%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:20:23 AM UTC 2026
% Result : Unsatisfiable 99.43s 28.10s
% Output : Refutation 100.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 16
% Syntax : Number of formulae : 189 ( 100 unt; 0 typ; 0 def)
% Number of atoms : 300 ( 299 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1879 ( 208 ~; 111 |; 0 &;1560 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 257 ( 0 ^; 257 !; 0 ?; 257 :)
% Comments :
%------------------------------------------------------------------------------
thf(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(identity_decl,type,
identity: $i ).
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(lifteq,[status(thm)],[26]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(lifteq,[status(thm)],[36]) ).
thf(253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( D @ ( C @ least_upper_bound ) ) )
| ( ( A @ ( B @ least_upper_bound ) @ ( C @ greatest_lower_bound ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[29,37]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
!= ( D @ ( C @ greatest_lower_bound ) ) )
| ( A
= ( C @ ( D @ greatest_lower_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[254,25]) ).
thf(539,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[538:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ least_upper_bound ) ))]]) ).
thf(573,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= B ),
inference(simp,[status(thm)],[539]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lub_absorbtion) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(lifteq,[status(thm)],[34]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
!= ( D @ ( C @ least_upper_bound ) ) )
| ( A
= ( C @ ( D @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,29]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ greatest_lower_bound ) ))]]) ).
thf(244,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= A ),
inference(simp,[status(thm)],[201]) ).
thf(1,negated_conjecture,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22a) ).
thf(17,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(19,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(449,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) )
| ( A
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[244,19]) ).
thf(474,plain,
! [A: $i] :
( ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( A @ ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[449]) ).
thf(497,plain,
! [A: $i] :
( ( A @ ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[474]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ least_upper_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub2) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ least_upper_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ least_upper_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(2049,plain,
! [A: $i] :
( ( A @ ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[497,49]) ).
thf(2103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( C @ ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) ) )
| ( B
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[573,2049]) ).
thf(2104,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2103:[bind(A,$thf( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) )),bind(B,$thf( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) )),bind(C,$thf( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) ))]]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_lub1) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(2311,plain,
( ( identity @ ( identity @ multiply ) @ ( b @ ( identity @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2104,45]) ).
thf(2314,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b @ ( identity @ multiply ) ) )
| ( ( identity @ ( identity @ multiply ) @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,2311]) ).
thf(2315,plain,
( ( identity @ ( identity @ multiply ) @ ( b @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2314:[bind(A,$thf( b ))]]) ).
thf(2406,plain,
( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2315,41]) ).
thf(2410,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( identity @ ( identity @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,2406]) ).
thf(2438,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ inverse )
!= a )
| ( identity != identity )
| ( identity != b ) ),
inference(simp,[status(thm)],[2410]) ).
thf(2463,plain,
( ( ( b @ inverse )
!= a )
| ( identity != b ) ),
inference(simp,[status(thm)],[2438]) ).
thf(2413,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) )
| ( ( A @ ( B @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2406]) ).
thf(2414,plain,
( ( b @ ( a @ multiply ) @ ( identity @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2413:[bind(A,$thf( b @ ( a @ multiply ) )),bind(B,$thf( identity ))]]) ).
thf(2772,plain,
( ( ( b @ ( a @ multiply ) )
!= identity )
| ( identity != b ) ),
inference(simp,[status(thm)],[2414]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiply ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( A @ multiply ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( D @ ( identity @ multiply ) )
= ( D @ ( C @ multiply ) @ ( B @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,43]) ).
thf(897,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= ( A @ ( identity @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( E )),bind(B,$thf( E @ inverse )),bind(C,$thf( E ))]]) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= ( A @ ( identity @ multiply ) ) ),
inference(simp,[status(thm)],[897]) ).
thf(2500,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[919,41]) ).
thf(2503,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[41,2500]) ).
thf(2504,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[2503:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(2886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2504,2500]) ).
thf(2887,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[2886:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity @ inverse ))]]) ).
thf(3490,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2887,2500]) ).
thf(3491,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[3490:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity @ inverse @ inverse ))]]) ).
thf(3451,plain,
! [B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ inverse @ multiply ) )
!= ( B @ ( B @ inverse @ multiply ) ) )
| ( A = identity ) ),
inference(paramod_ordered,[status(thm)],[2887,27]) ).
thf(3452,plain,
( ( identity @ inverse )
= identity ),
inference(pattern_uni,[status(thm)],[3451:[bind(A,$thf( identity @ inverse )),bind(B,$thf( identity @ inverse ))]]) ).
