%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC316+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 : n010.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 03:09:16 PM UTC 2026
% Result : Theorem 35.86s 5.85s
% Output : CNFRefutation 35.86s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f558ERROR: Could not build tree for root c_126581ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax25) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(app(X0,X1)) = hd(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax85) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ( neq(X0,nil)
& ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X0)
& ? [X9] :
( neq(nil,X0)
& hd(X0) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X0) = X7
& ssList(X8) )
& ssList(X7) )
& X1 = X6
& ssList(X6) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2 ) ) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ( neq(X0,nil)
& ? [X6] :
( ? [X7] :
( ? [X8] :
( neq(nil,X0)
& ? [X9] :
( neq(nil,X0)
& hd(X0) = X9
& cons(X9,nil) = X8
& ssItem(X9) )
& app(X7,X8) = X6
& tl(X0) = X7
& ssList(X8) )
& ssList(X7) )
& X1 = X6
& ssList(X6) ) )
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(X5,cons(X4,nil)) != X3
| app(cons(X4,nil),X5) != X2 ) ) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != 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(f120,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) != X0 ) ),
inference(ennf_transformation,[],[f18]) ).
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(f132,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ssList(app(X0,X1)) ) ),
inference(ennf_transformation,[],[f26]) ).
fof(f198,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f200,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f202,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| nil = X0
| hd(app(X0,X1)) = hd(X0) ) ),
inference(ennf_transformation,[],[f85]) ).
fof(f203,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| nil = X0
| hd(app(X0,X1)) = hd(X0) ) ),
inference(flattening,[],[f202]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ( ~ neq(X0,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X0)
| ! [X9] :
( ~ neq(nil,X0)
| hd(X0) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X0) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X1 != X6
| ~ ssList(X6) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) = X2 ) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ( ~ neq(X0,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X0)
| ! [X9] :
( ~ neq(nil,X0)
| hd(X0) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X0) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X1 != X6
| ~ ssList(X6) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) = X2 ) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f275,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f294,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f200]) ).
fof(f295,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( nil != app(X0,X1)
| ( nil = X0
& nil = X1 ) )
& ( nil != X0
| nil != X1
| nil = app(X0,X1) ) ) ) ),
inference(flattening,[],[f294]) ).
fof(f301,plain,
( ssList(sK56)
& ssList(sK57)
& ssList(sK58)
& ssList(sK59)
& ( ( ~ neq(sK59,nil)
& neq(sK57,nil) )
| sP6(sK57,sK58,sK59,sK56) )
& sK56 = sK58
& sK57 = sK59 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57,sK58,sK59]),skolemize(X0,sK56),skolemize(X1,sK57),skolemize(X2,sK58),skolemize(X3,sK59)],[f233]) ).
fof(f392,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f393,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
fof(f394,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f395,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) != X0 ),
inference(cnf_transformation,[],[f120]) ).
fof(f402,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssItem(hd(X0)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f403,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f128]) ).
fof(f404,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ssList(tl(X0)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f405,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f131]) ).
fof(f406,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ssList(app(X0,X1)) ),
inference(cnf_transformation,[],[f132]) ).
fof(f482,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f484,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f295]) ).
fof(f488,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1)) ),
inference(cnf_transformation,[],[f203]) ).
fof(f507,plain,
ssList(sK56),
inference(cnf_transformation,[],[f301]) ).
fof(f511,plain,
( ~ neq(sK59,nil)
| sP6(sK57,sK58,sK59,sK56) ),
inference(cnf_transformation,[],[f301]) ).
fof(f512,plain,
( neq(sK57,nil)
| sP6(sK57,sK58,sK59,sK56) ),
inference(cnf_transformation,[],[f301]) ).
fof(f513,plain,
sK56 = sK58,
inference(cnf_transformation,[],[f301]) ).
fof(f514,plain,
sK57 = sK59,
inference(cnf_transformation,[],[f301]) ).
fof(f515,plain,
( neq(sK59,nil)
| sP6(sK59,sK58,sK59,sK58) ),
inference(definition_unfolding,[],[f512,f514,f513,f514]) ).
