TSTP Solution File: COM023+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : COM023+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 29 16:38:26 EDT 2024
% Result : Theorem 0.21s 0.54s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : COM023+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 02:26:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.54 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.nEZb3WcVX9/cvc5---1.0.5_22092.smt2
% 0.21/0.54 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.nEZb3WcVX9/cvc5---1.0.5_22092.smt2
% 0.21/0.54 (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)))
% 0.21/0.54 (assume a1 (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) true)))
% 0.21/0.54 (assume a2 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aReductOfIn0 W2 W0 W1) (tptp.aElement0 W2))))))
% 0.21/0.54 (assume a3 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (tptp.iLess0 W0 W1) true))))
% 0.21/0.54 (assume a4 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2)) (=> (tptp.sdtmndtplgtdt0 W0 W1 W2) true))))
% 0.21/0.54 (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2)) (= (tptp.sdtmndtplgtdt0 W0 W1 W2) (or (tptp.aReductOfIn0 W2 W0 W1) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.aReductOfIn0 W3 W0 W1) (tptp.sdtmndtplgtdt0 W3 W1 W2))))))))
% 0.21/0.54 (assume a6 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3)) (=> (and (tptp.sdtmndtplgtdt0 W0 W1 W2) (tptp.sdtmndtplgtdt0 W2 W1 W3)) (tptp.sdtmndtplgtdt0 W0 W1 W3)))))
% 0.21/0.54 (assume a7 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2)) (= (tptp.sdtmndtasgtdt0 W0 W1 W2) (or (= W0 W2) (tptp.sdtmndtplgtdt0 W0 W1 W2))))))
% 0.21/0.54 (assume a8 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3)) (=> (and (tptp.sdtmndtasgtdt0 W0 W1 W2) (tptp.sdtmndtasgtdt0 W2 W1 W3)) (tptp.sdtmndtasgtdt0 W0 W1 W3)))))
% 0.21/0.54 (assume a9 (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))
% 0.21/0.54 (assume a10 (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isLocallyConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.aReductOfIn0 W2 W1 W0) (tptp.aReductOfIn0 W3 W1 W0)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))
% 0.21/0.54 (assume a11 (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isTerminating0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2)) (=> (tptp.sdtmndtplgtdt0 W1 W0 W2) (tptp.iLess0 W2 W1))))))))
% 0.21/0.54 (assume a12 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aRewritingSystem0 W1)) (forall ((W2 $$unsorted)) (= (tptp.aNormalFormOfIn0 W2 W0 W1) (and (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 W1 W2) (not (exists ((W3 $$unsorted)) (tptp.aReductOfIn0 W3 W2 W1)))))))))
% 0.21/0.54 (assume a13 (forall ((W0 $$unsorted)) (=> (and (tptp.aRewritingSystem0 W0) (tptp.isTerminating0 W0)) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (exists ((W2 $$unsorted)) (tptp.aNormalFormOfIn0 W2 W1 W0)))))))
% 0.21/0.54 (assume a14 (tptp.aRewritingSystem0 tptp.xR))
% 0.21/0.54 (assume a15 (and (tptp.isLocallyConfluent0 tptp.xR) (tptp.isTerminating0 tptp.xR)))
% 0.21/0.54 (assume a16 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))
% 0.21/0.54 (assume a17 (not (tptp.isConfluent0 tptp.xR)))
% 0.21/0.54 (assume a18 true)
% 0.21/0.54 (step t1 (cl (not (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))) :rule or_pos)
% 0.21/0.54 (step t2 (cl (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))) (not (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))))) :rule reordering :premises (t1))
% 0.21/0.54 (step t3 (cl (not (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))) (tptp.isConfluent0 tptp.xR) (not (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))) :rule equiv_pos1)
% 0.21/0.54 (step t4 (cl (tptp.isConfluent0 tptp.xR) (not (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))) (not (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule reordering :premises (t3))
% 0.21/0.54 (step t5 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))) :rule hole :args ((forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))) (= W0 W1) (= W1 W2) (= W2 W3) (= W3 W4)))
