TSTP Solution File: SEU681^2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 03:43:19 EDT 2024
% Result : Theorem 58.59s 9.75s
% Output : Refutation 58.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 18
% Syntax : Number of formulae : 55 ( 11 unt; 14 typ; 3 def)
% Number of atoms : 145 ( 26 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 543 ( 55 ~; 45 |; 6 &; 396 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 112 ( 3 ^ 103 !; 6 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $o ).
thf(cartprodmempair1_def,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) ) ) ) ).
thf(breln_type,type,
breln: $i > $i > $i > $o ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $i > $i ).
thf(sk2_type,type,
sk2: $i > $i > $i > $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 > $o ).
thf(sk7_type,type,
sk7: $i ).
thf(1,conjecture,
( subsetE
=> ( cartprodmempair1
=> ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(2,negated_conjecture,
~ ( subsetE
=> ( cartprodmempair1
=> ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(11,plain,
subset @ sk5 @ ( cartprod @ sk3 @ sk4 ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
in @ sk7 @ sk5,
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( in @ C @ A )
| ( in @ C @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ( in @ C @ B )
| ( ( in @ sk7 @ sk5 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[9,8]) ).
thf(81,plain,
! [A: $i] :
( ~ ( subset @ sk5 @ A )
| ( in @ sk7 @ A ) ),
inference(pattern_uni,[status(thm)],[80:[bind(A,$thf( sk5 )),bind(B,$thf( B )),bind(C,$thf( sk7 ))]]) ).
thf(102,plain,
! [A: $i] :
( ~ ( subset @ sk5 @ A )
| ( in @ sk7 @ A ) ),
inference(simp,[status(thm)],[81]) ).
thf(113,plain,
! [A: $i] :
( ( in @ sk7 @ A )
| ( ( subset @ sk5 @ ( cartprod @ sk3 @ sk4 ) )
!= ( subset @ sk5 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,102]) ).
thf(114,plain,
in @ sk7 @ ( cartprod @ sk3 @ sk4 ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( cartprod @ sk3 @ sk4 ))]]) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartprod @ A @ B ) )
| ( C
= ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) )
= C )
| ~ ( in @ C @ ( cartprod @ A @ B ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) )
= C )
| ~ ( in @ C @ ( cartprod @ A @ B ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( kpair @ ( sk1 @ C @ B @ A ) @ ( sk2 @ C @ B @ A ) )
= C )
| ( ( in @ sk7 @ ( cartprod @ sk3 @ sk4 ) )
!= ( in @ C @ ( cartprod @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,15]) ).
thf(146,plain,
( ( kpair @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ ( sk2 @ sk7 @ sk4 @ sk3 ) )
= sk7 ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 )),bind(C,$thf( sk7 ))]]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ~ ( in @ ( kpair @ A @ B ) @ sk5 )
| ( sk6 @ ( kpair @ A @ B ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ~ ( in @ ( kpair @ A @ B ) @ sk5 )
| ( sk6 @ ( kpair @ A @ B ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( sk6 @ ( kpair @ A @ B ) )
| ( ( in @ ( kpair @ A @ B ) @ sk5 )
!= ( in @ sk7 @ sk5 ) ) ),
inference(paramod_ordered,[status(thm)],[9,13]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( sk6 @ ( kpair @ A @ B ) )
| ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( ( kpair @ A @ B )
!= sk7 )
| ( sk5 != sk5 ) ),
inference(simp,[status(thm)],[26]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( sk6 @ ( kpair @ A @ B ) )
| ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( ( kpair @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[37]) ).
thf(12,plain,
~ ( sk6 @ sk7 ),
inference(cnf,[status(esa)],[4]) ).
thf(3226,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( ( kpair @ A @ B )
!= sk7 )
| ( ( sk6 @ ( kpair @ A @ B ) )
!= ( sk6 @ sk7 ) ) ),
inference(paramod_ordered,[status(thm)],[43,12]) ).
thf(3333,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( ( kpair @ A @ B )
!= sk7 )
| ( ( kpair @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[3226]) ).
thf(3361,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( ( kpair @ A @ B )
!= sk7 ) ),
inference(simp,[status(thm)],[3333]) ).
thf(5566,plain,
! [B: $i,A: $i] :
( ~ ( in @ A @ sk3 )
| ~ ( in @ B @ sk4 )
| ( ( kpair @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ ( sk2 @ sk7 @ sk4 @ sk3 ) )
!= ( kpair @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[146,3361]) ).
thf(5567,plain,
( ~ ( in @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ sk3 )
| ~ ( in @ ( sk2 @ sk7 @ sk4 @ sk3 ) @ sk4 ) ),
inference(pattern_uni,[status(thm)],[5566:[bind(A,$thf( sk1 @ sk7 @ sk4 @ sk3 )),bind(B,$thf( sk2 @ sk7 @ sk4 @ sk3 ))]]) ).
thf(7,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A ) ),
inference(cnf,[status(esa)],[4]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk1 @ C @ B @ A ) @ A ) ),
inference(simp,[status(thm)],[7]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk1 @ C @ B @ A ) @ A )
| ( ( in @ sk7 @ ( cartprod @ sk3 @ sk4 ) )
!= ( in @ C @ ( cartprod @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,17]) ).
thf(363,plain,
in @ ( sk1 @ sk7 @ sk4 @ sk3 ) @ sk3,
inference(pattern_uni,[status(thm)],[362:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 )),bind(C,$thf( sk7 ))]]) ).
thf(6,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk2 @ C @ B @ A ) @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ ( cartprod @ A @ B ) )
| ( in @ ( sk2 @ C @ B @ A ) @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ ( sk2 @ C @ B @ A ) @ B )
| ( ( in @ sk7 @ ( cartprod @ sk3 @ sk4 ) )
!= ( in @ C @ ( cartprod @ A @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[114,16]) ).
thf(142,plain,
in @ ( sk2 @ sk7 @ sk4 @ sk3 ) @ sk4,
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 )),bind(C,$thf( sk7 ))]]) ).
thf(6068,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[5567,363,142]) ).
thf(6069,plain,
$false,
inference(simp,[status(thm)],[6068]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n007.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun May 19 15:32:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.99/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.07 % [INFO] Parsing done (141ms).
% 1.30/1.09 % [INFO] Running in sequential loop mode.
% 1.67/1.41 % [INFO] nitpick registered as external prover.
% 1.67/1.42 % [INFO] Scanning for conjecture ...
% 2.05/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.58 % [INFO] Type checking passed.
% 2.05/1.59 % [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 ...
% 58.59/9.73 % [INFO] Killing All external provers ...
% 58.59/9.74 % Time passed: 9250ms (effective reasoning time: 8640ms)
% 58.59/9.74 % 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)>
% 58.59/9.74 % Axioms used in derivation (0):
% 58.59/9.74 % No. of inferences in proof: 38
% 58.59/9.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9250 ms resp. 8640 ms w/o parsing
% 58.59/9.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 58.59/9.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------