%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD024-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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 : 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 07:10:21 AM UTC 2026
% Result : Unsatisfiable 140.89s 37.68s
% Output : Refutation 137.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 31
% Syntax : Number of formulae : 341 ( 98 unt; 0 typ; 0 def)
% Number of atoms : 1080 ( 294 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 2933 ( 523 ~; 399 |; 0 &;2011 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 280 ( 0 ^; 280 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(b_decl,type,
b: $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(a_decl,type,
a: $i ).
thf(defined_decl,type,
defined: $i > $o ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(7,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(42,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(67,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(68,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[67]) ).
thf(133,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[42,68]) ).
thf(134,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( additive_identity ))]]) ).
thf(161,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[135,68]) ).
thf(162,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[161]) ).
thf(163,plain,
additive_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[162:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(791,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[163,68]) ).
thf(792,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[791]) ).
thf(793,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[792:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(71,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(142,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[71,68]) ).
thf(143,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( a ))]]) ).
thf(171,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[144,68]) ).
thf(172,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
a @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(848,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[173,68]) ).
thf(849,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[848]) ).
thf(850,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[849:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(1153,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[850,68]) ).
thf(1154,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1153]) ).
thf(1155,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1154:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ equalish ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_order_relation) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ equalish ) )
| ~ ( B @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
~ ( multiplicative_identity @ ( additive_identity @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(87,plain,
~ ( multiplicative_identity @ ( additive_identity @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(88,plain,
~ ( multiplicative_identity @ ( additive_identity @ equalish ) ),
inference(polarity_switch,[status(thm)],[87]) ).
thf(12,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(51,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(52,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(2128,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[71,52]) ).
thf(2129,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[2128]) ).
thf(2130,plain,
additive_identity @ ( a @ additive_inverse @ ( a @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[2129:[bind(A,$thf( a ))]]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_equality) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(2215,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ~ $true
| ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[2130,48]) ).
thf(2216,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( a @ additive_inverse @ ( a @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[2215]) ).
thf(2217,plain,
a @ additive_inverse @ ( a @ add ) @ ( additive_identity @ equalish ),
inference(pattern_uni,[status(thm)],[2216:[bind(A,$thf( additive_identity )),bind(B,$thf( a @ additive_inverse @ ( a @ add ) ))]]) ).
thf(2492,plain,
( ( ( a @ additive_inverse @ ( a @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2217,88]) ).
thf(2493,plain,
( ( a @ additive_inverse @ ( a @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[2492]) ).
thf(2509,plain,
( ( ( a @ additive_inverse @ ( a @ add ) )
!= multiplicative_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2512,plain,
( ( a @ additive_inverse @ ( a @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[2509]) ).
thf(30,axiom,
b @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(86,plain,
b @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_equality) ).
thf(43,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(1379,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[86,44]) ).
thf(1380,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1379]) ).
thf(1381,plain,
b @ ( b @ equalish ),
inference(pattern_uni,[status(thm)],[1380:[bind(A,$thf( b ))]]) ).
thf(1433,plain,
( ( ( b @ ( b @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1381,88]) ).
thf(1434,plain,
( ( b @ ( b @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1433]) ).
thf(1437,plain,
( ( multiplicative_identity != b )
| ( b != additive_identity ) ),
inference(simp,[status(thm)],[1434]) ).
thf(3,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(35,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(127,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[35,68]) ).
thf(128,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[127]) ).
thf(129,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(1368,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[129,44]) ).
thf(1369,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1368]) ).
thf(1370,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1369:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(1493,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1370,88]) ).
thf(1494,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1493]) ).
thf(1497,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( multiplicative_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[1494]) ).
thf(1373,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[71,44]) ).
thf(1374,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1373]) ).
thf(1375,plain,
a @ ( a @ equalish ),
inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( a ))]]) ).
thf(1422,plain,
( ( ( a @ ( a @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1375,88]) ).
thf(1423,plain,
( ( a @ ( a @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1426,plain,
( ( multiplicative_identity != a )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[1423]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_equality) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ equalish ) )
| ~ ( C @ ( A @ equalish ) )
| ( B @ ( A @ equalish ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(151,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[129,68]) ).
