%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD050-4 : 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 : n006.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 07:10:28 AM UTC 2026
% Result : Unsatisfiable 9.63s 8.95s
% Output : Refutation 9.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 38
% Syntax : Number of formulae : 140 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 396 ( 55 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 1179 ( 210 ~; 196 |; 0 &; 773 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 196 ( 0 ^; 196 !; 0 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(b_decl,type,
b: $i ).
thf(d_decl,type,
d: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(s_decl,type,
s: $i ).
thf(k_decl,type,
k: $i ).
thf(c_decl,type,
c: $i ).
thf(less_or_equal_decl,type,
less_or_equal: $i > $i > $o ).
thf(defined_decl,type,
defined: $i > $o ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(9,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(52,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
thf(62,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(63,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(cnf,[status(esa)],[62]) ).
thf(118,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[52,63]) ).
thf(119,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[118]) ).
thf(120,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(2,negated_conjecture,
~ ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_8) ).
thf(42,plain,
~ ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(84,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(38,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(102,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(45,plain,
~ ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[42]) ).
thf(136,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[63,45]) ).
thf(137,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ~ ( d @ defined )
| ( d @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( d ))]]) ).
thf(25,axiom,
d @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_is_defined) ).
thf(79,plain,
d @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(164,plain,
( ~ $true
| ( d @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[138,79]) ).
thf(165,plain,
d @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[164]) ).
thf(10,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(53,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)],[10]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
thf(77,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ sum ) ) )
| ~ ( F @ ( B @ ( E @ sum ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,negated_conjecture,
~ ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_12) ).
thf(41,plain,
~ ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ product ) ) )
| ~ ( C @ ( additive_identity @ less_or_equal ) )
| ~ ( B @ ( additive_identity @ less_or_equal ) )
| ( A @ ( additive_identity @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_multiplication) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ product ) ) )
| ~ ( C @ ( additive_identity @ less_or_equal ) )
| ~ ( B @ ( additive_identity @ less_or_equal ) )
| ( A @ ( additive_identity @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ less_or_equal ) )
| ~ ( B @ ( A @ less_or_equal ) )
| ( B @ ( A @ ( additive_identity @ sum ) ) ) ),
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 @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(50,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[50]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_multiplication) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
b @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(101,plain,
b @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
thf(88,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ ( A @ ( A @ multiplicative_inverse @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,negated_conjecture,
k @ ( d @ ( a @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_10) ).
thf(44,plain,
k @ ( d @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(46,plain,
~ ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) ),
inference(polarity_switch,[status(thm)],[41]) ).
thf(104,plain,
( ( ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) )
!= ( k @ ( d @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44,46]) ).
thf(105,plain,
( ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) )
!= ( k @ ( d @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(110,plain,
( ( k != s )
| ( ( d @ multiplicative_inverse )
!= d )
| ( c != a ) ),
inference(simp,[status(thm)],[105]) ).
thf(33,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
thf(93,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ product ) ) )
| ~ ( A @ ( G @ ( D @ product ) ) )
| ~ ( C @ ( G @ ( F @ product ) ) )
| ~ ( F @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,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(57,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
c @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_is_defined) ).
thf(61,plain,
c @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(204,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[101,51]) ).
thf(205,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
b @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( b ))]]) ).
thf(32,axiom,
k @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_is_defined) ).
thf(92,plain,
k @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(17,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( A @ ( E @ ( D @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_2) ).
thf(65,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( D @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( A @ ( E @ ( D @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(35,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(97,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(16,axiom,
s @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_is_defined) ).
thf(64,plain,
s @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_7) ).
thf(40,plain,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(47,plain,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[40]) ).
thf(171,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[120,47]) ).
thf(172,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[171]) ).
thf(177,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != b )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[172]) ).
thf(180,plain,
( ( multiplicative_identity != b )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[177]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
thf(71,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(7,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(48,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)],[7]) ).
thf(49,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)],[48]) ).
thf(173,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[120,45]) ).
thf(174,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( d @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[173]) ).
thf(178,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != d )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[174]) ).
thf(181,plain,
( ( multiplicative_identity != d )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[178]) ).
thf(29,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ sum ) ) )
| ~ ( B @ ( F @ ( D @ sum ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
thf(86,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ sum ) ) )
| ~ ( B @ ( F @ ( D @ sum ) ) )
| ~ ( E @ ( D @ ( A @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,negated_conjecture,
s @ ( b @ multiplicative_inverse @ ( a @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_9) ).
thf(43,plain,
s @ ( b @ multiplicative_inverse @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(106,plain,
( ( ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) )
!= ( s @ ( b @ multiplicative_inverse @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,46]) ).
thf(107,plain,
( ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) )
!= ( s @ ( b @ multiplicative_inverse @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(111,plain,
( ( s != s )
| ( ( d @ multiplicative_inverse )
!= ( b @ multiplicative_inverse ) )
| ( c != a ) ),
inference(simp,[status(thm)],[107]) ).
thf(113,plain,
( ( ( d @ multiplicative_inverse )
!= ( b @ multiplicative_inverse ) )
| ( c != a ) ),
inference(simp,[status(thm)],[111]) ).
thf(23,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(76,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,negated_conjecture,
k @ ( c @ ( b @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_11) ).
thf(39,plain,
k @ ( c @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(98,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[97]) ).
thf(207,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[61,51]) ).
thf(208,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[207]) ).
