%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP185-3 : 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 : n015.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 92.36s 21.92s
% Output : Refutation 92.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 177 ( 107 unt; 0 typ; 0 def)
% Number of atoms : 268 ( 267 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1704 ( 165 ~; 91 |; 0 &;1448 @)
% ( 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 : 270 ( 0 ^; 270 !; 0 ?; 270 :)
% Comments :
%------------------------------------------------------------------------------
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i ).
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(inverse_decl,type,
inverse: $i > $i ).
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(2,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(lifteq,[status(thm)],[20]) ).
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(1024,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)],[21,43]) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= ( A @ ( identity @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[1024:[bind(A,$thf( E )),bind(B,$thf( E @ inverse )),bind(C,$thf( E ))]]) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= ( A @ ( identity @ multiply ) ) ),
inference(simp,[status(thm)],[1025]) ).
thf(3331,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ multiply ) @ ( B @ inverse @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[1043,41]) ).
thf(3361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[41,3331]) ).
thf(3362,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[3361:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(3904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ multiply ) )
!= ( C @ ( B @ multiply ) ) )
| ( ( D @ ( A @ multiply ) )
= ( D @ ( C @ multiply ) @ ( B @ multiply ) ) ) ),
inference(paramod_ordered,[status(thm)],[3362,43]) ).
thf(3905,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( identity @ inverse @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
inference(pattern_uni,[status(thm)],[3904:[bind(A,$thf( A )),bind(B,$thf( identity @ inverse )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).
thf(4010,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( identity @ inverse @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
inference(simp,[status(thm)],[3905]) ).
thf(3913,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( A @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3362,3331]) ).
thf(3914,plain,
! [A: $i] :
( ( A @ ( identity @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[3913:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity @ inverse ))]]) ).
thf(4279,plain,
! [B: $i,A: $i] :
( ( ( A @ ( identity @ inverse @ inverse @ multiply ) )
!= ( B @ ( B @ inverse @ multiply ) ) )
| ( A = identity ) ),
inference(paramod_ordered,[status(thm)],[3914,21]) ).
thf(4280,plain,
( ( identity @ inverse )
= identity ),
inference(pattern_uni,[status(thm)],[4279:[bind(A,$thf( identity @ inverse )),bind(B,$thf( identity @ inverse ))]]) ).
thf(7182,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( identity @ multiply ) )
= ( B @ ( A @ multiply ) ) ),
inference(rewrite,[status(thm)],[4010,4280]) ).
thf(3,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(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(1,negated_conjecture,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p22b) ).
thf(17,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
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 ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
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 ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,19]) ).
thf(107,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( a @ multiply ) @ ( identity @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( b @ ( a @ multiply ) )),bind(B,$thf( identity ))]]) ).
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(6533,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ ( identity @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[107,49]) ).
thf(11,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(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(7,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(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(195,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)],[31,23]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ greatest_lower_bound ) ))]]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= A ),
inference(simp,[status(thm)],[196]) ).
thf(386,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)],[39,219]) ).
thf(387,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[386:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(8,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(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) ) )
| ( A
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,19]) ).
thf(252,plain,
! [A: $i] :
( ( ( A @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(257,plain,
! [A: $i] :
( ( 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)],[252]) ).
thf(10,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(36,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)],[10]) ).
thf(37,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)],[36]) ).
thf(2070,plain,
! [A: $i] :
( ( A @ ( identity @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[257,49,37]) ).
thf(2080,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
!= ( C @ ( identity @ least_upper_bound ) ) )
| ( ( A @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[31,2070]) ).
thf(2081,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2080:[bind(A,$thf( identity )),bind(B,$thf( E )),bind(C,$thf( E @ ( identity @ greatest_lower_bound ) ))]]) ).
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(2428,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2081,41,45]) ).
thf(2462,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,2428]) ).
thf(2563,plain,
! [A: $i] :
( ( A
!= ( identity @ ( a @ multiply ) ) )
| ( A
!= ( b @ ( a @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) )
!= identity )
| ( A
!= ( b @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[2462]) ).
thf(2584,plain,
( ( ( identity @ ( a @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[2563]) ).
thf(2675,plain,
! [A: $i] :
( ( ( A @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( identity @ ( a @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( A != identity ) ),
inference(paramod_ordered,[status(thm)],[29,2584]) ).
thf(2712,plain,
( ( identity != identity )
| ( identity != b )
| ( identity != b )
| ( a != a ) ),
inference(simp,[status(thm)],[2675]) ).
