TSTP Solution File: SEU492^1 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU492^1 : TPTP v8.2.0. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 03:37:48 EDT 2024
% Result : Theorem 15.22s 4.59s
% Output : Refutation 15.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 26
% Syntax : Number of formulae : 94 ( 30 unt; 22 typ; 3 def)
% Number of atoms : 214 ( 51 equ; 0 cnn)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 602 ( 123 ~; 58 |; 24 &; 362 @)
% ( 0 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 19 con; 0-2 aty)
% Number of variables : 123 ( 23 ^ 100 !; 0 ?; 123 :)
% Comments :
%------------------------------------------------------------------------------
thf(irrefl_type,type,
irrefl: ( $i > $i > $o ) > $o ).
thf(irrefl_def,definition,
( irrefl
= ( ^ [A: $i > $i > $o] :
! [B: $i] :
~ ( A @ B @ B ) ) ) ).
thf(trans_type,type,
trans: ( $i > $i > $o ) > $o ).
thf(trans_def,definition,
( trans
= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ).
thf(so_type,type,
so: ( $i > $i > $o ) > $o ).
thf(so_def,definition,
( so
= ( ^ [A: $i > $i > $o] :
( ( asymm @ A )
& ( trans @ A ) ) ) ) ).
thf(sk1_type,type,
sk1: $i > $i > $o ).
thf(sk2_type,type,
sk2: $i > $i > $o ).
thf(sk3_type,type,
sk3: $i > $i > $o ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(sk6_type,type,
sk6: $i ).
thf(sk7_type,type,
sk7: $i ).
thf(sk8_type,type,
sk8: $i ).
thf(sk9_type,type,
sk9: $i ).
thf(sk10_type,type,
sk10: $i ).
thf(sk11_type,type,
sk11: $i ).
thf(sk12_type,type,
sk12: $i ).
thf(sk14_type,type,
sk14: $i ).
thf(sk16_type,type,
sk16: $i ).
thf(sk17_type,type,
sk17: $i ).
thf(sk18_type,type,
sk18: $i ).
thf(sk19_type,type,
sk19: $i ).
thf(sk20_type,type,
sk20: $i ).
thf(sk21_type,type,
sk21: $i ).
thf(1,conjecture,
( so
= ( ^ [A: $i > $i > $o] :
( ( irrefl @ A )
& ( trans @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',alternative_definition_of_strict_order) ).
thf(2,negated_conjecture,
( so
!= ( ^ [A: $i > $i > $o] :
( ( irrefl @ A )
& ( trans @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ^ [A: $i > $i > $o] :
( ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) )
!= ( ^ [A: $i > $i > $o] :
( ! [B: $i] :
~ ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i > $i > $o] :
( ! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) )
!= ( ^ [A: $i > $i > $o] :
( ! [B: $i] :
~ ( A @ B @ B )
& ! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(5,plain,
( ( ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) )
!= ( ^ [A: $i > $i > $o] :
! [B: $i] :
~ ( A @ B @ B ) ) )
| ( ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) )
!= ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i,D: $i] :
( ( ( A @ B @ C )
& ( A @ C @ D ) )
=> ( A @ B @ D ) ) ) ) ),
inference(simp,[status(thm)],[4]) ).
thf(7,plain,
( ( ^ [A: $i > $i > $o] :
! [B: $i,C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) )
!= ( ^ [A: $i > $i > $o] :
! [B: $i] :
~ ( A @ B @ B ) ) ),
inference(simp,[status(thm)],[5]) ).
thf(8,plain,
( ( ^ [A: $i > $i > $o,B: $i] :
! [C: $i] :
( ( A @ B @ C )
=> ~ ( A @ C @ B ) ) )
!= ( ^ [A: $i > $i > $o,B: $i] :
~ ( A @ B @ B ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) )
!= ( ~ ( sk3 @ sk4 @ sk4 ) ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(18,plain,
( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(21,plain,
! [A: $i] :
( ~ ( sk3 @ sk4 @ sk4 )
| ~ ( sk3 @ sk4 @ A )
| ~ ( sk3 @ A @ sk4 ) ),
inference(cnf,[status(esa)],[18]) ).
thf(176,plain,
! [A: $i] :
( ~ ( sk3 @ sk4 @ sk4 )
| ~ ( sk3 @ A @ sk4 )
| ( ( sk3 @ sk4 @ A )
!= ( sk3 @ sk4 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[21]) ).
thf(179,plain,
( ~ ( sk3 @ sk4 @ sk4 )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( sk4 ))]]) ).
thf(184,plain,
~ ( sk3 @ sk4 @ sk4 ),
inference(simp,[status(thm)],[179]) ).
thf(189,plain,
( ( ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) )
!= ~ $false ),
inference(rewrite,[status(thm)],[10,184]) ).
thf(190,plain,
~ ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ),
inference(simp,[status(thm)],[189]) ).
thf(195,plain,
sk3 @ sk21 @ sk4,
inference(cnf,[status(esa)],[190]) ).