thf(152,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[151]) ).
thf(153,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[152:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(710,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[153,68]) ).
thf(711,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[710]) ).
thf(712,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[711:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(1009,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[712,68]) ).
thf(1010,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1009]) ).
thf(1011,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1010:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1273,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1011,68]) ).
thf(1274,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1273]) ).
thf(1275,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1274:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1093,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[793,68]) ).
thf(1094,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1093]) ).
thf(1095,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1094:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_order_relation) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(2143,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[35,52]) ).
thf(2144,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[2143]) ).
thf(2145,plain,
additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[2144:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(2231,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ~ $true
| ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[2145,48]) ).
thf(2232,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[2231]) ).
thf(2233,plain,
multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( additive_identity @ equalish ),
inference(pattern_uni,[status(thm)],[2232:[bind(A,$thf( additive_identity )),bind(B,$thf( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) ))]]) ).
thf(2513,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2233,88]) ).
thf(2514,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[2513]) ).
thf(2529,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) )
!= multiplicative_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[2514]) ).
thf(2531,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[2529]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(83,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) ) ),
inference(cnf,[status(esa)],[82]) ).
thf(181,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true
| ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[83,88]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[181]) ).
thf(257,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ add ) @ add ) )
!= multiplicative_identity )
| ( ( C @ ( B @ add ) @ ( A @ add ) )
!= additive_identity )
| ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[182]) ).
thf(2103,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[42,52]) ).
thf(2104,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[2103]) ).
thf(2105,plain,
additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[2104:[bind(A,$thf( additive_identity ))]]) ).
thf(2183,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ~ $true
| ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[2105,48]) ).
thf(2184,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[2183]) ).
thf(2185,plain,
additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ equalish ),
inference(pattern_uni,[status(thm)],[2184:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity @ additive_inverse @ ( additive_identity @ add ) ))]]) ).
thf(2,negated_conjecture,
~ ( b @ ( a @ equalish ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_equal_to_b_4) ).
thf(33,plain,
~ ( b @ ( a @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(34,plain,
~ ( b @ ( a @ equalish ) ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true
| ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[83,34]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ add ) @ add ) @ ( C @ ( B @ add ) @ ( A @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[210]) ).
thf(258,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ add ) @ add ) )
!= b )
| ( ( C @ ( B @ add ) @ ( A @ add ) )
!= a )
| ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[211]) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( C @ defined ) )
| ( ( C @ ( B @ ( A @ add ) @ add ) )
!= b )
| ( ( C @ ( B @ add ) @ ( A @ add ) )
!= a )
| ~ $true
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[42,258]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( C @ defined ) )
| ( ( C @ ( B @ ( A @ add ) @ add ) )
!= b )
| ( ( C @ ( B @ add ) @ ( A @ add ) )
!= a )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[430]) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( B @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( B @ add ) @ ( A @ add ) )
!= a )
| ~ ( B @ defined )
| ~ ( A @ defined ) ),
inference(pattern_uni,[status(thm)],[431:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( additive_identity ))]]) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ( ( additive_identity @ ( B @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( B @ add ) @ ( A @ add ) )
!= a )
| ~ $true
| ~ ( A @ defined ) ),
inference(paramod_ordered,[status(thm)],[42,432]) ).
thf(519,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ defined )
!= ( B @ defined ) )
| ( ( additive_identity @ ( B @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( B @ add ) @ ( A @ add ) )
!= a )
| ~ ( A @ defined ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ ( A @ defined ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(932,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[129,520]) ).
thf(933,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[932]) ).
thf(934,plain,
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ additive_inverse @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( multiplicative_identity @ additive_inverse @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[933:[bind(A,$thf( multiplicative_identity @ additive_inverse ))]]) ).
thf(947,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[135,520]) ).
thf(948,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[947]) ).
