%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : FLD012-4 : 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 : n020.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 07:10:17 AM UTC 2026
% Result : Unsatisfiable 38.14s 8.85s
% Output : Refutation 32.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 35
% Syntax : Number of formulae : 147 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 455 ( 77 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 1385 ( 255 ~; 236 |; 0 &; 894 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 8 con; 0-3 aty)
% Number of variables : 216 ( 0 ^; 216 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(u_decl,type,
u: $i ).
thf(multiplicative_inverse_decl,type,
multiplicative_inverse: $i > $i ).
thf(v_decl,type,
v: $i ).
thf(multiplicative_identity_decl,type,
multiplicative_identity: $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(multiply_decl,type,
multiply: $i > $i > $i ).
thf(add_decl,type,
add: $i > $i > $i ).
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(69,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(1,negated_conjecture,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_5) ).
thf(37,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(41,plain,
~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[37]) ).
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(44,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(5,negated_conjecture,
~ ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_product_9) ).
thf(36,plain,
~ ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,plain,
~ ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ),
inference(polarity_switch,[status(thm)],[36]) ).
thf(4,negated_conjecture,
v @ ( b @ multiplicative_inverse @ ( a @ multiplicative_inverse @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_8) ).
thf(40,plain,
v @ ( b @ multiplicative_inverse @ ( a @ multiplicative_inverse @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,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(79,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)],[26]) ).
thf(12,axiom,
multiplicative_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
thf(56,plain,
multiplicative_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
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(60,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(61,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(cnf,[status(esa)],[60]) ).
thf(140,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[56,61]) ).
thf(141,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[140]) ).
thf(142,plain,
( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(2,negated_conjecture,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_6) ).
thf(38,plain,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,plain,
~ ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[38]) ).
thf(10,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(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
v @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_is_defined) ).
thf(57,plain,
v @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
thf(46,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ additive_inverse @ defined ) ),
inference(cnf,[status(esa)],[46]) ).
thf(342,plain,
! [A: $i] :
( ( ( v @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[57,47]) ).
thf(343,plain,
! [A: $i] :
( ( ( v @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[342]) ).
thf(344,plain,
v @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[343:[bind(A,$thf( v ))]]) ).
thf(33,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(93,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)],[33]) ).
thf(196,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)],[142,42]) ).
thf(197,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[196]) ).
thf(208,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != b )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[197]) ).
thf(211,plain,
( ( multiplicative_identity != b )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[208]) ).
thf(351,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[56,47]) ).
thf(352,plain,
! [A: $i] :
( ( ( multiplicative_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[351]) ).
thf(353,plain,
multiplicative_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[352:[bind(A,$thf( multiplicative_identity ))]]) ).
thf(31,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(89,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ product ) ) )
| ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
additive_identity @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
thf(74,plain,
additive_identity @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(29,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(85,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(70,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)],[69]) ).
thf(32,axiom,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
thf(91,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(92,plain,
~ ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(polarity_switch,[status(thm)],[91]) ).
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(65,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(146,plain,
! [A: $i] :
( ( ( v @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ~ $true
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[57,61]) ).
thf(147,plain,
! [A: $i] :
( ( ( v @ defined )
!= ( A @ defined ) )
| ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[146]) ).
thf(148,plain,
( ( additive_identity @ ( v @ ( additive_identity @ sum ) ) )
| ( v @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( v ))]]) ).
thf(300,plain,
( ( ( additive_identity @ ( v @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( v @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[148,42]) ).
thf(301,plain,
( ( ( additive_identity @ ( v @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ( v @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[300]) ).
thf(320,plain,
( ( additive_identity != additive_identity )
| ( v != b )
| ( additive_identity != additive_identity )
| ( v @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[301]) ).
thf(328,plain,
( ( v != b )
| ( v @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[320]) ).
thf(25,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(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ sum ) ) )
| ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(204,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[142,92]) ).
thf(205,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( multiplicative_identity @ ( additive_identity @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[204]) ).
thf(209,plain,
( ( multiplicative_identity != additive_identity )
| ( multiplicative_identity != additive_identity )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[205]) ).
thf(212,plain,
( ( multiplicative_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[209]) ).
thf(35,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
thf(96,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
a @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
thf(73,plain,
a @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(101,plain,
( ( ( v @ ( b @ multiplicative_inverse @ ( a @ multiplicative_inverse @ product ) ) )
!= ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,43]) ).
