TSTP Solution File: NUM765^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM765^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n021.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 10:45:37 EDT 2024
% Result : Theorem 5.61s 2.29s
% Output : Refutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 6 unt; 8 typ; 0 def)
% Number of atoms : 128 ( 8 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 469 ( 57 ~; 35 |; 0 &; 346 @)
% ( 0 <=>; 31 =>; 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 : 68 ( 0 ^ 68 !; 0 ?; 68 :)
% 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 > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(8,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( ~ ( moref @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65a) ).
thf(24,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( ~ ( moref @ A @ B )
=> ( eq @ A @ B ) )
=> ( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(25,plain,
! [A: frac,B: frac] :
( ( ~ ( moref @ A @ B )
=> ( eq @ A @ B ) )
=> ! [C: frac,D: frac] :
( ( moref @ C @ D )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[24]) ).
thf(27,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[25]) ).
thf(1,conjecture,
( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz66) ).
thf(2,negated_conjecture,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ( ~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) )
=> ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
~ ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(cnf,[status(esa)],[9]) ).
thf(325,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( moref @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,11]) ).
thf(326,plain,
( ~ ( eq @ x @ y )
| ~ ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(3,axiom,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m) ).
thf(12,plain,
( ~ ( moref @ x @ y )
=> ( eq @ x @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
( ( moref @ x @ y )
| ( eq @ x @ y ) ),
inference(cnf,[status(esa)],[12]) ).
thf(4,axiom,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',n) ).
thf(14,plain,
( ~ ( moref @ z @ u )
=> ( eq @ z @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
( ( moref @ z @ u )
| ( eq @ z @ u ) ),
inference(cnf,[status(esa)],[14]) ).
thf(7,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( ~ ( moref @ C @ D )
=> ( eq @ C @ D ) )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz65b) ).
thf(20,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( moref @ A @ B )
=> ( ( ~ ( moref @ C @ D )
=> ( eq @ C @ D ) )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,plain,
! [A: frac,B: frac] :
( ( moref @ A @ B )
=> ! [C: frac,D: frac] :
( ( ~ ( moref @ C @ D )
=> ( eq @ C @ D ) )
=> ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[20]) ).
thf(22,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(75,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( eq @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[22,11]) ).
thf(76,plain,
( ~ ( moref @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(99,plain,
( ( moref @ z @ u )
| ~ ( moref @ x @ y )
| ( ( eq @ z @ u )
!= ( eq @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[15,76]) ).
thf(100,plain,
( ( moref @ z @ u )
| ~ ( moref @ x @ y ) ),
inference(pattern_uni,[status(thm)],[99:[]]) ).
thf(23,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(205,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( moref @ A @ B )
| ~ ( moref @ C @ D )
| ( ( moref @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( moref @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,11]) ).
thf(206,plain,
( ~ ( moref @ x @ y )
| ~ ( moref @ z @ u ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(238,plain,
( ~ ( moref @ x @ y )
| ( ( moref @ z @ u )
!= ( moref @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[100,206]) ).
thf(239,plain,
~ ( moref @ x @ y ),
inference(pattern_uni,[status(thm)],[238:[]]) ).
thf(258,plain,
( $false
| ( eq @ x @ y ) ),
inference(rewrite,[status(thm)],[13,239]) ).
thf(259,plain,
eq @ x @ y,
inference(simp,[status(thm)],[258]) ).
thf(6,axiom,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz56) ).
thf(17,plain,
! [A: frac,B: frac,C: frac,D: frac] :
( ( eq @ A @ B )
=> ( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac,D: frac] :
( ( eq @ C @ D )
=> ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(10,plain,
~ ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ),
inference(cnf,[status(esa)],[9]) ).
thf(32,plain,
! [D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ C @ D )
| ( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ D ) )
!= ( eq @ ( pf @ x @ z ) @ ( pf @ y @ u ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,10]) ).
thf(33,plain,
( ~ ( eq @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z )),bind(D,$thf( u ))]]) ).
thf(50,plain,
( ( moref @ x @ y )
| ~ ( eq @ z @ u )
| ( ( eq @ x @ y )
!= ( eq @ x @ y ) ) ),
inference(paramod_ordered,[status(thm)],[13,33]) ).
thf(51,plain,
( ( moref @ x @ y )
| ~ ( eq @ z @ u ) ),
inference(pattern_uni,[status(thm)],[50:[]]) ).
thf(66,plain,
( ( moref @ z @ u )
| ( moref @ x @ y )
| ( ( eq @ z @ u )
!= ( eq @ z @ u ) ) ),
inference(paramod_ordered,[status(thm)],[15,51]) ).
thf(67,plain,
( ( moref @ z @ u )
| ( moref @ x @ y ) ),
inference(pattern_uni,[status(thm)],[66:[]]) ).
thf(262,plain,
( ( moref @ z @ u )
| $false ),
inference(rewrite,[status(thm)],[67,239]) ).
thf(263,plain,
moref @ z @ u,
inference(simp,[status(thm)],[262]) ).
thf(358,plain,
( ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[326,259,263]) ).
thf(359,plain,
$false,
inference(simp,[status(thm)],[358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : NUM765^1 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n021.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Mon May 6 19:29:09 EDT 2024
% 0.17/0.38 % CPUTime :
% 1.02/0.92 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.05 % [INFO] Parsing done (135ms).
% 1.23/1.06 % [INFO] Running in sequential loop mode.
% 1.70/1.26 % [INFO] nitpick registered as external prover.
% 1.70/1.26 % [INFO] Scanning for conjecture ...
% 1.70/1.31 % [INFO] Found a conjecture and 6 axioms. Running axiom selection ...
% 1.93/1.33 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 1.93/1.35 % [INFO] Problem is higher-order (TPTP THF).
% 1.93/1.36 % [INFO] Type checking passed.
% 1.93/1.36 % [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 ...
% 5.61/2.28 % [INFO] Killing All external provers ...
% 5.61/2.28 % Time passed: 1738ms (effective reasoning time: 1218ms)
% 5.61/2.29 % 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)>
% 5.61/2.29 % Axioms used in derivation (5): satz65b, n, m, satz65a, satz56
% 5.61/2.29 % No. of inferences in proof: 46
% 5.61/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1738 ms resp. 1218 ms w/o parsing
% 5.61/2.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.61/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------