%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n007.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 07:31:40 AM UTC 2026
% Result : Unsatisfiable 21.32s 5.72s
% Output : Refutation 21.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 103 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 358 ( 89 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1058 ( 204 ~; 183 |; 0 &; 671 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 264 ( 0 ^; 264 !; 0 ?; 264 :)
% Comments :
%------------------------------------------------------------------------------
thf(idQa_decl,type,
idQa: $i ).
thf(idQa_Q__idQ_idQa_decl,type,
idQa_Q__idQ_idQa: $i ).
thf(less_equal_decl,type,
less_equal: $i > $i > $o ).
thf(quotient_decl,type,
quotient: $i > $i > $i > $o ).
thf(zero_decl,type,
zero: $i ).
thf(identity_decl,type,
identity: $i ).
thf(divide_decl,type,
divide: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(idQ_idQa_decl,type,
idQ_idQa: $i ).
thf(1,negated_conjecture,
idQa != idQa_Q__idQ_idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_idQa_equals_idQa_Q__idQ_idQa) ).
thf(14,plain,
idQa != idQa_Q__idQ_idQa,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,axiom,
idQ_idQa @ ( idQa @ ( identity @ quotient ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQa) ).
thf(35,plain,
idQ_idQa @ ( idQa @ ( identity @ quotient ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
thf(23,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(64,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( idQ_idQa @ ( idQa @ ( identity @ quotient ) ) )
!= ( H @ ( D @ ( C @ quotient ) ) ) )
| ( H @ ( G @ less_equal ) )
| ~ $true
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(paramod_ordered,[status(thm)],[35,24]) ).
thf(65,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( idQ_idQa @ ( idQa @ ( identity @ quotient ) ) )
!= ( H @ ( D @ ( C @ quotient ) ) ) )
| ( H @ ( G @ less_equal ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( idQ_idQa @ ( E @ less_equal ) )
| ~ ( E @ ( C @ ( D @ quotient ) ) )
| ~ ( D @ ( idQa @ ( A @ quotient ) ) )
| ~ ( C @ ( idQa @ ( B @ quotient ) ) )
| ~ ( identity @ ( B @ ( A @ quotient ) ) ) ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( identity )),bind(D,$thf( idQa )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( idQ_idQa ))]]) ).
thf(102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( idQ_idQa @ ( E @ less_equal ) )
| ~ ( E @ ( C @ ( D @ quotient ) ) )
| ~ ( D @ ( idQa @ ( A @ quotient ) ) )
| ~ ( C @ ( idQa @ ( B @ quotient ) ) )
| ~ ( identity @ ( B @ ( A @ quotient ) ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ less_equal ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divisor_existence) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ less_equal ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ less_equal ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
thf(25,plain,
! [A: $i] : ( A @ ( zero @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
idQa_Q__idQ_idQa @ ( idQ_idQa @ ( idQa @ quotient ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_idQ_idQa) ).
thf(36,plain,
idQa_Q__idQ_idQa @ ( idQ_idQa @ ( idQa @ quotient ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(885,plain,
! [C: $i,B: $i,A: $i] :
( ( ( idQa_Q__idQ_idQa @ ( idQ_idQa @ ( idQa @ quotient ) ) )
!= ( C @ ( B @ ( A @ quotient ) ) ) )
| ( A @ ( C @ less_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,22]) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ( ( idQa_Q__idQ_idQa @ ( idQ_idQa @ ( idQa @ quotient ) ) )
!= ( C @ ( B @ ( A @ quotient ) ) ) )
| ( A @ ( C @ less_equal ) ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
idQa @ ( idQa_Q__idQ_idQa @ less_equal ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( idQa )),bind(B,$thf( idQ_idQa )),bind(C,$thf( idQa_Q__idQ_idQa ))]]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_equal ) )
| ~ ( B @ ( A @ less_equal ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(1791,plain,
! [B: $i,A: $i] :
( ( ( idQa @ ( idQa_Q__idQ_idQa @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ~ ( A @ ( B @ less_equal ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[887,28]) ).
thf(1792,plain,
! [B: $i,A: $i] :
( ( ( idQa @ ( idQa_Q__idQ_idQa @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ~ ( A @ ( B @ less_equal ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1791]) ).
thf(1793,plain,
( ~ ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) )
| ( idQa_Q__idQ_idQa = idQa ) ),
inference(pattern_uni,[status(thm)],[1792:[bind(A,$thf( idQa_Q__idQ_idQa )),bind(B,$thf( idQa ))]]) ).
thf(15,plain,
idQa != idQa_Q__idQ_idQa,
inference(polarity_switch,[status(thm)],[14]) ).
thf(16,plain,
idQa_Q__idQ_idQa != idQa,
inference(lifteq,[status(thm)],[15]) ).
