%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU138+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 : n004.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 02:55:33 PM UTC 2026
% Result : Theorem 18.11s 3.42s
% Output : CNFRefutation 18.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 218 ( 38 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 278 ( 109 ~; 123 |; 42 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 123 ( 0 sgn 115 !; 8 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f9,axiom,
! [X0,X1,X2] :
( X2 = set_difference(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( ~ in(X3,X1)
& in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(f44,conjecture,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f69,plain,
? [X0,X1] : set_intersection2(X0,X1) != set_difference(X0,set_difference(X0,X1)),
inference(ennf_transformation,[],[f45]) ).
fof(f85,plain,
set_intersection2(sK1,sK2) != set_difference(sK1,set_difference(sK1,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f69]) ).
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(sK5(X0,X1,X2),X2)
| ( ~ in(sK5(X0,X1,X2),X1)
& in(sK5(X0,X1,X2),X0) ) )
& ( ~ in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0) ) )
| X2 = set_difference(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f94]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(flattening,[],[f100]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ( set_intersection2(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_intersection2(X0,X1) ) ),
inference(rectify,[],[f101]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( set_intersection2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| ( in(X4,X1)
& in(X4,X0) ) )
& ( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ) ) )
& ( ( ( in(sK7(X0,X1,X2),X2)
| ( in(sK7(X0,X1,X2),X1)
& in(sK7(X0,X1,X2),X0) ) )
& ( ~ in(sK7(X0,X1,X2),X2)
| ~ in(sK7(X0,X1,X2),X1)
| ~ in(sK7(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(X3,sK7(X0,X1,X2))],[f102]) ).
fof(f132,plain,
set_intersection2(sK1,sK2) != set_difference(sK1,set_difference(sK1,sK2)),
inference(cnf_transformation,[],[f85]) ).
fof(f149,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| ~ in(X4,X2)
| ~ in(X4,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f151,plain,
! [X2,X0,X1,X4] :
( set_difference(X0,X1) != X2
| in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f95]) ).
fof(f152,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X1)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f153,plain,
! [X2,X0,X1] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f154,plain,
! [X2,X0,X1] :
( ~ in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X1)
| ~ in(sK5(X0,X1,X2),X0)
| set_difference(X0,X1) = X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f166,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f167,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X2)
| in(X4,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f168,plain,
! [X2,X0,X1,X4] :
( set_intersection2(X0,X1) != X2
| ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,X2) ),
inference(cnf_transformation,[],[f103]) ).
fof(f189,plain,
! [X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_difference(X0,X1)) ),
inference(equality_resolution,[],[f151]) ).
fof(f191,plain,
! [X0,X1,X4] :
( ~ in(X4,set_difference(X0,X1))
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f149]) ).
fof(f195,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| ~ in(X4,X0)
| in(X4,set_intersection2(X0,X1)) ),
inference(equality_resolution,[],[f168]) ).
fof(f196,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X0) ),
inference(equality_resolution,[],[f167]) ).
fof(f197,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f166]) ).
tcf(c_69,negated_conjecture,
set_difference(sK1,set_difference(sK1,sK2)) != set_intersection2(sK1,sK2),
inference(cnf_transformation,[],[f132]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1,X2),X1)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK5(X0,X1,X2),X2)
| ~ in(sK5(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f154]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1,X2),X2)
| in(sK5(X0,X1,X2),X0)
| ( set_difference(X0,X1) = X2 ) ),
inference(cnf_transformation,[],[f153]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK5(X0,X1,X2),X2)
| ( set_difference(X0,X1) = X2 )
| ~ in(sK5(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| in(X0,set_difference(X1,X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ in(X0,X2)
| ~ in(X0,set_difference(X1,X2)) ),
inference(cnf_transformation,[],[f191]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f195]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f196]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ in(X0,set_intersection2(X1,X2)) ),
inference(cnf_transformation,[],[f197]) ).
tcf(c_3210,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1)
| in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,sK2))
| ( set_difference(sK1,set_difference(sK1,sK2)) = set_intersection2(sK1,sK2) ) ),
inference(instantiation,[status(thm)],[c_87]) ).
