%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET596+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 : n002.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 02:47:29 PM UTC 2026
% Result : Theorem 2.26s 1.28s
% Output : CNFRefutation 2.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 26 unt; 2 def)
% Number of atoms : 181 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 139 ( 60 ~; 52 |; 19 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 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; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 102 !; 8 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( subset(X0,empty_set)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_of_empty_set_is_empty_set) ).
fof(f2,axiom,
! [X0,X1,X2] :
( subset(X0,X1)
=> subset(intersection(X0,X2),intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_of_subset) ).
fof(f3,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f4,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(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(f7,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( intersection(X1,X2) = empty_set
& subset(X0,X1) )
=> intersection(X0,X2) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th55) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( intersection(X1,X2) = empty_set
& subset(X0,X1) )
=> intersection(X0,X2) = empty_set ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| subset(intersection(X0,X2),intersection(X1,X2)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f16,plain,
? [X0,X1,X2] :
( intersection(X1,X2) = empty_set
& subset(X0,X1)
& empty_set != intersection(X0,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f17,plain,
? [X0,X1,X2] :
( intersection(X1,X2) = empty_set
& subset(X0,X1)
& empty_set != intersection(X0,X2) ),
inference(flattening,[],[f16]) ).
fof(f18,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,[],[f4]) ).
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(flattening,[],[f18]) ).
fof(f20,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(f21,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,[],[f20]) ).
fof(f22,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))],[f21]) ).
fof(f28,plain,
( empty_set = intersection(sK3,sK4)
& subset(sK2,sK3)
& empty_set != intersection(sK2,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f17]) ).
fof(f29,plain,
! [X0] :
( ~ subset(X0,empty_set)
| empty_set = X0 ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ subset(X0,X1)
| subset(intersection(X0,X2),intersection(X1,X2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f31,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f3]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,intersection(X0,X1))
| member(X2,X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| member(X2,intersection(X0,X1)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f35,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ member(X3,X0)
| member(X3,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f36,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f37,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f7]) ).
fof(f47,plain,
empty_set = intersection(sK3,sK4),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
subset(sK2,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f49,plain,
empty_set != intersection(sK2,sK4),
inference(cnf_transformation,[],[f28]) ).
tcf(c_49,plain,
! [X0: $i] :
( ( X0 = empty_set )
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( subset(intersection(X0,X2),intersection(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_51,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_65,negated_conjecture,
intersection(sK2,sK4) != empty_set,
inference(cnf_transformation,[],[f49]) ).
tcf(c_66,negated_conjecture,
subset(sK2,sK3),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,negated_conjecture,
intersection(sK3,sK4) = empty_set,
inference(cnf_transformation,[],[f47]) ).
tcf(c_142,plain,
intersection(sK4,sK3) = empty_set,
inference(demodulation,[status(thm)],[c_67,c_61]) ).
tcf(c_325,definition,
iPr_def_10 = intersection(sK4,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_326,definition,
iPr_def_11 = intersection(sK2,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_327,plain,
iPr_def_10 = empty_set,
inference(demodulation,[status(thm)],[c_142,c_325]) ).
tcf(c_328,negated_conjecture,
subset(sK2,sK3),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_329,negated_conjecture,
iPr_def_11 != empty_set,
inference(demodulation,[status(thm)],[c_65,c_326]) ).
tcf(c_541,plain,
! [X0: $i] : ~ member(X0,iPr_def_10),
inference(light_normalisation,[status(thm)],[c_51,c_327]) ).
tcf(c_542,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ subset(X0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_49,c_327]) ).
tcf(c_559,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_326,c_53]) ).
tcf(c_574,plain,
! [X0: $i] :
( member(X0,sK4)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_326,c_54]) ).
tcf(c_591,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK2) ),
inference(superposition,[status(thm)],[c_56,c_559]) ).
tcf(c_599,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK4) ),
inference(superposition,[status(thm)],[c_56,c_574]) ).
tcf(c_612,plain,
subset(iPr_def_11,sK4),
inference(superposition,[status(thm)],[c_599,c_55]) ).
