%------------------------------------------------------------------------------
% File : SNARK---20120808r022
% Problem : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run-snark %s %d
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:35:08 EDT 2022
% Result : Unsatisfiable 16.24s 16.47s
% Output : Refutation 16.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of clauses : 104 ( 104 unt; 0 nHn; 29 RR)
% Number of literals : 104 ( 103 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 153 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(ifeq_axiom,axiom,
ifeq2(X,X,Y,Z) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X,X,Y,Z) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(left_identity,axiom,
product(identity,X,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(right_identity,axiom,
product(X,identity,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
cnf(left_inverse,axiom,
product(inverse(X),X,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(right_inverse,axiom,
product(X,inverse(X),identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
cnf(total_function1,axiom,
product(X,Y,multiply(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
cnf(total_function2,axiom,
ifeq2(product(X,Y,Z),true,ifeq2(product(X,Y,U),true,U,Z),Z) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
cnf(associativity1,axiom,
ifeq(product(X,Y,Z),true,ifeq(product(U,Y,V),true,ifeq(product(W,U,X),true,product(W,V,Z),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(associativity2,axiom,
ifeq(product(X,Y,Z),true,ifeq(product(U,Z,V),true,ifeq(product(U,X,W),true,product(W,Y,V),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(x_cubed_is_identity_1,hypothesis,
ifeq(product(X,X,Y),true,product(X,Y,identity),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_1) ).
cnf(a_times_b_is_c,negated_conjecture,
product(a,b,c) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
cnf(c_times_inverse_a_is_d,negated_conjecture,
product(c,inverse(a),d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_times_inverse_a_is_d) ).
cnf(d_times_inverse_b_is_h,negated_conjecture,
product(d,inverse(b),h) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_times_inverse_b_is_h) ).
cnf(h_times_b_is_j,negated_conjecture,
product(h,b,j) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',h_times_b_is_j) ).
cnf(j_times_inverse_h_is_k,negated_conjecture,
product(j,inverse(h),k) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',j_times_inverse_h_is_k) ).
cnf(prove_k_times_inverse_b_is_e,negated_conjecture,
product(k,inverse(b),identity) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(20,plain,
product(X,multiply(X,X),identity) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[x_cubed_is_identity_1,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(26,plain,
ifeq2(product(X,identity,Y),true,X,Y) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[total_function2,right_identity,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(30,plain,
ifeq2(product(X,identity,Y),true,Y,X) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[total_function2,right_identity,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(41,plain,
ifeq2(product(X,Y,Z),true,multiply(X,Y),Z) = Z,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[total_function2,total_function1,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(42,plain,
ifeq2(product(X,Y,Z),true,Z,multiply(X,Y)) = multiply(X,Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[total_function2,total_function1,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(44,plain,
ifeq(product(X,b,Y),true,ifeq(product(Z,X,h),true,product(Z,Y,j),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,h_times_b_is_j,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(45,plain,
ifeq(product(X,b,Y),true,ifeq(product(Z,X,a),true,product(Z,Y,c),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,a_times_b_is_c,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(46,plain,
ifeq(product(X,Y,Z),true,ifeq(product(U,X,identity),true,product(U,Z,Y),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,left_identity,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(53,plain,
ifeq(product(c,X,Y),true,ifeq(product(b,X,Z),true,product(a,Z,Y),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,a_times_b_is_c,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(60,plain,
ifeq(product(X,inverse(h),Y),true,ifeq(product(Z,X,j),true,product(Z,Y,k),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,j_times_inverse_h_is_k,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(62,plain,
ifeq(product(X,inverse(a),Y),true,ifeq(product(Z,X,c),true,product(Z,Y,d),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,c_times_inverse_a_is_d,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(79,plain,
ifeq(product(multiply(X,Y),Z,U),true,ifeq(product(Y,Z,V),true,product(X,V,U),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity1,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(92,plain,
ifeq(product(X,Y,identity),true,ifeq(product(Z,X,U),true,product(U,Y,Z),true),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[associativity2,right_identity,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(151,plain,
X = multiply(X,identity),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[26,total_function1,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(157,plain,
multiply(X,multiply(X,X)) = identity,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,20,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(201,plain,
ifeq(product(inverse(b),b,X),true,product(d,X,j),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[44,d_times_inverse_b_is_h,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(203,plain,
ifeq(product(X,Y,h),true,product(X,multiply(Y,b),j),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[44,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(213,plain,
product(d,identity,j) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[201,left_inverse,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(215,plain,
j = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,213,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(226,plain,
ifeq(product(X,inverse(h),Y),true,ifeq(product(Z,X,d),true,product(Z,Y,k),true),true) = true,
inference('REWRITE',[status(thm)],[60,215,theory(equality)]) ).