thf(949,plain,
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ additive_inverse @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( additive_identity @ additive_inverse @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[948:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ less_or_equal ) )
| ~ ( A @ ( additive_identity @ less_or_equal ) )
| ( B @ ( A @ multiply ) @ ( additive_identity @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ less_or_equal ) )
| ~ ( A @ ( additive_identity @ less_or_equal ) )
| ( B @ ( A @ multiply ) @ ( additive_identity @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( additive_identity @ less_or_equal ) )
| ~ ( A @ ( additive_identity @ less_or_equal ) )
| ( B @ ( A @ multiply ) @ ( additive_identity @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(15,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_or_equal ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ less_or_equal ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(935,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[71,520]) ).
thf(936,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[935]) ).
thf(937,plain,
( ( ( additive_identity @ ( additive_identity @ ( a @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( a @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[936:[bind(A,$thf( a ))]]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ multiply ) @ multiply ) @ ( C @ ( B @ multiply ) @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication) ).
thf(84,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ defined )
| ~ ( B @ defined )
| ~ ( A @ defined )
| ( C @ ( B @ ( A @ multiply ) @ multiply ) @ ( C @ ( B @ multiply ) @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(58,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(cnf,[status(esa)],[57]) ).
thf(3073,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[42,58]) ).
thf(3074,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[3073]) ).
thf(3075,plain,
additive_identity @ ( additive_identity @ ( additive_identity @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[3074:[bind(A,$thf( additive_identity ))]]) ).
thf(145,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[86,68]) ).
thf(146,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
b @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( b ))]]) ).
thf(1528,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true
| ~ ( A @ ( B @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[48,34]) ).
thf(1529,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ ( A @ ( B @ equalish ) ) ),
inference(simp,[status(thm)],[1528]) ).
thf(1530,plain,
~ ( a @ ( b @ equalish ) ),
inference(pattern_uni,[status(thm)],[1529:[bind(A,$thf( a )),bind(B,$thf( b ))]]) ).
thf(2179,plain,
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ) )
!= ( a @ ( b @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2105,1530]) ).
thf(2180,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ) )
!= ( a @ ( b @ equalish ) ) ),
inference(simp,[status(thm)],[2179]) ).
thf(2190,plain,
( ( a != additive_identity )
| ( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) )
!= b ) ),
inference(simp,[status(thm)],[2180]) ).
thf(1333,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1095,68]) ).
thf(1334,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1333]) ).
thf(1335,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1334:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2000,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1335,68]) ).
thf(2001,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[2000]) ).
thf(2002,plain,
additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[2001:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(365,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[147,68]) ).
thf(366,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[365]) ).
thf(367,plain,
b @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[366:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(905,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[367,68]) ).
thf(906,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[905]) ).
thf(907,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[906:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(1213,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[907,68]) ).
thf(1214,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1213]) ).
thf(1215,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1214:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(61,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(24,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(74,plain,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(2125,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[86,52]) ).
thf(2126,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ additive_inverse @ ( A @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[2125]) ).
thf(2127,plain,
additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[2126:[bind(A,$thf( b ))]]) ).
thf(2195,plain,
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ) )
!= ( a @ ( b @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2127,1530]) ).
thf(2196,plain,
( ( additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ) )
!= ( a @ ( b @ equalish ) ) ),
inference(simp,[status(thm)],[2195]) ).
thf(2205,plain,
( ( a != additive_identity )
| ( ( b @ additive_inverse @ ( b @ add ) )
!= b ) ),
inference(simp,[status(thm)],[2196]) ).
thf(950,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35,520]) ).
thf(951,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[950]) ).
thf(952,plain,
( ( ( additive_identity @ ( additive_identity @ ( multiplicative_identity @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( multiplicative_identity @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[951:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplication) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1400,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[163,44]) ).
thf(1401,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1402,plain,
additive_identity @ additive_inverse @ additive_inverse @ ( additive_identity @ additive_inverse @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1401:[bind(A,$thf( additive_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(1495,plain,
( ( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1370,34]) ).
thf(1496,plain,
( ( multiplicative_identity @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[1495]) ).
