TSTP Solution File: SEU781^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.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 03:39:50 EDT 2024
% Result : Theorem 3.22s 1.98s
% Output : Refutation 3.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 13 ( 3 unt; 7 typ; 2 def)
% Number of atoms : 48 ( 2 equ; 0 cnn)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 181 ( 2 ~; 0 |; 4 &; 135 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 1 ^ 31 !; 2 ?; 34 :)
% 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(breln1_type,type,
breln1: $i > $i > $o ).
thf(breln1_def,definition,
( breln1
= ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).
thf(breln1compset_type,type,
breln1compset: $i > $i > $i > $i ).
thf(breln1compE_type,type,
breln1compE: $o ).
thf(breln1compE_def,definition,
( breln1compE
= ( ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) ) ) ) ).
thf(1,conjecture,
( breln1compE
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ! [F: $o] :
( ! [G: $i] :
( ( in @ G @ A )
=> ( ( in @ ( kpair @ D @ G ) @ B )
=> ( ( in @ ( kpair @ G @ E ) @ C )
=> F ) ) )
=> F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1compEex) ).
thf(2,negated_conjecture,
~ ( breln1compE
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i] :
( ( breln1 @ A @ C )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ! [F: $o] :
( ! [G: $i] :
( ( in @ G @ A )
=> ( ( in @ ( kpair @ D @ G ) @ B )
=> ( ( in @ ( kpair @ G @ E ) @ C )
=> F ) ) )
=> F ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ? [F: $i] :
( ( in @ F @ A )
& ( in @ ( kpair @ D @ F ) @ B )
& ( in @ ( kpair @ F @ E ) @ C ) ) ) ) ) ) )
=> ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i] :
( ( subset @ C @ ( cartprod @ A @ A ) )
=> ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
=> ! [F: $o] :
( ! [G: $i] :
( ( in @ G @ A )
=> ( ( in @ ( kpair @ D @ G ) @ B )
=> ( ( in @ ( kpair @ G @ E ) @ C )
=> F ) ) )
=> F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% 0.17/0.19 % Command : run_Leo-III %s %d
% 0.18/0.41 % Computer : n002.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8042.1875MB
% 0.18/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.25/0.41 % CPULimit : 300
% 0.25/0.41 % WCLimit : 300
% 0.25/0.41 % DateTime : Sun May 19 18:18:24 EDT 2024
% 0.25/0.41 % CPUTime :
% 1.02/0.95 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.28/1.08 % [INFO] Parsing done (132ms).
% 1.28/1.10 % [INFO] Running in sequential loop mode.
% 1.70/1.37 % [INFO] eprover registered as external prover.
% 1.70/1.37 % [INFO] cvc4 registered as external prover.
% 1.70/1.38 % [INFO] Scanning for conjecture ...
% 2.00/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.00/1.49 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.00/1.49 % [INFO] Problem is higher-order (TPTP THF).
% 2.00/1.50 % [INFO] Type checking passed.
% 2.00/1.50 % [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 ...
% 3.22/1.98 % External prover 'e' found a proof!
% 3.22/1.98 % [INFO] Killing All external provers ...
% 3.22/1.98 % Time passed: 1398ms (effective reasoning time: 879ms)
% 3.22/1.98 % 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)>
% 3.22/1.98 % Axioms used in derivation (0):
% 3.22/1.98 % No. of inferences in proof: 4
% 3.22/1.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1398 ms resp. 879 ms w/o parsing
% 3.22/2.03 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.22/2.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------