%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:25:19 AM UTC 2026
% Result : Unsatisfiable 7.10s 3.08s
% Output : Refutation 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 74
% Syntax : Number of formulae : 149 ( 101 unt; 0 typ; 0 def)
% Number of atoms : 259 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1172 ( 112 ~; 110 |; 0 &; 950 @)
% ( 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 : 11 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 278 ( 0 ^; 278 !; 0 ?; 278 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(equalish_decl,type,
equalish: $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(57,axiom,
a @ ( d @ add ) @ ( a @ ( a @ ( b @ add ) @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(152,plain,
a @ ( d @ add ) @ ( a @ ( a @ ( b @ add ) @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution3) ).
thf(118,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ sum ) ) )
| ~ ( A @ ( D @ ( C @ sum ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ equalish ) )
| ~ ( C @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_left_cancellation) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ equalish ) )
| ~ ( C @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(50,axiom,
b @ ( d @ add ) @ ( b @ ( a @ add ) @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(143,plain,
b @ ( d @ add ) @ ( b @ ( a @ add ) @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(12,axiom,
! [B: $i,A: $i] : ( A @ ( B @ add ) @ ( B @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(90,plain,
! [B: $i,A: $i] : ( A @ ( B @ add ) @ ( B @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(45,axiom,
d @ ( a @ multiply ) @ ( a @ ( c @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(138,plain,
d @ ( a @ multiply ) @ ( a @ ( c @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(19,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( B @ ( A @ multiply ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(101,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( B @ ( A @ multiply ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ sum ) ) )
| ~ ( F @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(88,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ sum ) ) )
| ~ ( F @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(72,axiom,
a @ ( c @ add ) @ ( a @ ( b @ add ) @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(170,plain,
a @ ( c @ add ) @ ( a @ ( b @ add ) @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution2) ).
thf(115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ product ) ) )
| ~ ( D @ ( A @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,axiom,
! [A: $i] : ( A @ ( A @ ( A @ multiply ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(120,plain,
! [A: $i] : ( A @ ( A @ ( A @ multiply ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(49,axiom,
b @ ( d @ multiply ) @ ( c @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(142,plain,
b @ ( d @ multiply ) @ ( c @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(26,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(110,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( C @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(35,axiom,
! [A: $i] : ( A @ ( d @ multiply ) @ ( A @ ( a @ multiply ) @ ( b @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(125,plain,
! [A: $i] : ( A @ ( d @ multiply ) @ ( A @ ( a @ multiply ) @ ( b @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(61,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(157,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ multiply ) @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(67,axiom,
c @ ( c @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(164,plain,
c @ ( c @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(23,axiom,
! [A: $i] : ( additive_identity @ ( A @ ( additive_identity @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity1) ).
thf(106,plain,
! [A: $i] : ( additive_identity @ ( A @ ( additive_identity @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ add ) @ ( A @ ( C @ add ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution2) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ add ) @ ( A @ ( C @ add ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(8,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(84,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ sum ) ) )
| ~ ( D @ ( A @ ( C @ sum ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution2) ).
thf(147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ sum ) ) )
| ~ ( D @ ( A @ ( C @ sum ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(40,axiom,
c @ ( b @ add ) @ ( b @ ( a @ ( b @ add ) @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(132,plain,
c @ ( b @ add ) @ ( b @ ( a @ ( b @ add ) @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ sum ) ) )
| ~ ( D @ ( C @ ( A @ sum ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_substitution1) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ sum ) ) )
| ~ ( D @ ( C @ ( A @ sum ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(30,axiom,
a @ ( d @ multiply ) @ ( a @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(117,plain,
a @ ( d @ multiply ) @ ( a @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ add ) @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion2) ).
