%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU141+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 : n002.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 02:55:34 PM UTC 2026
% Result : Theorem 3.93s 1.29s
% Output : CNFRefutation 3.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 79 ( 33 unt; 1 def)
% Number of atoms : 170 ( 70 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 45 ~; 45 |; 7 &)
% ( 5 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 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 : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 92 !; 4 ?; 23 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f11,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_intersection2(X0,X1) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7_xboole_0) ).
fof(f12,axiom,
! [X0,X1] :
( proper_subset(X0,X1)
<=> ( X0 != X1
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(f27,axiom,
! [X0,X1] :
( disjoint(X0,X1)
=> disjoint(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(f35,axiom,
! [X0] : set_intersection2(X0,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(f39,axiom,
! [X0,X1] : subset(set_difference(X0,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
fof(f40,axiom,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).
fof(f41,axiom,
! [X0,X1] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_xboole_1) ).
fof(f42,axiom,
! [X0] : set_difference(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
fof(f45,axiom,
! [X0,X1] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_xboole_1) ).
fof(f47,axiom,
! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
fof(f50,axiom,
! [X0,X1] :
~ ( proper_subset(X1,X0)
& subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t60_xboole_1) ).
fof(f55,conjecture,
! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(f56,negated_conjecture,
~ ! [X0,X1] :
( disjoint(X0,X1)
<=> set_difference(X0,X1) = X0 ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 != X1
& subset(X0,X1) )
=> proper_subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f69,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(ennf_transformation,[],[f65]) ).
fof(f70,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(flattening,[],[f69]) ).
fof(f73,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f87,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f92,plain,
? [X0,X1] :
( disjoint(X0,X1)
<~> set_difference(X0,X1) = X0 ),
inference(ennf_transformation,[],[f56]) ).
fof(f116,plain,
! [X0,X1] :
( ( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set )
& ( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f122,plain,
! [X0,X1] :
( ( empty_set != set_difference(X0,X1)
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ) ),
inference(nnf_transformation,[],[f40]) ).
fof(f125,plain,
? [X0,X1] :
( ( disjoint(X0,X1)
| set_difference(X0,X1) = X0 )
& ( ~ disjoint(X0,X1)
| set_difference(X0,X1) != X0 ) ),
inference(nnf_transformation,[],[f92]) ).
fof(f126,plain,
( ( disjoint(sK10,sK11)
| sK10 = set_difference(sK10,sK11) )
& ( ~ disjoint(sK10,sK11)
| sK10 != set_difference(sK10,sK11) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f125]) ).
fof(f129,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f157,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| set_intersection2(X0,X1) = empty_set ),
inference(cnf_transformation,[],[f116]) ).
fof(f158,plain,
! [X0,X1] :
( set_intersection2(X0,X1) != empty_set
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f159,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f171,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f179,plain,
! [X0] : empty_set = set_intersection2(X0,empty_set),
inference(cnf_transformation,[],[f35]) ).
fof(f184,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f39]) ).
fof(f185,plain,
! [X0,X1] :
( empty_set != set_difference(X0,X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f122]) ).
fof(f187,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X0,set_difference(X1,X0)),
inference(cnf_transformation,[],[f41]) ).
fof(f188,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f42]) ).
fof(f193,plain,
! [X0,X1] : set_difference(X0,X1) = set_difference(set_union2(X0,X1),X1),
inference(cnf_transformation,[],[f45]) ).
fof(f195,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
inference(cnf_transformation,[],[f47]) ).
fof(f199,plain,
! [X0,X1] :
( ~ proper_subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f204,plain,
( disjoint(sK10,sK11)
| sK10 = set_difference(sK10,sK11) ),
inference(cnf_transformation,[],[f126]) ).
fof(f205,plain,
( ~ disjoint(sK10,sK11)
| sK10 != set_difference(sK10,sK11) ),
inference(cnf_transformation,[],[f126]) ).
fof(f215,plain,
! [X0,X1] :
( empty_set != set_difference(X0,set_difference(X0,X1))
| disjoint(X0,X1) ),
inference(definition_unfolding,[],[f158,f195]) ).
fof(f216,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| empty_set = set_difference(X0,set_difference(X0,X1)) ),
inference(definition_unfolding,[],[f157,f195]) ).
fof(f222,plain,
! [X0] : empty_set = set_difference(X0,set_difference(X0,empty_set)),
inference(definition_unfolding,[],[f179,f195]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| ( set_difference(X0,set_difference(X0,X1)) != empty_set ) ),
inference(cnf_transformation,[],[f215]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( ( set_difference(X0,set_difference(X0,X1)) = empty_set )
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f216]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( proper_subset(X0,X1)
| ( X0 = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f159]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[],[f171]) ).
tcf(c_101,plain,
! [X0: $i] : set_difference(X0,set_difference(X0,empty_set)) = empty_set,
inference(cnf_transformation,[],[f222]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[],[f184]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ( set_difference(X0,X1) != empty_set ) ),
inference(cnf_transformation,[],[f185]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] : set_union2(X0,set_difference(X1,X0)) = set_union2(X0,X1),
inference(cnf_transformation,[],[f187]) ).
tcf(c_110,plain,
! [X0: $i] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[],[f188]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : set_difference(set_union2(X0,X1),X1) = set_difference(X0,X1),
inference(cnf_transformation,[],[f193]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ proper_subset(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_125,negated_conjecture,
( ~ disjoint(sK10,sK11)
| ( set_difference(sK10,sK11) != sK10 ) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_126,negated_conjecture,
( disjoint(sK10,sK11)
| ( set_difference(sK10,sK11) = sK10 ) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_733,plain,
! [X0: $i] : set_difference(X0,X0) = empty_set,
inference(light_normalisation,[status(thm)],[c_101,c_110]) ).
