TSTP Solution File: GRP158-1 by Leo-III-SAT---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.10
% Problem : GRP158-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 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 10:33:07 EDT 2024
% Result : Unsatisfiable 18.66s 4.37s
% Output : Refutation 18.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 30 unt; 6 typ; 0 def)
% Number of atoms : 42 ( 41 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 233 ( 19 ~; 6 |; 0 &; 208 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 52 ( 0 ^ 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(c_type,type,
c: $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i ).
thf(9,axiom,
( ( greatest_lower_bound @ a @ b )
= a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_mono2b_1) ).
thf(35,plain,
( ( greatest_lower_bound @ a @ b )
= a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
( ( greatest_lower_bound @ a @ b )
= a ),
inference(lifteq,[status(thm)],[35]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( ( greatest_lower_bound @ B @ A )
= a )
| ( ( greatest_lower_bound @ a @ b )
!= ( greatest_lower_bound @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[36,42]) ).
thf(265,plain,
( ( greatest_lower_bound @ b @ a )
= a ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( ( least_upper_bound @ A @ a )
= A )
| ( ( greatest_lower_bound @ b @ a )
!= ( greatest_lower_bound @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[265,34]) ).
thf(336,plain,
( ( least_upper_bound @ b @ a )
= b ),
inference(pattern_uni,[status(thm)],[335:[bind(A,$thf( b )),bind(B,$thf( a ))]]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) )
= ( multiply @ A @ ( least_upper_bound @ B @ C ) ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[37]) ).
thf(1,negated_conjecture,
( ( greatest_lower_bound @ ( multiply @ c @ a ) @ ( multiply @ c @ b ) )
!= ( multiply @ c @ a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ax_mono2b) ).
thf(18,plain,
( ( greatest_lower_bound @ ( multiply @ c @ a ) @ ( multiply @ c @ b ) )
!= ( multiply @ c @ a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,plain,
( ( greatest_lower_bound @ ( multiply @ c @ a ) @ ( multiply @ c @ b ) )
!= ( multiply @ c @ a ) ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( greatest_lower_bound @ ( multiply @ c @ a ) @ ( multiply @ c @ b ) )
!= ( multiply @ c @ a ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A
!= ( multiply @ c @ a ) )
| ( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
!= ( greatest_lower_bound @ ( multiply @ c @ a ) @ ( multiply @ c @ b ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,20]) ).
thf(214,plain,
! [A: $i] :
( ( ( multiply @ c @ a )
!= ( multiply @ c @ a ) )
| ( ( least_upper_bound @ ( multiply @ c @ a ) @ A )
!= ( multiply @ c @ b ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(223,plain,
! [A: $i] :
( ( least_upper_bound @ ( multiply @ c @ a ) @ A )
!= ( multiply @ c @ b ) ),
inference(simp,[status(thm)],[214]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( least_upper_bound @ A @ B )
!= ( multiply @ c @ b ) )
| ( ( least_upper_bound @ B @ A )
!= ( least_upper_bound @ ( multiply @ c @ a ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[22,223]) ).
thf(232,plain,
! [A: $i] :
( ( least_upper_bound @ A @ ( multiply @ c @ a ) )
!= ( multiply @ c @ b ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( multiply @ c @ a )),bind(C,$thf( A ))]]) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ ( least_upper_bound @ B @ C ) )
!= ( multiply @ c @ b ) )
| ( ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) )
!= ( least_upper_bound @ D @ ( multiply @ c @ a ) ) ) ),
inference(paramod_ordered,[status(thm)],[48,232]) ).
thf(903,plain,
! [A: $i] :
( ( multiply @ c @ ( least_upper_bound @ A @ a ) )
!= ( multiply @ c @ b ) ),
inference(pattern_uni,[status(thm)],[902:[bind(A,$thf( c )),bind(B,$thf( F )),bind(C,$thf( a )),bind(D,$thf( multiply @ c @ F ))]]) ).
thf(920,plain,
! [A: $i] :
( ( multiply @ c @ ( least_upper_bound @ A @ a ) )
!= ( multiply @ c @ b ) ),
inference(simp,[status(thm)],[903]) ).
thf(2095,plain,
! [A: $i] :
( ( least_upper_bound @ b @ a )
!= ( least_upper_bound @ A @ a ) ),
inference(paramod_ordered,[status(thm)],[336,920]) ).
thf(2096,plain,
$false,
inference(pattern_uni,[status(thm)],[2095:[bind(A,$thf( b ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP158-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n021.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 23:52:09 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.93/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.01 % [INFO] Parsing done (149ms).
% 1.28/1.02 % [INFO] Running in sequential loop mode.
% 1.76/1.32 % [INFO] nitpick registered as external prover.
% 1.76/1.33 % [INFO] Scanning for conjecture ...
% 2.01/1.39 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.01/1.43 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.16/1.45 % [INFO] Problem is propositional (TPTP CNF).
% 2.21/1.46 % [INFO] Type checking passed.
% 2.21/1.46 % [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 ...
% 18.66/4.35 % [INFO] Killing All external provers ...
% 18.66/4.36 % Time passed: 3837ms (effective reasoning time: 3320ms)
% 18.66/4.36 % 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)>
% 18.66/4.37 % Axioms used in derivation (6): monotony_lub1, ax_mono2b_1, symmetry_of_glb, glb_absorbtion, lub_absorbtion, symmetry_of_lub
% 18.66/4.37 % No. of inferences in proof: 36
% 18.66/4.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3837 ms resp. 3320 ms w/o parsing
% 18.66/4.41 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.66/4.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------