TSTP Solution File: SEV045^5 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SEV045^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 04:10:49 EDT 2024
% Result : Theorem 9.10s 2.74s
% Output : Refutation 9.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 55 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 196 ( 23 equ; 0 cnn)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 615 ( 62 ~; 49 |; 15 &; 450 @)
% ( 0 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 4 con; 0-3 aty)
% Number of variables : 115 ( 0 ^ 115 !; 0 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(g_type,type,
g: a > b ).
thf(f_type,type,
f: a > b ).
thf(cQ_type,type,
cQ: a > b > b > $o ).
thf(cP_type,type,
cP: a > a > $o ).
thf(sk1_type,type,
sk1: a ).
thf(sk2_type,type,
sk2: a ).
thf(1,conjecture,
( ! [A: a] :
( ( cP @ A @ A )
=> ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) )
=> ( ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) )
=> ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cP @ B @ A ) )
& ! [A: a,B: a,C: a] :
( ( ( cP @ A @ B )
& ( cP @ B @ C ) )
=> ( cP @ A @ C ) ) )
=> ( ( ! [A: a] :
( ( cP @ A @ A )
=> ( ! [B: b,C: b] :
( ( cQ @ A @ B @ C )
=> ( cQ @ A @ C @ B ) )
& ! [B: b,C: b,D: b] :
( ( ( cQ @ A @ B @ C )
& ( cQ @ A @ C @ D ) )
=> ( cQ @ A @ B @ D ) ) ) )
& ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( ( cQ @ A )
= ( cQ @ B ) ) ) )
=> ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cQ @ A @ ( f @ A ) @ ( g @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM509_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a] :
( ( cP @ A @ A )
=> ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) )
=> ( ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) )
=> ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cP @ B @ A ) )
& ! [A: a,B: a,C: a] :
( ( ( cP @ A @ B )
& ( cP @ B @ C ) )
=> ( cP @ A @ C ) ) )
=> ( ( ! [A: a] :
( ( cP @ A @ A )
=> ( ! [B: b,C: b] :
( ( cQ @ A @ B @ C )
=> ( cQ @ A @ C @ B ) )
& ! [B: b,C: b,D: b] :
( ( ( cQ @ A @ B @ C )
& ( cQ @ A @ C @ D ) )
=> ( cQ @ A @ B @ D ) ) ) )
& ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( ( cQ @ A )
= ( cQ @ B ) ) ) )
=> ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cQ @ A @ ( f @ A ) @ ( g @ B ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a] :
( ( cP @ A @ A )
=> ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) )
=> ( ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) )
=> ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cP @ B @ A ) )
& ! [A: a,B: a,C: a] :
( ( ( cP @ A @ B )
& ( cP @ B @ C ) )
=> ( cP @ A @ C ) ) )
=> ( ( ! [A: a] :
( ( cP @ A @ A )
=> ( ! [B: b,C: b] :
( ( cQ @ A @ B @ C )
=> ( cQ @ A @ C @ B ) )
& ! [B: b,C: b,D: b] :
( ( ( cQ @ A @ B @ C )
& ( cQ @ A @ C @ D ) )
=> ( cQ @ A @ B @ D ) ) ) )
& ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( ( cQ @ A )
= ( cQ @ B ) ) ) )
=> ! [A: a,B: a] :
( ( cP @ A @ B )
=> ( cQ @ A @ ( f @ A ) @ ( g @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
cP @ sk1 @ sk2,
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
! [B: a,A: a] :
( ~ ( cP @ A @ B )
| ( ( cQ @ A )
= ( cQ @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(14,plain,
! [B: a,A: a] :
( ( ( cQ @ A )
= ( cQ @ B ) )
| ~ ( cP @ A @ B ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(15,plain,
! [B: a,A: a] :
( ( ( cQ @ A )
= ( cQ @ B ) )
| ~ ( cP @ A @ B ) ),
inference(simp,[status(thm)],[14]) ).
thf(64,plain,
! [B: a,A: a] :
( ( ( cQ @ A )
= ( cQ @ B ) )
| ( ( cP @ sk1 @ sk2 )
!= ( cP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,15]) ).
