%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC354-1 : 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 03:09:26 PM UTC 2026
% Result : Unsatisfiable 115.05s 16.49s
% Output : CNFRefutation 115.06s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f253ERROR: Could not build tree for root c_228401ERROR: 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(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(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(f208,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_9) ).
fof(f210,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_11) ).
fof(f211,negated_conjecture,
( ~ neq(sk4,nil)
| ~ segmentP(sk2,sk1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f216,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,[],[f208,f204]) ).
fof(f218,plain,
( ~ neq(sk4,nil)
| ~ segmentP(sk4,sk3) ),
inference(definition_unfolding,[],[f211,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,[],[f216]) ).
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,[],[f210]) ).
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_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_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_436,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,
( ( 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_439,negated_conjecture,
( ~ segmentP(sk4,sk3)
| ~ neq(sk4,nil) ),
inference(cnf_transformation,[],[f218]) ).
tcf(c_555,negated_conjecture,
~ segmentP(sk4,sk3),
inference(global_subsumption_just,[status(thm)],[c_439,c_435,c_439]) ).
tcf(c_563,negated_conjecture,
neq(sk4,nil),
inference(global_subsumption_just,[status(thm)],[c_436,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_438,c_435,c_438]) ).
tcf(c_799,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_2982,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != nil )
| ( X0 != sk4 ) ),
inference(resolution_lifted,[status(thm)],[c_563,c_360]) ).
tcf(c_2983,plain,
( ~ ssList(sk4)
| ( sk4 != nil ) ),
inference(unflattening,[status(thm)],[c_2982]) ).
tcf(c_2984,plain,
sk4 != nil,
inference(global_subsumption_just,[status(thm)],[c_2983,c_434,c_2983]) ).
tcf(c_3008,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_3009,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_3008]) ).
tcf(c_3010,plain,
( ~ ssList(cons(hd(sk4),nil))
| ~ ssItem(hd(sk4))
| ( cons(hd(sk4),nil) = sk3 ) ),
inference(global_subsumption_just,[status(thm)],[c_3009,c_434,c_253,c_2983,c_3009]) ).
tcf(c_3011,plain,
( ( cons(hd(sk4),nil) = sk3 )
| ~ ssItem(hd(sk4))
| ~ ssList(cons(hd(sk4),nil)) ),
inference(renaming,[status(thm)],[c_3010]) ).
tcf(c_6521,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_317]) ).
tcf(c_6522,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_317]) ).
tcf(c_6523,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_317]) ).
tcf(c_6524,definition,
iPr_def_12 = hd(sk4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_6525,definition,
iPr_def_13 = cons(iPr_def_12,nil),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_6526,plain,
( ( iPr_def_13 = sk3 )
| ~ ssItem(iPr_def_12)
| ~ ssList(iPr_def_13) ),
inference(demodulation,[status(thm)],[c_3011,c_6524,c_6525]) ).
tcf(c_6527,plain,
sk4 != nil,
inference(demodulation,[status(thm)],[c_2984]) ).
tcf(c_6528,negated_conjecture,
~ segmentP(sk4,sk3),
inference(demodulation,[status(thm)],[c_555]) ).
tcf(c_6529,negated_conjecture,
ssList(sk4),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_6530,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_433]) ).
tcf(c_9510,plain,
( ssItem(iPr_def_12)
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_6524,c_323]) ).
tcf(c_9511,plain,
ssItem(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_9510,c_6527,c_6529]) ).
tcf(c_9566,plain,
( ssList(iPr_def_13)
| ~ ssItem(iPr_def_12)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_6525,c_331]) ).
tcf(c_9570,plain,
ssList(iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_9566,c_9511,c_253]) ).
tcf(c_9915,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_331,c_361]) ).
tcf(c_9919,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_9915,c_253]) ).
tcf(c_10243,plain,
( ssList(tl(sk4))
| ( sk4 = nil )
| ~ ssList(sk4) ),
inference(instantiation,[status(thm)],[c_322]) ).
tcf(c_10577,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6529,c_349]) ).
tcf(c_10611,plain,
( ( sk4 = nil )
| ( cons(iPr_def_12,tl(sk4)) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_10577,c_6524]) ).