thf(5025,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[3491,3452]) ).
thf(2407,plain,
( ( identity != identity )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[2406]) ).
thf(2478,plain,
( ( b @ ( a @ multiply ) )
!= b ),
inference(simp,[status(thm)],[2407]) ).
thf(3485,plain,
! [A: $i] :
( ( ( A @ ( identity @ inverse @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[2887,2478]) ).
thf(3534,plain,
( ( b @ ( identity @ inverse @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) ),
inference(simp,[status(thm)],[3485]) ).
thf(4234,plain,
( ( b @ ( identity @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) ),
inference(rewrite,[status(thm)],[3534,3452]) ).
thf(2507,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( identity @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[27,2500]) ).
thf(2508,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[2507:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ inverse ))]]) ).
thf(2608,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ multiply ) )
= A ),
inference(simp,[status(thm)],[2508]) ).
thf(3015,plain,
! [A: $i] :
( ( ( identity @ ( A @ inverse @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[2608,2478]) ).
thf(3044,plain,
( ( identity != b )
| ( ( b @ inverse @ inverse )
!= a ) ),
inference(simp,[status(thm)],[3015]) ).
thf(196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) )
!= ( D @ ( C @ greatest_lower_bound ) ) )
| ( ( A @ ( B @ greatest_lower_bound ) @ ( C @ least_upper_bound ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,35]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
!= ( D @ ( C @ least_upper_bound ) ) )
| ( A
= ( C @ ( D @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[197,29]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ greatest_lower_bound ) ))]]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= B ),
inference(simp,[status(thm)],[354]) ).
thf(796,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) )
!= ( D @ ( C @ greatest_lower_bound ) ) )
| ( ( D @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[25,422]) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[796:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3019,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( A @ inverse @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[2608,2500]) ).
thf(3020,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
= identity ),
inference(pattern_uni,[status(thm)],[3019:[bind(A,$thf( E )),bind(B,$thf( identity )),bind(C,$thf( E @ inverse @ inverse ))]]) ).
thf(3088,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
= identity ),
inference(simp,[status(thm)],[3020]) ).
thf(3000,plain,
! [A: $i] :
( ( ( identity @ ( A @ inverse @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( A @ ( identity @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[2608,2414]) ).
thf(3055,plain,
! [A: $i] :
( ( identity != b )
| ( ( A @ inverse @ inverse )
!= a )
| ( A != identity )
| ( identity != b ) ),
inference(simp,[status(thm)],[3000]) ).
thf(3107,plain,
( ( ( identity @ inverse @ inverse )
!= a )
| ( identity != b ) ),
inference(simp,[status(thm)],[3055]) ).
thf(3644,plain,
( ( ( identity @ inverse )
!= a )
| ( identity != b ) ),
inference(rewrite,[status(thm)],[3107,3452]) ).
thf(56,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( A @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,19]) ).
thf(64,plain,
! [A: $i] :
( ( A
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( identity @ ( a @ least_upper_bound ) )
!= identity )
| ( ( A @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(73,plain,
( ( ( identity @ ( a @ least_upper_bound ) )
!= identity )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) )
= ( C @ ( B @ ( A @ least_upper_bound ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_lub) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) )
= ( C @ ( B @ ( A @ least_upper_bound ) @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ least_upper_bound ) @ least_upper_bound ) )
= ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(3116,plain,
( ( ( identity @ ( a @ least_upper_bound ) )
!= identity )
| ( ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[73,39,45]) ).
thf(2,axiom,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb1) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
!= ( D @ ( C @ greatest_lower_bound ) ) )
| ( A
= ( C @ ( D @ greatest_lower_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,25]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ least_upper_bound ) ))]]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= A ),
inference(simp,[status(thm)],[264]) ).
thf(2061,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( C @ ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) ) )
| ( A
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[282,2049]) ).
thf(2062,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2061:[bind(A,$thf( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) )),bind(B,$thf( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) )),bind(C,$thf( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) ))]]) ).
thf(2186,plain,
( ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2062,45]) ).
thf(2187,plain,
( ( ( identity @ ( a @ multiply ) )
!= identity )
| ( ( b @ ( a @ multiply ) )
!= ( b @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[2186]) ).
thf(2264,plain,
( ( identity @ ( a @ multiply ) )
!= identity ),
inference(simp,[status(thm)],[2187]) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(lifteq,[status(thm)],[20]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(4236,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b @ ( identity @ inverse @ multiply ) ) )
| ( A
!= ( b @ ( a @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,4234]) ).
