%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU201+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 : n007.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 02:55:52 PM UTC 2026
% Result : Theorem 29.42s 4.81s
% Output : CNFRefutation 29.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 13 unt; 0 def)
% Number of atoms : 177 ( 35 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 80 ~; 93 |; 29 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 99 ( 0 sgn 94 !; 5 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f23,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(f112,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t115_relat_1) ).
fof(f117,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_relat_1) ).
fof(f118,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_rng(relation_rng_restriction(X0,X1)) = set_intersection2(relation_rng(X1),X0) ),
inference(negated_conjecture,[status(cth)],[f117]) ).
fof(f162,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f216,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( in(X0,relation_rng(relation_rng_restriction(X1,X2)))
<=> ( in(X0,relation_rng(X2))
& in(X0,X1) ) ) ),
inference(ennf_transformation,[],[f112]) ).
fof(f221,plain,
? [X0,X1] :
( relation(X1)
& relation_rng(relation_rng_restriction(X0,X1)) != set_intersection2(relation_rng(X1),X0) ),
inference(ennf_transformation,[],[f118]) ).
fof(f363,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ) ),
inference(nnf_transformation,[],[f216]) ).
fof(f364,plain,
! [X0,X1,X2] :
( ~ relation(X2)
| ( ( ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| ( in(X0,relation_rng(X2))
& in(X0,X1) ) )
& ( ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ) ) ),
inference(flattening,[],[f363]) ).
fof(f365,plain,
( relation(sK2)
& relation_rng(relation_rng_restriction(sK1,sK2)) != set_intersection2(relation_rng(sK2),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f221]) ).
fof(f443,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,[],[f23]) ).
fof(f444,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,[],[f443]) ).
fof(f445,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,[],[f444]) ).
fof(f446,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(sK42(X0,X1,X2),X2)
| ( in(sK42(X0,X1,X2),X1)
& in(sK42(X0,X1,X2),X0) ) )
& ( ~ in(sK42(X0,X1,X2),X2)
| ~ in(sK42(X0,X1,X2),X1)
| ~ in(sK42(X0,X1,X2),X0) ) )
| X2 = set_intersection2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(X3,sK42(X0,X1,X2))],[f445]) ).
fof(f493,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,relation_rng(X2)) ),
inference(cnf_transformation,[],[f364]) ).
fof(f494,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f364]) ).
fof(f495,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_rng(X2))
| ~ in(X0,X1)
| in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f364]) ).
fof(f501,plain,
relation(sK2),
inference(cnf_transformation,[],[f365]) ).
fof(f502,plain,
relation_rng(relation_rng_restriction(sK1,sK2)) != set_intersection2(relation_rng(sK2),sK1),
inference(cnf_transformation,[],[f365]) ).
fof(f555,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f162]) ).
fof(f717,plain,
! [X2,X0,X1] :
( in(sK42(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X1)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f446]) ).
fof(f718,plain,
! [X2,X0,X1] :
( in(sK42(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f446]) ).
fof(f719,plain,
! [X2,X0,X1] :
( ~ in(sK42(X0,X1,X2),X2)
| ~ in(sK42(X0,X1,X2),X1)
| ~ in(sK42(X0,X1,X2),X0)
| set_intersection2(X0,X1) = X2 ),
inference(cnf_transformation,[],[f446]) ).
fof(f720,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f805,plain,
relation_rng(relation_rng_restriction(sK1,sK2)) != set_difference(relation_rng(sK2),set_difference(relation_rng(sK2),sK1)),
inference(definition_unfolding,[],[f502,f555]) ).
fof(f873,plain,
! [X2,X0,X1] :
( ~ in(sK42(X0,X1,X2),X2)
| ~ in(sK42(X0,X1,X2),X1)
| ~ in(sK42(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f719,f555]) ).
fof(f874,plain,
! [X2,X0,X1] :
( in(sK42(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X0)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f718,f555]) ).
fof(f875,plain,
! [X2,X0,X1] :
( in(sK42(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X1)
| set_difference(X0,set_difference(X0,X1)) = X2 ),
inference(definition_unfolding,[],[f717,f555]) ).
fof(f879,plain,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(definition_unfolding,[],[f720,f555,f555]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(relation_rng_restriction(X2,X1)))
| ~ relation(X1)
| ~ in(X0,X2)
| ~ in(X0,relation_rng(X1)) ),
inference(cnf_transformation,[],[f495]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X1)
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f494]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,relation_rng(X2))
| ~ relation(X2)
| ~ in(X0,relation_rng(relation_rng_restriction(X1,X2))) ),
inference(cnf_transformation,[],[f493]) ).
tcf(c_80,negated_conjecture,
set_difference(relation_rng(sK2),set_difference(relation_rng(sK2),sK1)) != relation_rng(relation_rng_restriction(sK1,sK2)),
inference(cnf_transformation,[],[f805]) ).
tcf(c_81,negated_conjecture,
relation(sK2),
inference(cnf_transformation,[],[f501]) ).