cnf(254,plain,
ifeq(product(X,Y,h),true,product(X,multiply(Y,b),d),true) = true,
inference('REWRITE',[status(thm)],[203,215,theory(equality)]) ).
cnf(436,plain,
ifeq(product(X,Y,a),true,product(X,multiply(Y,b),c),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[45,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(515,plain,
ifeq(product(inverse(X),Y,Z),true,product(X,Z,Y),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[46,right_inverse,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(630,plain,
product(X,identity,inverse(inverse(X))) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[515,right_inverse,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(631,plain,
product(X,multiply(inverse(X),Y),Y) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[515,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(634,plain,
inverse(inverse(X)) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[30,630,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(636,plain,
multiply(X,multiply(inverse(X),Y)) = Y,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,631,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(637,plain,
product(X,multiply(multiply(inverse(X),h),b),d) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[254,631,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(638,plain,
product(X,multiply(multiply(inverse(X),a),b),c) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[436,631,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(653,plain,
multiply(inverse(X),multiply(X,Y)) = Y,
inference('PARAMODULATE',[status(thm)],[636,634,theory(equality)]) ).
cnf(654,plain,
X = multiply(inverse(X),inverse(X)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[636,157,theory(equality)]),151,theory(equality)]) ).
cnf(655,plain,
multiply(X,X) = inverse(X),
inference('PARAMODULATE',[status(thm)],[636,654,theory(equality)]) ).
cnf(762,plain,
product(X,d,multiply(multiply(X,h),b)) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[515,637,theory(equality)]),ifeq_axiom_001,634,theory(equality)]) ).
cnf(776,plain,
multiply(multiply(X,h),b) = multiply(X,d),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,762,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(779,plain,
multiply(inverse(multiply(X,h)),multiply(X,d)) = b,
inference('PARAMODULATE',[status(thm)],[653,776,theory(equality)]) ).
cnf(809,plain,
product(X,c,multiply(multiply(X,a),b)) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[515,638,theory(equality)]),ifeq_axiom_001,634,theory(equality)]) ).
cnf(825,plain,
multiply(multiply(X,a),b) = multiply(X,c),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,809,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(828,plain,
multiply(inverse(multiply(X,a)),multiply(X,c)) = b,
inference('PARAMODULATE',[status(thm)],[653,825,theory(equality)]) ).
cnf(927,plain,
multiply(inverse(multiply(d,h)),inverse(d)) = b,
inference('PARAMODULATE',[status(thm)],[779,655,theory(equality)]) ).
cnf(932,plain,
multiply(inverse(multiply(c,a)),inverse(c)) = b,
inference('PARAMODULATE',[status(thm)],[828,655,theory(equality)]) ).
cnf(1127,plain,
ifeq(product(b,X,Y),true,product(a,Y,multiply(c,X)),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[53,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(1211,plain,
product(a,multiply(b,X),multiply(c,X)) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[1127,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(1217,plain,
multiply(a,multiply(b,X)) = multiply(c,X),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,1211,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(2342,plain,
ifeq(product(X,inverse(Y),Z),true,product(Z,Y,X),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[92,left_inverse,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(2637,plain,
product(multiply(X,inverse(Y)),Y,X) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2342,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(2645,plain,
multiply(multiply(X,inverse(Y)),Y) = X,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,2637,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(2681,plain,
multiply(multiply(X,Y),inverse(Y)) = X,
inference('PARAMODULATE',[status(thm)],[2645,634,theory(equality)]) ).
cnf(2685,plain,
multiply(b,d) = inverse(multiply(d,h)),
inference('PARAMODULATE',[status(thm)],[2645,927,theory(equality)]) ).
cnf(2817,plain,
multiply(inverse(multiply(X,Y)),X) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[653,2681,theory(equality)]) ).
cnf(2859,plain,
multiply(X,inverse(multiply(Y,X))) = inverse(Y),
inference('PARAMODULATE',[status(thm)],[2681,653,theory(equality)]) ).
cnf(2861,plain,
multiply(multiply(X,d),inverse(b)) = multiply(X,h),
inference('PARAMODULATE',[status(thm)],[2681,776,theory(equality)]) ).
cnf(3257,plain,
multiply(inverse(X),inverse(Y)) = inverse(multiply(Y,X)),
inference('PARAMODULATE',[status(thm)],[2681,2817,theory(equality)]) ).