thf(102,plain,
( ( v @ ( b @ multiplicative_inverse @ ( a @ multiplicative_inverse @ product ) ) )
!= ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( ( v != v )
| ( ( u @ multiplicative_inverse )
!= ( b @ multiplicative_inverse ) )
| ( ( a @ multiplicative_inverse )
!= multiplicative_identity ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
( ( ( u @ multiplicative_inverse )
!= ( b @ multiplicative_inverse ) )
| ( ( a @ multiplicative_inverse )
!= multiplicative_identity ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
( ( u != b )
| ( ( a @ multiplicative_inverse )
!= multiplicative_identity ) ),
inference(simp,[status(thm)],[104]) ).
thf(3,negated_conjecture,
u @ ( b @ ( a @ product ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_7) ).
thf(39,plain,
u @ ( b @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(118,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ $true
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[70,43]) ).
thf(119,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ product ) ) )
!= ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) ) )
| ~ ( C @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( D @ product ) ) )
| ~ ( A @ ( E @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( u @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( u @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( multiplicative_identity )),bind(B,$thf( u @ multiplicative_inverse )),bind(C,$thf( v )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G ))]]) ).
thf(135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( v @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( u @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( C @ ( u @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(231,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( u @ ( b @ ( a @ product ) ) )
!= ( C @ ( u @ multiplicative_inverse @ ( A @ product ) ) ) )
| ~ ( v @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( u @ multiplicative_inverse @ ( B @ product ) ) )
| ~ $true
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,135]) ).
thf(232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( u @ ( b @ ( a @ product ) ) )
!= ( C @ ( u @ multiplicative_inverse @ ( A @ product ) ) ) )
| ~ ( v @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( u @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( u != C )
| ( ( u @ multiplicative_inverse )
!= b )
| ( a != A )
| ~ ( v @ ( D @ ( C @ sum ) ) )
| ~ ( D @ ( u @ multiplicative_inverse @ ( B @ product ) ) )
| ~ ( multiplicative_identity @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[232]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( ( u @ multiplicative_inverse )
!= b )
| ~ ( v @ ( B @ ( u @ sum ) ) )
| ~ ( B @ ( u @ multiplicative_inverse @ ( A @ product ) ) )
| ~ ( multiplicative_identity @ ( A @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[259]) ).
thf(45,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)],[44]) ).
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(71,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(11,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(54,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)],[11]) ).
thf(34,axiom,
b @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
thf(95,plain,
b @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(348,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[95,47]) ).
thf(349,plain,
! [A: $i] :
( ( ( b @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[348]) ).
thf(350,plain,
b @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[349:[bind(A,$thf( b ))]]) ).
thf(27,axiom,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ defined )
| ( A @ ( A @ ( multiplicative_identity @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(206,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[142,41]) ).
thf(207,plain,
( ( ( additive_identity @ ( multiplicative_identity @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[206]) ).
thf(210,plain,
( ( additive_identity != additive_identity )
| ( multiplicative_identity != a )
| ( additive_identity != additive_identity )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[207]) ).
thf(213,plain,
( ( multiplicative_identity != a )
| ( multiplicative_identity @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[210]) ).
thf(310,plain,
( ( ( additive_identity @ ( v @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( v @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[148,41]) ).
thf(311,plain,
( ( ( additive_identity @ ( v @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ( v @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[310]) ).
thf(322,plain,
( ( additive_identity != additive_identity )
| ( v != a )
| ( additive_identity != additive_identity )
| ( v @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[311]) ).
thf(330,plain,
( ( v != a )
| ( v @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[322]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( ( u @ ( b @ ( a @ product ) ) )
!= ( B @ ( u @ multiplicative_inverse @ ( A @ product ) ) ) )
| ( ( u @ multiplicative_inverse )
!= b )
| ~ ( v @ ( B @ ( u @ sum ) ) )
| ~ $true
| ~ ( multiplicative_identity @ ( A @ ( a @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[39,264]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( ( u @ ( b @ ( a @ product ) ) )
!= ( B @ ( u @ multiplicative_inverse @ ( A @ product ) ) ) )
| ( ( u @ multiplicative_inverse )
!= b )
| ~ ( v @ ( B @ ( u @ sum ) ) )
| ~ ( multiplicative_identity @ ( A @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( u != B )
| ( ( u @ multiplicative_inverse )
!= b )
| ( a != A )
| ( ( u @ multiplicative_inverse )
!= b )
| ~ ( v @ ( B @ ( u @ sum ) ) )
| ~ ( multiplicative_identity @ ( A @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(299,plain,
( ( ( u @ multiplicative_inverse )
!= b )
| ~ ( v @ ( u @ ( u @ sum ) ) )
| ~ ( multiplicative_identity @ ( a @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(8,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(48,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)],[8]) ).
