%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET626+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 : 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 02:47:37 PM UTC 2026
% Result : Theorem 1.01s 1.38s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 7 unt; 1 def)
% Number of atoms : 87 ( 1 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 85 ( 36 ~; 31 |; 14 &)
% ( 2 <=>; 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 52 !; 6 ?; 16 :)
% 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] :
( intersect(X0,X1)
<=> ? [X2] :
( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersect_defn) ).
fof(f6,conjecture,
! [X0,X1,X2] :
( intersect(X0,intersection(X1,X2))
=> intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th102) ).
fof(f7,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,intersection(X1,X2))
=> intersect(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f9,plain,
? [X0,X1,X2] :
( intersect(X0,intersection(X1,X2))
& ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f10,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(f11,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,[],[f10]) ).
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(f18,plain,
( intersect(sK2,intersection(sK3,sK4))
& ~ intersect(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f9]) ).
fof(f20,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
intersect(sK2,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
~ intersect(sK2,sK3),
inference(cnf_transformation,[],[f18]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_59,negated_conjecture,
~ intersect(sK2,sK3),
inference(cnf_transformation,[],[f32]) ).
tcf(c_60,negated_conjecture,
intersect(sK2,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f31]) ).
tcf(c_166,definition,
iPr_def_10 = intersection(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_167,negated_conjecture,
intersect(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_60,c_166]) ).
tcf(c_353,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_166,c_50]) ).
tcf(c_410,plain,
! [X0: $i] :
( member(sK0(X0,iPr_def_10),sK3)
| ~ intersect(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_54,c_353]) ).
tcf(c_426,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X0,X2)
| ~ intersect(X0,X1)
| ~ member(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_53,c_52]) ).
tcf(c_737,plain,
! [X0: $i] :
( intersect(X0,sK3)
| ~ intersect(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_410,c_426]) ).
tcf(c_764,plain,
( intersect(sK2,sK3)
| ~ intersect(sK2,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_737]) ).
tcf(c_765,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_764,c_167,c_59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET626+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.42 % Computer : n015.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Thu Sep 24 11:33:10 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.48 Running first-order theorem proving
% 0.16/0.48 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
% 0.16/0.49
% 0.16/0.49 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.49
% 0.16/0.49 % Detected problem language: tptp
% 0.16/0.51 % Proving...
% 1.01/1.38 % SZS status Started for theBenchmark.p
% 1.01/1.38 % SZS status Theorem for theBenchmark.p
% 1.01/1.38
% 1.01/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.01/1.38
% 1.01/1.38 % ------ iProver source info
% 1.01/1.38
% 1.01/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 1.01/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.01/1.38 % git: non_committed_changes: false
% 1.01/1.38
% 1.01/1.38 % ------ Parsing...
% 1.01/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.01/1.38
% 1.01/1.38 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.01/1.38
% 1.01/1.38 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.01/1.38
% 1.01/1.38 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.01/1.38 % ------ Proving...
% 1.01/1.38 % ------ Problem Properties
% 1.01/1.38
% 1.01/1.38 %
% 1.01/1.38 % clauses 13
% 1.01/1.38 % conjectures 2
% 1.01/1.38 % EPR 4
% 1.01/1.38 % Horn 12
% 1.01/1.38 % unary 4
% 1.01/1.38 % binary 5
% 1.01/1.38 % lits 26
% 1.01/1.38 % lits eq 4
% 1.01/1.38 % fd_pure 0
% 1.01/1.38 % fd_pseudo 0
% 1.01/1.38 % fd_cond 0
% 1.01/1.38 % fd_pseudo_cond 2
% 1.01/1.38 % AC symbols 0
% 1.01/1.38
% 1.01/1.38 % ------ Schedule dynamic 5 is on
% 1.01/1.38
% 1.01/1.38 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.01/1.38
% 1.01/1.38
% 1.01/1.38 % ------
% 1.01/1.38 % Current options:
% 1.01/1.38 % ------
% 1.01/1.38
% 1.01/1.38
% 1.01/1.38 %
% 1.01/1.38
% 1.01/1.38 % ------ Proving...
% 1.01/1.38 %
% 1.01/1.38
% 1.01/1.38 % SZS status Theorem for theBenchmark.p
% 1.01/1.38
% 1.01/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.01/1.38
% 1.01/1.38
%------------------------------------------------------------------------------