thf(209,plain,
( ( sk3 @ sk21 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ),
inference(paramod_ordered,[status(thm)],[195,184]) ).
thf(210,plain,
( ( sk21 != sk4 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[209]) ).
thf(211,plain,
sk21 != sk4,
inference(simp,[status(thm)],[210]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) ) )
!= ( ! [A: $i] :
~ ( sk2 @ A @ A ) ) ),
inference(func_ext,[status(esa)],[7]) ).
thf(13,plain,
( ! [A: $i,B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) )
| ! [A: $i] :
~ ( sk2 @ A @ A ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk2 @ C @ C )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ B @ A ) ),
inference(cnf,[status(esa)],[13]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sk2 @ C @ C )
| ~ ( sk2 @ A @ B )
| ( ( sk2 @ B @ A )
!= ( sk2 @ C @ C ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[16]) ).
thf(126,plain,
! [A: $i] :
( ~ ( sk2 @ A @ A )
| ~ ( sk2 @ A @ A ) ),
inference(pattern_uni,[status(thm)],[123:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(133,plain,
! [A: $i] :
~ ( sk2 @ A @ A ),
inference(simp,[status(thm)],[126]) ).
thf(6,plain,
( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) )
!= ( ! [A: $i] :
~ ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ),
inference(func_ext,[status(esa)],[4]) ).
thf(36,plain,
( ( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) )
!= ( ! [A: $i] :
~ ( sk1 @ A @ A ) ) )
| ( ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) )
!= ( ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ) ),
inference(simp,[status(thm)],[6]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) )
!= ( ! [A: $i] :
~ ( sk1 @ A @ A ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(67,plain,
( ~ ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) )
| ~ ! [A: $i] :
~ ( sk1 @ A @ A ) ),
inference(bool_ext,[status(thm)],[39]) ).
thf(69,plain,
( ( sk1 @ sk20 @ sk20 )
| ( sk1 @ sk19 @ sk18 ) ),
inference(cnf,[status(esa)],[67]) ).
thf(107,plain,
( ( sk1 @ sk19 @ sk18 )
| ( ( sk1 @ sk20 @ sk20 )
!= ( sk1 @ sk19 @ sk18 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[69]) ).
thf(109,plain,
( ( sk1 @ sk19 @ sk18 )
| ( sk20 != sk19 )
| ( sk20 != sk18 ) ),
inference(simp,[status(thm)],[107]) ).
thf(12,plain,
( ~ ! [A: $i,B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) )
| ~ ! [A: $i] :
~ ( sk2 @ A @ A ) ),
inference(bool_ext,[status(thm)],[9]) ).
thf(14,plain,
( ( sk2 @ sk7 @ sk7 )
| ( sk2 @ sk6 @ sk5 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(135,plain,
( $false
| ( sk2 @ sk6 @ sk5 ) ),
inference(rewrite,[status(thm)],[14,133]) ).
thf(136,plain,
sk2 @ sk6 @ sk5,
inference(simp,[status(thm)],[135]) ).
thf(139,plain,
! [A: $i] :
( ( sk2 @ sk6 @ sk5 )
!= ( sk2 @ A @ A ) ),
inference(paramod_ordered,[status(thm)],[136,133]) ).
thf(145,plain,
! [A: $i] :
( ( sk6 != A )
| ( sk5 != A ) ),
inference(simp,[status(thm)],[139]) ).
thf(148,plain,
sk6 != sk5,
inference(simp,[status(thm)],[145]) ).
thf(17,plain,
( ~ ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) )
| ~ ~ ( sk3 @ sk4 @ sk4 ) ),
inference(bool_ext,[status(thm)],[10]) ).
thf(19,plain,
( ( sk3 @ sk4 @ sk4 )
| ( sk3 @ sk8 @ sk4 ) ),
inference(cnf,[status(esa)],[17]) ).
thf(193,plain,
( $false
| ( sk3 @ sk8 @ sk4 ) ),
inference(rewrite,[status(thm)],[19,184]) ).
thf(194,plain,
sk3 @ sk8 @ sk4,
inference(simp,[status(thm)],[193]) ).
thf(11,plain,
( ( ^ [A: $i] :
! [B: $i] :
( ( sk2 @ A @ B )
=> ~ ( sk2 @ B @ A ) ) )
!= ( ^ [A: $i] :
~ ( sk2 @ A @ A ) ) ),
inference(simp,[status(thm)],[9]) ).
thf(37,plain,
( ~ ( ! [A: $i,B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) )
| ~ ( ! [A: $i] :
~ ( sk1 @ A @ A )
& ! [A: $i,B: $i,C: $i] :
( ( ( sk1 @ A @ B )
& ( sk1 @ B @ C ) )
=> ( sk1 @ A @ C ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(40,plain,
( ( sk1 @ sk14 @ sk14 )
| ( sk1 @ sk16 @ sk17 )
| ( sk1 @ sk9 @ sk10 )
| ( sk1 @ sk11 @ sk12 ) ),
inference(cnf,[status(esa)],[37]) ).
