%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC355+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 : n001.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 03:09:26 PM UTC 2026
% Result : Theorem 3.33s 1.17s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f207ERROR: Could not build tree for root c_3917ERROR: MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax7) ).
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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( neq(X3,nil)
| ~ neq(X1,nil) )
& ( segmentP(X1,X0)
| ! [X4] :
( ssItem(X4)
=> app(X2,cons(X4,nil)) != X3 )
| ~ 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) )
& ( segmentP(X1,X0)
| ! [X4] :
( ssItem(X4)
=> app(X2,cons(X4,nil)) != X3 )
| ~ 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) )
| ( ~ segmentP(X1,X0)
& ? [X4] :
( ssItem(X4)
& app(X2,cons(X4,nil)) = X3 )
& 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) )
| ( ~ segmentP(X1,X0)
& ? [X4] :
( ssItem(X4)
& app(X2,cons(X4,nil)) = X3 )
& neq(X1,nil) ) )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f108,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssItem(X1)
| ssList(cons(X1,X0)) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f129,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f130,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ~ neq(sK3,nil)
& neq(sK1,nil) )
| ( ~ segmentP(sK1,sK0)
& ssItem(sK4)
& sK3 = app(sK2,cons(sK4,nil))
& neq(sK1,nil) ) )
& sK0 = sK2
& sK1 = sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f99]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f129]) ).
fof(f139,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(rectify,[],[f138]) ).
fof(f140,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ segmentP(X0,X1)
| ( app(app(sK9(X0,X1),X1),sK10(X0,X1)) = X0
& ssList(sK10(X0,X1))
& ssList(sK9(X0,X1)) ) )
& ( ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) )
| segmentP(X0,X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X4,sK9(X0,X1)),skolemize(X5,sK10(X0,X1))],[f139]) ).
fof(f141,plain,
ssList(sK0),
inference(cnf_transformation,[],[f130]) ).
fof(f142,plain,
ssList(sK1),
inference(cnf_transformation,[],[f130]) ).
fof(f145,plain,
( ~ neq(sK3,nil)
| ~ segmentP(sK1,sK0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f147,plain,
( ~ neq(sK3,nil)
| ssItem(sK4) ),
inference(cnf_transformation,[],[f130]) ).
fof(f149,plain,
( ~ neq(sK3,nil)
| sK3 = app(sK2,cons(sK4,nil)) ),
inference(cnf_transformation,[],[f130]) ).
fof(f153,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f130]) ).
fof(f154,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f130]) ).
fof(f167,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| ssList(cons(X1,X0)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f175,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f181,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f192,plain,
! [X2,X3,X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1) ),
inference(cnf_transformation,[],[f140]) ).
fof(f198,plain,
( ~ neq(sK3,nil)
| ~ segmentP(sK3,sK2) ),
inference(definition_unfolding,[],[f145,f154,f153]) ).
fof(f199,plain,
ssList(sK3),
inference(definition_unfolding,[],[f142,f154]) ).
fof(f200,plain,
ssList(sK2),
inference(definition_unfolding,[],[f141,f153]) ).
fof(f206,plain,
! [X2,X3,X1] :
( ~ ssList(app(app(X2,X1),X3))
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(app(app(X2,X1),X3),X1) ),
inference(equality_resolution,[],[f192]) ).
tcf(c_49,negated_conjecture,
neq(sK3,nil),
inference(cnf_transformation,[],[f207]) ).
tcf(c_51,negated_conjecture,
( ( app(sK2,cons(sK4,nil)) = sK3 )
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f149]) ).
tcf(c_53,negated_conjecture,
( ssItem(sK4)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f147]) ).
tcf(c_55,negated_conjecture,
( ~ segmentP(sK3,sK2)
| ~ neq(sK3,nil) ),
inference(cnf_transformation,[],[f198]) ).
tcf(c_58,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f199]) ).
tcf(c_59,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f200]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f167]) ).
tcf(c_80,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f175]) ).
tcf(c_86,plain,
ssList(nil),
inference(cnf_transformation,[],[f181]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i,X2: $i] :
( segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_130,negated_conjecture,
~ segmentP(sK3,sK2),
inference(global_subsumption_just,[status(thm)],[c_55,c_49,c_55]) ).
tcf(c_136,negated_conjecture,
app(sK2,cons(sK4,nil)) = sK3,
inference(global_subsumption_just,[status(thm)],[c_51,c_49,c_51]) ).
tcf(c_1715,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_59,c_80]) ).
tcf(c_2073,plain,
! [X0: $i] :
( ssList(cons(sK4,X0))
| ~ ssItem(sK4)
| ~ ssList(X0) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_2074,plain,
( ssList(cons(sK4,nil))
| ~ ssList(nil)
| ~ ssItem(sK4) ),
inference(instantiation,[status(thm)],[c_2073]) ).
tcf(c_3403,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_1715,c_94]) ).
tcf(c_3427,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(sK2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_3403,c_1715]) ).
tcf(c_3428,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3427,c_59,c_86]) ).
tcf(c_3893,plain,
( segmentP(sK3,sK2)
| ~ ssList(cons(sK4,nil))
| ~ ssList(app(sK2,cons(sK4,nil))) ),
inference(superposition,[status(thm)],[c_136,c_3428]) ).
tcf(c_3900,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK3)
| ~ ssList(cons(sK4,nil)) ),
inference(light_normalisation,[status(thm)],[c_3893,c_136]) ).
tcf(c_3901,plain,
~ ssList(cons(sK4,nil)),
inference(forward_subsumption_resolution,[status(thm)],[c_3900,c_130,c_58]) ).
tcf(c_3917,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3901,c_2074,c_53,c_49,c_86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC355+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 17:53:54 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 3.33/1.17 % SZS status Started for theBenchmark.p
% 3.33/1.17 % SZS status Theorem for theBenchmark.p
% 3.33/1.17
% 3.33/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.33/1.17
% 3.33/1.17 % ------ iProver source info
% 3.33/1.17
% 3.33/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 3.33/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.33/1.17 % git: non_committed_changes: false
% 3.33/1.17
% 3.33/1.17 % ------ Parsing...
% 3.33/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.33/1.17
% 3.33/1.17 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.33/1.17
% 3.33/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.33/1.17
% 3.33/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.33/1.17 % ------ Proving...
% 3.33/1.17 % ------ Problem Properties
% 3.33/1.17
% 3.33/1.17 %
% 3.33/1.17 % clauses 40
% 3.33/1.17 % conjectures 5
% 3.33/1.17 % EPR 15
% 3.33/1.17 % Horn 37
% 3.33/1.17 % unary 12
% 3.33/1.17 % binary 4
% 3.33/1.17 % lits 119
% 3.33/1.17 % lits eq 30
% 3.33/1.17 % fd_pure 0
% 3.33/1.17 % fd_pseudo 0
% 3.33/1.17 % fd_cond 5
% 3.33/1.17 % fd_pseudo_cond 5
% 3.33/1.17 % AC symbols 0
% 3.33/1.17
% 3.33/1.17 % ------ Schedule dynamic 5 is on
% 3.33/1.17
% 3.33/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.33/1.17
% 3.33/1.17
% 3.33/1.17 % ------
% 3.33/1.17 % Current options:
% 3.33/1.17 % ------
% 3.33/1.17
% 3.33/1.17
% 3.33/1.17 %
% 3.33/1.17
% 3.33/1.17 % ------ Proving...
% 3.33/1.17 %
% 3.33/1.17
% 3.33/1.17 % SZS status Theorem for theBenchmark.p
% 3.33/1.17
% 3.33/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.33/1.17
%------------------------------------------------------------------------------