%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG041-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n008.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 17:41:34 EDT 2024

% Result   : Unsatisfiable 3.52s 3.70s
% Output   : Proof 3.54s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem    : RNG041-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.14  % Command    : do_cvc5 %s %d
% 0.15/0.35  % Computer : n008.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit   : 300
% 0.15/0.35  % WCLimit    : 300
% 0.15/0.35  % DateTime   : Sat May 25 21:10:39 EDT 2024
% 0.15/0.35  % CPUTime    : 
% 0.21/0.49  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.50  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 3.52/3.70  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.JhWtawOK9J/cvc5---1.0.5_8716.smt2
% 3.52/3.70  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.JhWtawOK9J/cvc5---1.0.5_8716.smt2
% 3.54/3.70  (assume a0 (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)))
% 3.54/3.70  (assume a1 (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)))
% 3.54/3.70  (assume a2 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.product X Y (tptp.multiply X Y))))
% 3.54/3.70  (assume a3 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.sum X Y (tptp.add X Y))))
% 3.54/3.70  (assume a4 (forall ((X $$unsorted)) (tptp.sum (tptp.additive_inverse X) X tptp.additive_identity)))
% 3.54/3.70  (assume a5 (forall ((X $$unsorted)) (tptp.sum X (tptp.additive_inverse X) tptp.additive_identity)))
% 3.54/3.70  (assume a6 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum Y Z V)) (not (tptp.sum U Z W)) (tptp.sum X V W))))
% 3.54/3.70  (assume a7 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum Y Z V)) (not (tptp.sum X V W)) (tptp.sum U Z W))))
% 3.54/3.70  (assume a8 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted)) (or (not (tptp.sum X Y Z)) (tptp.sum Y X Z))))
% 3.54/3.70  (assume a9 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product U Z W)) (tptp.product X V W))))
% 3.54/3.70  (assume a10 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))))
% 3.54/3.70  (assume a11 (forall ((X $$unsorted) (Y $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product X Y V1)) (not (tptp.product X Z V2)) (not (tptp.sum Y Z V3)) (not (tptp.product X V3 V4)) (tptp.sum V1 V2 V4))))
% 3.54/3.70  (assume a12 (forall ((X $$unsorted) (Y $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product X Y V1)) (not (tptp.product X Z V2)) (not (tptp.sum Y Z V3)) (not (tptp.sum V1 V2 V4)) (tptp.product X V3 V4))))
% 3.54/3.70  (assume a13 (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))))
% 3.54/3.70  (assume a14 (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.sum V1 V2 V4)) (tptp.product V3 X V4))))
% 3.54/3.70  (assume a15 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))))
% 3.54/3.70  (assume a16 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product X Y V)) (= U V))))
% 3.54/3.70  (assume a17 (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)))
% 3.54/3.70  (assume a18 (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)))
% 3.54/3.70  (assume a19 (forall ((A $$unsorted)) (tptp.product A tptp.multiplicative_identity A)))
% 3.54/3.70  (assume a20 (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)))
% 3.54/3.70  (assume a21 (forall ((A $$unsorted)) (or (tptp.product A (tptp.h A) tptp.multiplicative_identity) (= A tptp.additive_identity))))
% 3.54/3.70  (assume a22 (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= A tptp.additive_identity))))
% 3.54/3.70  (assume a23 (tptp.product tptp.a tptp.b tptp.additive_identity))
% 3.54/3.70  (assume a24 (not (= tptp.a tptp.additive_identity)))
% 3.54/3.70  (assume a25 (not (= tptp.b tptp.additive_identity)))
% 3.54/3.70  (step t1 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V)))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t2)
% 3.54/3.70  (assume t2.a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))))
% 3.54/3.70  (step t2.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V)))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)))) :rule forall_inst :args ((:= X tptp.additive_identity) (:= Y tptp.additive_identity) (:= U tptp.additive_identity) (:= V tptp.b)))
% 3.54/3.70  (step t2.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V)))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) :rule or :premises (t2.t1))
% 3.54/3.70  (step t2.t3 (cl (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) :rule resolution :premises (t2.t2 t2.a0))
% 3.54/3.70  (step t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V)))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) :rule subproof :discharge (t2.a0))
% 3.54/3.70  (step t3 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) :rule resolution :premises (t1 t2))
