%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC380+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 : n015.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 03:09:32 PM UTC 2026
% Result : Theorem 0.63s 6.29s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f209ERROR: Could not build tree for root c_2506ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(cons(X5,nil),X6) != X3
| cons(X5,nil) != X2 ) ) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ 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) )
& ( ! [X5] :
( ssItem(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(cons(X5,nil),X6) != X3
| cons(X5,nil) != X2 ) ) )
| ? [X4] :
( memberP(X1,X4)
& cons(X4,nil) = X0
& ssItem(X4) )
| ~ neq(X1,nil) ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X3
& cons(X5,nil) = X2 ) )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X3
& cons(X5,nil) = X2 ) )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f100,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ) ),
inference(ennf_transformation,[],[f81]) ).
fof(f129,plain,
( ssList(sK3)
& ssList(sK4)
& ssList(sK5)
& ssList(sK6)
& ( ( ~ neq(sK6,nil)
& neq(sK4,nil) )
| sP0(sK4,sK3,sK5,sK6) )
& sK3 = sK5
& sK4 = sK6 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f125]) ).
fof(f153,plain,
( ~ neq(sK6,nil)
| sP0(sK4,sK3,sK5,sK6) ),
inference(cnf_transformation,[],[f129]) ).
fof(f154,plain,
( neq(sK4,nil)
| sP0(sK4,sK3,sK5,sK6) ),
inference(cnf_transformation,[],[f129]) ).
fof(f155,plain,
sK3 = sK5,
inference(cnf_transformation,[],[f129]) ).
fof(f156,plain,
sK4 = sK6,
inference(cnf_transformation,[],[f129]) ).
fof(f160,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f195,plain,
( neq(sK6,nil)
| sP0(sK6,sK5,sK5,sK6) ),
inference(definition_unfolding,[],[f154,f156,f155,f156]) ).
fof(f196,plain,
( ~ neq(sK6,nil)
| sP0(sK6,sK5,sK5,sK6) ),
inference(definition_unfolding,[],[f153,f156,f155]) ).
tcf(c_55,negated_conjecture,
( neq(sK6,nil)
| sP0(sK6,sK5,sK5,sK6) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_56,negated_conjecture,
( sP0(sK6,sK5,sK5,sK6)
| ~ neq(sK6,nil) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( ( app(cons(X0,nil),X1) = cons(X0,X1) )
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f160]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f209]) ).
tcf(c_126,negated_conjecture,
sP0(sK6,sK5,sK5,sK6),
inference(global_subsumption_just,[status(thm)],[c_55,c_55,c_56]) ).
tcf(c_128,negated_conjecture,
sP0(sK6,sK5,sK5,sK6),
inference(global_subsumption_just,[status(thm)],[c_56,c_126]) ).
fof(f124,definition,
! [X1,X0,X2,X3] :
( ~ sP0(X1,X0,X2,X3)
| ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X3
& cons(X5,nil) = X2 ) )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f125,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ~ neq(X3,nil)
& neq(X1,nil) )
| sP0(X1,X0,X2,X3) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(definition_folding,[],[f99,f124]) ).
fof(f126,plain,
! [X1,X0,X2,X3] :
( ~ sP0(X1,X0,X2,X3)
| ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X3
& cons(X5,nil) = X2 ) )
& ! [X4] :
( ~ memberP(X1,X4)
| cons(X4,nil) != X0
| ~ ssItem(X4) )
& neq(X1,nil) ) ),
inference(nnf_transformation,[],[f124]) ).
fof(f127,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X3
& cons(X5,nil) = X2 ) )
& ! [X4] :
( ~ memberP(X0,X4)
| cons(X4,nil) != X1
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(rectify,[],[f126]) ).
fof(f128,plain,
! [X0,X1,X2,X3] :
( ~ sP0(X0,X1,X2,X3)
| ( ssItem(sK1(X2,X3))
& ssList(sK2(X2,X3))
& app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X3
& cons(sK1(X2,X3),nil) = X2
& ! [X4] :
( ~ memberP(X0,X4)
| cons(X4,nil) != X1
| ~ ssItem(X4) )
& neq(X0,nil) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X5,sK1(X2,X3)),skolemize(X6,sK2(X2,X3))],[f127]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssItem(sK1(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| ssList(sK2(X2,X3)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f145,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X3 ),
inference(cnf_transformation,[],[f128]) ).
fof(f146,plain,
! [X2,X3,X0,X1] :
( ~ sP0(X0,X1,X2,X3)
| cons(sK1(X2,X3),nil) = X2 ),
inference(cnf_transformation,[],[f128]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X4] :
( ~ sP0(X0,X1,X2,X3)
| ~ memberP(X0,X4)
| cons(X4,nil) != X1
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f128]) ).
fof(f199,plain,
! [X2,X3,X0,X4] :
( ~ sP0(X0,cons(X4,nil),X2,X3)
| ~ memberP(X0,X4)
| ~ ssItem(X4) ),
inference(equality_resolution,[],[f147]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X1)
| ~ memberP(X0,X1)
| ~ sP0(X0,cons(X1,nil),X2,X3) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK1(X2,X3),nil) = X2 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f146]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X3 )
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK2(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X2,X3))
| ~ sP0(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_716,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssItem(sK1(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_128]) ).
tcf(c_717,plain,
ssItem(sK1(sK5,sK6)),
inference(unflattening,[status(thm)],[c_716]) ).
