%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET347+4 : 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 : n018.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 02:47:08 PM UTC 2026
% Result : Theorem 3.03s 1.31s
% Output : CNFRefutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 13 unt; 0 def)
% Number of atoms : 92 ( 2 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 103 ( 46 ~; 36 |; 15 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn 54 !; 5 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(f2,axiom,
! [X0,X1] :
( equal_set(X0,X1)
<=> ( subset(X1,X0)
& subset(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(f6,axiom,
! [X0] : ~ member(X0,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(f10,axiom,
! [X0,X1] :
( member(X0,sum(X1))
<=> ? [X2] :
( member(X0,X2)
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(f12,conjecture,
equal_set(sum(empty_set),empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI38) ).
fof(f13,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
~ equal_set(sum(empty_set),empty_set),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( subset(X1,X0)
& subset(X0,X1) )
=> equal_set(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f17,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(flattening,[],[f17]) ).
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,[],[f16]) ).
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(f33,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ? [X2] :
( member(X0,X2)
& member(X2,X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f34,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ? [X3] :
( member(X0,X3)
& member(X3,X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(rectify,[],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ( member(X0,sK1(X0,X1))
& member(sK1(X0,X1),X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1))],[f34]) ).
fof(f40,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f42,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f6]) ).
fof(f61,plain,
! [X0,X1] :
( ~ member(X0,sum(X1))
| member(sK1(X0,X1),X1) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
~ equal_set(sum(empty_set),empty_set),
inference(cnf_transformation,[],[f14]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK0(X0,X1),X0) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( equal_set(X0,X1)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_61,plain,
! [X0: $i] : ~ member(X0,empty_set),
inference(cnf_transformation,[],[f51]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( member(sK1(X0,X1),X1)
| ~ member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_76,negated_conjecture,
~ equal_set(sum(empty_set),empty_set),
inference(cnf_transformation,[],[f66]) ).
tcf(c_422,plain,
! [X0: $i,X1: $i] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| ( X1 != empty_set )
| ( sum(empty_set) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_76]) ).
tcf(c_423,plain,
( ~ subset(empty_set,sum(empty_set))
| ~ subset(sum(empty_set),empty_set) ),
inference(unflattening,[status(thm)],[c_422]) ).
tcf(c_488,plain,
( ~ subset(empty_set,sum(empty_set))
| ~ subset(sum(empty_set),empty_set) ),
inference(prop_impl_just,[status(thm)],[c_423]) ).
tcf(c_1283,plain,
! [X0: $i] : subset(empty_set,X0),
inference(superposition,[status(thm)],[c_50,c_61]) ).
tcf(c_1298,plain,
~ subset(sum(empty_set),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[c_488,c_1283]) ).
tcf(c_1401,plain,
! [X0: $i] : ~ member(X0,sum(empty_set)),
inference(superposition,[status(thm)],[c_71,c_61]) ).
tcf(c_1423,plain,
! [X0: $i] : subset(sum(empty_set),X0),
inference(superposition,[status(thm)],[c_50,c_1401]) ).
tcf(c_1426,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_1298,c_1423]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET347+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Thu Sep 24 10:41:35 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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...
% 3.03/1.31 % SZS status Started for theBenchmark.p
% 3.03/1.31 % SZS status Theorem for theBenchmark.p
% 3.03/1.31
% 3.03/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.03/1.31
% 3.03/1.31 % ------ iProver source info
% 3.03/1.31
% 3.03/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.03/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.03/1.31 % git: non_committed_changes: false
% 3.03/1.31
% 3.03/1.31 % ------ Parsing...
% 3.03/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.03/1.31
% 3.03/1.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.03/1.31
% 3.03/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.03/1.31
% 3.03/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.03/1.31 % ------ Proving...
% 3.03/1.31 % ------ Problem Properties
% 3.03/1.31
% 3.03/1.31 %
% 3.03/1.31 % clauses 27
% 3.03/1.31 % conjectures 0
% 3.03/1.31 % EPR 2
% 3.03/1.31 % Horn 22
% 3.03/1.31 % unary 4
% 3.03/1.31 % binary 16
% 3.03/1.31 % lits 57
% 3.03/1.31 % lits eq 3
% 3.03/1.31 % fd_pure 0
% 3.03/1.31 % fd_pseudo 0
% 3.03/1.31 % fd_cond 0
% 3.03/1.31 % fd_pseudo_cond 2
% 3.03/1.31 % AC symbols 0
% 3.03/1.31
% 3.03/1.31 % ------ Schedule dynamic 5 is on
% 3.03/1.31
% 3.03/1.31 % ------ no conjectures: strip conj schedule
% 3.03/1.31
% 3.03/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.03/1.31
% 3.03/1.31
% 3.03/1.31 % ------
% 3.03/1.31 % Current options:
% 3.03/1.31 % ------
% 3.03/1.31
% 3.03/1.31
% 3.03/1.31 %
% 3.03/1.31
% 3.03/1.31 % ------ Proving...
% 3.03/1.31 %
% 3.03/1.31
% 3.03/1.31 % SZS status Theorem for theBenchmark.p
% 3.03/1.31
% 3.03/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.03/1.31
% 3.03/1.31
%------------------------------------------------------------------------------