TSTP Solution File: GRP184-2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GRP184-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 12.05s 3.15s
% Output : Refutation 12.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 25
% Syntax : Number of formulae : 110 ( 72 unt; 6 typ; 0 def)
% Number of atoms : 145 ( 144 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 688 ( 73 ~; 41 |; 0 &; 574 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 143 ( 0 ^; 143 !; 0 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i ).
thf(a_type,type,
a: $i ).
thf(identity_type,type,
identity: $i ).
thf(inverse_type,type,
inverse: $i > $i ).
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i ).
thf(11,axiom,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_2) ).
thf(41,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(42,plain,
! [A: $i] :
( ( inverse @ ( inverse @ A ) )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(6,axiom,
( ( inverse @ identity )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_1) ).
thf(31,plain,
( ( inverse @ identity )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
( ( inverse @ identity )
= identity ),
inference(lifteq,[status(thm)],[31]) ).
thf(2,axiom,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(23,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [A: $i] :
( ( greatest_lower_bound @ A @ A )
= A ),
inference(lifteq,[status(thm)],[23]) ).
thf(1,negated_conjecture,
( ( multiply @ ( least_upper_bound @ a @ identity ) @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) )
!= ( multiply @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) @ ( least_upper_bound @ a @ identity ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p21) ).
thf(20,plain,
( ( multiply @ ( least_upper_bound @ a @ identity ) @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) )
!= ( multiply @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) @ ( least_upper_bound @ a @ identity ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(21,plain,
( ( multiply @ ( least_upper_bound @ a @ identity ) @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) )
!= ( multiply @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) @ ( least_upper_bound @ a @ identity ) ) ),
inference(polarity_switch,[status(thm)],[20]) ).
thf(22,plain,
( ( multiply @ ( least_upper_bound @ a @ identity ) @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) )
!= ( multiply @ ( inverse @ ( greatest_lower_bound @ a @ identity ) ) @ ( least_upper_bound @ a @ identity ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(78,plain,
( ( ( least_upper_bound @ a @ identity )
!= ( inverse @ ( greatest_lower_bound @ a @ identity ) ) )
| ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(109,plain,
( ( least_upper_bound @ a @ identity )
!= ( inverse @ ( greatest_lower_bound @ a @ identity ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(112,plain,
! [A: $i] :
( ( A
!= ( least_upper_bound @ a @ identity ) )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ ( greatest_lower_bound @ a @ identity ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,109]) ).
thf(115,plain,
( ( greatest_lower_bound @ a @ identity )
!= ( inverse @ ( least_upper_bound @ a @ identity ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(119,plain,
! [A: $i] :
( ( A
!= ( inverse @ ( least_upper_bound @ a @ identity ) ) )
| ( ( greatest_lower_bound @ A @ A )
!= ( greatest_lower_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[24,115]) ).
thf(131,plain,
( ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= a )
| ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= identity ) ),
inference(simp,[status(thm)],[119]) ).
thf(343,plain,
( ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= a )
| ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= ( inverse @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[32,131]) ).
thf(361,plain,
( ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= a )
| ( ( least_upper_bound @ a @ identity )
!= identity ) ),
inference(simp,[status(thm)],[343]) ).
thf(377,plain,
! [A: $i] :
( ( A != a )
| ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ ( least_upper_bound @ a @ identity ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,361]) ).
thf(385,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( least_upper_bound @ a @ identity )
!= ( inverse @ a ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(352,plain,
! [A: $i] :
( ( A != a )
| ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= identity )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ ( least_upper_bound @ a @ identity ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,131]) ).
thf(357,plain,
( ( ( inverse @ ( least_upper_bound @ a @ identity ) )
!= identity )
| ( ( least_upper_bound @ a @ identity )
!= ( inverse @ a ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(17,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(53,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)],[17]) ).
thf(15,axiom,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(49,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(10,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(39,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,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(35,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)],[8]) ).
thf(14,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(47,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ B )
= ( greatest_lower_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(4,axiom,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(27,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ A )
= identity ),
inference(lifteq,[status(thm)],[27]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( multiply @ A @ B )
= identity )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,28]) ).
thf(72,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= identity ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( C )),bind(B,$thf( inverse @ C ))]]) ).
