TSTP Solution File: NUM739^1 by Leo-III-SAT---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM739^1 : 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 10:45:27 EDT 2024
% Result : Theorem 21.79s 4.31s
% Output : Refutation 21.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 72 ( 15 unt; 7 typ; 0 def)
% Number of atoms : 173 ( 15 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 450 ( 68 ~; 56 |; 0 &; 304 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 82 ( 0 ^ 82 !; 0 ?; 82 :)
% 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(moref_type,type,
moref: frac > frac > $o ).
thf(eq_type,type,
eq: frac > frac > $o ).
thf(4,axiom,
eq @ x @ z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(15,plain,
eq @ x @ z,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz38) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ( eq @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,plain,
! [B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ B @ A ) ),
inference(cnf,[status(esa)],[21]) ).
thf(189,plain,
! [B: frac,A: frac] :
( ( eq @ B @ A )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,22]) ).
thf(190,plain,
eq @ z @ x,
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(18,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] :
( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(miniscope,[status(thm)],[18]) ).
thf(20,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( eq @ A @ C ) ),
inference(cnf,[status(esa)],[19]) ).
thf(50,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ B @ C )
| ( eq @ A @ C )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,20]) ).
thf(51,plain,
! [A: frac] :
( ~ ( eq @ z @ A )
| ( eq @ x @ A ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(57,plain,
! [A: frac] :
( ~ ( eq @ z @ A )
| ( eq @ x @ A ) ),
inference(simp,[status(thm)],[51]) ).
thf(689,plain,
! [A: frac] :
( ( eq @ x @ A )
| ( ( eq @ z @ x )
!= ( eq @ z @ A ) ) ),
inference(paramod_ordered,[status(thm)],[190,57]) ).
thf(690,plain,
eq @ x @ x,
inference(pattern_uni,[status(thm)],[689:[bind(A,$thf( x ))]]) ).
thf(5,axiom,
eq @ y @ u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).
thf(16,plain,
eq @ y @ u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,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(23,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)],[9]) ).
thf(24,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)],[23]) ).
thf(25,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)],[24]) ).
thf(297,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ( moref @ C @ D )
| ( ( eq @ y @ u )
!= ( eq @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,25]) ).
thf(298,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ~ ( eq @ A @ B )
| ( moref @ B @ u ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( C )),bind(D,$thf( u ))]]) ).
thf(323,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ~ ( eq @ A @ B )
| ( moref @ B @ u ) ),
inference(simp,[status(thm)],[298]) ).
thf(4677,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ( moref @ B @ u )
| ( ( eq @ x @ x )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[690,323]) ).
thf(4678,plain,
( ~ ( moref @ x @ y )
| ( moref @ x @ u ) ),
inference(pattern_uni,[status(thm)],[4677:[bind(A,$thf( x )),bind(B,$thf( x ))]]) ).
thf(3,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m) ).
thf(13,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[13]) ).
thf(46,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ A @ C )
| ( ( eq @ y @ u )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,20]) ).
thf(47,plain,
! [A: frac] :
( ~ ( eq @ A @ y )
| ( eq @ A @ u ) ),
inference(pattern_uni,[status(thm)],[46:[bind(A,$thf( A )),bind(B,$thf( y )),bind(C,$thf( u ))]]) ).
thf(62,plain,
! [A: frac] :
( ( moref @ x @ y )
| ( eq @ A @ u )
| ( ( eq @ x @ y )
!= ( eq @ A @ y ) ) ),
inference(paramod_ordered,[status(thm)],[14,47]) ).
thf(63,plain,
( ( moref @ x @ y )
| ( eq @ x @ u ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( x ))]]) ).
thf(1,conjecture,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz46) ).
thf(2,negated_conjecture,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
~ ( eq @ z @ u ),
inference(cnf,[status(esa)],[10]) ).
thf(48,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( ( eq @ A @ C )
!= ( eq @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[20,11]) ).
thf(49,plain,
! [A: frac] :
( ~ ( eq @ z @ A )
| ~ ( eq @ A @ u ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( z )),bind(B,$thf( B )),bind(C,$thf( u ))]]) ).
thf(56,plain,
! [A: frac] :
( ~ ( eq @ z @ A )
| ~ ( eq @ A @ u ) ),
inference(simp,[status(thm)],[49]) ).
thf(236,plain,
! [A: frac] :
( ~ ( eq @ A @ u )
| ( ( eq @ z @ x )
!= ( eq @ z @ A ) ) ),
inference(paramod_ordered,[status(thm)],[190,56]) ).
