%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GRP193-2 : 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 : n010.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 07:20:26 AM UTC 2026
% Result : Unsatisfiable 15.39s 10.76s
% Output : Refutation 13.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 114 ( 79 unt; 0 typ; 0 def)
% Number of atoms : 168 ( 167 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 727 ( 86 ~; 54 |; 0 &; 587 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 128 ( 0 ^; 128 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(greatest_lower_bound_decl,type,
greatest_lower_bound: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(least_upper_bound_decl,type,
least_upper_bound: $i > $i > $i ).
thf(identity_decl,type,
identity: $i ).
thf(inverse_decl,type,
inverse: $i > $i ).
thf(20,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(61,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)],[20]) ).
thf(16,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(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( identity @ multiply ) )
= A ),
inference(lifteq,[status(thm)],[55]) ).
thf(1,negated_conjecture,
( ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p8_9b) ).
thf(22,plain,
( ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,plain,
( ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(24,plain,
( ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(100,plain,
! [A: $i] :
( ( ( A @ ( identity @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( ( A @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,24]) ).
thf(104,plain,
! [A: $i] :
( ( A != c )
| ( identity != b )
| ( A != c )
| ( a != a ) ),
inference(simp,[status(thm)],[100]) ).
thf(109,plain,
identity != b,
inference(simp,[status(thm)],[104]) ).
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(41,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(13,axiom,
( ( b @ ( a @ greatest_lower_bound ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_4) ).
thf(47,plain,
( ( b @ ( a @ greatest_lower_bound ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(48,plain,
( ( b @ ( a @ greatest_lower_bound ) )
= identity ),
inference(lifteq,[status(thm)],[47]) ).
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(39,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(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ greatest_lower_bound ) )
!= ( B @ ( A @ greatest_lower_bound ) ) )
| ( ( identity @ ( A @ least_upper_bound ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[48,40]) ).
thf(231,plain,
( ( identity @ ( a @ least_upper_bound ) )
= a ),
inference(pattern_uni,[status(thm)],[230:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(2,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(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) )
= ( A @ ( B @ least_upper_bound ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ( ( identity @ ( a @ least_upper_bound ) )
!= ( B @ ( A @ least_upper_bound ) ) )
| ( ( A @ ( B @ least_upper_bound ) )
= a ) ),
inference(paramod_ordered,[status(thm)],[231,26]) ).
thf(266,plain,
( ( a @ ( identity @ least_upper_bound ) )
= a ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( a )),bind(B,$thf( identity ))]]) ).
thf(4,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(29,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)],[4]) ).
thf(30,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)],[29]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( a @ ( identity @ least_upper_bound ) )
!= ( B @ ( A @ least_upper_bound ) ) )
| ( ( C @ ( a @ least_upper_bound ) )
= ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[266,30]) ).
thf(362,plain,
! [A: $i] :
( ( A @ ( a @ least_upper_bound ) @ ( identity @ least_upper_bound ) )
= ( A @ ( a @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[361:[bind(A,$thf( identity )),bind(B,$thf( a ))]]) ).
thf(372,plain,
! [A: $i] :
( ( A @ ( a @ least_upper_bound ) @ ( identity @ least_upper_bound ) )
= ( A @ ( a @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[362]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ least_upper_bound ) @ ( A @ greatest_lower_bound ) )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( a @ least_upper_bound ) @ ( identity @ least_upper_bound ) )
!= ( C @ ( B @ least_upper_bound ) ) )
| ( ( A @ ( a @ least_upper_bound ) @ ( B @ greatest_lower_bound ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[372,42]) ).
thf(735,plain,
! [A: $i] :
( ( A @ ( a @ least_upper_bound ) @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(pattern_uni,[status(thm)],[734:[bind(A,$thf( E )),bind(B,$thf( identity )),bind(C,$thf( E @ ( a @ least_upper_bound ) ))]]) ).
thf(799,plain,
! [A: $i] :
( ( A @ ( a @ least_upper_bound ) @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(simp,[status(thm)],[735]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
thf(35,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( a @ least_upper_bound ) )
!= ( B @ ( A @ least_upper_bound ) ) )
| ( ( C @ ( a @ least_upper_bound ) )
= ( C @ ( B @ least_upper_bound ) @ ( A @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[231,30]) ).
