%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU155+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:55:38 PM UTC 2026
% Result : Theorem 8.01s 6.74s
% Output : CNFRefutation 8.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 111 ( 8 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 132 ( 50 ~; 51 |; 24 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 56 !; 11 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f14,axiom,
! [X0,X1] :
( X1 = union(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,X0)
& in(X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
fof(f40,conjecture,
! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> subset(X0,union(X1)) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f91,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f101,plain,
? [X0,X1] :
( in(X0,X1)
& ~ subset(X0,union(X1)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f147,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,[],[f91]) ).
fof(f148,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,[],[f147]) ).
fof(f149,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK5(X0,X1),X0)
& ~ in(sK5(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X2,sK5(X0,X1))],[f148]) ).
fof(f154,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) )
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X3] :
( in(X3,X0)
& in(X2,X3) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f155,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ? [X7] :
( in(X7,X0)
& in(X5,X7) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| ? [X4] :
( in(X4,X0)
& in(X2,X4) ) )
& ( ~ in(X2,X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(X2,X3) ) ) )
| X1 = union(X0) ) ),
inference(rectify,[],[f154]) ).
fof(f156,plain,
! [X0,X1] :
( ( union(X0) != X1
| ! [X5] :
( ( ~ in(X5,X1)
| ( in(sK9(X0,X5),X0)
& in(X5,sK9(X0,X5)) ) )
& ( ! [X6] :
( ~ in(X6,X0)
| ~ in(X5,X6) )
| in(X5,X1) ) ) )
& ( ( ( in(sK7(X0,X1),X1)
| ( in(sK8(X0,X1),X0)
& in(sK7(X0,X1),sK8(X0,X1)) ) )
& ( ~ in(sK7(X0,X1),X1)
| ! [X3] :
( ~ in(X3,X0)
| ~ in(sK7(X0,X1),X3) ) ) )
| X1 = union(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f155]) ).
fof(f166,plain,
( in(sK11,sK12)
& ~ subset(sK11,union(sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f101]) ).
fof(f206,plain,
! [X0,X1] :
( in(sK5(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f207,plain,
! [X0,X1] :
( ~ in(sK5(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f149]) ).
fof(f216,plain,
! [X0,X1,X6,X5] :
( union(X0) != X1
| ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,X1) ),
inference(cnf_transformation,[],[f156]) ).
fof(f247,plain,
in(sK11,sK12),
inference(cnf_transformation,[],[f166]) ).
fof(f248,plain,
~ subset(sK11,union(sK12)),
inference(cnf_transformation,[],[f166]) ).
fof(f349,plain,
! [X0,X6,X5] :
( ~ in(X6,X0)
| ~ in(X5,X6)
| in(X5,union(X0)) ),
inference(equality_resolution,[],[f216]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK5(X0,X1),X1) ),
inference(cnf_transformation,[],[f207]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK5(X0,X1),X0) ),
inference(cnf_transformation,[],[f206]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,union(X2))
| ~ in(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f349]) ).
tcf(c_121,negated_conjecture,
~ subset(sK11,union(sK12)),
inference(cnf_transformation,[],[f248]) ).
tcf(c_122,negated_conjecture,
in(sK11,sK12),
inference(cnf_transformation,[],[f247]) ).
tcf(c_3846,plain,
( subset(sK11,union(sK12))
| ~ in(sK5(sK11,union(sK12)),union(sK12)) ),
inference(instantiation,[status(thm)],[c_79]) ).
tcf(c_3852,plain,
( subset(sK11,union(sK12))
| in(sK5(sK11,union(sK12)),sK11) ),
inference(instantiation,[status(thm)],[c_80]) ).
tcf(c_3953,plain,
! [X0: $i] :
( in(X0,union(sK12))
| ~ in(sK11,sK12)
| ~ in(X0,sK11) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_4855,plain,
( in(sK5(sK11,union(sK12)),union(sK12))
| ~ in(sK11,sK12)
| ~ in(sK5(sK11,union(sK12)),sK11) ),
inference(instantiation,[status(thm)],[c_3953]) ).
tcf(c_4856,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_4855,c_3852,c_3846,c_121,c_122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU155+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.37 % Computer : n001.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Thu Sep 24 13:04:13 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 8.01/6.74 % SZS status Started for theBenchmark.p
% 8.01/6.74 % SZS status Theorem for theBenchmark.p
% 8.01/6.74
% 8.01/6.74 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 8.01/6.74
% 8.01/6.74 % ------ iProver source info
% 8.01/6.74
% 8.01/6.74 % git: date: 2026-07-19 20:42:38 +0200
% 8.01/6.74 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 8.01/6.74 % git: non_committed_changes: false
% 8.01/6.74
% 8.01/6.74 % ------ Parsing...
% 8.01/6.74 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 8.01/6.74
% 8.01/6.74 % ------ 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 %
% 8.01/6.74
% 8.01/6.74 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 8.01/6.74
% 8.01/6.74 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 8.01/6.74 % ------ Proving...
% 8.01/6.74 % ------ Problem Properties
% 8.01/6.74
% 8.01/6.74 %
% 8.01/6.74 % clauses 109
% 8.01/6.74 % conjectures 2
% 8.01/6.74 % EPR 22
% 8.01/6.74 % Horn 84
% 8.01/6.74 % unary 26
% 8.01/6.74 % binary 45
% 8.01/6.74 % lits 235
% 8.01/6.74 % lits eq 69
% 8.01/6.74 % fd_pure 0
% 8.01/6.74 % fd_pseudo 0
% 8.01/6.74 % fd_cond 3
% 8.01/6.74 % fd_pseudo_cond 29
% 8.01/6.74 % AC symbols 0
% 8.01/6.74
% 8.01/6.74 % ------ Input Options Time Limit: Unbounded
% 8.01/6.74
% 8.01/6.74
% 8.01/6.74 % ------
% 8.01/6.74 % Current options:
% 8.01/6.74 % ------
% 8.01/6.74
% 8.01/6.74
% 8.01/6.74 %
% 8.01/6.74
% 8.01/6.74 % ------ Proving...
% 8.01/6.74 %
% 8.01/6.74
% 8.01/6.74 % SZS status Theorem for theBenchmark.p
% 8.01/6.74
% 8.01/6.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 8.01/6.75
% 8.01/6.75
%------------------------------------------------------------------------------