thf(65,plain,
( ( cQ @ sk2 )
= ( cQ @ sk1 ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(71,plain,
! [B: b,A: b] :
( ( cQ @ sk2 @ A @ B )
= ( cQ @ sk1 @ A @ B ) ),
inference(func_ext,[status(esa)],[65]) ).
thf(11,plain,
! [A: a] :
( ~ ( cP @ A @ A )
| ( cQ @ A @ ( f @ A ) @ ( g @ A ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(115,plain,
! [C: a,B: b,A: b] :
( ~ ( cP @ C @ C )
| ( cQ @ sk1 @ A @ B )
| ( ( cQ @ sk2 @ A @ B )
!= ( cQ @ C @ ( f @ C ) @ ( g @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[71,11]) ).
thf(116,plain,
( ~ ( cP @ sk2 @ sk2 )
| ( cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( f @ sk2 )),bind(B,$thf( g @ sk2 )),bind(C,$thf( sk2 ))]]) ).
thf(8,plain,
! [B: a,A: a] :
( ~ ( cP @ A @ B )
| ( cP @ B @ A ) ),
inference(cnf,[status(esa)],[3]) ).
thf(18,plain,
! [B: a,A: a] :
( ~ ( cP @ A @ B )
| ( cP @ B @ A ) ),
inference(simp,[status(thm)],[8]) ).
thf(22,plain,
! [B: a,A: a] :
( ( cP @ B @ A )
| ( ( cP @ sk1 @ sk2 )
!= ( cP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,18]) ).
thf(23,plain,
cP @ sk2 @ sk1,
inference(pattern_uni,[status(thm)],[22:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(9,plain,
! [C: a,B: a,A: a] :
( ~ ( cP @ A @ B )
| ~ ( cP @ B @ C )
| ( cP @ A @ C ) ),
inference(cnf,[status(esa)],[3]) ).
thf(16,plain,
! [C: a,B: a,A: a] :
( ~ ( cP @ A @ B )
| ~ ( cP @ B @ C )
| ( cP @ A @ C ) ),
inference(simp,[status(thm)],[9]) ).
thf(228,plain,
! [C: a,B: a,A: a] :
( ~ ( cP @ A @ B )
| ( cP @ A @ C )
| ( ( cP @ sk1 @ sk2 )
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[5,16]) ).
thf(229,plain,
! [A: a] :
( ~ ( cP @ A @ sk1 )
| ( cP @ A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[228:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( sk2 ))]]) ).
thf(419,plain,
! [A: a] :
( ( cP @ A @ sk2 )
| ( ( cP @ sk2 @ sk1 )
!= ( cP @ A @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[23,229]) ).
thf(420,plain,
cP @ sk2 @ sk2,
inference(pattern_uni,[status(thm)],[419:[bind(A,$thf( sk2 ))]]) ).
thf(447,plain,
( ~ $true
| ( cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ) ) ),
inference(rewrite,[status(thm)],[116,420]) ).
thf(448,plain,
cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ),
inference(simp,[status(thm)],[447]) ).
thf(4,plain,
! [D: b,C: b,B: b,A: a] :
( ~ ( cP @ A @ A )
| ~ ( cQ @ A @ B @ C )
| ~ ( cQ @ A @ C @ D )
| ( cQ @ A @ B @ D ) ),
inference(cnf,[status(esa)],[3]) ).
thf(19,plain,
! [D: b,C: b,B: b,A: a] :
( ~ ( cP @ A @ A )
| ~ ( cQ @ A @ B @ C )
| ~ ( cQ @ A @ C @ D )
| ( cQ @ A @ B @ D ) ),
inference(simp,[status(thm)],[4]) ).
thf(7,plain,
~ ( cQ @ sk1 @ ( f @ sk1 ) @ ( g @ sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(27,plain,
! [D: b,C: b,B: b,A: a] :
( ~ ( cP @ A @ A )
| ~ ( cQ @ A @ B @ C )
| ~ ( cQ @ A @ C @ D )
| ( ( cQ @ A @ B @ D )
!= ( cQ @ sk1 @ ( f @ sk1 ) @ ( g @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,7]) ).