thf(85,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ add ) @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(102,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( B @ ( F @ product ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(44,axiom,
c @ ( b @ ( a @ ( c @ multiply ) @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(137,plain,
c @ ( b @ ( a @ ( c @ multiply ) @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(68,axiom,
! [A: $i] : ( d @ ( A @ multiply ) @ ( a @ ( b @ ( A @ multiply ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(165,plain,
! [A: $i] : ( d @ ( A @ multiply ) @ ( a @ ( b @ ( A @ multiply ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ equalish ) )
| ~ ( C @ ( B @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(97,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( F @ ( A @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(156,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(71,axiom,
d @ ( a @ ( b @ multiply ) @ equalish ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(169,plain,
d @ ( a @ ( b @ multiply ) @ equalish ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(48,axiom,
! [A: $i] : ( additive_identity @ ( additive_identity @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_identity2) ).
thf(141,plain,
! [A: $i] : ( additive_identity @ ( additive_identity @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(25,axiom,
c @ ( a @ add ) @ ( b @ ( a @ add ) @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(109,plain,
c @ ( a @ add ) @ ( b @ ( a @ add ) @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3,negated_conjecture,
~ ( d @ ( c @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
thf(77,plain,
~ ( d @ ( c @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] : ( c @ ( A @ multiply ) @ ( b @ ( a @ ( A @ multiply ) @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(96,plain,
! [A: $i] : ( c @ ( A @ multiply ) @ ( b @ ( a @ ( A @ multiply ) @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(74,axiom,
d @ ( a @ ( d @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(173,plain,
d @ ( a @ ( d @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( C @ ( A @ add ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ add ) @ ( C @ ( A @ add ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(37,axiom,
d @ ( b @ add ) @ ( a @ ( b @ add ) @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(128,plain,
d @ ( b @ add ) @ ( a @ ( b @ add ) @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(22,axiom,
! [A: $i] : ( additive_identity @ ( A @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(105,plain,
! [A: $i] : ( additive_identity @ ( A @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ product ) ) )
| ~ ( A @ ( D @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).
thf(166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ product ) ) )
| ~ ( A @ ( D @ ( C @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(64,axiom,
d @ ( a @ ( b @ ( d @ multiply ) @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(161,plain,
d @ ( a @ ( b @ ( d @ multiply ) @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(55,axiom,
c @ ( a @ multiply ) @ ( b @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(149,plain,
c @ ( a @ multiply ) @ ( b @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(51,axiom,
c @ ( b @ ( c @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(144,plain,
c @ ( b @ ( c @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(10,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ sum ) ) )
| ~ ( F @ ( E @ ( A @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(86,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ sum ) ) )
| ~ ( F @ ( E @ ( A @ sum ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(63,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(159,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( B @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( A @ sum ) ) )
| ~ ( E @ ( B @ ( D @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(81,plain,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
d @ ( a @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a) ).
thf(76,plain,
d @ ( a @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
d @ ( a @ add ) @ ( a @ ( b @ ( a @ add ) @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(140,plain,
d @ ( a @ add ) @ ( a @ ( b @ ( a @ add ) @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(13,axiom,
! [A: $i] : ( additive_identity @ ( A @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(91,plain,
! [A: $i] : ( additive_identity @ ( A @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(59,axiom,
d @ ( d @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(155,plain,
d @ ( d @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(42,axiom,
! [A: $i] : ( A @ ( additive_identity @ ( A @ add ) @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(135,plain,
! [A: $i] : ( A @ ( additive_identity @ ( A @ add ) @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ add ) @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion1) ).
thf(80,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ add ) @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(65,axiom,
b @ ( c @ add ) @ ( b @ ( b @ ( a @ add ) @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(162,plain,
b @ ( c @ add ) @ ( b @ ( b @ ( a @ add ) @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( A @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution1) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( A @ product ) ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(34,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(123,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(52,axiom,
c @ ( b @ multiply ) @ ( b @ ( d @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(145,plain,
c @ ( b @ multiply ) @ ( b @ ( d @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_substitution1) ).
