%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWC032+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 : n013.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 03:07:36 PM UTC 2026
% Result : Theorem 4.02s 1.28s
% Output : CNFRefutation 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 189 ( 110 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 224 ( 77 ~; 71 |; 61 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 38 !; 18 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
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(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)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [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/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ( ( nil = X1
| nil != X0 )
& ( nil = X0
| nil != X1 ) )
| ( nil = X2
& nil != X3 )
| ! [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 != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [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 != X1
& nil = X0 )
| ( nil != X0
& nil = X1 ) )
& ( nil != X2
| nil = X3 )
& ? [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(f109,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(ennf_transformation,[],[f84]) ).
fof(f110,plain,
! [X0] :
( ~ ssList(X0)
| ! [X1] :
( ~ ssList(X1)
| ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
inference(ennf_transformation,[],[f83]) ).
fof(f155,plain,
( ssList(sK0)
& ssList(sK1)
& ssList(sK2)
& ssList(sK3)
& ( ( nil != sK1
& nil = sK0 )
| ( nil != sK0
& nil = sK1 ) )
& ( nil != sK2
| nil = sK3 )
& 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(f158,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(f159,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,[],[f158]) ).
fof(f169,plain,
ssList(sK0),
inference(cnf_transformation,[],[f155]) ).
fof(f173,plain,
( nil != sK1
| nil != sK0 ),
inference(cnf_transformation,[],[f155]) ).
fof(f176,plain,
( nil = sK0
| nil = sK1 ),
inference(cnf_transformation,[],[f155]) ).
fof(f177,plain,
( nil != sK2
| nil = sK3 ),
inference(cnf_transformation,[],[f155]) ).
fof(f178,plain,
ssList(sK4),
inference(cnf_transformation,[],[f155]) ).
fof(f181,plain,
sK3 = app(sK2,sK4),
inference(cnf_transformation,[],[f155]) ).
fof(f182,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f155]) ).
fof(f183,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f155]) ).
fof(f197,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f109]) ).
fof(f199,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| nil != app(X0,X1)
| nil = X1 ),
inference(cnf_transformation,[],[f159]) ).
fof(f245,plain,
( nil = sK2
| nil = sK3 ),
inference(definition_unfolding,[],[f176,f183,f182]) ).
fof(f248,plain,
( nil != sK3
| nil != sK2 ),
inference(definition_unfolding,[],[f173,f182,f183]) ).
fof(f250,plain,
ssList(sK2),
inference(definition_unfolding,[],[f169,f182]) ).
tcf(c_49,negated_conjecture,
app(sK2,sK4) = sK3,
inference(cnf_transformation,[],[f181]) ).
tcf(c_52,negated_conjecture,
ssList(sK4),
inference(cnf_transformation,[],[f178]) ).
tcf(c_53,negated_conjecture,
( ( sK3 = nil )
| ( sK2 != nil ) ),
inference(cnf_transformation,[],[f177]) ).
tcf(c_54,negated_conjecture,
( ( sK2 = nil )
| ( sK3 = nil ) ),
inference(cnf_transformation,[],[f245]) ).
tcf(c_55,negated_conjecture,
( ( sK2 != nil )
| ( sK3 != nil ) ),
inference(cnf_transformation,[],[f248]) ).
tcf(c_59,negated_conjecture,
ssList(sK2),
inference(cnf_transformation,[],[f250]) ).
tcf(c_73,plain,
! [X0: $i] :
( ( app(X0,nil) = X0 )
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] :
( ( X1 = nil )
| ~ ssList(X1)
| ~ ssList(X0)
| ( app(X0,X1) != nil ) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_152,negated_conjecture,
sK3 = nil,
inference(global_subsumption_just,[status(thm)],[c_54,c_54,c_53]) ).
tcf(c_154,negated_conjecture,
sK3 = nil,
inference(global_subsumption_just,[status(thm)],[c_53,c_152]) ).
tcf(c_158,negated_conjecture,
sK2 != nil,
inference(global_subsumption_just,[status(thm)],[c_55,c_54,c_53,c_55]) ).
tcf(c_595,plain,
app(sK2,sK4) = nil,
inference(light_normalisation,[status(thm)],[c_49,c_154]) ).
tcf(c_2885,plain,
app(sK2,nil) = sK2,
inference(superposition,[status(thm)],[c_59,c_73]) ).
tcf(c_3644,plain,
( ( sK4 = nil )
| ~ ssList(sK4)
| ~ ssList(sK2) ),
inference(superposition,[status(thm)],[c_595,c_75]) ).
tcf(c_3652,plain,
sK4 = nil,
inference(forward_subsumption_resolution,[status(thm)],[c_3644,c_52,c_59]) ).
tcf(c_3656,plain,
app(sK2,nil) = nil,
inference(demodulation,[status(thm)],[c_595,c_3652]) ).
tcf(c_3666,plain,
sK2 = nil,
inference(demodulation,[status(thm)],[c_2885,c_3656]) ).
tcf(c_3667,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3666,c_158]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC032+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 16:00:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.41
% 0.09/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.41
% 0.09/0.41 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 4.02/1.28 % SZS status Started for theBenchmark.p
% 4.02/1.28 % SZS status Theorem for theBenchmark.p
% 4.02/1.28
% 4.02/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.02/1.28
% 4.02/1.28 % ------ iProver source info
% 4.02/1.28
% 4.02/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 4.02/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.02/1.28 % git: non_committed_changes: false
% 4.02/1.28
% 4.02/1.28 % ------ Parsing...
% 4.02/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.02/1.28
% 4.02/1.28 % ------ Preprocessing... sup_sim: 3 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 %
% 4.02/1.28
% 4.02/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.02/1.28
% 4.02/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.02/1.28 % ------ Proving...
% 4.02/1.28 % ------ Problem Properties
% 4.02/1.28
% 4.02/1.28 %
% 4.02/1.28 % clauses 64
% 4.02/1.28 % conjectures 6
% 4.02/1.28 % EPR 19
% 4.02/1.28 % Horn 41
% 4.02/1.28 % unary 12
% 4.02/1.28 % binary 5
% 4.02/1.28 % lits 214
% 4.02/1.28 % lits eq 57
% 4.02/1.28 % fd_pure 0
% 4.02/1.28 % fd_pseudo 0
% 4.02/1.28 % fd_cond 15
% 4.02/1.28 % fd_pseudo_cond 7
% 4.02/1.28 % AC symbols 0
% 4.02/1.28
% 4.02/1.28 % ------ Schedule dynamic 5 is on
% 4.02/1.28
% 4.02/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.02/1.28
% 4.02/1.28
% 4.02/1.28 % ------
% 4.02/1.28 % Current options:
% 4.02/1.28 % ------
% 4.02/1.28
% 4.02/1.28
% 4.02/1.28 %
% 4.02/1.28
% 4.02/1.28 % ------ Proving...
% 4.02/1.28 %
% 4.02/1.28
% 4.02/1.28 % SZS status Theorem for theBenchmark.p
% 4.02/1.28
% 4.02/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.02/1.28
% 4.02/1.28
%------------------------------------------------------------------------------