%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC027+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 03:07:34 PM UTC 2026
% Result : Theorem 1.31s 1.20s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f552ERROR: Could not build tree for root c_13747ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax3) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax38) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| 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)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( ( nil != X2
| nil != X3 )
& ! [X4] :
( ssItem(X4)
=> ( ? [X5] :
( leq(X4,X5)
& memberP(X3,X5)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f99,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( memberP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f148,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f201,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f221,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( nil != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( ( nil = X2
& nil = X3 )
| ? [X4] :
( ssItem(X4)
& ! [X5] :
( ~ leq(X4,X5)
| ~ memberP(X3,X5)
| X4 = X5
| ~ ssItem(X5) )
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(X2,cons(X1,X3)) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f99]) ).
fof(f235,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(X4,cons(X1,X5)) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(rectify,[],[f234]) ).
fof(f236,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ( ( ~ memberP(X0,X1)
| ( app(sK8(X0,X1),cons(X1,sK9(X0,X1))) = X0
& ssList(sK9(X0,X1))
& ssList(sK8(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| memberP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X4,sK8(X0,X1)),skolemize(X5,sK9(X0,X1))],[f235]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ( nil != sK54
& nil = sK53 )
| ( nil != sK53
& nil = sK54 ) )
& ( ( nil = sK55
& nil = sK56 )
| ( ssItem(sK57)
& ! [X5] :
( ~ leq(sK57,X5)
| ~ memberP(sK56,X5)
| sK57 = X5
| ~ ssItem(X5) )
& memberP(sK56,sK57)
& sK55 = cons(sK57,nil) ) )
& sK53 = sK55
& sK54 = sK56 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57)],[f222]) ).
fof(f305,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1) ),
inference(cnf_transformation,[],[f236]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f419,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f201]) ).
fof(f496,plain,
ssList(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f500,plain,
( nil != sK54
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK53
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( nil = sK55
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( nil = sK56
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
( nil = sK55
| memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
( nil = sK56
| memberP(sK56,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( nil = sK55
| sK55 = cons(sK57,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
( nil = sK56
| sK55 = cons(sK57,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f513,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f514,plain,
( nil = sK55
| nil = sK56 ),
inference(definition_unfolding,[],[f503,f513,f512]) ).
fof(f517,plain,
( nil != sK56
| nil != sK55 ),
inference(definition_unfolding,[],[f500,f512,f513]) ).
fof(f519,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f512]) ).
fof(f521,plain,
! [X2,X3,X1] :
( ~ ssList(app(X2,cons(X1,X3)))
| ~ ssItem(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(app(X2,cons(X1,X3)),X1) ),
inference(equality_resolution,[],[f305]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( memberP(app(X0,cons(X1,X2)),X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(cnf_transformation,[],[f521]) ).
tcf(c_141,plain,
ssList(nil),
inference(cnf_transformation,[],[f389]) ).
tcf(c_171,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[],[f419]) ).
tcf(c_229,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(cnf_transformation,[],[f552]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
( ( nil = sK56 )
| ( cons(sK57,nil) = sK55 ) ),
inference(cnf_transformation,[],[f511]) ).
tcf(c_247,negated_conjecture,
( ( nil = sK55 )
| ( cons(sK57,nil) = sK55 ) ),
inference(cnf_transformation,[],[f510]) ).
tcf(c_248,negated_conjecture,
( memberP(sK56,sK57)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f509]) ).
tcf(c_249,negated_conjecture,
( memberP(sK56,sK57)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f508]) ).
tcf(c_252,negated_conjecture,
( ssItem(sK57)
| ( nil = sK56 ) ),
inference(cnf_transformation,[],[f505]) ).
tcf(c_253,negated_conjecture,
( ssItem(sK57)
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f504]) ).
tcf(c_254,negated_conjecture,
( ( nil = sK56 )
| ( nil = sK55 ) ),
inference(cnf_transformation,[],[f514]) ).
tcf(c_255,negated_conjecture,
( ( nil != sK56 )
| ( nil != sK55 ) ),
inference(cnf_transformation,[],[f517]) ).
tcf(c_259,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f519]) ).
tcf(c_300,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_368,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_253,c_253,c_252,c_255]) ).
tcf(c_370,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_252,c_368]) ).
tcf(c_378,negated_conjecture,
memberP(sK56,sK57),
inference(global_subsumption_just,[status(thm)],[c_249,c_249,c_248,c_255]) ).
tcf(c_380,negated_conjecture,
memberP(sK56,sK57),
inference(global_subsumption_just,[status(thm)],[c_248,c_378]) ).
tcf(c_382,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_229,c_141,c_300]) ).
tcf(c_384,negated_conjecture,
cons(sK57,nil) = sK55,
inference(global_subsumption_just,[status(thm)],[c_247,c_255,c_247,c_246]) ).
