%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET575+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 : n006.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 02:47:25 PM UTC 2026
% Result : Theorem 0.22s 11.36s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 21 ( 3 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 63 ( 28 ~; 21 |; 11 &)
% ( 1 <=>; 2 =>; 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 28 !; 7 ?; 6 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
fof(f3,conjecture,
! [X0,X1] :
( intersect(X0,X1)
=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th15) ).
fof(f4,negated_conjecture,
~ ! [X0,X1] :
( intersect(X0,X1)
=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f6,plain,
? [X0,X1] :
( intersect(X0,X1)
& ! [X2] :
( ~ member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f7,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,[],[f1]) ).
fof(f8,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,[],[f7]) ).
fof(f9,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))],[f8]) ).
fof(f10,plain,
( intersect(sK1,sK2)
& ! [X2] :
( ~ member(X2,sK2)
| ~ member(X2,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f6]) ).
fof(f11,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f15,plain,
intersect(sK1,sK2),
inference(cnf_transformation,[],[f10]) ).
fof(f16,plain,
! [X2] :
( ~ member(X2,sK2)
| ~ member(X2,sK1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( ~ member(X0,sK2)
| ~ member(X0,sK1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_54,negated_conjecture,
intersect(sK1,sK2),
inference(cnf_transformation,[],[f15]) ).
tcf(c_83,negated_conjecture,
! [X0: $i] :
( ~ member(X0,sK2)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_85,plain,
( member(sK0(sK1,sK2),sK1)
| ~ intersect(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_86,plain,
( member(sK0(sK1,sK2),sK2)
| ~ intersect(sK1,sK2) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_92,plain,
( ~ member(sK0(sK1,sK2),sK2)
| ~ member(sK0(sK1,sK2),sK1) ),
inference(instantiation,[status(thm)],[c_83]) ).
tcf(c_93,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_92,c_86,c_85,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET575+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.45 % Computer : n006.cluster.edu
% 0.10/10.45 % Model : x86_64 x86_64
% 0.10/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.45 % Memory : 8046.5625MB
% 0.10/10.45 % OS : Linux 6.8.0-71-generic
% 0.10/10.45 % CPULimit : 300
% 0.10/10.45 % WCLimit : 300
% 0.10/10.45 % DateTime : Thu Sep 24 11:19:41 UTC 2026
% 0.10/10.45 % CPUTime :
% 0.10/10.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/10.49 Running first-order theorem proving
% 0.10/10.49 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
% 0.15/10.50
% 0.15/10.50 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.50
% 0.15/10.51 % Detected problem language: tptp
% 0.15/10.52 % Proving...
% 0.22/11.36 % SZS status Started for theBenchmark.p
% 0.22/11.36 % SZS status Theorem for theBenchmark.p
% 0.22/11.36
% 0.22/11.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.22/11.36
% 0.22/11.36 % ------ iProver source info
% 0.22/11.36
% 0.22/11.36 % git: date: 2026-07-19 20:42:38 +0200
% 0.22/11.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.22/11.36 % git: non_committed_changes: false
% 0.22/11.36
% 0.22/11.36 % ------ Parsing...
% 0.22/11.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.22/11.36
% 0.22/11.36 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.22/11.36
% 0.22/11.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.22/11.36 % ------ Proving...
% 0.22/11.36 % ------ Problem Properties
% 0.22/11.36
% 0.22/11.36 %
% 0.22/11.36 % clauses 6
% 0.22/11.36 % conjectures 2
% 0.22/11.36 % EPR 4
% 0.22/11.36 % Horn 6
% 0.22/11.36 % unary 1
% 0.22/11.36 % binary 4
% 0.22/11.36 % lits 12
% 0.22/11.36 % lits eq 0
% 0.22/11.36 % fd_pure 0
% 0.22/11.36 % fd_pseudo 0
% 0.22/11.36 % fd_cond 0
% 0.22/11.36 % fd_pseudo_cond 0
% 0.22/11.36 % AC symbols 0
% 0.22/11.36
% 0.22/11.36 % ------ Schedule dynamic 5 is on
% 0.22/11.36
% 0.22/11.36 % ------ no equalities: superposition off
% 0.22/11.36
% 0.22/11.36 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.22/11.36
% 0.22/11.36
% 0.22/11.36 % ------
% 0.22/11.36 % Current options:
% 0.22/11.36 % ------
% 0.22/11.36
% 0.22/11.36
% 0.22/11.36 %
% 0.22/11.36
% 0.22/11.36 % ------ Proving...
% 0.22/11.36 %
% 0.22/11.36
% 0.22/11.36 % SZS status Theorem for theBenchmark.p
% 0.22/11.36
% 0.22/11.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.22/11.36
% 0.22/11.36
%------------------------------------------------------------------------------