%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GRP039-4 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n015.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 16:50:33 EDT 2024

% Result   : Unsatisfiable 51.65s 51.90s
% Output   : Proof 51.65s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : GRP039-4 : TPTP v8.2.0. Released v1.0.0.
% 0.07/0.15  % Command    : do_cvc5 %s %d
% 0.14/0.36  % Computer : n015.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Sun May 26 18:47:24 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.21/0.52  %----Proving TF0_NAR, FOF, or CNF
% 0.36/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 10.35/10.54  --- Run --no-e-matching --full-saturate-quant at 5...
% 15.35/15.57  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 20.35/20.60  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.47/25.65  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 30.49/30.68  --- Run --trigger-sel=max --full-saturate-quant at 5...
% 35.46/35.70  --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 5...
% 40.42/40.74  --- Run --multi-trigger-cache --full-saturate-quant at 5...
% 45.77/46.01  --- Run --prenex-quant=none --full-saturate-quant at 5...
% 50.76/51.05  --- Run --enum-inst-interleave --decision=internal --full-saturate-quant at 5...
% 51.65/51.90  % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.NRVGJjnBoj/cvc5---1.0.5_22735.smt2
% 51.65/51.90  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.NRVGJjnBoj/cvc5---1.0.5_22735.smt2
% 51.65/51.91  (assume a0 (forall ((X $$unsorted)) (tptp.product tptp.identity X X)))
% 51.65/51.91  (assume a1 (forall ((X $$unsorted)) (tptp.product X tptp.identity X)))
% 51.65/51.91  (assume a2 (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)))
% 51.65/51.91  (assume a3 (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)))
% 51.65/51.91  (assume a4 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.product X Y (tptp.multiply X Y))))
% 51.65/51.91  (assume a5 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y Z)) (not (tptp.product X Y W)) (= Z W))))
% 51.65/51.91  (assume a6 (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))))
% 51.65/51.91  (assume a7 (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))))
% 51.65/51.91  (assume a8 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 51.65/51.91  (assume a9 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))))
% 51.65/51.91  (assume a10 (tptp.subgroup_member tptp.identity))
% 51.65/51.91  (assume a11 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))))
% 51.65/51.91  (assume a12 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))))
% 51.65/51.91  (assume a13 (tptp.subgroup_member tptp.b))
% 51.65/51.91  (assume a14 (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c))
% 51.65/51.91  (assume a15 (tptp.product tptp.a tptp.c tptp.d))
% 51.65/51.91  (assume a16 (not (tptp.subgroup_member tptp.d)))
% 51.65/51.91  (step t1 (cl (not (or (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) :rule or_pos)
% 51.65/51.91  (step t2 (cl (not (tptp.product tptp.a tptp.c tptp.d)) (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d) (not (or (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)))) :rule reordering :premises (t1))
% 51.65/51.91  (step t3 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) (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)
% 51.65/51.91  (anchor :step t4)
% 51.65/51.91  (assume t4.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))))
% 51.65/51.91  (step t4.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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)))) :rule forall_inst :args ((:= X tptp.a) (:= Y (tptp.inverse tptp.a)) (:= U tptp.identity) (:= Z (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (:= V tptp.c) (:= W tptp.d)))
% 51.65/51.91  (step t4.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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) :rule or :premises (t4.t1))
% 51.65/51.91  (step t4.t3 (cl (or (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) :rule resolution :premises (t4.t2 t4.a0))
% 51.65/51.91  (step t4 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) :rule subproof :discharge (t4.a0))
% 51.65/51.91  (step t5 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) (or (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) :rule resolution :premises (t3 t4))
% 51.65/51.91  (step t6 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) (not (or (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)))) :rule implies_neg2)
% 51.65/51.91  (step t7 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) (=> (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)))) :rule resolution :premises (t5 t6))
% 51.65/51.91  (step t8 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)))) :rule contraction :premises (t7))
% 51.65/51.91  (step t9 (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.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) :rule implies :premises (t8))
% 51.65/51.91  (step t10 (cl (or (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d))) :rule resolution :premises (t9 a7))
