%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET631+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 : n011.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 02:47:38 PM UTC 2026
% Result : Theorem 2.13s 1.17s
% Output : CNFRefutation 2.13s
% 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 : 86 ( 37 ~; 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,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_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(f4,conjecture,
! [X0,X1,X2] :
( intersect(X0,difference(X1,X2))
=> intersect(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th113) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( intersect(X0,difference(X1,X2))
=> intersect(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f7,plain,
? [X0,X1,X2] :
( intersect(X0,difference(X1,X2))
& ~ intersect(X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f8,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,[],[f1]) ).
fof(f9,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,[],[f8]) ).
fof(f10,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(f11,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,[],[f10]) ).
fof(f12,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))],[f11]) ).
fof(f13,plain,
( intersect(sK1,difference(sK2,sK3))
& ~ intersect(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f7]) ).
fof(f15,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
intersect(sK1,difference(sK2,sK3)),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
~ intersect(sK1,sK2),
inference(cnf_transformation,[],[f13]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( intersect(X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_56,negated_conjecture,
~ intersect(sK1,sK2),
inference(cnf_transformation,[],[f22]) ).
tcf(c_57,negated_conjecture,
intersect(sK1,difference(sK2,sK3)),
inference(cnf_transformation,[],[f21]) ).
tcf(c_98,definition,
iPr_def_10 = difference(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_99,negated_conjecture,
intersect(sK1,iPr_def_10),
inference(demodulation,[status(thm)],[c_57,c_98]) ).
tcf(c_256,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_98,c_50]) ).
tcf(c_293,plain,
! [X0: $i] :
( member(sK0(X0,iPr_def_10),sK2)
| ~ intersect(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_54,c_256]) ).
tcf(c_324,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_514,plain,
! [X0: $i] :
( intersect(X0,sK2)
| ~ intersect(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_293,c_324]) ).
tcf(c_529,plain,
( intersect(sK1,sK2)
| ~ intersect(sK1,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_514]) ).
tcf(c_530,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_529,c_99,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET631+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 11:31:13 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.42
% 0.08/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.42
% 0.08/0.42 % Detected problem language: tptp
% 0.08/0.43 % Proving...
% 2.13/1.17 % SZS status Started for theBenchmark.p
% 2.13/1.17 % SZS status Theorem for theBenchmark.p
% 2.13/1.17
% 2.13/1.17 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.13/1.17
% 2.13/1.17 % ------ iProver source info
% 2.13/1.17
% 2.13/1.17 % git: date: 2026-07-19 20:42:38 +0200
% 2.13/1.17 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.13/1.17 % git: non_committed_changes: false
% 2.13/1.17
% 2.13/1.17 % ------ Parsing...
% 2.13/1.17 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.13/1.17
% 2.13/1.17 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 2.13/1.17
% 2.13/1.17 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.13/1.17
% 2.13/1.17 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.13/1.17 % ------ Proving...
% 2.13/1.17 % ------ Problem Properties
% 2.13/1.17
% 2.13/1.17 %
% 2.13/1.17 % clauses 10
% 2.13/1.17 % conjectures 2
% 2.13/1.17 % EPR 4
% 2.13/1.17 % Horn 9
% 2.13/1.17 % unary 3
% 2.13/1.17 % binary 5
% 2.13/1.17 % lits 19
% 2.13/1.17 % lits eq 1
% 2.13/1.17 % fd_pure 0
% 2.13/1.17 % fd_pseudo 0
% 2.13/1.17 % fd_cond 0
% 2.13/1.17 % fd_pseudo_cond 0
% 2.13/1.17 % AC symbols 0
% 2.13/1.17
% 2.13/1.17 % ------ Schedule dynamic 5 is on
% 2.13/1.17
% 2.13/1.17 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.13/1.17
% 2.13/1.17
% 2.13/1.17 % ------
% 2.13/1.17 % Current options:
% 2.13/1.17 % ------
% 2.13/1.17
% 2.13/1.17
% 2.13/1.17 %
% 2.13/1.17
% 2.13/1.17 % ------ Proving...
% 2.13/1.17 %
% 2.13/1.17
% 2.13/1.17 % SZS status Theorem for theBenchmark.p
% 2.13/1.17
% 2.13/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.13/1.17
% 2.13/1.17
%------------------------------------------------------------------------------