thf(2132,plain,
~ ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ),
inference(simplifyReflect,[status(thm)],[1793,16]) ).
thf(2137,plain,
! [A: $i] :
( ( ( A @ ( zero @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,2132]) ).
thf(2138,plain,
! [A: $i] :
( ( A @ ( zero @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2163,plain,
! [A: $i] :
( ( A != idQa_Q__idQ_idQa )
| ( zero != idQa ) ),
inference(simp,[status(thm)],[2138]) ).
thf(2166,plain,
zero != idQa,
inference(simp,[status(thm)],[2163]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal) ).
thf(17,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ ( A @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(895,plain,
! [B: $i,A: $i] :
( ( ( idQa @ ( idQa_Q__idQ_idQa @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ( zero @ ( B @ ( A @ quotient ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[887,18]) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( ( idQa @ ( idQa_Q__idQ_idQa @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ( zero @ ( B @ ( A @ quotient ) ) ) ),
inference(simp,[status(thm)],[895]) ).
thf(897,plain,
zero @ ( idQa @ ( idQa_Q__idQ_idQa @ quotient ) ),
inference(pattern_uni,[status(thm)],[896:[bind(A,$thf( idQa_Q__idQ_idQa )),bind(B,$thf( idQa ))]]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_quotient) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ less_equal ) )
| ~ ( zero @ ( B @ ( A @ quotient ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( ( idQa_Q__idQ_idQa @ ( idQ_idQa @ ( idQa @ quotient ) ) )
!= ( zero @ ( B @ ( A @ quotient ) ) ) )
| ( B @ ( A @ less_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[36,20]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( ( idQa_Q__idQ_idQa @ ( idQ_idQa @ ( idQa @ quotient ) ) )
!= ( zero @ ( B @ ( A @ quotient ) ) ) )
| ( B @ ( A @ less_equal ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( zero != idQa_Q__idQ_idQa )
| ( idQ_idQa != B )
| ( idQa != A )
| ( B @ ( A @ less_equal ) ) ),
inference(simp,[status(thm)],[354]) ).
thf(364,plain,
( ( zero != idQa_Q__idQ_idQa )
| ( idQ_idQa @ ( idQa @ less_equal ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( ( idQ_idQa @ ( idQa @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ( zero @ ( B @ ( A @ quotient ) ) )
| ~ $true
| ( zero != idQa_Q__idQ_idQa ) ),
inference(paramod_ordered,[status(thm)],[364,18]) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( ( idQ_idQa @ ( idQa @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ( zero @ ( B @ ( A @ quotient ) ) )
| ( zero != idQa_Q__idQ_idQa ) ),
inference(simp,[status(thm)],[780]) ).
thf(782,plain,
( ( zero @ ( idQ_idQa @ ( idQa @ quotient ) ) )
| ( zero != idQa_Q__idQ_idQa ) ),
inference(pattern_uni,[status(thm)],[781:[bind(A,$thf( idQa )),bind(B,$thf( idQ_idQa ))]]) ).
thf(8,axiom,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_is_largest) ).
thf(29,plain,
! [A: $i] : ( identity @ ( A @ less_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( A @ less_equal ) )
!= ( C @ ( B @ less_equal ) ) )
| ( zero @ ( C @ ( B @ quotient ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,18]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( identity @ ( A @ less_equal ) )
!= ( C @ ( B @ less_equal ) ) )
| ( zero @ ( C @ ( B @ quotient ) ) ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
! [A: $i] : ( zero @ ( identity @ ( A @ quotient ) ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( identity ))]]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ less_equal ) )
!= ( C @ ( B @ less_equal ) ) )
| ( zero @ ( C @ ( B @ quotient ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,18]) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ less_equal ) )
!= ( C @ ( B @ less_equal ) ) )
| ( zero @ ( C @ ( B @ quotient ) ) ) ),
inference(simp,[status(thm)],[258]) ).
thf(260,plain,
! [A: $i] : ( zero @ ( A @ ( zero @ quotient ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(11,axiom,
idQa @ ( a @ ( identity @ quotient ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_divide_a) ).
thf(34,plain,
idQa @ ( a @ ( identity @ quotient ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(9,axiom,
! [B: $i,A: $i] : ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',closure) ).
thf(30,plain,
! [B: $i,A: $i] : ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) )
!= ( E @ ( D @ ( C @ quotient ) ) ) )
| ( C @ ( E @ less_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30,22]) ).
thf(889,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ divide ) @ ( B @ ( A @ quotient ) ) )
!= ( E @ ( D @ ( C @ quotient ) ) ) )
| ( C @ ( E @ less_equal ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( G @ ( F @ divide ) ))]]) ).
thf(891,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ divide ) @ less_equal ) ),
inference(simp,[status(thm)],[890]) ).
