%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET638+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 : n026.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 02:47:39 PM UTC 2026
% Result : Theorem 3.30s 6.30s
% Output : CNFRefutation 3.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 46 unt; 2 def)
% Number of atoms : 115 ( 38 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 59 ( 24 ~; 15 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 79 !; 8 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : subset(intersection(X0,X1),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).
fof(f2,axiom,
! [X0,X1] :
( subset(X0,X1)
=> intersection(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).
fof(f3,axiom,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
fof(f4,axiom,
! [X0,X1,X2] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_distributes_over_union) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f10,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f15,conjecture,
! [X0,X1,X2] :
( ( intersection(X0,X2) = empty_set
& subset(X0,union(X1,X2)) )
=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th120) ).
fof(f16,negated_conjecture,
~ ! [X0,X1,X2] :
( ( intersection(X0,X2) = empty_set
& subset(X0,union(X1,X2)) )
=> subset(X0,X1) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(ennf_transformation,[],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f19,plain,
? [X0,X1,X2] :
( intersection(X0,X2) = empty_set
& subset(X0,union(X1,X2))
& ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f20,plain,
? [X0,X1,X2] :
( intersection(X0,X2) = empty_set
& subset(X0,union(X1,X2))
& ~ subset(X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f25,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,[],[f18]) ).
fof(f26,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,[],[f25]) ).
fof(f27,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))],[f26]) ).
fof(f33,plain,
( empty_set = intersection(sK2,sK4)
& subset(sK2,union(sK3,sK4))
& ~ subset(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f20]) ).
fof(f34,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[],[f1]) ).
fof(f35,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| intersection(X0,X1) = X0 ),
inference(cnf_transformation,[],[f17]) ).
fof(f36,plain,
! [X0] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f37,plain,
! [X2,X0,X1] : intersection(X0,union(X1,X2)) = union(intersection(X0,X1),intersection(X0,X2)),
inference(cnf_transformation,[],[f4]) ).
fof(f41,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f51,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f10]) ).
fof(f52,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f58,plain,
empty_set = intersection(sK2,sK4),
inference(cnf_transformation,[],[f33]) ).
fof(f59,plain,
subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f33]) ).
fof(f60,plain,
~ subset(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( intersection(X0,X1) = X0 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_51,plain,
! [X0: $i] : union(X0,empty_set) = X0,
inference(cnf_transformation,[],[f36]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] : union(intersection(X0,X1),intersection(X0,X2)) = intersection(X0,union(X1,X2)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f41]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f52]) ).
tcf(c_71,negated_conjecture,
~ subset(sK2,sK3),
inference(cnf_transformation,[],[f60]) ).
tcf(c_72,negated_conjecture,
subset(sK2,union(sK3,sK4)),
inference(cnf_transformation,[],[f59]) ).
tcf(c_73,negated_conjecture,
intersection(sK2,sK4) = empty_set,
inference(cnf_transformation,[],[f58]) ).
tcf(c_393,definition,
iPr_def_10 = intersection(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_394,definition,
iPr_def_11 = union(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_395,negated_conjecture,
iPr_def_10 = empty_set,
inference(demodulation,[status(thm)],[c_73,c_393]) ).
tcf(c_396,negated_conjecture,
subset(sK2,iPr_def_11),
inference(demodulation,[status(thm)],[c_72,c_394]) ).
tcf(c_397,negated_conjecture,
~ subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_657,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_56,c_395]) ).
tcf(c_658,plain,
! [X0: $i] : union(X0,iPr_def_10) = X0,
inference(light_normalisation,[status(thm)],[c_51,c_395]) ).
tcf(c_662,plain,
! [X0: $i] : subset(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_61,c_657]) ).
tcf(c_664,plain,
! [X0: $i] : union(iPr_def_10,X0) = X0,
inference(superposition,[status(thm)],[c_658,c_66]) ).
tcf(c_669,plain,
! [X0: $i,X1: $i] : subset(intersection(X0,X1),X1),
inference(superposition,[status(thm)],[c_67,c_49]) ).
tcf(c_766,plain,
intersection(sK2,iPr_def_11) = sK2,
inference(superposition,[status(thm)],[c_396,c_50]) ).