thf(99,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiply ) @ ( C @ ( A @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(21,axiom,
d @ ( d @ ( a @ multiply ) @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(104,plain,
d @ ( d @ ( a @ multiply ) @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(62,axiom,
c @ ( b @ ( a @ multiply ) @ equalish ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(158,plain,
c @ ( b @ ( a @ multiply ) @ equalish ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(28,axiom,
b @ ( c @ multiply ) @ ( b @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(114,plain,
b @ ( c @ multiply ) @ ( b @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ equalish ) )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum_right_concellation) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ equalish ) )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(46,axiom,
! [A: $i] : ( A @ ( A @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(139,plain,
! [A: $i] : ( A @ ( A @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1,negated_conjecture,
c @ ( b @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
thf(75,plain,
c @ ( b @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(82,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(70,axiom,
c @ ( c @ ( b @ multiply ) @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(168,plain,
c @ ( c @ ( b @ multiply ) @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(53,axiom,
d @ ( b @ multiply ) @ ( a @ ( b @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(146,plain,
d @ ( b @ multiply ) @ ( a @ ( b @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ multiply ) @ ( A @ ( C @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_substitution2) ).
thf(107,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ multiply ) @ ( A @ ( C @ multiply ) @ equalish ) )
| ~ ( B @ ( A @ equalish ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(79,plain,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(94,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ equalish ) )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(36,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(126,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,axiom,
a @ ( c @ multiply ) @ ( d @ ( a @ product ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(136,plain,
a @ ( c @ multiply ) @ ( d @ ( a @ product ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(39,axiom,
! [A: $i] : ( A @ ( A @ equalish ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(131,plain,
! [A: $i] : ( A @ ( A @ equalish ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(66,axiom,
! [B: $i,A: $i] : ( A @ ( B @ multiply ) @ ( A @ ( b @ multiply ) @ ( a @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(163,plain,
! [B: $i,A: $i] : ( A @ ( B @ multiply ) @ ( A @ ( b @ multiply ) @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(212,plain,
$false,
inference(e,[status(thm)],[152,118,150,143,90,138,101,88,170,115,120,142,153,110,125,157,164,106,121,84,147,132,133,117,85,102,137,165,92,97,156,169,141,109,77,96,173,129,128,105,166,161,149,144,86,159,81,76,140,91,155,135,80,162,112,123,145,99,104,158,114,171,139,75,82,168,146,107,79,94,126,136,131,163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n007.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 05:49:24 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.68/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.13/0.97 % [INFO] Parsing done (195ms).
% 1.13/0.98 % [INFO] Running in sequential loop mode.
% 2.18/1.31 % [INFO] eprover registered as external prover.
% 2.18/1.32 % [INFO] Scanning for conjecture ...
% 2.40/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 71 axioms. Running axiom selection ...
% 2.40/1.48 % [INFO] Axiom selection finished. Selected 71 axioms (removed 0 axioms).
% 2.64/1.59 % [INFO] Problem is propositional (TPTP CNF).
% 2.64/1.60 % [INFO] Type checking passed.
% 2.95/1.60 % [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 ...
% 7.10/3.08 % External prover 'e' found a proof!
% 7.10/3.08 % [INFO] Killing All external provers ...
% 7.10/3.08 % Time passed: 2578ms (effective reasoning time: 2091ms)
% 7.10/3.08 % Axioms used in derivation (71): clause37, sum_left_cancellation, additive_identity1, multiplication_is_well_defined, multiplicative_identity1, associativity_of_multiplication2, clause33, associativity_of_addition2, clause60, clause71, clause65, clause43, clause32, clause54, clause59, product_substitution2, clause48, addition_is_well_defined, clause55, clause66, closure_of_addition, clause70, distributivity3, clause49, sum_substitution2, absorbtion2, clause42, commutativity_of_addition, clause64, multiply_substitution1, product_substitution3, additive_identity2, clause38, distributivity2, associativity_of_addition1, clause53, reflexivity, clause34, absorbtion1, sum_substitution3, sum_right_concellation, clause69, product_substitution1, multiply_substitution2, clause68, distributivity1, clause41, clause39, add_substitution1, clause57, multiplicative_identity2, clause35, closure_of_multiplication, clause52, clause63, clause46, clause44, clause50, transitivity, clause58, associativity_of_multiplication1, clause56, clause67, clause45, distributivity4, clause40, clause51, clause47, clause36, add_substitution2, sum_substitution1
% 7.10/3.08 % No. of inferences in proof: 149
% 7.10/3.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2578 ms resp. 2091 ms w/o parsing
% 7.59/3.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.59/3.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------