TSTP Solution File: GRP185-3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP185-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 : Fri May 19 11:13:26 EDT 2023
% Result : Unsatisfiable 51.65s 10.43s
% Output : Refutation 51.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 23
% Syntax : Number of formulae : 105 ( 65 unt; 7 typ; 0 def)
% Number of atoms : 148 ( 147 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 741 ( 76 ~; 50 |; 0 &; 615 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 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 : 184 ( 0 ^; 184 !; 0 ?; 184 :)
% Comments :
%------------------------------------------------------------------------------
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i ).
thf(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(identity_type,type,
identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(3,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(22,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(8,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(32,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( greatest_lower_bound @ C @ ( least_upper_bound @ B @ A ) )
= C )
| ( ( least_upper_bound @ A @ B )
!= ( least_upper_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,33]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
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(38,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(39,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( greatest_lower_bound @ D @ C ) )
| ( ( greatest_lower_bound @ A @ ( least_upper_bound @ B @ A ) )
!= ( greatest_lower_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[243,39]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ ( least_upper_bound @ A @ B ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[460:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( least_upper_bound @ E @ F ))]]) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ ( least_upper_bound @ A @ B ) @ B )
= B ),
inference(simp,[status(thm)],[461]) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( greatest_lower_bound @ ( least_upper_bound @ B @ A ) @ D )
= D )
| ( ( least_upper_bound @ A @ B )
!= ( least_upper_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,472]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ ( least_upper_bound @ B @ A ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[1082:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( greatest_lower_bound @ D @ C ) )
| ( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
!= ( greatest_lower_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[33,39]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ ( least_upper_bound @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( least_upper_bound @ E @ F ))]]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ ( least_upper_bound @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[281]) ).
thf(12,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(40,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( greatest_lower_bound @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( greatest_lower_bound @ ( greatest_lower_bound @ A @ B ) @ C )
= ( greatest_lower_bound @ A @ ( greatest_lower_bound @ B @ C ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(7,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(30,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( multiply @ A @ B ) @ C )
= ( multiply @ A @ ( multiply @ B @ C ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ A @ ( greatest_lower_bound @ B @ C ) )
= ( greatest_lower_bound @ ( multiply @ A @ B ) @ ( multiply @ A @ C ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(195,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)],[31,23]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( greatest_lower_bound @ E @ F ))]]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[196]) ).
thf(386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( least_upper_bound @ ( greatest_lower_bound @ B @ A ) @ C )
= C )
| ( ( greatest_lower_bound @ A @ B )
!= ( greatest_lower_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[39,219]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ B @ A ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[386:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( least_upper_bound @ ( greatest_lower_bound @ B @ A ) @ C )
= C )
| ( ( greatest_lower_bound @ A @ B )
!= ( greatest_lower_bound @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[39,387]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ B @ A ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[802:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(697,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( greatest_lower_bound @ ( least_upper_bound @ B @ A ) @ C )
= C )
| ( ( least_upper_bound @ A @ B )
!= ( least_upper_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[23,285]) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ ( least_upper_bound @ B @ A ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[697:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(24,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( least_upper_bound @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( least_upper_bound @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( least_upper_bound @ A @ ( least_upper_bound @ B @ C ) )
= ( least_upper_bound @ ( least_upper_bound @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( least_upper_bound @ ( least_upper_bound @ A @ B ) @ C )
= ( least_upper_bound @ A @ ( least_upper_bound @ B @ C ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(25,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ C )
= C )
| ( ( greatest_lower_bound @ B @ A )
!= ( greatest_lower_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[39,219]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ B )
= B ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(1,negated_conjecture,
( ( greatest_lower_bound @ ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) @ ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) ) )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22b) ).
thf(17,plain,
( ( greatest_lower_bound @ ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) @ ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) ) )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,plain,
( ( greatest_lower_bound @ ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) @ ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) ) )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(19,plain,
( ( greatest_lower_bound @ ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) @ ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) ) )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(56,plain,
! [A: $i] :
( ( A
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) )
| ( ( greatest_lower_bound @ A @ A )
!= ( greatest_lower_bound @ ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) @ ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(65,plain,
( ( ( least_upper_bound @ ( multiply @ a @ b ) @ identity )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) )
| ( ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(73,plain,
( ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) )
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) ),
inference(simp,[status(thm)],[65]) ).
thf(84,plain,
! [A: $i] :
( ( A
!= ( least_upper_bound @ ( multiply @ a @ b ) @ identity ) )
| ( ( multiply @ identity @ A )
!= ( multiply @ ( least_upper_bound @ a @ identity ) @ ( least_upper_bound @ b @ identity ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,73]) ).
thf(89,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( least_upper_bound @ ( multiply @ a @ b ) @ identity )
!= ( least_upper_bound @ b @ identity ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(114,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( multiply @ a @ b )
!= b )
| ( identity != identity ) ),
inference(simp,[status(thm)],[89]) ).
thf(144,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( multiply @ a @ b )
!= b ) ),
inference(simp,[status(thm)],[114]) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( A != identity )
| ( ( multiply @ a @ b )
!= b )
| ( ( least_upper_bound @ ( greatest_lower_bound @ B @ A ) @ A )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[387,144]) ).
thf(834,plain,
! [A: $i] :
( ( ( multiply @ a @ b )
!= b )
| ( ( greatest_lower_bound @ A @ identity )
!= a )
| ( identity != identity ) ),
inference(simp,[status(thm)],[767]) ).
thf(838,plain,
! [A: $i] :
( ( ( multiply @ a @ b )
!= b )
| ( ( greatest_lower_bound @ A @ identity )
!= a ) ),
inference(simp,[status(thm)],[834]) ).
