%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET600+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 : n019.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 02:47:30 PM UTC 2026
% Result : Theorem 2.55s 1.30s
% Output : CNFRefutation 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 75 ( 14 unt; 1 def)
% Number of atoms : 266 ( 88 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 233 ( 87 ~; 103 |; 33 &)
% ( 8 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 94 !; 10 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( member(X2,union(X0,X1))
<=> ( member(X2,X1)
| member(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(f5,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(f8,axiom,
! [X0,X1] :
( X0 = X1
<=> ! [X2] :
( member(X2,X0)
<=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(f9,conjecture,
! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( X1 = empty_set
& X0 = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th59) ).
fof(f10,negated_conjecture,
~ ! [X0,X1] :
( union(X0,X1) = empty_set
<=> ( X1 = empty_set
& X0 = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0,X1] :
( union(X0,X1) = empty_set
<~> ( X1 = empty_set
& X0 = empty_set ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f13,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,[],[f1]) ).
fof(f14,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,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1] :
( ( X0 != X1
| ( subset(X1,X0)
& subset(X0,X1) ) )
& ( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ) ),
inference(flattening,[],[f15]) ).
fof(f17,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,[],[f11]) ).
fof(f18,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,[],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X2] :
( ( ~ member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X1)
| member(X2,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ? [X2] :
( ( member(X2,X0)
| member(X2,X1) )
& ( ~ member(X2,X0)
| ~ member(X2,X1) ) )
| X0 = X1 ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( X0 != X1
| ! [X3] :
( ( ~ member(X3,X0)
| member(X3,X1) )
& ( ~ member(X3,X1)
| member(X3,X0) ) ) )
& ( ( ( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) )
& ( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1) ) )
| X0 = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f21]) ).
fof(f23,plain,
? [X0,X1] :
( ( union(X0,X1) = empty_set
| ( X1 = empty_set
& X0 = empty_set ) )
& ( union(X0,X1) != empty_set
| empty_set != X1
| empty_set != X0 ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f24,plain,
? [X0,X1] :
( ( union(X0,X1) = empty_set
| ( X1 = empty_set
& X0 = empty_set ) )
& ( union(X0,X1) != empty_set
| empty_set != X1
| empty_set != X0 ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( ( empty_set = union(sK2,sK3)
| ( empty_set = sK3
& empty_set = sK2 ) )
& ( empty_set != union(sK2,sK3)
| empty_set != sK3
| empty_set != sK2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f24]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X2,X0)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f32,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f35,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f36,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
! [X0,X1] :
( member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
( empty_set = union(sK2,sK3)
| empty_set = sK3 ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
( empty_set = union(sK2,sK3)
| empty_set = sK2 ),
inference(cnf_transformation,[],[f25]) ).
fof(f44,plain,
( empty_set != union(sK2,sK3)
| empty_set != sK3
| empty_set != sK2 ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| member(sK1(X0,X1),X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_63,negated_conjecture,
( ( empty_set != sK3 )
| ( empty_set != sK2 )
| ( union(sK2,sK3) != empty_set ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_64,negated_conjecture,
( ( empty_set = sK2 )
| ( union(sK2,sK3) = empty_set ) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_65,negated_conjecture,
( ( empty_set = sK3 )
| ( union(sK2,sK3) = empty_set ) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_331,definition,
iPr_def_10 = union(sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_332,negated_conjecture,
( ( iPr_def_10 = empty_set )
| ( empty_set = sK3 ) ),
inference(demodulation,[status(thm)],[c_65,c_331]) ).
tcf(c_333,negated_conjecture,
( ( iPr_def_10 = empty_set )
| ( empty_set = sK2 ) ),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_334,negated_conjecture,
( ( iPr_def_10 != empty_set )
| ( empty_set != sK3 )
| ( empty_set != sK2 ) ),
inference(demodulation,[status(thm)],[c_63]) ).
tcf(c_537,plain,
( ( empty_set = iPr_def_10 )
| ( union(empty_set,sK3) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_333,c_331]) ).
tcf(c_547,plain,
( ( empty_set = iPr_def_10 )
| ( union(empty_set,empty_set) = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_332,c_537]) ).
tcf(c_566,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_58,c_52]) ).
tcf(c_573,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_331,c_49]) ).
tcf(c_586,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK3) ),
inference(superposition,[status(thm)],[c_331,c_50]) ).
tcf(c_603,plain,
! [X0: $i] :
( subset(sK2,X0)
| member(sK0(sK2,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_58,c_573]) ).
tcf(c_612,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK0(sK3,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_58,c_586]) ).
tcf(c_640,plain,
! [X0: $i] :
( subset(sK3,X0)
| member(sK0(empty_set,X0),iPr_def_10)
| ( empty_set = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_332,c_612]) ).
tcf(c_658,plain,
subset(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_603,c_57]) ).
