%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET355+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 : n008.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 02:47:09 PM UTC 2026
% Result : Theorem 1.41s 6.62s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 7 unt; 0 def)
% Number of atoms : 68 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 27 ~; 23 |; 11 &)
% ( 2 <=>; 5 =>; 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 : 46 ( 0 sgn 40 !; 6 ?; 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(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,
! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI43) ).
fof(f13,negated_conjecture,
~ ! [X0,X1] :
( member(X1,X0)
=> subset(X1,sum(X0)) ),
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(X1,sum(X0)) ),
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,
( member(sK1,sK0)
& ~ subset(sK1,sum(sK0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f15]) ).
fof(f18,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(f19,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(f20,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,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( ~ member(X0,sum(X1))
| ( member(X0,sK3(X0,X1))
& member(sK3(X0,X1),X1) ) )
& ( ! [X2] :
( ~ member(X0,X2)
| ~ member(X2,X1) )
| member(X0,sum(X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1))],[f20]) ).
fof(f22,plain,
member(sK1,sK0),
inference(cnf_transformation,[],[f17]) ).
fof(f23,plain,
~ subset(sK1,sum(sK0)),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X0,X1] :
( member(sK2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1] :
( ~ member(sK2(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ member(X0,X2)
| ~ member(X2,X1)
| member(X0,sum(X1)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_49,negated_conjecture,
~ subset(sK1,sum(sK0)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_50,negated_conjecture,
member(sK1,sK0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ member(sK2(X0,X1),X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| member(sK2(X0,X1),X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,sum(X2))
| ~ member(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_87,plain,
member(sK2(sK1,sum(sK0)),sK1),
inference(resolution,[status(thm)],[c_49,c_52]) ).
tcf(c_91,plain,
~ member(sK2(sK1,sum(sK0)),sum(sK0)),
inference(resolution,[status(thm)],[c_49,c_51]) ).
tcf(c_119,plain,
! [X0: $i] :
( member(sK2(sK1,sum(sK0)),sum(X0))
| ~ member(sK1,X0)
| ~ member(sK2(sK1,sum(sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_53]) ).
tcf(c_120,plain,
( member(sK2(sK1,sum(sK0)),sum(sK0))
| ~ member(sK1,sK0)
| ~ member(sK2(sK1,sum(sK0)),sK1) ),
inference(instantiation,[status(thm)],[c_119]) ).
tcf(c_121,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_120,c_91,c_87,c_50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET355+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/5.80 % Computer : n008.cluster.edu
% 0.11/5.80 % Model : x86_64 x86_64
% 0.11/5.80 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.80 % Memory : 8046.5625MB
% 0.11/5.80 % OS : Linux 6.8.0-71-generic
% 0.11/5.80 % CPULimit : 300
% 0.14/5.80 % WCLimit : 300
% 0.14/5.80 % DateTime : Thu Sep 24 10:42:33 UTC 2026
% 0.14/5.80 % CPUTime :
% 0.14/5.80 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.84 Running first-order theorem proving
% 0.14/5.84 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
% 0.14/5.85
% 0.14/5.85 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.85
% 0.14/5.85 % Detected problem language: tptp
% 0.14/5.86 % Proving...
% 1.41/6.62 % SZS status Started for theBenchmark.p
% 1.41/6.62 % SZS status Theorem for theBenchmark.p
% 1.41/6.62
% 1.41/6.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.41/6.62
% 1.41/6.62 % ------ iProver source info
% 1.41/6.62
% 1.41/6.62 % git: date: 2026-07-19 20:42:38 +0200
% 1.41/6.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.41/6.62 % git: non_committed_changes: false
% 1.41/6.62
% 1.41/6.62 % ------ Parsing...
% 1.41/6.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.41/6.62
% 1.41/6.62 % ------ 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 %
% 1.41/6.62
% 1.41/6.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.41/6.62 % ------ Proving...
% 1.41/6.62 % ------ Problem Properties
% 1.41/6.62
% 1.41/6.62 %
% 1.41/6.62 % clauses 6
% 1.41/6.62 % conjectures 1
% 1.41/6.62 % EPR 1
% 1.41/6.62 % Horn 6
% 1.41/6.62 % unary 3
% 1.41/6.62 % binary 2
% 1.41/6.62 % lits 10
% 1.41/6.62 % lits eq 0
% 1.41/6.62 % fd_pure 0
% 1.41/6.62 % fd_pseudo 0
% 1.41/6.62 % fd_cond 0
% 1.41/6.62 % fd_pseudo_cond 0
% 1.41/6.62 % AC symbols 0
% 1.41/6.62
% 1.41/6.62 % ------ Schedule dynamic 5 is on
% 1.41/6.62
% 1.41/6.62 % ------ no equalities: superposition off
% 1.41/6.62
% 1.41/6.62 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.41/6.62
% 1.41/6.62
% 1.41/6.62 % ------
% 1.41/6.62 % Current options:
% 1.41/6.62 % ------
% 1.41/6.62
% 1.41/6.62
% 1.41/6.62 %
% 1.41/6.62
% 1.41/6.62 % ------ Proving...
% 1.41/6.62 %
% 1.41/6.62
% 1.41/6.62 % SZS status Theorem for theBenchmark.p
% 1.41/6.62
% 1.41/6.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.41/6.62
% 1.41/6.62
%------------------------------------------------------------------------------