%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP206-1 : TPTP v8.2.0. Released v2.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n026.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed May 29 16:53:51 EDT 2024

% Result   : Unsatisfiable 10.80s 11.13s
% Output   : Proof 10.80s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP206-1 : TPTP v8.2.0. Released v2.3.0.
% 0.07/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n026.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Sun May 26 18:23:54 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.79/10.98  --- Run --no-e-matching --full-saturate-quant at 5...
% 10.80/11.13  % SZS status Unsatisfiable for /export/starexec/sandbox2/tmp/tmp.BChwx7UGGG/cvc5---1.0.5_31856.smt2
% 10.80/11.13  % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.BChwx7UGGG/cvc5---1.0.5_31856.smt2
% 10.80/11.14  (assume a0 (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)))
% 10.80/11.14  (assume a1 (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X)))
% 10.80/11.14  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply X (tptp.left_division X Y)) Y)))
% 10.80/11.14  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.left_division X (tptp.multiply X Y)) Y)))
% 10.80/11.14  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply (tptp.right_division X Y) Y) X)))
% 10.80/11.14  (assume a5 (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.right_division (tptp.multiply X Y) Y) X)))
% 10.80/11.14  (assume a6 (forall ((X $$unsorted)) (= (tptp.multiply X (tptp.right_inverse X)) tptp.identity)))
% 10.80/11.14  (assume a7 (forall ((X $$unsorted)) (= (tptp.multiply (tptp.left_inverse X) X) tptp.identity)))
% 10.80/11.14  (assume a8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))))
% 10.80/11.14  (assume a9 (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))
% 10.80/11.14  (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t2)
% 10.80/11.14  (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))))
% 10.80/11.14  (step t2.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.multiply tptp.b tptp.c)) (:= Z tptp.identity)))
% 10.80/11.14  (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) :rule or :premises (t2.t1))
% 10.80/11.14  (step t2.t3 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t2.t2 t2.a0))
% 10.80/11.14  (step t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) :rule subproof :discharge (t2.a0))
% 10.80/11.14  (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) :rule resolution :premises (t1 t2))
% 10.80/11.14  (step t4 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule implies_neg2)
% 10.80/11.14  (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t3 t4))
% 10.80/11.14  (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t5))
% 10.80/11.14  (step t7 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) :rule implies :premises (t6))
% 10.80/11.14  (step t8 (cl (not (= (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))))) (not (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) (or (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule equiv_pos2)
% 10.80/11.14  (step t9 (cl (= (= (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) true) (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) :rule equiv_simplify)
% 10.80/11.14  (step t10 (cl (not (= (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) true)) (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule equiv1 :premises (t9))
% 10.80/11.14  (step t11 (cl (= (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))))) :rule all_simplify)
% 10.80/11.14  (step t12 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule refl)
% 10.80/11.14  (step t13 (cl (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule all_simplify)
% 10.80/11.14  (step t14 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) :rule cong :premises (t12 t13))
% 10.80/11.14  (step t15 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) true)) :rule all_simplify)
% 10.80/11.14  (step t16 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) true)) :rule trans :premises (t14 t15))
% 10.80/11.14  (step t17 (cl (= (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) true)) :rule trans :premises (t11 t16))
% 10.80/11.14  (step t18 (cl (= (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule resolution :premises (t10 t17))
% 10.80/11.14  (step t19 (cl (= (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))))) :rule refl)
% 10.80/11.14  (step t20 (cl (= (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))))) :rule refl)
% 10.80/11.14  (step t21 (cl (= (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))))) :rule refl)
% 10.80/11.14  (step t22 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))))) :rule refl)
% 10.80/11.14  (step t23 (cl (= (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule refl)
% 10.80/11.14  (step t24 (cl (= (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))))) :rule cong :premises (t18 t19 t20 t21 t22 t23))
% 10.80/11.14  (step t25 (cl (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) :rule and_neg)
% 10.80/11.14  (step t26 (cl (=> (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t27)
