TSTP Solution File: SET108-6 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SET108-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.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 03:05:25 EDT 2024
% Result : Unsatisfiable 145.78s 26.04s
% Output : Refutation 145.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 25 ( 10 unt; 8 typ; 0 def)
% Number of atoms : 27 ( 11 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 181 ( 17 ~; 8 |; 0 &; 156 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 ^ 19 !; 0 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(member_type,type,
member: $i > $i > $o ).
thf(ordered_pair_type,type,
ordered_pair: $i > $i > $i ).
thf(y_type,type,
y: $i ).
thf(z_type,type,
z: $i ).
thf(cross_product_type,type,
cross_product: $i > $i > $i ).
thf(universal_class_type,type,
universal_class: $i ).
thf(first_type,type,
first: $i > $i ).
thf(second_type,type,
second: $i > $i ).
thf(1,negated_conjecture,
member @ ( ordered_pair @ y @ z ) @ ( cross_product @ universal_class @ universal_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_1) ).
thf(94,plain,
member @ ( ordered_pair @ y @ z ) @ ( cross_product @ universal_class @ universal_class ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartesian_product4) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A ) ),
inference(cnf,[status(esa)],[209]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
= A )
| ~ ( member @ A @ ( cross_product @ B @ C ) ) ),
inference(lifteq,[status(thm)],[210]) ).
thf(2,negated_conjecture,
~ ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_existence_of_1st_and_2nd_1_2) ).
thf(95,plain,
~ ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(96,plain,
~ ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) ),
inference(polarity_switch,[status(thm)],[95]) ).
thf(292,plain,
( ( member @ ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) @ ( cross_product @ universal_class @ universal_class ) )
!= ( member @ ( ordered_pair @ y @ z ) @ ( cross_product @ universal_class @ universal_class ) ) ),
inference(paramod_ordered,[status(thm)],[94,96]) ).
thf(293,plain,
( ( ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) )
!= ( ordered_pair @ y @ z ) )
| ( ( cross_product @ universal_class @ universal_class )
!= ( cross_product @ universal_class @ universal_class ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(294,plain,
( ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) )
!= ( ordered_pair @ y @ z ) ),
inference(simp,[status(thm)],[293]) ).
thf(58523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( cross_product @ B @ C ) )
| ( A
!= ( ordered_pair @ y @ z ) )
| ( ( ordered_pair @ ( first @ A ) @ ( second @ A ) )
!= ( ordered_pair @ ( first @ ( ordered_pair @ y @ z ) ) @ ( second @ ( ordered_pair @ y @ z ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[211,294]) ).
thf(58524,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( ordered_pair @ y @ z ) @ ( cross_product @ A @ B ) )
| ( ( ordered_pair @ y @ z )
!= ( ordered_pair @ y @ z ) ) ),
inference(pattern_uni,[status(thm)],[58523:[bind(A,$thf( ordered_pair @ y @ z )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).
thf(58685,plain,
! [B: $i,A: $i] :
~ ( member @ ( ordered_pair @ y @ z ) @ ( cross_product @ A @ B ) ),
inference(simp,[status(thm)],[58524]) ).
thf(58989,plain,
$false,
inference(rewrite,[status(thm)],[94,58685]) ).
thf(58990,plain,
$false,
inference(simp,[status(thm)],[58989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET108-6 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n024.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 12:39:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.93/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.51/1.06 % [INFO] Parsing done (156ms).
% 1.51/1.07 % [INFO] Running in sequential loop mode.
% 2.00/1.27 % [INFO] nitpick registered as external prover.
% 2.00/1.27 % [INFO] Scanning for conjecture ...
% 2.00/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 2.32/1.39 % [INFO] Axiom selection finished. Selected 91 axioms (removed 0 axioms).
% 2.64/1.46 % [INFO] Problem is propositional (TPTP CNF).
% 2.64/1.47 % [INFO] Type checking passed.
% 2.64/1.47 % [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 ...
% 145.78/26.04 % [INFO] Killing All external provers ...
% 145.78/26.04 % Time passed: 25506ms (effective reasoning time: 24968ms)
% 145.78/26.04 % Axioms used in derivation (1): cartesian_product4
% 145.78/26.04 % No. of inferences in proof: 17
% 145.78/26.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 25506 ms resp. 24968 ms w/o parsing
% 145.78/26.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 145.78/26.06 % [INFO] Killing All external provers ...
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