thf(2,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(20,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(28,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(115,plain,
! [A: $i] :
( ( A != identity )
| ( ( least_upper_bound @ ( multiply @ a @ b ) @ identity )
!= ( least_upper_bound @ b @ identity ) )
| ( ( least_upper_bound @ A @ A )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[29,89]) ).
thf(128,plain,
( ( ( multiply @ a @ b )
!= b )
| ( identity != identity )
| ( identity != a )
| ( identity != identity ) ),
inference(simp,[status(thm)],[115]) ).
thf(137,plain,
( ( ( multiply @ a @ b )
!= b )
| ( identity != a ) ),
inference(simp,[status(thm)],[128]) ).
thf(147,plain,
! [A: $i] :
( ( A != b )
| ( identity != a )
| ( ( multiply @ identity @ A )
!= ( multiply @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[41,137]) ).
thf(150,plain,
( ( identity != a )
| ( identity != a )
| ( b != b ) ),
inference(simp,[status(thm)],[147]) ).
thf(152,plain,
identity != a,
inference(simp,[status(thm)],[150]) ).
thf(21,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(lifteq,[status(thm)],[20]) ).
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(44,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(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(lifteq,[status(thm)],[44]) ).
thf(5,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(26,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)],[5]) ).
thf(27,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)],[26]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( identity = B )
| ( ( multiply @ ( inverse @ A ) @ A )
!= ( multiply @ identity @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,41]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( identity = B )
| ( ( inverse @ A )
!= identity )
| ( A != B ) ),
inference(simp,[status(thm)],[50]) ).
thf(54,plain,
! [A: $i] :
( ( identity = A )
| ( ( inverse @ A )
!= identity ) ),
inference(simp,[status(thm)],[52]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( least_upper_bound @ A @ B ) @ C )
= ( least_upper_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( least_upper_bound @ A @ B ) @ C )
= ( least_upper_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( multiply @ ( least_upper_bound @ A @ B ) @ C )
= ( least_upper_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(117,plain,
! [A: $i] :
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( least_upper_bound @ identity @ identity )
!= ( least_upper_bound @ b @ identity ) )
| ( ( multiply @ ( inverse @ A ) @ A )
!= ( multiply @ a @ b ) ) ),
inference(paramod_ordered,[status(thm)],[21,89]) ).
thf(133,plain,
! [A: $i] :
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( identity != b )
| ( identity != identity )
| ( ( inverse @ A )
!= a )
| ( A != b ) ),
inference(simp,[status(thm)],[117]) ).
thf(140,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( identity != b )
| ( ( inverse @ b )
!= a ) ),
inference(simp,[status(thm)],[133]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( A != identity )
| ( ( least_upper_bound @ ( multiply @ a @ b ) @ identity )
!= ( least_upper_bound @ b @ identity ) )
| ( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[219,89]) ).
thf(396,plain,
! [A: $i] :
( ( ( multiply @ a @ b )
!= b )
| ( identity != identity )
| ( ( greatest_lower_bound @ identity @ A )
!= a )
| ( identity != identity ) ),
inference(simp,[status(thm)],[360]) ).
thf(414,plain,
! [A: $i] :
( ( ( multiply @ a @ b )
!= b )
| ( ( greatest_lower_bound @ identity @ A )
!= a ) ),
inference(simp,[status(thm)],[396]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( least_upper_bound @ C @ ( greatest_lower_bound @ B @ A ) )
= C )
| ( ( greatest_lower_bound @ A @ B )
!= ( greatest_lower_bound @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[39,31]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(30540,plain,
$false,
inference(e,[status(thm)],[1083,285,41,35,31,43,47,803,472,698,42,24,37,25,389,838,20,46,152,29,89,243,21,33,28,38,45,17,32,34,22,44,27,54,144,49,219,39,387,140,48,414,40,26,23,36,30,273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP185-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.10/0.12 % Command : run_Leo-III %s %d
% 0.12/0.30 % Computer : n032.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8042.1875MB
% 0.12/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Fri May 19 01:39:20 EDT 2023
% 0.12/0.31 % CPUTime :
% 0.81/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.13/0.95 % [INFO] Parsing done (140ms).
% 1.13/0.96 % [INFO] Running in sequential loop mode.
% 1.67/1.21 % [INFO] eprover registered as external prover.
% 1.67/1.21 % [INFO] cvc4 registered as external prover.
% 1.67/1.21 % [INFO] Scanning for conjecture ...
% 1.74/1.27 % [INFO] Found a conjecture and 15 axioms. Running axiom selection ...
% 1.74/1.31 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 1.96/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 1.96/1.33 % [INFO] Type checking passed.
% 1.96/1.33 % [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 ...
% 51.65/10.43 % External prover 'e' found a proof!
% 51.65/10.43 % [INFO] Killing All external provers ...
% 51.65/10.43 % Time passed: 9989ms (effective reasoning time: 9467ms)
% 51.65/10.43 % 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)>
% 51.65/10.43 % Axioms used in derivation (15): associativity, monotony_lub1, idempotence_of_lub, monotony_glb1, left_inverse, symmetry_of_glb, monotony_glb2, glb_absorbtion, idempotence_of_gld, associativity_of_glb, symmetry_of_lub, monotony_lub2, left_identity, associativity_of_lub, lub_absorbtion
% 51.65/10.43 % No. of inferences in proof: 98
% 51.65/10.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9989 ms resp. 9467 ms w/o parsing
% 51.65/10.48 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 51.65/10.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------