TSTP Solution File: SET025-8 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET025-8 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:04:57 EDT 2024
% Result : Unsatisfiable 127.37s 23.75s
% Output : Refutation 127.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 12 unt; 6 typ; 0 def)
% Number of atoms : 27 ( 9 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 69 ( 16 ~; 7 |; 0 &; 46 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 ^ 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(little_set_type,type,
little_set: $i > $o ).
thf(a_type,type,
a: $i ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(ordered_pair_predicate_type,type,
ordered_pair_predicate: $i > $o ).
thf(f2_type,type,
f2: $i > $i ).
thf(f3_type,type,
f3: $i > $i ).
thf(77,axiom,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A
= ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_predicate3) ).
thf(324,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A
= ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(325,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A
= ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) ) ) ),
inference(cnf,[status(esa)],[324]) ).
thf(326,plain,
! [A: $i] :
( ( ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) )
= A )
| ~ ( ordered_pair_predicate @ A ) ),
inference(lifteq,[status(thm)],[325]) ).
thf(108,axiom,
! [B: $i,A: $i] : ( little_set @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pairs_are_small1) ).
thf(398,plain,
! [B: $i,A: $i] : ( little_set @ ( ordered_pair @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(1,negated_conjecture,
~ ( little_set @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_predicate_is_small) ).
thf(150,plain,
~ ( little_set @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(151,plain,
~ ( little_set @ a ),
inference(polarity_switch,[status(thm)],[150]) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( little_set @ ( ordered_pair @ A @ B ) )
!= ( little_set @ a ) ),
inference(paramod_ordered,[status(thm)],[398,151]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( ordered_pair @ A @ B )
!= a ),
inference(simp,[status(thm)],[507]) ).
thf(72509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A != a )
| ( ( ordered_pair @ ( f2 @ A ) @ ( f3 @ A ) )
!= ( ordered_pair @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[326,508]) ).
thf(72510,plain,
! [A: $i] :
( ~ ( ordered_pair_predicate @ A )
| ( A != a ) ),
inference(pattern_uni,[status(thm)],[72509:[bind(A,$thf( E )),bind(B,$thf( f2 @ E )),bind(C,$thf( f3 @ E ))]]) ).
thf(72644,plain,
~ ( ordered_pair_predicate @ a ),
inference(simp,[status(thm)],[72510]) ).
thf(129,axiom,
ordered_pair_predicate @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_ordered_pair_predicate) ).
thf(457,plain,
ordered_pair_predicate @ a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(72673,plain,
~ $true,
inference(rewrite,[status(thm)],[72644,457]) ).
thf(72674,plain,
$false,
inference(simp,[status(thm)],[72673]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET025-8 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n006.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 13:18:09 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.83/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.47/1.01 % [INFO] Parsing done (156ms).
% 1.47/1.02 % [INFO] Running in sequential loop mode.
% 1.89/1.21 % [INFO] nitpick registered as external prover.
% 1.89/1.22 % [INFO] Scanning for conjecture ...
% 1.98/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 152 axioms. Running axiom selection ...
% 2.27/1.35 % [INFO] Axiom selection finished. Selected 148 axioms (removed 4 axioms).
% 2.54/1.44 % [INFO] Problem is propositional (TPTP CNF).
% 2.54/1.45 % [INFO] Type checking passed.
% 2.54/1.45 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 127.37/23.75 % [INFO] Killing All external provers ...
% 127.37/23.75 % Time passed: 23221ms (effective reasoning time: 22725ms)
% 127.37/23.75 % Axioms used in derivation (3): ordered_pair_predicate3, ordered_pairs_are_small1, an_ordered_pair_predicate
% 127.37/23.75 % No. of inferences in proof: 18
% 127.37/23.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 23221 ms resp. 22725 ms w/o parsing
% 127.37/23.77 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 127.37/23.77 % [INFO] Killing All external provers ...
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