fof(f516,plain,
( ~ neq(sK59,nil)
| sP6(sK59,sK58,sK59,sK58) ),
inference(definition_unfolding,[],[f511,f514,f513]) ).
fof(f518,plain,
ssList(sK58),
inference(definition_unfolding,[],[f507,f513]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f392]) ).
tcf(c_140,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f393]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f394]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( ~ ssList(X1)
| ~ ssItem(X0)
| ( cons(X0,X1) != X1 ) ),
inference(cnf_transformation,[],[f395]) ).
tcf(c_149,plain,
! [X0: $i] :
( ssItem(hd(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f402]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( ( hd(cons(X0,X1)) = X0 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f403]) ).
tcf(c_151,plain,
! [X0: $i] :
( ssList(tl(X0))
| ( X0 = nil )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f404]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] :
( ( tl(cons(X0,X1)) = X1 )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f405]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f406]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f484]) ).
tcf(c_233,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ( hd(app(X0,X1)) = hd(X0) )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f488]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(tl(X0))
| ~ ssItem(hd(X0))
| ~ neq(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(cons(hd(X0),nil))
| ~ ssList(app(tl(X0),cons(hd(X0),nil)))
| ~ sP6(app(tl(X0),cons(hd(X0),nil)),X1,X2,X0) ),
inference(cnf_transformation,[],[f558]) ).
tcf(c_252,negated_conjecture,
( neq(sK59,nil)
| sP6(sK59,sK58,sK59,sK58) ),
inference(cnf_transformation,[],[f515]) ).
tcf(c_253,negated_conjecture,
( sP6(sK59,sK58,sK59,sK58)
| ~ neq(sK59,nil) ),
inference(cnf_transformation,[],[f516]) ).
tcf(c_257,negated_conjecture,
ssList(sK58),
inference(cnf_transformation,[],[f518]) ).
tcf(c_376,negated_conjecture,
sP6(sK59,sK58,sK59,sK58),
inference(global_subsumption_just,[status(thm)],[c_252,c_252,c_253]) ).
tcf(c_378,negated_conjecture,
sP6(sK59,sK58,sK59,sK58),
inference(global_subsumption_just,[status(thm)],[c_253,c_376]) ).
tcf(c_834,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(tl(X0))
| ~ ssItem(hd(X0))
| ~ neq(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(cons(hd(X0),nil))
| ~ sP6(app(tl(X0),cons(hd(X0),nil)),X1,X2,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_251,c_153]) ).
tcf(c_3293,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ ssList(tl(X0))
| ~ ssItem(hd(X0))
| ~ neq(nil,X0)
| ~ neq(X0,nil)
| ~ ssList(cons(hd(X0),nil))
| ( X2 != sK59 )
| ( X1 != sK58 )
| ( X0 != sK58 )
| ( app(tl(X0),cons(hd(X0),nil)) != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_834,c_378]) ).
tcf(c_3294,plain,
( ~ ssList(tl(sK58))
| ~ ssItem(hd(sK58))
| ~ neq(sK58,nil)
| ~ neq(nil,sK58)
| ~ ssList(cons(hd(sK58),nil))
| ( app(tl(sK58),cons(hd(sK58),nil)) != sK59 ) ),
inference(unflattening,[status(thm)],[c_3293]) ).
tcf(c_8984,definition,
iPr_def_10 = tl(sK58),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_8985,definition,
iPr_def_11 = hd(sK58),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_8986,definition,
iPr_def_12 = cons(iPr_def_11,nil),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_8987,definition,
iPr_def_13 = app(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_8988,definition,
iPr_def_14 = sK54(sK58,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_8989,definition,
iPr_def_15 = cons(iPr_def_14,nil),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_8990,definition,
iPr_def_16 = sK55(sK58,sK59),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_8991,definition,
iPr_def_17 = app(iPr_def_15,iPr_def_16),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_8992,definition,
iPr_def_18 = app(iPr_def_16,iPr_def_15),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_8993,plain,
( ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ ssItem(iPr_def_11)
| ~ neq(sK58,nil)
| ~ neq(nil,sK58)
| ( iPr_def_13 != sK59 ) ),
inference(demodulation,[status(thm)],[c_3294,c_8985,c_8986,c_8984,c_8987]) ).
