TSTP Solution File: RNG039-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : RNG039-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:49:09 EDT 2023
% Result : Unsatisfiable 3.77s 1.88s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 70
% Syntax : Number of formulae : 131 ( 99 unt; 10 typ; 0 def)
% Number of atoms : 187 ( 16 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 848 ( 68 ~; 66 |; 0 &; 714 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 182 ( 0 ^; 182 !; 0 ?; 182 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_type,type,
product: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(c_type,type,
c: $i ).
thf(d_type,type,
d: $i ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(add_type,type,
add: $i > $i > $i ).
thf(additive_identity_type,type,
additive_identity: $i ).
thf(additive_inverse_type,type,
additive_inverse: $i > $i ).
thf(multiply_type,type,
multiply: $i > $i > $i ).
thf(25,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication1) ).
thf(97,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ C @ D @ F )
| ( product @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(51,axiom,
! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause57) ).
thf(129,plain,
! [A: $i] : ( product @ ( multiply @ A @ b ) @ a @ ( multiply @ A @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(42,axiom,
product @ b @ d @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause40) ).
thf(118,plain,
product @ b @ d @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(17,axiom,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(86,plain,
! [A: $i] : ( sum @ ( additive_inverse @ A ) @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,negated_conjecture,
c != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
thf(63,plain,
c != d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(49,axiom,
! [B: $i,A: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause44) ).
thf(127,plain,
! [B: $i,A: $i] : ( product @ a @ ( multiply @ b @ A ) @ ( multiply @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(58,axiom,
product @ ( add @ b @ a ) @ b @ ( add @ b @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause68) ).
thf(138,plain,
product @ ( add @ b @ a ) @ b @ ( add @ b @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(19,axiom,
! [A: $i] :
( ( multiply @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause35) ).
thf(88,plain,
! [A: $i] :
( ( multiply @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(39,axiom,
product @ b @ a @ ( multiply @ b @ d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause58) ).
thf(115,plain,
product @ b @ a @ ( multiply @ b @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
! [B: $i,A: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause43) ).
thf(120,plain,
! [B: $i,A: $i] : ( product @ A @ ( multiply @ A @ B ) @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(34,axiom,
product @ ( add @ a @ b ) @ a @ ( add @ a @ d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause70) ).
thf(110,plain,
product @ ( add @ a @ b ) @ a @ ( add @ a @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(47,axiom,
product @ ( multiply @ d @ b ) @ a @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause59) ).
thf(125,plain,
product @ ( multiply @ d @ b ) @ a @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(22,axiom,
! [B: $i,A: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause52) ).
thf(93,plain,
! [B: $i,A: $i] : ( product @ ( multiply @ A @ B ) @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(11,axiom,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(78,plain,
! [A: $i] : ( sum @ A @ additive_identity @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(45,axiom,
( ( multiply @ b @ a )
= d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause37) ).
thf(121,plain,
( ( multiply @ b @ a )
= d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ A @ E @ F )
| ( sum @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition2) ).
thf(84,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ A @ E @ F )
| ( sum @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,negated_conjecture,
product @ a @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_b) ).
thf(61,plain,
product @ a @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(53,axiom,
product @ a @ ( multiply @ b @ c ) @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause46) ).
thf(133,plain,
product @ a @ ( multiply @ b @ c ) @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(40,axiom,
! [A: $i] : ( product @ A @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause71) ).
thf(116,plain,
! [A: $i] : ( product @ A @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(8,axiom,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(74,plain,
! [A: $i] : ( sum @ additive_identity @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
product @ a @ b @ ( multiply @ a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause54) ).
thf(117,plain,
product @ a @ b @ ( multiply @ a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(28,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_multiplication2) ).
thf(102,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ B @ D @ E )
| ~ ( product @ A @ E @ F )
| ( product @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(57,axiom,
product @ b @ ( add @ b @ a ) @ ( add @ b @ d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause66) ).
thf(137,plain,
product @ b @ ( add @ b @ a ) @ ( add @ b @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(33,axiom,
product @ c @ a @ ( multiply @ a @ d ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause60) ).
thf(109,plain,
product @ c @ a @ ( multiply @ a @ d ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(24,axiom,
product @ a @ ( add @ a @ b ) @ ( add @ a @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause64) ).
thf(96,plain,
product @ a @ ( add @ a @ b ) @ ( add @ a @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(54,axiom,
product @ a @ ( add @ b @ a ) @ ( add @ c @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause63) ).
thf(134,plain,
product @ a @ ( add @ b @ a ) @ ( add @ c @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7,axiom,
! [A: $i] : ( sum @ A @ A @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause32) ).
thf(73,plain,
! [A: $i] : ( sum @ A @ A @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,axiom,
product @ a @ c @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause39) ).
thf(128,plain,
product @ a @ c @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(30,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( product @ A @ F @ G )
| ( sum @ C @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(105,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( product @ A @ F @ G )
| ( sum @ C @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(37,axiom,
product @ c @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause41) ).
thf(113,plain,
product @ c @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(10,axiom,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause33) ).
thf(76,plain,
! [A: $i] :
( ( add @ A @ additive_identity )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(60,axiom,
product @ d @ a @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause42) ).
thf(140,plain,
product @ d @ a @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(21,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ A @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(91,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ D @ E )
| ~ ( sum @ B @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ A @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(4,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ C @ D @ F )
| ( sum @ A @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition1) ).
thf(66,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ~ ( sum @ B @ D @ E )
| ~ ( sum @ C @ D @ F )
| ( sum @ A @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,axiom,
product @ ( multiply @ c @ a ) @ b @ c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause55) ).
thf(108,plain,
product @ ( multiply @ c @ a ) @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ A @ B @ D )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(55,axiom,
product @ b @ ( multiply @ a @ d ) @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause49) ).
