%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET704+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 : n007.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 02:47:50 PM UTC 2026
% Result : Theorem 3.50s 1.15s
% Output : CNFRefutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 71 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 71 ( 28 ~; 24 |; 10 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 44 !; 5 ?; 8 :)
% 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(f11,axiom,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( member(X2,X1)
=> member(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',product) ).
fof(f12,conjecture,
! [X0,X1] :
( member(X1,X0)
=> subset(product(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI42) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(product(X0),X1) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( ! [X2] :
( member(X2,X0)
=> member(X2,X1) )
=> subset(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f15,plain,
? [X0,X1] :
( member(X1,X0)
& ~ subset(product(X0),X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| subset(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f17,plain,
! [X0,X1] :
( member(X0,product(X1))
<=> ! [X2] :
( ~ member(X2,X1)
| member(X0,X2) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f18,plain,
( member(sK1,sK0)
& ~ subset(product(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f19,plain,
! [X0,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))],[f16]) ).
fof(f20,plain,
! [X0,X1] :
( ( ~ member(X0,product(X1))
| ! [X2] :
( ~ member(X2,X1)
| member(X0,X2) ) )
& ( ? [X2] :
( member(X2,X1)
& ~ member(X0,X2) )
| member(X0,product(X1)) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ member(X0,product(X1))
| ! [X3] :
( ~ member(X3,X1)
| member(X0,X3) ) )
& ( ? [X2] :
( member(X2,X1)
& ~ member(X0,X2) )
| member(X0,product(X1)) ) ),
inference(rectify,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ( ~ member(X0,product(X1))
| ! [X3] :
( ~ member(X3,X1)
| member(X0,X3) ) )
& ( ( member(sK3(X0,X1),X1)
& ~ member(X0,sK3(X0,X1)) )
| member(X0,product(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f21]) ).
fof(f23,plain,
member(sK1,sK0),
inference(cnf_transformation,[],[f18]) ).
fof(f24,plain,
~ subset(product(sK0),sK1),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f26,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X3,X0,X1] :
( ~ member(X0,product(X1))
| ~ member(X3,X1)
| member(X0,X3) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_49,negated_conjecture,
~ subset(product(sK0),sK1),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,negated_conjecture,
member(sK1,sK0),
inference(cnf_transformation,[],[f23]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X2,X1)
| ~ member(X0,product(X1)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_86,plain,
member(sK2(product(sK0),sK1),product(sK0)),
inference(resolution,[status(thm)],[c_49,c_52]) ).
tcf(c_90,plain,
~ member(sK2(product(sK0),sK1),sK1),
inference(resolution,[status(thm)],[c_49,c_51]) ).
tcf(c_116,plain,
! [X0: $i] :
( member(X0,sK1)
| ~ member(sK1,sK0)
| ~ member(X0,product(sK0)) ),
inference(instantiation,[status(thm)],[c_55]) ).
tcf(c_124,plain,
( member(sK2(product(sK0),sK1),sK1)
| ~ member(sK1,sK0)
| ~ member(sK2(product(sK0),sK1),product(sK0)) ),
inference(instantiation,[status(thm)],[c_116]) ).
tcf(c_125,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_124,c_90,c_86,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET704+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.33 % Computer : n007.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Thu Sep 24 11:41:25 UTC 2026
% 0.08/0.33 % CPUTime :
% 0.08/0.33 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 Running first-order theorem proving
% 0.11/0.37 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
% 0.11/0.38
% 0.11/0.38 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.38
% 0.11/0.38 % Detected problem language: tptp
% 0.11/0.40 % Proving...
% 3.50/1.15 % SZS status Started for theBenchmark.p
% 3.50/1.15 % SZS status Theorem for theBenchmark.p
% 3.50/1.15
% 3.50/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.50/1.15
% 3.50/1.15 % ------ iProver source info
% 3.50/1.15
% 3.50/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 3.50/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.50/1.15 % git: non_committed_changes: false
% 3.50/1.15
% 3.50/1.15 % ------ Parsing...
% 3.50/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.50/1.15
% 3.50/1.15 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.50/1.15
% 3.50/1.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.50/1.15 % ------ Proving...
% 3.50/1.15 % ------ Problem Properties
% 3.50/1.15
% 3.50/1.15 %
% 3.50/1.15 % clauses 6
% 3.50/1.15 % conjectures 1
% 3.50/1.15 % EPR 1
% 3.50/1.15 % Horn 5
% 3.50/1.15 % unary 3
% 3.50/1.15 % binary 2
% 3.50/1.15 % lits 10
% 3.50/1.15 % lits eq 0
% 3.50/1.15 % fd_pure 0
% 3.50/1.15 % fd_pseudo 0
% 3.50/1.15 % fd_cond 0
% 3.50/1.15 % fd_pseudo_cond 0
% 3.50/1.15 % AC symbols 0
% 3.50/1.15
% 3.50/1.15 % ------ Schedule dynamic 5 is on
% 3.50/1.15
% 3.50/1.15 % ------ no equalities: superposition off
% 3.50/1.15
% 3.50/1.15 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.50/1.15
% 3.50/1.15
% 3.50/1.15 % ------
% 3.50/1.15 % Current options:
% 3.50/1.15 % ------
% 3.50/1.15
% 3.50/1.15
% 3.50/1.15 %
% 3.50/1.15
% 3.50/1.15 % ------ Proving...
% 3.50/1.15 %
% 3.50/1.15
% 3.50/1.15 % SZS status Theorem for theBenchmark.p
% 3.50/1.15
% 3.50/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.50/1.15
% 3.50/1.15
%------------------------------------------------------------------------------