tcf(c_8999,negated_conjecture,
ssList(sK58),
inference(demodulation,[status(thm)],[c_257]) ).
tcf(c_12505,plain,
( ssList(iPr_def_12)
| ~ ssList(nil)
| ~ ssItem(iPr_def_11) ),
inference(superposition,[status(thm)],[c_8986,c_140]) ).
tcf(c_12506,plain,
( ssList(iPr_def_15)
| ~ ssList(nil)
| ~ ssItem(iPr_def_14) ),
inference(superposition,[status(thm)],[c_8989,c_140]) ).
tcf(c_12511,plain,
( ssList(iPr_def_12)
| ~ ssItem(iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12505,c_141]) ).
tcf(c_13288,plain,
( ~ ssList(nil)
| ~ ssItem(iPr_def_14)
| ( nil != iPr_def_15 ) ),
inference(superposition,[status(thm)],[c_8989,c_142]) ).
tcf(c_16619,plain,
( ( nil = iPr_def_15 )
| ~ ssList(iPr_def_16)
| ~ ssList(iPr_def_15)
| ( nil != iPr_def_17 ) ),
inference(superposition,[status(thm)],[c_8991,c_231]) ).
fof(f232,definition,
! [X1,X2,X3,X0] :
( ~ sP6(X1,X2,X3,X0)
| ( ( ~ neq(X0,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X0)
| ! [X9] :
( ~ neq(nil,X0)
| hd(X0) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X0) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X1 != X6
| ~ ssList(X6) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) = X2 ) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f233,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP6(X1,X2,X3,X0) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f222,f232]) ).
fof(f298,plain,
! [X1,X2,X3,X0] :
( ~ sP6(X1,X2,X3,X0)
| ( ( ~ neq(X0,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X0)
| ! [X9] :
( ~ neq(nil,X0)
| hd(X0) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X0) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X1 != X6
| ~ ssList(X6) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X3
& app(cons(X4,nil),X5) = X2 ) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f299,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X0 != X6
| ~ ssList(X6) ) )
& ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(X5,cons(X4,nil)) = X2
& app(cons(X4,nil),X5) = X1 ) )
& neq(X0,nil) ) ),
inference(rectify,[],[f298]) ).
fof(f300,plain,
! [X0,X1,X2,X3] :
( ~ sP6(X0,X1,X2,X3)
| ( ( ~ neq(X3,nil)
| ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ neq(nil,X3)
| ! [X9] :
( ~ neq(nil,X3)
| hd(X3) != X9
| cons(X9,nil) != X8
| ~ ssItem(X9) )
| app(X7,X8) != X6
| tl(X3) != X7
| ~ ssList(X8) )
| ~ ssList(X7) )
| X0 != X6
| ~ ssList(X6) ) )
& ssItem(sK54(X1,X2))
& ssList(sK55(X1,X2))
& app(sK55(X1,X2),cons(sK54(X1,X2),nil)) = X2
& app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X1
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54,sK55]),skolemize(X4,sK54(X1,X2)),skolemize(X5,sK55(X1,X2))],[f299]) ).
fof(f502,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssItem(sK54(X1,X2)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f503,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| ssList(sK55(X1,X2)) ),
inference(cnf_transformation,[],[f300]) ).
fof(f504,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| app(sK55(X1,X2),cons(sK54(X1,X2),nil)) = X2 ),
inference(cnf_transformation,[],[f300]) ).
fof(f505,plain,
! [X2,X3,X0,X1] :
( ~ sP6(X0,X1,X2,X3)
| app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X1 ),
inference(cnf_transformation,[],[f300]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X1 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_248,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK55(X1,X2),cons(sK54(X1,X2),nil)) = X2 )
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK55(X1,X2))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f503]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X1,X2))
| ~ sP6(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_3268,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK54(X1,X2))
| ( X3 != sK58 )
| ( X2 != sK59 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_378]) ).