thf(28,plain,
! [A: b] :
( ~ ( cP @ sk1 @ sk1 )
| ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ~ ( cQ @ sk1 @ A @ ( g @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk1 )),bind(B,$thf( f @ sk1 )),bind(C,$thf( C )),bind(D,$thf( g @ sk2 ))]]) ).
thf(44,plain,
! [A: b] :
( ~ ( cP @ sk1 @ sk1 )
| ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ~ ( cQ @ sk1 @ A @ ( g @ sk2 ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(52,plain,
! [A: b] :
( ~ ( cP @ sk1 @ sk1 )
| ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
!= ( cQ @ sk1 @ ( f @ sk1 ) @ A ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[44]) ).
thf(53,plain,
! [A: b] :
( ~ ( cP @ sk1 @ sk1 )
| ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
!= ( cQ @ sk1 @ ( f @ sk1 ) @ A ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(250,plain,
! [C: a,B: a,A: a] :
( ~ ( cP @ A @ B )
| ( cP @ A @ C )
| ( ( cP @ sk2 @ sk1 )
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[23,16]) ).
thf(251,plain,
! [A: a] :
( ~ ( cP @ A @ sk2 )
| ( cP @ A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( sk1 ))]]) ).
thf(860,plain,
! [A: a] :
( ( cP @ A @ sk1 )
| ( ( cP @ sk1 @ sk2 )
!= ( cP @ A @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[5,251]) ).
thf(861,plain,
cP @ sk1 @ sk1,
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( sk1 ))]]) ).
thf(1043,plain,
! [A: b] :
( ~ $true
| ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
!= ( cQ @ sk1 @ ( f @ sk1 ) @ A ) ) ),
inference(rewrite,[status(thm)],[53,861]) ).
thf(1044,plain,
! [A: b] :
( ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ( ( cQ @ sk1 @ A @ ( g @ sk2 ) )
!= ( cQ @ sk1 @ ( f @ sk1 ) @ A ) ) ),
inference(simp,[status(thm)],[1043]) ).
thf(1073,plain,
! [A: b] :
( ~ ( cQ @ sk1 @ ( f @ sk1 ) @ A )
| ( ( cQ @ sk1 @ ( f @ sk2 ) @ ( g @ sk2 ) )
!= ( cQ @ sk1 @ A @ ( g @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[448,1044]) ).
thf(1074,plain,
~ ( cQ @ sk1 @ ( f @ sk1 ) @ ( f @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1073:[bind(A,$thf( f @ sk2 ))]]) ).
thf(10,plain,
! [B: a,A: a] :
( ~ ( cP @ A @ B )
| ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(13,plain,
! [B: a,A: a] :
( ~ ( cP @ A @ B )
| ( cQ @ A @ ( f @ A ) @ ( f @ B ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(151,plain,
! [B: a,A: a] :
( ( cQ @ A @ ( f @ A ) @ ( f @ B ) )
| ( ( cP @ sk1 @ sk2 )
!= ( cP @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[5,13]) ).
thf(152,plain,
cQ @ sk1 @ ( f @ sk1 ) @ ( f @ sk2 ),
inference(pattern_uni,[status(thm)],[151:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1182,plain,
~ $true,
inference(rewrite,[status(thm)],[1074,152]) ).
thf(1183,plain,
$false,
inference(simp,[status(thm)],[1182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEV045^5 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.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 18:50:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.89/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (109ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.56/1.19 % [INFO] nitpick registered as external prover.
% 1.56/1.19 % [INFO] Scanning for conjecture ...
% 1.72/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.97/1.28 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.97/1.29 % [INFO] Problem is higher-order (TPTP THF).
% 1.97/1.29 % [INFO] Type checking passed.
% 1.97/1.29 % [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 ...
% 9.10/2.72 % [INFO] Killing All external provers ...
% 9.10/2.73 % Time passed: 2199ms (effective reasoning time: 1740ms)
% 9.10/2.74 % 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)>
% 9.10/2.74 % Axioms used in derivation (0):
% 9.10/2.74 % No. of inferences in proof: 47
% 9.10/2.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2199 ms resp. 1740 ms w/o parsing
% 9.13/2.80 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.13/2.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------