thf(135,plain,
product @ b @ ( multiply @ a @ d ) @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(36,axiom,
product @ b @ ( add @ a @ b ) @ ( add @ d @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause65) ).
thf(112,plain,
product @ b @ ( add @ a @ b ) @ ( add @ d @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ F @ B @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
thf(123,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( sum @ C @ E @ G )
| ( product @ F @ B @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(26,axiom,
product @ a @ b @ ( multiply @ c @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause45) ).
thf(99,plain,
product @ a @ b @ ( multiply @ c @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause38) ).
thf(87,plain,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(29,axiom,
! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause47) ).
thf(104,plain,
! [A: $i] : ( product @ b @ ( multiply @ a @ A ) @ ( multiply @ d @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(38,axiom,
product @ d @ b @ ( multiply @ b @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause56) ).
thf(114,plain,
product @ d @ b @ ( multiply @ b @ c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(59,axiom,
product @ ( add @ b @ a ) @ a @ ( add @ d @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause69) ).
thf(139,plain,
product @ ( add @ b @ a ) @ a @ ( add @ d @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(9,axiom,
! [B: $i,A: $i] : ( sum @ A @ ( add @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion1) ).
thf(75,plain,
! [B: $i,A: $i] : ( sum @ A @ ( add @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,axiom,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(119,plain,
! [B: $i,A: $i] : ( product @ A @ B @ ( multiply @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(14,axiom,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(82,plain,
! [B: $i,A: $i] : ( sum @ A @ B @ ( add @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,axiom,
product @ a @ d @ ( multiply @ c @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause51) ).
thf(107,plain,
product @ a @ d @ ( multiply @ c @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(12,axiom,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(79,plain,
! [A: $i] : ( sum @ A @ ( additive_inverse @ A ) @ additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(23,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( product @ F @ B @ G )
| ( sum @ C @ E @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity3) ).
thf(94,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( product @ A @ B @ C )
| ~ ( product @ D @ B @ E )
| ~ ( sum @ A @ D @ F )
| ~ ( product @ F @ B @ G )
| ( sum @ C @ E @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(48,axiom,
product @ ( add @ a @ b ) @ b @ ( add @ c @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause67) ).
thf(126,plain,
product @ ( add @ a @ b ) @ b @ ( add @ c @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(56,axiom,
product @ b @ a @ ( multiply @ d @ a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause48) ).
thf(136,plain,
product @ b @ a @ ( multiply @ d @ a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(5,axiom,
! [A: $i] :
( ( add @ A @ A )
= additive_identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause34) ).
thf(68,plain,
! [A: $i] :
( ( add @ A @ A )
= additive_identity ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,negated_conjecture,
product @ b @ a @ d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a) ).
thf(62,plain,
product @ b @ a @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [B: $i,A: $i] : ( sum @ ( add @ A @ B ) @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorbtion2) ).
thf(83,plain,
! [B: $i,A: $i] : ( sum @ ( add @ A @ B ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(27,axiom,
( ( multiply @ a @ b )
= c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause36) ).
thf(100,plain,
( ( multiply @ a @ b )
= c ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(20,axiom,
! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause53) ).
thf(90,plain,
! [A: $i] : ( product @ ( multiply @ A @ a ) @ b @ ( multiply @ A @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(35,axiom,
product @ b @ c @ ( multiply @ d @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause50) ).
thf(111,plain,
product @ b @ c @ ( multiply @ d @ b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(141,plain,
$false,
inference(e,[status(thm)],[97,129,118,86,63,127,138,88,115,120,110,125,93,78,121,84,61,133,116,74,117,102,70,137,109,96,134,73,128,105,113,76,140,91,66,108,130,135,80,112,123,99,87,104,114,139,75,119,82,107,79,94,126,136,68,62,83,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG039-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 20:19:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (140ms).
% 1.18/0.99 % [INFO] Running in sequential loop mode.
% 1.83/1.19 % [INFO] eprover registered as external prover.
% 1.86/1.19 % [INFO] cvc4 registered as external prover.
% 1.86/1.20 % [INFO] Scanning for conjecture ...
% 1.95/1.26 % [INFO] Found a conjecture and 57 axioms. Running axiom selection ...
% 2.17/1.31 % [INFO] Axiom selection finished. Selected 57 axioms (removed 0 axioms).
% 2.17/1.35 % [INFO] Problem is propositional (TPTP CNF).
% 2.17/1.35 % [INFO] Type checking passed.
% 2.17/1.35 % [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 ...
% 3.77/1.87 % External prover 'e' found a proof!
% 3.77/1.87 % [INFO] Killing All external provers ...
% 3.77/1.88 % Time passed: 1354ms (effective reasoning time: 881ms)
% 3.77/1.88 % Solved by 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)>
% 3.77/1.88 % Axioms used in derivation (57): clause37, clause49, additive_identity1, associativity_of_multiplication2, clause34, clause69, clause57, clause33, associativity_of_addition2, clause60, clause71, clause65, clause43, clause32, clause54, clause59, clause48, addition_is_well_defined, clause55, clause66, closure_of_addition, clause70, distributivity3, absorbtion2, clause42, commutativity_of_addition, clause64, additive_identity2, clause38, distributivity2, associativity_of_addition1, clause53, left_inverse, multiplication_is_well_defined, absorbtion1, right_inverse, clause68, distributivity1, clause41, clause39, clause35, closure_of_multiplication, clause52, clause63, clause46, clause44, clause50, clause58, associativity_of_multiplication1, clause56, clause67, clause45, distributivity4, clause40, clause51, clause47, clause36
% 3.77/1.88 % No. of inferences in proof: 121
% 3.77/1.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1354 ms resp. 881 ms w/o parsing
% 4.10/1.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.10/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------