TSTP Solution File: GRP030-1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : GRP030-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n003.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 16:50:30 EDT 2024
% Result : Unsatisfiable 0.22s 0.57s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.14 % Problem : GRP030-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n003.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 19:43:54 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.22/0.52 %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.53 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/tmp/tmp.6YyrcXJDB5/cvc5---1.0.5_6146.smt2
% 0.22/0.57 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.6YyrcXJDB5/cvc5---1.0.5_6146.smt2
% 0.40/0.58 (assume a0 (forall ((X $$unsorted) (Y $$unsorted)) (tptp.product X Y (tptp.multiply X Y))))
% 0.40/0.58 (assume a1 (forall ((X $$unsorted) (Y $$unsorted) (Z $$unsorted) (W $$unsorted)) (or (not (tptp.product X Y Z)) (not (tptp.product X Y W)) (= Z W))))
% 0.40/0.58 (assume a2 (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))))
% 0.40/0.58 (assume a3 (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))))
% 0.40/0.58 (assume a4 (forall ((A $$unsorted)) (tptp.product tptp.identity A A)))
% 0.40/0.58 (assume a5 (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)))
% 0.40/0.58 (assume a6 (not (tptp.product tptp.a tptp.identity tptp.a)))
% 0.40/0.58 (step t1 (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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity 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 X V W)) (tptp.product U Z W)))) :rule implies_neg1)
% 0.40/0.58 (anchor :step t2)
% 0.40/0.58 (assume t2.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))))
% 0.40/0.58 (step t2.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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y tptp.identity) (:= U tptp.a) (:= Z tptp.identity) (:= V tptp.identity) (:= W tptp.a)))
% 0.40/0.58 (step t2.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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) :rule or :premises (t2.t1))
% 0.40/0.58 (step t2.t3 (cl (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) :rule resolution :premises (t2.t2 t2.a0))
% 0.40/0.58 (step 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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) :rule subproof :discharge (t2.a0))
% 0.40/0.58 (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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) :rule resolution :premises (t1 t2))
% 0.40/0.58 (step t4 (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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)))) :rule implies_neg2)
% 0.40/0.58 (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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity 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 X V W)) (tptp.product U Z W))) (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)))) :rule resolution :premises (t3 t4))
% 0.40/0.58 (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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)))) :rule contraction :premises (t5))
% 0.40/0.58 (step t7 (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.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) :rule implies :premises (t6))
% 0.40/0.58 (step t8 (cl (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)) :rule or_pos)
% 0.40/0.58 (step t9 (cl (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a))) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (tptp.product tptp.a tptp.identity tptp.a)) :rule contraction :premises (t8))
% 0.40/0.58 (step t10 (cl (tptp.product tptp.a tptp.identity tptp.a) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)))) :rule reordering :premises (t9))
% 0.40/0.58 (step t11 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.identity tptp.identity)) (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) :rule implies_neg1)
% 0.40/0.58 (anchor :step t12)
% 0.40/0.58 (assume t12.a0 (forall ((A $$unsorted)) (tptp.product tptp.identity A A)))
% 0.40/0.58 (step t12.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.identity tptp.identity))) :rule forall_inst :args ((:= A tptp.identity)))
% 0.40/0.58 (step t12.t2 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.identity tptp.identity)) :rule or :premises (t12.t1))
% 0.40/0.58 (step t12.t3 (cl (tptp.product tptp.identity tptp.identity tptp.identity)) :rule resolution :premises (t12.t2 t12.a0))
% 0.40/0.58 (step t12 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.identity tptp.identity)) :rule subproof :discharge (t12.a0))
% 0.40/0.58 (step t13 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.identity tptp.identity)) (tptp.product tptp.identity tptp.identity tptp.identity)) :rule resolution :premises (t11 t12))
% 0.40/0.58 (step t14 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product tptp.identity tptp.identity tptp.identity))) :rule implies_neg2)
% 0.40/0.58 (step t15 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.identity tptp.identity)) (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.identity tptp.identity))) :rule resolution :premises (t13 t14))
% 0.40/0.58 (step t16 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.identity tptp.identity))) :rule contraction :premises (t15))
% 0.40/0.58 (step t17 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.identity tptp.identity)) :rule implies :premises (t16))
% 0.40/0.58 (step t18 (cl (tptp.product tptp.identity tptp.identity tptp.identity)) :rule resolution :premises (t17 a4))
% 0.40/0.58 (step t19 (cl (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) :rule or_pos)
% 0.40/0.58 (step t20 (cl (not (tptp.product tptp.identity tptp.a tptp.a)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a) (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)))) :rule reordering :premises (t19))
% 0.40/0.58 (step t21 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.a tptp.a)) (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) :rule implies_neg1)
% 0.40/0.58 (anchor :step t22)
% 0.40/0.58 (assume t22.a0 (forall ((A $$unsorted)) (tptp.product tptp.identity A A)))
% 0.40/0.58 (step t22.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.a tptp.a))) :rule forall_inst :args ((:= A tptp.a)))
% 0.40/0.58 (step t22.t2 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.a tptp.a)) :rule or :premises (t22.t1))
% 0.40/0.58 (step t22.t3 (cl (tptp.product tptp.identity tptp.a tptp.a)) :rule resolution :premises (t22.t2 t22.a0))