thf(209,plain,
c @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( c ))]]) ).
thf(108,plain,
( ( ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) )
!= ( k @ ( c @ ( b @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,46]) ).
thf(109,plain,
( ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) )
!= ( k @ ( c @ ( b @ product ) ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(112,plain,
( ( k != s )
| ( ( d @ multiplicative_inverse )
!= c )
| ( c != b ) ),
inference(simp,[status(thm)],[109]) ).
thf(121,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[61,63]) ).
thf(122,plain,
! [A: $i] :
( ( ( c @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
| ( c @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( c ))]]) ).
thf(133,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[63,47]) ).
thf(134,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[133]) ).
thf(135,plain,
( ~ ( b @ defined )
| ( b @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( b ))]]) ).
thf(149,plain,
( ~ $true
| ( b @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[135,101]) ).
thf(150,plain,
b @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[149]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
thf(67,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(72,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ sum ) ) )
| ~ ( A @ ( E @ ( C @ sum ) ) )
| ~ ( D @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility_of_order_relation_and_addition) ).
thf(99,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ sum ) ) )
| ~ ( A @ ( E @ ( C @ sum ) ) )
| ~ ( D @ ( C @ less_or_equal ) )
| ( B @ ( A @ less_or_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(22,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(75,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(216,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[75,51]) ).
thf(217,plain,
! [A: $i] :
( ( ( a @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[216]) ).
thf(218,plain,
a @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[217:[bind(A,$thf( a ))]]) ).
thf(11,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(55,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(114,plain,
( ( d != b )
| ( c != a ) ),
inference(simp,[status(thm)],[113]) ).
thf(27,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ product ) ) )
| ~ ( B @ ( F @ ( D @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
thf(82,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ product ) ) )
| ~ ( B @ ( F @ ( D @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(186,plain,
( ( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( c @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[123,47]) ).
thf(187,plain,
( ( ( additive_identity @ ( c @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[186]) ).
thf(192,plain,
( ( additive_identity != additive_identity )
| ( c != b )
| ( additive_identity != additive_identity )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[187]) ).
thf(195,plain,
( ( c != b )
| ( c @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[192]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality_of_addition) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(281,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) ) )
| ~ $true
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[72,46]) ).
thf(282,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( s @ ( d @ multiplicative_inverse @ ( c @ product ) ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( s @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( d @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( d @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( c @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( c )),bind(B,$thf( d @ multiplicative_inverse )),bind(C,$thf( s )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( s @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( d @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( d @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( c @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(213,plain,
! [A: $i] :
( ( ( k @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[92,51]) ).
thf(214,plain,
! [A: $i] :
( ( ( k @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[213]) ).
thf(215,plain,
k @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( k ))]]) ).
thf(679,plain,
$false,
inference(e,[status(thm)],[120,42,84,102,165,53,77,41,73,80,51,69,101,88,52,110,46,93,57,61,206,92,65,97,45,64,180,44,59,71,49,181,86,113,76,39,98,209,112,123,48,63,150,95,50,67,72,43,99,218,40,55,114,75,82,79,195,47,62,90,337,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : FLD050-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.26/5.73 % Computer : n006.cluster.edu
% 0.26/5.73 % Model : x86_64 x86_64
% 0.26/5.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/5.73 % Memory : 8046.5625MB
% 0.26/5.73 % OS : Linux 6.8.0-71-generic
% 0.26/5.73 % CPULimit : 300
% 0.26/5.73 % WCLimit : 300
% 0.26/5.73 % DateTime : Sun Sep 27 02:29:50 UTC 2026
% 0.26/5.73 % CPUTime :
% 0.26/5.73 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.11/6.32 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.46/6.53 % [INFO] Parsing done (211ms).
% 1.46/6.55 % [INFO] Running in sequential loop mode.
% 2.19/6.95 % [INFO] eprover registered as external prover.
% 2.19/6.96 % [INFO] Scanning for conjecture ...
% 2.47/7.05 % [INFO] Found a conjecture (or negated_conjecture) and 32 axioms. Running axiom selection ...
% 2.47/7.13 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 2.68/7.17 % [INFO] Problem is propositional (TPTP CNF).
% 2.68/7.18 % [INFO] Type checking passed.
% 2.68/7.18 % [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 ...
% 9.63/8.94 % External prover 'e' found a proof!
% 9.63/8.94 % [INFO] Killing All external provers ...
% 9.63/8.95 % Time passed: 3073ms (effective reasoning time: 2389ms)
% 9.63/8.95 % Axioms used in derivation (32): associativity_addition_1, existence_of_identity_multiplication, transitivity_of_order_relation, totality_of_multiplication, c_is_defined, compatibility_of_order_relation_and_multiplication, well_definedness_of_multiplication, existence_of_identity_addition, associativity_multiplication_1, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, distributivity_2, well_definedness_of_additive_identity, s_is_defined, a_is_defined, k_is_defined, d_is_defined, antisymmetry_of_order_relation, b_is_defined, totality_of_order_relation, existence_of_inverse_multiplication, well_definedness_of_multiplicative_identity, well_definedness_of_additive_inverse, distributivity_1, associativity_addition_2, commutativity_addition, associativity_multiplication_2, different_identities, well_definedness_of_multiplicative_inverse
% 9.63/8.95 % No. of inferences in proof: 140
% 9.63/8.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3073 ms resp. 2389 ms w/o parsing
% 9.63/9.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.63/9.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------