%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : RNG001-4 : 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 : n018.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 08:25:09 AM UTC 2026
% Result : Unsatisfiable 71.29s 18.60s
% Output : Refutation 57.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 20
% Syntax : Number of formulae : 316 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 1159 ( 330 equ; 0 cnn)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 4714 ( 871 ~; 711 |; 0 &;3132 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 1000 ( 0 ^;1000 !; 0 ?;1000 :)
% Comments :
%------------------------------------------------------------------------------
thf(product_decl,type,
product: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(additive_identity_decl,type,
additive_identity: $i ).
thf(sum_decl,type,
sum: $i > $i > $i > $o ).
thf(add_decl,type,
add: $i > $i > $i ).
thf(additive_inverse_decl,type,
additive_inverse: $i > $i ).
thf(multiply_decl,type,
multiply: $i > $i > $i ).
thf(20,axiom,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity1) ).
thf(58,plain,
! [A: $i] : ( A @ ( A @ ( additive_identity @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation1) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) )
| ( B = D ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( C @ ( B @ sum ) ) ) )
| ~ ( D @ ( E @ ( B @ sum ) ) )
| ~ $true
| ( C = E ) ),
inference(paramod_ordered,[status(thm)],[58,25]) ).
thf(264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( additive_identity @ sum ) ) )
!= ( D @ ( C @ ( B @ sum ) ) ) )
| ~ ( D @ ( E @ ( B @ sum ) ) )
| ( C = E ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( additive_identity @ sum ) ) )
| ( A = B ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( A )),bind(B,$thf( additive_identity )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( additive_identity @ sum ) ) )
| ( A = B ) ),
inference(simp,[status(thm)],[265]) ).
thf(17,axiom,
! [A: $i] : ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(54,plain,
! [A: $i] : ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_multiplication) ).
thf(55,plain,
! [B: $i,A: $i] : ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(1,negated_conjecture,
~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_times_additive_id_is_additive_id) ).
thf(21,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(22,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ product ) ) ),
inference(polarity_switch,[status(thm)],[21]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55,22]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ product ) ) ) ),
inference(simp,[status(thm)],[178]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != additive_identity )
| ( A != a ) ),
inference(simp,[status(thm)],[179]) ).
thf(203,plain,
( ( additive_identity @ ( a @ multiply ) )
!= additive_identity ),
inference(simp,[status(thm)],[198]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( B
!= ( additive_identity @ ( a @ multiply ) ) )
| ( A != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,203]) ).
thf(390,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( A @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[389:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(435,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(565,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,435]) ).
thf(566,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[565]) ).
thf(622,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[566]) ).
thf(638,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[622]) ).
thf(651,plain,
! [B: $i,A: $i] :
( ( B
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse ) )
| ( A != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,638]) ).
thf(652,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( A @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[651:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse ))]]) ).
thf(682,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[652]) ).
thf(1179,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,682]) ).
thf(1180,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[1179]) ).
thf(1248,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[1180]) ).
thf(1265,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[1248]) ).
thf(1307,plain,
! [B: $i,A: $i] :
( ( B
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ) )
| ( A != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,1265]) ).
thf(1308,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( A @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[1307:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(1349,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[1308]) ).
thf(2301,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,1349]) ).
thf(2302,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2301]) ).
thf(2420,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[2302]) ).
thf(2450,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[2420]) ).
thf(2458,plain,
! [B: $i,A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( B != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,2450]) ).
thf(2459,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[2458:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse )),bind(B,$thf( B ))]]) ).
thf(2540,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[2459]) ).
thf(13,axiom,
! [A: $i] : ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_inverse) ).
thf(47,plain,
! [A: $i] : ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(414,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( B @ ( C @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[47,301]) ).
thf(415,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( B @ ( C @ ( additive_identity @ sum ) ) ) )
| ( B = C ) ),
inference(simp,[status(thm)],[414]) ).
thf(416,plain,
( ( additive_identity @ additive_inverse )
= additive_identity ),
inference(pattern_uni,[status(thm)],[415:[bind(A,$thf( additive_identity )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ additive_inverse ))]]) ).
thf(467,plain,
! [B: $i,A: $i] :
( ( A
!= ( additive_identity @ additive_inverse ) )
| ( B = additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,416]) ).
thf(468,plain,
! [A: $i] :
( ( A = additive_identity )
| ~ ( additive_identity @ additive_inverse @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[467:[bind(A,$thf( additive_identity @ additive_inverse )),bind(B,$thf( B ))]]) ).
thf(483,plain,
! [A: $i] :
( ( A = additive_identity )
| ~ ( additive_identity @ additive_inverse @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(5062,plain,
! [A: $i] :
( ( A = additive_identity )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(rewrite,[status(thm)],[483,416]) ).
thf(2470,plain,
! [B: $i,A: $i] :
( ( B
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( A != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,2450]) ).
thf(2471,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( A @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[2470:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2544,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[2471]) ).