% 51.65/51.91  (step t11 (cl (=> (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t12)
% 51.65/51.91  (assume t12.a0 (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)))
% 51.65/51.91  (step t12.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity))) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity))) :rule forall_inst :args ((:= X tptp.a)))
% 51.65/51.91  (step t12.t2 (cl (not (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity))) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) :rule or :premises (t12.t1))
% 51.65/51.91  (step t12.t3 (cl (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) :rule resolution :premises (t12.t2 t12.a0))
% 51.65/51.91  (step t12 (cl (not (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity))) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) :rule subproof :discharge (t12.a0))
% 51.65/51.91  (step t13 (cl (=> (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) :rule resolution :premises (t11 t12))
% 51.65/51.91  (step t14 (cl (=> (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity))) :rule implies_neg2)
% 51.65/51.91  (step t15 (cl (=> (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) (=> (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity))) :rule resolution :premises (t13 t14))
% 51.65/51.91  (step t16 (cl (=> (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity)) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity))) :rule contraction :premises (t15))
% 51.65/51.91  (step t17 (cl (not (forall ((X $$unsorted)) (tptp.product X (tptp.inverse X) tptp.identity))) (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) :rule implies :premises (t16))
% 51.65/51.91  (step t18 (cl (tptp.product tptp.a (tptp.inverse tptp.a) tptp.identity)) :rule resolution :premises (t17 a3))
% 51.65/51.91  (step t19 (cl (not (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d)) :rule or_pos)
% 51.65/51.91  (step t20 (cl (tptp.subgroup_member tptp.d) (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (not (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d)))) :rule reordering :premises (t19))
% 51.65/51.91  (step t21 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t22)
% 51.65/51.91  (assume t22.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))))
% 51.65/51.91  (step t22.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d)))) :rule forall_inst :args ((:= A tptp.identity) (:= B (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (:= C tptp.d)))
% 51.65/51.91  (step t22.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) :rule or :premises (t22.t1))
% 51.65/51.91  (step t22.t3 (cl (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) :rule resolution :premises (t22.t2 t22.a0))
% 51.65/51.91  (step t22 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) :rule subproof :discharge (t22.a0))
% 51.65/51.91  (step t23 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) :rule resolution :premises (t21 t22))
% 51.65/51.91  (step t24 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) (not (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d)))) :rule implies_neg2)
% 51.65/51.91  (step t25 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d)))) :rule resolution :premises (t23 t24))
% 51.65/51.91  (step t26 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d)))) :rule contraction :premises (t25))
% 51.65/51.91  (step t27 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) :rule implies :premises (t26))
% 51.65/51.91  (step t28 (cl (or (not (tptp.subgroup_member tptp.identity)) (not (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c))) (not (tptp.product tptp.identity (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.d)) (tptp.subgroup_member tptp.d))) :rule resolution :premises (t27 a9))
% 51.65/51.91  (step t29 (cl (not (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))) :rule or_pos)
% 51.65/51.91  (step t30 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member tptp.c) (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (not (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule reordering :premises (t29))
% 51.65/51.91  (step t31 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t32)
% 51.65/51.91  (assume t32.a0 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))))
% 51.65/51.91  (step t32.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= A (tptp.inverse tptp.a)) (:= B tptp.c)))
% 51.65/51.91  (step t32.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule or :premises (t32.t1))
% 51.65/51.91  (step t32.t3 (cl (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t32.t2 t32.a0))
% 51.65/51.91  (step t32 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule subproof :discharge (t32.a0))
% 51.65/51.91  (step t33 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t31 t32))
% 51.65/51.91  (step t34 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule implies_neg2)
% 51.65/51.91  (step t35 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule resolution :premises (t33 t34))
% 51.65/51.91  (step t36 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule contraction :premises (t35))
