TSTP Solution File: SEU781^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---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 : n008.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 31.97s 6.21s
% Output : Refutation 32.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 48 ( 12 unt; 14 typ; 2 def)
% Number of atoms : 153 ( 6 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 715 ( 77 ~; 69 |; 4 &; 525 @)
% ( 0 <=>; 40 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-5 aty)
% Number of variables : 69 ( 1 ^ 66 !; 2 ?; 69 :)
% 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(sk1_type,type,
sk1: $i > $i > $i > $i > $i > $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $o ).
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/sandbox/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(12,plain,
in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( cartprod @ A @ A ) )
| ~ ( subset @ C @ ( cartprod @ A @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ A )
| ~ ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
| ( in @ ( kpair @ ( sk1 @ E @ D @ C @ B @ A ) @ E ) @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( cartprod @ A @ A ) )
| ~ ( subset @ C @ ( cartprod @ A @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ A )
| ( in @ ( kpair @ ( sk1 @ E @ D @ C @ B @ A ) @ E ) @ C )
| ( ( in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ) )
!= ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,9]) ).
thf(621,plain,
( ~ ( subset @ sk3 @ ( cartprod @ sk2 @ sk2 ) )
| ~ ( subset @ sk4 @ ( cartprod @ sk2 @ sk2 ) )
| ~ ( in @ sk5 @ sk2 )
| ~ ( in @ sk6 @ sk2 )
| ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[620:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind(E,$thf( sk6 ))]]) ).
thf(4,plain,
in @ sk5 @ sk2,
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
subset @ sk4 @ ( cartprod @ sk2 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
subset @ sk3 @ ( cartprod @ sk2 @ sk2 ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
in @ sk6 @ sk2,
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( cartprod @ A @ A ) )
| ~ ( subset @ C @ ( cartprod @ A @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ A )
| ~ ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
| ( in @ ( sk1 @ E @ D @ C @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(165,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( cartprod @ A @ A ) )
| ~ ( subset @ C @ ( cartprod @ A @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ A )
| ( in @ ( sk1 @ E @ D @ C @ B @ A ) @ A )
| ( ( in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ) )
!= ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,13]) ).
thf(166,plain,
( ~ ( subset @ sk3 @ ( cartprod @ sk2 @ sk2 ) )
| ~ ( subset @ sk4 @ ( cartprod @ sk2 @ sk2 ) )
| ~ ( in @ sk5 @ sk2 )
| ~ ( in @ sk6 @ sk2 )
| ( in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2 ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind(E,$thf( sk6 ))]]) ).
thf(456,plain,
( ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2 ) ),
inference(rewrite,[status(thm)],[166,4,5,6,7]) ).
thf(457,plain,
in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2,
inference(simp,[status(thm)],[456]) ).
thf(10,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
| ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
| sk7 ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
| ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
| sk7 ),
inference(simp,[status(thm)],[10]) ).
thf(11,plain,
~ sk7,
inference(cnf,[status(esa)],[3]) ).
thf(174,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
| ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[14,11]) ).
thf(175,plain,
! [A: $i] :
( ~ ( in @ A @ sk2 )
| ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
| ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 ) ),
inference(simp,[status(thm)],[174]) ).
thf(482,plain,
! [A: $i] :
( ~ ( in @ ( kpair @ sk5 @ A ) @ sk3 )
| ~ ( in @ ( kpair @ A @ sk6 ) @ sk4 )
| ( ( in @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk2 )
!= ( in @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[457,175]) ).
thf(483,plain,
( ~ ( in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3 )
| ~ ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ))]]) ).
thf(8,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( cartprod @ A @ A ) )
| ~ ( subset @ C @ ( cartprod @ A @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ A )
| ~ ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) )
| ( in @ ( kpair @ D @ ( sk1 @ E @ D @ C @ B @ A ) ) @ B ) ),
inference(cnf,[status(esa)],[3]) ).
thf(260,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( subset @ B @ ( cartprod @ A @ A ) )
| ~ ( subset @ C @ ( cartprod @ A @ A ) )
| ~ ( in @ D @ A )
| ~ ( in @ E @ A )
| ( in @ ( kpair @ D @ ( sk1 @ E @ D @ C @ B @ A ) ) @ B )
| ( ( in @ ( kpair @ sk5 @ sk6 ) @ ( breln1compset @ sk2 @ sk3 @ sk4 ) )
!= ( in @ ( kpair @ D @ E ) @ ( breln1compset @ A @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,8]) ).
thf(261,plain,
( ~ ( subset @ sk3 @ ( cartprod @ sk2 @ sk2 ) )
| ~ ( subset @ sk4 @ ( cartprod @ sk2 @ sk2 ) )
| ~ ( in @ sk5 @ sk2 )
| ~ ( in @ sk6 @ sk2 )
| ( in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3 ) ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 )),bind(C,$thf( sk4 )),bind(D,$thf( sk5 )),bind(E,$thf( sk6 ))]]) ).
thf(1688,plain,
( ~ $true
| ~ $true
| ~ $true
| ~ $true
| ( in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3 ) ),
inference(rewrite,[status(thm)],[261,4,5,6,7]) ).
thf(1689,plain,
in @ ( kpair @ sk5 @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) ) @ sk3,
inference(simp,[status(thm)],[1688]) ).
thf(1690,plain,
( ~ $true
| ~ ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ) ),
inference(rewrite,[status(thm)],[483,1689]) ).
thf(1691,plain,
~ ( in @ ( kpair @ ( sk1 @ sk6 @ sk5 @ sk4 @ sk3 @ sk2 ) @ sk6 ) @ sk4 ),
inference(simp,[status(thm)],[1690]) ).
thf(2073,plain,
( ~ $true
| ~ $true
| ~ $true
| ~ $true
| $false ),
inference(rewrite,[status(thm)],[621,4,5,6,7,1691]) ).
thf(2074,plain,
$false,
inference(simp,[status(thm)],[2073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% 0.02/0.11 % Command : run_Leo-III %s %d
% 0.11/0.31 % Computer : n008.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sun May 19 18:18:09 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.94/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.10 % [INFO] Parsing done (178ms).
% 1.29/1.12 % [INFO] Running in sequential loop mode.
% 1.94/1.48 % [INFO] nitpick registered as external prover.
% 1.94/1.49 % [INFO] Scanning for conjecture ...
% 2.08/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.27/1.65 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.27/1.65 % [INFO] Problem is higher-order (TPTP THF).
% 2.27/1.65 % [INFO] Type checking passed.
% 2.27/1.65 % [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 ...
% 31.97/6.20 % [INFO] Killing All external provers ...
% 31.97/6.20 % Time passed: 5741ms (effective reasoning time: 5076ms)
% 31.97/6.21 % 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)>
% 31.97/6.21 % Axioms used in derivation (0):
% 31.97/6.21 % No. of inferences in proof: 32
% 31.97/6.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5741 ms resp. 5076 ms w/o parsing
% 32.24/6.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.24/6.38 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------