%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC166-1 : 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 : n003.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 03:08:11 PM UTC 2026
% Result : Unsatisfiable 18.34s 3.85s
% Output : CNFRefutation 18.34s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f244ERROR: Could not build tree for root c_54861ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause8) ).
fof(f47,axiom,
! [X0] : ssItem(skaf44(X0)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause47) ).
fof(f50,axiom,
! [X0,X1] : ssList(skaf46(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause50) ).
fof(f52,axiom,
! [X0,X1] : ssList(skaf43(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause52) ).
fof(f53,axiom,
! [X0,X1] : ssList(skaf42(X0,X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause53) ).
fof(f65,axiom,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause65) ).
fof(f71,axiom,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause71) ).
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(f77,axiom,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause77) ).
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(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(f103,axiom,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause101) ).
fof(f104,axiom,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause102) ).
fof(f105,plain,
! [X0,X1] :
( X0 = X1
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(reorient_equations,[],[f104]) ).
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(f123,axiom,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause119) ).
fof(f124,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(reorient_equations,[],[f123]) ).
fof(f136,axiom,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause128) ).
fof(f137,plain,
! [X0,X1] :
( X0 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(reorient_equations,[],[f136]) ).
fof(f142,axiom,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause131) ).
fof(f144,axiom,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause133) ).
fof(f152,axiom,
! [X2,X0,X1] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause141) ).
fof(f154,axiom,
! [X2,X0,X1] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause143) ).
fof(f163,axiom,
! [X2,X0,X1] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause151) ).
fof(f173,axiom,
! [X2,X0,X1] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause161) ).
fof(f174,plain,
! [X2,X0,X1] :
( X0 = X2
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(reorient_equations,[],[f173]) ).
fof(f182,axiom,
! [X0,X1] :
( app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ memberP(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001-0.ax',clause169) ).
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,
singletonP(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_10) ).
fof(f210,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_11) ).
fof(f211,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_12) ).
fof(f212,plain,
sk1 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(reorient_equations,[],[f211]) ).
fof(f213,negated_conjecture,
~ neq(sk5,sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_13) ).
fof(f216,plain,
sk3 = app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8),
inference(definition_unfolding,[],[f212,f205]) ).
fof(f224,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(equality_resolution,[],[f119]) ).
fof(f227,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[],[f154]) ).
fof(f234,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_254,plain,
ssList(nil),
inference(cnf_transformation,[],[f8]) ).
tcf(c_293,plain,
! [X0: $i] : ssItem(skaf44(X0)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[],[f50]) ).
tcf(c_298,plain,
! [X0: $i,X1: $i] : ssList(skaf43(X0,X1)),
inference(cnf_transformation,[],[f52]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] : ssList(skaf42(X0,X1)),
inference(cnf_transformation,[],[f53]) ).
tcf(c_311,plain,
! [X0: $i] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_317,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] :
( duplicatefreeP(X0)
| ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_319,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_323,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_331,plain,
! [X0: $i,X1: $i] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X1,X0)) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( ~ ssItem(X0)
| ~ ssList(X1)
| ( cons(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_347,plain,
! [X0: $i] :
( ( cons(skaf44(X0),nil) = X0 )
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_362,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(cnf_transformation,[],[f224]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f124]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_377,plain,
! [X0: $i,X1: $i] :
( ( app(skaf46(X0,X1),X1) = X0 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_379,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ( app(tl(X1),X0) = tl(app(X1,X0)) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_384,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X1,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f244]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_389,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f227]) ).
tcf(c_397,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != app(X2,X1) ) ),
inference(cnf_transformation,[],[f163]) ).
tcf(c_407,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(X1,X2)
| ( X0 = X2 )
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[],[f174]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] :
( ( app(skaf42(X0,X1),cons(X1,skaf43(X1,X0))) = X0 )
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_425,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,[],[f234]) ).
tcf(c_434,negated_conjecture,
ssList(sk3),
inference(cnf_transformation,[],[f202]) ).