% 3.54/3.70  (step t4 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) (not (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)))) :rule implies_neg2)
% 3.54/3.70  (step t5 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)))) :rule resolution :premises (t3 t4))
% 3.54/3.70  (step t6 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)))) :rule contraction :premises (t5))
% 3.54/3.70  (step t7 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (V $$unsorted)) (or (not (tptp.sum X Y U)) (not (tptp.sum X Y V)) (= U V)))) (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) :rule implies :premises (t6))
% 3.54/3.70  (step t8 (cl (not (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b))) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)) :rule or_pos)
% 3.54/3.70  (step t9 (cl (= tptp.additive_identity tptp.b) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (not (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)))) :rule reordering :premises (t8))
% 3.54/3.70  (step t10 (cl (not (= tptp.additive_identity tptp.b))) :rule not_symm :premises (a25))
% 3.54/3.70  (step t11 (cl (=> (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t12)
% 3.54/3.70  (assume t12.a0 (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)))
% 3.54/3.70  (step t12.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X))) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity))) :rule forall_inst :args ((:= X tptp.additive_identity)))
% 3.54/3.70  (step t12.t2 (cl (not (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X))) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) :rule or :premises (t12.t1))
% 3.54/3.70  (step t12.t3 (cl (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) :rule resolution :premises (t12.t2 t12.a0))
% 3.54/3.70  (step t12 (cl (not (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X))) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) :rule subproof :discharge (t12.a0))
% 3.54/3.70  (step t13 (cl (=> (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) :rule resolution :premises (t11 t12))
% 3.54/3.70  (step t14 (cl (=> (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity))) :rule implies_neg2)
% 3.54/3.70  (step t15 (cl (=> (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (=> (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity))) :rule resolution :premises (t13 t14))
% 3.54/3.70  (step t16 (cl (=> (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity))) :rule contraction :premises (t15))
% 3.54/3.70  (step t17 (cl (not (forall ((X $$unsorted)) (tptp.sum tptp.additive_identity X X))) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) :rule implies :premises (t16))
% 3.54/3.70  (step t18 (cl (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) :rule resolution :premises (t17 a0))
% 3.54/3.70  (step t19 (cl (not (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) :rule or_pos)
% 3.54/3.70  (step t20 (cl (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (not (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)))) :rule reordering :premises (t19))
% 3.54/3.70  (step t21 (cl (=> (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t22)
% 3.54/3.70  (assume t22.a0 (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)))
% 3.54/3.70  (step t22.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X))) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity))) :rule forall_inst :args ((:= X tptp.multiplicative_identity)))
% 3.54/3.70  (step t22.t2 (cl (not (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X))) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) :rule or :premises (t22.t1))
% 3.54/3.70  (step t22.t3 (cl (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) :rule resolution :premises (t22.t2 t22.a0))
% 3.54/3.70  (step t22 (cl (not (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X))) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) :rule subproof :discharge (t22.a0))
% 3.54/3.70  (step t23 (cl (=> (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) :rule resolution :premises (t21 t22))
% 3.54/3.70  (step t24 (cl (=> (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity))) :rule implies_neg2)
% 3.54/3.70  (step t25 (cl (=> (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (=> (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity))) :rule resolution :premises (t23 t24))
% 3.54/3.70  (step t26 (cl (=> (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X)) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity))) :rule contraction :premises (t25))
% 3.54/3.70  (step t27 (cl (not (forall ((X $$unsorted)) (tptp.sum X tptp.additive_identity X))) (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) :rule implies :premises (t26))
% 3.54/3.70  (step t28 (cl (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) :rule resolution :premises (t27 a1))