thf(1498,plain,
( ( ( multiplicative_identity @ additive_inverse )
!= b )
| ( ( multiplicative_identity @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[1496]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_addition) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1391,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[135,44]) ).
thf(1392,plain,
! [A: $i] :
( ( ( additive_identity @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1393,plain,
additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1392:[bind(A,$thf( additive_identity @ additive_inverse ))]]) ).
thf(3107,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[86,58]) ).
thf(3108,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[3107]) ).
thf(3109,plain,
b @ ( b @ ( additive_identity @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[3108:[bind(A,$thf( b ))]]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_order_relation) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ less_or_equal ) )
| ~ ( C @ ( A @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(1507,plain,
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1393,34]) ).
thf(1508,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[1507]) ).
thf(1510,plain,
( ( ( additive_identity @ additive_inverse )
!= b )
| ( ( additive_identity @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[1508]) ).
thf(1696,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1215,68]) ).
thf(1697,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1696]) ).
thf(1698,plain,
b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1697:[bind(A,$thf( b @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1,negated_conjecture,
a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity_equals_add_3) ).
thf(32,plain,
a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_addition) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1424,plain,
( ( ( a @ ( a @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1375,34]) ).
thf(1425,plain,
( ( a @ ( a @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[1424]) ).
thf(1427,plain,
( ( a != b )
| ( a != a ) ),
inference(simp,[status(thm)],[1425]) ).
thf(1428,plain,
a != b,
inference(simp,[status(thm)],[1427]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ add ) @ ( B @ ( A @ add ) @ equalish ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(1633,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1155,68]) ).
thf(1634,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1633]) ).
thf(1635,plain,
a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1634:[bind(A,$thf( a @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_equality_and_multiplication) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(1376,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[144,44]) ).
thf(1377,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1376]) ).
thf(1378,plain,
a @ additive_inverse @ ( a @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1377:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(1499,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1378,88]) ).
thf(1500,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1499]) ).
thf(1503,plain,
( ( ( a @ additive_inverse )
!= multiplicative_identity )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[1500]) ).
thf(1347,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[153,44]) ).
thf(1348,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(1349,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ ( multiplicative_identity @ additive_inverse @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1348:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse ))]]) ).
thf(2241,plain,
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2185,88]) ).
thf(2242,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[2241]) ).
thf(2253,plain,
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) )
!= multiplicative_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[2242]) ).
thf(2257,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[2253]) ).
thf(1350,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[147,44]) ).
thf(1351,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1350]) ).
thf(1352,plain,
b @ additive_inverse @ ( b @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1351:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(1489,plain,
( ( ( b @ additive_inverse @ ( b @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1352,34]) ).
thf(1490,plain,
( ( b @ additive_inverse @ ( b @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[1489]) ).
thf(1492,plain,
( ( ( b @ additive_inverse )
!= b )
| ( ( b @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[1490]) ).
thf(25,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( multiplicative_identity @ ( A @ multiplicative_inverse @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(76,plain,
! [A: $i] :
( ( additive_identity @ ( A @ equalish ) )
| ~ ( A @ defined )
| ( multiplicative_identity @ ( A @ multiplicative_inverse @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(cnf,[status(esa)],[38]) ).
thf(3205,plain,
( ( ( b @ ( b @ ( additive_identity @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3109,34]) ).
thf(3206,plain,
( ( b @ ( b @ ( additive_identity @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[3205]) ).
thf(3217,plain,
( ( b != b )
| ( ( b @ ( additive_identity @ add ) )
!= a ) ),
inference(simp,[status(thm)],[3206]) ).
thf(3219,plain,
( ( b @ ( additive_identity @ add ) )
!= a ),
inference(simp,[status(thm)],[3217]) ).
thf(941,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[86,520]) ).
thf(942,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[941]) ).
thf(943,plain,
( ( ( additive_identity @ ( additive_identity @ ( b @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( b @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[942:[bind(A,$thf( b ))]]) ).
thf(1394,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[35,44]) ).
thf(1395,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1394]) ).