tcf(c_436,negated_conjecture,
singletonP(sk3),
inference(cnf_transformation,[],[f206]) ).
tcf(c_437,negated_conjecture,
ssItem(sk5),
inference(cnf_transformation,[],[f207]) ).
tcf(c_438,negated_conjecture,
ssItem(sk6),
inference(cnf_transformation,[],[f208]) ).
tcf(c_439,negated_conjecture,
ssList(sk7),
inference(cnf_transformation,[],[f209]) ).
tcf(c_440,negated_conjecture,
ssList(sk8),
inference(cnf_transformation,[],[f210]) ).
tcf(c_441,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk3,
inference(cnf_transformation,[],[f216]) ).
tcf(c_442,negated_conjecture,
~ neq(sk5,sk6),
inference(cnf_transformation,[],[f213]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_389,c_331]) ).
tcf(c_2728,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssItem(X1)
| ~ ssItem(X0)
| ( X1 != sk6 )
| ( X0 != sk5 ) ),
inference(resolution_lifted,[status(thm)],[c_442,c_348]) ).
tcf(c_2729,plain,
( ( sk5 = sk6 )
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(unflattening,[status(thm)],[c_2728]) ).
tcf(c_2730,plain,
sk5 = sk6,
inference(global_subsumption_just,[status(thm)],[c_2729,c_438,c_437,c_2729]) ).
tcf(c_4930,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),sk8) = sk3,
inference(light_normalisation,[status(thm)],[c_441,c_2730]) ).
tcf(c_9393,plain,
! [X0: $i] :
( ~ iPr_def_10
| ssItem(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_318]) ).
tcf(c_9394,plain,
! [X0: $i] :
( ~ iPr_def_11
| ~ ssList(X0)
| duplicatefreeP(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_318]) ).
tcf(c_9395,plain,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_318]) ).
tcf(c_9396,definition,
iPr_def_12 = cons(sk5,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_9397,definition,
iPr_def_13 = app(sk7,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_9398,definition,
iPr_def_14 = app(iPr_def_13,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_9399,definition,
iPr_def_15 = app(iPr_def_14,sk8),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_9400,plain,
iPr_def_15 = sk3,
inference(demodulation,[status(thm)],[c_4930,c_9396,c_9397,c_9398,c_9399]) ).
tcf(c_9402,negated_conjecture,
ssList(sk8),
inference(demodulation,[status(thm)],[c_440]) ).
tcf(c_9403,negated_conjecture,
ssList(sk7),
inference(demodulation,[status(thm)],[c_439]) ).
tcf(c_9404,negated_conjecture,
ssItem(sk5),
inference(demodulation,[status(thm)],[c_437]) ).
tcf(c_9405,negated_conjecture,
singletonP(sk3),
inference(demodulation,[status(thm)],[c_436]) ).
tcf(c_9407,negated_conjecture,
ssList(sk3),
inference(demodulation,[status(thm)],[c_434]) ).
tcf(c_11920,plain,
singletonP(iPr_def_15),
inference(light_normalisation,[status(thm)],[c_9405,c_9400]) ).
tcf(c_11921,plain,
ssList(iPr_def_15),
inference(light_normalisation,[status(thm)],[c_9407,c_9400]) ).
tcf(c_12008,plain,
app(sk8,nil) = sk8,
inference(superposition,[status(thm)],[c_9402,c_319]) ).
tcf(c_12303,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7) ),
inference(superposition,[status(thm)],[c_9397,c_331]) ).
tcf(c_12304,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_9398,c_331]) ).
tcf(c_12321,plain,
( ssList(iPr_def_13)
| ~ ssList(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12303,c_9403]) ).
tcf(c_12324,plain,
( ssList(iPr_def_14)
| ~ ssList(iPr_def_12) ),
inference(backward_subsumption_resolution,[status(thm)],[c_12304,c_12321]) ).
tcf(c_12346,plain,
( ssList(iPr_def_12)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_9396,c_332]) ).