% 0.40/0.58 (step t22 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.a tptp.a)) :rule subproof :discharge (t22.a0))
% 0.40/0.58 (step t23 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product tptp.identity tptp.a tptp.a)) :rule resolution :premises (t21 t22))
% 0.40/0.58 (step t24 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.a tptp.a)) (not (tptp.product tptp.identity tptp.a tptp.a))) :rule implies_neg2)
% 0.40/0.58 (step t25 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.a tptp.a)) (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.a tptp.a))) :rule resolution :premises (t23 t24))
% 0.40/0.58 (step t26 (cl (=> (forall ((A $$unsorted)) (tptp.product tptp.identity A A)) (tptp.product tptp.identity tptp.a tptp.a))) :rule contraction :premises (t25))
% 0.40/0.58 (step t27 (cl (not (forall ((A $$unsorted)) (tptp.product tptp.identity A A))) (tptp.product tptp.identity tptp.a tptp.a)) :rule implies :premises (t26))
% 0.40/0.58 (step t28 (cl (tptp.product tptp.identity tptp.a tptp.a)) :rule resolution :premises (t27 a4))
% 0.40/0.58 (step t29 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) :rule implies_neg1)
% 0.40/0.58 (anchor :step t30)
% 0.40/0.58 (assume t30.a0 (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)))
% 0.40/0.58 (step t30.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule forall_inst :args ((:= A tptp.a)))
% 0.40/0.58 (step t30.t2 (cl (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule or :premises (t30.t1))
% 0.40/0.58 (step t30.t3 (cl (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule resolution :premises (t30.t2 t30.a0))
% 0.40/0.58 (step t30 (cl (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule subproof :discharge (t30.a0))
% 0.40/0.58 (step t31 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule resolution :premises (t29 t30))
% 0.40/0.58 (step t32 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A 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)
% 0.40/0.58 (step t33 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule resolution :premises (t31 t32))
% 0.40/0.58 (step t34 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity))) :rule contraction :premises (t33))
% 0.40/0.58 (step t35 (cl (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule implies :premises (t34))
% 0.40/0.58 (step t36 (cl (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) :rule resolution :premises (t35 a5))
% 0.40/0.58 (step t37 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) :rule implies_neg1)
% 0.40/0.58 (anchor :step t38)
% 0.40/0.58 (assume t38.a0 (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)))
% 0.40/0.58 (step t38.t1 (cl (or (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity))) :rule forall_inst :args ((:= A (tptp.inverse tptp.a))))
% 0.40/0.58 (step t38.t2 (cl (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) :rule or :premises (t38.t1))
% 0.40/0.58 (step t38.t3 (cl (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) :rule resolution :premises (t38.t2 t38.a0))
% 0.40/0.58 (step t38 (cl (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) :rule subproof :discharge (t38.a0))
% 0.40/0.58 (step t39 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) :rule resolution :premises (t37 t38))
% 0.40/0.58 (step t40 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity))) :rule implies_neg2)
% 0.40/0.58 (step t41 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity))) :rule resolution :premises (t39 t40))
% 0.40/0.58 (step t42 (cl (=> (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity))) :rule contraction :premises (t41))
% 0.40/0.58 (step t43 (cl (not (forall ((A $$unsorted)) (tptp.product (tptp.inverse A) A tptp.identity))) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) :rule implies :premises (t42))
% 0.40/0.58 (step t44 (cl (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) :rule resolution :premises (t43 a5))
% 0.40/0.58 (step t45 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity 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)
% 0.40/0.58 (anchor :step t46)
% 0.40/0.58 (assume t46.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))))
% 0.40/0.58 (step t46.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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)))) :rule forall_inst :args ((:= X (tptp.inverse (tptp.inverse tptp.a))) (:= Y (tptp.inverse tptp.a)) (:= U tptp.identity) (:= Z tptp.a) (:= V tptp.identity) (:= W tptp.a)))
% 0.40/0.58 (step t46.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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) :rule or :premises (t46.t1))
% 0.40/0.58 (step t46.t3 (cl (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) :rule resolution :premises (t46.t2 t46.a0))
% 0.40/0.58 (step t46 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) :rule subproof :discharge (t46.a0))
% 0.40/0.58 (step t47 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) :rule resolution :premises (t45 t46))
% 0.40/0.58 (step t48 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)))) :rule implies_neg2)
% 0.40/0.58 (step t49 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity 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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)))) :rule resolution :premises (t47 t48))
% 0.40/0.58 (step t50 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)))) :rule contraction :premises (t49))
% 0.40/0.58 (step t51 (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.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) :rule implies :premises (t50))
% 0.40/0.58 (step t52 (cl (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) (tptp.inverse tptp.a) tptp.identity)) (not (tptp.product (tptp.inverse tptp.a) tptp.a tptp.identity)) (not (tptp.product tptp.identity tptp.a tptp.a)) (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a))) :rule resolution :premises (t51 a2))
% 0.40/0.58 (step t53 (cl (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) :rule resolution :premises (t20 t28 t36 t44 t52))
% 0.40/0.58 (step t54 (cl (not (or (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (not (tptp.product tptp.identity tptp.identity tptp.identity)) (not (tptp.product (tptp.inverse (tptp.inverse tptp.a)) tptp.identity tptp.a)) (tptp.product tptp.a tptp.identity tptp.a)))) :rule resolution :premises (t10 a6 t18 t53))
% 0.40/0.58 (step t55 (cl) :rule resolution :premises (t7 t54 a3))
% 0.40/0.58
% 0.40/0.58 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.6YyrcXJDB5/cvc5---1.0.5_6146.smt2
% 0.40/0.58 % cvc5---1.0.5 exiting
% 0.40/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------