% 3.54/3.70  (step t29 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t30)
% 3.54/3.70  (assume t30.a0 (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)))
% 3.54/3.70  (step t30.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity))) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity))) :rule forall_inst :args ((:= A tptp.b)))
% 3.54/3.70  (step t30.t2 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity))) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) :rule or :premises (t30.t1))
% 3.54/3.70  (step t30.t3 (cl (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) :rule resolution :premises (t30.t2 t30.a0))
% 3.54/3.70  (step t30 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity))) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) :rule subproof :discharge (t30.a0))
% 3.54/3.70  (step t31 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) :rule resolution :premises (t29 t30))
% 3.54/3.70  (step t32 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity))) :rule implies_neg2)
% 3.54/3.70  (step t33 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (=> (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity))) :rule resolution :premises (t31 t32))
% 3.54/3.70  (step t34 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity)) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity))) :rule contraction :premises (t33))
% 3.54/3.70  (step t35 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.additive_identity A tptp.additive_identity))) (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) :rule implies :premises (t34))
% 3.54/3.70  (step t36 (cl (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) :rule resolution :premises (t35 a17))
% 3.54/3.70  (step t37 (cl (not (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) :rule or_pos)
% 3.54/3.70  (step t38 (cl (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity) (not (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)))) :rule reordering :premises (t37))
% 3.54/3.70  (step t39 (cl (not (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a)) :rule or_pos)
% 3.54/3.70  (step t40 (cl (= tptp.additive_identity tptp.a) (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (not (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a)))) :rule reordering :premises (t39))
% 3.54/3.70  (step t41 (cl (not (= tptp.additive_identity tptp.a))) :rule not_symm :premises (a24))
% 3.54/3.70  (step t42 (cl (=> (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t43)
% 3.54/3.70  (assume t43.a0 (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))))
% 3.54/3.70  (step t43.t1 (cl (or (not (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a)))) :rule forall_inst :args ((:= A tptp.a)))
% 3.54/3.70  (step t43.t2 (cl (not (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) :rule or :premises (t43.t1))
% 3.54/3.70  (step t43.t3 (cl (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) :rule resolution :premises (t43.t2 t43.a0))
% 3.54/3.70  (step t43 (cl (not (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) :rule subproof :discharge (t43.a0))
% 3.54/3.70  (step t44 (cl (=> (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) :rule resolution :premises (t42 t43))
% 3.54/3.70  (step t45 (cl (=> (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) (not (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a)))) :rule implies_neg2)
% 3.54/3.70  (step t46 (cl (=> (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) (=> (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a)))) :rule resolution :premises (t44 t45))
% 3.54/3.70  (step t47 (cl (=> (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a)))) :rule contraction :premises (t46))
% 3.54/3.70  (step t48 (cl (not (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) :rule implies :premises (t47))
% 3.54/3.70  (step t49 (cl (not (= (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= A tptp.additive_identity))) (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))))) (not (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= A tptp.additive_identity)))) (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) :rule equiv_pos2)
% 3.54/3.70  (anchor :step t50 :args ((A $$unsorted) (:= A A)))
% 3.54/3.70  (step t50.t1 (cl (= A A)) :rule refl)
% 3.54/3.70  (step t50.t2 (cl (= (tptp.product (tptp.h A) A tptp.multiplicative_identity) (tptp.product (tptp.h A) A tptp.multiplicative_identity))) :rule refl)
% 3.54/3.70  (step t50.t3 (cl (= (= A tptp.additive_identity) (= tptp.additive_identity A))) :rule all_simplify)
% 3.54/3.70  (step t50.t4 (cl (= (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= A tptp.additive_identity)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) :rule cong :premises (t50.t2 t50.t3))
