%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n015.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 02:47:39 PM UTC 2026
% Result : Theorem 3.32s 6.30s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 77 ( 8 unt; 0 def)
% Number of atoms : 211 ( 33 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 230 ( 96 ~; 101 |; 24 &)
% ( 7 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 123 !; 9 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f5,axiom,
! [X0,X1] :
( not_equal(X0,X1)
<=> X0 != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_equal_defn) ).
fof(f7,axiom,
! [X0,X1] :
( intersect(X0,X1)
=> intersect(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
fof(f9,conjecture,
! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th119) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
<=> not_equal(intersection(X0,X1),empty_set) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
? [X0,X1] :
( intersect(X0,X1)
<~> not_equal(intersection(X0,X1),empty_set) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,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(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(flattening,[],[f13]) ).
fof(f15,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,[],[f2]) ).
fof(f16,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,[],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ not_equal(X0,X1)
| X0 != X1 )
& ( X0 = X1
| not_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f5]) ).
fof(f22,plain,
? [X0,X1] :
( ( intersect(X0,X1)
| not_equal(intersection(X0,X1),empty_set) )
& ( ~ intersect(X0,X1)
| ~ not_equal(intersection(X0,X1),empty_set) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f23,plain,
( ( intersect(sK2,sK3)
| not_equal(intersection(sK2,sK3),empty_set) )
& ( ~ intersect(sK2,sK3)
| ~ not_equal(intersection(sK2,sK3),empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f28,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f30,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( ~ not_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( X0 = X1
| not_equal(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| intersect(X1,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f39,plain,
( intersect(sK2,sK3)
| not_equal(intersection(sK2,sK3),empty_set) ),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
( ~ intersect(sK2,sK3)
| ~ not_equal(intersection(sK2,sK3),empty_set) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
! [X1] : ~ not_equal(X1,X1),
inference(equality_resolution,[],[f35]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f30]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,plain,
! [X0: $i] : ~ not_equal(X0,X0),
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_62,negated_conjecture,
( ~ intersect(sK2,sK3)
| ~ not_equal(intersection(sK2,sK3),empty_set) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,negated_conjecture,
( intersect(sK2,sK3)
| not_equal(intersection(sK2,sK3),empty_set) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_74,plain,
( ~ not_equal(intersection(sK2,sK3),empty_set)
| ~ intersect(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_75,plain,
( ~ intersect(sK2,sK3)
| ~ not_equal(intersection(sK2,sK3),empty_set) ),
inference(renaming,[status(thm)],[c_74]) ).
tcf(c_76,plain,
( not_equal(intersection(sK2,sK3),empty_set)
| intersect(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_77,plain,
( intersect(sK2,sK3)
| not_equal(intersection(sK2,sK3),empty_set) ),
inference(renaming,[status(thm)],[c_76]) ).
tcf(c_94,plain,
! [X0: $i,X1: $i] :
( not_equal(X0,X1)
| ( X0 = X1 ) ),
inference(prop_impl_just,[status(thm)],[c_58]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ intersect(sK2,sK3)
| ( X1 != empty_set )
| ( intersection(sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_94,c_75]) ).
tcf(c_255,plain,
( ( intersection(sK2,sK3) = empty_set )
| ~ intersect(sK2,sK3) ),
inference(unflattening,[status(thm)],[c_254]) ).
tcf(c_262,plain,
! [X0: $i] :
( intersect(sK2,sK3)
| ( X0 != empty_set )
| ( intersection(sK2,sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_77]) ).
tcf(c_263,plain,
( intersect(sK2,sK3)
| ( intersection(sK2,sK3) != empty_set ) ),
inference(unflattening,[status(thm)],[c_262]) ).
tcf(c_274,plain,
( ( intersection(sK2,sK3) != empty_set )
| intersect(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_263]) ).
tcf(c_275,plain,
( intersect(sK2,sK3)
| ( intersection(sK2,sK3) != empty_set ) ),
inference(renaming,[status(thm)],[c_274]) ).
tcf(c_276,plain,
( ( intersection(sK2,sK3) = empty_set )
| ~ intersect(sK2,sK3) ),
inference(prop_impl_just,[status(thm)],[c_255]) ).
tcf(c_750,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK0(intersection(X0,X1),X2),X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_53,c_50]) ).
tcf(c_782,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ intersect(X0,X1)
| ~ member(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_54,c_52]) ).
tcf(c_817,plain,
! [X0: $i] :
( member(sK1(X0,empty_set),X0)
| ( X0 = empty_set ) ),
inference(superposition,[status(thm)],[c_57,c_55]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i] :
( member(sK1(intersection(X0,X1),empty_set),X1)
| ( intersection(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_817,c_51]) ).