% 51.65/51.91  (step t37 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.product A (tptp.element_in_O2 A B) B) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule implies :premises (t36))
% 51.65/51.91  (step t38 (cl (or (tptp.product (tptp.inverse tptp.a) (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c) tptp.c) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t37 a12))
% 51.65/51.91  (step t39 (cl (not (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))) :rule or_pos)
% 51.65/51.91  (step t40 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (not (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule reordering :premises (t39))
% 51.65/51.91  (step t41 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t42)
% 51.65/51.91  (assume t42.a0 (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))))
% 51.65/51.91  (step t42.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= A (tptp.inverse tptp.a)) (:= B tptp.c)))
% 51.65/51.91  (step t42.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule or :premises (t42.t1))
% 51.65/51.91  (step t42.t3 (cl (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t42.t2 t42.a0))
% 51.65/51.91  (step t42 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule subproof :discharge (t42.a0))
% 51.65/51.91  (step t43 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t41 t42))
% 51.65/51.91  (step t44 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule implies_neg2)
% 51.65/51.91  (step t45 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule resolution :premises (t43 t44))
% 51.65/51.91  (step t46 (cl (=> (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule contraction :premises (t45))
% 51.65/51.91  (step t47 (cl (not (forall ((A $$unsorted) (B $$unsorted)) (or (tptp.subgroup_member (tptp.element_in_O2 A B)) (tptp.subgroup_member B) (tptp.subgroup_member A)))) (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule implies :premises (t46))
% 51.65/51.91  (step t48 (cl (or (tptp.subgroup_member (tptp.element_in_O2 (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t47 a11))
% 51.65/51.91  (step t49 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member tptp.c) (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member tptp.c)) :rule resolution :premises (t2 t10 t18 a15 t20 t28 a16 a10 t30 t38 t40 t48))
% 51.65/51.91  (step t50 (cl (tptp.subgroup_member (tptp.inverse tptp.a)) (tptp.subgroup_member tptp.c)) :rule contraction :premises (t49))
% 51.65/51.91  (step t51 (cl (not (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c)) :rule or_pos)
% 51.65/51.91  (step t52 (cl (not (tptp.subgroup_member tptp.b)) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (tptp.subgroup_member tptp.c) (not (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c)))) :rule reordering :premises (t51))
% 51.65/51.91  (step t53 (cl (not (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c))) :rule or_pos)
% 51.65/51.91  (step t54 (cl (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)) (not (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c))))) :rule reordering :premises (t53))
% 51.65/51.91  (step t55 (cl (not (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a)) :rule or_pos)
% 51.65/51.91  (step t56 (cl (not (tptp.subgroup_member tptp.b)) (tptp.subgroup_member tptp.a) (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (not (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a)))) :rule reordering :premises (t55))
% 51.65/51.91  (step t57 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t58)
% 51.65/51.91  (assume t58.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))))
% 51.65/51.91  (step t58.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c)))) :rule forall_inst :args ((:= A tptp.b) (:= B (tptp.inverse tptp.a)) (:= C tptp.c)))
% 51.65/51.91  (step t58.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) :rule or :premises (t58.t1))
% 51.65/51.91  (step t58.t3 (cl (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) :rule resolution :premises (t58.t2 t58.a0))
% 51.65/51.91  (step t58 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) :rule subproof :discharge (t58.a0))
% 51.65/51.91  (step t59 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) :rule resolution :premises (t57 t58))
% 51.65/51.91  (step t60 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) (not (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c)))) :rule implies_neg2)
% 51.65/51.91  (step t61 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c)))) :rule resolution :premises (t59 t60))
% 51.65/51.91  (step t62 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c)))) :rule contraction :premises (t61))
% 51.65/51.91  (step t63 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) :rule implies :premises (t62))
% 51.65/51.91  (step t64 (cl (or (not (tptp.subgroup_member tptp.b)) (not (tptp.subgroup_member (tptp.inverse tptp.a))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (tptp.subgroup_member tptp.c))) :rule resolution :premises (t63 a9))
% 51.65/51.91  (step t65 (cl (not (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d)) :rule or_pos)
