%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO893^11 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n027.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 Jun 3 09:13:43 AM UTC 2026 % Result : Theorem 0.35s 0.58s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO893^11 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n027.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 01:09:06 EDT 2026 % 0.16/0.34 % CPUTime : % 0.25/0.50 %----Proving TH0 % 0.35/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.35/0.58 % SZS status Theorem % 0.35/0.58 % SZS output start Proof % 0.35/0.58 ( % 0.35/0.58 (declare-sort tptp.mworld 0) % 0.35/0.58 (declare-const tptp.mactual tptp.mworld) % 0.35/0.58 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.35/0.58 (declare-const tptp.p (-> tptp.mworld Bool)) % 0.35/0.58 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.35/0.58 (define tptp.mnot () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.35/0.58 (define tptp.mand () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.58 (define tptp.mor () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.58 (define tptp.mimplies () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.58 (define tptp.mequiv () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "B" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "A" (-> tptp.mworld Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.35/0.58 (define tptp.mbox () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.35/0.58 (define tptp.mdia () (let ((_let_1 (@var "V" tptp.mworld))) (let ((_let_2 (@var "Phi" (-> tptp.mworld Bool)))) (let ((_let_3 (@var "W" tptp.mworld))) (lambda (@list _let_2 _let_3) (exists (@list _let_1) (and (_ (_ tptp.mrel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.35/0.58 (define @t1 () (@var "W" tptp.mworld)) % 0.35/0.58 (define @t2 () (_ tptp.mrel @t1)) % 0.35/0.58 (define @t3 () (@list @t1)) % 0.35/0.58 (define @t4 () (@var "V" tptp.mworld)) % 0.35/0.58 (define @t5 () (@var "U" tptp.mworld)) % 0.35/0.58 (define @t6 () (_ @t2 @t4)) % 0.35/0.58 (define @t7 () (not (_ tptp.mlocal (_ (_ tptp.mequiv (_ tptp.mnot (_ tptp.mbox (_ tptp.mdia (_ tptp.mbox tptp.p))))) (_ tptp.mdia (_ tptp.mbox (_ tptp.mdia (_ tptp.mnot tptp.p)))))))) % 0.35/0.58 (define @t8 () (@var "Phi" (-> tptp.mworld Bool))) % 0.35/0.58 (define @t9 () (lambda (@list @t8) (_ @t8 tptp.mactual))) % 0.35/0.58 (define @t10 () (@var "A" (-> tptp.mworld Bool))) % 0.35/0.58 (define @t11 () (_ @t10 @t1)) % 0.35/0.58 (define @t12 () (lambda (@list @t10 @t1) (not @t11))) % 0.35/0.58 (define @t13 () (@var "B" (-> tptp.mworld Bool))) % 0.35/0.58 (define @t14 () (_ @t13 @t1)) % 0.35/0.58 (define @t15 () (@list @t10 @t13 @t1)) % 0.35/0.58 (define @t16 () (lambda @t15 (and @t11 @t14))) % 0.35/0.58 (define @t17 () (lambda @t15 (or @t11 @t14))) % 0.35/0.58 (define @t18 () (lambda @t15 (=> @t11 @t14))) % 0.35/0.58 (define @t19 () (lambda @t15 (= @t11 @t14))) % 0.35/0.58 (define @t20 () (_ @t8 @t4)) % 