% 10.80/11.14  (assume t27.a0 (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))
% 10.80/11.14  (assume t27.a1 (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))
% 10.80/11.14  (assume t27.a2 (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))
% 10.80/11.14  (assume t27.a3 (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))
% 10.80/11.14  (assume t27.a4 (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))
% 10.80/11.14  (step t27.t1 (cl (=> (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t27.t2)
% 10.80/11.14  (assume t27.t2.a0 (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))
% 10.80/11.14  (assume t27.t2.a1 (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))
% 10.80/11.14  (assume t27.t2.a2 (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))
% 10.80/11.14  (assume t27.t2.a3 (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))
% 10.80/11.14  (assume t27.t2.a4 (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))
% 10.80/11.14  (step t27.t2.t1 (cl (= (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule equiv_simplify)
% 10.80/11.14  (step t27.t2.t2 (cl (not (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false)) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule equiv1 :premises (t27.t2.t1))
% 10.80/11.14  (step t27.t2.t3 (cl (not (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) false) (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false))) (not (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) false)) (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false)) :rule equiv_pos2)
% 10.80/11.14  (step t27.t2.t4 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) false) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)))))) :rule all_simplify)
% 10.80/11.14  (step t27.t2.t5 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule all_simplify)
% 10.80/11.14  (step t27.t2.t6 (cl (= (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule cong :premises (t27.t2.t5))
% 10.80/11.14  (step t27.t2.t7 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) false) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule trans :premises (t27.t2.t4 t27.t2.t6))
% 10.80/11.14  (step t27.t2.t8 (cl (= (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule all_simplify)
% 10.80/11.14  (step t27.t2.t9 (cl (= (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false))) :rule symm :premises (t27.t2.t8))
% 10.80/11.14  (step t27.t2.t10 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) false) (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false))) :rule trans :premises (t27.t2.t7 t27.t2.t9))
% 10.80/11.14  (step t27.t2.t11 (cl (= (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)))) :rule refl)
% 10.80/11.14  (step t27.t2.t12 (cl (= tptp.identity tptp.identity)) :rule refl)
% 10.80/11.14  (step t27.t2.t13 (cl (= (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)) (tptp.left_division tptp.identity tptp.a))) :rule symm :premises (t27.t2.a1))
% 10.80/11.14  (step t27.t2.t14 (cl (= tptp.a (tptp.left_division tptp.identity tptp.a))) :rule trans :premises (t27.t2.a0 t27.t2.t13))
% 10.80/11.14  (step t27.t2.t15 (cl (= (tptp.multiply tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule cong :premises (t27.t2.t12 t27.t2.t14))
% 10.80/11.14  (step t27.t2.t16 (cl (= (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)) tptp.a)) :rule symm :premises (t27.t2.a0))
% 10.80/11.14  (step t27.t2.t17 (cl (= (tptp.multiply tptp.identity tptp.a) tptp.a)) :rule trans :premises (t27.t2.t15 t27.t2.t16))
% 10.80/11.14  (step t27.t2.t18 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a))) :rule cong :premises (t27.t2.t11 t27.t2.t17))
% 10.80/11.14  (step t27.t2.t19 (cl (= tptp.a tptp.a)) :rule refl)
% 10.80/11.14  (step t27.t2.t20 (cl (= (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) (tptp.multiply tptp.b tptp.c))) :rule symm :premises (t27.t2.a4))
% 10.80/11.14  (step t27.t2.t21 (cl (= (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) :rule cong :premises (t27.t2.t20 t27.t2.t19))
% 10.80/11.14  (step t27.t2.t22 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) :rule cong :premises (t27.t2.t19 t27.t2.t21))
% 10.80/11.14  (step t27.t2.t23 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule symm :premises (t27.t2.a3))
% 10.80/11.14  (step t27.t2.t24 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule trans :premises (t27.t2.t22 t27.t2.t23))
% 10.80/11.14  (step t27.t2.t25 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule cong :premises (t27.t2.t18 t27.t2.t24))
% 10.80/11.14  (step t27.t2.t26 (cl (= (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) false) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) :rule equiv_simplify)
% 10.80/11.14  (step t27.t2.t27 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) false) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) :rule equiv2 :premises (t27.t2.t26))
% 10.80/11.14  (step t27.t2.t28 (cl (not (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))))) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule not_not)