% 0.21/0.54 (step t6 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))))) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))) :rule equiv1 :premises (t5))
% 0.21/0.54 (step t7 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))))) :rule equiv_pos2)
% 0.21/0.54 (anchor :step t8 :args ((W0 $$unsorted) (:= W0 W0) (W1 $$unsorted) (:= W1 W1) (W2 $$unsorted) (:= W2 W2)))
% 0.21/0.54 (step t8.t1 (cl (= W0 W0)) :rule refl)
% 0.21/0.54 (step t8.t2 (cl (= W1 W1)) :rule refl)
% 0.21/0.54 (step t8.t3 (cl (= W2 W2)) :rule refl)
% 0.21/0.54 (step t8.t4 (cl (= (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)))) :rule refl)
% 0.21/0.54 (step t8.t5 (cl (= (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))) (not (forall ((W3 $$unsorted)) (not (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))) :rule all_simplify)
% 0.21/0.54 (step t8.t6 (cl (= (forall ((W3 $$unsorted)) (not (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))) (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))) :rule all_simplify)
% 0.21/0.54 (step t8.t7 (cl (= (not (forall ((W3 $$unsorted)) (not (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))) :rule cong :premises (t8.t6))
% 0.21/0.54 (step t8.t8 (cl (= (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))) :rule trans :premises (t8.t5 t8.t7))
% 0.21/0.54 (step t8.t9 (cl (= (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))))) :rule cong :premises (t8.t4 t8.t8))
% 0.21/0.54 (step t8 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))))) :rule bind)
% 0.21/0.54 (step t9 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))))) :rule all_simplify)
% 0.21/0.54 (step t10 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.sdtmndtasgtdt0 W0 tptp.xR W1) (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 tptp.xR W3) (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3))))))))) :rule trans :premises (t8 t9))
% 0.21/0.54 (step t11 (cl (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W1)) (not (tptp.sdtmndtasgtdt0 W0 tptp.xR W2)) (not (forall ((W3 $$unsorted)) (or (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W3)))))))) :rule resolution :premises (t7 t10 a16))
% 0.21/0.54 (step t12 (cl (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))) :rule resolution :premises (t6 t11))
% 0.21/0.54 (step t13 (cl (not (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule resolution :premises (t4 a17 t12))
% 0.21/0.54 (step t14 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) :rule implies_neg1)
% 0.21/0.54 (anchor :step t15)
% 0.21/0.54 (assume t15.a0 (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))))
% 0.21/0.54 (step t15.t1 (cl (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))))) :rule forall_inst :args ((:= W0 tptp.xR)))
% 0.21/0.54 (step t15.t2 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule or :premises (t15.t1))
% 0.21/0.54 (step t15.t3 (cl (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule resolution :premises (t15.t2 t15.a0))
% 0.21/0.54 (step t15 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule subproof :discharge (t15.a0))
% 0.21/0.54 (step t16 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule resolution :premises (t14 t15))
% 0.21/0.54 (step t17 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) (not (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))))) :rule implies_neg2)
% 0.21/0.54 (step t18 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) (=> (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))))) :rule resolution :premises (t16 t17))
% 0.21/0.54 (step t19 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4))))))))))) :rule contraction :premises (t18))
% 0.21/0.54 (step t20 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule implies :premises (t19))
% 0.21/0.54 (step t21 (cl (not (= (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))))) (not (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) :rule equiv_pos2)
% 0.21/0.54 (anchor :step t22 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.21/0.54 (step t22.t1 (cl (= W0 W0)) :rule refl)