tcf(c_386,negated_conjecture,
cons(sK57,nil) = sK55,
inference(global_subsumption_just,[status(thm)],[c_246,c_384]) ).
tcf(c_9745,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_9747,negated_conjecture,
iPr_def_10 = sK55,
inference(demodulation,[status(thm)],[c_386,c_9745]) ).
tcf(c_9748,negated_conjecture,
memberP(sK56,sK57),
inference(demodulation,[status(thm)],[c_380]) ).
tcf(c_9749,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_370]) ).
tcf(c_9750,negated_conjecture,
ssList(sK55),
inference(demodulation,[status(thm)],[c_259]) ).
tcf(c_9753,negated_conjecture,
( ( nil = sK56 )
| ( nil = sK55 ) ),
inference(demodulation,[status(thm)],[c_254]) ).
tcf(c_13478,plain,
ssList(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_9750,c_9747]) ).
tcf(c_13479,plain,
( ( nil = iPr_def_10 )
| ( nil = sK56 ) ),
inference(light_normalisation,[status(thm)],[c_9753,c_9747]) ).
tcf(c_13482,plain,
( memberP(nil,sK57)
| ( nil = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_13479,c_9748]) ).
tcf(c_13585,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,nil))) ),
inference(superposition,[status(thm)],[c_9745,c_54]) ).
tcf(c_13586,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(nil)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_13585,c_9745]) ).
tcf(c_13587,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_13586,c_141,c_9749]) ).
tcf(c_13642,plain,
( ( nil = iPr_def_10 )
| ~ ssItem(sK57) ),
inference(superposition,[status(thm)],[c_13482,c_171]) ).
tcf(c_13643,plain,
nil = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_13642,c_9749]) ).
tcf(c_13645,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(demodulation,[status(thm)],[c_171,c_13643]) ).
tcf(c_13662,plain,
app(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_382,c_13643]) ).
tcf(c_13723,plain,
( memberP(iPr_def_10,sK57)
| ~ ssList(iPr_def_10)
| ~ ssList(app(iPr_def_10,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_13662,c_13587]) ).
tcf(c_13724,plain,
( memberP(iPr_def_10,sK57)
| ~ ssList(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_13723,c_13662]) ).
tcf(c_13725,plain,
memberP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_13724,c_13478]) ).
tcf(c_13746,plain,
~ ssItem(sK57),
inference(superposition,[status(thm)],[c_13725,c_13645]) ).
tcf(c_13747,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_13746,c_9749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC027+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.38 % Computer : n020.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Thu Sep 24 16:00:03 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 0.13/0.44
% 0.13/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.44
% 0.13/0.44 % Detected problem language: tptp
% 0.13/0.45 % Proving...
% 1.31/1.20 % SZS status Started for theBenchmark.p
% 1.31/1.20 % SZS status Theorem for theBenchmark.p
% 1.31/1.20
% 1.31/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.31/1.20
% 1.31/1.20 % ------ iProver source info
% 1.31/1.20
% 1.31/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 1.31/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.31/1.20 % git: non_committed_changes: false
% 1.31/1.20
% 1.31/1.20 % ------ Parsing...
% 1.31/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.31/1.20
% 1.31/1.20 % ------ 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: 4 0s sf_e pe_s pe_e %
% 1.31/1.20
% 1.31/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.31/1.20
% 1.31/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.31/1.20 % ------ Proving...
% 1.31/1.20 % ------ Problem Properties
% 1.31/1.20
% 1.31/1.20 %
% 1.31/1.20 % clauses 189
% 1.31/1.20 % conjectures 8
% 1.31/1.20 % EPR 57
% 1.31/1.20 % Horn 120
% 1.31/1.20 % unary 22
% 1.31/1.20 % binary 42
% 1.31/1.20 % lits 632
% 1.31/1.20 % lits eq 85
% 1.31/1.20 % fd_pure 0
% 1.31/1.20 % fd_pseudo 0
% 1.31/1.20 % fd_cond 22
% 1.31/1.20 % fd_pseudo_cond 14
% 1.31/1.20 % AC symbols 0
% 1.31/1.20
% 1.31/1.20 % ------ Schedule dynamic 5 is on
% 1.31/1.20
% 1.31/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.31/1.20
% 1.31/1.20
% 1.31/1.20 % ------
% 1.31/1.20 % Current options:
% 1.31/1.20 % ------
% 1.31/1.20
% 1.31/1.20
% 1.31/1.20 %
% 1.31/1.20
% 1.31/1.20 % ------ Proving...
% 1.31/1.20 %
% 1.31/1.20
% 1.31/1.20 % SZS status Theorem for theBenchmark.p
% 1.31/1.20
% 1.31/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.31/1.20
%------------------------------------------------------------------------------