% 51.65/51.91  (step t66 (cl (tptp.subgroup_member tptp.d) (not (tptp.product tptp.a tptp.c tptp.d)) (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d)))) :rule reordering :premises (t65))
% 51.65/51.91  (step t67 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t68)
% 51.65/51.91  (assume t68.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))))
% 51.65/51.91  (step t68.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d)))) :rule forall_inst :args ((:= A tptp.a) (:= B tptp.c) (:= C tptp.d)))
% 51.65/51.91  (step t68.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) :rule or :premises (t68.t1))
% 51.65/51.91  (step t68.t3 (cl (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) :rule resolution :premises (t68.t2 t68.a0))
% 51.65/51.91  (step t68 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) :rule subproof :discharge (t68.a0))
% 51.65/51.91  (step t69 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) :rule resolution :premises (t67 t68))
% 51.65/51.91  (step t70 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) (not (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d)))) :rule implies_neg2)
% 51.65/51.91  (step t71 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d)))) :rule resolution :premises (t69 t70))
% 51.65/51.91  (step t72 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d)))) :rule contraction :premises (t71))
% 51.65/51.91  (step t73 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) :rule implies :premises (t72))
% 51.65/51.91  (step t74 (cl (or (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.c)) (not (tptp.product tptp.a tptp.c tptp.d)) (tptp.subgroup_member tptp.d))) :rule resolution :premises (t73 a9))
% 51.65/51.91  (step t75 (cl (not (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))) :rule or_pos)
% 51.65/51.91  (step t76 (cl (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)) (not (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule reordering :premises (t75))
% 51.65/51.91  (step t77 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t78)
% 51.65/51.91  (assume t78.a0 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 51.65/51.91  (step t78.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule forall_inst :args ((:= X tptp.a)))
% 51.65/51.91  (step t78.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule or :premises (t78.t1))
% 51.65/51.91  (step t78.t3 (cl (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t78.t2 t78.a0))
% 51.65/51.91  (step t78 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule subproof :discharge (t78.a0))
% 51.65/51.91  (step t79 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t77 t78))
% 51.65/51.91  (step t80 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (not (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule implies_neg2)
% 51.65/51.91  (step t81 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule resolution :premises (t79 t80))
% 51.65/51.91  (step t82 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a))))) :rule contraction :premises (t81))
% 51.65/51.91  (step t83 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule implies :premises (t82))
% 51.65/51.91  (step t84 (cl (or (not (tptp.subgroup_member tptp.a)) (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t83 a8))
% 51.65/51.91  (step t85 (cl (not (tptp.subgroup_member tptp.a)) (not (tptp.subgroup_member tptp.a))) :rule resolution :premises (t52 t64 a14 a13 t66 t74 a16 a15 t76 t84))
% 51.65/51.91  (step t86 (cl (not (tptp.subgroup_member tptp.a))) :rule contraction :premises (t85))
% 51.65/51.91  (step t87 (cl (not (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) :rule or_pos)
% 51.65/51.91  (step t88 (cl (not (tptp.product tptp.identity tptp.a tptp.a)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a) (not (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)))) :rule reordering :premises (t87))
% 51.65/51.91  (step t89 (cl (=> (forall ((X $$unsorted)) (tptp.product tptp.identity X X)) (tptp.product tptp.identity tptp.a tptp.a)) (forall ((X $$unsorted)) (tptp.product tptp.identity X X))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t90)
% 51.65/51.91  (assume t90.a0 (forall ((X $$unsorted)) (tptp.product tptp.identity X X)))
% 51.65/51.91  (step t90.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product tptp.identity X X))) (tptp.product tptp.identity tptp.a tptp.a))) :rule forall_inst :args ((:= X tptp.a)))
% 51.65/51.91  (step t90.t2 (cl (not (forall ((X $$unsorted)) (tptp.product tptp.identity X X))) (tptp.product tptp.identity tptp.a tptp.a)) :rule or :premises (t90.t1))
% 51.65/51.91  (step t90.t3 (cl (tptp.product tptp.identity tptp.a tptp.a)) :rule resolution :premises (t90.t2 t90.a0))
% 51.65/51.91  (step t90 (cl (not (forall ((X $$unsorted)) (tptp.product tptp.identity X X))) (tptp.product tptp.identity tptp.a tptp.a)) :rule subproof :discharge (t90.a0))
% 51.65/51.91  (step t91 (cl (=> (forall ((X $$unsorted)) (tptp.product tptp.identity X X)) (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product tptp.identity tptp.a tptp.a)) :rule resolution :premises (t89 t90))