thf(4227,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,2544]) ).
thf(4228,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4227]) ).
thf(4411,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[4228]) ).
thf(4424,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[4411]) ).
thf(4508,plain,
! [B: $i,A: $i] :
( ( B
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( A != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,4424]) ).
thf(4509,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( A @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[4508:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(4637,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[4509]) ).
thf(6429,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,4637]) ).
thf(6430,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[6429]) ).
thf(6493,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[6430]) ).
thf(6508,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[6493]) ).
thf(6755,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5062,6508]) ).
thf(6756,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[6755]) ).
thf(6757,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[6756:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(11893,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,6757]) ).
thf(11894,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11893]) ).
thf(11985,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[11894]) ).
thf(12039,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[11985]) ).
thf(12286,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5062,12039]) ).
thf(12287,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12286]) ).
thf(12288,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[12287:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(10,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(41,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)],[10]) ).
thf(42,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(cnf,[status(esa)],[41]) ).
thf(59,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( E @ ( C @ sum ) ) )
!= ( M @ ( K @ ( I @ sum ) ) ) )
| ( N @ ( L @ ( J @ sum ) ) )
| ~ ( N @ ( M @ ( H @ product ) ) )
| ~ $true
| ~ ( L @ ( K @ ( H @ product ) ) )
| ~ ( J @ ( I @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,42]) ).
thf(60,plain,
! [N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( E @ ( C @ sum ) ) )
!= ( M @ ( K @ ( I @ sum ) ) ) )
| ( N @ ( L @ ( J @ sum ) ) )
| ~ ( N @ ( M @ ( H @ product ) ) )
| ~ ( L @ ( K @ ( H @ product ) ) )
| ~ ( J @ ( I @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[59]) ).
thf(61,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ sum ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( C )),bind(J,$thf( J )),bind(K,$thf( E )),bind(L,$thf( L )),bind(M,$thf( G ))]]) ).
thf(83,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( K @ ( J @ ( I @ sum ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(115,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( K @ ( G @ ( H @ product ) ) )
!= ( I @ ( C @ ( H @ product ) ) ) )
| ( K @ ( J @ ( I @ sum ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[83]) ).
thf(117,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( I @ sum ) ) )
| ~ ( H @ ( D @ ( G @ product ) ) )
| ~ ( I @ ( F @ ( G @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( C @ ( B @ sum ) ) )
| ~ ( D @ ( C @ ( A @ product ) ) )
| ~ ( F @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( K ))]]) ).
thf(138,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( I @ sum ) ) )
| ~ ( H @ ( D @ ( G @ product ) ) )
| ~ ( I @ ( F @ ( G @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( C @ ( B @ sum ) ) )
| ~ ( D @ ( C @ ( A @ product ) ) )
| ~ ( F @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( B
!= ( additive_identity @ additive_inverse ) )
| ( A = additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,416]) ).
thf(472,plain,
! [A: $i] :
( ( A = additive_identity )
| ~ ( A @ ( additive_identity @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[471:[bind(A,$thf( A )),bind(B,$thf( additive_identity @ additive_inverse ))]]) ).
thf(3066,plain,
! [A: $i] :
( ( A = additive_identity )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(rewrite,[status(thm)],[472,416]) ).
thf(12,axiom,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity2) ).
thf(46,plain,
! [A: $i] : ( A @ ( additive_identity @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( B != a )
| ~ ( additive_identity @ ( additive_identity @ ( A @ product ) ) )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,22]) ).
thf(361,plain,
! [A: $i] :
( ~ ( additive_identity @ ( additive_identity @ ( A @ product ) ) )
| ~ ( A @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( A )),bind(B,$thf( a ))]]) ).
thf(9966,plain,
! [B: $i,A: $i] :
( ( ( A @ ( additive_identity @ ( A @ sum ) ) )
!= ( B @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( B @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[46,361]) ).
thf(9967,plain,
! [B: $i,A: $i] :
( ( ( A @ ( additive_identity @ ( A @ sum ) ) )
!= ( B @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[9966]) ).
thf(10098,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( additive_identity != a )
| ( A != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[9967]) ).
thf(10155,plain,
( ( additive_identity != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) ) ),
inference(simp,[status(thm)],[10098]) ).
thf(10974,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) ) )
| ( additive_identity != a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55,10155]) ).
thf(10975,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) ) )
| ( additive_identity != a ) ),
inference(simp,[status(thm)],[10974]) ).
thf(10976,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != additive_identity )
| ( A != additive_identity )
| ( additive_identity != a ) ),
inference(simp,[status(thm)],[10975]) ).
thf(10997,plain,
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( additive_identity != a ) ),
inference(simp,[status(thm)],[10976]) ).
thf(11105,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != additive_identity )
| ( additive_identity != a )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3066,10997]) ).
thf(11106,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != a )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11105]) ).
thf(11107,plain,
( ( additive_identity != a )
| ~ ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[11106:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(11120,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != additive_identity )
| ( additive_identity != a )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5062,10997]) ).