thf(2743,plain,
identity != b,
inference(simp,[status(thm)],[2712]) ).
thf(802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) )
!= ( C @ ( D @ greatest_lower_bound ) ) )
| ( ( C @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[39,387]) ).
thf(803,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[802:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(3357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( identity @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[21,3331]) ).
thf(3358,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[3357:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ inverse ))]]) ).
thf(3453,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ multiply ) )
= A ),
inference(simp,[status(thm)],[3358]) ).
thf(4122,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)],[3453,3331]) ).
thf(4123,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
= identity ),
inference(pattern_uni,[status(thm)],[4122:[bind(A,$thf( E )),bind(B,$thf( identity )),bind(C,$thf( E @ inverse @ inverse ))]]) ).
thf(4212,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
= identity ),
inference(simp,[status(thm)],[4123]) ).
thf(4954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ inverse @ inverse @ multiply ) )
!= ( B @ ( C @ multiply ) ) )
| ( ( identity @ ( C @ inverse @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[4212,3331]) ).
thf(4955,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ inverse @ inverse @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[4954:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ inverse @ inverse @ inverse ))]]) ).
thf(5078,plain,
! [A: $i] :
( ( identity @ ( A @ inverse @ inverse @ inverse @ inverse @ multiply ) )
= A ),
inference(simp,[status(thm)],[4955]) ).
thf(5319,plain,
! [A: $i] :
( ( A @ inverse @ inverse )
= A ),
inference(rewrite,[status(thm)],[5078,3453]) ).
thf(5320,plain,
! [A: $i] :
( ( identity @ ( A @ multiply ) )
= A ),
inference(rewrite,[status(thm)],[3453,5319]) ).
thf(242,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)],[23,33]) ).
thf(243,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[242:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(460,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)],[243,39]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[460:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ least_upper_bound ) ))]]) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= B ),
inference(simp,[status(thm)],[461]) ).
thf(1082,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)],[23,472]) ).
thf(1083,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[1082:[bind(A,$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] :
( ( ( 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)],[33,39]) ).
thf(281,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ least_upper_bound ) ))]]) ).
thf(285,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ least_upper_bound ) @ greatest_lower_bound ) )
= A ),
inference(simp,[status(thm)],[281]) ).
thf(697,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)],[23,285]) ).
thf(698,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ least_upper_bound ) @ greatest_lower_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[697:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(58,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 @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,19]) ).
thf(71,plain,
! [A: $i] :
( ( A != identity )
| ( A
!= ( b @ ( a @ multiply ) ) )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( A @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(79,plain,
( ( ( b @ ( a @ multiply ) )
!= identity )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( b @ ( a @ multiply ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[71]) ).
thf(5770,plain,
( ( ( b @ ( a @ multiply ) )
!= identity )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[79,49]) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(lifteq,[status(thm)],[24]) ).
thf(5352,plain,
( ( ( b @ ( a @ multiply ) )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) )
!= identity ) ),
inference(rewrite,[status(thm)],[2584,5320]) ).
thf(388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ greatest_lower_bound ) )
!= ( D @ ( C @ greatest_lower_bound ) ) )
| ( ( C @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[39,219]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ greatest_lower_bound ) @ least_upper_bound ) )
= B ),
inference(pattern_uni,[status(thm)],[388:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(56,plain,
! [A: $i] :
( ( ( A @ ( A @ greatest_lower_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) ) )
| ( A
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[25,19]) ).
thf(65,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(73,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(84,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)],[41,73]) ).
thf(89,plain,
( ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( identity @ ( a @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[84]) ).
thf(114,plain,
( ( identity != identity )
| ( ( b @ ( a @ multiply ) )
!= b )
| ( ( identity @ ( a @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[89]) ).
thf(144,plain,
( ( ( b @ ( a @ multiply ) )
!= b )
| ( ( identity @ ( a @ least_upper_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[114]) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ greatest_lower_bound ) @ least_upper_bound ) )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( b @ ( a @ multiply ) )
!= b )
| ( A != identity ) ),
inference(paramod_ordered,[status(thm)],[387,144]) ).
thf(834,plain,
! [A: $i] :
( ( identity != identity )
| ( ( identity @ ( A @ greatest_lower_bound ) )
!= a )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[767]) ).
thf(838,plain,
! [A: $i] :
( ( ( identity @ ( A @ greatest_lower_bound ) )
!= a )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[834]) ).
thf(5348,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( a @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2428,5320]) ).
thf(6951,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( a @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[5348,37]) ).