% 10.80/11.14  (step t27.t2.t29 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) false) (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule resolution :premises (t27.t2.t27 t27.t2.t28))
% 10.80/11.14  (step t27.t2.t30 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) false)) :rule resolution :premises (t27.t2.t29 t27.t2.a2))
% 10.80/11.14  (step t27.t2.t31 (cl (= (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a))) false)) :rule trans :premises (t27.t2.t25 t27.t2.t30))
% 10.80/11.14  (step t27.t2.t32 (cl (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))) false)) :rule resolution :premises (t27.t2.t3 t27.t2.t10 t27.t2.t31))
% 10.80/11.14  (step t27.t2.t33 (cl (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t27.t2.t2 t27.t2.t32))
% 10.80/11.14  (step t27.t2 (cl (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule subproof :discharge (t27.t2.a0 t27.t2.a1 t27.t2.a2 t27.t2.a3 t27.t2.a4))
% 10.80/11.14  (step t27.t3 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule and_pos)
% 10.80/11.14  (step t27.t4 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule and_pos)
% 10.80/11.14  (step t27.t5 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule and_pos)
% 10.80/11.14  (step t27.t6 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) :rule and_pos)
% 10.80/11.14  (step t27.t7 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule and_pos)
% 10.80/11.14  (step t27.t8 (cl (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))))) :rule resolution :premises (t27.t2 t27.t3 t27.t4 t27.t5 t27.t6 t27.t7))
% 10.80/11.14  (step t27.t9 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule reordering :premises (t27.t8))
% 10.80/11.14  (step t27.t10 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t27.t9))
% 10.80/11.14  (step t27.t11 (cl (=> (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t27.t1 t27.t10))
% 10.80/11.14  (step t27.t12 (cl (=> (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule implies_neg2)
% 10.80/11.14  (step t27.t13 (cl (=> (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (=> (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t27.t11 t27.t12))
% 10.80/11.14  (step t27.t14 (cl (=> (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule contraction :premises (t27.t13))
% 10.80/11.14  (step t27.t15 (cl (not (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule implies :premises (t27.t14))
% 10.80/11.14  (step t27.t16 (cl (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule and_neg)
% 10.80/11.14  (step t27.t17 (cl (and (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule resolution :premises (t27.t16 t27.a1 t27.a2 t27.a0 t27.a4 t27.a3))
% 10.80/11.14  (step t27.t18 (cl (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t27.t15 t27.t17))
% 10.80/11.14  (step t27 (cl (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule subproof :discharge (t27.a0 t27.a1 t27.a2 t27.a3 t27.a4))
% 10.80/11.14  (step t28 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule and_pos)
% 10.80/11.14  (step t29 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule and_pos)
% 10.80/11.14  (step t30 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule and_pos)
% 10.80/11.14  (step t31 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule and_pos)
% 10.80/11.14  (step t32 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) :rule and_pos)
% 10.80/11.14  (step t33 (cl (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))))) :rule resolution :premises (t27 t28 t29 t30 t31 t32))
% 10.80/11.14  (step t34 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule reordering :premises (t33))
% 10.80/11.14  (step t35 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule contraction :premises (t34))
% 10.80/11.14  (step t36 (cl (=> (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t26 t35))
% 10.80/11.14  (step t37 (cl (=> (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule implies_neg2)
% 10.80/11.14  (step t38 (cl (=> (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (=> (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t36 t37))
% 10.80/11.14  (step t39 (cl (=> (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule contraction :premises (t38))
% 10.80/11.14  (step t40 (cl (not (and (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule implies :premises (t39))
% 10.80/11.14  (step t41 (cl (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t25 t40))
% 10.80/11.14  (step t42 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))))) :rule or_neg)
% 10.80/11.14  (step t43 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))))) :rule or_neg)
% 10.80/11.14  (step t44 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))))) :rule or_neg)
% 10.80/11.14  (step t45 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))))) :rule or_neg)
% 10.80/11.14  (step t46 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))))) :rule or_neg)
% 10.80/11.14  (step t47 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (not (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule or_neg)
% 10.80/11.14  (step t48 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t41 t42 t43 t44 t45 t46 t47))
% 10.80/11.14  (step t49 (cl (or (not (not (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule contraction :premises (t48))
