%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC217+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 : n007.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 03:08:54 PM UTC 2026
% Result : Theorem 2.96s 1.29s
% Output : CNFRefutation 2.96s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f544ERROR: Could not build tree for root c_15841ERROR: 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(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
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)
=> ( ( neq(X3,nil)
& ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| ( nil = X3
& nil != X2 )
| neq(X0,nil)
| ~ 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)
& ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X3,X4)
| cons(X4,nil) != X2 ) ) )
| ( nil = X3
& nil != X2 )
| neq(X0,nil)
| ~ neq(X1,nil)
| 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(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
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)
& ( ~ neq(X3,nil)
| ? [X4] :
( ssItem(X4)
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& ( nil != X3
| nil = X2 )
& ~ neq(X0,nil)
& 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)
| ? [X4] :
( ssItem(X4)
& memberP(X3,X4)
& cons(X4,nil) = X2 ) )
& ( nil != X3
| nil = X2 )
& ~ neq(X0,nil)
& neq(X1,nil)
& 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(f273,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( ssList(sK53)
& ssList(sK54)
& ssList(sK55)
& ssList(sK56)
& ( ~ neq(sK56,nil)
| ( ssItem(sK57)
& memberP(sK56,sK57)
& sK55 = cons(sK57,nil) ) )
& ( nil != sK56
| nil = sK55 )
& ~ neq(sK53,nil)
& neq(sK54,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(f387,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f273]) ).
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,
( ~ neq(sK56,nil)
| ssItem(sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ~ neq(sK56,nil)
| sK55 = cons(sK57,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
~ neq(sK53,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f505,f507]) ).
fof(f509,plain,
~ neq(sK55,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f511,plain,
ssList(sK55),
inference(definition_unfolding,[],[f496,f506]) ).
fof(f513,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,[],[f513]) ).
tcf(c_138,plain,
! [X0: $i,X1: $i] :
( neq(X0,X1)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f387]) ).
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,[],[f544]) ).
tcf(c_232,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f482]) ).
tcf(c_246,negated_conjecture,
neq(sK56,nil),
inference(cnf_transformation,[],[f508]) ).
tcf(c_247,negated_conjecture,
~ neq(sK55,nil),
inference(cnf_transformation,[],[f509]) ).
tcf(c_249,negated_conjecture,
( ( cons(sK57,nil) = sK55 )
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f502]) ).
tcf(c_251,negated_conjecture,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f500]) ).
tcf(c_255,negated_conjecture,
ssList(sK55),
inference(cnf_transformation,[],[f511]) ).
tcf(c_296,plain,
( ( app(nil,nil) = nil )
| ~ ssList(nil) ),
inference(instantiation,[status(thm)],[c_232]) ).
tcf(c_362,negated_conjecture,
ssItem(sK57),
inference(global_subsumption_just,[status(thm)],[c_251,c_246,c_251]) ).
tcf(c_372,plain,
app(nil,nil) = nil,
inference(global_subsumption_just,[status(thm)],[c_229,c_141,c_296]) ).
tcf(c_374,negated_conjecture,
cons(sK57,nil) = sK55,
inference(global_subsumption_just,[status(thm)],[c_249,c_246,c_249]) ).
tcf(c_3219,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ( X1 != nil )
| ( X0 != sK55 ) ),
inference(resolution_lifted,[status(thm)],[c_138,c_247]) ).
tcf(c_3220,plain,
( ( sK55 = nil )
| ~ ssList(sK55)
| ~ ssList(nil) ),
inference(unflattening,[status(thm)],[c_3219]) ).
tcf(c_3221,plain,
sK55 = nil,
inference(global_subsumption_just,[status(thm)],[c_3220,c_255,c_141,c_3220]) ).
tcf(c_6111,plain,
cons(sK57,nil) = nil,
inference(light_normalisation,[status(thm)],[c_374,c_3221]) ).
tcf(c_12866,definition,
iPr_def_10 = cons(sK57,nil),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_12867,plain,
iPr_def_10 = nil,
inference(demodulation,[status(thm)],[c_6111,c_12866]) ).
