%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% 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 02:47:37 PM UTC 2026
% Result : Theorem 2.33s 11.21s
% Output : CNFRefutation 2.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 2 def)
% Number of atoms : 113 ( 4 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 108 ( 48 ~; 38 |; 17 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 sgn 69 !; 5 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
fof(f3,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f4,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f8,conjecture,
! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_and_difference_disjoint) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] : disjoint(intersection(X0,X1),difference(X0,X1)),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
=> disjoint(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f11,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,plain,
? [X0,X1] : ~ disjoint(intersection(X0,X1),difference(X0,X1)),
inference(ennf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(nnf_transformation,[],[f1]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ member(X2,intersection(X0,X1))
| ( member(X2,X1)
& member(X2,X0) ) )
& ( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(nnf_transformation,[],[f2]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ~ member(X2,difference(X0,X1))
| ( ~ member(X2,X1)
& member(X2,X0) ) )
& ( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X2] :
( member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f19,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ? [X3] :
( member(X3,X1)
& member(X3,X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ intersect(X0,X1)
| ( member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) )
| intersect(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f19]) ).
fof(f24,plain,
~ disjoint(intersection(sK2,sK3),difference(sK2,sK3)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f13]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f31,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f41,plain,
~ disjoint(intersection(sK2,sK3),difference(sK2,sK3)),
inference(cnf_transformation,[],[f24]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_63,negated_conjecture,
~ disjoint(intersection(sK2,sK3),difference(sK2,sK3)),
inference(cnf_transformation,[],[f41]) ).
tcf(c_207,plain,
! [X0: $i,X1: $i] :
( intersect(X0,X1)
| ( difference(sK2,sK3) != X1 )
| ( intersection(sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_63]) ).
tcf(c_208,plain,
intersect(intersection(sK2,sK3),difference(sK2,sK3)),
inference(unflattening,[status(thm)],[c_207]) ).
tcf(c_338,definition,
iPr_def_10 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_339,definition,
iPr_def_11 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_340,plain,
intersect(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_208,c_339,c_338]) ).
tcf(c_599,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_338,c_51]) ).
tcf(c_653,plain,
! [X0: $i] :
( member(sK0(iPr_def_10,X0),sK3)
| ~ intersect(iPr_def_10,X0) ),
inference(superposition,[status(thm)],[c_56,c_599]) ).
tcf(c_703,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_339,c_54]) ).
tcf(c_719,plain,
! [X0: $i] :
( ~ intersect(iPr_def_10,X0)
| ~ member(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_653,c_703]) ).
tcf(c_987,plain,
~ intersect(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_57,c_719]) ).
tcf(c_988,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_987,c_340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET629+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.40 % Computer : n002.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.11/10.40 % WCLimit : 300
% 0.11/10.40 % DateTime : Thu Sep 24 11:33:30 UTC 2026
% 0.11/10.40 % CPUTime :
% 0.11/10.40 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.44 Running first-order theorem proving
% 0.11/10.44 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
% 0.11/10.45
% 0.11/10.45 % ======== iProver multi-core TPTP/SMT =========
% 0.11/10.45
% 0.11/10.45 % Detected problem language: tptp
% 0.11/10.46 % Proving...
% 2.33/11.21 % SZS status Started for theBenchmark.p
% 2.33/11.21 % SZS status Theorem for theBenchmark.p
% 2.33/11.21
% 2.33/11.21 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.33/11.21
% 2.33/11.21 % ------ iProver source info
% 2.33/11.21
% 2.33/11.21 % git: date: 2026-07-19 20:42:38 +0200
% 2.33/11.21 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.33/11.21 % git: non_committed_changes: false
% 2.33/11.21
% 2.33/11.21 % ------ Parsing...
% 2.33/11.21 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.33/11.21
% 2.33/11.21 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.33/11.21
% 2.33/11.21 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.33/11.21
% 2.33/11.21 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.33/11.21 % ------ Proving...
% 2.33/11.21 % ------ Problem Properties
% 2.33/11.21
% 2.33/11.21 %
% 2.33/11.21 % clauses 16
% 2.33/11.21 % conjectures 0
% 2.33/11.21 % EPR 3
% 2.33/11.21 % Horn 14
% 2.33/11.21 % unary 4
% 2.33/11.21 % binary 7
% 2.33/11.21 % lits 33
% 2.33/11.21 % lits eq 5
% 2.33/11.21 % fd_pure 0
% 2.33/11.21 % fd_pseudo 0
% 2.33/11.21 % fd_cond 0
% 2.33/11.21 % fd_pseudo_cond 2
% 2.33/11.21 % AC symbols 0
% 2.33/11.21
% 2.33/11.21 % ------ Schedule dynamic 5 is on
% 2.33/11.21
% 2.33/11.21 % ------ no conjectures: strip conj schedule
% 2.33/11.21
% 2.33/11.21 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.33/11.21
% 2.33/11.21
% 2.33/11.21 % ------
% 2.33/11.21 % Current options:
% 2.33/11.21 % ------
% 2.33/11.21
% 2.33/11.21
% 2.33/11.21 %
% 2.33/11.21
% 2.33/11.21 % ------ Proving...
% 2.33/11.21 %
% 2.33/11.21
% 2.33/11.21 % SZS status Theorem for theBenchmark.p
% 2.33/11.21
% 2.33/11.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.33/11.21
% 2.33/11.21
%------------------------------------------------------------------------------