thf(75,plain,
! [A: $i] :
( ( multiply @ A @ ( inverse @ A ) )
= identity ),
inference(simp,[status(thm)],[72]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21_3) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( inverse @ ( multiply @ A @ B ) )
= ( multiply @ ( inverse @ B ) @ ( inverse @ A ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( inverse @ ( multiply @ A @ B ) )
= identity )
| ( ( multiply @ ( inverse @ B ) @ ( inverse @ A ) )
!= ( multiply @ C @ ( inverse @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,75]) ).
thf(227,plain,
! [A: $i] :
( ( inverse @ ( multiply @ ( inverse @ A ) @ A ) )
= identity ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( inverse @ E )),bind(B,$thf( E )),bind(C,$thf( inverse @ E ))]]) ).
thf(269,plain,
! [A: $i] :
( ( inverse @ ( multiply @ ( inverse @ A ) @ A ) )
= identity ),
inference(simp,[status(thm)],[227]) ).
thf(9,axiom,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(37,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(38,plain,
! [A: $i] :
( ( least_upper_bound @ A @ A )
= A ),
inference(lifteq,[status(thm)],[37]) ).
thf(113,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= ( inverse @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[32,109]) ).
thf(116,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( greatest_lower_bound @ a @ identity )
!= identity ) ),
inference(simp,[status(thm)],[113]) ).
thf(120,plain,
! [A: $i] :
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( A != identity )
| ( ( greatest_lower_bound @ A @ A )
!= ( greatest_lower_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[24,116]) ).
thf(125,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( identity != a )
| ( identity != identity ) ),
inference(simp,[status(thm)],[120]) ).
thf(139,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( identity != a ) ),
inference(simp,[status(thm)],[125]) ).
thf(182,plain,
! [A: $i] :
( ( A != identity )
| ( identity != a )
| ( ( least_upper_bound @ A @ A )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[38,139]) ).
thf(184,plain,
( ( identity != a )
| ( identity != a )
| ( identity != identity ) ),
inference(simp,[status(thm)],[182]) ).
thf(185,plain,
identity != a,
inference(simp,[status(thm)],[184]) ).
thf(13,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(45,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)],[13]) ).
thf(46,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)],[45]) ).
thf(19,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(57,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)],[19]) ).
thf(5,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(29,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ B )
= ( least_upper_bound @ B @ A ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(7,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(33,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[33]) ).
thf(395,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)],[30,34]) ).
thf(396,plain,
! [B: $i,A: $i] :
( ( greatest_lower_bound @ A @ ( least_upper_bound @ B @ A ) )
= A ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(480,plain,
! [A: $i] :
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( A
!= ( inverse @ a ) )
| ( ( least_upper_bound @ A @ A )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[38,385]) ).
thf(484,plain,
( ( ( least_upper_bound @ a @ identity )
!= identity )
| ( ( inverse @ a )
!= a )
| ( ( inverse @ a )
!= identity ) ),
inference(simp,[status(thm)],[480]) ).
thf(162,plain,
! [A: $i] :
( ( A
!= ( inverse @ ( greatest_lower_bound @ a @ identity ) ) )
| ( ( least_upper_bound @ A @ A )
!= ( least_upper_bound @ a @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[38,109]) ).
thf(168,plain,
( ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= a )
| ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= identity ) ),
inference(simp,[status(thm)],[162]) ).
thf(595,plain,
( ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= a )
| ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= ( inverse @ identity ) ) ),
inference(paramod_ordered,[status(thm)],[32,168]) ).
thf(612,plain,
( ( ( inverse @ ( greatest_lower_bound @ a @ identity ) )
!= a )
| ( ( greatest_lower_bound @ a @ identity )
!= identity ) ),
inference(simp,[status(thm)],[595]) ).
thf(622,plain,
! [A: $i] :
( ( A != a )
| ( ( greatest_lower_bound @ a @ identity )
!= identity )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ ( greatest_lower_bound @ a @ identity ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,612]) ).
thf(633,plain,
( ( ( greatest_lower_bound @ a @ identity )
!= identity )
| ( ( greatest_lower_bound @ a @ identity )
!= ( inverse @ a ) ) ),
inference(simp,[status(thm)],[622]) ).
