TSTP Solution File: NUM754^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM754^1 : TPTP v8.1.2. 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 7 10:45:32 EDT 2024
% Result : Theorem 5.34s 2.14s
% Output : Refutation 5.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 14
% Syntax : Number of formulae : 36 ( 12 unt; 8 typ; 0 def)
% Number of atoms : 69 ( 4 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 262 ( 25 ~; 18 |; 0 &; 204 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 54 ( 0 ^ 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(frac_type,type,
frac: $tType ).
thf(x_type,type,
x: frac ).
thf(y_type,type,
y: frac ).
thf(z_type,type,
z: frac ).
thf(u_type,type,
u: frac ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(moref_type,type,
moref: frac > frac > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(3,axiom,
eq @ x @ y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e) ).
thf(9,plain,
eq @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
moref @ z @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(10,plain,
moref @ z @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62g) ).
thf(14,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac,D: frac] :
( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[14]) ).
thf(16,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(76,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
| ( ( moref @ z @ u )
!= ( moref @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[10,16]) ).
thf(77,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( moref @ ( pf @ A @ z ) @ ( pf @ B @ u ) ) ),
inference(pattern_uni,[status(thm)],[76:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(128,plain,
! [B: frac,A: frac] :
( ( moref @ ( pf @ A @ z ) @ ( pf @ B @ u ) )
| ( ( eq @ x @ y )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[9,77]) ).
thf(129,plain,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( x )),bind(B,$thf( y ))]]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz44) ).
thf(11,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac] :
( ( eq @ A @ C )
=> ! [D: frac] :
( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[11]) ).
thf(13,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( moref @ C @ D ) ),
inference(cnf,[status(esa)],[12]) ).
thf(1,conjecture,
moref @ ( pf @ z @ x ) @ ( pf @ u @ y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz62h) ).
thf(2,negated_conjecture,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( ( moref @ C @ D )
!= ( moref @ ( pf @ z @ x ) @ ( pf @ u @ y ) ) ) ),
inference(paramod_ordered,[status(thm)],[13,8]) ).
thf(34,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ ( pf @ z @ x ) )
| ~ ( eq @ B @ ( pf @ u @ y ) ) ),
inference(pattern_uni,[status(thm)],[33:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( pf @ z @ x )),bind(D,$thf( pf @ u @ y ))]]) ).
thf(210,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ ( pf @ z @ x ) )
| ~ ( eq @ B @ ( pf @ u @ y ) )
| ( ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
!= ( moref @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[129,34]) ).
thf(211,plain,
( ~ ( eq @ ( pf @ x @ z ) @ ( pf @ z @ x ) )
| ~ ( eq @ ( pf @ y @ u ) @ ( pf @ u @ y ) ) ),
inference(pattern_uni,[status(thm)],[210:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ y @ u ))]]) ).
thf(7,axiom,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz58) ).
thf(17,plain,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
! [B: frac,A: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
inference(cnf,[status(esa)],[17]) ).
thf(263,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[211,18]) ).
thf(264,plain,
$false,
inference(simp,[status(thm)],[263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM754^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 19:42:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.88/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (113ms).
% 1.18/0.97 % [INFO] Running in sequential loop mode.
% 1.48/1.17 % [INFO] nitpick registered as external prover.
% 1.48/1.17 % [INFO] Scanning for conjecture ...
% 1.67/1.22 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.79/1.24 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.79/1.25 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/1.26 % [INFO] Type checking passed.
% 1.79/1.26 % [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 ...
% 5.34/2.14 % [INFO] Killing All external provers ...
% 5.34/2.14 % Time passed: 1612ms (effective reasoning time: 1164ms)
% 5.34/2.14 % 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)>
% 5.34/2.14 % Axioms used in derivation (5): e, satz62g, satz44, m, satz58
% 5.34/2.14 % No. of inferences in proof: 28
% 5.34/2.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1612 ms resp. 1164 ms w/o parsing
% 5.34/2.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.34/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------