tcf(c_3269,plain,
ssItem(sK54(sK58,sK59)),
inference(unflattening,[status(thm)],[c_3268]) ).
tcf(c_3273,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK55(X1,X2))
| ( X3 != sK58 )
| ( X2 != sK59 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_249,c_378]) ).
tcf(c_3274,plain,
ssList(sK55(sK58,sK59)),
inference(unflattening,[status(thm)],[c_3273]) ).
tcf(c_3278,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(sK55(X1,X2),cons(sK54(X1,X2),nil)) = X2 )
| ( X3 != sK58 )
| ( X2 != sK59 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_248,c_378]) ).
tcf(c_3279,plain,
app(sK55(sK58,sK59),cons(sK54(sK58,sK59),nil)) = sK59,
inference(unflattening,[status(thm)],[c_3278]) ).
tcf(c_3283,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(cons(sK54(X1,X2),nil),sK55(X1,X2)) = X1 )
| ( X3 != sK58 )
| ( X2 != sK59 )
| ( X1 != sK58 )
| ( X0 != sK59 ) ),
inference(resolution_lifted,[status(thm)],[c_247,c_378]) ).
tcf(c_3284,plain,
app(cons(sK54(sK58,sK59),nil),sK55(sK58,sK59)) = sK58,
inference(unflattening,[status(thm)],[c_3283]) ).
tcf(c_8995,plain,
iPr_def_17 = sK58,
inference(demodulation,[status(thm)],[c_3284,c_8990,c_8988,c_8989,c_8991]) ).
tcf(c_8996,plain,
iPr_def_18 = sK59,
inference(demodulation,[status(thm)],[c_3279,c_8992]) ).
tcf(c_8997,plain,
ssList(iPr_def_16),
inference(demodulation,[status(thm)],[c_3274]) ).
tcf(c_8998,plain,
ssItem(iPr_def_14),
inference(demodulation,[status(thm)],[c_3269]) ).
tcf(c_11953,plain,
ssList(iPr_def_17),
inference(light_normalisation,[status(thm)],[c_8999,c_8995]) ).
tcf(c_11956,plain,
( ~ ssList(iPr_def_12)
| ~ ssList(iPr_def_10)
| ~ ssItem(iPr_def_11)
| ~ neq(iPr_def_17,nil)
| ~ neq(nil,iPr_def_17)
| ( iPr_def_13 != iPr_def_18 ) ),
inference(light_normalisation,[status(thm)],[c_8993,c_8995,c_8996]) ).
tcf(c_11967,plain,
tl(iPr_def_17) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_8984,c_8995]) ).
tcf(c_12024,plain,
hd(iPr_def_17) = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_8985,c_8995]) ).
tcf(c_12510,plain,
ssList(iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_12506,c_141,c_8998]) ).
tcf(c_12552,plain,
( ssItem(iPr_def_11)
| ( nil = iPr_def_17 )
| ~ ssList(iPr_def_17) ),
inference(superposition,[status(thm)],[c_12024,c_149]) ).
tcf(c_12553,plain,
( ssItem(iPr_def_11)
| ( nil = iPr_def_17 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12552,c_11953]) ).
tcf(c_12562,plain,
( ~ ssList(iPr_def_10)
| ~ ssItem(iPr_def_11)
| ~ neq(iPr_def_17,nil)
| ~ neq(nil,iPr_def_17)
| ( iPr_def_13 != iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11956,c_12511]) ).
tcf(c_12629,plain,
( ssList(iPr_def_10)
| ( nil = iPr_def_17 )
| ~ ssList(iPr_def_17) ),
inference(superposition,[status(thm)],[c_11967,c_151]) ).
tcf(c_12632,plain,
( ssList(iPr_def_10)
| ( nil = iPr_def_17 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_12629,c_11953]) ).
tcf(c_13291,plain,
nil != iPr_def_15,
inference(forward_subsumption_resolution,[status(thm)],[c_13288,c_141,c_8998]) ).
tcf(c_13336,plain,
! [X0: $i] :
( ( hd(cons(iPr_def_14,X0)) = iPr_def_14 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_8998,c_150]) ).