% 10.80/11.14  (step t50 (cl (or (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a)))))) :rule resolution :premises (t8 t24 t49))
% 10.80/11.14  (step t51 (cl (= (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) tptp.a) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule or :premises (t50))
% 10.80/11.14  (step t52 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t53)
% 10.80/11.14  (assume t53.a0 (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))))
% 10.80/11.14  (step t53.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule forall_inst :args ((:= X tptp.identity) (:= Y tptp.a)))
% 10.80/11.14  (step t53.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule or :premises (t53.t1))
% 10.80/11.14  (step t53.t3 (cl (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule resolution :premises (t53.t2 t53.a0))
% 10.80/11.14  (step t53 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule subproof :discharge (t53.a0))
% 10.80/11.14  (step t54 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule resolution :premises (t52 t53))
% 10.80/11.14  (step t55 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule implies_neg2)
% 10.80/11.14  (step t56 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule resolution :premises (t54 t55))
% 10.80/11.14  (step t57 (cl (=> (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule contraction :premises (t56))
% 10.80/11.14  (step t58 (cl (not (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule implies :premises (t57))
% 10.80/11.14  (step t59 (cl (not (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply X (tptp.left_division X Y)) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))))) (not (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply X (tptp.left_division X Y)) Y))) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) :rule equiv_pos2)
% 10.80/11.14  (anchor :step t60 :args ((X $$unsorted) (:= X X) (Y $$unsorted) (:= Y Y)))
% 10.80/11.14  (step t60.t1 (cl (= X X)) :rule refl)
% 10.80/11.14  (step t60.t2 (cl (= Y Y)) :rule refl)
% 10.80/11.14  (step t60.t3 (cl (= (= (tptp.multiply X (tptp.left_division X Y)) Y) (= Y (tptp.multiply X (tptp.left_division X Y))))) :rule all_simplify)
% 10.80/11.14  (step t60 (cl (= (forall ((X $$unsorted) (Y $$unsorted)) (= (tptp.multiply X (tptp.left_division X Y)) Y)) (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y)))))) :rule bind)
% 10.80/11.14  (step t61 (cl (forall ((X $$unsorted) (Y $$unsorted)) (= Y (tptp.multiply X (tptp.left_division X Y))))) :rule resolution :premises (t59 t60 a2))
% 10.80/11.14  (step t62 (cl (= tptp.a (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule resolution :premises (t58 t61))
% 10.80/11.14  (step t63 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t64)
% 10.80/11.14  (assume t64.a0 (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))
% 10.80/11.14  (step t64.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule forall_inst :args ((:= X (tptp.left_division tptp.identity tptp.a))))
% 10.80/11.14  (step t64.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule or :premises (t64.t1))
% 10.80/11.14  (step t64.t3 (cl (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule resolution :premises (t64.t2 t64.a0))
% 10.80/11.14  (step t64 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule subproof :discharge (t64.a0))
% 10.80/11.14  (step t65 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule resolution :premises (t63 t64))
% 10.80/11.14  (step t66 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (not (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule implies_neg2)
% 10.80/11.14  (step t67 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule resolution :premises (t65 t66))
% 10.80/11.14  (step t68 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a))))) :rule contraction :premises (t67))
% 10.80/11.14  (step t69 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule implies :premises (t68))
% 10.80/11.14  (step t70 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) (not (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X))) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule equiv_pos2)
% 10.80/11.14  (anchor :step t71 :args ((X $$unsorted) (:= X X)))
% 10.80/11.14  (step t71.t1 (cl (= X X)) :rule refl)
% 10.80/11.14  (step t71.t2 (cl (= (= (tptp.multiply tptp.identity X) X) (= X (tptp.multiply tptp.identity X)))) :rule all_simplify)
% 10.80/11.14  (step t71 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply tptp.identity X) X)) (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X))))) :rule bind)
% 10.80/11.14  (step t72 (cl (forall ((X $$unsorted)) (= X (tptp.multiply tptp.identity X)))) :rule resolution :premises (t70 t71 a0))
% 10.80/11.14  (step t73 (cl (= (tptp.left_division tptp.identity tptp.a) (tptp.multiply tptp.identity (tptp.left_division tptp.identity tptp.a)))) :rule resolution :premises (t69 t72))
% 10.80/11.14  (step t74 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t75)
% 10.80/11.14  (assume t75.a0 (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))))