tcf(c_290,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = X2 )
| ~ in(sK42(X0,X1,X2),X2)
| ~ in(sK42(X0,X1,X2),X1)
| ~ in(sK42(X0,X1,X2),X0) ),
inference(cnf_transformation,[],[f873]) ).
tcf(c_291,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK42(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X0)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f874]) ).
tcf(c_292,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(sK42(X0,X1,X2),X2)
| in(sK42(X0,X1,X2),X1)
| ( set_difference(X0,set_difference(X0,X1)) = X2 ) ),
inference(cnf_transformation,[],[f875]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
inference(cnf_transformation,[],[f879]) ).
tcf(c_3454,plain,
set_difference(sK1,set_difference(sK1,relation_rng(sK2))) != relation_rng(relation_rng_restriction(sK1,sK2)),
inference(demodulation,[status(thm)],[c_80,c_296]) ).
tcf(c_15226,plain,
( in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),sK1)
| in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,sK2)))
| ( set_difference(sK1,set_difference(sK1,relation_rng(sK2))) = relation_rng(relation_rng_restriction(sK1,sK2)) ) ),
inference(instantiation,[status(thm)],[c_291]) ).
tcf(c_15230,plain,
( in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,sK2)))
| ( set_difference(sK1,set_difference(sK1,relation_rng(sK2))) = relation_rng(relation_rng_restriction(sK1,sK2)) ) ),
inference(instantiation,[status(thm)],[c_292]) ).
tcf(c_15366,plain,
( ( set_difference(sK1,set_difference(sK1,relation_rng(sK2))) = relation_rng(relation_rng_restriction(sK1,sK2)) )
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),sK1)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_290]) ).
tcf(c_20121,plain,
( in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2))
| ~ relation(sK2)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_20122,plain,
( in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),sK1)
| ~ relation(sK2)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,sK2))) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_31248,plain,
! [X0: $i] :
( in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,X0)))
| ~ relation(X0)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),sK1)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(X0)) ),
inference(instantiation,[status(thm)],[c_72]) ).
tcf(c_64482,plain,
( in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(relation_rng_restriction(sK1,sK2)))
| ~ relation(sK2)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),sK1)
| ~ in(sK42(sK1,relation_rng(sK2),relation_rng(relation_rng_restriction(sK1,sK2))),relation_rng(sK2)) ),
inference(instantiation,[status(thm)],[c_31248]) ).
tcf(c_64483,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_64482,c_20121,c_20122,c_15366,c_15230,c_15226,c_3454,c_81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU201+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n007.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 13:07:22 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 0.14/0.42
% 0.14/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.42
% 0.14/0.42 % Detected problem language: tptp
% 0.14/0.43 % Proving...
% 29.42/4.81 % SZS status Started for theBenchmark.p
% 29.42/4.81 % SZS status Theorem for theBenchmark.p
% 29.42/4.81
% 29.42/4.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 29.42/4.81
% 29.42/4.81 % ------ iProver source info
% 29.42/4.81
% 29.42/4.81 % git: date: 2026-07-19 20:42:38 +0200
% 29.42/4.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 29.42/4.81 % git: non_committed_changes: false
% 29.42/4.81
% 29.42/4.81 % ------ Parsing...
% 29.42/4.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 29.42/4.81
% 29.42/4.81 % ------ Preprocessing... sup_sim: 37 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 %
% 29.42/4.81
% 29.42/4.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 29.42/4.81
% 29.42/4.81 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 29.42/4.81 % ------ Proving...
% 29.42/4.81 % ------ Problem Properties
% 29.42/4.81
% 29.42/4.81 %
% 29.42/4.81 % clauses 281
% 29.42/4.81 % conjectures 1
% 29.42/4.81 % EPR 34
% 29.42/4.81 % Horn 228
% 29.42/4.81 % unary 45
% 29.42/4.81 % binary 99
% 29.42/4.81 % lits 727
% 29.42/4.81 % lits eq 144
% 29.42/4.81 % fd_pure 0
% 29.42/4.81 % fd_pseudo 0
% 29.42/4.81 % fd_cond 10
% 29.42/4.81 % fd_pseudo_cond 59
% 29.42/4.81 % AC symbols 0
% 29.42/4.81
% 29.42/4.81 % ------ Schedule dynamic 5 is on
% 29.42/4.81
% 29.42/4.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 29.42/4.81
% 29.42/4.81
% 29.42/4.81 % ------
% 29.42/4.81 % Current options:
% 29.42/4.81 % ------
% 29.42/4.81
% 29.42/4.81
% 29.42/4.81 %
% 29.42/4.81
% 29.42/4.81 % ------ Proving...
% 29.42/4.81 %
% 29.42/4.81
% 29.42/4.81 % SZS status Theorem for theBenchmark.p
% 29.42/4.81
% 29.42/4.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 29.42/4.81
% 29.42/4.81
%------------------------------------------------------------------------------