thf(1396,plain,
multiplicative_identity @ ( multiplicative_identity @ equalish ),
inference(pattern_uni,[status(thm)],[1395:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(1773,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[1275,68]) ).
thf(1774,plain,
! [A: $i] :
( ( ( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[1773]) ).
thf(1775,plain,
multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[1774:[bind(A,$thf( multiplicative_identity @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(1362,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[42,44]) ).
thf(1363,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1362]) ).
thf(1364,plain,
additive_identity @ ( additive_identity @ equalish ),
inference(pattern_uni,[status(thm)],[1363:[bind(A,$thf( additive_identity ))]]) ).
thf(2197,plain,
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2127,34]) ).
thf(2198,plain,
( ( additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[2197]) ).
thf(2207,plain,
( ( b != additive_identity )
| ( ( b @ additive_inverse @ ( b @ add ) )
!= a ) ),
inference(simp,[status(thm)],[2198]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_of_order_relation) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(920,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[147,520]) ).
thf(921,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[920]) ).
thf(922,plain,
( ( ( additive_identity @ ( additive_identity @ ( b @ additive_inverse @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( b @ additive_inverse @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[921:[bind(A,$thf( b @ additive_inverse ))]]) ).
thf(1561,plain,
( ( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( a @ ( b @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,1530]) ).
thf(1562,plain,
( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( a @ ( b @ equalish ) ) ),
inference(simp,[status(thm)],[1561]) ).
thf(1583,plain,
( ( ( a @ additive_inverse @ ( b @ add ) )
!= a )
| ( b != additive_identity ) ),
inference(simp,[status(thm)],[1562]) ).
thf(1417,plain,
( ( ( b @ ( a @ equalish ) )
!= ( additive_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1364,34]) ).
thf(1418,plain,
( ( b @ ( a @ equalish ) )
!= ( additive_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1417]) ).
thf(1420,plain,
( ( b != additive_identity )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[1418]) ).
thf(1505,plain,
( ( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1393,88]) ).
thf(1506,plain,
( ( additive_identity @ additive_inverse @ ( additive_identity @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1509,plain,
( ( ( additive_identity @ additive_inverse )
!= multiplicative_identity )
| ( ( additive_identity @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[1506]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( C @ defined )
| ~ ( A @ defined )
| ( B @ ( C @ ( A @ add ) @ multiply ) @ ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( C @ defined )
| ~ ( A @ defined )
| ( B @ ( C @ ( A @ add ) @ multiply ) @ ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ add ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3110,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[71,58]) ).
thf(3111,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ ( additive_identity @ add ) @ equalish ) ) ),
inference(simp,[status(thm)],[3110]) ).
thf(3112,plain,
a @ ( a @ ( additive_identity @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[3111:[bind(A,$thf( a ))]]) ).
thf(89,plain,
( ( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,88]) ).
thf(90,plain,
( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(93,plain,
( ( ( a @ additive_inverse @ ( b @ add ) )
!= multiplicative_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[90]) ).
thf(95,plain,
( ( a @ additive_inverse @ ( b @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[93]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ equalish ) )
| ~ ( B @ defined )
| ( B @ ( C @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(1482,plain,
( ( ( multiplicative_identity @ ( multiplicative_identity @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1396,34]) ).
thf(1483,plain,
( ( multiplicative_identity @ ( multiplicative_identity @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[1482]) ).
thf(1485,plain,
( ( multiplicative_identity != b )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[1483]) ).
thf(1501,plain,
( ( ( a @ additive_inverse @ ( a @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1378,34]) ).
thf(1502,plain,
( ( a @ additive_inverse @ ( a @ additive_inverse @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[1501]) ).
thf(1504,plain,
( ( ( a @ additive_inverse )
!= b )
| ( ( a @ additive_inverse )
!= a ) ),
inference(simp,[status(thm)],[1502]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( A @ ( B @ multiply ) @ ( B @ ( A @ multiply ) @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1415,plain,
( ( ( multiplicative_identity @ ( additive_identity @ equalish ) )
!= ( additive_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1364,88]) ).
thf(1416,plain,
( ( multiplicative_identity @ ( additive_identity @ equalish ) )
!= ( additive_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1415]) ).