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(115,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)],[29,89]) ).
thf(128,plain,
( ( identity != identity )
| ( identity != a )
| ( identity != identity )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[115]) ).
thf(137,plain,
( ( identity != a )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[128]) ).
thf(147,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( b @ ( a @ multiply ) ) )
| ( identity != a )
| ( A != b ) ),
inference(paramod_ordered,[status(thm)],[41,137]) ).
thf(150,plain,
( ( b != b )
| ( identity != a )
| ( identity != a ) ),
inference(simp,[status(thm)],[147]) ).
thf(152,plain,
identity != a,
inference(simp,[status(thm)],[150]) ).
thf(5324,plain,
! [B: $i,A: $i] :
( ( ( A @ inverse @ inverse )
!= ( B @ inverse ) )
| ( ( B @ ( A @ multiply ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[5319,21]) ).
thf(5325,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= identity ),
inference(pattern_uni,[status(thm)],[5324:[bind(A,$thf( C )),bind(B,$thf( C @ inverse ))]]) ).
thf(5343,plain,
! [A: $i] :
( ( A @ inverse @ ( A @ multiply ) )
= identity ),
inference(simp,[status(thm)],[5325]) ).
thf(2457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) )
| ( ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,2428]) ).
thf(2458,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ least_upper_bound ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2457:[bind(A,$thf( b @ ( a @ multiply ) )),bind(B,$thf( identity @ ( a @ multiply ) )),bind(C,$thf( identity @ ( b @ least_upper_bound ) ))]]) ).
thf(3078,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ least_upper_bound ) )
!= identity )
| ( ( b @ ( a @ multiply ) )
!= ( b @ ( a @ multiply ) ) ) ),
inference(simp,[status(thm)],[2458]) ).
thf(3234,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ least_upper_bound ) )
!= identity ),
inference(simp,[status(thm)],[3078]) ).
thf(3725,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ least_upper_bound ) ) )
| ( ( A @ ( B @ least_upper_bound ) )
!= identity ) ),
inference(paramod_ordered,[status(thm)],[23,3234]) ).
thf(3726,plain,
( ( identity @ ( a @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ least_upper_bound ) )
!= identity ),
inference(pattern_uni,[status(thm)],[3725:[bind(A,$thf( identity @ ( a @ multiply ) )),bind(B,$thf( identity @ ( b @ least_upper_bound ) ))]]) ).
thf(3787,plain,
( ( identity @ ( a @ multiply ) @ ( identity @ least_upper_bound ) @ ( b @ least_upper_bound ) )
!= identity ),
inference(rewrite,[status(thm)],[3726,37]) ).
thf(5349,plain,
( ( a @ ( identity @ least_upper_bound ) @ ( b @ least_upper_bound ) )
!= identity ),
inference(rewrite,[status(thm)],[3787,5320]) ).
thf(5334,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ inverse @ inverse )
!= ( C @ inverse ) )
| ( ( B @ ( C @ multiply ) @ ( A @ multiply ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[5319,3331]) ).
thf(5335,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ inverse @ multiply ) @ ( B @ multiply ) )
= A ),
inference(pattern_uni,[status(thm)],[5334:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ inverse ))]]) ).
thf(5345,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ inverse @ multiply ) @ ( B @ multiply ) )
= A ),
inference(simp,[status(thm)],[5335]) ).
thf(61,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 ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,19]) ).
thf(67,plain,
! [A: $i] :
( ( A != b )
| ( ( A @ inverse )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( identity @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(75,plain,
( ( ( b @ inverse )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( identity @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(4544,plain,
( ( ( b @ inverse )
!= a )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ ( identity @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(rewrite,[status(thm)],[75,49,29]) ).
thf(5482,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( a @ ( identity @ least_upper_bound ) ) )
| ( ( A @ ( B @ least_upper_bound ) @ ( b @ least_upper_bound ) )
!= identity ) ),
inference(paramod_ordered,[status(thm)],[23,5349]) ).
thf(5483,plain,
( ( identity @ ( a @ least_upper_bound ) @ ( b @ least_upper_bound ) )
!= identity ),
inference(pattern_uni,[status(thm)],[5482:[bind(A,$thf( identity )),bind(B,$thf( a ))]]) ).
thf(9,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(34,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)],[9]) ).
thf(5,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(26,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)],[5]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ greatest_lower_bound ) @ multiply ) )
= ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( B @ ( identity @ multiply ) ) )
| ( identity = B ) ),
inference(paramod_ordered,[status(thm)],[21,41]) ).
