%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n017.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 02:55:10 PM UTC 2026
% Result : Theorem 3.15s 1.28s
% Output : CNFRefutation 3.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 30 unt; 2 def)
% Number of atoms : 126 ( 36 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 34 ~; 27 |; 18 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 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 : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 55 !; 6 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(f6,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f26,axiom,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( one_to_one(X2)
=> relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t121_funct_1) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( one_to_one(X2)
& disjoint(X0,X1) )
=> disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t125_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( ( function(X2)
& relation(X2) )
=> ( ( one_to_one(X2)
& disjoint(X0,X1) )
=> disjoint(relation_image(X2,X0),relation_image(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> relation_image(X0,empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t149_relat_1) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ one_to_one(X2)
| relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ function(X2)
| ~ relation(X2)
| ~ one_to_one(X2)
| relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ),
inference(flattening,[],[f53]) ).
fof(f55,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& one_to_one(X2)
& disjoint(X0,X1)
& ~ disjoint(relation_image(X2,X0),relation_image(X2,X1)) ),
inference(ennf_transformation,[],[f28]) ).
fof(f56,plain,
? [X0,X1,X2] :
( function(X2)
& relation(X2)
& one_to_one(X2)
& disjoint(X0,X1)
& ~ disjoint(relation_image(X2,X0),relation_image(X2,X1)) ),
inference(flattening,[],[f55]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| relation_image(X0,empty_set) = empty_set ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f80,plain,
( function(sK13)
& relation(sK13)
& one_to_one(sK13)
& disjoint(sK11,sK12)
& ~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12,sK13]),skolemize(X0,sK11),skolemize(X1,sK12),skolemize(X2,sK13)],[f56]) ).
fof(f87,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f88,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f68]) ).
fof(f89,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ function(X2)
| ~ relation(X2)
| ~ one_to_one(X2)
| relation_image(X2,set_intersection2(X0,X1)) = set_intersection2(relation_image(X2,X0),relation_image(X2,X1)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f121,plain,
function(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f122,plain,
relation(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
one_to_one(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
disjoint(sK11,sK12),
inference(cnf_transformation,[],[f80]) ).
fof(f125,plain,
~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)),
inference(cnf_transformation,[],[f80]) ).
fof(f126,plain,
! [X0] :
( ~ relation(X0)
| empty_set = relation_image(X0,empty_set) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[],[f87]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_intersection2(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(X0,X1) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),relation_image(X0,X2)) = relation_image(X0,set_intersection2(X1,X2)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f120]) ).
tcf(c_87,negated_conjecture,
~ disjoint(relation_image(sK13,sK11),relation_image(sK13,sK12)),
inference(cnf_transformation,[],[f125]) ).
tcf(c_88,negated_conjecture,
disjoint(sK11,sK12),
inference(cnf_transformation,[],[f124]) ).
tcf(c_89,negated_conjecture,
one_to_one(sK13),
inference(cnf_transformation,[],[f123]) ).
tcf(c_90,negated_conjecture,
relation(sK13),
inference(cnf_transformation,[],[f122]) ).
tcf(c_91,negated_conjecture,
function(sK13),
inference(cnf_transformation,[],[f121]) ).
tcf(c_92,plain,
! [X0: $i] :
( ( relation_image(X0,empty_set) = empty_set )
| ~ relation(X0) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_525,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( set_intersection2(relation_image(X0,X1),relation_image(X0,X2)) = relation_image(X0,set_intersection2(X1,X2)) )
| ~ relation(X0)
| ~ function(X0)
| ( X0 != sK13 ) ),
inference(resolution_lifted,[status(thm)],[c_86,c_89]) ).
tcf(c_526,plain,
! [X0: $i,X1: $i] :
( ( set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1)) = relation_image(sK13,set_intersection2(X0,X1)) )
| ~ relation(sK13)
| ~ function(sK13) ),
inference(unflattening,[status(thm)],[c_525]) ).
tcf(c_528,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1)) = relation_image(sK13,set_intersection2(X0,X1)),
inference(global_subsumption_just,[status(thm)],[c_526,c_91,c_90,c_526]) ).
tcf(c_852,definition,
iPr_def_10 = relation_image(sK13,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_853,definition,
iPr_def_11 = relation_image(sK13,sK12),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i] : set_intersection2(relation_image(sK13,X0),relation_image(sK13,X1)) = relation_image(sK13,set_intersection2(X0,X1)),
inference(demodulation,[status(thm)],[c_528]) ).
