%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET585+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 : n003.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 02:47:27 PM UTC 2026
% Result : Theorem 2.05s 1.28s
% Output : CNFRefutation 2.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 11 unt; 2 def)
% Number of atoms : 102 ( 2 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 91 ( 36 ~; 35 |; 15 &)
% ( 4 <=>; 1 =>; 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 : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 68 ( 0 sgn 63 !; 5 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(f5,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(f6,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f11,conjecture,
! [X0,X1,X2] : subset(intersection(X0,X1),union(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_subset_of_union) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] : subset(intersection(X0,X1),union(X0,X2)),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f16,plain,
? [X0,X1,X2] : ~ subset(intersection(X0,X1),union(X0,X2)),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) )
& ( ( ~ member(X2,X1)
& ~ member(X2,X0) )
| member(X2,union(X0,X1)) ) ),
inference(flattening,[],[f17]) ).
fof(f19,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,[],[f5]) ).
fof(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ member(X3,X0)
| member(X3,X1) ) )
& ( ( member(sK0(X0,X1),X0)
& ~ member(sK0(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f22]) ).
fof(f27,plain,
~ subset(intersection(sK2,sK3),union(sK2,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f16]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f39,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
~ subset(intersection(sK2,sK3),union(sK2,sK4)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_66,negated_conjecture,
~ subset(intersection(sK2,sK3),union(sK2,sK4)),
inference(cnf_transformation,[],[f47]) ).
tcf(c_215,definition,
iPr_def_10 = intersection(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_216,definition,
iPr_def_11 = union(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_217,negated_conjecture,
~ subset(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_66,c_216,c_215]) ).
tcf(c_467,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_216,c_52]) ).
tcf(c_517,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_215,c_56]) ).
tcf(c_527,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK2) ),
inference(superposition,[status(thm)],[c_59,c_517]) ).
tcf(c_534,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),iPr_def_11) ),
inference(superposition,[status(thm)],[c_527,c_467]) ).
tcf(c_596,plain,
subset(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_534,c_58]) ).
tcf(c_597,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_596,c_217]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET585+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.37 % Computer : n003.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Thu Sep 24 11:23:09 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 0.13/0.42
% 0.13/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.42
% 0.13/0.42 % Detected problem language: tptp
% 0.13/0.43 % Proving...
% 2.05/1.28 % SZS status Started for theBenchmark.p
% 2.05/1.28 % SZS status Theorem for theBenchmark.p
% 2.05/1.28
% 2.05/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.05/1.28
% 2.05/1.28 % ------ iProver source info
% 2.05/1.28
% 2.05/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.05/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.05/1.28 % git: non_committed_changes: false
% 2.05/1.28
% 2.05/1.28 % ------ Parsing...
% 2.05/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.05/1.28
% 2.05/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.05/1.28 % ------ Proving...
% 2.05/1.28 % ------ Problem Properties
% 2.05/1.28
% 2.05/1.28 %
% 2.05/1.28 % clauses 20
% 2.05/1.28 % conjectures 1
% 2.05/1.28 % EPR 4
% 2.05/1.28 % Horn 17
% 2.05/1.28 % unary 8
% 2.05/1.28 % binary 6
% 2.05/1.28 % lits 38
% 2.05/1.28 % lits eq 6
% 2.05/1.28 % fd_pure 0
% 2.05/1.28 % fd_pseudo 0
% 2.05/1.28 % fd_cond 0
% 2.05/1.28 % fd_pseudo_cond 2
% 2.05/1.28 % AC symbols 0
% 2.05/1.28
% 2.05/1.28 % ------ Schedule dynamic 5 is on
% 2.05/1.28
% 2.05/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 % ------
% 2.05/1.28 % Current options:
% 2.05/1.28 % ------
% 2.05/1.28
% 2.05/1.28
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % ------ Proving...
% 2.05/1.28 %
% 2.05/1.28
% 2.05/1.28 % SZS status Theorem for theBenchmark.p
% 2.05/1.28
% 2.05/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.05/1.28
% 2.05/1.28
%------------------------------------------------------------------------------