TSTP Solution File: NUM759^1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : NUM759^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 10:45:34 EDT 2024
% Result : Theorem 9.46s 2.98s
% Output : Refutation 9.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 13 unt; 6 typ; 0 def)
% Number of atoms : 63 ( 5 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 243 ( 16 ~; 14 |; 0 &; 204 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 ^ 54 !; 1 ?; 55 :)
% 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(eq_type,type,
eq: frac > frac > $o ).
thf(pf_type,type,
pf: frac > frac > frac ).
thf(6,axiom,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz58) ).
thf(15,plain,
! [A: frac,B: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(16,plain,
! [B: frac,A: frac] : ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) ),
inference(cnf,[status(esa)],[15]) ).
thf(3,axiom,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(8,plain,
eq @ ( pf @ z @ x ) @ ( pf @ z @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(12,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ A @ B )
=> ( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,plain,
! [A: frac,B: frac] :
( ( eq @ A @ B )
=> ! [C: frac] :
( ( eq @ B @ C )
=> ( eq @ A @ C ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ A @ B )
| ~ ( eq @ B @ C )
| ( eq @ A @ C ) ),
inference(cnf,[status(esa)],[13]) ).
thf(31,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ B @ C )
| ( eq @ A @ C )
| ( ( eq @ ( pf @ z @ x ) @ ( pf @ z @ y ) )
!= ( eq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[8,14]) ).
thf(32,plain,
! [A: frac] :
( ~ ( eq @ ( pf @ z @ y ) @ A )
| ( eq @ ( pf @ z @ x ) @ A ) ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( pf @ z @ x )),bind(B,$thf( pf @ z @ y )),bind(C,$thf( C ))]]) ).
thf(37,plain,
! [A: frac] :
( ~ ( eq @ ( pf @ z @ y ) @ A )
| ( eq @ ( pf @ z @ x ) @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(346,plain,
! [C: frac,B: frac,A: frac] :
( ( eq @ ( pf @ z @ x ) @ C )
| ( ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) )
!= ( eq @ ( pf @ z @ y ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[16,37]) ).
thf(347,plain,
eq @ ( pf @ z @ x ) @ ( pf @ y @ z ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( z )),bind(B,$thf( y )),bind(C,$thf( pf @ y @ z ))]]) ).
thf(27,plain,
! [E: frac,D: frac,C: frac,B: frac,A: frac] :
( ~ ( eq @ D @ E )
| ( eq @ C @ E )
| ( ( eq @ ( pf @ A @ B ) @ ( pf @ B @ A ) )
!= ( eq @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[16,14]) ).
thf(28,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ ( pf @ B @ C ) @ A )
| ( eq @ ( pf @ C @ B ) @ A ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( pf @ I @ H )),bind(D,$thf( pf @ H @ I )),bind(E,$thf( E ))]]) ).
thf(41,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ ( pf @ B @ C ) @ A )
| ( eq @ ( pf @ C @ B ) @ A ) ),
inference(simp,[status(thm)],[28]) ).
thf(722,plain,
! [C: frac,B: frac,A: frac] :
( ( eq @ ( pf @ C @ B ) @ A )
| ( ( eq @ ( pf @ z @ x ) @ ( pf @ y @ z ) )
!= ( eq @ ( pf @ B @ C ) @ A ) ) ),
inference(paramod_ordered,[status(thm)],[347,41]) ).
thf(723,plain,
eq @ ( pf @ x @ z ) @ ( pf @ y @ z ),
inference(pattern_uni,[status(thm)],[722:[bind(A,$thf( pf @ y @ z )),bind(B,$thf( z )),bind(C,$thf( x ))]]) ).
thf(4,axiom,
! [A: frac,B: frac,C: frac] :
( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
=> ( eq @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63b) ).
thf(9,plain,
! [A: frac,B: frac,C: frac] :
( ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
=> ( eq @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,plain,
! [A: frac,B: frac] :
( ? [C: frac] : ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
=> ( eq @ A @ B ) ),
inference(miniscope,[status(thm)],[9]) ).
thf(11,plain,
! [C: frac,B: frac,A: frac] :
( ~ ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) )
| ( eq @ A @ B ) ),
inference(cnf,[status(esa)],[10]) ).
thf(807,plain,
! [C: frac,B: frac,A: frac] :
( ( eq @ A @ B )
| ( ( eq @ ( pf @ x @ z ) @ ( pf @ y @ z ) )
!= ( eq @ ( pf @ A @ C ) @ ( pf @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[723,11]) ).
thf(808,plain,
eq @ x @ y,
inference(pattern_uni,[status(thm)],[807:[bind(A,$thf( x )),bind(B,$thf( y )),bind(C,$thf( z ))]]) ).
thf(1,conjecture,
eq @ x @ y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz63e) ).
thf(2,negated_conjecture,
~ ( eq @ x @ y ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( eq @ x @ y ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(869,plain,
$false,
inference(rewrite,[status(thm)],[808,7]) ).
thf(870,plain,
$false,
inference(simp,[status(thm)],[869]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM759^1 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n025.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Mon May 6 20:01:24 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.09/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.37/1.09 % [INFO] Parsing done (146ms).
% 1.37/1.10 % [INFO] Running in sequential loop mode.
% 1.82/1.34 % [INFO] nitpick registered as external prover.
% 1.82/1.34 % [INFO] Scanning for conjecture ...
% 1.99/1.39 % [INFO] Found a conjecture and 4 axioms. Running axiom selection ...
% 1.99/1.41 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.99/1.43 % [INFO] Problem is higher-order (TPTP THF).
% 1.99/1.43 % [INFO] Type checking passed.
% 1.99/1.43 % [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 ...
% 9.46/2.97 % [INFO] Killing All external provers ...
% 9.46/2.97 % Time passed: 2426ms (effective reasoning time: 1871ms)
% 9.46/2.97 % 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)>
% 9.46/2.98 % Axioms used in derivation (4): satz58, e, satz39, satz63b
% 9.46/2.98 % No. of inferences in proof: 30
% 9.46/2.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2426 ms resp. 1871 ms w/o parsing
% 9.46/3.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.46/3.06 % [INFO] Killing All external provers ...
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