cnf(3258,plain,
inverse(multiply(c,multiply(c,a))) = b,
inference('REWRITE',[status(thm)],[932,3257,theory(equality)]) ).
cnf(3260,plain,
multiply(inverse(X),Y) = inverse(multiply(inverse(Y),X)),
inference('PARAMODULATE',[status(thm)],[2645,2817,theory(equality)]) ).
cnf(3320,plain,
multiply(X,inverse(Y)) = inverse(multiply(Y,inverse(X))),
inference('PARAMODULATE',[status(thm)],[636,2859,theory(equality)]) ).
cnf(3546,plain,
inverse(multiply(b,d)) = multiply(d,h),
inference('PARAMODULATE',[status(thm)],[634,2685,theory(equality)]) ).
cnf(3757,plain,
inverse(b) = multiply(c,multiply(c,a)),
inference('PARAMODULATE',[status(thm)],[634,3258,theory(equality)]) ).
cnf(4342,plain,
inverse(multiply(multiply(b,d),d)) = h,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[653,3546,theory(equality)]),3257,theory(equality)]) ).
cnf(5361,plain,
inverse(h) = multiply(multiply(b,d),d),
inference('PARAMODULATE',[status(thm)],[634,4342,theory(equality)]) ).
cnf(5472,plain,
inverse(multiply(b,h)) = multiply(multiply(b,d),h),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2861,5361,theory(equality)]),3257,theory(equality)]) ).
cnf(7950,plain,
ifeq(product(X,Y,c),true,product(X,multiply(Y,inverse(a)),d),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[62,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(7977,plain,
product(multiply(c,inverse(X)),multiply(X,inverse(a)),d) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7950,2637,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(7995,plain,
product(multiply(c,a),a,d) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7977,655,theory(equality)]),634,theory(equality)]) ).
cnf(7996,plain,
multiply(multiply(c,inverse(X)),multiply(X,inverse(a))) = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,7977,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(8028,plain,
multiply(multiply(c,a),a) = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,7995,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(8128,plain,
multiply(d,b) = multiply(multiply(c,a),c),
inference('PARAMODULATE',[status(thm)],[825,8028,theory(equality)]) ).
cnf(8137,plain,
multiply(multiply(c,X),inverse(multiply(a,X))) = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[7996,634,theory(equality)]),3257,theory(equality)]) ).
cnf(8186,plain,
multiply(d,multiply(a,X)) = multiply(c,X),
inference('PARAMODULATE',[status(thm)],[2645,8137,theory(equality)]) ).
cnf(8235,plain,
multiply(inverse(d),multiply(c,X)) = multiply(a,X),
inference('PARAMODULATE',[status(thm)],[653,8186,theory(equality)]) ).
cnf(8531,plain,
inverse(multiply(b,d)) = multiply(a,multiply(c,a)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[8235,3757,theory(equality)]),3257,theory(equality)]) ).
cnf(12969,plain,
ifeq(product(X,Y,d),true,product(X,multiply(Y,inverse(h)),k),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[226,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(13006,plain,
product(multiply(d,inverse(X)),multiply(X,inverse(h)),k) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[12969,2637,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(13034,plain,
multiply(multiply(d,inverse(X)),multiply(X,inverse(h))) = k,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[41,13006,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(13074,plain,
inverse(multiply(inverse(h),multiply(b,d))) = k,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[13034,655,theory(equality)]),3260,3546,634,theory(equality)]) ).
cnf(13098,plain,
inverse(k) = multiply(inverse(h),multiply(b,d)),
inference('PARAMODULATE',[status(thm)],[634,13074,theory(equality)]) ).
cnf(23525,plain,
ifeq(product(multiply(X,Y),Z,U),true,product(X,multiply(Y,Z),U),true) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[79,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(24237,plain,
product(X,multiply(Y,Z),multiply(multiply(X,Y),Z)) = true,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[23525,total_function1,theory(equality)]),ifeq_axiom_001,theory(equality)]) ).
cnf(24620,plain,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[42,24237,theory(equality)]),ifeq_axiom,theory(equality)]) ).
cnf(25864,plain,
multiply(inverse(X),Y) = multiply(X,multiply(X,Y)),
inference('PARAMODULATE',[status(thm)],[24620,655,theory(equality)]) ).
cnf(26009,plain,
multiply(multiply(X,a),multiply(b,Y)) = multiply(X,multiply(c,Y)),
inference('PARAMODULATE',[status(thm)],[24620,1217,theory(equality)]) ).
