%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET002+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 : n013.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 02:45:57 PM UTC 2026
% Result : Theorem 1.11s 1.29s
% Output : CNFRefutation 1.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 11 unt; 0 def)
% Number of atoms : 21 ( 11 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 9 ~; 4 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 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 : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 13 !; 1 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subset(X0,X1)
=> union(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_union) ).
fof(f6,axiom,
! [X0] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
fof(f8,conjecture,
! [X0] : union(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idempotency_of_union) ).
fof(f9,negated_conjecture,
~ ! [X0] : union(X0,X0) = X0,
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| union(X0,X1) = X1 ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
? [X0] : union(X0,X0) != X0,
inference(ennf_transformation,[],[f9]) ).
fof(f23,plain,
sK2 != union(sK2,sK2),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f12]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| union(X0,X1) = X1 ),
inference(cnf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f40,plain,
sK2 != union(sK2,sK2),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ( union(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_60,plain,
! [X0: $i] : subset(X0,X0),
inference(cnf_transformation,[],[f35]) ).
tcf(c_63,negated_conjecture,
union(sK2,sK2) != sK2,
inference(cnf_transformation,[],[f40]) ).
tcf(c_64,plain,
subset(sK2,sK2),
inference(instantiation,[status(thm)],[c_60]) ).
tcf(c_67,plain,
( ( union(sK2,sK2) = sK2 )
| ~ subset(sK2,sK2) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_68,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_67,c_63,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 09:03:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.45 % Proving...
% 1.11/1.29 % SZS status Started for theBenchmark.p
% 1.11/1.29 % SZS status Theorem for theBenchmark.p
% 1.11/1.29
% 1.11/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.11/1.29
% 1.11/1.29 % ------ iProver source info
% 1.11/1.29
% 1.11/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.11/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.11/1.29 % git: non_committed_changes: false
% 1.11/1.29
% 1.11/1.29 % ------ Parsing...
% 1.11/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.11/1.29
% 1.11/1.29 % ------ Preprocessing...%
% 1.11/1.29
% 1.11/1.29 % SZS status Theorem for theBenchmark.p
% 1.11/1.29
% 1.11/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.11/1.29
% 1.11/1.29
%------------------------------------------------------------------------------