tcf(c_1774,definition,
iPr_def_10 = set_difference(sK10,sK11),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_1775,negated_conjecture,
( disjoint(sK10,sK11)
| ( iPr_def_10 = sK10 ) ),
inference(demodulation,[status(thm)],[c_126,c_1774]) ).
tcf(c_1776,negated_conjecture,
( ~ disjoint(sK10,sK11)
| ( iPr_def_10 != sK10 ) ),
inference(demodulation,[status(thm)],[c_125]) ).
tcf(c_2979,plain,
subset(iPr_def_10,sK10),
inference(superposition,[status(thm)],[c_1774,c_106]) ).
tcf(c_2996,plain,
( disjoint(sK11,sK10)
| ( sK10 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1775,c_93]) ).
tcf(c_3003,plain,
( disjoint(sK10,sK11)
| ( sK10 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2996,c_93]) ).
tcf(c_3127,plain,
set_union2(sK11,sK10) = set_union2(sK11,iPr_def_10),
inference(superposition,[status(thm)],[c_1774,c_109]) ).
tcf(c_3219,plain,
set_union2(sK10,sK11) = set_union2(iPr_def_10,sK11),
inference(demodulation,[status(thm)],[c_3127,c_51]) ).
tcf(c_3623,plain,
set_difference(set_union2(iPr_def_10,sK11),sK11) = set_difference(sK10,sK11),
inference(superposition,[status(thm)],[c_3219,c_115]) ).
tcf(c_3643,plain,
set_difference(set_union2(iPr_def_10,sK11),sK11) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_3623,c_1774]) ).
tcf(c_3933,plain,
( proper_subset(iPr_def_10,sK10)
| ( sK10 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_2979,c_81]) ).
tcf(c_4146,plain,
( subset(sK10,iPr_def_10)
| ( set_difference(sK10,iPr_def_10) != empty_set ) ),
inference(instantiation,[status(thm)],[c_108]) ).
tcf(c_4237,plain,
( ( sK10 = iPr_def_10 )
| ~ subset(sK10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3933,c_120]) ).
tcf(c_4772,plain,
set_difference(iPr_def_10,sK11) = iPr_def_10,
inference(demodulation,[status(thm)],[c_3643,c_115]) ).
tcf(c_4773,plain,
( disjoint(iPr_def_10,sK11)
| ( set_difference(iPr_def_10,iPr_def_10) != empty_set ) ),
inference(superposition,[status(thm)],[c_4772,c_79]) ).
tcf(c_4797,plain,
disjoint(iPr_def_10,sK11),
inference(ground_joinability,[status(thm)],[c_4773,c_733]) ).
tcf(c_4980,plain,
( ( sK10 = iPr_def_10 )
| ( set_difference(sK10,set_difference(sK10,sK11)) = empty_set ) ),
inference(superposition,[status(thm)],[c_3003,c_80]) ).
tcf(c_4995,plain,
( ( sK10 = iPr_def_10 )
| ( set_difference(sK10,iPr_def_10) = empty_set ) ),
inference(light_normalisation,[status(thm)],[c_4980,c_1774]) ).
tcf(c_5272,plain,
sK10 = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_4237,c_4146,c_4237,c_4995]) ).
tcf(c_5297,plain,
( ~ disjoint(iPr_def_10,sK11)
| ( iPr_def_10 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_1776,c_5272]) ).
tcf(c_5309,plain,
~ disjoint(iPr_def_10,sK11),
inference(equality_resolution_simp,[status(thm)],[c_5297]) ).
tcf(c_5310,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5309,c_4797]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU141+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n002.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 12:57:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 3.93/1.29 % SZS status Started for theBenchmark.p
% 3.93/1.29 % SZS status Theorem for theBenchmark.p
% 3.93/1.29
% 3.93/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.93/1.29
% 3.93/1.29 % ------ iProver source info
% 3.93/1.29
% 3.93/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 3.93/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.93/1.29 % git: non_committed_changes: false
% 3.93/1.29
% 3.93/1.29 % ------ Parsing...
% 3.93/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.93/1.29
% 3.93/1.29 % ------ Preprocessing... sup_sim: 3 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 %
% 3.93/1.29
% 3.93/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.93/1.29
% 3.93/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.93/1.29 % ------ Proving...
% 3.93/1.29 % ------ Problem Properties
% 3.93/1.29
% 3.93/1.29 %
% 3.93/1.29 % clauses 73
% 3.93/1.29 % conjectures 2
% 3.93/1.29 % EPR 23
% 3.93/1.29 % Horn 57
% 3.93/1.29 % unary 19
% 3.93/1.29 % binary 31
% 3.93/1.29 % lits 153
% 3.93/1.29 % lits eq 35
% 3.93/1.29 % fd_pure 0
% 3.93/1.29 % fd_pseudo 0
% 3.93/1.29 % fd_cond 3
% 3.93/1.29 % fd_pseudo_cond 14
% 3.93/1.29 % AC symbols 0
% 3.93/1.29
% 3.93/1.29 % ------ Schedule dynamic 5 is on
% 3.93/1.29
% 3.93/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.93/1.29
% 3.93/1.29
% 3.93/1.29 % ------
% 3.93/1.29 % Current options:
% 3.93/1.29 % ------
% 3.93/1.29
% 3.93/1.29
% 3.93/1.29 %
% 3.93/1.29
% 3.93/1.29 % ------ Proving...
% 3.93/1.29 %
% 3.93/1.29
% 3.93/1.29 % SZS status Theorem for theBenchmark.p
% 3.93/1.29
% 3.93/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.93/1.29
% 3.93/1.29
%------------------------------------------------------------------------------