%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC310+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:09:15 PM UTC 2026
% Result : Theorem 7.36s 2.27s
% Output : CNFRefutation 7.36s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f559ERROR: Could not build tree for root c_24038ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax27) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X1)
& ? [X9] :
( neq(nil,X1)
& hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X1) = X7
& ssList(X8) )
& ssList(X7) )
& X0 = X6
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ( ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X1)
& ? [X9] :
( neq(nil,X1)
& hd(X1) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X1) = X7
& ssList(X8) )
& ssList(X7) )
& X0 = X6
& ssList(X6) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ! [X5] :
( app(X5,cons(X4,nil)) != X2
| app(cons(X4,nil),X5) != X3
| ~ ssList(X5) ) ) )
| ( nil = X3
& nil != X2 )
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f119,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f126,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(ennf_transformation,[],[f22]) ).
fof(f127,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(flattening,[],[f126]) ).
fof(f128,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ) ),
inference(ennf_transformation,[],[f23]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f130,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(flattening,[],[f129]) ).
fof(f131,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f133,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ! [X2] :
( ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
inference(ennf_transformation,[],[f27]) ).
fof(f134,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ( ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X1)
| ! [X9] :
( ~ neq(nil,X1)
| hd(X1) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X1) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X0 != X6
| ~ ssList(X6) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X3
& ssList(X5) ) ) )
& ( nil != X3
| nil = X2 )
& X0 = X2
& X1 = X3
& ssList(X3) ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f272,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f295,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ( ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,sK54)
| ! [X9] :
( ~ neq(nil,sK54)
| hd(sK54) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(sK54) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| sK53 != X6
| ~ ssList(X6) )
& neq(sK54,nil) )
| ( nil != sK53
& nil = sK54 ) )
& ( ~ neq(sK56,nil)
| ( ssItem(sK57)
& sK55 = app(sK58,cons(sK57,nil))
& sK56 = app(cons(sK57,nil),sK58)
& ssList(sK58) ) )
& ( nil != sK56
| nil = sK55 )
& sK53 = sK55
& sK54 = sK56
& ssList(sK56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58)],[f221]) ).
fof(f386,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f388,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f396,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f397,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f398,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f399,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f401,plain,
! [X2,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f134]) ).
fof(f495,plain,
ssList(sK53),
inference(cnf_transformation,[],[f295]) ).
fof(f496,plain,
ssList(sK54),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( neq(sK54,nil)
| nil != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( neq(sK54,nil)
| nil = sK54 ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
( ~ neq(sK56,nil)
| sK55 = app(sK58,cons(sK57,nil)) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( ~ neq(sK56,nil)
| sK56 = app(cons(sK57,nil),sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
( ~ neq(sK56,nil)
| ssList(sK58) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
( nil != sK56
| nil = sK55 ),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
( neq(sK56,nil)
| nil = sK56 ),
inference(definition_unfolding,[],[f501,f508,f508]) ).
fof(f512,plain,
( neq(sK56,nil)
| nil != sK55 ),
inference(definition_unfolding,[],[f499,f507,f508]) ).
fof(f514,plain,
ssList(sK56),
inference(definition_unfolding,[],[f496,f508]) ).
fof(f515,plain,
ssList(sK55),
inference(definition_unfolding,[],[f495,f507]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f386]) ).
tcf(c_139,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f553]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f387]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f388]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f396]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f397]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X0,X1)) = X1 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f399]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cons(X0,app(X2,X1)) = app(cons(X0,X2),X1) )
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f401]) ).
tcf(c_155,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( nil != sK56 ) ),
inference(cnf_transformation,[],[f506]) ).
tcf(c_248,negated_conjecture,
( ssList(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_249,negated_conjecture,
( ( app(cons(sK57,nil),sK58) = sK56 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_250,negated_conjecture,
( ( app(sK58,cons(sK57,nil)) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_251,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_252,negated_conjecture,
( neq(sK56,nil)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_253,negated_conjecture,
( ( nil = sK56 )
| ~ ssList(sK55)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(cnf_transformation,[],[f558]) ).
tcf(c_254,negated_conjecture,
( neq(sK56,nil)
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f512]) ).
tcf(c_255,negated_conjecture,
( ~ ssList(sK55)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( nil != sK55 )
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(cnf_transformation,[],[f559]) ).
tcf(c_257,negated_conjecture,
ssList(sK56),
inference(cnf_transformation,[],[f514]) ).
tcf(c_258,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f515]) ).
tcf(c_365,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_251,c_251,c_252,c_254,c_247]) ).
tcf(c_367,negated_conjecture,
ssList(sK58),
inference(global_subsumption_just,[status(thm)],[c_248,c_248,c_252,c_254,c_247]) ).
tcf(c_377,negated_conjecture,
neq(sK56,nil),
inference(global_subsumption_just,[status(thm)],[c_254,c_252,c_254,c_247]) ).