thf(4248,plain,
( ( b @ ( identity @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) @ ( identity @ multiply ) ) ),
inference(simp,[status(thm)],[4236]) ).
thf(4725,plain,
( ( b @ ( identity @ multiply ) )
!= ( b @ ( a @ multiply ) ) ),
inference(rewrite,[status(thm)],[4248,41,3452]) ).
thf(61,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( A @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,19]) ).
thf(66,plain,
! [A: $i] :
( ( A != identity )
| ( A != b )
| ( ( A @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(75,plain,
( ( identity != b )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(3647,plain,
( ( identity != b )
| ( ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) )
!= ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[75,39,45]) ).
thf(455,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) )
!= ( D @ ( C @ greatest_lower_bound ) ) )
| ( ( C @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[25,244]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[455:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4729,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( b @ ( identity @ multiply ) ) )
| ( ( b @ ( a @ multiply ) )
!= identity ) ),
inference(paramod_ordered,[status(thm)],[27,4725]) ).
thf(4743,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ inverse )
!= identity )
| ( ( b @ ( a @ multiply ) )
!= identity ) ),
inference(simp,[status(thm)],[4729]) ).
thf(4750,plain,
( ( ( b @ inverse )
!= identity )
| ( ( b @ ( a @ multiply ) )
!= identity ) ),
inference(simp,[status(thm)],[4743]) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,19]) ).
thf(70,plain,
! [A: $i] :
( ( A
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( A @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(79,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(5263,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( identity @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[79,39,45]) ).
thf(62,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) )
| ( A
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,19]) ).
thf(72,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(80,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(81,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( A
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,80]) ).
thf(86,plain,
( ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( identity @ ( a @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[81]) ).
thf(105,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( A != identity ) ),
inference(paramod_ordered,[status(thm)],[33,86]) ).
thf(112,plain,
( ( identity != identity )
| ( identity != a )
| ( identity != identity )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[105]) ).
thf(122,plain,
( ( identity != a )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[112]) ).
thf(129,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( identity != a )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[41,122]) ).
thf(132,plain,
( ( b != b )
| ( identity != a )
| ( identity != a ) ),
inference(simp,[status(thm)],[129]) ).
thf(134,plain,
identity != a,
inference(simp,[status(thm)],[132]) ).
thf(688,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( D @ ( C @ least_upper_bound ) ) )
| ( ( C @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[29,282]) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[688:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ greatest_lower_bound ) )
= ( C @ ( B @ ( A @ greatest_lower_bound ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_glb) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ greatest_lower_bound ) )
= ( C @ ( B @ ( A @ greatest_lower_bound ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1136,plain,
( ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[80,45]) ).
thf(1786,plain,
( ( identity @ ( identity @ multiply ) @ ( identity @ ( a @ multiply ) @ least_upper_bound ) @ ( b @ ( identity @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[1136,49]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( B @ ( identity @ multiply ) ) )
| ( identity = B ) ),
inference(paramod_ordered,[status(thm)],[27,41]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( ( A @ inverse )
!= identity )
| ( identity = B ) ),
inference(simp,[status(thm)],[50]) ).
thf(54,plain,
! [A: $i] :
( ( ( A @ inverse )
!= identity )
| ( identity = A ) ),
inference(simp,[status(thm)],[52]) ).
thf(4848,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
!= ( identity @ ( a @ multiply ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[3088,2186]) ).
thf(4849,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
!= ( identity @ ( a @ multiply ) ) ),
inference(simp,[status(thm)],[4848]) ).
thf(4865,plain,
! [A: $i] :
( ( A != identity )
| ( ( A @ inverse @ inverse @ inverse )
!= a ) ),
inference(simp,[status(thm)],[4849]) ).
thf(4941,plain,
( ( identity @ inverse @ inverse @ inverse )
!= a ),
inference(simp,[status(thm)],[4865]) ).
thf(5011,plain,
( ( identity @ inverse @ inverse )
!= a ),
inference(rewrite,[status(thm)],[4941,3452]) ).
thf(71,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(2624,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ),
inference(rewrite,[status(thm)],[71,33,39]) ).
thf(1043,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( D @ ( C @ least_upper_bound ) ) )
| ( ( D @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[29,573]) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[1043:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(83,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( A @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,80]) ).