% 51.65/51.91  (step t92 (cl (=> (forall ((X $$unsorted)) (tptp.product tptp.identity X X)) (tptp.product tptp.identity tptp.a tptp.a)) (not (tptp.product tptp.identity tptp.a tptp.a))) :rule implies_neg2)
% 51.65/51.91  (step t93 (cl (=> (forall ((X $$unsorted)) (tptp.product tptp.identity X X)) (tptp.product tptp.identity tptp.a tptp.a)) (=> (forall ((X $$unsorted)) (tptp.product tptp.identity X X)) (tptp.product tptp.identity tptp.a tptp.a))) :rule resolution :premises (t91 t92))
% 51.65/51.91  (step t94 (cl (=> (forall ((X $$unsorted)) (tptp.product tptp.identity X X)) (tptp.product tptp.identity tptp.a tptp.a))) :rule contraction :premises (t93))
% 51.65/51.91  (step t95 (cl (not (forall ((X $$unsorted)) (tptp.product tptp.identity X X))) (tptp.product tptp.identity tptp.a tptp.a)) :rule implies :premises (t94))
% 51.65/51.91  (step t96 (cl (tptp.product tptp.identity tptp.a tptp.a)) :rule resolution :premises (t95 a0))
% 51.65/51.91  (step t97 (cl (not (or (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b)) :rule or_pos)
% 51.65/51.91  (step t98 (cl (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b) (not (or (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b)))) :rule reordering :premises (t97))
% 51.65/51.91  (step t99 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t100)
% 51.65/51.91  (assume t100.a0 (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)))
% 51.65/51.91  (step t100.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule forall_inst :args ((:= X tptp.a)))
% 51.65/51.91  (step t100.t2 (cl (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule or :premises (t100.t1))
% 51.65/51.91  (step t100.t3 (cl (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule resolution :premises (t100.t2 t100.a0))
% 51.65/51.91  (step t100 (cl (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule subproof :discharge (t100.a0))
% 51.65/51.91  (step t101 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule resolution :premises (t99 t100))
% 51.65/51.91  (step t102 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule implies_neg2)
% 51.65/51.91  (step t103 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule resolution :premises (t101 t102))
% 51.65/51.91  (step t104 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule contraction :premises (t103))
% 51.65/51.91  (step t105 (cl (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule implies :premises (t104))
% 51.65/51.91  (step t106 (cl (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule resolution :premises (t105 a2))
% 51.65/51.91  (step t107 (cl (=> (forall ((X $$unsorted)) (tptp.product X tptp.identity X)) (tptp.product tptp.b tptp.identity tptp.b)) (forall ((X $$unsorted)) (tptp.product X tptp.identity X))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t108)
% 51.65/51.91  (assume t108.a0 (forall ((X $$unsorted)) (tptp.product X tptp.identity X)))
% 51.65/51.91  (step t108.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product X tptp.identity X))) (tptp.product tptp.b tptp.identity tptp.b))) :rule forall_inst :args ((:= X tptp.b)))
% 51.65/51.91  (step t108.t2 (cl (not (forall ((X $$unsorted)) (tptp.product X tptp.identity X))) (tptp.product tptp.b tptp.identity tptp.b)) :rule or :premises (t108.t1))
% 51.65/51.91  (step t108.t3 (cl (tptp.product tptp.b tptp.identity tptp.b)) :rule resolution :premises (t108.t2 t108.a0))
% 51.65/51.91  (step t108 (cl (not (forall ((X $$unsorted)) (tptp.product X tptp.identity X))) (tptp.product tptp.b tptp.identity tptp.b)) :rule subproof :discharge (t108.a0))
% 51.65/51.91  (step t109 (cl (=> (forall ((X $$unsorted)) (tptp.product X tptp.identity X)) (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.b tptp.identity tptp.b)) :rule resolution :premises (t107 t108))
% 51.65/51.91  (step t110 (cl (=> (forall ((X $$unsorted)) (tptp.product X tptp.identity X)) (tptp.product tptp.b tptp.identity tptp.b)) (not (tptp.product tptp.b tptp.identity tptp.b))) :rule implies_neg2)
% 51.65/51.91  (step t111 (cl (=> (forall ((X $$unsorted)) (tptp.product X tptp.identity X)) (tptp.product tptp.b tptp.identity tptp.b)) (=> (forall ((X $$unsorted)) (tptp.product X tptp.identity X)) (tptp.product tptp.b tptp.identity tptp.b))) :rule resolution :premises (t109 t110))
% 51.65/51.91  (step t112 (cl (=> (forall ((X $$unsorted)) (tptp.product X tptp.identity X)) (tptp.product tptp.b tptp.identity tptp.b))) :rule contraction :premises (t111))
% 51.65/51.91  (step t113 (cl (not (forall ((X $$unsorted)) (tptp.product X tptp.identity X))) (tptp.product tptp.b tptp.identity tptp.b)) :rule implies :premises (t112))
% 51.65/51.91  (step t114 (cl (tptp.product tptp.b tptp.identity tptp.b)) :rule resolution :premises (t113 a1))
% 51.65/51.91  (step t115 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) (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)
% 51.65/51.91  (anchor :step t116)
% 51.65/51.91  (assume t116.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))))