thf(1419,plain,
( ( multiplicative_identity != additive_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1421,plain,
multiplicative_identity != additive_identity,
inference(simp,[status(thm)],[1419]) ).
thf(2199,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ~ $true
| ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[2127,48]) ).
thf(2200,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( b @ additive_inverse @ ( b @ add ) @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[2199]) ).
thf(2201,plain,
b @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ),
inference(pattern_uni,[status(thm)],[2200:[bind(A,$thf( additive_identity )),bind(B,$thf( b @ additive_inverse @ ( b @ add ) ))]]) ).
thf(2471,plain,
( ( ( b @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2201,88]) ).
thf(2472,plain,
( ( b @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[2471]) ).
thf(2487,plain,
( ( ( b @ additive_inverse @ ( b @ add ) )
!= multiplicative_identity )
| ( additive_identity != additive_identity ) ),
inference(simp,[status(thm)],[2472]) ).
thf(2490,plain,
( ( b @ additive_inverse @ ( b @ add ) )
!= multiplicative_identity ),
inference(simp,[status(thm)],[2487]) ).
thf(1388,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[367,44]) ).
thf(1389,plain,
! [A: $i] :
( ( ( b @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1388]) ).
thf(1390,plain,
b @ additive_inverse @ additive_inverse @ ( b @ additive_inverse @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1389:[bind(A,$thf( b @ additive_inverse @ additive_inverse ))]]) ).
thf(1487,plain,
( ( ( b @ additive_inverse @ ( b @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1352,88]) ).
thf(1488,plain,
( ( b @ additive_inverse @ ( b @ additive_inverse @ equalish ) )
!= ( multiplicative_identity @ ( additive_identity @ equalish ) ) ),
inference(simp,[status(thm)],[1487]) ).
thf(1491,plain,
( ( ( b @ additive_inverse )
!= multiplicative_identity )
| ( ( b @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[1488]) ).
thf(1525,plain,
! [B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ~ $true
| ( B @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[32,48]) ).
thf(1526,plain,
! [B: $i,A: $i] :
( ( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( A @ ( B @ equalish ) ) )
| ( B @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1525]) ).
thf(1527,plain,
additive_identity @ ( a @ additive_inverse @ ( b @ add ) @ equalish ),
inference(pattern_uni,[status(thm)],[1526:[bind(A,$thf( a @ additive_inverse @ ( b @ add ) )),bind(B,$thf( additive_identity ))]]) ).
thf(91,plain,
( ( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[32,34]) ).
thf(92,plain,
( ( a @ additive_inverse @ ( b @ add ) @ ( additive_identity @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[91]) ).
thf(94,plain,
( ( ( a @ additive_inverse @ ( b @ add ) )
!= b )
| ( a != additive_identity ) ),
inference(simp,[status(thm)],[92]) ).
thf(926,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42,520]) ).
thf(927,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[926]) ).
thf(928,plain,
( ( ( additive_identity @ ( additive_identity @ ( additive_identity @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( additive_identity @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[927:[bind(A,$thf( additive_identity ))]]) ).
thf(2181,plain,
( ( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2105,34]) ).
thf(2182,plain,
( ( additive_identity @ ( additive_identity @ additive_inverse @ ( additive_identity @ add ) @ equalish ) )
!= ( b @ ( a @ equalish ) ) ),
inference(simp,[status(thm)],[2181]) ).
thf(2191,plain,
( ( b != additive_identity )
| ( ( additive_identity @ additive_inverse @ ( additive_identity @ add ) )
!= a ) ),
inference(simp,[status(thm)],[2182]) ).
thf(1365,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ ( A @ equalish ) ) ),
inference(paramod_ordered,[status(thm)],[173,44]) ).
thf(1366,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( A @ ( A @ equalish ) ) ),
inference(simp,[status(thm)],[1365]) ).
thf(1367,plain,
a @ additive_inverse @ additive_inverse @ ( a @ additive_inverse @ additive_inverse @ equalish ),
inference(pattern_uni,[status(thm)],[1366:[bind(A,$thf( a @ additive_inverse @ additive_inverse ))]]) ).
