%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET162+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 02:46:48 PM UTC 2026
% Result : Theorem 2.06s 1.28s
% Output : CNFRefutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 45 ( 18 unt; 1 def)
% Number of atoms : 123 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 47 ~; 45 |; 15 &)
% ( 4 <=>; 1 =>; 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 : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn 70 !; 3 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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(f2,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(f4,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
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(f9,conjecture,
! [X0] : union(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_empty_set) ).
fof(f10,negated_conjecture,
~ ! [X0] : union(X0,empty_set) = X0,
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] : union(X0,empty_set) != X0,
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(f23,plain,
sK2 != union(sK2,empty_set),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ member(X2,union(X0,X1))
| member(X2,X1)
| member(X2,X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| member(X2,union(X0,X1)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f30,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f33,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f34,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f40,plain,
sK2 != union(sK2,empty_set),
inference(cnf_transformation,[],[f23]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,union(X2,X1))
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f27]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_63,negated_conjecture,
union(sK2,empty_set) != sK2,
inference(cnf_transformation,[],[f40]) ).
tcf(c_127,plain,
union(empty_set,sK2) != sK2,
inference(demodulation,[status(thm)],[c_63,c_56]) ).
tcf(c_278,definition,
iPr_def_10 = union(empty_set,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_279,plain,
iPr_def_10 != sK2,
inference(demodulation,[status(thm)],[c_127,c_278]) ).
tcf(c_461,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,sK2) ),
inference(superposition,[status(thm)],[c_278,c_50]) ).
tcf(c_506,plain,
! [X0: $i] :
( member(X0,sK2)
| member(X0,empty_set)
| ~ member(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_278,c_51]) ).
tcf(c_507,plain,
! [X0: $i] :
( member(X0,sK2)
| ~ member(X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_506,c_52]) ).
tcf(c_529,plain,
! [X0: $i] :
( subset(sK2,X0)
| member(sK0(sK2,X0),iPr_def_10) ),
inference(superposition,[status(thm)],[c_58,c_461]) ).
tcf(c_537,plain,
! [X0: $i] :
( subset(iPr_def_10,X0)
| member(sK0(iPr_def_10,X0),sK2) ),
inference(superposition,[status(thm)],[c_58,c_507]) ).
tcf(c_552,plain,
subset(sK2,iPr_def_10),
inference(superposition,[status(thm)],[c_529,c_57]) ).
tcf(c_569,plain,
subset(iPr_def_10,sK2),
inference(superposition,[status(thm)],[c_537,c_57]) ).
tcf(c_578,plain,
( ( iPr_def_10 = sK2 )
| ~ subset(iPr_def_10,sK2)
| ~ subset(sK2,iPr_def_10) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_579,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_578,c_569,c_552,c_279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET162+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 10:08:04 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 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
% 0.04/0.40
% 0.04/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.40
% 0.04/0.41 % Detected problem language: tptp
% 0.04/0.42 % Proving...
% 2.06/1.28 % SZS status Started for theBenchmark.p
% 2.06/1.28 % SZS status Theorem for theBenchmark.p
% 2.06/1.28
% 2.06/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.06/1.28
% 2.06/1.28 % ------ iProver source info
% 2.06/1.28
% 2.06/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.06/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.06/1.28 % git: non_committed_changes: false
% 2.06/1.28
% 2.06/1.28 % ------ Parsing...
% 2.06/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.06/1.28
% 2.06/1.28 % ------ 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 %
% 2.06/1.28
% 2.06/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.06/1.28
% 2.06/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.06/1.28 % ------ Proving...
% 2.06/1.28 % ------ Problem Properties
% 2.06/1.28
% 2.06/1.28 %
% 2.06/1.28 % clauses 14
% 2.06/1.28 % conjectures 0
% 2.06/1.28 % EPR 5
% 2.06/1.28 % Horn 11
% 2.06/1.28 % unary 5
% 2.06/1.28 % binary 4
% 2.06/1.28 % lits 28
% 2.06/1.28 % lits eq 6
% 2.06/1.28 % fd_pure 0
% 2.06/1.28 % fd_pseudo 0
% 2.06/1.28 % fd_cond 0
% 2.06/1.28 % fd_pseudo_cond 3
% 2.06/1.28 % AC symbols 0
% 2.06/1.28
% 2.06/1.28 % ------ Schedule dynamic 5 is on
% 2.06/1.28
% 2.06/1.28 % ------ no conjectures: strip conj schedule
% 2.06/1.28
% 2.06/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.06/1.28
% 2.06/1.28
% 2.06/1.28 % ------
% 2.06/1.28 % Current options:
% 2.06/1.28 % ------
% 2.06/1.28
% 2.06/1.28
% 2.06/1.28 %
% 2.06/1.28
% 2.06/1.28 % ------ Proving...
% 2.06/1.28 %
% 2.06/1.28
% 2.06/1.28 % SZS status Theorem for theBenchmark.p
% 2.06/1.28
% 2.06/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.06/1.28
% 2.06/1.28
%------------------------------------------------------------------------------