tcf(c_12350,plain,
ssList(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_12346,c_9404,c_254]) ).
tcf(c_12383,plain,
ssList(iPr_def_13),
inference(global_subsumption_just,[status(thm)],[c_12321,c_12321,c_12350]) ).
tcf(c_12394,plain,
ssList(iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_12324,c_12324,c_12350]) ).
tcf(c_12396,plain,
( duplicatefreeP(iPr_def_14)
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_12394,c_9394]) ).
tcf(c_12398,plain,
app(iPr_def_14,nil) = iPr_def_14,
inference(superposition,[status(thm)],[c_12394,c_319]) ).
tcf(c_12577,plain,
( memberP(iPr_def_12,sk5)
| ~ ssItem(sk5)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_9396,c_384]) ).
tcf(c_12578,plain,
memberP(iPr_def_12,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_12577,c_9404,c_254]) ).
tcf(c_12645,plain,
( rearsegP(iPr_def_15,sk8)
| ~ ssList(iPr_def_14)
| ~ ssList(sk8) ),
inference(superposition,[status(thm)],[c_9399,c_805]) ).
tcf(c_12648,plain,
( rearsegP(sk8,nil)
| ~ ssList(nil)
| ~ ssList(sk8) ),
inference(superposition,[status(thm)],[c_12008,c_805]) ).
tcf(c_12676,plain,
rearsegP(sk8,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_12648,c_254,c_9402]) ).
tcf(c_12679,plain,
rearsegP(iPr_def_15,sk8),
inference(forward_subsumption_resolution,[status(thm)],[c_12645,c_12394,c_9402]) ).
tcf(c_12704,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_332,c_362]) ).
tcf(c_12708,plain,
! [X0: $i] :
( singletonP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12704,c_254]) ).
tcf(c_12723,plain,
! [X0: $i] :
( ( tl(cons(X0,nil)) = nil )
| ~ ssItem(X0) ),
inference(superposition,[status(thm)],[c_254,c_342]) ).
tcf(c_13152,plain,
( ~ ssItem(sk5)
| ~ ssList(nil)
| ( nil != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_9396,c_344]) ).
tcf(c_13153,plain,
nil != iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_13152,c_9404,c_254]) ).
tcf(c_13167,plain,
( ( cons(skaf44(iPr_def_15),nil) = iPr_def_15 )
| ~ ssList(iPr_def_15) ),
inference(superposition,[status(thm)],[c_11920,c_347]) ).
tcf(c_13168,plain,
cons(skaf44(iPr_def_15),nil) = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_13167,c_11921]) ).
tcf(c_13929,plain,
( duplicatefreeP(iPr_def_15)
| ~ ssItem(skaf44(iPr_def_15)) ),
inference(superposition,[status(thm)],[c_13168,c_311]) ).
tcf(c_13936,plain,
duplicatefreeP(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_13929,c_293]) ).
tcf(c_14455,plain,
( ( nil = iPr_def_12 )
| ~ ssList(iPr_def_13)
| ~ ssList(iPr_def_12)
| ( nil != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_9398,c_365]) ).
tcf(c_14480,plain,
nil != iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_14455,c_13153,c_12383,c_12350]) ).
tcf(c_15727,plain,
( ( sk8 = nil )
| ~ ssList(nil)
| ~ ssList(sk8)
| ~ rearsegP(nil,sk8) ),
inference(superposition,[status(thm)],[c_12676,c_374]) ).
tcf(c_15752,plain,
( ( sk8 = nil )
| ~ rearsegP(nil,sk8) ),
inference(forward_subsumption_resolution,[status(thm)],[c_15727,c_254,c_9402]) ).
tcf(c_16032,plain,
( ( app(skaf46(iPr_def_15,sk8),sk8) = iPr_def_15 )
| ~ ssList(iPr_def_15)
| ~ ssList(sk8) ),
inference(superposition,[status(thm)],[c_12679,c_377]) ).