thf(11121,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != a )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11120]) ).
thf(11122,plain,
( ( additive_identity != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[11121:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(19,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(56,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)],[19]) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( B @ ( C @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( B = C ) ),
inference(paramod_ordered,[status(thm)],[54,301]) ).
thf(375,plain,
! [C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( B @ ( C @ ( additive_identity @ sum ) ) ) )
| ( B = C ) ),
inference(simp,[status(thm)],[374]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( additive_identity != B )
| ( A != C )
| ( ( A @ additive_inverse )
!= additive_identity )
| ( B = C ) ),
inference(simp,[status(thm)],[375]) ).
thf(456,plain,
! [A: $i] :
( ( ( A @ additive_inverse )
!= additive_identity )
| ( additive_identity = A ) ),
inference(simp,[status(thm)],[431]) ).
thf(2555,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( C @ additive_inverse ) )
| ( B != additive_identity )
| ( additive_identity = C )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,456]) ).
thf(2556,plain,
! [B: $i,A: $i] :
( ( A != additive_identity )
| ( additive_identity = B )
| ~ ( B @ additive_inverse @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( D @ additive_inverse )),bind(B,$thf( B )),bind(C,$thf( D ))]]) ).
thf(2574,plain,
! [A: $i] :
( ( additive_identity = A )
| ~ ( A @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2556]) ).
thf(15252,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( A @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2574,12039]) ).
thf(15253,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( A @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[15252]) ).
thf(15254,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[15253:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(2557,plain,
! [C: $i,B: $i,A: $i] :
( ( B
!= ( C @ additive_inverse ) )
| ( A != additive_identity )
| ( additive_identity = C )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,456]) ).
thf(2558,plain,
! [B: $i,A: $i] :
( ( A != additive_identity )
| ( additive_identity = B )
| ~ ( A @ ( B @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[2557:[bind(A,$thf( A )),bind(B,$thf( D @ additive_inverse )),bind(C,$thf( D ))]]) ).
thf(2575,plain,
! [A: $i] :
( ( additive_identity = A )
| ~ ( additive_identity @ ( A @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[2558]) ).
thf(4,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(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(5458,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ sum ) ) )
!= ( additive_identity @ ( D @ ( additive_identity @ sum ) ) ) )
| ( D = additive_identity )
| ~ $true
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,5062]) ).
thf(5459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( B @ sum ) ) )
!= ( additive_identity @ ( D @ ( additive_identity @ sum ) ) ) )
| ( D = additive_identity )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[5458]) ).
thf(5460,plain,
! [A: $i] :
( ( A = additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[5459:[bind(A,$thf( A )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity )),bind(D,$thf( A ))]]) ).
thf(12210,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,12039]) ).
thf(12211,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[12210]) ).
thf(12212,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[12211:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(16,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(52,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)],[16]) ).
thf(57,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(cnf,[status(esa)],[56]) ).
thf(65,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( additive_identity @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( H @ ( F @ ( D @ sum ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ $true
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[58,42]) ).
thf(66,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( additive_identity @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( H @ ( F @ ( D @ sum ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(67,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( A @ ( B @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( additive_identity @ ( B @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[66:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( additive_identity )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( F )),bind(G,$thf( A ))]]) ).
thf(78,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( A @ ( B @ product ) ) )
| ~ ( D @ ( A @ ( B @ product ) ) )
| ~ ( C @ ( additive_identity @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(7224,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,6508]) ).
thf(7225,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[7224]) ).
thf(7226,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[7225:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(116,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( K @ ( G @ ( H @ product ) ) )
!= ( J @ ( E @ ( H @ product ) ) ) )
| ( K @ ( J @ ( I @ sum ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[83]) ).
thf(128,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( I @ ( H @ sum ) ) )
| ~ ( I @ ( F @ ( G @ product ) ) )
| ~ ( H @ ( C @ ( G @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( G )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( K ))]]) ).
thf(132,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( I @ ( H @ sum ) ) )
| ~ ( I @ ( F @ ( G @ product ) ) )
| ~ ( H @ ( C @ ( G @ product ) ) )
| ~ ( F @ ( E @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( B @ sum ) ) )
| ~ ( F @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(113,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( K @ ( G @ ( H @ product ) ) )
!= ( E @ ( D @ ( A @ product ) ) ) )
| ( K @ ( J @ ( I @ sum ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[83]) ).
thf(129,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( H @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( D @ ( C @ ( E @ product ) ) )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( H @ ( D @ ( E @ product ) ) )
| ~ ( B @ ( A @ ( E @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( K ))]]) ).
thf(133,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ sum ) ) )
| ~ ( G @ ( H @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( D @ ( C @ ( E @ product ) ) )
| ~ ( C @ ( D @ ( A @ sum ) ) )
| ~ ( H @ ( D @ ( E @ product ) ) )
| ~ ( B @ ( A @ ( E @ product ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(1297,plain,
! [B: $i,A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ) )
| ( B != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,1265]) ).