tcf(c_858,plain,
! [X0: $i,X1: $i] :
( intersect(X0,X1)
| ( X0 = empty_set )
| ~ member(sK1(X0,empty_set),X1) ),
inference(superposition,[status(thm)],[c_817,c_52]) ).
tcf(c_891,plain,
( member(sK0(sK2,sK3),sK2)
| ~ intersect(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_1105,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X2,X0)
| ~ intersect(intersection(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_750,c_782]) ).
tcf(c_1544,plain,
! [X0: $i,X1: $i] :
( intersect(intersection(X0,X1),X1)
| ( intersection(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_856,c_858]) ).
tcf(c_1612,plain,
! [X0: $i,X1: $i] :
( intersect(X1,X0)
| ( intersection(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_1544,c_1105]) ).
tcf(c_1661,plain,
! [X0: $i,X1: $i] :
( intersect(X0,X1)
| ( intersection(X0,X1) = empty_set ) ),
inference(superposition,[status(thm)],[c_1612,c_61]) ).
tcf(c_1765,plain,
intersect(sK2,sK3),
inference(backward_subsumption_resolution,[status(thm)],[c_275,c_1661]) ).
tcf(c_1766,plain,
intersection(sK2,sK3) = empty_set,
inference(backward_subsumption_resolution,[status(thm)],[c_276,c_1661]) ).
tcf(c_1812,plain,
! [X0: $i] :
( member(X0,empty_set)
| ~ member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_1766,c_49]) ).
tcf(c_1828,plain,
! [X0: $i] :
( ~ member(X0,sK3)
| ~ member(X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1812,c_55]) ).
tcf(c_1839,plain,
! [X0: $i] :
( ~ intersect(X0,sK3)
| ~ member(sK0(X0,sK3),sK2) ),
inference(superposition,[status(thm)],[c_54,c_1828]) ).
tcf(c_1876,plain,
( ~ intersect(sK2,sK3)
| ~ member(sK0(sK2,sK3),sK2) ),
inference(instantiation,[status(thm)],[c_1839]) ).
tcf(c_1877,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1876,c_1765,c_891]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET637+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.39 % Computer : n015.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Thu Sep 24 11:35:02 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.44
% 0.15/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/5.44
% 0.15/5.44 % Detected problem language: tptp
% 0.15/5.45 % Proving...
% 3.32/6.30 % SZS status Started for theBenchmark.p
% 3.32/6.30 % SZS status Theorem for theBenchmark.p
% 3.32/6.30
% 3.32/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.32/6.30
% 3.32/6.30 % ------ iProver source info
% 3.32/6.30
% 3.32/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.32/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.32/6.30 % git: non_committed_changes: false
% 3.32/6.30
% 3.32/6.30 % ------ Parsing...
% 3.32/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.32/6.30
% 3.32/6.30 % ------ 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 %
% 3.32/6.30
% 3.32/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.32/6.30
% 3.32/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.32/6.30 % ------ Proving...
% 3.32/6.30 % ------ Problem Properties
% 3.32/6.30
% 3.32/6.30 %
% 3.32/6.30 % clauses 13
% 3.32/6.30 % conjectures 0
% 3.32/6.30 % EPR 3
% 3.32/6.30 % Horn 12
% 3.32/6.30 % unary 2
% 3.32/6.30 % binary 7
% 3.32/6.30 % lits 28
% 3.32/6.30 % lits eq 5
% 3.32/6.30 % fd_pure 0
% 3.32/6.30 % fd_pseudo 0
% 3.32/6.30 % fd_cond 0
% 3.32/6.30 % fd_pseudo_cond 2
% 3.32/6.30 % AC symbols 0
% 3.32/6.30
% 3.32/6.30 % ------ Schedule dynamic 5 is on
% 3.32/6.30
% 3.32/6.30 % ------ no conjectures: strip conj schedule
% 3.32/6.30
% 3.32/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.32/6.30
% 3.32/6.30
% 3.32/6.30 % ------
% 3.32/6.30 % Current options:
% 3.32/6.30 % ------
% 3.32/6.30
% 3.32/6.30
% 3.32/6.30 %
% 3.32/6.30
% 3.32/6.30 % ------ Proving...
% 3.32/6.30 %
% 3.32/6.30
% 3.32/6.30 % SZS status Theorem for theBenchmark.p
% 3.32/6.30
% 3.32/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.32/6.31
% 3.32/6.31
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