% 51.65/51.91  (step t116.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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b)))) :rule forall_inst :args ((:= X tptp.b) (:= Y (tptp.inverse tptp.a)) (:= U tptp.c) (:= Z tptp.a) (:= V tptp.identity) (:= W tptp.b)))
% 51.65/51.91  (step t116.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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) :rule or :premises (t116.t1))
% 51.65/51.91  (step t116.t3 (cl (or (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) :rule resolution :premises (t116.t2 t116.a0))
% 51.65/51.91  (step t116 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) :rule subproof :discharge (t116.a0))
% 51.65/51.91  (step t117 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) (or (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) :rule resolution :premises (t115 t116))
% 51.65/51.91  (step t118 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) (not (or (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b)))) :rule implies_neg2)
% 51.65/51.91  (step t119 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) (=> (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b)))) :rule resolution :premises (t117 t118))
% 51.65/51.91  (step t120 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b)))) :rule contraction :premises (t119))
% 51.65/51.91  (step t121 (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.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) :rule implies :premises (t120))
% 51.65/51.91  (step t122 (cl (or (not (tptp.product tptp.b (tptp.inverse tptp.a) tptp.c)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.b tptp.identity tptp.b)) (tptp.product tptp.c tptp.a tptp.b))) :rule resolution :premises (t121 a7))
% 51.65/51.91  (step t123 (cl (tptp.product tptp.c tptp.a tptp.b)) :rule resolution :premises (t98 a14 t106 t114 t122))
% 51.65/51.91  (step t124 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t125)
% 51.65/51.91  (assume t125.a0 (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)))
% 51.65/51.91  (step t125.t1 (cl (or (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity))) :rule forall_inst :args ((:= X tptp.c)))
% 51.65/51.91  (step t125.t2 (cl (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) :rule or :premises (t125.t1))
% 51.65/51.91  (step t125.t3 (cl (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) :rule resolution :premises (t125.t2 t125.a0))
% 51.65/51.91  (step t125 (cl (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) :rule subproof :discharge (t125.a0))
% 51.65/51.91  (step t126 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) :rule resolution :premises (t124 t125))
% 51.65/51.91  (step t127 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity))) :rule implies_neg2)
% 51.65/51.91  (step t128 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity))) :rule resolution :premises (t126 t127))
% 51.65/51.91  (step t129 (cl (=> (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity)) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity))) :rule contraction :premises (t128))
% 51.65/51.91  (step t130 (cl (not (forall ((X $$unsorted)) (tptp.product (tptp.inverse X) X tptp.identity))) (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) :rule implies :premises (t129))
% 51.65/51.91  (step t131 (cl (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) :rule resolution :premises (t130 a2))
% 51.65/51.91  (step t132 (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 U Z W)) (tptp.product X V W))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) (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)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t133)
% 51.65/51.91  (assume t133.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 U Z W)) (tptp.product X V W))))
% 51.65/51.91  (step t133.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 U Z W)) (tptp.product X V W)))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)))) :rule forall_inst :args ((:= X (tptp.inverse tptp.c)) (:= Y tptp.c) (:= U tptp.identity) (:= Z tptp.a) (:= V tptp.b) (:= W tptp.a)))
% 51.65/51.91  (step t133.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 U Z W)) (tptp.product X V W)))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) :rule or :premises (t133.t1))
% 51.65/51.91  (step t133.t3 (cl (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) :rule resolution :premises (t133.t2 t133.a0))
% 51.65/51.91  (step t133 (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 U Z W)) (tptp.product X V W)))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) :rule subproof :discharge (t133.a0))
% 51.65/51.91  (step t134 (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 U Z W)) (tptp.product X V W))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) :rule resolution :premises (t132 t133))
% 51.65/51.91  (step t135 (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 U Z W)) (tptp.product X V W))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) (not (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)))) :rule implies_neg2)