% 3.54/3.70  (step t50 (cl (= (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= A tptp.additive_identity))) (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A))))) :rule bind)
% 3.54/3.70  (step t51 (cl (forall ((A $$unsorted)) (or (tptp.product (tptp.h A) A tptp.multiplicative_identity) (= tptp.additive_identity A)))) :rule resolution :premises (t49 t50 a22))
% 3.54/3.70  (step t52 (cl (or (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity) (= tptp.additive_identity tptp.a))) :rule resolution :premises (t48 t51))
% 3.54/3.70  (step t53 (cl (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) :rule resolution :premises (t40 t41 t52))
% 3.54/3.70  (step t54 (cl (=> (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t55)
% 3.54/3.70  (assume t55.a0 (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)))
% 3.54/3.70  (step t55.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity))) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity))) :rule forall_inst :args ((:= A (tptp.h tptp.a))))
% 3.54/3.70  (step t55.t2 (cl (not (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity))) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) :rule or :premises (t55.t1))
% 3.54/3.70  (step t55.t3 (cl (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) :rule resolution :premises (t55.t2 t55.a0))
% 3.54/3.70  (step t55 (cl (not (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity))) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) :rule subproof :discharge (t55.a0))
% 3.54/3.70  (step t56 (cl (=> (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) :rule resolution :premises (t54 t55))
% 3.54/3.70  (step t57 (cl (=> (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity))) :rule implies_neg2)
% 3.54/3.70  (step t58 (cl (=> (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (=> (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity))) :rule resolution :premises (t56 t57))
% 3.54/3.70  (step t59 (cl (=> (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity)) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity))) :rule contraction :premises (t58))
% 3.54/3.70  (step t60 (cl (not (forall ((A $$unsorted)) (tptp.product A tptp.additive_identity tptp.additive_identity))) (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) :rule implies :premises (t59))
% 3.54/3.70  (step t61 (cl (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) :rule resolution :premises (t60 a18))
% 3.54/3.70  (step t62 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W)))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t63)
% 3.54/3.70  (assume t63.a0 (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))))
% 3.54/3.70  (step t63.t1 (cl (or (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W)))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)))) :rule forall_inst :args ((:= X (tptp.h tptp.a)) (:= Y tptp.a) (:= U tptp.multiplicative_identity) (:= Z tptp.b) (:= V tptp.additive_identity) (:= W tptp.additive_identity)))
% 3.54/3.70  (step t63.t2 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W)))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) :rule or :premises (t63.t1))
% 3.54/3.70  (step t63.t3 (cl (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) :rule resolution :premises (t63.t2 t63.a0))
% 3.54/3.70  (step t63 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W)))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) :rule subproof :discharge (t63.a0))
% 3.54/3.70  (step t64 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) :rule resolution :premises (t62 t63))
% 3.54/3.70  (step t65 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) (not (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)))) :rule implies_neg2)
% 3.54/3.70  (step t66 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)))) :rule resolution :premises (t64 t65))
% 3.54/3.70  (step t67 (cl (=> (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)))) :rule contraction :premises (t66))
% 3.54/3.70  (step t68 (cl (not (forall ((X $$unsorted) (Y $$unsorted) (U $$unsorted) (Z $$unsorted) (V $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y U)) (not (tptp.product Y Z V)) (not (tptp.product X V W)) (tptp.product U Z W)))) (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) :rule implies :premises (t67))
% 3.54/3.70  (step t69 (cl (or (not (tptp.product (tptp.h tptp.a) tptp.a tptp.multiplicative_identity)) (not (tptp.product tptp.a tptp.b tptp.additive_identity)) (not (tptp.product (tptp.h tptp.a) tptp.additive_identity tptp.additive_identity)) (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity))) :rule resolution :premises (t68 a10))
% 3.54/3.70  (step t70 (cl (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) :rule resolution :premises (t38 a23 t53 t61 t69))
% 3.54/3.70  (step t71 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t72)