tcf(c_13448,plain,
! [X0: $i] :
( ( nil = iPr_def_17 )
| ( tl(cons(iPr_def_11,X0)) = X0 )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12553,c_152]) ).
tcf(c_13586,plain,
hd(cons(iPr_def_14,nil)) = iPr_def_14,
inference(superposition,[status(thm)],[c_141,c_13336]) ).
tcf(c_13597,plain,
hd(iPr_def_15) = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_13586,c_8989]) ).
tcf(c_14197,plain,
( ( nil = iPr_def_17 )
| ( tl(cons(iPr_def_11,iPr_def_16)) = iPr_def_16 ) ),
inference(superposition,[status(thm)],[c_8997,c_13448]) ).
tcf(c_16635,plain,
nil != iPr_def_17,
inference(forward_subsumption_resolution,[status(thm)],[c_16619,c_13291,c_8997,c_12510]) ).
tcf(c_16647,plain,
tl(cons(iPr_def_11,iPr_def_16)) = iPr_def_16,
inference(backward_subsumption_resolution,[status(thm)],[c_14197,c_16635]) ).
tcf(c_16674,plain,
ssList(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_12632,c_16635]) ).
tcf(c_16683,plain,
ssItem(iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_12553,c_16635]) ).
tcf(c_16700,plain,
( ~ ssItem(iPr_def_11)
| ~ neq(iPr_def_17,nil)
| ~ neq(nil,iPr_def_17)
| ( iPr_def_13 != iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_12562,c_16674]) ).
tcf(c_16714,plain,
( ~ neq(iPr_def_17,nil)
| ~ neq(nil,iPr_def_17)
| ( iPr_def_13 != iPr_def_18 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_16700,c_16683]) ).
tcf(c_16756,plain,
! [X0: $i] :
( ( app(cons(iPr_def_11,nil),X0) = cons(iPr_def_11,X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_16683,c_227]) ).
tcf(c_16759,plain,
! [X0: $i] :
( ( cons(iPr_def_11,X0) = app(iPr_def_12,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_16756,c_8986]) ).
tcf(c_18170,plain,
! [X0: $i] :
( ( nil = iPr_def_15 )
| ( hd(app(iPr_def_15,X0)) = hd(iPr_def_15) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_12510,c_233]) ).
tcf(c_18177,plain,
! [X0: $i] :
( ( nil = iPr_def_15 )
| ( hd(app(iPr_def_15,X0)) = iPr_def_14 )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_18170,c_13597]) ).
tcf(c_18178,plain,
! [X0: $i] :
( ( hd(app(iPr_def_15,X0)) = iPr_def_14 )
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_18177,c_13291]) ).
tcf(c_43237,plain,
hd(app(iPr_def_15,iPr_def_16)) = iPr_def_14,
inference(superposition,[status(thm)],[c_8997,c_18178]) ).
tcf(c_43254,plain,
iPr_def_11 = iPr_def_14,
inference(light_normalisation,[status(thm)],[c_43237,c_8991,c_12024]) ).
tcf(c_43406,plain,
cons(iPr_def_11,nil) = iPr_def_15,
inference(demodulation,[status(thm)],[c_8989,c_43254]) ).
tcf(c_43409,plain,
iPr_def_12 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_43406,c_8986]) ).
tcf(c_43460,plain,
app(iPr_def_16,iPr_def_12) = iPr_def_18,
inference(demodulation,[status(thm)],[c_8992,c_43409]) ).
tcf(c_43461,plain,
app(iPr_def_12,iPr_def_16) = iPr_def_17,
inference(demodulation,[status(thm)],[c_8991,c_43409]) ).
tcf(c_56334,plain,
cons(iPr_def_11,iPr_def_16) = app(iPr_def_12,iPr_def_16),
inference(superposition,[status(thm)],[c_8997,c_16759]) ).
tcf(c_56351,plain,
cons(iPr_def_11,iPr_def_16) = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_56334,c_43461]) ).
