TSTP Solution File: GRP175-2 by Leo-III-SAT---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : GRP175-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n028.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 : Mon May 20 21:03:30 EDT 2024
% Result : Unsatisfiable 238.77s 37.02s
% Output : Refutation 238.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 62 ( 43 unt; 7 typ; 0 def)
% Number of atoms : 69 ( 68 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 361 ( 32 ~; 14 |; 0 &; 315 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 91 ( 0 ^ 91 !; 0 ?; 91 :)
% Comments :
%------------------------------------------------------------------------------
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i ).
thf(identity_type,type,
identity: $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(inverse_type,type,
inverse: $i > $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(17,axiom,
( ( greatest_lower_bound @ identity @ b )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p06b_1) ).
thf(51,plain,
( ( greatest_lower_bound @ identity @ b )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(52,plain,
( ( greatest_lower_bound @ identity @ b )
= identity ),
inference(lifteq,[status(thm)],[51]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(338,plain,
! [B: $i,A: $i] :
( ( ( greatest_lower_bound @ B @ A )
= identity )
| ( ( greatest_lower_bound @ identity @ b )
!= ( greatest_lower_bound @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52,40]) ).
thf(339,plain,
( ( greatest_lower_bound @ b @ identity )
= identity ),
inference(pattern_uni,[status(thm)],[338:[bind(A,$thf( identity )),bind(B,$thf( b ))]]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( greatest_lower_bound @ A @ B ) @ C )
= ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( greatest_lower_bound @ A @ B ) @ C )
= ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( greatest_lower_bound @ A @ B ) @ C )
= ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiply @ identity @ C )
= ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) )
| ( ( greatest_lower_bound @ b @ identity )
!= ( greatest_lower_bound @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[339,32]) ).
thf(438,plain,
! [A: $i] :
( ( greatest_lower_bound @ ( multiply @ b @ A ) @ ( multiply @ identity @ A ) )
= ( multiply @ identity @ A ) ),
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( b )),bind(B,$thf( identity ))]]) ).
thf(465,plain,
! [A: $i] :
( ( greatest_lower_bound @ ( multiply @ b @ A ) @ ( multiply @ identity @ A ) )
= ( multiply @ identity @ A ) ),
inference(simp,[status(thm)],[438]) ).
thf(12,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(41,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(42,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(33111,plain,
! [A: $i] :
( ( greatest_lower_bound @ ( multiply @ b @ A ) @ A )
= A ),
inference(rewrite,[status(thm)],[465,42]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/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(2,axiom,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
file('/export/starexec/sandbox2/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(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( least_upper_bound @ D @ C ) )
| ( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
!= ( least_upper_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[34,22]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( greatest_lower_bound @ E @ F ))]]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[157]) ).
thf(6,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(29,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(lifteq,[status(thm)],[29]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
thf(45,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)],[14]) ).
thf(46,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)],[45]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[35]) ).
thf(1,negated_conjecture,
( ( greatest_lower_bound @ identity @ ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) )
!= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p06b) ).
thf(18,plain,
( ( greatest_lower_bound @ identity @ ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) )
!= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(19,plain,
( ( greatest_lower_bound @ identity @ ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) )
!= identity ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(20,plain,
( ( greatest_lower_bound @ identity @ ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) )
!= identity ),
inference(lifteq,[status(thm)],[19]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( A != identity )
| ( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
!= ( greatest_lower_bound @ identity @ ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,20]) ).
thf(235,plain,
! [A: $i] :
( ( identity != identity )
| ( ( least_upper_bound @ identity @ A )
!= ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(242,plain,
! [A: $i] :
( ( least_upper_bound @ identity @ A )
!= ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiply @ A @ ( least_upper_bound @ B @ C ) )
!= ( multiply @ ( inverse @ a ) @ ( multiply @ b @ a ) ) )
| ( ( least_upper_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) )
!= ( least_upper_bound @ identity @ D ) ) ),
inference(paramod_ordered,[status(thm)],[46,242]) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( inverse @ a ) )
| ( ( least_upper_bound @ B @ C )
!= ( multiply @ b @ a ) )
| ( ( multiply @ A @ B )
!= identity )
| ( ( multiply @ A @ C )
!= D ) ),
inference(simp,[status(thm)],[829]) ).
thf(844,plain,
! [B: $i,A: $i] :
( ( ( least_upper_bound @ A @ B )
!= ( multiply @ b @ a ) )
| ( ( multiply @ ( inverse @ a ) @ A )
!= identity ) ),
inference(simp,[status(thm)],[832]) ).
thf(84458,plain,
! [C: $i,B: $i,A: $i] :
( ( ( least_upper_bound @ B @ C )
!= ( multiply @ b @ a ) )
| ( ( multiply @ ( inverse @ A ) @ A )
!= ( multiply @ ( inverse @ a ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,844]) ).
thf(84459,plain,
! [A: $i] :
( ( least_upper_bound @ a @ A )
!= ( multiply @ b @ a ) ),
inference(pattern_uni,[status(thm)],[84458:[bind(A,$thf( a )),bind(B,$thf( a ))]]) ).
thf(84518,plain,
! [A: $i] :
( ( least_upper_bound @ a @ A )
!= ( multiply @ b @ a ) ),
inference(simp,[status(thm)],[84459]) ).
thf(90654,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( multiply @ b @ a ) )
| ( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
!= ( least_upper_bound @ a @ C ) ) ),
inference(paramod_ordered,[status(thm)],[166,84518]) ).
thf(90768,plain,
! [B: $i,A: $i] :
( ( ( greatest_lower_bound @ ( multiply @ b @ a ) @ A )
!= a )
| ( ( multiply @ b @ a )
!= B ) ),
inference(simp,[status(thm)],[90654]) ).
thf(90861,plain,
! [A: $i] :
( ( greatest_lower_bound @ ( multiply @ b @ a ) @ A )
!= a ),
inference(simp,[status(thm)],[90768]) ).
thf(91724,plain,
! [B: $i,A: $i] :
( ( A != a )
| ( ( greatest_lower_bound @ ( multiply @ b @ A ) @ A )
!= ( greatest_lower_bound @ ( multiply @ b @ a ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33111,90861]) ).
thf(91725,plain,
a != a,
inference(pattern_uni,[status(thm)],[91724:[bind(A,$thf( a )),bind(B,$thf( a ))]]) ).
thf(91794,plain,
$false,
inference(simp,[status(thm)],[91725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP175-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n028.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Sun May 19 04:49:23 EDT 2024
% 0.16/0.36 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (132ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.73/1.24 % [INFO] nitpick registered as external prover.
% 1.73/1.25 % [INFO] Scanning for conjecture ...
% 1.73/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 1.91/1.34 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.91/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 1.91/1.36 % [INFO] Type checking passed.
% 1.91/1.36 % [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 ...
% 238.77/37.02 % [INFO] Killing All external provers ...
% 238.77/37.02 % Time passed: 36511ms (effective reasoning time: 36022ms)
% 238.77/37.02 % Axioms used in derivation (9): monotony_lub1, left_identity, left_inverse, symmetry_of_glb, monotony_glb2, glb_absorbtion, lub_absorbtion, symmetry_of_lub, p06b_1
% 238.77/37.02 % No. of inferences in proof: 55
% 238.77/37.02 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36511 ms resp. 36022 ms w/o parsing
% 238.77/37.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 238.77/37.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------