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(63,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(9,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(50,plain,
! [B: $i,A: $i] :
( ~ ( B @ defined )
| ~ ( A @ defined )
| ( B @ ( A @ multiply ) @ defined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
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(67,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(357,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ~ $true
| ( A @ additive_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[74,47]) ).
thf(358,plain,
! [A: $i] :
( ( ( additive_identity @ defined )
!= ( A @ defined ) )
| ( A @ additive_inverse @ defined ) ),
inference(simp,[status(thm)],[357]) ).
thf(359,plain,
additive_identity @ additive_inverse @ defined,
inference(pattern_uni,[status(thm)],[358:[bind(A,$thf( additive_identity ))]]) ).
thf(143,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)],[61,42]) ).
thf(144,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( b @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
( ~ ( b @ defined )
| ( b @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( b ))]]) ).
thf(176,plain,
( ~ $true
| ( b @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[145,95]) ).
thf(177,plain,
b @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[176]) ).
thf(157,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(paramod_ordered,[status(thm)],[61,41]) ).
thf(158,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( additive_identity @ sum ) ) )
!= ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( A @ defined )
| ( A @ multiplicative_inverse @ defined ) ),
inference(simp,[status(thm)],[157]) ).
thf(159,plain,
( ~ ( a @ defined )
| ( a @ multiplicative_inverse @ defined ) ),
inference(pattern_uni,[status(thm)],[158:[bind(A,$thf( a ))]]) ).
thf(181,plain,
( ~ $true
| ( a @ multiplicative_inverse @ defined ) ),
inference(rewrite,[status(thm)],[159,73]) ).
thf(182,plain,
a @ multiplicative_inverse @ defined,
inference(simp,[status(thm)],[181]) ).
thf(30,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(87,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)],[30]) ).
thf(24,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(75,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)],[24]) ).
thf(14,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(58,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)],[14]) ).
thf(16,axiom,
u @ defined,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_defined) ).
thf(62,plain,
u @ defined,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,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(83,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)],[28]) ).
thf(98,plain,
( ( ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( u @ ( b @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,43]) ).
thf(99,plain,
( ( v @ ( u @ multiplicative_inverse @ ( multiplicative_identity @ product ) ) )
!= ( u @ ( b @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
( ( v != u )
| ( ( u @ multiplicative_inverse )
!= b )
| ( multiplicative_identity != a ) ),
inference(simp,[status(thm)],[99]) ).
thf(12735,plain,
$false,
inference(e,[status(thm)],[69,41,44,43,40,36,79,56,142,42,37,52,344,46,93,57,211,353,61,89,74,60,85,38,70,92,65,328,77,212,96,73,105,148,264,45,71,54,350,81,39,213,91,330,135,299,48,63,95,50,67,359,177,182,87,104,75,58,47,62,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD012-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 02:22:33 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.36/1.21 % [INFO] Parsing done (237ms).
% 1.36/1.22 % [INFO] Running in sequential loop mode.
% 2.05/1.62 % [INFO] eprover registered as external prover.
% 2.05/1.62 % [INFO] Scanning for conjecture ...
% 2.22/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 30 axioms. Running axiom selection ...
% 2.22/1.79 % [INFO] Axiom selection finished. Selected 30 axioms (removed 0 axioms).
% 2.40/1.84 % [INFO] Problem is propositional (TPTP CNF).
% 2.40/1.84 % [INFO] Type checking passed.
% 2.40/1.85 % [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 ...
% 38.14/8.85 % External prover 'e' found a proof!
% 38.14/8.85 % [INFO] Killing All external provers ...
% 38.14/8.85 % Time passed: 8319ms (effective reasoning time: 7620ms)
% 38.14/8.85 % Axioms used in derivation (30): associativity_addition_1, existence_of_identity_multiplication, transitivity_of_order_relation, totality_of_multiplication, well_definedness_of_additive_identity, compatibility_of_order_relation_and_multiplication, a_is_defined, well_definedness_of_multiplication, existence_of_identity_addition, associativity_multiplication_1, antisymmetry_of_order_relation, totality_of_addition, commutativity_multiplication, existence_of_inverse_addition, well_definedness_of_addition, compatibility_of_order_relation_and_addition, 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, u_is_defined, v_is_defined, distributivity_2
% 38.14/8.85 % No. of inferences in proof: 147
% 38.14/8.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 8319 ms resp. 7620 ms w/o parsing
% 32.58/8.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.58/8.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------