TSTP Solution File: SEU778^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU778^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 03:43:45 EDT 2024
% Result : Theorem 3.03s 1.73s
% Output : Refutation 3.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 21 ( 6 unt; 11 typ; 3 def)
% Number of atoms : 32 ( 3 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 113 ( 4 ~; 0 |; 6 &; 94 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-3 aty)
% Number of variables : 28 ( 10 ^ 15 !; 3 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(dpsetconstr_type,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(breln1_def,definition,
( breln1
= ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).
thf(setOfPairsIsBReln1_type,type,
setOfPairsIsBReln1: $o ).
thf(setOfPairsIsBReln1_def,definition,
( setOfPairsIsBReln1
= ( ! [A: $i,B: $i > $i > $o] : ( breln1 @ A @ ( dpsetconstr @ A @ A @ B ) ) ) ) ).
thf(breln1compset_type,type,
breln1compset: $i > $i > $i > $i ).
thf(breln1compset_def,definition,
( breln1compset
= ( ^ [A: $i,B: $i,C: $i] :
( dpsetconstr @ A @ A
@ ^ [D: $i,E: $i] :
? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(1,conjecture,
( setOfPairsIsBReln1
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( breln1 @ A @ ( breln1compset @ A @ B @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compprop) ).
thf(2,negated_conjecture,
~ ( setOfPairsIsBReln1
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ( breln1 @ A @ ( breln1compset @ A @ B @ C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $i > $o] : ( subset @ ( dpsetconstr @ A @ A @ B ) @ ( cartprod @ A @ A ) )
=> ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ( subset
@ ( dpsetconstr @ A @ A
@ ^ [D: $i,E: $i] :
? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) )
@ ( cartprod @ A @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( subset
@ ( dpsetconstr @ sk1 @ sk1
@ ^ [A: $i,B: $i] :
? [C: $i] :
( ( in @ C @ sk1 )
& ( in @ ( kpair @ A @ C ) @ sk2 )
& ( in @ ( kpair @ C @ B ) @ sk3 ) ) )
@ ( cartprod @ sk1 @ sk1 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
! [B: $i > $i > $o,A: $i] : ( subset @ ( dpsetconstr @ A @ A @ B ) @ ( cartprod @ A @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
~ $true,
inference(rewrite,[status(thm)],[4,7]) ).
thf(15,plain,
$false,
inference(simp,[status(thm)],[14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU778^2 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n026.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 : Sun May 19 18:06:39 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.87/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.14/0.98 % [INFO] Parsing done (122ms).
% 1.14/0.99 % [INFO] Running in sequential loop mode.
% 1.63/1.21 % [INFO] nitpick registered as external prover.
% 1.63/1.22 % [INFO] Scanning for conjecture ...
% 1.77/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.98/1.31 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.98/1.31 % [INFO] Problem is higher-order (TPTP THF).
% 1.98/1.31 % [INFO] Type checking passed.
% 1.98/1.32 % [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 ...
% 3.03/1.73 % [INFO] Killing All external provers ...
% 3.03/1.73 % Time passed: 1213ms (effective reasoning time: 734ms)
% 3.03/1.73 % Solved by 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)>
% 3.03/1.73 % Axioms used in derivation (0):
% 3.03/1.73 % No. of inferences in proof: 7
% 3.03/1.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1213 ms resp. 734 ms w/o parsing
% 3.03/1.76 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.03/1.76 % [INFO] Killing All external provers ...
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