thf(88,plain,
! [A: $i] :
( ( A != identity )
| ( A != b )
| ( ( A @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(91,plain,
( ( identity != b )
| ( ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(5767,plain,
( ( identity != b )
| ( ( b @ ( identity @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[91,49]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ greatest_lower_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ greatest_lower_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ greatest_lower_bound ) )
= ( C @ ( B @ ( A @ greatest_lower_bound ) @ multiply ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ greatest_lower_bound ) @ greatest_lower_bound ) )
= ( C @ ( B @ greatest_lower_bound ) @ ( A @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(4756,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( b @ inverse )
!= identity )
| ( identity != identity ) ),
inference(paramod_ordered,[status(thm)],[27,4750]) ).
thf(4757,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( b @ inverse )
!= identity ) ),
inference(simp,[status(thm)],[4756]) ).
thf(4769,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ inverse )
!= a )
| ( ( b @ inverse )
!= identity ) ),
inference(simp,[status(thm)],[4757]) ).
thf(4777,plain,
( ( ( b @ inverse )
!= a )
| ( ( b @ inverse )
!= identity ) ),
inference(simp,[status(thm)],[4769]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,19]) ).
thf(67,plain,
! [A: $i] :
( ( A != identity )
| ( A
!= ( b @ ( a @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(76,plain,
( ( ( b @ ( a @ multiply ) )
!= identity )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(3875,plain,
( ( ( b @ ( a @ multiply ) )
!= identity )
| ( ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[76,45]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ greatest_lower_bound ) )
= ( C @ ( B @ greatest_lower_bound ) @ ( A @ multiply ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(4787,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( identity != identity )
| ( identity != b ) ),
inference(paramod_ordered,[status(thm)],[3088,2772]) ).
thf(4788,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( identity != b ) ),
inference(simp,[status(thm)],[4787]) ).
thf(4884,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ inverse @ inverse @ inverse )
!= a )
| ( identity != b ) ),
inference(simp,[status(thm)],[4788]) ).
thf(4955,plain,
( ( ( b @ inverse @ inverse @ inverse )
!= a )
| ( identity != b ) ),
inference(simp,[status(thm)],[4884]) ).
thf(82,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= identity ) ),
inference(paramod_ordered,[status(thm)],[27,80]) ).
thf(87,plain,
! [A: $i] :
( ( A
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( A @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[82]) ).
thf(90,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[87]) ).
thf(59,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( identity @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,19]) ).
thf(68,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ inverse )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( identity @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(77,plain,
( ( ( b @ inverse )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( identity @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(4274,plain,
( ( ( b @ inverse )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ least_upper_bound ) @ ( identity @ least_upper_bound ) )
!= ( identity @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[77,39,45]) ).
thf(25464,plain,
$false,
inference(e,[status(thm)],[2463,2772,41,5025,3452,4234,3044,797,42,24,3088,37,25,3644,3116,20,2049,46,29,2264,21,2414,33,28,38,197,4725,3647,456,4750,5263,134,244,45,573,689,17,32,34,22,44,27,1786,54,5011,49,2311,2478,2624,39,1044,35,48,282,5767,31,2500,43,40,2406,26,2608,23,36,30,422,4777,2186,3875,47,4955,90,254,4274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP185-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/5.52 % Computer : n020.cluster.edu
% 0.25/5.52 % Model : x86_64 x86_64
% 0.25/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.52 % Memory : 8046.5625MB
% 0.25/5.52 % OS : Linux 6.8.0-71-generic
% 0.25/5.52 % CPULimit : 300
% 0.25/5.52 % WCLimit : 300
% 0.25/5.52 % DateTime : Fri Sep 25 14:36:56 UTC 2026
% 0.25/5.52 % CPUTime :
% 0.25/5.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.37/6.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/6.65 % [INFO] Parsing done (285ms).
% 1.85/6.67 % [INFO] Running in sequential loop mode.
% 2.89/7.26 % [INFO] eprover registered as external prover.
% 2.89/7.27 % [INFO] Scanning for conjecture ...
% 3.25/7.40 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 3.25/7.49 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 3.43/7.52 % [INFO] Problem is propositional (TPTP CNF).
% 3.43/7.53 % [INFO] Type checking passed.
% 3.43/7.54 % [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 ...
% 99.43/28.09 % External prover 'e' found a proof!
% 99.43/28.10 % [INFO] Killing All external provers ...
% 99.43/28.10 % Time passed: 22371ms (effective reasoning time: 21416ms)
% 99.43/28.10 % 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
% 99.43/28.10 % No. of inferences in proof: 189
% 99.43/28.10 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 22371 ms resp. 21416 ms w/o parsing
% 100.14/28.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 100.14/28.23 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------