thf(273,plain,
! [A: $i] :
( ( A @ ( identity @ least_upper_bound ) @ ( a @ least_upper_bound ) )
= ( A @ ( a @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( a )),bind(B,$thf( identity ))]]) ).
thf(281,plain,
! [A: $i] :
( ( A @ ( identity @ least_upper_bound ) @ ( a @ least_upper_bound ) )
= ( A @ ( a @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ greatest_lower_bound ) @ ( A @ least_upper_bound ) )
!= ( C @ ( identity @ least_upper_bound ) ) )
| ( ( A @ ( a @ least_upper_bound ) )
= ( C @ ( a @ least_upper_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,281]) ).
thf(393,plain,
! [A: $i] :
( ( A @ ( identity @ greatest_lower_bound ) @ ( a @ least_upper_bound ) )
= ( identity @ ( a @ least_upper_bound ) ) ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( identity )),bind(B,$thf( E )),bind(C,$thf( E @ ( identity @ greatest_lower_bound ) ))]]) ).
thf(428,plain,
! [A: $i] :
( ( A @ ( identity @ greatest_lower_bound ) @ ( a @ least_upper_bound ) )
= ( identity @ ( a @ least_upper_bound ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(440,plain,
! [A: $i] :
( ( A @ ( identity @ greatest_lower_bound ) @ ( a @ least_upper_bound ) )
= a ),
inference(rewrite,[status(thm)],[428,231]) ).
thf(465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( identity @ greatest_lower_bound ) @ ( a @ least_upper_bound ) )
!= ( C @ ( B @ least_upper_bound ) ) )
| ( ( B @ ( C @ least_upper_bound ) )
= a ) ),
inference(paramod_ordered,[status(thm)],[440,26]) ).
thf(466,plain,
! [A: $i] :
( ( a @ ( A @ ( identity @ greatest_lower_bound ) @ least_upper_bound ) )
= a ),
inference(pattern_uni,[status(thm)],[465:[bind(A,$thf( E )),bind(B,$thf( a )),bind(C,$thf( E @ ( identity @ greatest_lower_bound ) ))]]) ).
thf(490,plain,
! [A: $i] :
( ( a @ ( A @ ( identity @ greatest_lower_bound ) @ least_upper_bound ) )
= a ),
inference(simp,[status(thm)],[466]) ).
thf(11,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(43,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)],[11]) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( A @ inverse @ multiply ) )
= identity ),
inference(lifteq,[status(thm)],[35]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( A @ inverse @ multiply ) )
!= ( c @ ( b @ multiply ) ) )
| ( ( identity @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,24]) ).
thf(120,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ inverse )
!= b )
| ( ( identity @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(126,plain,
( ( ( c @ inverse )
!= b )
| ( ( identity @ ( a @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(860,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ least_upper_bound ) )
!= ( C @ ( a @ least_upper_bound ) ) )
| ( ( B @ ( A @ least_upper_bound ) @ ( identity @ greatest_lower_bound ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[26,799]) ).
thf(861,plain,
! [A: $i] :
( ( a @ ( A @ least_upper_bound ) @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(pattern_uni,[status(thm)],[860:[bind(A,$thf( A )),bind(B,$thf( a )),bind(C,$thf( A ))]]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ greatest_lower_bound ) )
= ( A @ ( B @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(1232,plain,
! [B: $i,A: $i] :
( ( ( b @ ( a @ greatest_lower_bound ) )
!= ( B @ ( A @ greatest_lower_bound ) ) )
| ( ( A @ ( B @ greatest_lower_bound ) )
= identity ) ),
inference(paramod_ordered,[status(thm)],[48,54]) ).
thf(1233,plain,
( ( a @ ( b @ greatest_lower_bound ) )
= identity ),
inference(pattern_uni,[status(thm)],[1232:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(8,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(37,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)],[8]) ).
thf(15,axiom,
( ( b @ ( identity @ greatest_lower_bound ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_2) ).
thf(51,plain,
( ( b @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(52,plain,
( ( b @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(lifteq,[status(thm)],[51]) ).
thf(18,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(57,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)],[18]) ).
thf(12,axiom,
( ( c @ ( a @ greatest_lower_bound ) @ ( b @ ( a @ greatest_lower_bound ) @ multiply ) @ ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) @ greatest_lower_bound ) )
= ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_5) ).