thf(1967,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ divide ) @ less_equal ) )
!= ( D @ ( C @ less_equal ) ) )
| ( zero @ ( D @ ( C @ quotient ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[891,18]) ).
thf(1968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ divide ) @ less_equal ) )
!= ( D @ ( C @ less_equal ) ) )
| ( zero @ ( D @ ( C @ quotient ) ) ) ),
inference(simp,[status(thm)],[1967]) ).
thf(1969,plain,
! [B: $i,A: $i] : ( zero @ ( A @ ( B @ ( A @ divide ) @ quotient ) ) ),
inference(pattern_uni,[status(thm)],[1968:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ divide ) )),bind(D,$thf( E ))]]) ).
thf(1973,plain,
! [B: $i,A: $i] : ( zero @ ( A @ ( B @ ( A @ divide ) @ quotient ) ) ),
inference(simp,[status(thm)],[1969]) ).
thf(2155,plain,
( ( ( idQ_idQa @ ( idQa @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) )
| ~ $true
| ( zero != idQa_Q__idQ_idQa ) ),
inference(paramod_ordered,[status(thm)],[364,2132]) ).
thf(2156,plain,
( ( ( idQ_idQa @ ( idQa @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) )
| ( zero != idQa_Q__idQ_idQa ) ),
inference(simp,[status(thm)],[2155]) ).
thf(2161,plain,
( ( idQ_idQa != idQa_Q__idQ_idQa )
| ( idQa != idQa )
| ( zero != idQa_Q__idQ_idQa ) ),
inference(simp,[status(thm)],[2156]) ).
thf(2165,plain,
( ( idQ_idQa != idQa_Q__idQ_idQa )
| ( zero != idQa_Q__idQ_idQa ) ),
inference(simp,[status(thm)],[2161]) ).
thf(345,plain,
! [B: $i,A: $i] :
( ( ( idQ_idQa @ ( idQa @ ( identity @ quotient ) ) )
!= ( zero @ ( B @ ( A @ quotient ) ) ) )
| ( B @ ( A @ less_equal ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,20]) ).
thf(346,plain,
! [B: $i,A: $i] :
( ( ( idQ_idQa @ ( idQa @ ( identity @ quotient ) ) )
!= ( zero @ ( B @ ( A @ quotient ) ) ) )
| ( B @ ( A @ less_equal ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ( idQ_idQa != zero )
| ( idQa != B )
| ( identity != A )
| ( B @ ( A @ less_equal ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(363,plain,
( ( idQ_idQa != zero )
| ( idQa @ ( identity @ less_equal ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(2153,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ divide ) @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[891,2132]) ).
thf(2154,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ divide ) @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) ),
inference(simp,[status(thm)],[2153]) ).
thf(2157,plain,
! [B: $i,A: $i] :
( ( A != idQa_Q__idQ_idQa )
| ( ( B @ ( A @ divide ) )
!= idQa ) ),
inference(simp,[status(thm)],[2154]) ).
thf(2167,plain,
! [A: $i] :
( ( A @ ( idQa_Q__idQ_idQa @ divide ) )
!= idQa ),
inference(simp,[status(thm)],[2157]) ).
thf(229,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( B @ ( A @ quotient ) ) )
!= ( identity @ ( D @ ( C @ quotient ) ) ) )
| ( idQ_idQa @ ( G @ less_equal ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( idQa @ ( C @ quotient ) ) )
| ~ ( E @ ( idQa @ ( D @ quotient ) ) )
| ~ $true
| ~ ( B @ ( A @ less_equal ) ) ),
inference(paramod_ordered,[status(thm)],[18,102]) ).
thf(230,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( zero @ ( B @ ( A @ quotient ) ) )
!= ( identity @ ( D @ ( C @ quotient ) ) ) )
| ( idQ_idQa @ ( G @ less_equal ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( idQa @ ( C @ quotient ) ) )
| ~ ( E @ ( idQa @ ( D @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(261,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( identity != zero )
| ( B != D )
| ( A != C )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( idQa @ ( C @ quotient ) ) )
| ~ ( E @ ( idQa @ ( D @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) )
| ( idQ_idQa @ ( G @ less_equal ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( identity != zero )
| ~ ( E @ ( C @ ( D @ quotient ) ) )
| ~ ( D @ ( idQa @ ( A @ quotient ) ) )
| ~ ( C @ ( idQa @ ( B @ quotient ) ) )
| ~ ( B @ ( A @ less_equal ) )
| ( idQ_idQa @ ( E @ less_equal ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( ( idQa @ ( identity @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ( zero @ ( B @ ( A @ quotient ) ) )
| ~ $true
| ( idQ_idQa != zero ) ),
inference(paramod_ordered,[status(thm)],[363,18]) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( ( idQa @ ( identity @ less_equal ) )
!= ( B @ ( A @ less_equal ) ) )
| ( zero @ ( B @ ( A @ quotient ) ) )
| ( idQ_idQa != zero ) ),
inference(simp,[status(thm)],[773]) ).