thf(15,plain,
( ( sk2 @ sk7 @ sk7 )
| ( sk2 @ sk5 @ sk6 ) ),
inference(cnf,[status(esa)],[12]) ).
thf(137,plain,
( $false
| ( sk2 @ sk5 @ sk6 ) ),
inference(rewrite,[status(thm)],[15,133]) ).
thf(138,plain,
sk2 @ sk5 @ sk6,
inference(simp,[status(thm)],[137]) ).
thf(29,plain,
( ( sk3 @ sk4 @ sk4 )
| ( ( sk3 @ sk8 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(32,plain,
( ( sk3 @ sk4 @ sk4 )
| ( sk8 != sk4 )
| ( sk4 != sk4 ) ),
inference(simp,[status(thm)],[29]) ).
thf(33,plain,
( ( sk3 @ sk4 @ sk4 )
| ( sk8 != sk4 ) ),
inference(simp,[status(thm)],[32]) ).
thf(72,plain,
( ( sk8 != sk4 )
| ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[33,10]) ).
thf(73,plain,
( ( sk8 != sk4 )
| ! [A: $i] :
( ( sk3 @ sk4 @ A )
=> ~ ( sk3 @ A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[72:[]]) ).
thf(74,plain,
! [A: $i] :
( ~ ( sk3 @ sk4 @ A )
| ~ ( sk3 @ A @ sk4 )
| ( sk8 != sk4 ) ),
inference(cnf,[status(esa)],[73]) ).
thf(86,plain,
! [A: $i] :
( ( sk8 != sk4 )
| ~ ( sk3 @ A @ sk4 )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33,74]) ).
thf(87,plain,
( ( sk8 != sk4 )
| ~ ( sk3 @ sk4 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( sk4 ))]]) ).
thf(100,plain,
( ( sk8 != sk4 )
| ( ( sk3 @ sk4 @ sk4 )
!= ( sk3 @ sk4 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[33,87]) ).
thf(101,plain,
sk8 != sk4,
inference(pattern_uni,[status(thm)],[100:[]]) ).
thf(196,plain,
sk3 @ sk4 @ sk21,
inference(cnf,[status(esa)],[190]) ).
thf(70,plain,
( ( sk1 @ sk20 @ sk20 )
| ( sk1 @ sk18 @ sk19 ) ),
inference(cnf,[status(esa)],[67]) ).
thf(20,plain,
( ( sk3 @ sk4 @ sk4 )
| ( sk3 @ sk4 @ sk8 ) ),
inference(cnf,[status(esa)],[17]) ).
thf(191,plain,
( $false
| ( sk3 @ sk4 @ sk8 ) ),
inference(rewrite,[status(thm)],[20,184]) ).
thf(192,plain,
sk3 @ sk4 @ sk8,
inference(simp,[status(thm)],[191]) ).
thf(163,plain,
( ( sk1 @ sk18 @ sk19 )
| ( ( sk1 @ sk20 @ sk20 )
!= ( sk1 @ sk18 @ sk19 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[70]) ).
thf(165,plain,
( ( sk1 @ sk18 @ sk19 )
| ( sk20 != sk18 )
| ( sk20 != sk19 ) ),
inference(simp,[status(thm)],[163]) ).
thf(66,plain,
( ( ^ [A: $i] :
! [B: $i] :
( ( sk1 @ A @ B )
=> ~ ( sk1 @ B @ A ) ) )
!= ( ^ [A: $i] :
~ ( sk1 @ A @ A ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(108,plain,
( ( sk1 @ sk19 @ sk18 )
| ( ( sk1 @ sk20 @ sk20 )
!= ( sk1 @ sk19 @ sk18 ) ) ),
inference(simp,[status(thm)],[107]) ).
thf(254,plain,
$false,
inference(e,[status(thm)],[211,133,6,9,109,148,3,194,16,11,40,8,69,138,101,184,196,70,192,165,7,39,66,108,4,136,195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SEU492^1 : TPTP v8.2.0. Released v3.6.0.
% 0.05/0.14 % Command : run_Leo-III %s %d
% 0.12/0.34 % Computer : n012.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 17:15:09 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.83/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.02 % [INFO] Parsing done (172ms).
% 1.21/1.03 % [INFO] Running in sequential loop mode.
% 1.77/1.29 % [INFO] eprover registered as external prover.
% 1.77/1.29 % [INFO] cvc4 registered as external prover.
% 1.77/1.30 % [INFO] Scanning for conjecture ...
% 2.10/1.45 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.48 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.48 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.48 % [INFO] Type checking passed.
% 2.10/1.48 % [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 ...
% 15.22/4.58 % External prover 'e' found a proof!
% 15.22/4.58 % [INFO] Killing All external provers ...
% 15.22/4.59 % Time passed: 4103ms (effective reasoning time: 3556ms)
% 15.22/4.59 % 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)>
% 15.22/4.59 % Axioms used in derivation (0):
% 15.22/4.59 % No. of inferences in proof: 69
% 15.22/4.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4103 ms resp. 3556 ms w/o parsing
% 15.22/4.64 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.22/4.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------