tcf(c_16072,plain,
app(skaf46(iPr_def_15,sk8),sk8) = iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_16032,c_11921,c_9402]) ).
tcf(c_16803,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssList(iPr_def_12)
| ~ ssList(sk7)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_9397,c_387]) ).
tcf(c_16844,plain,
! [X0: $i] :
( memberP(iPr_def_13,X0)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_16803,c_12350,c_9403]) ).
tcf(c_17440,plain,
! [X0: $i] :
( ( X0 = nil )
| ( app(tl(X0),sk8) = tl(app(X0,sk8)) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_9402,c_379]) ).
tcf(c_18277,plain,
( memberP(iPr_def_13,sk5)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_12578,c_16844]) ).
tcf(c_18278,plain,
memberP(iPr_def_13,sk5),
inference(forward_subsumption_resolution,[status(thm)],[c_18277,c_9404]) ).
tcf(c_19893,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ~ ssList(iPr_def_14)
| ~ ssList(sk8)
| ~ ssList(X0)
| ( app(X0,sk8) != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_9399,c_397]) ).
tcf(c_19997,plain,
! [X0: $i] :
( ( X0 = iPr_def_14 )
| ~ ssList(X0)
| ( app(X0,sk8) != iPr_def_15 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_19893,c_12394,c_9402]) ).
tcf(c_20719,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sk5 )
| ~ ssItem(sk5)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_9396,c_407]) ).
tcf(c_20727,plain,
! [X0: $i] :
( memberP(nil,X0)
| ( X0 = sk5 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_20719,c_9404,c_254]) ).
tcf(c_22525,plain,
( ( app(skaf42(iPr_def_13,sk5),cons(sk5,skaf43(sk5,iPr_def_13))) = iPr_def_13 )
| ~ ssItem(sk5)
| ~ ssList(iPr_def_13) ),
inference(superposition,[status(thm)],[c_18278,c_415]) ).
tcf(c_22526,plain,
app(skaf42(iPr_def_13,sk5),cons(sk5,skaf43(sk5,iPr_def_13))) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_22525,c_9404,c_12383]) ).
tcf(c_25122,plain,
! [X0: $i] :
( ~ ssItem(sk5)
| ~ ssList(X0)
| ~ ssList(skaf42(iPr_def_13,sk5))
| ~ ssList(skaf43(sk5,iPr_def_13))
| ~ ssList(app(iPr_def_13,cons(sk5,X0)))
| ~ duplicatefreeP(app(app(skaf42(iPr_def_13,sk5),cons(sk5,skaf43(sk5,iPr_def_13))),cons(sk5,X0))) ),
inference(superposition,[status(thm)],[c_22526,c_425]) ).
tcf(c_25170,plain,
! [X0: $i] :
( ~ ssItem(sk5)
| ~ ssList(X0)
| ~ ssList(skaf42(iPr_def_13,sk5))
| ~ ssList(skaf43(sk5,iPr_def_13))
| ~ duplicatefreeP(app(iPr_def_13,cons(sk5,X0)))
| ~ ssList(app(iPr_def_13,cons(sk5,X0))) ),
inference(light_normalisation,[status(thm)],[c_25122,c_22526]) ).
tcf(c_25171,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ duplicatefreeP(app(iPr_def_13,cons(sk5,X0)))
| ~ ssList(app(iPr_def_13,cons(sk5,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_25170,c_9404,c_299,c_298]) ).
tcf(c_27708,plain,
( singletonP(iPr_def_12)
| ~ ssItem(sk5) ),
inference(superposition,[status(thm)],[c_9396,c_12708]) ).
tcf(c_27711,plain,
singletonP(iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_27708,c_9404]) ).
tcf(c_27715,plain,
( ( cons(skaf44(iPr_def_12),nil) = iPr_def_12 )
| ~ ssList(iPr_def_12) ),
inference(superposition,[status(thm)],[c_27711,c_347]) ).
tcf(c_27716,plain,
cons(skaf44(iPr_def_12),nil) = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_27715,c_12350]) ).
