%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC110+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 : n009.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 03:07:56 PM UTC 2026
% Result : Theorem 3.92s 1.35s
% Output : CNFRefutation 3.92s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named f223ERROR: Could not build tree for root c_5000ERROR: 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(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(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).
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(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| 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)
=> ( ( ( ( segmentP(X1,X0)
& neq(X0,nil) )
| ~ neq(X1,nil) )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3 ) )
| 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)
& ( ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ssList(X0)
& ? [X1] :
( ssList(X1)
& ? [X2] :
( ssList(X2)
& ? [X3] :
( ssList(X3)
& ( ( ( ~ segmentP(X1,X0)
| ~ neq(X0,nil) )
& neq(X1,nil) )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f118,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( neq(X0,X1)
<=> X0 != X1 ) ) ),
inference(ennf_transformation,[],[f15]) ).
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(f133,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( ( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil) )
& neq(sK1,nil) )
| ( nil != sK0
& nil = sK1 ) )
& ( nil != sK2
| nil = sK3 )
& ssList(sK4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK2)
& sK3 = app(sK2,sK4)
& 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(f136,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,[],[f110]) ).
fof(f137,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,[],[f136]) ).
fof(f138,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( ( ~ neq(X0,X1)
| X0 != X1 )
& ( X0 = X1
| neq(X0,X1) ) ) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f141,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(f142,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,[],[f141]) ).
fof(f143,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))],[f142]) ).
fof(f147,plain,
ssList(sK0),
inference(cnf_transformation,[],[f133]) ).
fof(f148,plain,
ssList(sK1),
inference(cnf_transformation,[],[f133]) ).
fof(f152,plain,
( neq(sK1,nil)
| nil != sK0 ),
inference(cnf_transformation,[],[f133]) ).
fof(f153,plain,
( ~ segmentP(sK1,sK0)
| ~ neq(sK0,nil)
| nil = sK1 ),
inference(cnf_transformation,[],[f133]) ).
fof(f155,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f133]) ).
fof(f156,plain,
ssList(sK4),
inference(cnf_transformation,[],[f133]) ).
fof(f159,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f133]) ).
fof(f160,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f133]) ).
fof(f161,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f133]) ).
fof(f176,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X0 ),
inference(cnf_transformation,[],[f137]) ).
fof(f182,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f185,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 = X1
| neq(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
fof(f188,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f199,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,[],[f143]) ).
fof(f210,plain,
( ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil)
| nil = sK3 ),
inference(definition_unfolding,[],[f153,f161,f160,f161,f160]) ).
fof(f211,plain,
( neq(sK3,nil)
| nil != sK2 ),
inference(definition_unfolding,[],[f152,f160,f161]) ).
fof(f213,plain,
ssList(sK3),
inference(definition_unfolding,[],[f148,f161]) ).
fof(f214,plain,
ssList(sK2),
inference(definition_unfolding,[],[f147,f160]) ).
fof(f220,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,[],[f199]) ).
tcf(c_49,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f159]) ).
tcf(c_52,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f156]) ).
tcf(c_53,negated_conjecture,
( ( sK3 = nil )
| ( sK2 != nil ) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_55,negated_conjecture,
( ( sK3 = nil )
| ~ segmentP(sK3,sK2)
| ~ neq(sK2,nil) ),
inference(cnf_transformation,[],[f210]) ).
tcf(c_56,negated_conjecture,
( neq(sK3,nil)
| ( sK2 != nil ) ),
inference(cnf_transformation,[],[f211]) ).
tcf(c_60,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f213]) ).
tcf(c_61,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f214]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( ( X0 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f176]) ).
tcf(c_82,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( neq(X1,X0)
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_85,plain,
! [X0: $i] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(cnf_transformation,[],[f223]) ).
tcf(c_88,plain,
ssList(nil),
inference(cnf_transformation,[],[f188]) ).
tcf(c_96,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,[],[f220]) ).
tcf(c_864,plain,
! [X0: $i] :
( ~ ssList(X0)
| ( sK2 != nil )
| ( X0 != nil )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_85]) ).
tcf(c_865,plain,
( ~ ssList(sK3)
| ( sK2 != nil )
| ( sK3 != nil ) ),
inference(unflattening,[status(thm)],[c_864]) ).