cnf(26014,plain,
inverse(multiply(b,d)) = multiply(inverse(a),multiply(b,a)),
inference('REWRITE',[status(thm)],[8531,655,26009,theory(equality)]) ).
cnf(27892,plain,
inverse(multiply(X,multiply(Y,X))) = multiply(multiply(Y,X),Y),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25864,2681,theory(equality)]),3257,theory(equality)]) ).
cnf(27893,plain,
multiply(d,b) = multiply(b,d),
inference('REWRITE',[status(thm)],[8128,634,26014,655,26009,27892,theory(equality)]) ).
cnf(28245,plain,
k = inverse(multiply(multiply(b,h),inverse(multiply(b,d)))),
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[25864,5472,theory(equality)]),3320,634,13098,3260,theory(equality)]) ).
cnf(28271,plain,
multiply(b,h) = d,
inference('REWRITE',[status(thm)],[inference('PARAMODULATE',[status(thm)],[2681,27893,theory(equality)]),2861,theory(equality)]) ).
cnf(28546,plain,
k = b,
inference('REWRITE',[status(thm)],[28245,634,2681,3320,28271,theory(equality)]) ).
cnf(28547,plain,
$false,
inference('REWRITE',[status(thm)],[prove_k_times_inverse_b_is_e,right_inverse,28546,theory(equality)]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP002-10 : TPTP v8.1.0. Released v7.3.0.
% 0.12/0.12 % Command : run-snark %s %d
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 17:34:56 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.44 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 *
% 0.18/0.45 *
% 0.18/0.46 #<PACKAGE "SNARK-USER">
% 0.18/0.46 *
% 0.18/0.46 SNARK-TPTP-OPTIONS
% 0.18/0.46 *
% 0.18/0.46 ((AGENDA-LENGTH-LIMIT NIL) (AGENDA-LENGTH-BEFORE-SIMPLIFICATION-LIMIT NIL)
% 0.18/0.46 (USE-HYPERRESOLUTION T) (USE-UR-RESOLUTION T) (USE-PARAMODULATION T)
% 0.18/0.46 (USE-FACTORING :POS)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-HYPERRESOLUTION 'LITERAL-ORDERING-P)
% 0.18/0.46 (USE-LITERAL-ORDERING-WITH-PARAMODULATION 'LITERAL-ORDERING-P)
% 0.18/0.46 (ORDERING-FUNCTIONS>CONSTANTS T) (ASSERT-CONTEXT :CURRENT)
% 0.18/0.46 (RUN-TIME-LIMIT 300) (LISTEN-FOR-COMMANDS NIL)
% 0.18/0.46 (USE-CLOSURE-WHEN-SATISFIABLE T) (PRINT-ROWS-WHEN-GIVEN NIL)
% 0.18/0.46 (PRINT-ROWS-WHEN-DERIVED NIL) (PRINT-UNORIENTABLE-ROWS NIL)
% 0.18/0.46 (PRINT-ROW-WFFS-PRETTILY NIL) (PRINT-FINAL-ROWS :TPTP)
% 0.18/0.46 (PRINT-OPTIONS-WHEN-STARTING NIL) (USE-VARIABLE-NAME-SORTS NIL)
% 0.18/0.46 (USE-PURITY-TEST T) (USE-RELEVANCE-TEST T) (DECLARE-TPTP-SYMBOLS1)
% 0.18/0.46 (DECLARE-TPTP-SYMBOLS2))
% 0.18/0.46 *
% 0.18/0.46 "."
% 0.18/0.46 *
% 0.18/0.46 ; Begin refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T17:34:57
% 0.18/0.46 ; Running SNARK from /davis/home/graph/tptp/Systems/SNARK---20120808r022/Source/snark-system.lisp in SBCL 1.0.12 on n006.cluster.edu at 2022-06-13T17:34:57
% 16.24/16.47
% 16.24/16.47
% 16.24/16.47 #||
% 16.24/16.47 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.24/16.47 % SZS output start Refutation
% See solution above
% 16.33/16.55 ||#
% 16.33/16.55
% 16.33/16.55 ; Summary of computation:
% 16.33/16.55 ; 120949 formulas have been input or derived (from 2154 formulas).
% 16.33/16.55 ; 28547 (24%) were retained. Of these,
% 16.33/16.55 ; 12368 (43%) were simplified or subsumed later,
% 16.33/16.55 ; 16179 (57%) are still being kept.