% 51.65/51.91  (step t136 (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 U Z W)) (tptp.product X V W))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) (=> (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))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)))) :rule resolution :premises (t134 t135))
% 51.65/51.91  (step t137 (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 U Z W)) (tptp.product X V W))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)))) :rule contraction :premises (t136))
% 51.65/51.91  (step t138 (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 U Z W)) (tptp.product X V W)))) (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) :rule implies :premises (t137))
% 51.65/51.91  (step t139 (cl (or (not (tptp.product (tptp.inverse tptp.c) tptp.c tptp.identity)) (not (tptp.product tptp.c tptp.a tptp.b)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a))) :rule resolution :premises (t138 a6))
% 51.65/51.91  (step t140 (cl (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) :rule resolution :premises (t88 t96 t123 t131 t139))
% 51.65/51.91  (step t141 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t142)
% 51.65/51.91  (assume t142.a0 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))))
% 51.65/51.91  (step t142.t1 (cl (or (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a)))) :rule forall_inst :args ((:= A (tptp.inverse tptp.c)) (:= B tptp.b) (:= C tptp.a)))
% 51.65/51.91  (step t142.t2 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) :rule or :premises (t142.t1))
% 51.65/51.91  (step t142.t3 (cl (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) :rule resolution :premises (t142.t2 t142.a0))
% 51.65/51.91  (step t142 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) :rule subproof :discharge (t142.a0))
% 51.65/51.91  (step t143 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) :rule resolution :premises (t141 t142))
% 51.65/51.91  (step t144 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) (not (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a)))) :rule implies_neg2)
% 51.65/51.91  (step t145 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a)))) :rule resolution :premises (t143 t144))
% 51.65/51.91  (step t146 (cl (=> (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a)))) :rule contraction :premises (t145))
% 51.65/51.91  (step t147 (cl (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (or (not (tptp.subgroup_member A)) (not (tptp.subgroup_member B)) (not (tptp.product A B C)) (tptp.subgroup_member C)))) (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) :rule implies :premises (t146))
% 51.65/51.91  (step t148 (cl (or (not (tptp.subgroup_member (tptp.inverse tptp.c))) (not (tptp.subgroup_member tptp.b)) (not (tptp.product (tptp.inverse tptp.c) tptp.b tptp.a)) (tptp.subgroup_member tptp.a))) :rule resolution :premises (t147 a9))
% 51.65/51.91  (step t149 (cl (not (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule resolution :premises (t56 a13 t86 t140 t148))
% 51.65/51.91  (step t150 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) :rule implies_neg1)
% 51.65/51.91  (anchor :step t151)
% 51.65/51.91  (assume t151.a0 (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))))
% 51.65/51.91  (step t151.t1 (cl (or (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c))))) :rule forall_inst :args ((:= X tptp.c)))
% 51.65/51.91  (step t151.t2 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule or :premises (t151.t1))
% 51.65/51.91  (step t151.t3 (cl (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule resolution :premises (t151.t2 t151.a0))
% 51.65/51.91  (step t151 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule subproof :discharge (t151.a0))
% 51.65/51.91  (step t152 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule resolution :premises (t150 t151))
% 51.65/51.91  (step t153 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) (not (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c))))) :rule implies_neg2)
% 51.65/51.91  (step t154 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c))))) :rule resolution :premises (t152 t153))
% 51.65/51.91  (step t155 (cl (=> (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X)))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c))))) :rule contraction :premises (t154))
% 51.65/51.91  (step t156 (cl (not (forall ((X $$unsorted)) (or (not (tptp.subgroup_member X)) (tptp.subgroup_member (tptp.inverse X))))) (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule implies :premises (t155))
% 51.65/51.91  (step t157 (cl (or (not (tptp.subgroup_member tptp.c)) (tptp.subgroup_member (tptp.inverse tptp.c)))) :rule resolution :premises (t156 a8))
% 51.65/51.91  (step t158 (cl (not (tptp.subgroup_member tptp.c))) :rule resolution :premises (t54 t149 t157))
% 51.65/51.91  (step t159 (cl (not (tptp.subgroup_member (tptp.inverse tptp.a)))) :rule resolution :premises (t52 a13 a14 t158 t64))
% 51.65/51.91  (step t160 (cl) :rule resolution :premises (t50 t159 t158))
% 51.65/51.91  
% 51.65/51.91  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.NRVGJjnBoj/cvc5---1.0.5_22735.smt2
% 51.65/51.92  % cvc5---1.0.5 exiting
% 51.65/51.92  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------