tcf(c_855,negated_conjecture,
relation(sK13),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_856,negated_conjecture,
disjoint(sK11,sK12),
inference(demodulation,[status(thm)],[c_88]) ).
tcf(c_857,negated_conjecture,
~ disjoint(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_87,c_853,c_852]) ).
tcf(c_1470,plain,
! [X0: $i] : set_intersection2(iPr_def_10,relation_image(sK13,X0)) = relation_image(sK13,set_intersection2(sK11,X0)),
inference(superposition,[status(thm)],[c_852,c_854]) ).
tcf(c_1483,plain,
! [X0: $i] : set_intersection2(relation_image(sK13,X0),iPr_def_11) = relation_image(sK13,set_intersection2(X0,sK12)),
inference(superposition,[status(thm)],[c_853,c_854]) ).
tcf(c_1510,plain,
! [X0: $i] : set_intersection2(iPr_def_11,relation_image(sK13,X0)) = relation_image(sK13,set_intersection2(X0,sK12)),
inference(demodulation,[status(thm)],[c_1483,c_53]) ).
tcf(c_1515,plain,
set_intersection2(iPr_def_10,relation_image(sK13,sK12)) = set_intersection2(iPr_def_11,relation_image(sK13,sK11)),
inference(superposition,[status(thm)],[c_1510,c_1470]) ).
tcf(c_1517,plain,
set_intersection2(iPr_def_10,iPr_def_11) = set_intersection2(iPr_def_11,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_1515,c_852,c_853]) ).
tcf(c_1600,plain,
( disjoint(iPr_def_10,iPr_def_11)
| ( set_intersection2(iPr_def_10,iPr_def_11) != empty_set ) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_1964,plain,
relation_image(sK13,empty_set) = empty_set,
inference(superposition,[status(thm)],[c_855,c_92]) ).
tcf(c_2228,plain,
set_intersection2(sK11,sK12) = empty_set,
inference(superposition,[status(thm)],[c_856,c_55]) ).
tcf(c_2381,plain,
set_intersection2(iPr_def_11,relation_image(sK13,sK11)) = relation_image(sK13,empty_set),
inference(superposition,[status(thm)],[c_2228,c_1510]) ).
tcf(c_2382,plain,
set_intersection2(iPr_def_10,iPr_def_11) = empty_set,
inference(light_normalisation,[status(thm)],[c_2381,c_852,c_1517,c_1964]) ).
tcf(c_2384,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2382,c_1600,c_857]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU056+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:35:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 3.15/1.28 % SZS status Started for theBenchmark.p
% 3.15/1.28 % SZS status Theorem for theBenchmark.p
% 3.15/1.28
% 3.15/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.15/1.28
% 3.15/1.28 % ------ iProver source info
% 3.15/1.28
% 3.15/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 3.15/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.15/1.28 % git: non_committed_changes: false
% 3.15/1.28
% 3.15/1.28 % ------ Parsing...
% 3.15/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.15/1.28
% 3.15/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.15/1.28
% 3.15/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.15/1.28
% 3.15/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.15/1.28 % ------ Proving...
% 3.15/1.28 % ------ Problem Properties
% 3.15/1.28
% 3.15/1.28 %
% 3.15/1.28 % clauses 45
% 3.15/1.28 % conjectures 3
% 3.15/1.28 % EPR 24
% 3.15/1.28 % Horn 43
% 3.15/1.28 % unary 28
% 3.15/1.28 % binary 12
% 3.15/1.28 % lits 67
% 3.15/1.28 % lits eq 13
% 3.15/1.28 % fd_pure 0
% 3.15/1.28 % fd_pseudo 0
% 3.15/1.28 % fd_cond 1
% 3.15/1.28 % fd_pseudo_cond 1
% 3.15/1.28 % AC symbols 0
% 3.15/1.28
% 3.15/1.28 % ------ Schedule dynamic 5 is on
% 3.15/1.28
% 3.15/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.15/1.28
% 3.15/1.28
% 3.15/1.28 % ------
% 3.15/1.28 % Current options:
% 3.15/1.28 % ------
% 3.15/1.28
% 3.15/1.28
% 3.15/1.28 %
% 3.15/1.28
% 3.15/1.28 % ------ Proving...
% 3.15/1.28 %
% 3.15/1.28
% 3.15/1.28 % SZS status Theorem for theBenchmark.p
% 3.15/1.28
% 3.15/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.15/1.28
% 3.15/1.28
%------------------------------------------------------------------------------