tcf(c_10612,plain,
cons(iPr_def_12,tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_10611,c_6527]) ).
tcf(c_10905,plain,
! [X0: $i] :
( ( app(cons(X0,nil),sk4) = cons(X0,sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6529,c_365]) ).
tcf(c_11099,plain,
app(cons(iPr_def_12,nil),sk4) = cons(iPr_def_12,sk4),
inference(superposition,[status(thm)],[c_9511,c_10905]) ).
tcf(c_11100,plain,
cons(iPr_def_12,sk4) = app(iPr_def_13,sk4),
inference(light_normalisation,[status(thm)],[c_11099,c_6525]) ).
tcf(c_15366,plain,
! [X0: $i,X1: $i] :
( ( cons(X1,app(sk4,X0)) = app(cons(X1,sk4),X0) )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_6529,c_402]) ).
tcf(c_17711,plain,
! [X0: $i] :
( ( cons(X0,app(sk4,sk4)) = app(cons(X0,sk4),sk4) )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_6529,c_15366]) ).
tcf(c_17947,plain,
cons(iPr_def_12,app(sk4,sk4)) = app(cons(iPr_def_12,sk4),sk4),
inference(superposition,[status(thm)],[c_9511,c_17711]) ).
tcf(c_26945,plain,
( ssList(cons(iPr_def_12,sk4))
| ~ ssList(iPr_def_13)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_11100,c_330]) ).
tcf(c_26965,plain,
ssList(cons(iPr_def_12,sk4)),
inference(forward_subsumption_resolution,[status(thm)],[c_26945,c_9570,c_6529]) ).
tcf(c_27105,plain,
app(nil,cons(iPr_def_12,sk4)) = cons(iPr_def_12,sk4),
inference(superposition,[status(thm)],[c_26965,c_319]) ).
tcf(c_28895,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_27105,c_424]) ).
tcf(c_28923,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_28895,c_27105]) ).
tcf(c_28924,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_28923,c_9511,c_253,c_6529]) ).
tcf(c_29537,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_10612,c_28924]) ).
tcf(c_29545,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_29537,c_10612,c_17947]) ).
tcf(c_90070,plain,
( ssList(cons(iPr_def_12,app(sk4,sk4)))
| ~ ssList(sk4)
| ~ ssList(cons(iPr_def_12,sk4)) ),
inference(superposition,[status(thm)],[c_17947,c_330]) ).
tcf(c_90111,plain,
ssList(cons(iPr_def_12,app(sk4,sk4))),
inference(forward_subsumption_resolution,[status(thm)],[c_90070,c_6529,c_26965]) ).
tcf(c_90387,plain,
( duplicatefreeP(cons(iPr_def_12,app(sk4,sk4)))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_90111,c_6522]) ).
tcf(c_91217,plain,
~ iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_90387,c_434,c_2983,c_10243,c_29545,c_90111,c_90387]) ).
tcf(c_91219,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_6523,c_91217]) ).
tcf(c_91236,plain,
! [X0: $i] : ssItem(X0),
inference(backward_subsumption_resolution,[status(thm)],[c_6521,c_91219]) ).
tcf(c_91359,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_365,c_91236]) ).
tcf(c_91369,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_342,c_91236]) ).
tcf(c_91370,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_341,c_91236]) ).
tcf(c_156128,plain,
iPr_def_13 = sk3,
inference(global_subsumption_just,[status(thm)],[c_6526,c_6526,c_9511,c_9570]) ).
tcf(c_156130,plain,
~ segmentP(sk4,iPr_def_13),
inference(demodulation,[status(thm)],[c_6528,c_156128]) ).
tcf(c_156131,plain,
ssList(iPr_def_13),
inference(demodulation,[status(thm)],[c_6530,c_156128]) ).
tcf(c_156250,plain,
app(nil,iPr_def_13) = iPr_def_13,
inference(superposition,[status(thm)],[c_156131,c_319]) ).
tcf(c_156668,plain,
! [X0: $i] : singletonP(cons(X0,nil)),
inference(global_subsumption_just,[status(thm)],[c_361,c_434,c_2983,c_6521,c_6523,c_9919,c_10243,c_29545,c_90111,c_90387]) ).
