TSTP Solution File: NUM753^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 10:45:31 EDT 2024
% Result : Theorem 11.89s 3.15s
% Output : Refutation 11.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 44 ( 14 unt; 8 typ; 0 def)
% Number of atoms : 85 ( 5 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 322 ( 33 ~; 21 |; 0 &; 250 @)
% ( 0 <=>; 18 =>; 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 : 69 ( 0 ^ 69 !; 0 ?; 69 :)
% 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 > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(8,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz56) ).
thf(20,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac,D: frac] :
( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(4,axiom,
moref @ z @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(11,plain,
moref @ z @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac] :
( ( moref @ A @ B )
=> ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62d) ).
thf(15,plain,
! [A: frac,B: frac,C: frac] :
( ( moref @ A @ B )
=> ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac] : ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) ) ),
inference(miniscope,[status(thm)],[15]) ).
thf(17,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(55,plain,
! [C: frac,B: frac,A: frac] :
( ( moref @ ( pf @ C @ A ) @ ( pf @ C @ B ) )
| ( ( moref @ z @ u )
!= ( moref @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11,17]) ).
thf(56,plain,
! [A: frac] : ( moref @ ( pf @ A @ z ) @ ( pf @ A @ u ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( z )),bind(B,$thf( u ))]]) ).
thf(61,plain,
! [A: frac] : ( moref @ ( pf @ A @ z ) @ ( pf @ A @ u ) ),
inference(simp,[status(thm)],[56]) ).
thf(7,axiom,
! [A: frac] : ( eq @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz37) ).
thf(18,plain,
! [A: frac] : ( eq @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [A: frac] : ( eq @ A @ A ),
inference(cnf,[status(esa)],[18]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz44) ).
thf(12,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( eq @ A @ C )
=> ( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac] :
( ( eq @ A @ C )
=> ! [D: frac] :
( ( eq @ B @ D )
=> ( moref @ C @ D ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( moref @ C @ D ) ),
inference(cnf,[status(esa)],[13]) ).
thf(1,conjecture,
moref @ ( pf @ x @ z ) @ ( pf @ y @ u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz62g) ).
thf(2,negated_conjecture,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ~ ( eq @ B @ D )
| ( ( moref @ C @ D )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[14,9]) ).
thf(32,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ ( pf @ x @ z ) )
| ~ ( eq @ B @ ( pf @ y @ u ) ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( pf @ x @ z )),bind(D,$thf( pf @ y @ u ))]]) ).
thf(68,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( moref @ B @ C )
| ~ ( eq @ C @ ( pf @ y @ u ) )
| ( ( eq @ A @ A )
!= ( eq @ B @ ( pf @ x @ z ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,32]) ).
thf(69,plain,
! [A: frac] :
( ~ ( moref @ ( pf @ x @ z ) @ A )
| ~ ( eq @ A @ ( pf @ y @ u ) ) ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( pf @ x @ z )),bind(B,$thf( pf @ x @ z )),bind(C,$thf( C ))]]) ).
thf(79,plain,
! [A: frac] :
( ~ ( moref @ ( pf @ x @ z ) @ A )
| ~ ( eq @ A @ ( pf @ y @ u ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(297,plain,
! [B: frac,A: frac] :
( ~ ( eq @ B @ ( pf @ y @ u ) )
| ( ( moref @ ( pf @ A @ z ) @ ( pf @ A @ u ) )
!= ( moref @ ( pf @ x @ z ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[61,79]) ).
thf(298,plain,
~ ( eq @ ( pf @ x @ u ) @ ( pf @ y @ u ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( x )),bind(B,$thf( pf @ x @ u ))]]) ).
thf(347,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq @ ( pf @ x @ u ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,298]) ).
thf(348,plain,
( ~ ( eq @ x @ y )
| ~ ( eq @ u @ u ) ),
inference(pattern_uni,[status(thm)],[347:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( u )),bind(D,$thf( u ))]]) ).
thf(3,axiom,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(10,plain,
eq @ x @ y,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(454,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[348,19,10]) ).
thf(455,plain,
$false,
inference(simp,[status(thm)],[454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : NUM753^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.13 % Command : run_Leo-III %s %d
% 0.12/0.33 % Computer : n023.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 : Mon May 6 19:27:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.93/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.94 % [INFO] Parsing done (116ms).
% 1.21/0.95 % [INFO] Running in sequential loop mode.
% 1.58/1.15 % [INFO] nitpick registered as external prover.
% 1.58/1.15 % [INFO] Scanning for conjecture ...
% 1.67/1.20 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.67/1.22 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.84/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 1.84/1.24 % [INFO] Type checking passed.
% 1.84/1.24 % [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 ...
% 11.89/3.13 % [INFO] Killing All external provers ...
% 11.89/3.15 % Time passed: 2641ms (effective reasoning time: 2187ms)
% 11.89/3.15 % 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)>
% 11.89/3.15 % Axioms used in derivation (6): e, satz62d, m, satz37, satz44, satz56
% 11.89/3.15 % No. of inferences in proof: 36
% 11.89/3.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2641 ms resp. 2187 ms w/o parsing
% 11.99/3.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.99/3.20 % [INFO] Killing All external provers ...
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