% 3.54/3.70  (assume t72.a0 (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)))
% 3.54/3.70  (step t72.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A))) (tptp.product tptp.multiplicative_identity tptp.b tptp.b))) :rule forall_inst :args ((:= A tptp.b)))
% 3.54/3.70  (step t72.t2 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A))) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) :rule or :premises (t72.t1))
% 3.54/3.70  (step t72.t3 (cl (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) :rule resolution :premises (t72.t2 t72.a0))
% 3.54/3.70  (step t72 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A))) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) :rule subproof :discharge (t72.a0))
% 3.54/3.70  (step t73 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) :rule resolution :premises (t71 t72))
% 3.54/3.70  (step t74 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b))) :rule implies_neg2)
% 3.54/3.70  (step t75 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (=> (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b))) :rule resolution :premises (t73 t74))
% 3.54/3.70  (step t76 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A)) (tptp.product tptp.multiplicative_identity tptp.b tptp.b))) :rule contraction :premises (t75))
% 3.54/3.70  (step t77 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.multiplicative_identity A A))) (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) :rule implies :premises (t76))
% 3.54/3.70  (step t78 (cl (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) :rule resolution :premises (t77 a20))
% 3.54/3.70  (step t79 (cl (=> (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4)))) :rule implies_neg1)
% 3.54/3.70  (anchor :step t80)
% 3.54/3.70  (assume t80.a0 (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))))
% 3.54/3.70  (step t80.t1 (cl (or (not (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4)))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)))) :rule forall_inst :args ((:= Y tptp.multiplicative_identity) (:= X tptp.b) (:= V1 tptp.additive_identity) (:= Z tptp.additive_identity) (:= V2 tptp.additive_identity) (:= V3 tptp.multiplicative_identity) (:= V4 tptp.b)))
% 3.54/3.71  (step t80.t2 (cl (not (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4)))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) :rule or :premises (t80.t1))
% 3.54/3.71  (step t80.t3 (cl (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) :rule resolution :premises (t80.t2 t80.a0))
% 3.54/3.71  (step t80 (cl (not (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4)))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) :rule subproof :discharge (t80.a0))
% 3.54/3.71  (step t81 (cl (=> (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) :rule resolution :premises (t79 t80))
% 3.54/3.71  (step t82 (cl (=> (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) (not (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)))) :rule implies_neg2)
% 3.54/3.71  (step t83 (cl (=> (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) (=> (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)))) :rule resolution :premises (t81 t82))
% 3.54/3.71  (step t84 (cl (=> (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)))) :rule contraction :premises (t83))
% 3.54/3.71  (step t85 (cl (not (forall ((Y $$unsorted) (X $$unsorted) (V1 $$unsorted) (Z $$unsorted) (V2 $$unsorted) (V3 $$unsorted) (V4 $$unsorted)) (or (not (tptp.product Y X V1)) (not (tptp.product Z X V2)) (not (tptp.sum Y Z V3)) (not (tptp.product V3 X V4)) (tptp.sum V1 V2 V4)))) (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) :rule implies :premises (t84))
% 3.54/3.71  (step t86 (cl (or (not (tptp.product tptp.multiplicative_identity tptp.b tptp.additive_identity)) (not (tptp.product tptp.additive_identity tptp.b tptp.additive_identity)) (not (tptp.sum tptp.multiplicative_identity tptp.additive_identity tptp.multiplicative_identity)) (not (tptp.product tptp.multiplicative_identity tptp.b tptp.b)) (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b))) :rule resolution :premises (t85 a13))
% 3.54/3.71  (step t87 (cl (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) :rule resolution :premises (t20 t28 t36 t70 t78 t86))
% 3.54/3.71  (step t88 (cl (not (or (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.additive_identity)) (not (tptp.sum tptp.additive_identity tptp.additive_identity tptp.b)) (= tptp.additive_identity tptp.b)))) :rule resolution :premises (t9 t10 t18 t87))
% 3.54/3.71  (step t89 (cl) :rule resolution :premises (t7 t88 a15))
% 3.54/3.71  
% 3.54/3.71  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.JhWtawOK9J/cvc5---1.0.5_8716.smt2
% 3.54/3.71  % cvc5---1.0.5 exiting
% 3.54/3.71  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------