thf(45,plain,
( ( c @ ( a @ greatest_lower_bound ) @ ( b @ ( a @ greatest_lower_bound ) @ multiply ) @ ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) @ greatest_lower_bound ) )
= ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(46,plain,
( ( c @ ( a @ greatest_lower_bound ) @ ( b @ ( a @ greatest_lower_bound ) @ multiply ) @ ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) @ greatest_lower_bound ) )
= ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(44,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)],[43]) ).
thf(952,plain,
( ( c @ ( a @ greatest_lower_bound ) @ ( b @ ( a @ greatest_lower_bound ) @ multiply ) @ ( c @ ( b @ multiply ) @ greatest_lower_bound ) @ ( a @ greatest_lower_bound ) )
= ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) ) ),
inference(rewrite,[status(thm)],[46,44]) ).
thf(6,axiom,
( ( a @ ( identity @ greatest_lower_bound ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_1) ).
thf(33,plain,
( ( a @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_lub) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ least_upper_bound ) )
= A ),
inference(lifteq,[status(thm)],[27]) ).
thf(38,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)],[37]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_of_gld) ).
thf(31,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
! [A: $i] :
( ( A @ ( A @ greatest_lower_bound ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(34,plain,
( ( a @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(lifteq,[status(thm)],[33]) ).
thf(19,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(59,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)],[19]) ).
thf(14,axiom,
( ( c @ ( identity @ greatest_lower_bound ) )
= identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p8_9b_3) ).
thf(49,plain,
( ( c @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(50,plain,
( ( c @ ( identity @ greatest_lower_bound ) )
= identity ),
inference(lifteq,[status(thm)],[49]) ).
thf(92,plain,
( ( ( c @ ( b @ multiply ) @ ( a @ greatest_lower_bound ) )
!= ( b @ ( a @ greatest_lower_bound ) ) )
| ( ( c @ ( a @ greatest_lower_bound ) )
!= identity ) ),
inference(paramod_ordered,[status(thm)],[48,24]) ).
thf(95,plain,
( ( ( c @ ( b @ multiply ) )
!= b )
| ( a != a )
| ( ( c @ ( a @ greatest_lower_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[92]) ).
thf(99,plain,
( ( ( c @ ( b @ multiply ) )
!= b )
| ( ( c @ ( a @ greatest_lower_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[95]) ).
thf(174,plain,
( ( ( c @ ( identity @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) )
| ( ( c @ ( b @ multiply ) )
!= b )
| ( identity != identity ) ),
inference(paramod_ordered,[status(thm)],[50,99]) ).
thf(175,plain,
( ( ( c @ ( identity @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) )
| ( ( c @ ( b @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[174]) ).
thf(182,plain,
( ( c != c )
| ( identity != a )
| ( ( c @ ( b @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[175]) ).
thf(187,plain,
( ( identity != a )
| ( ( c @ ( b @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[182]) ).
thf(89,plain,
( ( ( c @ ( b @ multiply ) )
!= c )
| ( a != a ) ),
inference(simp,[status(thm)],[24]) ).
thf(98,plain,
( ( c @ ( b @ multiply ) )
!= c ),
inference(simp,[status(thm)],[89]) ).
thf(21,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(63,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)],[21]) ).
thf(121,plain,
! [A: $i] :
( ( A != c )
| ( ( A @ inverse )
!= b )
| ( identity != c )
| ( a != a ) ),
inference(simp,[status(thm)],[115]) ).
thf(127,plain,
( ( ( c @ inverse )
!= b )
| ( identity != c ) ),
inference(simp,[status(thm)],[121]) ).
thf(895,plain,
( ( ( a @ ( identity @ greatest_lower_bound ) )
!= ( identity @ ( a @ greatest_lower_bound ) ) )
| ( ( c @ inverse )
!= b )
| ( ( c @ ( a @ greatest_lower_bound ) )
!= identity ) ),
inference(paramod_ordered,[status(thm)],[34,126]) ).
thf(909,plain,
( ( identity != a )
| ( identity != a )
| ( ( c @ inverse )
!= b )
| ( ( c @ ( a @ greatest_lower_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[895]) ).