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(2441,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ least_upper_bound ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ least_upper_bound ) ) )
| ( ( A @ ( B @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[23,2428]) ).
thf(2442,plain,
( ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ ( identity @ ( b @ least_upper_bound ) @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[2441:[bind(A,$thf( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) )),bind(B,$thf( identity @ ( b @ least_upper_bound ) ))]]) ).
thf(2763,plain,
( ( identity @ ( a @ multiply ) @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ ( identity @ least_upper_bound ) @ ( b @ least_upper_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2442,37]) ).
thf(5346,plain,
( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= ( a @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ ( identity @ least_upper_bound ) @ ( b @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[2763,5320]) ).
thf(62,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 ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,19]) ).
thf(72,plain,
! [A: $i] :
( ( A
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( identity @ ( a @ least_upper_bound ) )
!= identity )
| ( ( A @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(80,plain,
( ( ( identity @ ( a @ least_upper_bound ) )
!= identity )
| ( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(35,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)],[34]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ greatest_lower_bound ) @ 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)],[219,89]) ).
thf(396,plain,
! [A: $i] :
( ( identity != identity )
| ( ( A @ ( identity @ greatest_lower_bound ) )
!= a )
| ( identity != identity )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[360]) ).
thf(414,plain,
! [A: $i] :
( ( ( A @ ( identity @ greatest_lower_bound ) )
!= a )
| ( ( b @ ( a @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[396]) ).
thf(5351,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( a @ least_upper_bound ) )
!= identity ),
inference(rewrite,[status(thm)],[3234,5320]) ).
thf(272,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)],[39,31]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) ) )
| ( ( identity @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,19]) ).
thf(68,plain,
! [A: $i] :
( ( A
!= ( identity @ ( b @ least_upper_bound ) ) )
| ( ( A @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(76,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(4777,plain,
( ( ( identity @ ( b @ least_upper_bound ) @ inverse )
!= ( identity @ ( a @ least_upper_bound ) ) )
| ( ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) )
!= identity ) ),
inference(rewrite,[status(thm)],[76,698]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ greatest_lower_bound ) @ ( A @ multiply ) )
= ( C @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(64,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ ( a @ least_upper_bound ) @ multiply ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(3494,plain,
( ( identity @ ( b @ least_upper_bound ) @ ( identity @ multiply ) @ ( identity @ ( b @ least_upper_bound ) @ ( a @ multiply ) @ least_upper_bound ) @ ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) @ greatest_lower_bound ) )
!= ( identity @ ( b @ ( a @ multiply ) @ least_upper_bound ) ) ),
inference(rewrite,[status(thm)],[64,49,25]) ).
thf(44696,plain,
$false,
inference(e,[status(thm)],[7182,41,6533,387,31,2743,803,5320,1083,472,698,42,24,5770,37,25,5352,389,838,20,6951,46,152,29,5343,89,243,21,33,28,5349,38,4280,285,5345,4544,5483,45,17,32,34,22,44,27,54,144,49,219,39,5346,80,35,48,414,5319,43,40,26,5351,3331,23,36,30,273,4777,2070,47,3494]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP185-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.12 % 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
% 0.22/0.47 % Computer : n015.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 14:39:29 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.00/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.14 % [INFO] Parsing done (173ms).
% 1.62/1.16 % [INFO] Running in sequential loop mode.
% 2.07/1.49 % [INFO] eprover registered as external prover.
% 2.07/1.49 % [INFO] Scanning for conjecture ...
% 2.34/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.59/1.62 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.59/1.65 % [INFO] Problem is propositional (TPTP CNF).
% 2.59/1.66 % [INFO] Type checking passed.
% 2.59/1.67 % [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 ...
% 92.36/21.91 % External prover 'e' found a proof!
% 92.36/21.91 % [INFO] Killing All external provers ...
% 92.36/21.91 % Time passed: 21300ms (effective reasoning time: 20750ms)
% 92.36/21.91 % 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
% 92.36/21.91 % No. of inferences in proof: 177
% 92.36/21.92 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21300 ms resp. 20750 ms w/o parsing
% 92.36/22.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 92.36/22.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------