tcf(c_721,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ssList(sK2(X2,X3))
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_128]) ).
tcf(c_722,plain,
ssList(sK2(sK5,sK6)),
inference(unflattening,[status(thm)],[c_721]) ).
tcf(c_726,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( app(cons(sK1(X2,X3),nil),sK2(X2,X3)) = X3 )
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_128]) ).
tcf(c_727,plain,
app(cons(sK1(sK5,sK6),nil),sK2(sK5,sK6)) = sK6,
inference(unflattening,[status(thm)],[c_726]) ).
tcf(c_731,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( cons(sK1(X2,X3),nil) = X2 )
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK5 )
| ( X0 != sK6 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_128]) ).
tcf(c_732,plain,
cons(sK1(sK5,sK6),nil) = sK5,
inference(unflattening,[status(thm)],[c_731]) ).
tcf(c_741,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ ssItem(X0)
| ~ memberP(X1,X0)
| ( X3 != sK6 )
| ( X2 != sK5 )
| ( X1 != sK6 )
| ( cons(X0,nil) != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_128]) ).
tcf(c_742,plain,
! [X0: $i] :
( ~ ssItem(X0)
| ~ memberP(sK6,X0)
| ( cons(X0,nil) != sK5 ) ),
inference(unflattening,[status(thm)],[c_741]) ).
tcf(c_1085,plain,
app(sK5,sK2(sK5,sK6)) = sK6,
inference(light_normalisation,[status(thm)],[c_727,c_732]) ).
tcf(c_1931,plain,
( ~ ssItem(sK1(sK5,sK6))
| ~ memberP(sK6,sK1(sK5,sK6)) ),
inference(superposition,[status(thm)],[c_732,c_742]) ).
tcf(c_1932,plain,
~ memberP(sK6,sK1(sK5,sK6)),
inference(forward_subsumption_resolution,[status(thm)],[c_1931,c_717]) ).
tcf(c_1982,plain,
! [X0: $i] :
( ( app(cons(sK1(sK5,sK6),nil),X0) = cons(sK1(sK5,sK6),X0) )
| ~ ssList(X0) ),
inference(superposition,[status(thm)],[c_717,c_64]) ).
tcf(c_1987,plain,
! [X0: $i] :
( ( cons(sK1(sK5,sK6),X0) = app(sK5,X0) )
| ~ ssList(X0) ),
inference(light_normalisation,[status(thm)],[c_1982,c_732]) ).
tcf(c_2112,plain,
cons(sK1(sK5,sK6),sK2(sK5,sK6)) = app(sK5,sK2(sK5,sK6)),
inference(superposition,[status(thm)],[c_722,c_1987]) ).
tcf(c_2114,plain,
cons(sK1(sK5,sK6),sK2(sK5,sK6)) = sK6,
inference(light_normalisation,[status(thm)],[c_2112,c_1085]) ).
tcf(c_2503,plain,
( memberP(sK6,sK1(sK5,sK6))
| ~ ssList(sK2(sK5,sK6))
| ~ ssItem(sK1(sK5,sK6)) ),
inference(superposition,[status(thm)],[c_2114,c_89]) ).
tcf(c_2506,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2503,c_1932,c_722,c_717]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC380+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n015.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 17:59:32 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 0.63/6.29 % SZS status Started for theBenchmark.p
% 0.63/6.29 % SZS status Theorem for theBenchmark.p
% 0.63/6.29
% 0.63/6.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.63/6.29
% 0.63/6.29 % ------ iProver source info
% 0.63/6.29
% 0.63/6.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.63/6.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.63/6.29 % git: non_committed_changes: false
% 0.63/6.29
% 0.63/6.29 % ------ Parsing...
% 0.63/6.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.63/6.29
% 0.63/6.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 1 sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.63/6.29
% 0.63/6.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.63/6.29
% 0.63/6.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.63/6.29 % ------ Proving...
% 0.63/6.29 % ------ Problem Properties
% 0.63/6.29
% 0.63/6.29 %
% 0.63/6.29 % clauses 42
% 0.63/6.29 % conjectures 2
% 0.63/6.29 % EPR 8
% 0.63/6.29 % Horn 37
% 0.63/6.29 % unary 12
% 0.63/6.29 % binary 3
% 0.63/6.29 % lits 130
% 0.63/6.29 % lits eq 31
% 0.63/6.29 % fd_pure 0
% 0.63/6.29 % fd_pseudo 0
% 0.63/6.29 % fd_cond 4
% 0.63/6.29 % fd_pseudo_cond 5
% 0.63/6.29 % AC symbols 0
% 0.63/6.29
% 0.63/6.29 % ------ Schedule dynamic 5 is on
% 0.63/6.29
% 0.63/6.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.63/6.29
% 0.63/6.29
% 0.63/6.29 % ------
% 0.63/6.29 % Current options:
% 0.63/6.29 % ------
% 0.63/6.29
% 0.63/6.29
% 0.63/6.29 %
% 0.63/6.29
% 0.63/6.29 % ------ Proving...
% 0.63/6.29 %
% 0.63/6.29
% 0.63/6.29 % SZS status Theorem for theBenchmark.p
% 0.63/6.29
% 0.63/6.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.63/6.29
% 0.63/6.29
%------------------------------------------------------------------------------