%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC372+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 03:09:30 PM UTC 2026
% Result : Theorem 2.56s 1.39s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 42 ( 20 unt; 0 def)
% Number of atoms : 200 ( 53 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 249 ( 91 ~; 83 |; 60 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 55 !; 26 ?; 7 :)
% 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/sandbox2/benchmark/Axioms/SWC001+0.ax',ax7) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWC001+0.ax',ax28) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| segmentP(X1,X0)
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(X2)
| app(X2,X4) != X3 ) )
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( nil = X2
& nil != X3 )
| segmentP(X1,X0)
| ! [X4] :
( ssList(X4)
=> ( ? [X5] :
( ? [X6] :
( ? [X7] :
( ? [X8] :
( lt(X7,X5)
& app(X8,cons(X7,nil)) = X2
& ssList(X8) )
& ssItem(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ strictorderedP(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)
& ( nil != X2
| nil = X3 )
& ~ segmentP(X1,X0)
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(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)
& ( nil != X2
| nil = X3 )
& ~ segmentP(X1,X0)
& ? [X4] :
( ssList(X4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != X2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(X2)
& app(X2,X4) = X3 )
& X0 = X2
& X1 = X3 ) ) ) ),
inference(flattening,[],[f98]) ).
fof(f116,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(ennf_transformation,[],[f28]) ).
fof(f127,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(f165,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( nil != sK2
| nil = sK3 )
& ~ segmentP(sK1,sK0)
& ssList(sK4)
& ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( ~ lt(X7,X5)
| app(X8,cons(X7,nil)) != sK2
| ~ ssList(X8) )
| ~ ssItem(X7) )
| app(cons(X5,nil),X6) != sK4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& strictorderedP(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(f171,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,[],[f127]) ).
fof(f172,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,[],[f171]) ).
fof(f173,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))],[f172]) ).
fof(f183,plain,
ssList(sK0),
inference(cnf_transformation,[],[f165]) ).
fof(f184,plain,
ssList(sK1),
inference(cnf_transformation,[],[f165]) ).
fof(f188,plain,
~ segmentP(sK1,sK0),
inference(cnf_transformation,[],[f165]) ).
fof(f189,plain,
ssList(sK4),
inference(cnf_transformation,[],[f165]) ).
fof(f192,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f165]) ).
fof(f193,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f165]) ).
fof(f194,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f165]) ).
fof(f215,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f116]) ).
fof(f217,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f228,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,[],[f173]) ).
fof(f267,plain,
~ segmentP(sK3,sK2),
inference(definition_unfolding,[],[f188,f194,f193]) ).
fof(f268,plain,
ssList(sK3),
inference(definition_unfolding,[],[f184,f194]) ).
fof(f269,plain,
ssList(sK2),
inference(definition_unfolding,[],[f183,f193]) ).
fof(f273,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,[],[f228]) ).
tcf(c_49,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f192]) ).
tcf(c_52,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f189]) ).
tcf(c_53,negated_conjecture,
~ segmentP(sK3,sK2),
inference(cnf_transformation,[],[f267]) ).
tcf(c_57,negated_conjecture,
ssList(sK3),
inference(cnf_transformation,[],[f268]) ).
tcf(c_58,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f269]) ).
tcf(c_79,plain,
! [X0: $i] :
( ( app(nil,X0) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_81,plain,
ssList(nil),
inference(cnf_transformation,[],[f217]) ).
tcf(c_89,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,[],[f273]) ).
tcf(c_3483,plain,
app(nil,sK2) = sK2,
inference(superposition,[status(thm)],[c_58,c_79]) ).
tcf(c_7532,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_3483,c_89]) ).
tcf(c_7547,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(nil)
| ~ ssList(sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(light_normalisation,[status(thm)],[c_7532,c_3483]) ).
tcf(c_7548,plain,
! [X0: $i] :
( segmentP(app(sK2,X0),sK2)
| ~ ssList(X0)
| ~ ssList(app(sK2,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_7547,c_81,c_58]) ).
tcf(c_7950,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(app(sK2,sK4)) ),
inference(superposition,[status(thm)],[c_49,c_7548]) ).
tcf(c_7957,plain,
( segmentP(sK3,sK2)
| ~ ssList(sK4)
| ~ ssList(sK3) ),
inference(light_normalisation,[status(thm)],[c_7950,c_49]) ).
tcf(c_7958,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7957,c_53,c_52,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC372+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.72 % Computer : n012.cluster.edu
% 0.03/0.72 % Model : x86_64 x86_64
% 0.03/0.72 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.72 % Memory : 8046.5625MB
% 0.03/0.72 % OS : Linux 6.8.0-71-generic
% 0.03/0.72 % CPULimit : 300
% 0.03/0.72 % WCLimit : 300
% 0.03/0.72 % DateTime : Thu Sep 24 17:53:39 UTC 2026
% 0.03/0.73 % CPUTime :
% 0.03/0.73 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.75 Running first-order theorem proving
% 0.03/0.75 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.75
% 0.03/0.75 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.75
% 0.03/0.75 % Detected problem language: tptp
% 0.03/0.76 % Proving...
% 2.56/1.39 % SZS status Started for theBenchmark.p
% 2.56/1.39 % SZS status Theorem for theBenchmark.p
% 2.56/1.39
% 2.56/1.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.56/1.39
% 2.56/1.39 % ------ iProver source info
% 2.56/1.39
% 2.56/1.39 % git: date: 2026-07-19 20:42:38 +0200
% 2.56/1.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.56/1.39 % git: non_committed_changes: false
% 2.56/1.39
% 2.56/1.39 % ------ Parsing...
% 2.56/1.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.56/1.39
% 2.56/1.39 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.56/1.39
% 2.56/1.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.56/1.39
% 2.56/1.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.56/1.39 % ------ Proving...
% 2.56/1.39 % ------ Problem Properties
% 2.56/1.39
% 2.56/1.39 %
% 2.56/1.39 % clauses 76
% 2.56/1.39 % conjectures 8
% 2.56/1.39 % EPR 26
% 2.56/1.39 % Horn 53
% 2.56/1.39 % unary 13
% 2.56/1.39 % binary 8
% 2.56/1.39 % lits 258
% 2.56/1.39 % lits eq 60
% 2.56/1.39 % fd_pure 0
% 2.56/1.39 % fd_pseudo 0
% 2.56/1.39 % fd_cond 16
% 2.56/1.39 % fd_pseudo_cond 8
% 2.56/1.39 % AC symbols 0
% 2.56/1.39
% 2.56/1.39 % ------ Schedule dynamic 5 is on
% 2.56/1.39
% 2.56/1.39 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.56/1.39
% 2.56/1.39
% 2.56/1.39 % ------
% 2.56/1.39 % Current options:
% 2.56/1.39 % ------
% 2.56/1.39
% 2.56/1.39
% 2.56/1.39 %
% 2.56/1.39
% 2.56/1.39 % ------ Proving...
% 2.56/1.39 %
% 2.56/1.39
% 2.56/1.39 % SZS status Theorem for theBenchmark.p
% 2.56/1.39
% 2.56/1.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.56/1.39
% 2.56/1.39
%------------------------------------------------------------------------------