tcf(c_56473,plain,
tl(iPr_def_17) = iPr_def_16,
inference(demodulation,[status(thm)],[c_16647,c_56351]) ).
tcf(c_56474,plain,
iPr_def_10 = iPr_def_16,
inference(light_normalisation,[status(thm)],[c_56473,c_11967]) ).
tcf(c_56491,plain,
app(iPr_def_10,iPr_def_12) = iPr_def_18,
inference(demodulation,[status(thm)],[c_43460,c_56474]) ).
tcf(c_56569,plain,
iPr_def_13 = iPr_def_18,
inference(light_normalisation,[status(thm)],[c_56491,c_8987]) ).
tcf(c_126563,plain,
( ~ neq(iPr_def_17,nil)
| ~ neq(nil,iPr_def_17) ),
inference(global_subsumption_just,[status(thm)],[c_16714,c_16714,c_56569]) ).
tcf(c_126569,plain,
( ( nil = iPr_def_17 )
| ~ ssList(iPr_def_17)
| ~ ssList(nil)
| ~ neq(iPr_def_17,nil) ),
inference(superposition,[status(thm)],[c_138,c_126563]) ).
tcf(c_126575,plain,
~ neq(iPr_def_17,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_126569,c_16635,c_11953,c_141]) ).
tcf(c_126576,plain,
( ( nil = iPr_def_17 )
| ~ ssList(iPr_def_17)
| ~ ssList(nil) ),
inference(superposition,[status(thm)],[c_138,c_126575]) ).
tcf(c_126581,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_126576,c_16635,c_11953,c_141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC316+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Thu Sep 24 17:35:13 UTC 2026
% 0.03/0.37 % CPUTime :
% 0.03/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.40 Running first-order theorem proving
% 0.03/0.40 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
% 0.03/0.42
% 0.03/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.42
% 0.03/0.42 % Detected problem language: tptp
% 0.03/0.43 % Proving...
% 35.86/5.85 % SZS status Started for theBenchmark.p
% 35.86/5.85 % SZS status Theorem for theBenchmark.p
% 35.86/5.85
% 35.86/5.85 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 35.86/5.85
% 35.86/5.85 % ------ iProver source info
% 35.86/5.85
% 35.86/5.85 % git: date: 2026-07-19 20:42:38 +0200
% 35.86/5.85 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 35.86/5.85 % git: non_committed_changes: false
% 35.86/5.85
% 35.86/5.85 % ------ Parsing...
% 35.86/5.85 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 35.86/5.85
% 35.86/5.85 % ------ 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 %
% 35.86/5.85
% 35.86/5.85 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 35.86/5.85
% 35.86/5.85 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 35.86/5.85 % ------ Proving...
% 35.86/5.85 % ------ Problem Properties
% 35.86/5.85
% 35.86/5.85 %
% 35.86/5.85 % clauses 201
% 35.86/5.85 % conjectures 2
% 35.86/5.85 % EPR 61
% 35.86/5.85 % Horn 131
% 35.86/5.85 % unary 32
% 35.86/5.85 % binary 42
% 35.86/5.85 % lits 652
% 35.86/5.85 % lits eq 92
% 35.86/5.85 % fd_pure 0
% 35.86/5.85 % fd_pseudo 0
% 35.86/5.85 % fd_cond 21
% 35.86/5.85 % fd_pseudo_cond 16
% 35.86/5.85 % AC symbols 0
% 35.86/5.85
% 35.86/5.85 % ------ Schedule dynamic 5 is on
% 35.86/5.85
% 35.86/5.85 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 35.86/5.85
% 35.86/5.85
% 35.86/5.85 % ------
% 35.86/5.85 % Current options:
% 35.86/5.85 % ------
% 35.86/5.85
% 35.86/5.85
% 35.86/5.85 %
% 35.86/5.85
% 35.86/5.85 % ------ Proving...
% 35.86/5.85 %
% 35.86/5.85
% 35.86/5.85 % SZS status Theorem for theBenchmark.p
% 35.86/5.85
% 35.86/5.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 35.86/5.86
% 35.86/5.86
%------------------------------------------------------------------------------