tcf(c_3211,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,sK2))
| ( set_difference(sK1,set_difference(sK1,sK2)) = set_intersection2(sK1,sK2) )
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_difference(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_88]) ).
tcf(c_3236,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_difference(sK1,sK2))
| ( set_difference(sK1,set_difference(sK1,sK2)) = set_intersection2(sK1,sK2) )
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_86]) ).
tcf(c_3630,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK2)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_3631,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_107]) ).
tcf(c_4335,plain,
! [X0: $i] :
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,X0))
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),X0) ),
inference(instantiation,[status(thm)],[c_106]) ).
tcf(c_4336,plain,
! [X0: $i] :
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),X0)
| in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_difference(sK1,X0))
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1) ),
inference(instantiation,[status(thm)],[c_89]) ).
tcf(c_9389,plain,
! [X0: $i] :
( ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK2)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_difference(X0,sK2)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_9393,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_intersection2(sK1,sK2))
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK2)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1) ),
inference(instantiation,[status(thm)],[c_4335]) ).
tcf(c_27402,plain,
( ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK2)
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_difference(sK1,sK2)) ),
inference(instantiation,[status(thm)],[c_9389]) ).
tcf(c_42931,plain,
( in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK2)
| in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),set_difference(sK1,sK2))
| ~ in(sK5(sK1,set_difference(sK1,sK2),set_intersection2(sK1,sK2)),sK1) ),
inference(instantiation,[status(thm)],[c_4336]) ).
tcf(c_42932,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_42931,c_27402,c_9393,c_3630,c_3631,c_3236,c_3211,c_3210,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU138+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.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 12:54:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.43 % Detected problem language: tptp
% 0.13/0.44 % Proving...
% 18.11/3.42 % SZS status Started for theBenchmark.p
% 18.11/3.42 % SZS status Theorem for theBenchmark.p
% 18.11/3.42
% 18.11/3.42 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 18.11/3.42
% 18.11/3.42 % ------ iProver source info
% 18.11/3.42
% 18.11/3.42 % git: date: 2026-07-19 20:42:38 +0200
% 18.11/3.42 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 18.11/3.42 % git: non_committed_changes: false
% 18.11/3.42
% 18.11/3.42 % ------ Parsing...
% 18.11/3.42 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 18.11/3.42
% 18.11/3.42 % ------ Preprocessing... sup_sim: 1 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 %
% 18.11/3.42
% 18.11/3.42 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 18.11/3.42
% 18.11/3.42 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 18.11/3.42 % ------ Proving...
% 18.11/3.42 % ------ Problem Properties
% 18.11/3.42
% 18.11/3.42 %
% 18.11/3.42 % clauses 69
% 18.11/3.42 % conjectures 1
% 18.11/3.42 % EPR 16
% 18.11/3.42 % Horn 55
% 18.11/3.42 % unary 20
% 18.11/3.42 % binary 28
% 18.11/3.42 % lits 142
% 18.11/3.42 % lits eq 33
% 18.11/3.42 % fd_pure 0
% 18.11/3.42 % fd_pseudo 0
% 18.11/3.42 % fd_cond 3
% 18.11/3.42 % fd_pseudo_cond 13
% 18.11/3.42 % AC symbols 0
% 18.11/3.42
% 18.11/3.42 % ------ Schedule dynamic 5 is on
% 18.11/3.42
% 18.11/3.42 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 18.11/3.42
% 18.11/3.42
% 18.11/3.42 % ------
% 18.11/3.42 % Current options:
% 18.11/3.42 % ------
% 18.11/3.42
% 18.11/3.42
% 18.11/3.42 %
% 18.11/3.42
% 18.11/3.42 % ------ Proving...
% 18.11/3.42 %
% 18.11/3.42
% 18.11/3.42 % SZS status Theorem for theBenchmark.p
% 18.11/3.42
% 18.11/3.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 18.11/3.42
% 18.11/3.42
%------------------------------------------------------------------------------