thf(1298,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[1297:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse )),bind(B,$thf( B ))]]) ).
thf(1345,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[1298]) ).
thf(643,plain,
! [B: $i,A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse ) )
| ( B != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,638]) ).
thf(644,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[643:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse )),bind(B,$thf( B ))]]) ).
thf(678,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[644]) ).
thf(10953,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3066,10155]) ).
thf(10954,plain,
! [A: $i] :
( ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[10953:[]]) ).
thf(10990,plain,
( ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( a @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[10954]) ).
thf(6,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(32,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)],[6]) ).
thf(33,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(cnf,[status(esa)],[32]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ~ ( C @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation2) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ~ ( C @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ~ ( C @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) )
| ( A = D ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_is_well_defined) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ sum ) ) )
| ~ ( C @ ( B @ ( A @ sum ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(99,plain,
! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( J @ ( I @ sum ) ) )
!= ( Q @ ( O @ ( M @ sum ) ) ) )
| ( V @ ( U @ ( T @ sum ) ) )
| ~ ( V @ ( R @ ( S @ product ) ) )
| ~ ( U @ ( P @ ( S @ product ) ) )
| ~ ( T @ ( N @ ( S @ product ) ) )
| ~ ( R @ ( Q @ ( L @ product ) ) )
| ~ $true
| ~ ( P @ ( O @ ( L @ product ) ) )
| ~ ( N @ ( M @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[83,83]) ).
thf(100,plain,
! [V: $i,U: $i,T: $i,S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( J @ ( I @ sum ) ) )
!= ( Q @ ( O @ ( M @ sum ) ) ) )
| ( V @ ( U @ ( T @ sum ) ) )
| ~ ( V @ ( R @ ( S @ product ) ) )
| ~ ( U @ ( P @ ( S @ product ) ) )
| ~ ( T @ ( N @ ( S @ product ) ) )
| ~ ( R @ ( Q @ ( L @ product ) ) )
| ~ ( P @ ( O @ ( L @ product ) ) )
| ~ ( N @ ( M @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( S @ ( R @ ( Q @ sum ) ) )
| ~ ( S @ ( O @ ( P @ product ) ) )
| ~ ( R @ ( N @ ( P @ product ) ) )
| ~ ( Q @ ( M @ ( P @ product ) ) )
| ~ ( O @ ( K @ ( L @ product ) ) )
| ~ ( N @ ( J @ ( L @ product ) ) )
| ~ ( M @ ( I @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( L )),bind(M,$thf( I )),bind(N,$thf( N )),bind(O,$thf( J )),bind(P,$thf( P )),bind(Q,$thf( K ))]]) ).
thf(137,plain,
! [S: $i,R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( S @ ( R @ ( Q @ sum ) ) )
| ~ ( S @ ( O @ ( P @ product ) ) )
| ~ ( R @ ( N @ ( P @ product ) ) )
| ~ ( Q @ ( M @ ( P @ product ) ) )
| ~ ( O @ ( K @ ( L @ product ) ) )
| ~ ( N @ ( J @ ( L @ product ) ) )
| ~ ( M @ ( I @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(469,plain,
! [B: $i,A: $i] :
( ( A != additive_identity )
| ( ( B @ additive_inverse )
= additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,416]) ).
thf(470,plain,
! [A: $i] :
( ( ( A @ additive_inverse )
= additive_identity )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[469:[bind(A,$thf( additive_identity ))]]) ).
thf(484,plain,
! [A: $i] :
( ( ( A @ additive_inverse )
= additive_identity )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[470]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_addition) ).
thf(31,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1413,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( E @ ( D @ ( C @ sum ) ) ) )
| ( E @ ( C @ ( D @ sum ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31,30]) ).
thf(1414,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( E @ ( D @ ( C @ sum ) ) ) )
| ( E @ ( C @ ( D @ sum ) ) ) ),
inference(simp,[status(thm)],[1413]) ).
thf(1415,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( A @ ( B @ sum ) ) ),
inference(pattern_uni,[status(thm)],[1414:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G )),bind(E,$thf( G @ ( F @ add ) ))]]) ).
thf(1457,plain,
! [B: $i,A: $i] : ( B @ ( A @ add ) @ ( A @ ( B @ sum ) ) ),
inference(simp,[status(thm)],[1415]) ).
thf(11008,plain,
! [B: $i,A: $i] :
( ( A != additive_identity )
| ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( B != a )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,10997]) ).
thf(11009,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[11008:[bind(A,$thf( additive_identity ))]]) ).
thf(11133,plain,
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11009]) ).
thf(1491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( A @ ( B @ sum ) ) )
!= ( C @ ( D @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( C = D ) ),
inference(paramod_ordered,[status(thm)],[1457,301]) ).
thf(1492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( A @ ( B @ sum ) ) )
!= ( C @ ( D @ ( additive_identity @ sum ) ) ) )
| ( C = D ) ),
inference(simp,[status(thm)],[1491]) ).
