%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET627+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 : n016.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 0.30s 1.07s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 12 unt; 0 def)
% Number of atoms : 49 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 48 ( 23 ~; 15 |; 7 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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 : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 30 !; 4 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f2,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,axiom,
! [X0,X1] :
( disjoint(X0,X1)
<=> ~ intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',disjoint_defn) ).
fof(f6,conjecture,
! [X0] : disjoint(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th104) ).
fof(f7,negated_conjecture,
~ ! [X0] : disjoint(X0,empty_set),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
=> disjoint(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f9,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f11,plain,
? [X0] : ~ disjoint(X0,empty_set),
inference(ennf_transformation,[],[f7]) ).
fof(f12,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(f13,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,[],[f12]) ).
fof(f14,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))],[f13]) ).
fof(f15,plain,
~ disjoint(sK1,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X0,sK1)],[f11]) ).
fof(f16,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X0,X1] :
( intersect(X0,X1)
| disjoint(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f22,plain,
~ disjoint(sK1,empty_set),
inference(cnf_transformation,[],[f15]) ).
tcf(c_49,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f16]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( disjoint(X0,X1)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,negated_conjecture,
~ disjoint(sK1,empty_set),
inference(cnf_transformation,[],[f22]) ).
tcf(c_85,plain,
intersect(sK1,empty_set),
inference(resolution,[status(thm)],[c_53,c_55]) ).
tcf(c_115,plain,
( member(sK0(sK1,empty_set),empty_set)
| ~ intersect(sK1,empty_set) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_120,plain,
~ member(sK0(sK1,empty_set),empty_set),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_121,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_120,c_115,c_85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET627+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 11:35:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.44 % Proving...
% 0.30/1.07 % SZS status Started for theBenchmark.p
% 0.30/1.07 % SZS status Theorem for theBenchmark.p
% 0.30/1.07
% 0.30/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.30/1.07
% 0.30/1.07 % ------ iProver source info
% 0.30/1.07
% 0.30/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.30/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.30/1.07 % git: non_committed_changes: false
% 0.30/1.07
% 0.30/1.07 % ------ Parsing...
% 0.30/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.30/1.07
% 0.30/1.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.30/1.07
% 0.30/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.30/1.07 % ------ Proving...
% 0.30/1.07 % ------ Problem Properties
% 0.30/1.07
% 0.30/1.07 %
% 0.30/1.07 % clauses 6
% 0.30/1.07 % conjectures 0
% 0.30/1.07 % EPR 4
% 0.30/1.07 % Horn 6
% 0.30/1.07 % unary 2
% 0.30/1.07 % binary 3
% 0.30/1.07 % lits 11
% 0.30/1.07 % lits eq 0
% 0.30/1.07 % fd_pure 0
% 0.30/1.07 % fd_pseudo 0
% 0.30/1.07 % fd_cond 0
% 0.30/1.07 % fd_pseudo_cond 0
% 0.30/1.07 % AC symbols 0
% 0.30/1.07
% 0.30/1.07 % ------ Schedule dynamic 5 is on
% 0.30/1.07
% 0.30/1.07 % ------ no conjectures: strip conj schedule
% 0.30/1.07
% 0.30/1.07 % ------ no equalities: superposition off
% 0.30/1.07
% 0.30/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.30/1.07
% 0.30/1.07
% 0.30/1.07 % ------
% 0.30/1.07 % Current options:
% 0.30/1.07 % ------
% 0.30/1.07
% 0.30/1.07
% 0.30/1.07 %
% 0.30/1.07
% 0.30/1.07 % ------ Proving...
% 0.30/1.07 %
% 0.30/1.07
% 0.30/1.07 % SZS status Theorem for theBenchmark.p
% 0.30/1.07
% 0.30/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.30/1.07
% 0.30/1.07
%------------------------------------------------------------------------------