tcf(c_12871,negated_conjecture,
ssItem(sK57),
inference(demodulation,[status(thm)],[c_362]) ).
tcf(c_15678,plain,
app(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_372,c_12867]) ).
tcf(c_15679,plain,
ssList(iPr_def_10),
inference(light_normalisation,[status(thm)],[c_141,c_12867]) ).
tcf(c_15701,plain,
cons(sK57,iPr_def_10) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_12866,c_12867]) ).
tcf(c_15779,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(iPr_def_10)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,cons(sK57,iPr_def_10))) ),
inference(superposition,[status(thm)],[c_15701,c_54]) ).
tcf(c_15780,plain,
! [X0: $i] :
( memberP(app(X0,iPr_def_10),sK57)
| ~ ssList(iPr_def_10)
| ~ ssItem(sK57)
| ~ ssList(X0)
| ~ ssList(app(X0,iPr_def_10)) ),
inference(light_normalisation,[status(thm)],[c_15779,c_15701]) ).
tcf(c_15781,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_15780,c_15679,c_12871]) ).
tcf(c_15816,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(iPr_def_10,X0) ),
inference(light_normalisation,[status(thm)],[c_171,c_12867]) ).
tcf(c_15837,plain,
( memberP(iPr_def_10,sK57)
| ~ ssList(iPr_def_10)
| ~ ssList(app(iPr_def_10,iPr_def_10)) ),
inference(superposition,[status(thm)],[c_15678,c_15781]) ).
tcf(c_15838,plain,
( memberP(iPr_def_10,sK57)
| ~ ssList(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_15837,c_15678]) ).
tcf(c_15839,plain,
memberP(iPr_def_10,sK57),
inference(forward_subsumption_resolution,[status(thm)],[c_15838,c_15679]) ).
tcf(c_15840,plain,
~ ssItem(sK57),
inference(superposition,[status(thm)],[c_15839,c_15816]) ).
tcf(c_15841,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_15840,c_12871]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC217+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 17:00:53 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.96/1.29 % SZS status Started for theBenchmark.p
% 2.96/1.29 % SZS status Theorem for theBenchmark.p
% 2.96/1.29
% 2.96/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.96/1.29
% 2.96/1.29 % ------ iProver source info
% 2.96/1.29
% 2.96/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.96/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.96/1.29 % git: non_committed_changes: false
% 2.96/1.29
% 2.96/1.29 % ------ Parsing...
% 2.96/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.96/1.29
% 2.96/1.29 % ------ 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: 5 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 2.96/1.29
% 2.96/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.96/1.29
% 2.96/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.96/1.29 % ------ Proving...
% 2.96/1.29 % ------ Problem Properties
% 2.96/1.29
% 2.96/1.29 %
% 2.96/1.29 % clauses 187
% 2.96/1.29 % conjectures 3
% 2.96/1.29 % EPR 55
% 2.96/1.29 % Horn 119
% 2.96/1.29 % unary 23
% 2.96/1.29 % binary 40
% 2.96/1.29 % lits 625
% 2.96/1.29 % lits eq 82
% 2.96/1.29 % fd_pure 0
% 2.96/1.29 % fd_pseudo 0
% 2.96/1.29 % fd_cond 21
% 2.96/1.29 % fd_pseudo_cond 14
% 2.96/1.29 % AC symbols 0
% 2.96/1.29
% 2.96/1.29 % ------ Schedule dynamic 5 is on
% 2.96/1.29
% 2.96/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.96/1.29
% 2.96/1.29
% 2.96/1.29 % ------
% 2.96/1.29 % Current options:
% 2.96/1.29 % ------
% 2.96/1.29
% 2.96/1.29
% 2.96/1.29 %
% 2.96/1.29
% 2.96/1.29 % ------ Proving...
% 2.96/1.29 %
% 2.96/1.29
% 2.96/1.29 % SZS status Theorem for theBenchmark.p
% 2.96/1.29
% 2.96/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.96/1.30
% 2.96/1.30
%------------------------------------------------------------------------------