thf(1493,plain,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
inference(pattern_uni,[status(thm)],[1492:[bind(A,$thf( E )),bind(B,$thf( additive_identity )),bind(C,$thf( additive_identity @ ( E @ add ) )),bind(D,$thf( E ))]]) ).
thf(1534,plain,
! [A: $i] :
( ( additive_identity @ ( A @ add ) )
= A ),
inference(simp,[status(thm)],[1493]) ).
thf(10043,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( B @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( B @ product ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,361]) ).
thf(10044,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( B @ ( a @ ( additive_identity @ sum ) ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[10043]) ).
thf(10097,plain,
! [B: $i,A: $i] :
( ( additive_identity != B )
| ( A != a )
| ( ( A @ additive_inverse )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[10044]) ).
thf(10154,plain,
( ( ( a @ additive_inverse )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) ) ),
inference(simp,[status(thm)],[10097]) ).
thf(53,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(cnf,[status(esa)],[52]) ).
thf(11081,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,10997]) ).
thf(11082,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[11081:[]]) ).
thf(11157,plain,
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[11082]) ).
thf(18883,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( A @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[2575,12039]) ).
thf(18884,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( A @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[18883]) ).
thf(18885,plain,
~ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[18884:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(62,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( additive_identity @ ( A @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( H @ ( F @ ( D @ sum ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ $true
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,42]) ).
thf(63,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( additive_identity @ ( A @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( H @ ( F @ ( D @ sum ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(64,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( A @ ( B @ product ) ) )
| ~ ( D @ ( additive_identity @ ( B @ product ) ) )
| ~ ( C @ ( A @ ( B @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( additive_identity )),bind(F,$thf( F )),bind(G,$thf( A ))]]) ).
thf(77,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ sum ) ) )
| ~ ( E @ ( A @ ( B @ product ) ) )
| ~ ( D @ ( additive_identity @ ( B @ product ) ) )
| ~ ( C @ ( A @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(96,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( L @ ( K @ ( J @ sum ) ) )
| ~ ( L @ ( H @ ( I @ product ) ) )
| ~ ( K @ ( F @ ( I @ product ) ) )
| ~ ( J @ ( D @ ( I @ product ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ $true
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,83]) ).
thf(97,plain,
! [L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( L @ ( K @ ( J @ sum ) ) )
| ~ ( L @ ( H @ ( I @ product ) ) )
| ~ ( K @ ( F @ ( I @ product ) ) )
| ~ ( J @ ( D @ ( I @ product ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ sum ) ) )
| ~ ( H @ ( D @ ( E @ product ) ) )
| ~ ( G @ ( C @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( D @ ( additive_identity @ ( A @ product ) ) )
| ~ ( C @ ( I @ additive_inverse @ ( A @ product ) ) )
| ~ ( B @ ( I @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( M )),bind(B,$thf( B )),bind(C,$thf( M )),bind(D,$thf( D )),bind(E,$thf( M @ additive_inverse )),bind(F,$thf( F )),bind(G,$thf( additive_identity ))]]) ).
thf(134,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ sum ) ) )
| ~ ( H @ ( D @ ( E @ product ) ) )
| ~ ( G @ ( C @ ( E @ product ) ) )
| ~ ( F @ ( B @ ( E @ product ) ) )
| ~ ( D @ ( additive_identity @ ( A @ product ) ) )
| ~ ( C @ ( I @ additive_inverse @ ( A @ product ) ) )
| ~ ( B @ ( I @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(10916,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,10155]) ).
thf(10917,plain,
! [A: $i] :
( ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[10916:[]]) ).
thf(10983,plain,
( ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( a @ sum ) ) ) ),
inference(simp,[status(thm)],[10917]) ).
thf(4611,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3066,4424]) ).
thf(4612,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[4611]) ).
thf(4613,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[4612:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplication_is_well_defined) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(44,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(7,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(34,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)],[7]) ).
thf(6925,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,2450]) ).
thf(6926,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[6925]) ).
thf(6927,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[6926:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(14,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(48,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)],[14]) ).
thf(49,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(cnf,[status(esa)],[48]) ).
thf(71,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( E @ ( D @ ( A @ product ) ) )
!= ( C @ ( B @ ( A @ product ) ) ) )
| ( G @ ( E @ ( C @ sum ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(75,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( D @ ( B @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( A )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(81,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( D @ ( B @ ( B @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[75]) ).
thf(9,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(39,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)],[9]) ).
thf(17615,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,12212]) ).
thf(17616,plain,
! [A: $i] :
( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ) ),
inference(simp,[status(thm)],[17615]) ).
thf(17633,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( ( A @ additive_inverse )
!= additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) ) ),
inference(simp,[status(thm)],[17616]) ).
thf(17661,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[17633]) ).
thf(20296,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,17661]) ).
thf(20297,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[20296]) ).