0.35/0.58 (define @t21 () (@list @t4)) % 0.35/0.58 (define @t22 () (forall @t21 (=> @t6 @t20))) % 0.35/0.58 (define @t23 () (@list @t8 @t1)) % 0.35/0.58 (define @t24 () (lambda @t23 @t22)) % 0.35/0.58 (define @t25 () (and @t6 @t20)) % 0.35/0.58 (define @t26 () (exists @t21 @t25)) % 0.35/0.58 (define @t27 () (lambda @t23 @t26)) % 0.35/0.58 (define @t28 () (@var "BOUND_VARIABLE_7780" tptp.mworld)) % 0.35/0.58 (define @t29 () (@var "BOUND_VARIABLE_7779" tptp.mworld)) % 0.35/0.58 (define @t30 () (@var "BOUND_VARIABLE_7778" tptp.mworld)) % 0.35/0.58 (define @t31 () (@list @t30 @t29 @t28)) % 0.35/0.58 (define @t32 () (@var "BOUND_VARIABLE_7669" tptp.mworld)) % 0.35/0.58 (define @t33 () (@var "BOUND_VARIABLE_7695" tptp.mworld)) % 0.35/0.58 (define @t34 () (@var "BOUND_VARIABLE_7585" tptp.mworld)) % 0.35/0.58 (define @t35 () (tptp.p @t34)) % 0.35/0.58 (define @t36 () (@var "BOUND_VARIABLE_7609" tptp.mworld)) % 0.35/0.58 (define @t37 () (@list @t34)) % 0.35/0.58 (define @t38 () (not (forall @t37 (or (not (tptp.mrel @t36 @t34)) @t35)))) % 0.35/0.58 (define @t39 () (@list @t36)) % 0.35/0.58 (define @t40 () (not (forall @t39 (or (not (tptp.mrel @t4 @t36)) @t38)))) % 0.35/0.58 (define @t41 () (not (tptp.mrel tptp.mactual @t4))) % 0.35/0.58 (define @t42 () (forall @t21 (or @t41 @t40))) % 0.35/0.58 (define @t43 () (tptp.p @t32)) % 0.35/0.58 (define @t44 () (@list @t32)) % 0.35/0.58 (define @t45 () (not (forall @t44 (or (not (tptp.mrel @t33 @t32)) @t43)))) % 0.35/0.58 (define @t46 () (@list @t33)) % 0.35/0.58 (define @t47 () (forall @t46 (or (not (tptp.mrel @t4 @t33)) @t45))) % 0.35/0.58 (define @t48 () (not @t47)) % 0.35/0.58 (define @t49 () (forall @t21 (or @t41 @t48))) % 0.35/0.58 (define @t50 () (not @t49)) % 0.35/0.58 (define @t51 () (not @t42)) % 0.35/0.58 (define @t52 () (tptp.mrel @t1 @t4)) % 0.35/0.58 (define @t53 () (not @t52)) % 0.35/0.58 (define @t54 () (not (forall @t21 (or @t53 @t48)))) % 0.35/0.58 (define @t55 () (forall @t21 (or @t53 @t40))) % 0.35/0.58 (define @t56 () (not @t55)) % 0.35/0.58 (define @t57 () (lambda @t3 (= @t56 @t54))) % 0.35/0.58 (define @t58 () (_ @t57 tptp.mactual)) % 0.35/0.58 (define @t59 () (lambda @t3 @t54)) % 0.35/0.58 (define @t60 () (_ @t59 @t1)) % 0.35/0.58 (define @t61 () (lambda @t3 (= @t60 @t56))) % 0.35/0.58 (define @t62 () (@list @t13 @t1)) % 0.35/0.58 (define @t63 () (not (forall @t44 (or (not (tptp.mrel @t4 @t32)) @t43)))) % 0.35/0.58 (define @t64 () (forall @t21 (or @t53 @t63))) % 0.35/0.58 (define @t65 () (@list @t4)) % 0.35/0.58 (define @t66 () (lambda @t3 @t64)) % 0.35/0.58 (define @t67 () (not (_ @t66 @t4))) % 0.35/0.58 (define @t68 () (or @t53 @t67)) % 0.35/0.58 (define @t69 () (forall @t21 @t68)) % 0.35/0.58 (define @t70 () (not @t69)) % 0.35/0.58 (define @t71 () (lambda @t3 @t70)) % 0.35/0.58 (define @t72 () (_ @t8 @t4)) % 0.35/0.58 (define @t73 () (lambda @t23 (not (forall @t21 (or @t53 (not @t72)))))) % 0.35/0.58 (define @t74 () (tptp.p @t4)) % 0.35/0.58 (define @t75 () (forall @t21 (or @t53 @t74))) % 0.35/0.58 (define @t76 () (not @t75)) % 0.35/0.58 (define @t77 () (lambda @t3 @t76)) % 0.35/0.58 (define @t78 () (or @t53 (_ @t77 @t4))) % 0.35/0.58 (define @t79 () (forall @t21 @t78)) % 0.35/0.58 (define @t80 () (lambda @t3 @t79)) % 0.35/0.58 (define @t81 () (lambda @t23 (forall @t21 (or @t53 @t72)))) % 0.35/0.58 (define @t82 () (_ tptp.p @t4)) % 0.35/0.58 (define @t83 () (or @t53 @t82)) % 0.35/0.58 (define @t84 () (lambda @t3 (not (_ tptp.p @t1)))) % 0.35/0.58 (define @t85 () (_ @t84 @t4)) % 0.35/0.58 (define @t86 () (not @t85)) % 0.35/0.58 (define @t87 () (or @t53 @t86)) % 0.35/0.58 (define @t88 () (forall @t21 @t87)) % 0.35/0.58 (define @t89 () (not @t88)) % 0.35/0.58 (define @t90 () (lambda @t3 @t89)) % 0.35/0.58 (define @t91 () (_ @t12 tptp.p)) % 0.35/0.58 (define @t92 () (lambda @t3 @t56)) % 0.35/0.58 (define @t93 () (_ @t92 @t1)) % 0.35/0.58 (define @t94 () (lambda @t62 (= @t93 @t14))) % 0.35/0.58 (define @t95 () (lambda @t3 @t55)) % 0.35/0.58 (define @t96 () (_ @t95 @t1)) % 0.35/0.58 (define @t97 () (not @t96)) % 0.35/0.58 (define @t98 () (lambda @t3 @t97)) % 0.35/0.58 (define @t99 () (forall @t37 (or (not (tptp.mrel @t4 @t34)) @t35))) % 0.35/0.58 (define @t100 () (forall @t21 (or @t53 (not @t99)))) % 0.35/0.58 (define @t101 () (not @t100)) % 0.35/0.58 (define @t102 () (lambda @t3 @t101)) % 0.35/0.58 (define @t103 () (or @t53 (_ @t102 @t4))) % 0.35/0.58 (define @t104 () (forall @t21 @t103)) % 0.35/0.58 (define @t105 () (lambda @t3 @t104)) % 0.35/0.58 (define @t106 () (lambda @t3 @t75)) % 0.35/0.58 (define @t107 () (not (_ @t106 @t4))) % 0.35/0.58 (define @t108 () (or @t53 @t107)) % 0.35/0.58 (define @t109 () (forall @t21 @t108)) % 0.35/0.58 (define @t110 () (not @t109)) % 0.35/0.58 (define @t111 () (lambda @t3 @t110)) % 0.35/0.58 (define @t112 () (_ @t81 tptp.p)) % 0.35/0.58 (define @t113 () (not @t20)) % 0.35/0.58 (define @t114 () (not @t6)) % 0.35/0.58 (define @t115 () (or @t114 @t113)) % 0.35/0.58 (define @t116 () (forall @t21 (not @t25))) % 0.35/0.58 (define @t117 () (not @t116)) % 0.35/0.58 (define @t118 () (or @t114 @t20)) % 0.35/0.58 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.35/0.58 (assume @p2 (forall (@list @t1 @t4 @t5) (=> (and (_ @t2 @t5) @t6) (_ (_ tptp.mrel @t5) @t4)))) % 0.35/0.58 (assume @p3 @t7) % 0.35/0.58 (assume @p4 true) % 0.35/0.58 (step @p5 (= tptp.mlocal @t9) :rule refl :args (@t9)) % 0.35/0.58 (step @p6 (= tptp.mnot @t12) :rule refl :args (@t12)) % 0.35/0.58 (step @p7 (= tptp.mand @t16) :rule refl :args (@t16)) % 0.35/0.58 (step @p8 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.35/0.58 (step @p9 (= tptp.mimplies @t18) :rule refl :args (@t18)) % 0.35/0.58 (step @p10 (= tptp.mequiv @t19) :rule refl :args (@t19)) % 0.35/0.58 (step @p11 (= tptp.mbox @t24) :rule refl :args (@t24)) % 0.35/0.58 (step @p12 (= tptp.mdia @t27) :rule refl :args (@t27)) % 0.35/0.58 (step @p13 :rule alpha_equiv :args ((forall (@list @t30) (or (not (tptp.mrel tptp.mactual @t30)) (not (forall (@list @t29) (or (not (tptp.mrel @t30 @t29)) (not (forall (@list @t28) (or (not (tptp.mrel @t29 @t28)) (tptp.p @t28))))))))) @t31 (@list @t4 @t33 @t32))) % 0.35/0.58 (step @p14 :rule alpha_equiv :args (@t42 (@list @t4 @t36 @t34) @t31)) % 0.35/0.58 (step @p15 :rule trans :premises (@p14 @p13)) % 0.35/0.58 (step @p16 :rule equiv_elim2 :premises (@p15)) % 0.35/0.58 (step @p17 :rule bool-double-not-elim :args (@t49)) % 0.35/0.58 (step @p18 :rule bool-double-not-elim :args (@t42)) % 0.35/0.58 (step @p19 :rule nary_cong :premises (@p18 @p17) :args ((or (not @t51) (not @t50)))) % 0.35/0.58 (step @p20 :rule beta-reduce :args ((= @t58 (= @t51 @t50)))) % 0.35/0.58 (step @p21 :rule beta-reduce :args ((= (_ @t9 @t57) @t58))) % 0.35/0.58 (step @p22 :rule trans :premises (@p21 @p20)) % 0.35/0.58 (step @p23 :rule beta-reduce :args ((= @t60 @t54))) % 0.35/0.58 (step @p24 :rule refl :args (@t56)) % 0.35/0.58 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t56 @t60))) % 0.35/0.58 (step @p26 :rule eq-symm :args (@t60 @t56)) % 0.35/0.58 (step @p27 :rule trans :premises (@p26 @p25)) % 0.35/0.58 (step @p28 :rule cong :premises (@p27) :args (@t61)) % 0.35/0.58 (step @p29 :rule beta-reduce :args ((= (_ (lambda @t62 (= @t14 @t56)) @t59) @t61))) % 0.35/0.58 (step @p30 :rule trans :premises (@p29 @p28)) % 0.35/0.58 (step @p31 :rule beta-reduce :args ((= (_ (lambda @t3 (forall @t46 (or (not (tptp.mrel @t1 @t33)) @t45))) @t4) @t47))) % 0.35/0.58 (step @p32 :rule refl :args (@t4)) % 0.35/0.58 (step @p33 :rule alpha_equiv :args (@t64 @t65 (@list @t33))) % 0.35/0.58 (step @p34 :rule cong :premises (@p33) :args (@t66)) % 0.35/0.58 (step @p35 :rule ho_cong :premises (@p34 @p32)) % 0.35/0.58 (step @p36 :rule trans :premises (@p35 @p31)) % 0.35/0.58 (step @p37 :rule cong :premises (@p36) :args (@t67)) % 0.35/0.58 (step @p38 :rule refl :args (@t53)) % 0.35/0.58 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t68)) % 0.35/0.58 (step @p40 :rule cong :premises (@p39) :args (@t69)) % 0.35/0.58 (step @p41 :rule cong :premises (@p40) :args (@t70)) % 0.35/0.58 (step @p42 :rule cong :premises (@p41) :args (@t71)) % 0.35/0.58 (step @p43 :rule beta-reduce :args ((= (_ @t73 @t66) @t71))) % 0.35/0.58 (step @p44 :rule trans :premises (@p43 @p42)) % 0.35/0.58 (step @p45 :rule beta-reduce :args ((= (_ (lambda @t3 (not (forall @t44 (or (not (tptp.mrel @t1 @t32)) @t43)))) @t4) @t63))) % 0.35/0.58 (step @p46 :rule alpha_equiv :args (@t75 @t65 (@list @t32))) % 0.35/0.58 (step @p47 :rule cong :premises (@p46) :args (@t76)) % 0.35/0.58 (step @p48 :rule cong :premises (@p47) :args (@t77)) % 0.35/0.58 (step @p49 :rule ho_cong :premises (@p48 @p32)) % 0.35/0.58 (step @p50 :rule trans :premises (@p49 @p45)) % 0.35/0.58 (step @p51 :rule nary_cong :premises (@p38 @p50) :args (@t78)) % 0.35/0.58 (step @p52 :rule cong :premises (@p51) :args (@t79)) % 0.35/0.58 (step @p53 :rule cong :premises (@p52) :args (@t80)) % 0.35/0.58 (step @p54 :rule beta-reduce :args ((= (_ @t81 @t77) @t80))) % 0.35/0.58 (step @p55 :rule trans :premises (@p54 @p53)) % 0.35/0.58 (step @p56 :rule refl :args (@t74)) % 0.35/0.58 (step @p57 :rule refl :args (@t82)) % 0.35/0.58 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t82 @t74))) % 0.35/0.58 (step @p59 :rule symm :premises (@p58)) % 0.35/0.58 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 0.35/0.58 (step @p61 :rule refl :args (@t53)) % 0.35/0.58 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t83)) % 0.35/0.58 (step @p63 :rule cong :premises (@p62) :args ((forall @t21 @t83))) % 0.35/0.58 (step @p64 :rule bool-double-not-elim :args (@t82)) % 0.35/0.58 (step @p65 :rule beta-reduce :args ((= @t85 (not @t82)))) % 0.35/0.58 (step @p66 :rule cong :premises (@p65) :args (@t86)) % 0.35/0.58 (step @p67 :rule trans :premises (@p66 @p64)) % 0.35/0.58 (step @p68 :rule nary_cong :premises (@p38 @p67) :args (@t87)) % 0.35/0.58 (step @p69 :rule cong :premises (@p68) :args (@t88)) % 0.35/0.58 (step @p70 :rule trans :premises (@p69 @p63)) % 0.35/0.58 (step @p71 :rule cong :premises (@p70) :args (@t89)) % 0.35/0.58 (step @p72 :rule cong :premises (@p71) :args (@t90)) % 0.35/0.58 (step @p73 :rule beta-reduce :args ((= (_ @t73 @t84) @t90))) % 0.35/0.58 (step @p74 :rule trans :premises (@p73 @p72)) % 0.35/0.58 (step @p75 :rule beta-reduce :args ((= @t91 @t84))) % 0.35/0.58 (step @p76 :rule refl :args (@t73)) % 0.35/0.58 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.35/0.58 (step @p78 :rule trans :premises (@p77 @p74)) % 0.35/0.58 (step @p79 :rule refl :args (@t81)) % 0.35/0.58 (step @p80 :rule ho_cong :premises (@p79 @p78)) % 0.35/0.58 (step @p81 :rule trans :premises (@p80 @p55)) % 0.35/0.58 (step @p82 :rule ho_cong :premises (@p76 @p81)) % 0.35/0.58 (step @p83 :rule trans :premises (@p82 @p44)) % 0.35/0.58 (step @p84 :rule beta-reduce :args ((= @t93 @t56))) % 0.35/0.58 (step @p85 :rule refl :args (@t14)) % 0.35/0.58 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t14 @t93))) % 0.35/0.58 (step @p87 :rule eq-symm :args (@t93 @t14)) % 0.35/0.58 (step @p88 :rule trans :premises (@p87 @p86)) % 0.35/0.58 (step @p89 :rule cong :premises (@p88) :args (@t94)) % 0.35/0.58 (step @p90 :rule beta-reduce :args ((= (_ @t19 @t92) @t94))) % 0.35/0.58 (step @p91 :rule trans :premises (@p90 @p89)) % 0.35/0.58 (step @p92 :rule beta-reduce :args ((= @t96 @t55))) % 0.35/0.58 (step @p93 :rule cong :premises (@p92) :args (@t97)) % 0.35/0.58 (step @p94 :rule cong :premises (@p93) :args (@t98)) % 0.35/0.58 (step @p95 :rule beta-reduce :args ((= (_ @t12 @t95) @t98))) % 0.35/0.58 (step @p96 :rule trans :premises (@p95 @p94)) % 0.35/0.58 (step @p97 :rule beta-reduce :args ((= (_ (lambda @t3 (not (forall @t39 (or (not (tptp.mrel @t1 @t36)) @t38)))) @t4) @t40))) % 0.35/0.58 (step @p98 :rule alpha_equiv :args (@t100 @t65 (@list @t36))) % 0.35/0.58 (step @p99 :rule cong :premises (@p98) :args (@t101)) % 0.35/0.58 (step @p100 :rule cong :premises (@p99) :args (@t102)) % 0.35/0.58 (step @p101 :rule ho_cong :premises (@p100 @p32)) % 