tcf(c_385,negated_conjecture,
app(sK58,cons(sK57,nil)) = sK55,
inference(global_subsumption_just,[status(thm)],[c_250,c_252,c_254,c_247,c_250]) ).
tcf(c_387,negated_conjecture,
app(cons(sK57,nil),sK58) = sK56,
inference(global_subsumption_just,[status(thm)],[c_249,c_252,c_254,c_247,c_249]) ).
tcf(c_395,negated_conjecture,
( ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_253,c_258,c_247,c_253,c_255]) ).
tcf(c_397,plain,
( ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 )
| ~ ssList(cons(hd(sK56),nil))
| ~ neq(nil,sK56)
| ~ ssItem(hd(sK56))
| ~ ssList(tl(sK56)) ),
inference(global_subsumption_just,[status(thm)],[c_255,c_395]) ).
tcf(c_398,negated_conjecture,
( ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ neq(nil,sK56)
| ~ ssList(cons(hd(sK56),nil))
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(renaming,[status(thm)],[c_397]) ).
tcf(c_3252,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( X1 != sK56 )
| ( X0 != nil )
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_398]) ).
tcf(c_3253,plain,
( ( nil = sK56 )
| ~ ssList(sK56)
| ~ ssList(nil)
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(unflattening,[status(thm)],[c_3252]) ).
tcf(c_3254,plain,
( ( nil = sK56 )
| ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(global_subsumption_just,[status(thm)],[c_3253,c_257,c_141,c_3253]) ).
tcf(c_3275,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( X0 != sK56 )
| ( X0 != nil ) ),
inference(resolution_lifted,[status(thm)],[c_139,c_377]) ).
tcf(c_3276,plain,
( ~ ssList(nil)
| ( nil != sK56 ) ),
inference(unflattening,[status(thm)],[c_3275]) ).
tcf(c_3277,plain,
nil != sK56,
inference(global_subsumption_just,[status(thm)],[c_3276,c_141,c_3276]) ).
tcf(c_3282,plain,
( ~ ssList(tl(sK56))
| ~ ssItem(hd(sK56))
| ~ ssList(cons(hd(sK56),nil))
| ( app(tl(sK56),cons(hd(sK56),nil)) != sK55 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_3254,c_3277]) ).
tcf(c_8892,definition,
iPr_def_10 = tl(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8893,definition,
iPr_def_11 = hd(sK56),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8894,definition,
iPr_def_12 = cons(iPr_def_11,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8895,definition,
iPr_def_13 = app(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8896,definition,
iPr_def_14 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_8897,definition,
iPr_def_15 = app(iPr_def_14,sK58),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_8898,definition,
iPr_def_16 = app(sK58,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_8899,plain,
( ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ ssItem(iPr_def_11)
| ( iPr_def_13 != sK55 ) ),
inference(demodulation,[status(thm)],[c_3282,c_8893,c_8894,c_8892,c_8895]) ).
tcf(c_8900,plain,
nil != sK56,
inference(demodulation,[status(thm)],[c_3277]) ).
tcf(c_8901,negated_conjecture,
iPr_def_15 = sK56,
inference(demodulation,[status(thm)],[c_387,c_8896,c_8897]) ).
tcf(c_8902,negated_conjecture,
iPr_def_16 = sK55,
inference(demodulation,[status(thm)],[c_385,c_8898]) ).
tcf(c_8903,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_367]) ).
tcf(c_8904,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_365]) ).
tcf(c_8906,negated_conjecture,
ssList(sK56),
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_11751,plain,
ssList(iPr_def_15),
inference(light_normalisation,[status(thm)],[c_8906,c_8901]) ).
tcf(c_11752,plain,
nil != iPr_def_15,
inference(light_normalisation,[status(thm)],[c_8900,c_8901]) ).
tcf(c_11753,plain,
( ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ ssItem(iPr_def_11)
| ( iPr_def_13 != iPr_def_16 ) ),
inference(light_normalisation,[status(thm)],[c_8899,c_8902]) ).
tcf(c_11762,plain,
tl(iPr_def_15) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_8892,c_8901]) ).
tcf(c_11819,plain,
hd(iPr_def_15) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8893,c_8901]) ).
tcf(c_12133,plain,
app(nil,sK58) = sK58,
inference(superposition,[status(thm)],[c_8903,c_155]) ).
tcf(c_12291,plain,
( ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssItem(iPr_def_11) ),
inference(superposition,[status(thm)],[c_8894,c_140]) ).
tcf(c_12294,plain,
( ssList(iPr_def_12)
| ~ ssItem(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12291,c_141]) ).
tcf(c_12336,plain,
( ssItem(iPr_def_11)
| ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15) ),
inference(superposition,[status(thm)],[c_11819,c_149]) ).
tcf(c_12337,plain,
ssItem(iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_12336,c_11752,c_11751]) ).
tcf(c_12342,plain,
( ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ( iPr_def_13 != iPr_def_16 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11753,c_12337]) ).