thf(20298,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[20297:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( C @ ( D @ ( additive_identity @ sum ) ) ) )
| ~ $true
| ( C = D ) ),
inference(paramod_ordered,[status(thm)],[31,301]) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ add ) @ ( B @ ( A @ sum ) ) )
!= ( C @ ( D @ ( additive_identity @ sum ) ) ) )
| ( C = D ) ),
inference(simp,[status(thm)],[380]) ).
thf(382,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( additive_identity )),bind(B,$thf( F )),bind(C,$thf( F @ ( additive_identity @ add ) )),bind(D,$thf( F ))]]) ).
thf(462,plain,
! [A: $i] :
( ( A @ ( additive_identity @ add ) )
= A ),
inference(simp,[status(thm)],[382]) ).
thf(103,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( G @ ( F @ ( A @ product ) ) )
!= ( C @ ( B @ ( A @ product ) ) ) )
| ( K @ ( J @ ( I @ sum ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[83]) ).
thf(130,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( G @ sum ) ) )
| ~ ( I @ ( E @ ( F @ product ) ) )
| ~ ( H @ ( C @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( F @ product ) ) )
| ~ ( D @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G ))]]) ).
thf(135,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( I @ ( H @ ( G @ sum ) ) )
| ~ ( I @ ( E @ ( F @ product ) ) )
| ~ ( H @ ( C @ ( F @ product ) ) )
| ~ ( G @ ( E @ ( F @ product ) ) )
| ~ ( D @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(73,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( G @ ( F @ ( A @ product ) ) )
!= ( E @ ( D @ ( A @ product ) ) ) )
| ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(74,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ sum ) ) )
| ~ ( D @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(80,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ sum ) ) )
| ~ ( D @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[74]) ).
thf(35,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(cnf,[status(esa)],[34]) ).
thf(25414,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,18885]) ).
thf(25415,plain,
! [A: $i] :
( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[25414]) ).
thf(25521,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[25415]) ).
thf(25597,plain,
( ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse )
!= additive_identity ),
inference(simp,[status(thm)],[25521]) ).
thf(11074,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != additive_identity )
| ( additive_identity != a )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,10997]) ).
thf(11075,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != a )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[11074]) ).
thf(11076,plain,
( ( additive_identity != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[11075:[bind(A,$thf( additive_identity @ ( additive_identity @ multiply ) ))]]) ).
thf(16200,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ sum ) ) ) )
| ( additive_identity != a )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,11076]) ).
thf(16201,plain,
! [A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ ( additive_identity @ multiply ) @ sum ) ) ) )
| ( additive_identity != a ) ),
inference(simp,[status(thm)],[16200]) ).
thf(16206,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( ( A @ additive_inverse )
!= additive_identity )
| ( A
!= ( additive_identity @ ( additive_identity @ multiply ) ) )
| ( additive_identity != a ) ),
inference(simp,[status(thm)],[16201]) ).
thf(16221,plain,
( ( ( additive_identity @ ( additive_identity @ multiply ) @ additive_inverse )
!= additive_identity )
| ( additive_identity != a ) ),
inference(simp,[status(thm)],[16206]) ).
thf(11016,plain,
! [B: $i,A: $i] :
( ( B != additive_identity )
| ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( A != a )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,10997]) ).
thf(11017,plain,
! [A: $i] :
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( A != a )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[11016:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(11137,plain,
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ~ ( a @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[11017]) ).
thf(15,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(50,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)],[15]) ).
thf(10969,plain,
! [A: $i] :
( ( additive_identity != additive_identity )
| ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5062,10155]) ).
thf(10970,plain,
! [A: $i] :
( ( A != a )
| ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( additive_identity @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[10969:[]]) ).
thf(10994,plain,
( ~ ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) )
| ~ ( additive_identity @ ( a @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[10970]) ).
thf(7262,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,4424]) ).
thf(7263,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[7262]) ).
thf(7264,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[7263:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(11327,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) ) )
| ( ( a @ additive_inverse )
!= additive_identity )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55,10154]) ).
thf(11328,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) @ ( B @ ( A @ product ) ) )
!= ( additive_identity @ ( additive_identity @ ( additive_identity @ product ) ) ) )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[11327]) ).
thf(11332,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiply ) )
!= additive_identity )
| ( B != additive_identity )
| ( A != additive_identity )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[11328]) ).
thf(11354,plain,
( ( ( additive_identity @ ( additive_identity @ multiply ) )
!= additive_identity )
| ( ( a @ additive_inverse )
!= additive_identity ) ),
inference(simp,[status(thm)],[11332]) ).
thf(40,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(cnf,[status(esa)],[39]) ).
thf(18691,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( B @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ( additive_identity = B )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,2575]) ).
thf(18692,plain,
! [B: $i,A: $i] :
( ( ( additive_identity @ ( A @ ( A @ additive_inverse @ sum ) ) )
!= ( additive_identity @ ( B @ additive_inverse @ ( additive_identity @ sum ) ) ) )
| ( additive_identity = B ) ),
inference(simp,[status(thm)],[18691]) ).