% 16.33/16.55 ;
% 16.33/16.55 ; Run time in seconds excluding printing time:
% 16.33/16.55 ; 0.003 0% Read assertion file (1 call)
% 16.33/16.55 ; 0.001 0% Assert (18 calls)
% 16.33/16.55 ; 4.626 29% Process new row (110,915 calls)
% 16.33/16.55 ; 0.336 2% Resolution (4,306 calls)
% 16.33/16.55 ; 2.380 15% Paramodulation (2,153 calls)
% 16.33/16.55 ; 5.007 31% Forward simplification (104,425 calls)
% 16.33/16.55 ; 2.565 16% Backward simplification (28,547 calls)
% 16.33/16.55 ; 0.710 4% Ordering (335,117 calls)
% 16.33/16.55 ; 0.000 0% Sortal reasoning (32 calls)
% 16.33/16.55 ; 0.000 0% Purity testing (1 call)
% 16.33/16.55 ; 0.388 2% Other
% 16.33/16.55 ; 16.016 Total
% 16.33/16.55 ; 16.094 Real time
% 16.33/16.55 ;
% 16.33/16.55 ; Term-hash-array has 72,504 terms in all.
% 16.33/16.55 ; Feature-vector-row-index has 0 entries (0 at peak, 0 added, 0 deleted).
% 16.33/16.55 ; Feature-vector-row-index has 1 node (1 at peak, 1 added, 0 deleted).
% 16.33/16.55 ; Path-index has 41,836 entries (59,685 at peak, 73,219 added, 31,383 deleted).
% 16.33/16.55 ; Path-index has 7,303 nodes (8,341 at peak, 11,882 added, 4,579 deleted).
% 16.33/16.55 ; Trie-index has 41,836 entries (59,685 at peak, 73,219 added, 31,383 deleted).
% 16.33/16.55 ; Trie-index has 284,199 nodes (408,800 at peak, 497,265 added, 213,066 deleted).
% 16.33/16.55 ; Retrieved 812,294 generalization terms in 844,184 calls.
% 16.33/16.55 ; Retrieved 56,010 instance terms in 28,790 calls.
% 16.33/16.55 ; Retrieved 651,510 unifiable terms in 22,280 calls.
% 16.33/16.55 ;
% 16.33/16.55 ; The agenda of backward simplifiable rows to process has 7199 entries:
% 16.33/16.55 ; 7199 with value 0
% 16.33/16.55 ; The agenda of rows to process has 413 entries:
% 16.33/16.55 ; 6 with value 21 51 with value 26 98 with value 30
% 16.33/16.55 ; 12 with value 22 60 with value 27 32 with value 31
% 16.33/16.55 ; 16 with value 23 11 with value 28 2 with value 32
% 16.33/16.55 ; 30 with value 24 58 with value 29 2 with value 36
% 16.33/16.55 ; 35 with value 25
% 16.33/16.55 ; The agenda of rows to give has 14967 entries:
% 16.33/16.55 ; 1 with value (4 17) 493 with value (4 27) 1068 with value (4 37)
% 16.33/16.55 ; 1 with value (4 18) 591 with value (4 28) 598 with value (4 38)
% 16.33/16.55 ; 1 with value (4 19) 764 with value (4 29) 236 with value (4 39)
% 16.33/16.55 ; 1 with value (4 20) 836 with value (4 30) 237 with value (4 40)
% 16.33/16.55 ; 6 with value (4 21) 1211 with value (4 31) 316 with value (4 41)
% 16.33/16.55 ; 13 with value (4 22) 1407 with value (4 32) 339 with value (4 42)
% 16.33/16.55 ; 17 with value (4 23) 1455 with value (4 33) 391 with value (4 43)
% 16.33/16.55 ; 40 with value (4 24) 1569 with value (4 34) 19 with value (4 44)
% 16.33/16.55 ; 44 with value (4 25) 1818 with value (4 35) 1 with value (4 45)
% 16.33/16.55 ; 103 with value (4 26) 1391 with value (4 36)
% 16.33/16.55 Evaluation took:
% 16.33/16.55 16.097 seconds of real time
% 16.33/16.55 14.65338 seconds of user run time
% 16.33/16.55 1.445472 seconds of system run time
% 16.33/16.55 [Run times include 4.139 seconds GC run time.]
% 16.33/16.55 0 calls to %EVAL
% 16.33/16.55 0 page faults and
% 16.33/16.55 939,774,584 bytes consed.
% 16.33/16.55 :PROOF-FOUND
% 16.33/16.55 ; End refute-file /export/starexec/sandbox2/benchmark/theBenchmark.p 2022-06-13T17:35:13
% 16.33/16.55 :PROOF-FOUND
% 16.33/16.55 *
%------------------------------------------------------------------------------