tcf(c_659,plain,
subset(sK3,iPr_def_10),
inference(superposition,[status(thm)],[c_612,c_57]) ).
tcf(c_681,plain,
! [X0: $i] :
( member(X0,empty_set)
| ( empty_set = iPr_def_10 )
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_547,c_51]) ).
tcf(c_687,plain,
! [X0: $i] :
( ( empty_set = iPr_def_10 )
| ~ member(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_681,c_52]) ).
tcf(c_753,plain,
( ( sK2 = iPr_def_10 )
| ~ subset(iPr_def_10,sK2) ),
inference(superposition,[status(thm)],[c_658,c_53]) ).
tcf(c_754,plain,
( ( sK3 = iPr_def_10 )
| ~ subset(iPr_def_10,sK3) ),
inference(superposition,[status(thm)],[c_659,c_53]) ).
tcf(c_835,plain,
~ member(sK1(iPr_def_10,empty_set),empty_set),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_865,plain,
! [X0: $i] :
( subset(sK3,X0)
| ( empty_set = iPr_def_10 ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_640,c_687]) ).
tcf(c_874,plain,
! [X0: $i] :
( member(sK1(iPr_def_10,X0),X0)
| ( empty_set = iPr_def_10 )
| ( X0 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_62,c_687]) ).
tcf(c_888,plain,
( member(sK1(iPr_def_10,empty_set),empty_set)
| ( empty_set = iPr_def_10 ) ),
inference(instantiation,[status(thm)],[c_874]) ).
tcf(c_889,plain,
empty_set = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_865,c_835,c_888]) ).
tcf(c_892,plain,
! [X0: $i] : subset(iPr_def_10,X0),
inference(demodulation,[status(thm)],[c_566,c_889]) ).
tcf(c_897,plain,
( ( iPr_def_10 != iPr_def_10 )
| ( sK3 != iPr_def_10 )
| ( sK2 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_334,c_889]) ).
tcf(c_900,plain,
( ( sK3 != iPr_def_10 )
| ( sK2 != iPr_def_10 ) ),
inference(equality_resolution_simp,[status(thm)],[c_897]) ).
tcf(c_994,plain,
sK2 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_753,c_892]) ).
tcf(c_997,plain,
( ( iPr_def_10 != iPr_def_10 )
| ( sK3 != iPr_def_10 ) ),
inference(demodulation,[status(thm)],[c_900,c_994]) ).
tcf(c_999,plain,
sK3 != iPr_def_10,
inference(equality_resolution_simp,[status(thm)],[c_997]) ).
tcf(c_1007,plain,
~ subset(iPr_def_10,sK3),
inference(global_subsumption_just,[status(thm)],[c_754,c_754,c_999]) ).
tcf(c_1009,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1007,c_892]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET600+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 11:24:05 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.55/1.30 % SZS status Started for theBenchmark.p
% 2.55/1.30 % SZS status Theorem for theBenchmark.p
% 2.55/1.30
% 2.55/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.55/1.30
% 2.55/1.30 % ------ iProver source info
% 2.55/1.30
% 2.55/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.55/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.55/1.30 % git: non_committed_changes: false
% 2.55/1.30
% 2.55/1.30 % ------ Parsing...
% 2.55/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.55/1.30
% 2.55/1.30 % ------ 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 %
% 2.55/1.30
% 2.55/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.55/1.30
% 2.55/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.55/1.30 % ------ Proving...
% 2.55/1.30 % ------ Problem Properties
% 2.55/1.30
% 2.55/1.30 %
% 2.55/1.30 % clauses 16
% 2.55/1.30 % conjectures 3
% 2.55/1.30 % EPR 7
% 2.55/1.30 % Horn 11
% 2.55/1.30 % unary 4
% 2.55/1.30 % binary 6
% 2.55/1.30 % lits 34
% 2.55/1.30 % lits eq 12
% 2.55/1.30 % fd_pure 0
% 2.55/1.30 % fd_pseudo 0
% 2.55/1.30 % fd_cond 0
% 2.55/1.30 % fd_pseudo_cond 3
% 2.55/1.30 % AC symbols 0
% 2.55/1.30
% 2.55/1.30 % ------ Schedule dynamic 5 is on
% 2.55/1.30
% 2.55/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.55/1.30
% 2.55/1.30
% 2.55/1.30 % ------
% 2.55/1.30 % Current options:
% 2.55/1.30 % ------
% 2.55/1.30
% 2.55/1.30
% 2.55/1.30 %
% 2.55/1.30
% 2.55/1.30 % ------ Proving...
% 2.55/1.30 %
% 2.55/1.30
% 2.55/1.30 % SZS status Theorem for theBenchmark.p
% 2.55/1.30
% 2.55/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.55/1.30
% 2.55/1.30
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