 0.16/0.40 % DateTime : Thu Sep 24 18:10:18 UTC 2026
% 0.16/0.40 % CPUTime :
% 0.16/0.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.44 Running first-order theorem proving
% 0.16/0.44 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
% 0.16/0.46
% 0.16/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.46
% 0.16/0.46 % Detected problem language: tptp
% 0.21/0.48 % Proving...
% 70.01/12.04 % SZS status Started for theBenchmark.p
% 70.01/12.04 % SZS status Unsatisfiable for theBenchmark.p
% 70.01/12.04
% 70.01/12.04 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 70.01/12.04
% 70.01/12.04 % ------ iProver source info
% 70.01/12.04
% 70.01/12.04 % git: date: 2026-07-19 20:42:38 +0200
% 70.01/12.04 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 70.01/12.04 % git: non_committed_changes: false
% 70.01/12.04
% 70.01/12.04 % ------ Parsing...% successful
% 70.01/12.04
% 70.01/12.04
% 70.01/12.04 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 70.01/12.04
% 70.01/12.04 % ------ 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 %
% 70.01/12.04
% 70.01/12.04 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 70.01/12.04
% 70.01/12.04 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 70.01/12.04 % ------ Proving...
% 70.01/12.04 % ------ Problem Properties
% 70.01/12.04
% 70.01/12.04 %
% 70.01/12.04 % clauses 187
% 70.01/12.04 % conjectures 3
% 70.01/12.04 % EPR 57
% 70.01/12.04 % Horn 159
% 70.01/12.04 % unary 66
% 70.01/12.04 % binary 21
% 70.01/12.04 % lits 558
% 70.01/12.04 % lits eq 78
% 70.01/12.04 % fd_pure 0
% 70.01/12.04 % fd_pseudo 0
% 70.01/12.04 % fd_cond 15
% 70.01/12.04 % fd_pseudo_cond 14
% 70.01/12.04 % AC symbols 0
% 70.01/12.04
% 70.01/12.04 % ------ Schedule dynamic 5 is on
% 70.01/12.04
% 70.01/12.04 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 70.01/12.04
% 70.01/12.04
% 70.01/12.04 % ------
% 70.01/12.04 % Current options:
% 70.01/12.04 % ------
% 70.01/12.04
% 70.01/12.04
% 70.01/12.04 %
% 70.01/12.04
% 70.01/12.04 % ------ Proving...
% 70.01/12.04 % Proof_search_loop: time out after: 4408 full_loop iterations
% 70.01/12.04
% 70.01/12.04 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 70.01/12.04
% 70.01/12.04
% 70.01/12.04 % ------
% 70.01/12.04 % Current options:
% 70.01/12.04 % ------
% 70.01/12.04
% 70.01/12.04
% 70.01/12.04 %
% 70.01/12.04
% 70.01/12.04 % ------ Proving...
% 70.01/12.04 %
% 70.01/12.04
% 70.01/12.04 % SZS status Unsatisfiable for theBenchmark.p
% 70.01/12.04
% 70.01/12.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 70.01/12.05
% 70.01/12.05
%------------------------------------------------------------------------------