tcf(c_12352,plain,
( ssList(iPr_def_10)
| ( nil = iPr_def_15 )
| ~ ssList(iPr_def_15) ),
inference(superposition,[status(thm)],[c_11762,c_151]) ).
tcf(c_12355,plain,
ssList(iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_12352,c_11752,c_11751]) ).
tcf(c_12364,plain,
iPr_def_13 != iPr_def_16,
inference(global_subsumption_just,[status(thm)],[c_12342,c_12294,c_12337,c_12342,c_12355]) ).
tcf(c_13465,plain,
! [X0: $i] :
( ( hd(cons(sK57,X0)) = sK57 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8904,c_150]) ).
tcf(c_13599,plain,
! [X0: $i] :
( ( tl(cons(sK57,X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8904,c_152]) ).
tcf(c_13753,plain,
hd(cons(sK57,sK58)) = sK57,
inference(superposition,[status(thm)],[c_8903,c_13465]) ).
tcf(c_13897,plain,
tl(cons(sK57,sK58)) = sK58,
inference(superposition,[status(thm)],[c_8903,c_13599]) ).
tcf(c_21261,plain,
! [X0: $i,X1: $i] :
( ( cons(sK57,app(X1,X0)) = app(cons(sK57,X1),X0) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8904,c_154]) ).
tcf(c_22203,plain,
! [X0: $i] :
( ( cons(sK57,app(X0,sK58)) = app(cons(sK57,X0),sK58) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8903,c_21261]) ).
tcf(c_22490,plain,
cons(sK57,app(nil,sK58)) = app(cons(sK57,nil),sK58),
inference(superposition,[status(thm)],[c_141,c_22203]) ).
tcf(c_22507,plain,
cons(sK57,sK58) = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_22490,c_8896,c_8897,c_12133]) ).
tcf(c_22602,plain,
tl(iPr_def_15) = sK58,
inference(demodulation,[status(thm)],[c_13897,c_22507]) ).
tcf(c_22603,plain,
hd(iPr_def_15) = sK57,
inference(demodulation,[status(thm)],[c_13753,c_22507]) ).
tcf(c_22607,plain,
sK57 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_22603,c_11819]) ).
tcf(c_22659,plain,
cons(iPr_def_11,nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_8896,c_22607]) ).
tcf(c_22661,plain,
iPr_def_12 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_22659,c_8894]) ).
tcf(c_22693,plain,
app(sK58,iPr_def_12) = iPr_def_16,
inference(demodulation,[status(thm)],[c_8898,c_22661]) ).
tcf(c_22760,plain,
sK58 = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_22602,c_11762]) ).
tcf(c_24038,plain,
$false,
inference(smt_impl_just,[status(thm)],[c_22760,c_22693,c_12364,c_8895]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC310+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.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 17:33:20 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 7.36/2.27 % SZS status Started for theBenchmark.p
% 7.36/2.27 % SZS status Theorem for theBenchmark.p
% 7.36/2.27
% 7.36/2.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 7.36/2.27
% 7.36/2.27 % ------ iProver source info
% 7.36/2.27
% 7.36/2.27 % git: date: 2026-07-19 20:42:38 +0200
% 7.36/2.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 7.36/2.27 % git: non_committed_changes: false
% 7.36/2.27
% 7.36/2.27 % ------ Parsing...
% 7.36/2.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 7.36/2.27
% 7.36/2.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 7.36/2.27
% 7.36/2.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 7.36/2.27
% 7.36/2.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 7.36/2.27 % ------ Proving...
% 7.36/2.27 % ------ Problem Properties
% 7.36/2.27
% 7.36/2.27 %
% 7.36/2.27 % clauses 195
% 7.36/2.27 % conjectures 6
% 7.36/2.27 % EPR 57
% 7.36/2.27 % Horn 127
% 7.36/2.27 % unary 30
% 7.36/2.27 % binary 40
% 7.36/2.27 % lits 636
% 7.36/2.27 % lits eq 89
% 7.36/2.27 % fd_pure 0
% 7.36/2.27 % fd_pseudo 0
% 7.36/2.27 % fd_cond 21
% 7.36/2.27 % fd_pseudo_cond 14
% 7.36/2.27 % AC symbols 0
% 7.36/2.27
% 7.36/2.27 % ------ Schedule dynamic 5 is on
% 7.36/2.27
% 7.36/2.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 7.36/2.27
% 7.36/2.27
% 7.36/2.27 % ------
% 7.36/2.27 % Current options:
% 7.36/2.27 % ------
% 7.36/2.27
% 7.36/2.27
% 7.36/2.27 %
% 7.36/2.27
% 7.36/2.27 % ------ Proving...
% 7.36/2.27 %
% 7.36/2.27
% 7.36/2.27 % SZS status Theorem for theBenchmark.p
% 7.36/2.27
% 7.36/2.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 7.36/2.28
% 7.36/2.28
%------------------------------------------------------------------------------