%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU133+2 : TPTP v9.3.1. Released v3.3.0.
% 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 02:55:31 PM UTC 2026
% Result : Theorem 3.45s 6.21s
% Output : CNFRefutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 10 unt; 1 def)
% Number of atoms : 119 ( 11 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 136 ( 52 ~; 52 |; 27 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 66 ( 0 sgn 59 !; 7 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f36,conjecture,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f54,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f67,plain,
? [X0,X1] : ~ subset(set_difference(X0,X1),X0),
inference(ennf_transformation,[],[f37]) ).
fof(f85,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f86,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f85]) ).
fof(f87,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK2(X0,X1),X0)
& ~ in(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f86]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( in(X3,X1)
| ~ in(X3,X0)
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(flattening,[],[f92]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| ( ~ in(X3,X1)
& in(X3,X0) ) )
& ( ~ in(X3,X2)
| in(X3,X1)
| ~ in(X3,X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ( set_difference(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( ~ in(X4,X1)
& in(X4,X0) ) )
& ( in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK4(X0,X1,X2),X2)
| ( ~ in(sK4(X0,X1,X2),X1)
& in(sK4(X0,X1,X2),X0) ) )
& ( ~ in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| ~ in(sK4(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f94]) ).
fof(f102,plain,
~ subset(set_difference(sK8,sK9),sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f67]) ).
fof(f120,plain,
! [X0,X1] :
( in(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f121,plain,
! [X0,X1] :
( ~ in(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f129,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f159,plain,
~ subset(set_difference(sK8,sK9),sK8),
inference(cnf_transformation,[],[f102]) ).
fof(f183,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f129]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f121]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f183]) ).
tcf(c_103,negated_conjecture,
~ subset(set_difference(sK8,sK9),sK8),
inference(cnf_transformation,[],[f159]) ).
tcf(c_1598,definition,
iPr_def_10 = set_difference(sK8,sK9),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1599,negated_conjecture,
~ subset(iPr_def_10,sK8),
inference(demodulation,[status(thm)],[c_103,c_1598]) ).
tcf(c_2934,plain,
! [X0: $i] :
( in(X0,sK8)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1598,c_76]) ).
tcf(c_2981,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| in(sK2(iPr_def_10,X0),sK8) ),
inference(superposition,[status(thm)],[c_64,c_2934]) ).
tcf(c_3034,plain,
subset(iPr_def_10,sK8),
inference(superposition,[status(thm)],[c_2981,c_63]) ).
tcf(c_3035,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3034,c_1599]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU133+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/5.39 % Computer : n001.cluster.edu
% 0.11/5.39 % Model : x86_64 x86_64
% 0.11/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.39 % Memory : 8046.5625MB
% 0.11/5.39 % OS : Linux 6.8.0-71-generic
% 0.11/5.39 % CPULimit : 300
% 0.11/5.39 % WCLimit : 300
% 0.11/5.40 % DateTime : Thu Sep 24 12:58:14 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.44 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
% 0.16/5.45
% 0.16/5.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.45
% 0.16/5.45 % Detected problem language: tptp
% 0.16/5.46 % Proving...
% 3.45/6.21 % SZS status Started for theBenchmark.p
% 3.45/6.21 % SZS status Theorem for theBenchmark.p
% 3.45/6.21
% 3.45/6.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.45/6.21
% 3.45/6.21 % ------ iProver source info
% 3.45/6.21
% 3.45/6.21 % git: date: 2026-07-19 20:42:38 +0200
% 3.45/6.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.45/6.21 % git: non_committed_changes: false
% 3.45/6.21
% 3.45/6.21 % ------ Parsing...
% 3.45/6.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.45/6.21
% 3.45/6.21 % ------ 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 %
% 3.45/6.21
% 3.45/6.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.45/6.21
% 3.45/6.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.45/6.21 % ------ Proving...
% 3.45/6.21 % ------ Problem Properties
% 3.45/6.21
% 3.45/6.21 %
% 3.45/6.21 % clauses 67
% 3.45/6.21 % conjectures 1
% 3.45/6.21 % EPR 17
% 3.45/6.21 % Horn 53
% 3.45/6.21 % unary 18
% 3.45/6.21 % binary 28
% 3.45/6.21 % lits 140
% 3.45/6.21 % lits eq 31
% 3.45/6.21 % fd_pure 0
% 3.45/6.21 % fd_pseudo 0
% 3.45/6.21 % fd_cond 3
% 3.45/6.21 % fd_pseudo_cond 13
% 3.45/6.21 % AC symbols 0
% 3.45/6.21
% 3.45/6.21 % ------ Schedule dynamic 5 is on
% 3.45/6.21
% 3.45/6.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.45/6.21
% 3.45/6.21
% 3.45/6.21 % ------
% 3.45/6.21 % Current options:
% 3.45/6.21 % ------
% 3.45/6.21
% 3.45/6.21
% 3.45/6.21 %
% 3.45/6.21
% 3.45/6.21 % ------ Proving...
% 3.45/6.21 %
% 3.45/6.21
% 3.45/6.21 % SZS status Theorem for theBenchmark.p
% 3.45/6.21
% 3.45/6.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.45/6.21
% 3.45/6.21
%------------------------------------------------------------------------------