% 0.21/0.54 (step t22.t2 (cl (= (tptp.aRewritingSystem0 W0) (tptp.aRewritingSystem0 W0))) :rule refl)
% 0.21/0.54 (step t22.t3 (cl (= (tptp.isConfluent0 W0) (tptp.isConfluent0 W0))) :rule refl)
% 0.21/0.54 (anchor :step t22.t4 :args ((W1 $$unsorted) (:= W1 W1) (W2 $$unsorted) (:= W2 W2) (W3 $$unsorted) (:= W3 W3)))
% 0.21/0.54 (step t22.t4.t1 (cl (= W1 W1)) :rule refl)
% 0.21/0.54 (step t22.t4.t2 (cl (= W2 W2)) :rule refl)
% 0.21/0.54 (step t22.t4.t3 (cl (= W3 W3)) :rule refl)
% 0.21/0.54 (step t22.t4.t4 (cl (= (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)))) :rule refl)
% 0.21/0.54 (step t22.t4.t5 (cl (= (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))) (not (forall ((W4 $$unsorted)) (not (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))))))) :rule all_simplify)
% 0.21/0.54 (step t22.t4.t6 (cl (= (forall ((W4 $$unsorted)) (not (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))) (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))) :rule all_simplify)
% 0.21/0.54 (step t22.t4.t7 (cl (= (not (forall ((W4 $$unsorted)) (not (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))))) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))) :rule cong :premises (t22.t4.t6))
% 0.21/0.54 (step t22.t4.t8 (cl (= (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))) :rule trans :premises (t22.t4.t5 t22.t4.t7))
% 0.21/0.54 (step t22.t4.t9 (cl (= (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))) :rule cong :premises (t22.t4.t4 t22.t4.t8))
% 0.21/0.54 (step t22.t4 (cl (= (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))))) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))) :rule bind)
% 0.21/0.54 (step t22.t5 (cl (= (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))) :rule all_simplify)
% 0.21/0.54 (step t22.t6 (cl (= (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))))) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))) :rule trans :premises (t22.t4 t22.t5))
% 0.21/0.54 (step t22.t7 (cl (= (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) :rule cong :premises (t22.t3 t22.t6))
% 0.21/0.54 (step t22.t8 (cl (= (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4))))))) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) :rule cong :premises (t22.t2 t22.t7))
% 0.21/0.54 (step t22 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))) (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))))) :rule bind)
% 0.21/0.54 (step t23 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))))) :rule all_simplify)
% 0.21/0.54 (step t24 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aRewritingSystem0 W0) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W1) (tptp.aElement0 W2) (tptp.aElement0 W3) (tptp.sdtmndtasgtdt0 W1 W0 W2) (tptp.sdtmndtasgtdt0 W1 W0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdtmndtasgtdt0 W2 W0 W4) (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4)))))))))))) :rule trans :premises (t22 t23))
% 0.21/0.54 (step t25 (cl (forall ((W0 $$unsorted)) (or (not (tptp.aRewritingSystem0 W0)) (= (tptp.isConfluent0 W0) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 W0 W2)) (not (tptp.sdtmndtasgtdt0 W1 W0 W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 W0 W4)) (not (tptp.sdtmndtasgtdt0 W3 W0 W4))))))))))) :rule resolution :premises (t21 t24 a9))
% 0.21/0.54 (step t26 (cl (or (not (tptp.aRewritingSystem0 tptp.xR)) (= (tptp.isConfluent0 tptp.xR) (forall ((W1 $$unsorted) (W2 $$unsorted) (W3 $$unsorted)) (or (not (tptp.aElement0 W1)) (not (tptp.aElement0 W2)) (not (tptp.aElement0 W3)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W2)) (not (tptp.sdtmndtasgtdt0 W1 tptp.xR W3)) (not (forall ((W4 $$unsorted)) (or (not (tptp.aElement0 W4)) (not (tptp.sdtmndtasgtdt0 W2 tptp.xR W4)) (not (tptp.sdtmndtasgtdt0 W3 tptp.xR W4)))))))))) :rule resolution :premises (t20 t25))
% 0.21/0.54 (step t27 (cl) :rule resolution :premises (t2 t13 t26 a14))
% 0.21/0.54
% 0.21/0.54 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.nEZb3WcVX9/cvc5---1.0.5_22092.smt2
% 0.21/0.54 % cvc5---1.0.5 exiting
% 0.21/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------