tcf(c_156670,plain,
singletonP(iPr_def_13),
inference(superposition,[status(thm)],[c_6525,c_156668]) ).
tcf(c_156671,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_341,c_91370]) ).
tcf(c_156679,plain,
! [X0: $i,X1: $i] : tl(cons(X0,skaf82(X1))) = skaf82(X1),
inference(superposition,[status(thm)],[c_258,c_156671]) ).
tcf(c_156729,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X1,X0)) = X1 )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_342,c_91369]) ).
tcf(c_156735,plain,
! [X0: $i] : hd(cons(X0,sk4)) = X0,
inference(superposition,[status(thm)],[c_6529,c_156729]) ).
tcf(c_156836,plain,
( ( cons(skaf44(iPr_def_13),nil) = iPr_def_13 )
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_156670,c_346]) ).
tcf(c_156837,plain,
cons(skaf44(iPr_def_13),nil) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_156836,c_156131]) ).
tcf(c_156932,plain,
( ( sk4 = nil )
| ( cons(hd(sk4),tl(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6529,c_349]) ).
tcf(c_156967,plain,
( ( sk4 = nil )
| ( cons(iPr_def_12,tl(sk4)) = sk4 ) ),
inference(light_normalisation,[status(thm)],[c_156932,c_6524]) ).
tcf(c_156968,plain,
cons(iPr_def_12,tl(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_156967,c_6527]) ).
tcf(c_157102,plain,
( ( sk4 = nil )
| ( cons(skaf83(sk4),skaf82(sk4)) = sk4 ) ),
inference(superposition,[status(thm)],[c_6529,c_354]) ).
tcf(c_157137,plain,
cons(skaf83(sk4),skaf82(sk4)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_157102,c_6527]) ).
tcf(c_157230,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X1,nil),X0) = cons(X1,X0) )
| ~ ssList(X0) ),
inference(global_subsumption_just,[status(thm)],[c_365,c_91359]) ).
tcf(c_157236,plain,
! [X0: $i] : app(cons(X0,nil),sk4) = cons(X0,sk4),
inference(superposition,[status(thm)],[c_6529,c_157230]) ).
tcf(c_157238,plain,
! [X0: $i,X1: $i] : app(cons(X0,nil),skaf82(X1)) = cons(X0,skaf82(X1)),
inference(superposition,[status(thm)],[c_258,c_157230]) ).
tcf(c_157450,plain,
cons(iPr_def_12,sk4) = app(iPr_def_13,sk4),
inference(superposition,[status(thm)],[c_6525,c_157236]) ).
tcf(c_157451,plain,
cons(skaf44(iPr_def_13),sk4) = app(iPr_def_13,sk4),
inference(superposition,[status(thm)],[c_156837,c_157236]) ).
tcf(c_157944,plain,
cons(skaf44(iPr_def_13),sk4) = cons(iPr_def_12,sk4),
inference(light_normalisation,[status(thm)],[c_157451,c_157450]) ).
tcf(c_157955,plain,
hd(cons(iPr_def_12,sk4)) = skaf44(iPr_def_13),
inference(superposition,[status(thm)],[c_157944,c_156735]) ).
tcf(c_157974,plain,
skaf44(iPr_def_13) = iPr_def_12,
inference(demodulation,[status(thm)],[c_157955,c_156735]) ).
tcf(c_157978,plain,
cons(iPr_def_12,nil) = iPr_def_13,
inference(demodulation,[status(thm)],[c_156837,c_157974]) ).
tcf(c_157979,plain,
skaf82(sk4) = tl(sk4),
inference(superposition,[status(thm)],[c_157137,c_156679]) ).
tcf(c_166847,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_156250,c_418]) ).
tcf(c_166876,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_166847,c_156250]) ).
tcf(c_166877,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_166876,c_156131,c_253]) ).
tcf(c_226322,plain,
! [X0: $i] : cons(iPr_def_12,skaf82(X0)) = app(iPr_def_13,skaf82(X0)),
inference(superposition,[status(thm)],[c_157978,c_157238]) ).
tcf(c_228024,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_226322,c_799]) ).