tcf(c_767,plain,
! [X0: $i] : intersection(iPr_def_10,X0) = iPr_def_10,
inference(superposition,[status(thm)],[c_662,c_50]) ).
tcf(c_844,plain,
intersection(iPr_def_11,sK2) = sK2,
inference(demodulation,[status(thm)],[c_766,c_67]) ).
tcf(c_856,plain,
! [X0: $i] : intersection(X0,iPr_def_10) = iPr_def_10,
inference(superposition,[status(thm)],[c_767,c_67]) ).
tcf(c_963,plain,
! [X0: $i] : intersection(sK2,union(sK4,X0)) = union(iPr_def_10,intersection(sK2,X0)),
inference(superposition,[status(thm)],[c_393,c_52]) ).
tcf(c_967,plain,
! [X0: $i,X1: $i] : intersection(X0,union(iPr_def_10,X1)) = union(iPr_def_10,intersection(X0,X1)),
inference(superposition,[status(thm)],[c_856,c_52]) ).
tcf(c_2617,plain,
! [X0: $i] : intersection(sK2,union(sK4,X0)) = intersection(sK2,X0),
inference(demodulation,[status(thm)],[c_963,c_664,c_967]) ).
tcf(c_2618,plain,
! [X0: $i] : intersection(sK2,union(X0,sK4)) = intersection(sK2,X0),
inference(superposition,[status(thm)],[c_66,c_2617]) ).
tcf(c_4439,plain,
intersection(sK2,sK3) = intersection(sK2,iPr_def_11),
inference(superposition,[status(thm)],[c_394,c_2618]) ).
tcf(c_4532,plain,
intersection(sK2,sK3) = sK2,
inference(demodulation,[status(thm)],[c_4439,c_67,c_844]) ).
tcf(c_4543,plain,
subset(sK2,sK3),
inference(superposition,[status(thm)],[c_4532,c_669]) ).
tcf(c_4562,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4543,c_397]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET638+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n026.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Thu Sep 24 11:35:00 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/5.42 Running first-order theorem proving
% 0.16/5.42 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 3.30/6.30 % SZS status Started for theBenchmark.p
% 3.30/6.30 % SZS status Theorem for theBenchmark.p
% 3.30/6.30
% 3.30/6.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.30/6.30
% 3.30/6.30 % ------ iProver source info
% 3.30/6.30
% 3.30/6.30 % git: date: 2026-07-19 20:42:38 +0200
% 3.30/6.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.30/6.30 % git: non_committed_changes: false
% 3.30/6.30
% 3.30/6.30 % ------ Parsing...
% 3.30/6.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.30/6.30
% 3.30/6.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.30/6.30
% 3.30/6.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.30/6.30
% 3.30/6.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.30/6.30 % ------ Proving...
% 3.30/6.30 % ------ Problem Properties
% 3.30/6.30
% 3.30/6.30 %
% 3.30/6.30 % clauses 25
% 3.30/6.30 % conjectures 3
% 3.30/6.30 % EPR 7
% 3.30/6.30 % Horn 22
% 3.30/6.30 % unary 12
% 3.30/6.30 % binary 7
% 3.30/6.30 % lits 44
% 3.30/6.30 % lits eq 11
% 3.30/6.30 % fd_pure 0
% 3.30/6.30 % fd_pseudo 0
% 3.30/6.30 % fd_cond 0
% 3.30/6.30 % fd_pseudo_cond 3
% 3.30/6.30 % AC symbols 0
% 3.30/6.30
% 3.30/6.30 % ------ Schedule dynamic 5 is on
% 3.30/6.30
% 3.30/6.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.30/6.30
% 3.30/6.30
% 3.30/6.30 % ------
% 3.30/6.30 % Current options:
% 3.30/6.30 % ------
% 3.30/6.30
% 3.30/6.30
% 3.30/6.30 %
% 3.30/6.30
% 3.30/6.30 % ------ Proving...
% 3.30/6.30 %
% 3.30/6.30
% 3.30/6.30 % SZS status Theorem for theBenchmark.p
% 3.30/6.30
% 3.30/6.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.30/6.30
% 3.30/6.30
%------------------------------------------------------------------------------