%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET606+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 : n005.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 02:47:32 PM UTC 2026
% Result : Theorem 0.90s 1.29s
% Output : CNFRefutation 4.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 78 ( 18 unt; 3 def)
% Number of atoms : 283 ( 31 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 210 ( 84 ~; 94 |; 23 &)
% ( 6 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 5 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 : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 132 ( 0 sgn 126 !; 6 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
<=> member(X2,X1) )
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
fof(f2,axiom,
! [X0,X1,X2] :
( member(X2,intersection(X0,X1))
<=> ( member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(f3,axiom,
! [X0,X1,X2] :
( member(X2,difference(X0,X1))
<=> ( ~ member(X2,X1)
& member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f7,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f9,conjecture,
! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_into_intersection) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] : difference(X0,intersection(X0,X1)) = difference(X0,X1),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
<~> member(X2,X1) )
| X0 = X1 ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
? [X0,X1] : difference(X0,X1) != difference(X0,intersection(X0,X1)),
inference(ennf_transformation,[],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ),
inference(nnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( ( ( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1) )
& ( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1) ) )
| X0 = X1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f14]) ).
fof(f16,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,[],[f2]) ).
fof(f17,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,[],[f16]) ).
fof(f18,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,[],[f3]) ).
fof(f19,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,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f20]) ).
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,[],[f12]) ).
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(sK2(X0,X1),X0)
& ~ member(sK2(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f26]) ).
fof(f28,plain,
difference(sK3,sK4) != difference(sK3,intersection(sK3,sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f13]) ).
fof(f29,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f30,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X0)
| ~ member(sK0(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| ~ member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X2,X0,X1] :
( ~ member(X2,difference(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| member(X2,difference(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f46,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f47,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
difference(sK3,sK4) != difference(sK3,intersection(sK3,sK4)),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(sK0(X0,X1),X1)
| ~ member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( member(sK0(X0,X1),X1)
| member(sK0(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,difference(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_67,negated_conjecture,
difference(sK3,intersection(sK3,sK4)) != difference(sK3,sK4),
inference(cnf_transformation,[],[f49]) ).
tcf(c_387,definition,
iPr_def_10 = intersection(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_388,definition,
iPr_def_11 = difference(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_389,definition,
iPr_def_12 = difference(sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_390,negated_conjecture,
iPr_def_11 != iPr_def_12,
inference(demodulation,[status(thm)],[c_67,c_389,c_387,c_388]) ).
tcf(c_650,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_387,c_51]) ).
tcf(c_667,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_387,c_53]) ).
tcf(c_677,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(difference(X0,X1),X2)
| member(sK2(difference(X0,X1),X2),X0) ),
inference(superposition,[status(thm)],[c_64,c_55]) ).
tcf(c_678,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_389,c_55]) ).
tcf(c_679,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_388,c_55]) ).
tcf(c_704,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,sK4) ),
inference(superposition,[status(thm)],[c_389,c_56]) ).
tcf(c_705,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_388,c_56]) ).
tcf(c_727,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK2(iPr_def_10,X0),sK4) ),
inference(superposition,[status(thm)],[c_64,c_667]) ).
tcf(c_773,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| ~ member(sK2(iPr_def_10,X0),iPr_def_12) ),
inference(superposition,[status(thm)],[c_727,c_704]) ).
tcf(c_788,plain,
! [X0: $i] :
( member(X0,iPr_def_12)
| member(X0,sK4)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_389,c_54]) ).
tcf(c_789,plain,
! [X0: $i] :
( member(X0,iPr_def_11)
| member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_388,c_54]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(X0,difference(X1,X2))
| member(sK2(X0,difference(X1,X2)),X2)
| ~ member(sK2(X0,difference(X1,X2)),X1) ),
inference(superposition,[status(thm)],[c_54,c_63]) ).
tcf(c_806,plain,
( ( iPr_def_11 = iPr_def_12 )
| ~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_12)
| ~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_11) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_839,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_12)
| member(sK0(iPr_def_11,iPr_def_12),iPr_def_11)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_889,plain,
! [X0: $i] :
( member(sK0(X0,iPr_def_12),sK3)
| member(sK0(X0,iPr_def_12),X0)
| ( X0 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_50,c_678]) ).