0.35/0.58 (step @p102 :rule trans :premises (@p101 @p97)) % 0.35/0.58 (step @p103 :rule nary_cong :premises (@p38 @p102) :args (@t103)) % 0.35/0.58 (step @p104 :rule cong :premises (@p103) :args (@t104)) % 0.35/0.58 (step @p105 :rule cong :premises (@p104) :args (@t105)) % 0.35/0.58 (step @p106 :rule beta-reduce :args ((= (_ @t81 @t102) @t105))) % 0.35/0.58 (step @p107 :rule trans :premises (@p106 @p105)) % 0.35/0.58 (step @p108 :rule beta-reduce :args ((= (_ (lambda @t3 (forall @t37 (or (not (tptp.mrel @t1 @t34)) @t35))) @t4) @t99))) % 0.35/0.58 (step @p109 :rule alpha_equiv :args (@t75 @t65 (@list @t34))) % 0.35/0.58 (step @p110 :rule cong :premises (@p109) :args (@t106)) % 0.35/0.58 (step @p111 :rule ho_cong :premises (@p110 @p32)) % 0.35/0.58 (step @p112 :rule trans :premises (@p111 @p108)) % 0.35/0.58 (step @p113 :rule cong :premises (@p112) :args (@t107)) % 0.35/0.58 (step @p114 :rule nary_cong :premises (@p38 @p113) :args (@t108)) % 0.35/0.58 (step @p115 :rule cong :premises (@p114) :args (@t109)) % 0.35/0.58 (step @p116 :rule cong :premises (@p115) :args (@t110)) % 0.35/0.58 (step @p117 :rule cong :premises (@p116) :args (@t111)) % 0.35/0.58 (step @p118 :rule beta-reduce :args ((= (_ @t73 @t106) @t111))) % 0.35/0.58 (step @p119 :rule trans :premises (@p118 @p117)) % 0.35/0.58 (step @p120 :rule beta-reduce :args ((= @t112 @t106))) % 0.35/0.58 (step @p121 :rule ho_cong :premises (@p76 @p120)) % 0.35/0.58 (step @p122 :rule trans :premises (@p121 @p119)) % 0.35/0.58 (step @p123 :rule ho_cong :premises (@p79 @p122)) % 0.35/0.58 (step @p124 :rule trans :premises (@p123 @p107)) % 0.35/0.58 (step @p125 :rule refl :args (@t12)) % 0.35/0.58 (step @p126 :rule ho_cong :premises (@p125 @p124)) % 0.35/0.58 (step @p127 :rule trans :premises (@p126 @p96)) % 0.35/0.58 (step @p128 :rule refl :args (@t19)) % 0.35/0.58 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.35/0.58 (step @p130 :rule trans :premises (@p129 @p91)) % 0.35/0.58 (step @p131 :rule ho_cong :premises (@p130 @p83)) % 0.35/0.58 (step @p132 :rule trans :premises (@p131 @p30)) % 0.35/0.58 (step @p133 :rule refl :args (@t9)) % 0.35/0.58 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.35/0.58 (step @p135 :rule trans :premises (@p134 @p22)) % 0.35/0.58 (step @p136 :rule cong :premises (@p135) :args ((not (_ @t9 (_ (_ @t19 (_ @t12 (_ @t81 (_ @t73 @t112)))) (_ @t73 (_ @t81 (_ @t73 @t91)))))))) % 0.35/0.58 (step @p137 :rule refl :args (tptp.p)) % 0.35/0.58 (step @p138 :rule ho_cong :premises (@p6 @p137)) % 0.35/0.58 (step @p139 :rule refl :args (@t72)) % 0.35/0.58 (step @p140 :rule refl :args (@t20)) % 0.35/0.58 (step @p141 :rule cong :premises (@p140 @p139) :args ((= @t20 @t72))) % 0.35/0.58 (step @p142 :rule symm :premises (@p141)) % 0.35/0.58 (step @p143 :rule eq_resolve :premises (@p140 @p142)) % 0.35/0.58 (step @p144 :rule cong :premises (@p143) :args (@t113)) % 0.35/0.58 (step @p145 :rule refl :args (@t52)) % 0.35/0.58 (step @p146 :rule refl :args (@t6)) % 0.35/0.58 