thf(50,plain,
! [A: $i] :
( ( multiply @ identity @ A )
= A ),
inference(lifteq,[status(thm)],[49]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( inverse @ A )
= ( multiply @ ( inverse @ C ) @ ( inverse @ B ) ) )
| ( ( multiply @ identity @ A )
!= ( multiply @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[50,26]) ).
thf(216,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ ( inverse @ identity ) )
= ( inverse @ A ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( A )),bind(B,$thf( identity )),bind(C,$thf( A ))]]) ).
thf(430,plain,
! [A: $i] :
( ( multiply @ ( inverse @ A ) @ identity )
= ( inverse @ A ) ),
inference(rewrite,[status(thm)],[216,32]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ( ( multiply @ A @ identity )
= ( inverse @ B ) )
| ( ( inverse @ ( inverse @ A ) )
!= ( inverse @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,430]) ).
thf(448,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= ( inverse @ ( inverse @ A ) ) ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( C )),bind(B,$thf( inverse @ C ))]]) ).
thf(463,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= ( inverse @ ( inverse @ A ) ) ),
inference(simp,[status(thm)],[448]) ).
thf(541,plain,
! [A: $i] :
( ( multiply @ A @ identity )
= A ),
inference(rewrite,[status(thm)],[463,42]) ).
thf(12,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(43,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)],[12]) ).
thf(44,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)],[43]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ A @ ( greatest_lower_bound @ A @ B ) )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(669,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)],[40,30]) ).
thf(670,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
= A ),
inference(pattern_uni,[status(thm)],[669:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( greatest_lower_bound @ E @ F ))]]) ).
thf(699,plain,
! [B: $i,A: $i] :
( ( least_upper_bound @ ( greatest_lower_bound @ A @ B ) @ A )
= A ),
inference(simp,[status(thm)],[670]) ).
thf(18,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(55,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)],[18]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( greatest_lower_bound @ ( multiply @ A @ C ) @ ( multiply @ B @ C ) )
= ( multiply @ ( greatest_lower_bound @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(16,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(51,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)],[16]) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( inverse @ A )
= ( multiply @ ( inverse @ C ) @ ( inverse @ B ) ) )
| ( ( multiply @ A @ identity )
!= ( multiply @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[541,26]) ).
thf(551,plain,
! [A: $i] :
( ( multiply @ ( inverse @ identity ) @ ( inverse @ A ) )
= ( inverse @ A ) ),
inference(pattern_uni,[status(thm)],[550:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(723,plain,
! [A: $i] :
( ( multiply @ identity @ ( inverse @ A ) )
= ( inverse @ A ) ),
inference(rewrite,[status(thm)],[551,32]) ).
thf(2300,plain,
$false,
inference(cvc4,[status(thm)],[385,357,53,109,41,49,39,35,48,75,115,269,185,42,24,37,25,20,46,57,29,396,116,33,28,38,484,361,633,541,45,32,34,22,44,27,50,31,612,43,699,40,26,55,23,36,168,30,51,723,131,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRP184-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 02:03:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (135ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 1.79/1.20 % [INFO] eprover registered as external prover.
% 1.79/1.20 % [INFO] cvc4 registered as external prover.
% 1.79/1.21 % [INFO] Scanning for conjecture ...
% 1.92/1.26 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.92/1.30 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.15/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 2.15/1.32 % [INFO] Type checking passed.
% 2.15/1.32 % [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 ...
% 12.05/3.15 % External prover 'cvc4' found a proof!
% 12.05/3.15 % [INFO] Killing All external provers ...
% 12.05/3.15 % Time passed: 2630ms (effective reasoning time: 2143ms)
% 12.05/3.15 % 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)>
% 12.05/3.15 % Axioms used in derivation (18): p21_2, associativity, monotony_lub1, idempotence_of_lub, monotony_glb1, left_inverse, monotony_glb2, glb_absorbtion, idempotence_of_gld, associativity_of_glb, p21_3, symmetry_of_lub, monotony_lub2, left_identity, p21_1, symmetry_of_glb, associativity_of_lub, lub_absorbtion
% 12.05/3.15 % No. of inferences in proof: 104
% 12.05/3.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2630 ms resp. 2143 ms w/o parsing
% 12.05/3.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.05/3.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------