tcf(c_1750,plain,
! [X0: $i,X1: $i] : subset(difference(X0,X1),X0),
inference(superposition,[status(thm)],[c_677,c_63]) ).
tcf(c_1852,plain,
! [X0: $i,X1: $i] :
( ( difference(X0,X1) = X0 )
| ~ subset(X0,difference(X0,X1)) ),
inference(superposition,[status(thm)],[c_1750,c_57]) ).
tcf(c_3285,plain,
! [X0: $i,X1: $i] :
( subset(X0,difference(X0,X1))
| member(sK2(X0,difference(X0,X1)),X1) ),
inference(superposition,[status(thm)],[c_64,c_792]) ).
tcf(c_4611,plain,
subset(iPr_def_10,difference(iPr_def_10,iPr_def_12)),
inference(superposition,[status(thm)],[c_3285,c_773]) ).
tcf(c_4733,plain,
difference(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_4611,c_1852]) ).
tcf(c_4785,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_12)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_4733,c_56]) ).
tcf(c_6897,plain,
( member(sK0(iPr_def_11,iPr_def_12),sK3)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_889,c_679]) ).
tcf(c_6902,plain,
member(sK0(iPr_def_11,iPr_def_12),sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_6897,c_390]) ).
tcf(c_7008,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_10)
| ~ member(sK0(iPr_def_11,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_6902,c_650]) ).
tcf(c_7009,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_11)
| member(sK0(iPr_def_11,iPr_def_12),iPr_def_10) ),
inference(superposition,[status(thm)],[c_6902,c_789]) ).
tcf(c_7010,plain,
( member(sK0(iPr_def_11,iPr_def_12),iPr_def_12)
| member(sK0(iPr_def_11,iPr_def_12),sK4) ),
inference(superposition,[status(thm)],[c_6902,c_788]) ).
tcf(c_7177,plain,
member(sK0(iPr_def_11,iPr_def_12),iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_7009,c_390,c_806,c_7010,c_7009,c_7008]) ).
tcf(c_7180,plain,
~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_12),
inference(superposition,[status(thm)],[c_7177,c_4785]) ).
tcf(c_7181,plain,
~ member(sK0(iPr_def_11,iPr_def_12),iPr_def_11),
inference(superposition,[status(thm)],[c_7177,c_705]) ).
tcf(c_7186,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7180,c_7181,c_839,c_390]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET606+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n005.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 11:25:32 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 0.90/1.29 % SZS status Started for theBenchmark.p
% 0.90/1.29 % SZS status Theorem for theBenchmark.p
% 0.90/1.29
% 0.90/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.90/1.29
% 0.90/1.29 % ------ iProver source info
% 0.90/1.29
% 0.90/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.90/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.90/1.29 % git: non_committed_changes: false
% 0.90/1.29
% 0.90/1.29 % ------ Parsing...
% 0.90/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.90/1.29
% 0.90/1.29 % ------ 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 %
% 0.90/1.29
% 0.90/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.90/1.29
% 0.90/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.90/1.29 % ------ Proving...
% 0.90/1.29 % ------ Problem Properties
% 0.90/1.29
% 0.90/1.29 %
% 0.90/1.29 % clauses 20
% 0.90/1.29 % conjectures 1
% 0.90/1.29 % EPR 4
% 0.90/1.29 % Horn 16
% 0.90/1.29 % unary 6
% 0.90/1.29 % binary 6
% 0.90/1.29 % lits 42
% 0.90/1.30 % lits eq 10
% 0.90/1.30 % fd_pure 0
% 0.90/1.30 % fd_pseudo 0
% 0.90/1.30 % fd_cond 0
% 0.90/1.30 % fd_pseudo_cond 5
% 0.90/1.30 % AC symbols 0
% 0.90/1.30
% 0.90/1.30 % ------ Schedule dynamic 5 is on
% 0.90/1.30
% 0.90/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 % ------
% 0.90/1.30 % Current options:
% 0.90/1.30 % ------
% 0.90/1.30
% 0.90/1.30
% 0.90/1.30 %
% 0.90/1.30
% 0.90/1.30 % ------ Proving...
% 0.90/1.30 %
% 0.90/1.30
% 0.90/1.30 % SZS status Theorem for theBenchmark.p
% 0.90/1.30
% 0.90/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.56/1.30
% 4.56/1.30
%------------------------------------------------------------------------------