tcf(c_228037,plain,
! [X0: $i] : frontsegP(cons(iPr_def_12,skaf82(X0)),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_228024,c_156131,c_258]) ).
tcf(c_228335,plain,
frontsegP(cons(iPr_def_12,tl(sk4)),iPr_def_13),
inference(superposition,[status(thm)],[c_157979,c_228037]) ).
tcf(c_228341,plain,
frontsegP(sk4,iPr_def_13),
inference(light_normalisation,[status(thm)],[c_228335,c_156968]) ).
tcf(c_228367,plain,
( ( app(iPr_def_13,skaf45(sk4,iPr_def_13)) = sk4 )
| ~ ssList(iPr_def_13)
| ~ ssList(sk4) ),
inference(superposition,[status(thm)],[c_228341,c_377]) ).
tcf(c_228372,plain,
app(iPr_def_13,skaf45(sk4,iPr_def_13)) = sk4,
inference(forward_subsumption_resolution,[status(thm)],[c_228367,c_156131,c_6529]) ).
tcf(c_228397,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_228372,c_166877]) ).
tcf(c_228400,plain,
( segmentP(sk4,iPr_def_13)
| ~ ssList(sk4)
| ~ ssList(skaf45(sk4,iPr_def_13)) ),
inference(light_normalisation,[status(thm)],[c_228397,c_228372]) ).
tcf(c_228401,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_228400,c_156130,c_6529,c_296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC354-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n020.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 17:49:04 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 115.05/16.49 % SZS status Started for theBenchmark.p
% 115.05/16.49 % SZS status Unsatisfiable for theBenchmark.p
% 115.05/16.49
% 115.05/16.49 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 115.05/16.49
% 115.05/16.49 % ------ iProver source info
% 115.05/16.49
% 115.05/16.49 % git: date: 2026-07-19 20:42:38 +0200
% 115.05/16.49 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 115.05/16.49 % git: non_committed_changes: false
% 115.05/16.49
% 115.05/16.49 % ------ Parsing...% successful
% 115.05/16.49
% 115.05/16.49
% 115.05/16.49 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 115.05/16.49
% 115.05/16.49 % ------ 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 %
% 115.05/16.49
% 115.05/16.49 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 115.05/16.49
% 115.05/16.49 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 115.05/16.49 % ------ Proving...
% 115.05/16.49 % ------ Problem Properties
% 115.05/16.49
% 115.05/16.49 %
% 115.05/16.49 % clauses 184
% 115.05/16.49 % conjectures 3
% 115.05/16.49 % EPR 57
% 115.05/16.49 % Horn 156
% 115.05/16.49 % unary 64
% 115.05/16.49 % binary 21
% 115.05/16.49 % lits 550
% 115.05/16.49 % lits eq 73
% 115.05/16.49 % fd_pure 0
% 115.05/16.49 % fd_pseudo 0
% 115.05/16.49 % fd_cond 15
% 115.05/16.49 % fd_pseudo_cond 14
% 115.05/16.49 % AC symbols 0
% 115.05/16.49
% 115.05/16.49 % ------ Schedule dynamic 5 is on
% 115.05/16.49
% 115.05/16.49 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 115.05/16.49
% 115.05/16.49
% 115.05/16.49 % ------
% 115.05/16.49 % Current options:
% 115.05/16.49 % ------
% 115.05/16.49
% 115.05/16.49
% 115.05/16.49 %
% 115.05/16.49
% 115.05/16.49 % ------ Proving...
% 115.05/16.49 % Proof_search_loop: time out after: 5387 full_loop iterations
% 115.05/16.49
% 115.05/16.49 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 115.05/16.49
% 115.05/16.49
% 115.05/16.49 % ------
% 115.05/16.49 % Current options:
% 115.05/16.49 % ------
% 115.05/16.49
% 115.05/16.49
% 115.05/16.49 %
% 115.05/16.49
% 115.05/16.49 % ------ Proving...
% 115.05/16.49 %
% 115.05/16.49
% 115.05/16.49 % SZS status Unsatisfiable for theBenchmark.p
% 115.05/16.49
% 115.05/16.49 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 115.06/16.50
% 115.06/16.50
%------------------------------------------------------------------------------