thf(775,plain,
( ( zero @ ( idQa @ ( identity @ quotient ) ) )
| ( idQ_idQa != zero ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( identity )),bind(B,$thf( idQa ))]]) ).
thf(2139,plain,
! [A: $i] :
( ( ( identity @ ( A @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29,2132]) ).
thf(2140,plain,
! [A: $i] :
( ( identity @ ( A @ less_equal ) )
!= ( idQa_Q__idQ_idQa @ ( idQa @ less_equal ) ) ),
inference(simp,[status(thm)],[2139]) ).
thf(2159,plain,
! [A: $i] :
( ( identity != idQa_Q__idQ_idQa )
| ( A != idQa ) ),
inference(simp,[status(thm)],[2140]) ).
thf(2170,plain,
identity != idQa_Q__idQ_idQa,
inference(simp,[status(thm)],[2159]) ).
thf(405,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ less_equal ) )
!= ( J @ ( I @ less_equal ) ) )
| ( identity != zero )
| ~ ( M @ ( K @ ( L @ quotient ) ) )
| ~ ( L @ ( idQa @ ( I @ quotient ) ) )
| ~ ( K @ ( idQa @ ( J @ quotient ) ) )
| ~ $true
| ( idQ_idQa @ ( M @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,262]) ).
thf(406,plain,
! [M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H @ ( G @ less_equal ) )
!= ( J @ ( I @ less_equal ) ) )
| ( identity != zero )
| ~ ( M @ ( K @ ( L @ quotient ) ) )
| ~ ( L @ ( idQa @ ( I @ quotient ) ) )
| ~ ( K @ ( idQa @ ( J @ quotient ) ) )
| ( idQ_idQa @ ( M @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(simp,[status(thm)],[405]) ).
thf(407,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( identity != zero )
| ~ ( K @ ( I @ ( J @ quotient ) ) )
| ~ ( J @ ( idQa @ ( G @ quotient ) ) )
| ~ ( I @ ( idQa @ ( H @ quotient ) ) )
| ( idQ_idQa @ ( K @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(pattern_uni,[status(thm)],[406:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( G )),bind(J,$thf( H ))]]) ).
thf(454,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( identity != zero )
| ~ ( K @ ( I @ ( J @ quotient ) ) )
| ~ ( J @ ( idQa @ ( G @ quotient ) ) )
| ~ ( I @ ( idQa @ ( H @ quotient ) ) )
| ( idQ_idQa @ ( K @ less_equal ) )
| ~ ( H @ ( D @ ( C @ quotient ) ) )
| ~ ( G @ ( E @ ( F @ quotient ) ) )
| ~ ( F @ ( D @ ( A @ quotient ) ) )
| ~ ( E @ ( D @ ( B @ quotient ) ) )
| ~ ( C @ ( B @ ( A @ quotient ) ) ) ),
inference(simp,[status(thm)],[407]) ).
thf(5348,plain,
$false,
inference(e,[status(thm)],[14,102,22,2166,897,782,24,25,20,228,29,260,28,21,2132,33,34,17,1973,35,18,887,2165,16,31,363,891,2167,26,23,36,262,30,19,775,2170,454,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.14/0.39 % Computer : n007.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Fri Sep 25 15:55:38 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.30/1.17 % [INFO] Parsing done (197ms).
% 1.30/1.19 % [INFO] Running in sequential loop mode.
% 1.95/1.58 % [INFO] eprover registered as external prover.
% 1.95/1.59 % [INFO] Scanning for conjecture ...
% 2.16/1.67 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.16/1.70 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.35/1.72 % [INFO] Problem is propositional (TPTP CNF).
% 2.35/1.73 % [INFO] Type checking passed.
% 2.35/1.73 % [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 ...
% 21.32/5.71 % External prover 'e' found a proof!
% 21.32/5.71 % [INFO] Killing All external provers ...
% 21.32/5.72 % Time passed: 5178ms (effective reasoning time: 4523ms)
% 21.32/5.72 % Axioms used in derivation (12): quotient_property, quotient_less_equal, identity_divide_a, closure, less_equal_and_equal, identity_divide_idQ_idQa, less_equal_quotient, identity_is_largest, divisor_existence, well_defined, identity_divide_idQa, zero_is_smallest
% 21.32/5.72 % No. of inferences in proof: 103
% 21.32/5.72 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5178 ms resp. 4523 ms w/o parsing
% 21.32/5.79 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.32/5.79 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------