thf(237,plain,
~ ( eq @ x @ u ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( x ))]]) ).
thf(259,plain,
( ( moref @ x @ y )
| $false ),
inference(rewrite,[status(thm)],[63,237]) ).
thf(260,plain,
moref @ x @ y,
inference(simp,[status(thm)],[259]) ).
thf(178,plain,
! [B: frac,A: frac] :
( ( eq @ B @ A )
| ( ( eq @ y @ u )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[16,22]) ).
thf(179,plain,
eq @ u @ y,
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( y )),bind(B,$thf( u ))]]) ).
thf(288,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ A @ C )
| ( moref @ C @ D )
| ( ( eq @ u @ y )
!= ( eq @ B @ D ) ) ),
inference(paramod_ordered,[status(thm)],[179,25]) ).
thf(289,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ u )
| ~ ( eq @ A @ B )
| ( moref @ B @ y ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( A )),bind(B,$thf( u )),bind(C,$thf( C )),bind(D,$thf( y ))]]) ).
thf(319,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ u )
| ~ ( eq @ A @ B )
| ( moref @ B @ y ) ),
inference(simp,[status(thm)],[289]) ).
thf(4267,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ u )
| ( moref @ B @ y )
| ( ( eq @ x @ z )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[15,319]) ).
thf(4268,plain,
( ~ ( moref @ x @ u )
| ( moref @ z @ y ) ),
inference(pattern_uni,[status(thm)],[4267:[bind(A,$thf( x )),bind(B,$thf( z ))]]) ).
thf(52,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ( eq @ A @ C )
| ( ( eq @ x @ z )
!= ( eq @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,20]) ).
thf(53,plain,
! [A: frac] :
( ~ ( eq @ A @ x )
| ( eq @ A @ z ) ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( A )),bind(B,$thf( x )),bind(C,$thf( z ))]]) ).
thf(566,plain,
! [A: frac] :
( ( eq @ A @ z )
| ( ( eq @ z @ x )
!= ( eq @ A @ x ) ) ),
inference(paramod_ordered,[status(thm)],[190,53]) ).
thf(567,plain,
eq @ z @ z,
inference(pattern_uni,[status(thm)],[566:[bind(A,$thf( z ))]]) ).
thf(4675,plain,
! [B: frac,A: frac] :
( ~ ( moref @ A @ y )
| ( moref @ B @ u )
| ( ( eq @ z @ z )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[567,323]) ).
thf(4676,plain,
( ~ ( moref @ z @ y )
| ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[4675:[bind(A,$thf( z )),bind(B,$thf( z ))]]) ).
thf(12,plain,
~ ( moref @ z @ u ),
inference(cnf,[status(esa)],[10]) ).
thf(7063,plain,
( ~ ( moref @ z @ y )
| $false ),
inference(rewrite,[status(thm)],[4676,12]) ).
thf(7064,plain,
~ ( moref @ z @ y ),
inference(simp,[status(thm)],[7063]) ).
thf(7065,plain,
( ~ ( moref @ x @ u )
| $false ),
inference(rewrite,[status(thm)],[4268,7064]) ).
thf(7066,plain,
~ ( moref @ x @ u ),
inference(simp,[status(thm)],[7065]) ).
thf(7207,plain,
( ~ $true
| $false ),
inference(rewrite,[status(thm)],[4678,260,7066]) ).
thf(7208,plain,
$false,
inference(simp,[status(thm)],[7207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM739^1 : TPTP v8.1.2. Released v3.7.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 6 19:50:39 EDT 2024
% 0.15/0.34 % CPUTime :
% 0.87/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.11/0.88 % [INFO] Parsing done (107ms).
% 1.11/0.89 % [INFO] Running in sequential loop mode.
% 1.51/1.08 % [INFO] nitpick registered as external prover.
% 1.51/1.08 % [INFO] Scanning for conjecture ...
% 1.51/1.13 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.68/1.15 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.68/1.16 % [INFO] Problem is higher-order (TPTP THF).
% 1.68/1.16 % [INFO] Type checking passed.
% 1.68/1.17 % [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 ...
% 21.79/4.30 % [INFO] Killing All external provers ...
% 21.79/4.31 % Time passed: 3799ms (effective reasoning time: 3416ms)
% 21.79/4.31 % 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)>
% 21.79/4.31 % Axioms used in derivation (6): e, f, satz39, m, satz44, satz38
% 21.79/4.31 % No. of inferences in proof: 65
% 21.79/4.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3799 ms resp. 3416 ms w/o parsing
% 21.97/4.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.97/4.40 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------