thf(19089,plain,
! [B: $i,A: $i] :
( ( additive_identity != additive_identity )
| ( A
!= ( B @ additive_inverse ) )
| ( ( A @ additive_inverse )
!= additive_identity )
| ( additive_identity = B ) ),
inference(simp,[status(thm)],[18692]) ).
thf(19173,plain,
! [A: $i] :
( ( ( A @ additive_inverse @ additive_inverse )
!= additive_identity )
| ( additive_identity = A ) ),
inference(simp,[status(thm)],[19089]) ).
thf(84,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( J @ ( I @ sum ) ) )
!= ( Q @ ( O @ ( M @ sum ) ) ) )
| ( R @ ( P @ ( N @ sum ) ) )
| ~ ( R @ ( Q @ ( L @ product ) ) )
| ~ $true
| ~ ( P @ ( O @ ( L @ product ) ) )
| ~ ( N @ ( M @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[83,42]) ).
thf(85,plain,
! [R: $i,Q: $i,P: $i,O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( K @ ( J @ ( I @ sum ) ) )
!= ( Q @ ( O @ ( M @ sum ) ) ) )
| ( R @ ( P @ ( N @ sum ) ) )
| ~ ( R @ ( Q @ ( L @ product ) ) )
| ~ ( P @ ( O @ ( L @ product ) ) )
| ~ ( N @ ( M @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(86,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( O @ ( N @ ( M @ sum ) ) )
| ~ ( O @ ( K @ ( L @ product ) ) )
| ~ ( N @ ( J @ ( L @ product ) ) )
| ~ ( M @ ( I @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[85:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( F )),bind(G,$thf( G )),bind(H,$thf( H )),bind(I,$thf( I )),bind(J,$thf( J )),bind(K,$thf( K )),bind(L,$thf( L )),bind(M,$thf( I )),bind(N,$thf( N )),bind(O,$thf( J )),bind(P,$thf( P )),bind(Q,$thf( K ))]]) ).
thf(139,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( O @ ( N @ ( M @ sum ) ) )
| ~ ( O @ ( K @ ( L @ product ) ) )
| ~ ( N @ ( J @ ( L @ product ) ) )
| ~ ( M @ ( I @ ( L @ product ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( J @ ( E @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(12266,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3066,12039]) ).
thf(12267,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[12266]) ).
thf(12268,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[12267:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(72,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( G @ ( F @ ( A @ product ) ) )
!= ( C @ ( B @ ( A @ product ) ) ) )
| ( G @ ( E @ ( C @ sum ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(76,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ sum ) ) )
| ~ ( D @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( G ))]]) ).
thf(82,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ sum ) ) )
| ~ ( D @ ( B @ ( D @ sum ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) ) )
| ( B != additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,203]) ).
thf(384,plain,
! [A: $i] :
( ( A != additive_identity )
| ~ ( additive_identity @ ( a @ multiply ) @ ( A @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( additive_identity @ ( a @ multiply ) )),bind(B,$thf( B ))]]) ).
thf(432,plain,
~ ( additive_identity @ ( a @ multiply ) @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(51,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(cnf,[status(esa)],[50]) ).
thf(108,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( J @ ( E @ ( H @ product ) ) )
!= ( C @ ( B @ ( A @ product ) ) ) )
| ( K @ ( J @ ( I @ sum ) ) )
| ~ ( K @ ( G @ ( H @ product ) ) )
| ~ ( I @ ( C @ ( H @ product ) ) )
| ~ ( G @ ( F @ ( A @ product ) ) )
| ~ ( F @ ( D @ ( B @ sum ) ) )
| ~ ( E @ ( D @ ( A @ product ) ) )
| ~ ( C @ ( B @ ( A @ product ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[83]) ).
thf(131,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ sum ) ) )
| ~ ( H @ ( D @ ( E @ product ) ) )
| ~ ( F @ ( G @ ( E @ product ) ) )
| ~ ( D @ ( C @ ( E @ product ) ) )
| ~ ( C @ ( A @ ( B @ sum ) ) )
| ~ ( B @ ( A @ ( E @ product ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( H )),bind(B,$thf( E )),bind(C,$thf( J ))]]) ).
thf(136,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( G @ ( F @ sum ) ) )
| ~ ( H @ ( D @ ( E @ product ) ) )
| ~ ( F @ ( G @ ( E @ product ) ) )
| ~ ( D @ ( C @ ( E @ product ) ) )
| ~ ( C @ ( A @ ( B @ sum ) ) )
| ~ ( B @ ( A @ ( E @ product ) ) )
| ~ ( G @ ( B @ ( E @ product ) ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(68,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( H @ ( F @ ( D @ sum ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ $true
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,42]) ).