tcf(c_624,plain,
! [X0: $i] :
( subset(intersection(X0,sK3),iPr_def_10)
| ~ subset(X0,sK4) ),
inference(superposition,[status(thm)],[c_325,c_50]) ).
tcf(c_665,plain,
! [X0: $i] :
( ( intersection(X0,sK3) = iPr_def_10 )
| ~ subset(X0,sK4) ),
inference(superposition,[status(thm)],[c_624,c_542]) ).
tcf(c_678,plain,
intersection(iPr_def_11,sK3) = iPr_def_10,
inference(superposition,[status(thm)],[c_612,c_665]) ).
tcf(c_692,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_328,c_57]) ).
tcf(c_717,plain,
( ( iPr_def_11 = empty_set )
| ~ subset(iPr_def_11,empty_set) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_868,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_11)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_678,c_52]) ).
tcf(c_875,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_11)
| ~ member(X0,sK3) ),
inference(forward_subsumption_resolution,[status(thm)],[c_868,c_541]) ).
tcf(c_891,plain,
! [X0: $i] :
( subset(iPr_def_11,X0)
| member(sK0(iPr_def_11,X0),sK3) ),
inference(superposition,[status(thm)],[c_591,c_692]) ).
tcf(c_924,plain,
subset(iPr_def_11,sK3),
inference(superposition,[status(thm)],[c_891,c_55]) ).
tcf(c_1023,plain,
! [X0: $i] :
( member(X0,sK3)
| ~ member(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_924,c_57]) ).
tcf(c_1125,plain,
! [X0: $i] : ~ member(X0,iPr_def_11),
inference(global_subsumption_just,[status(thm)],[c_1023,c_875,c_1023]) ).
tcf(c_1128,plain,
! [X0: $i] : subset(iPr_def_11,X0),
inference(superposition,[status(thm)],[c_56,c_1125]) ).
tcf(c_1141,plain,
subset(iPr_def_11,empty_set),
inference(instantiation,[status(thm)],[c_1128]) ).
tcf(c_1142,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1141,c_717,c_329]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET596+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n002.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 11:26:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.41
% 0.10/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.41
% 0.10/0.41 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 2.26/1.28 % SZS status Started for theBenchmark.p
% 2.26/1.28 % SZS status Theorem for theBenchmark.p
% 2.26/1.28
% 2.26/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.26/1.28
% 2.26/1.28 % ------ iProver source info
% 2.26/1.28
% 2.26/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.26/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.26/1.28 % git: non_committed_changes: false
% 2.26/1.28
% 2.26/1.28 % ------ Parsing...
% 2.26/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.26/1.28
% 2.26/1.28 % ------ Preprocessing... sup_sim: 1 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 %
% 2.26/1.28
% 2.26/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.26/1.28
% 2.26/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.26/1.28 % ------ Proving...
% 2.26/1.28 % ------ Problem Properties
% 2.26/1.28
% 2.26/1.28 %
% 2.26/1.28 % clauses 19
% 2.26/1.28 % conjectures 2
% 2.26/1.28 % EPR 8
% 2.26/1.28 % Horn 17
% 2.26/1.28 % unary 8
% 2.26/1.28 % binary 6
% 2.26/1.28 % lits 35
% 2.26/1.28 % lits eq 9
% 2.26/1.28 % fd_pure 0
% 2.26/1.28 % fd_pseudo 0
% 2.26/1.28 % fd_cond 1
% 2.26/1.28 % fd_pseudo_cond 3
% 2.26/1.28 % AC symbols 0
% 2.26/1.28
% 2.26/1.28 % ------ Schedule dynamic 5 is on
% 2.26/1.28
% 2.26/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.26/1.28
% 2.26/1.28
% 2.26/1.28 % ------
% 2.26/1.28 % Current options:
% 2.26/1.28 % ------
% 2.26/1.28
% 2.26/1.28
% 2.26/1.28 %
% 2.26/1.28
% 2.26/1.28 % ------ Proving...
% 2.26/1.28 %
% 2.26/1.28
% 2.26/1.28 % SZS status Theorem for theBenchmark.p
% 2.26/1.28
% 2.26/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.26/1.28
% 2.26/1.28
%------------------------------------------------------------------------------