% 10.80/11.14  (step t75.t1 (cl (or (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule forall_inst :args ((:= X (tptp.multiply tptp.b tptp.c))))
% 10.80/11.14  (step t75.t2 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule or :premises (t75.t1))
% 10.80/11.14  (step t75.t3 (cl (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule resolution :premises (t75.t2 t75.a0))
% 10.80/11.14  (step t75 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule subproof :discharge (t75.a0))
% 10.80/11.14  (step t76 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule resolution :premises (t74 t75))
% 10.80/11.14  (step t77 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (not (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule implies_neg2)
% 10.80/11.14  (step t78 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule resolution :premises (t76 t77))
% 10.80/11.14  (step t79 (cl (=> (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity)))) :rule contraction :premises (t78))
% 10.80/11.14  (step t80 (cl (not (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule implies :premises (t79))
% 10.80/11.14  (step t81 (cl (not (= (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X)) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))))) (not (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X))) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) :rule equiv_pos2)
% 10.80/11.14  (anchor :step t82 :args ((X $$unsorted) (:= X X)))
% 10.80/11.14  (step t82.t1 (cl (= X X)) :rule refl)
% 10.80/11.14  (step t82.t2 (cl (= (= (tptp.multiply X tptp.identity) X) (= X (tptp.multiply X tptp.identity)))) :rule all_simplify)
% 10.80/11.14  (step t82 (cl (= (forall ((X $$unsorted)) (= (tptp.multiply X tptp.identity) X)) (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity))))) :rule bind)
% 10.80/11.14  (step t83 (cl (forall ((X $$unsorted)) (= X (tptp.multiply X tptp.identity)))) :rule resolution :premises (t81 t82 a1))
% 10.80/11.14  (step t84 (cl (= (tptp.multiply tptp.b tptp.c) (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity))) :rule resolution :premises (t80 t83))
% 10.80/11.14  (step t85 (cl (not (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))))) (not (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) :rule equiv_pos2)
% 10.80/11.14  (step t86 (cl (= (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))))) :rule refl)
% 10.80/11.14  (step t87 (cl (= (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) :rule all_simplify)
% 10.80/11.14  (step t88 (cl (= (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))))) :rule cong :premises (t86 t87))
% 10.80/11.14  (step t89 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) :rule implies_neg1)
% 10.80/11.14  (anchor :step t90)
% 10.80/11.14  (assume t90.a0 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))))
% 10.80/11.14  (step t90.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule forall_inst :args ((:= X tptp.a) (:= Y tptp.b) (:= Z tptp.c)))
% 10.80/11.14  (step t90.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule or :premises (t90.t1))
% 10.80/11.14  (step t90.t3 (cl (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule resolution :premises (t90.t2 t90.a0))
% 10.80/11.14  (step t90 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule subproof :discharge (t90.a0))
% 10.80/11.14  (step t91 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) :rule resolution :premises (t89 t90))
% 10.80/11.14  (step t92 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule implies_neg2)
% 10.80/11.14  (step t93 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)))) (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule resolution :premises (t91 t92))
% 10.80/11.14  (step t94 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)) (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a))))) :rule contraction :premises (t93))
% 10.80/11.14  (step t95 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X)))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a))))) :rule resolution :premises (t85 t88 t94))
% 10.80/11.14  (step t96 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (= (tptp.multiply X (tptp.multiply (tptp.multiply Y Z) X)) (tptp.multiply (tptp.multiply X Y) (tptp.multiply Z X))))) (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) :rule implies :premises (t95))
% 10.80/11.14  (step t97 (cl (= (tptp.multiply (tptp.multiply tptp.a tptp.b) (tptp.multiply tptp.c tptp.a)) (tptp.multiply tptp.a (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.a)))) :rule resolution :premises (t96 a8))
% 10.80/11.14  (step t98 (cl (not (= (tptp.multiply tptp.a (tptp.multiply (tptp.multiply (tptp.multiply tptp.b tptp.c) tptp.identity) tptp.a)) (tptp.multiply (tptp.multiply tptp.a (tptp.multiply tptp.b tptp.c)) (tptp.multiply tptp.identity tptp.a))))) :rule resolution :premises (t51 a9 t62 t73 t84 t97))
% 10.80/11.14  (step t99 (cl) :rule resolution :premises (t7 t98 a8))
% 10.80/11.14  
% 10.80/11.14  % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.BChwx7UGGG/cvc5---1.0.5_31856.smt2
% 10.80/11.15  % cvc5---1.0.5 exiting
% 10.80/11.15  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------