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t6 @t52))) % 0.35/0.58 (step @p148 :rule symm :premises (@p147)) % 0.35/0.58 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.35/0.58 (step @p150 :rule cong :premises (@p149) :args (@t114)) % 0.35/0.58 (step @p151 :rule nary_cong :premises (@p150 @p144) :args (@t115)) % 0.35/0.58 (step @p152 :rule cong :premises (@p151) :args ((forall @t21 @t115))) % 0.35/0.58 (step @p153 :rule bool-and-de-morgan :args (@t6 @t20 true)) % 0.35/0.58 (step @p154 :rule cong :premises (@p153) :args (@t116)) % 0.35/0.58 (step @p155 :rule trans :premises (@p154 @p152)) % 0.35/0.58 (step @p156 :rule cong :premises (@p155) :args (@t117)) % 0.35/0.58 (step @p157 :rule exists-elim :args ((= @t26 @t117))) % 0.35/0.58 (step @p158 :rule trans :premises (@p157 @p156)) % 0.35/0.58 (step @p159 :rule cong :premises (@p158) :args (@t27)) % 0.35/0.58 (step @p160 :rule trans :premises (@p12 @p159)) % 0.35/0.58 (step @p161 :rule ho_cong :premises (@p160 @p138)) % 0.35/0.58 (step @p162 :rule nary_cong :premises (@p150 @p143) :args (@t118)) % 0.35/0.58 (step @p163 :rule cong :premises (@p162) :args ((forall @t21 @t118))) % 0.35/0.58 (step @p164 :rule bool-impl-elim :args (@t6 @t20)) % 0.35/0.58 (step @p165 :rule cong :premises (@p164) :args (@t22)) % 0.35/0.58 (step @p166 :rule trans :premises (@p165 @p163)) % 0.35/0.58 (step @p167 :rule cong :premises (@p166) :args (@t24)) % 0.35/0.58 (step @p168 :rule trans :premises (@p11 @p167)) % 0.35/0.58 (step @p169 :rule ho_cong :premises (@p168 @p161)) % 0.35/0.58 (step @p170 :rule ho_cong :premises (@p160 @p169)) % 0.35/0.58 (step @p171 :rule ho_cong :premises (@p168 @p137)) % 0.35/0.58 (step @p172 :rule ho_cong :premises (@p160 @p171)) % 0.35/0.58 (step @p173 :rule ho_cong :premises (@p168 @p172)) % 0.35/0.58 (step @p174 :rule ho_cong :premises (@p6 @p173)) % 0.35/0.58 (step @p175 :rule ho_cong :premises (@p10 @p174)) % 0.35/0.58 (step @p176 :rule ho_cong :premises (@p175 @p170)) % 0.35/0.58 (step @p177 :rule ho_cong :premises (@p5 @p176)) % 0.35/0.58 (step @p178 :rule cong :premises (@p177) :args (@t7)) % 0.35/0.58 (step @p179 :rule trans :premises (@p178 @p136)) % 0.35/0.58 (step @p180 :rule eq_resolve :premises (@p3 @p179)) % 0.35/0.58 (step @p181 :rule not_equiv_elim2 :premises (@p180)) % 0.35/0.58 (step @p182 :rule eq_resolve :premises (@p181 @p19)) % 0.35/0.58 (step @p183 :rule chain_m_resolution :premises (@p182 @p16) :args (@t42 (@list true) (@list @t49))) % 0.35/0.58 (step @p184 :rule equiv_elim1 :premises (@p15)) % 0.35/0.58 (step @p185 :rule chain_m_resolution :premises (@p184 @p183) :args (@t49 (@list false) (@list @t42))) % 0.35/0.58 (step @p186 :rule not_equiv_elim1 :premises (@p180)) % 0.35/0.58 (step @p187 false :rule chain_m_resolution :premises (@p186 @p185 @p183) :args (false (@list false false) (@list @t49 @t42))) % 0.35/0.58 ) % 0.35/0.58 % SZS output end Proof % 0.35/0.58 % cvc5 exiting %------------------------------------------------------------------------------