tcf(c_28071,plain,
( ( skaf46(iPr_def_15,sk8) = iPr_def_14 )
| ~ ssList(skaf46(iPr_def_15,sk8)) ),
inference(superposition,[status(thm)],[c_16072,c_19997]) ).
tcf(c_28072,plain,
skaf46(iPr_def_15,sk8) = iPr_def_14,
inference(forward_subsumption_resolution,[status(thm)],[c_28071,c_296]) ).
tcf(c_28076,plain,
app(iPr_def_14,sk8) = iPr_def_15,
inference(demodulation,[status(thm)],[c_16072,c_28072]) ).
tcf(c_28177,plain,
! [X0: $i] :
( ~ memberP(iPr_def_12,X0)
| ~ ssItem(X0)
| ( X0 = sk5 ) ),
inference(global_subsumption_just,[status(thm)],[c_20727,c_317,c_20727]) ).
tcf(c_28178,plain,
! [X0: $i] :
( ( X0 = sk5 )
| ~ ssItem(X0)
| ~ memberP(iPr_def_12,X0) ),
inference(renaming,[status(thm)],[c_28177]) ).
tcf(c_29533,plain,
( memberP(iPr_def_12,skaf44(iPr_def_12))
| ~ ssList(nil)
| ~ ssItem(skaf44(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_27716,c_384]) ).
tcf(c_29556,plain,
memberP(iPr_def_12,skaf44(iPr_def_12)),
inference(forward_subsumption_resolution,[status(thm)],[c_29533,c_254,c_293]) ).
tcf(c_29811,plain,
( ( skaf44(iPr_def_12) = sk5 )
| ~ ssItem(skaf44(iPr_def_12)) ),
inference(superposition,[status(thm)],[c_29556,c_28178]) ).
tcf(c_29814,plain,
skaf44(iPr_def_12) = sk5,
inference(forward_subsumption_resolution,[status(thm)],[c_29811,c_293]) ).
tcf(c_29817,plain,
cons(sk5,nil) = iPr_def_12,
inference(demodulation,[status(thm)],[c_27716,c_29814]) ).
tcf(c_31427,plain,
( ( nil = iPr_def_14 )
| ( app(tl(iPr_def_14),sk8) = tl(app(iPr_def_14,sk8)) ) ),
inference(superposition,[status(thm)],[c_12394,c_17440]) ).
tcf(c_31428,plain,
( ( nil = iPr_def_14 )
| ( app(tl(iPr_def_14),sk8) = tl(iPr_def_15) ) ),
inference(light_normalisation,[status(thm)],[c_31427,c_28076]) ).
tcf(c_31429,plain,
app(tl(iPr_def_14),sk8) = tl(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_31428,c_14480]) ).
tcf(c_32338,plain,
( ~ ssList(nil)
| ~ ssList(app(iPr_def_13,iPr_def_12))
| ~ duplicatefreeP(app(iPr_def_13,cons(sk5,nil))) ),
inference(superposition,[status(thm)],[c_29817,c_25171]) ).
tcf(c_32340,plain,
( ~ duplicatefreeP(iPr_def_14)
| ~ ssList(iPr_def_14)
| ~ ssList(nil) ),
inference(light_normalisation,[status(thm)],[c_32338,c_9398,c_29817]) ).
tcf(c_32341,plain,
~ duplicatefreeP(iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_32340,c_12394,c_254]) ).
tcf(c_32346,plain,
~ iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_12396,c_32341]) ).
tcf(c_32347,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_9395,c_32346]) ).
tcf(c_47942,plain,
( rearsegP(tl(iPr_def_15),sk8)
| ~ ssList(sk8)
| ~ ssList(tl(iPr_def_14)) ),
inference(superposition,[status(thm)],[c_31429,c_805]) ).
tcf(c_47955,plain,
( rearsegP(tl(iPr_def_15),sk8)
| ~ ssList(tl(iPr_def_14)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_47942,c_9402]) ).