tcf(c_866,plain,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_865,c_60,c_53,c_865]) ).
tcf(c_895,plain,
! [X0: $i,X1: $i] :
( ( sK3 = nil )
| ( X0 = X1 )
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK3,sK2)
| ( X1 != nil )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_84]) ).
tcf(c_896,plain,
( ( sK2 = nil )
| ( sK3 = nil )
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ segmentP(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_895]) ).
tcf(c_897,plain,
( ~ segmentP(sK3,sK2)
| ( sK3 = nil ) ),
inference(global_subsumption_just,[status(thm)],[c_896,c_61,c_88,c_866,c_896]) ).
tcf(c_898,plain,
( ( sK3 = nil )
| ~ segmentP(sK3,sK2) ),
inference(renaming,[status(thm)],[c_897]) ).
tcf(c_2854,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_61,c_82]) ).
tcf(c_3425,plain,
( ( sK2 = nil )
| ~ ssList(sK4)
| ~ ssList(sK2)
| ( sK3 != nil ) ),
inference(superposition,[status(thm)],[c_49,c_78]) ).
tcf(c_3433,plain,
sK3 != nil,
inference(forward_subsumption_resolution,[status(thm)],[c_3425,c_866,c_52,c_61]) ).
tcf(c_3436,plain,
~ segmentP(sK3,sK2),
inference(backward_subsumption_resolution,[status(thm)],[c_898,c_3433]) ).
tcf(c_4616,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK2),X0)) ),
inference(superposition,[status(thm)],[c_2854,c_96]) ).
tcf(c_4632,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_4616,c_2854]) ).
tcf(c_4633,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4632,c_88,c_61]) ).
tcf(c_4992,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(app(sK2,sK4)) ),
inference(superposition,[status(thm)],[c_49,c_4633]) ).
tcf(c_4999,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(light_normalisation,[status(thm)],[c_4992,c_49]) ).
tcf(c_5000,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4999,c_3436,c_52,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC110+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 16:26:44 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.45
% 0.14/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.45
% 0.14/0.45 % Detected problem language: tptp
% 0.14/0.46 % Proving...
% 3.92/1.35 % SZS status Started for theBenchmark.p
% 3.92/1.35 % SZS status Theorem for theBenchmark.p
% 3.92/1.35
% 3.92/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.92/1.35
% 3.92/1.35 % ------ iProver source info
% 3.92/1.35
% 3.92/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 3.92/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.92/1.35 % git: non_committed_changes: false
% 3.92/1.35
% 3.92/1.35 % ------ Parsing...
% 3.92/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.92/1.35
% 3.92/1.35 % ------ 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 %
% 3.92/1.35
% 3.92/1.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.92/1.35
% 3.92/1.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.92/1.35 % ------ Proving...
% 3.92/1.35 % ------ Problem Properties
% 3.92/1.35
% 3.92/1.35 %
% 3.92/1.35 % clauses 51
% 3.92/1.35 % conjectures 6
% 3.92/1.35 % EPR 17
% 3.92/1.35 % Horn 43
% 3.92/1.35 % unary 13
% 3.92/1.35 % binary 6
% 3.92/1.35 % lits 154
% 3.92/1.35 % lits eq 36
% 3.92/1.35 % fd_pure 0
% 3.92/1.35 % fd_pseudo 0
% 3.92/1.35 % fd_cond 5
% 3.92/1.35 % fd_pseudo_cond 6
% 3.92/1.35 % AC symbols 0
% 3.92/1.35
% 3.92/1.35 % ------ Schedule dynamic 5 is on
% 3.92/1.35
% 3.92/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.92/1.35
% 3.92/1.35
% 3.92/1.35 % ------
% 3.92/1.35 % Current options:
% 3.92/1.35 % ------
% 3.92/1.35
% 3.92/1.35
% 3.92/1.35 %
% 3.92/1.35
% 3.92/1.35 % ------ Proving...
% 3.92/1.35 %
% 3.92/1.35
% 3.92/1.35 % SZS status Theorem for theBenchmark.p
% 3.92/1.35
% 3.92/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.92/1.35
% 3.92/1.35
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