thf(938,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[144,520]) ).
thf(939,plain,
! [A: $i] :
( ( ( a @ additive_inverse @ defined )
!= ( A @ defined ) )
| ( ( additive_identity @ ( additive_identity @ ( A @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( A @ add ) )
!= a ) ),
inference(simp,[status(thm)],[938]) ).
thf(940,plain,
( ( ( additive_identity @ ( additive_identity @ ( a @ additive_inverse @ add ) @ add ) )
!= b )
| ( ( additive_identity @ ( additive_identity @ add ) @ ( a @ additive_inverse @ add ) )
!= a ) ),
inference(pattern_uni,[status(thm)],[939:[bind(A,$thf( a @ additive_inverse ))]]) ).
thf(54711,plain,
$false,
inference(e,[status(thm)],[793,65,1155,69,88,2512,1437,1497,1426,56,1275,153,1095,42,37,2531,257,52,2217,2185,934,949,46,57,78,937,84,2105,3075,147,2190,2002,1215,61,74,2205,952,38,1370,33,1402,1375,1498,53,1530,173,129,1393,3109,41,1510,1698,45,32,34,44,59,1428,54,144,1635,49,86,71,1503,1011,1349,2257,1492,76,39,3219,367,520,943,1381,1396,135,1775,1364,2207,80,922,35,1583,1420,1509,48,712,63,3112,95,50,67,907,2145,1485,43,1504,72,1421,87,2490,1390,40,258,55,2130,1491,58,82,432,36,2233,51,1527,2201,1335,94,928,2127,1352,1378,47,163,850,68,83,2191,1367,940]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD024-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 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
% 0.20/0.47 % Computer : n010.cluster.edu
% 0.20/0.47 % Model : x86_64 x86_64
% 0.20/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.47 % Memory : 8046.5625MB
% 0.20/0.47 % OS : Linux 6.8.0-71-generic
% 0.20/0.47 % CPULimit : 300
% 0.20/0.47 % WCLimit : 300
% 0.20/0.47 % DateTime : Sun Sep 27 02:24:16 UTC 2026
% 0.20/0.47 % CPUTime :
% 0.20/0.47 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
% 0.98/1.11 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.43/1.31 % [INFO] Parsing done (197ms).
% 1.43/1.33 % [INFO] Running in sequential loop mode.
% 2.13/1.71 % [INFO] eprover registered as external prover.
% 2.13/1.72 % [INFO] Scanning for conjecture ...
% 2.29/1.81 % [INFO] Found a conjecture (or negated_conjecture) and 29 axioms. Running axiom selection ...
% 2.29/1.88 % [INFO] Axiom selection finished. Selected 29 axioms (removed 0 axioms).
% 2.46/1.92 % [INFO] Problem is propositional (TPTP CNF).
% 2.46/1.92 % [INFO] Type checking passed.
% 2.46/1.93 % [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 ...
% 140.89/37.68 % External prover 'e' found a proof!
% 140.89/37.68 % [INFO] Killing All external provers ...
% 140.89/37.68 % Time passed: 37005ms (effective reasoning time: 36345ms)
% 140.89/37.68 % Axioms used in derivation (29): existence_of_identity_multiplication, transitivity_of_order_relation, associativity_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, well_definedness_of_multiplication, existence_of_identity_addition, transitivity_of_equality, reflexivity_of_equality, commutativity_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, distributivity, compatibility_of_equality_and_multiplication, a_is_defined, antisymmetry_of_order_relation, associativity_addition, b_is_defined, totality_of_order_relation, compatibility_of_equality_and_addition, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, symmetry_of_equality, different_identities, well_definedness_of_multiplicative_inverse, compatibility_of_equality_and_order_relation, compatibility_of_order_relation_and_addition
% 140.89/37.68 % No. of inferences in proof: 341
% 140.89/37.68 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 37005 ms resp. 36345 ms w/o parsing
% 137.80/37.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 137.80/37.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------