thf(916,plain,
( ( identity != a )
| ( ( c @ inverse )
!= b )
| ( ( c @ ( a @ greatest_lower_bound ) )
!= identity ) ),
inference(simp,[status(thm)],[909]) ).
thf(931,plain,
( ( ( c @ ( identity @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) )
| ( identity != a )
| ( ( c @ inverse )
!= b )
| ( identity != identity ) ),
inference(paramod_ordered,[status(thm)],[50,916]) ).
thf(932,plain,
( ( ( c @ ( identity @ greatest_lower_bound ) )
!= ( c @ ( a @ greatest_lower_bound ) ) )
| ( identity != a )
| ( ( c @ inverse )
!= b ) ),
inference(simp,[status(thm)],[931]) ).
thf(936,plain,
( ( c != c )
| ( identity != a )
| ( identity != a )
| ( ( c @ inverse )
!= b ) ),
inference(simp,[status(thm)],[932]) ).
thf(946,plain,
( ( identity != a )
| ( ( c @ inverse )
!= b ) ),
inference(simp,[status(thm)],[936]) ).
thf(168,plain,
( ( ( c @ ( a @ greatest_lower_bound ) )
!= ( b @ ( a @ greatest_lower_bound ) ) )
| ( ( c @ ( b @ multiply ) )
!= b )
| ( identity != identity ) ),
inference(paramod_ordered,[status(thm)],[48,99]) ).
thf(169,plain,
( ( ( c @ ( a @ greatest_lower_bound ) )
!= ( b @ ( a @ greatest_lower_bound ) ) )
| ( ( c @ ( b @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[168]) ).
thf(179,plain,
( ( c != b )
| ( a != a )
| ( ( c @ ( b @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[169]) ).
thf(186,plain,
( ( c != b )
| ( ( c @ ( b @ multiply ) )
!= b ) ),
inference(simp,[status(thm)],[179]) ).
thf(1590,plain,
$false,
inference(e,[status(thm)],[61,53,109,41,266,799,35,490,43,126,47,440,861,56,1233,42,24,37,25,52,372,57,29,952,33,28,38,45,32,34,22,44,59,281,27,54,49,187,39,98,48,63,50,127,31,231,99,40,26,946,186,55,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP193-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.11 % 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
% 0.23/5.71 % Computer : n010.cluster.edu
% 0.23/5.71 % Model : x86_64 x86_64
% 0.23/5.71 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/5.71 % Memory : 8046.5625MB
% 0.23/5.71 % OS : Linux 6.8.0-71-generic
% 0.23/5.71 % CPULimit : 300
% 0.23/5.71 % WCLimit : 300
% 0.23/5.71 % DateTime : Fri Sep 25 14:38:07 UTC 2026
% 0.23/5.71 % CPUTime :
% 0.23/5.71 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
% 1.42/6.54 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.97/6.83 % [INFO] Parsing done (287ms).
% 1.97/6.85 % [INFO] Running in sequential loop mode.
% 3.11/7.45 % [INFO] eprover registered as external prover.
% 3.11/7.46 % [INFO] Scanning for conjecture ...
% 3.31/7.59 % [INFO] Found a conjecture (or negated_conjecture) and 20 axioms. Running axiom selection ...
% 3.50/7.68 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 3.68/7.72 % [INFO] Problem is propositional (TPTP CNF).
% 3.68/7.73 % [INFO] Type checking passed.
% 3.68/7.74 % [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 ...
% 15.39/10.76 % External prover 'e' found a proof!
% 15.39/10.76 % [INFO] Killing All external provers ...
% 15.39/10.76 % Time passed: 4847ms (effective reasoning time: 3896ms)
% 15.39/10.76 % Axioms used in derivation (20): associativity, monotony_lub1, idempotence_of_lub, monotony_glb1, p8_9b_5, left_inverse, p8_9b_1, symmetry_of_glb, monotony_glb2, p8_9b_4, glb_absorbtion, idempotence_of_gld, associativity_of_glb, symmetry_of_lub, p8_9b_3, monotony_lub2, left_identity, p8_9b_2, associativity_of_lub, lub_absorbtion
% 15.39/10.76 % No. of inferences in proof: 114
% 15.39/10.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4847 ms resp. 3896 ms w/o parsing
% 13.80/10.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.80/10.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------