tcf(c_54484,plain,
! [X0: $i] : tl(cons(X0,nil)) = nil,
inference(global_subsumption_just,[status(thm)],[c_12723,c_9393,c_12723,c_32347]) ).
tcf(c_54489,plain,
tl(iPr_def_15) = nil,
inference(superposition,[status(thm)],[c_13168,c_54484]) ).
tcf(c_54539,plain,
( rearsegP(nil,sk8)
| ~ ssList(tl(iPr_def_14)) ),
inference(demodulation,[status(thm)],[c_47955,c_54489]) ).
tcf(c_54621,plain,
( rearsegP(nil,sk8)
| ( nil = iPr_def_14 )
| ~ ssList(iPr_def_14) ),
inference(superposition,[status(thm)],[c_323,c_54539]) ).
tcf(c_54622,plain,
rearsegP(nil,sk8),
inference(forward_subsumption_resolution,[status(thm)],[c_54621,c_14480,c_12394]) ).
tcf(c_54623,plain,
sk8 = nil,
inference(backward_subsumption_resolution,[status(thm)],[c_15752,c_54622]) ).
tcf(c_54812,plain,
app(iPr_def_14,nil) = iPr_def_15,
inference(demodulation,[status(thm)],[c_9399,c_54623]) ).
tcf(c_54814,plain,
iPr_def_14 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_54812,c_12398]) ).
tcf(c_54848,plain,
duplicatefreeP(iPr_def_14),
inference(demodulation,[status(thm)],[c_13936,c_54814]) ).
tcf(c_54861,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_54848,c_32341]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC166-1 : 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 : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 16:47:06 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.39 Running first-order theorem proving
% 0.09/0.39 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.42 % Proving...
% 18.34/3.85 % SZS status Started for theBenchmark.p
% 18.34/3.85 % SZS status Unsatisfiable for theBenchmark.p
% 18.34/3.85
% 18.34/3.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.34/3.85
% 18.34/3.85 % ------ iProver source info
% 18.34/3.85
% 18.34/3.85 % git: date: 2026-07-19 20:42:38 +0200
% 18.34/3.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.34/3.85 % git: non_committed_changes: false
% 18.34/3.85
% 18.34/3.85 % ------ Parsing...% successful
% 18.34/3.85
% 18.34/3.85
% 18.34/3.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.34/3.85
% 18.34/3.85 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 3 sf_s rm: 2 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 18.34/3.85
% 18.34/3.85 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.34/3.85
% 18.34/3.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.34/3.85 % ------ Proving...
% 18.34/3.85 % ------ Problem Properties
% 18.34/3.85
% 18.34/3.85 %
% 18.34/3.85 % clauses 189
% 18.34/3.85 % conjectures 6
% 18.34/3.85 % EPR 60
% 18.34/3.85 % Horn 161
% 18.34/3.85 % unary 70
% 18.34/3.85 % binary 21
% 18.34/3.85 % lits 553
% 18.34/3.85 % lits eq 75
% 18.34/3.85 % fd_pure 0
% 18.34/3.85 % fd_pseudo 0
% 18.34/3.85 % fd_cond 15
% 18.34/3.85 % fd_pseudo_cond 14
% 18.34/3.85 % AC symbols 0
% 18.34/3.85
% 18.34/3.85 % ------ Schedule dynamic 5 is on
% 18.34/3.85
% 18.34/3.85 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.34/3.85
% 18.34/3.85
% 18.34/3.85 % ------
% 18.34/3.85 % Current options:
% 18.34/3.85 % ------
% 18.34/3.85
% 18.34/3.85
% 18.34/3.85 %
% 18.34/3.85
% 18.34/3.85 % ------ Proving...
% 18.34/3.85 %
% 18.34/3.85
% 18.34/3.85 % SZS status Unsatisfiable for theBenchmark.p
% 18.34/3.85
% 18.34/3.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.34/3.86
% 18.34/3.86
%------------------------------------------------------------------------------