thf(69,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( additive_identity @ ( A @ additive_inverse @ ( A @ sum ) ) )
!= ( G @ ( E @ ( C @ sum ) ) ) )
| ( H @ ( F @ ( D @ sum ) ) )
| ~ ( H @ ( G @ ( B @ product ) ) )
| ~ ( F @ ( E @ ( B @ product ) ) )
| ~ ( D @ ( C @ ( B @ product ) ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ sum ) ) )
| ~ ( D @ ( additive_identity @ ( A @ product ) ) )
| ~ ( C @ ( E @ additive_inverse @ ( A @ product ) ) )
| ~ ( B @ ( E @ ( A @ product ) ) ) ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I )),bind(D,$thf( D )),bind(E,$thf( I @ additive_inverse )),bind(F,$thf( F )),bind(G,$thf( additive_identity ))]]) ).
thf(79,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ sum ) ) )
| ~ ( D @ ( additive_identity @ ( A @ product ) ) )
| ~ ( C @ ( E @ additive_inverse @ ( A @ product ) ) )
| ~ ( B @ ( E @ ( A @ product ) ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(473,plain,
! [B: $i,A: $i] :
( ( B != additive_identity )
| ( ( A @ additive_inverse )
= additive_identity )
| ~ ( A @ ( B @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[301,416]) ).
thf(474,plain,
! [A: $i] :
( ( ( A @ additive_inverse )
= additive_identity )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(pattern_uni,[status(thm)],[473:[bind(A,$thf( A )),bind(B,$thf( additive_identity ))]]) ).
thf(7276,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,203]) ).
thf(7277,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[7276]) ).
thf(7278,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ sum ) ) ),
inference(pattern_uni,[status(thm)],[7277:[bind(A,$thf( additive_identity @ ( a @ multiply ) ))]]) ).
thf(7023,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,638]) ).
thf(7024,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[7023]) ).
thf(7025,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[7024:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse ))]]) ).
thf(6737,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[3066,6508]) ).
thf(6738,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ) )
| ~ ( A @ ( additive_identity @ ( additive_identity @ sum ) ) ) ),
inference(simp,[status(thm)],[6737]) ).
thf(6739,plain,
~ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ ( additive_identity @ ( additive_identity @ sum ) ) ),
inference(pattern_uni,[status(thm)],[6738:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse @ additive_inverse ))]]) ).
thf(7001,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ) )
| ( additive_identity != additive_identity )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(paramod_ordered,[status(thm)],[5460,1265]) ).
thf(7002,plain,
! [A: $i] :
( ( A
!= ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ) )
| ~ ( additive_identity @ ( additive_identity @ ( A @ sum ) ) ) ),
inference(simp,[status(thm)],[7001]) ).
thf(7003,plain,
~ ( additive_identity @ ( additive_identity @ ( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse @ sum ) ) ),
inference(pattern_uni,[status(thm)],[7002:[bind(A,$thf( additive_identity @ ( a @ multiply ) @ additive_inverse @ additive_inverse ))]]) ).
thf(30897,plain,
$false,
inference(e,[status(thm)],[2540,12288,138,2544,11107,11122,56,15254,2575,42,12212,301,1265,25,4637,52,10997,638,46,416,57,78,29,7226,132,133,1345,678,2574,10990,33,28,38,21,137,484,361,435,5460,1457,682,456,11133,1534,10154,53,11157,18885,77,2450,41,134,10983,4613,45,32,34,10155,22,6927,54,49,6757,81,1349,39,3066,20298,462,135,80,35,25597,48,16221,11137,50,10994,7264,6508,5062,31,11354,43,12039,4424,203,11076,40,26,19173,55,139,12268,23,58,82,432,36,30,51,136,79,474,7278,7025,47,17661,83,6739,7003]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG001-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.08 % 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
% 0.12/0.39 % Computer : n018.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 05:45:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.92/0.88 % [INFO] Parsing done (162ms).
% 0.92/0.89 % [INFO] Running in sequential loop mode.
% 1.88/1.30 % [INFO] eprover registered as external prover.
% 1.88/1.31 % [INFO] Scanning for conjecture ...
% 2.08/1.40 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.08/1.46 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.29/1.50 % [INFO] Problem is propositional (TPTP CNF).
% 2.29/1.51 % [INFO] Type checking passed.
% 2.29/1.51 % [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 ...
% 69.08/18.59 % External prover 'e' found a proof!
% 69.08/18.60 % [INFO] Killing All external provers ...
% 71.29/18.60 % Time passed: 18102ms (effective reasoning time: 17699ms)
% 71.29/18.60 % Axioms used in derivation (19): addition_is_well_defined, cancellation1, commutativity_of_addition, additive_identity2, additive_identity1, associativity_of_multiplication2, right_inverse, distributivity1, closure_of_multiplication, associativity_of_addition2, associativity_of_multiplication1, distributivity4, closure_of_addition, distributivity3, distributivity2, associativity_of_addition1, left_inverse, multiplication_is_well_defined, cancellation2
% 71.29/18.60 % No. of inferences in proof: 316
% 71.29/18.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 18102 ms resp. 17699 ms w/o parsing
% 57.80/18.82 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.80/18.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------