%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO890^16 : TPTP v9.2.1. Released v8.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n029.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 09:13:42 AM UTC 2026 % Result : Theorem 0.40s 0.61s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SYO890^16 : TPTP v9.2.1. Released v8.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n029.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 01:09:02 EDT 2026 % 0.17/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 0.40/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.61 % SZS status Theorem % 0.40/0.61 % SZS output start Proof % 0.40/0.61 ( % 0.40/0.61 (declare-sort $$unsorted 0) % 0.40/0.61 (declare-sort tptp.mworld 0) % 0.40/0.61 (declare-const tptp.mactual tptp.mworld) % 0.40/0.61 (declare-const tptp.mrel (-> tptp.mworld tptp.mworld Bool)) % 0.40/0.61 (declare-const tptp.eiw_di (-> $$unsorted tptp.mworld Bool)) % 0.40/0.61 (declare-const tptp.e (-> $$unsorted tptp.mworld Bool)) % 0.40/0.61 (declare-const tptp.f (-> $$unsorted tptp.mworld Bool)) % 0.40/0.61 (define tptp.mlocal () (let ((_let_1 (@var "Phi" (-> tptp.mworld Bool)))) (lambda (@list _let_1) (_ _let_1 tptp.mactual)))) % 0.40/0.61 (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)))))) % 0.40/0.61 (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))))))) % 0.40/0.61 (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))))))) % 0.40/0.61 (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))))))) % 0.40/0.61 (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))))))) % 0.40/0.61 (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)))))))) % 0.40/0.61 (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)))))))) % 0.40/0.61 (define tptp.mforall_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.40/0.61 (define tptp.mexists_di () (let ((_let_1 (@var "W" tptp.mworld))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "A" (-> $$unsorted tptp.mworld Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (and (_ (_ tptp.eiw_di _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.40/0.61 (define @t1 () (@var "W" tptp.mworld)) % 0.40/0.61 (define @t2 () (_ tptp.mrel @t1)) % 0.40/0.61 (define @t3 () (@list @t1)) % 0.40/0.61 (define @t4 () (@var "U" tptp.mworld)) % 0.40/0.61 (define @t5 () (@var "V" tptp.mworld)) % 0.40/0.61 (define @t6 () (_ @t2 @t5)) % 0.40/0.61 (define @t7 () (@var "X" $$unsorted)) % 0.40/0.61 (define @t8 () (_ tptp.eiw_di @t7)) % 0.40/0.61 (define @t9 () (_ @t8 @t1)) % 0.40/0.61 (define @t10 () (@list @t7)) % 0.40/0.61 (define @t11 () (_ @t8 @t5)) % 0.40/0.61 (define @t12 () (and @t9 @t6)) % 0.40/0.61 (define @t13 () (@list @t1 @t5 @t7)) % 0.40/0.61 (define @t14 () (forall @t13 (=> @t12 @t11))) % 0.40/0.61 (define @t15 () (@var "__flatten_var_0" tptp.mworld)) % 0.40/0.61 (define @t16 () (_ tptp.f @t7)) % 0.40/0.61 (define @t17 () (@list @t7 @t15)) % 0.40/0.61 (define @t18 () (lambda @t17 (_ @t16 @t15))) % 0.40/0.61 (define @t19 () (_ tptp.e @t7)) % 0.40/0.61 (define @t20 () (lambda @t17 (_ (_ tptp.mbox (_ (_ tptp.mand @t19) @t16)) @t15))) % 0.40/0.61 (define @t21 () (not (_ tptp.mlocal (_ (_ tptp.mimplies (_ tptp.mexists_di @t20)) (_ tptp.mbox (_ tptp.mexists_di @t18)))))) % 0.40/0.61 (define @t22 () (@var "Phi" (-> tptp.mworld Bool))) % 0.40/0.61 (define @t23 () (lambda (@list @t22) (_ @t22 tptp.mactual))) % 0.40/0.61 (define @t24 () (@var "A" (-> tptp.mworld Bool))) % 0.40/0.61 (define @t25 () (_ @t24 @t1)) % 0.40/0.61 (define @t26 () (lambda (@list @t24 @t1) (not @t25))) % 0.40/0.61 (define @t27 () (@var "B" (-> tptp.mworld Bool))) % 0.40/0.61 (define @t28 () (_ @t27 @t1)) % 0.40/0.61 (define @t29 () (@list @t24 @t27 @t1)) % 0.40/0.61 (define @t30 () (lambda @t29 (and @t25 @t28))) % 0.40/0.61 (define @t31 () (lambda @t29 (or @t25 @t28))) % 0.40/0.61 (define @t32 () (lambda @t29 (=> @t25 @t28))) % 0.40/0.61 (define @t33 () (lambda @t29 (= @t25 @t28))) % 0.40/0.61 (define @t34 () (_ @t22 @t5)) % 0.40/0.61 (define @t35 () (@list @t5)) % 0.40/0.61 (define @t36 () (forall @t35 (=> @t6 @t34))) % 0.40/0.61 (define @t37 () (@list @t22 @t1)) % 0.40/0.61 (define @t38 () (lambda @t37 @t36)) % 0.40/0.61 (define @t39 () (lambda @t37 (exists @t35 (and @t6 @t34)))) % 0.40/0.61 (define @t40 () (@var "A" (-> $$unsorted tptp.mworld Bool))) % 0.40/0.61 (define @t41 () (_ (_ @t40 @t7) @t1)) % 0.40/0.61 (define @t42 () (@list @t40 @t1)) % 0.40/0.61 (define @t43 () (lambda @t42 (forall @t10 (=> @t9 @t41)))) % 0.40/0.61 (define @t44 () (and @t9 @t41)) % 0.40/0.61 (define @t45 () (exists @t10 @t44)) % 0.40/0.61 (define @t46 () (lambda @t42 @t45)) % 0.40/0.61 (define @t47 () (tptp.f @t7 @t5)) % 0.40/0.61 (define @t48 () (tptp.eiw_di @t7 @t5)) % 0.40/0.61 (define @t49 () (not (forall @t10 (or (not @t48) (not @t47))))) % 0.40/0.61 (define @t50 () (not (tptp.mrel tptp.mactual @t5))) % 0.40/0.61 (define @t51 () (forall @t35 (or @t50 @t49))) % 0.40/0.61 (define @t52 () (tptp.e @t7 @t5)) % 0.40/0.61 (define @t53 () (and @t52 @t47)) % 0.40/0.61 (define @t54 () (forall @t10 (or (not (tptp.eiw_di @t7 tptp.mactual)) (not (forall @t35 (or @t50 @t53)))))) % 0.40/0.61 (define @t55 () (tptp.mrel @t1 @t5)) % 0.40/0.61 (define @t56 () (not @t55)) % 0.40/0.61 (define @t57 () (forall @t35 (or @t56 @t49))) % 0.40/0.61 (define @t58 () (forall @t35 (or @t56 @t53))) % 0.40/0.61 (define @t59 () (tptp.eiw_di @t7 @t1)) % 0.40/0.61 (define @t60 () (not @t59)) % 0.40/0.61 (define @t61 () (not (forall @t10 (or @t60 (not @t58))))) % 0.40/0.61 (define @t62 () (lambda @t3 (=> @t61 @t57))) % 0.40/0.61 (define @t63 () (_ @t62 tptp.mactual)) % 0.40/0.61 (define @t64 () (lambda @t3 @t57)) % 0.40/0.61 (define @t65 () (_ @t64 @t1)) % 0.40/0.61 (define @t66 () (=> @t61 @t65)) % 0.40/0.61 (define @t67 () (lambda @t3 @t66)) % 0.40/0.61 (define @t68 () (@list @t27 @t1)) % 0.40/0.61 (define @t69 () (tptp.f @t7 @t1)) % 0.40/0.61 (define @t70 () (lambda @t3 (not (forall @t10 (or @t60 (not @t69)))))) % 0.40/0.61 (define @t71 () (_ @t70 @t5)) % 0.40/0.61 (define @t72 () (or @t56 @t71)) % 0.40/0.61 (define @t73 () (forall @t35 @t72)) % 0.40/0.61 (define @t74 () (lambda @t3 @t73)) % 0.40/0.61 (define @t75 () (_ @t22 @t5)) % 0.40/0.61 (define @t76 () (lambda @t37 (forall @t35 (or @t56 @t75)))) % 0.40/0.61 (define @t77 () (_ @t16 @t1)) % 0.40/0.61 (define @t78 () (not @t77)) % 0.40/0.61 (define @t79 () (or @t60 @t78)) % 0.40/0.61 (define @t80 () (_ @t18 @t7 @t1)) % 0.40/0.61 (define @t81 () (not @t80)) % 0.40/0.61 (define @t82 () (or @t60 @t81)) % 0.40/0.61 (define @t83 () (forall @t10 @t82)) % 0.40/0.61 (define @t84 () (not @t83)) % 0.40/0.61 (define @t85 () (lambda @t3 @t84)) % 0.40/0.61 (define @t86 () (_ @t40 @t7 @t1)) % 0.40/0.61 (define @t87 () (lambda @t42 (not (forall @t10 (or @t60 (not @t86)))))) % 0.40/0.61 (define @t88 () (_ @t87 @t18)) % 0.40/0.61 (define @t89 () (lambda @t3 @t61)) % 0.40/0.61 (define @t90 () (_ @t89 @t1)) % 0.40/0.61 (define @t91 () (=> @t90 @t28)) % 0.40/0.61 (define @t92 () (lambda @t68 @t91)) % 0.40/0.61 (define @t93 () (forall @t35 (or (not (tptp.mrel @t15 @t5)) @t53))) % 0.40/0.61 (define @t94 () (lambda @t17 @t93)) % 0.40/0.61 (define @t95 () (_ @t94 @t7 @t1)) % 0.40/0.61 (define @t96 () (not @t95)) % 0.40/0.61 (define @t97 () (or @t60 @t96)) % 0.40/0.61 (define @t98 () (forall @t10 @t97)) % 0.40/0.61 (define @t99 () (not @t98)) % 0.40/0.61 (define @t100 () (lambda @t3 @t99)) % 0.40/0.61 (define @t101 () (_ @t16 @t5)) % 0.40/0.61 (define @t102 () (_ @t19 @t5)) % 0.40/0.61 (define @t103 () (and @t102 @t101)) % 0.40/0.61 (define @t104 () (or @t56 @t103)) % 0.40/0.61 (define @t105 () (_ @t19 @t1)) % 0.40/0.61 (define @t106 () (lambda @t3 (and @t105 @t77))) % 0.40/0.61 (define @t107 () (_ @t106 @t5)) % 0.40/0.61 (define @t108 () (or @t56 @t107)) % 0.40/0.61 (define @t109 () (forall @t35 @t108)) % 0.40/0.61 (define @t110 () (lambda @t3 @t109)) % 0.40/0.61 (define @t111 () (lambda @t68 (and @t105 @t28))) % 0.40/0.61 (define @t112 () (_ @t30 @t19)) % 0.40/0.61 (define @t113 () (lambda @t17 (_ (_ @t76 (_ @t112 @t16)) @t15))) % 0.40/0.61 (define @t114 () (not @t41)) % 0.40/0.61 (define @t115 () (not @t9)) % 0.40/0.61 (define @t116 () (or @t115 @t114)) % 0.40/0.61 (define @t117 () (forall @t10 (not @t44))) % 0.40/0.61 (define @t118 () (not @t117)) % 0.40/0.61 (define @t119 () (not @t6)) % 0.40/0.61 (define @t120 () (or @t119 @t34)) % 0.40/0.61 (define @t121 () (@quantifiers_skolemize @t51 0)) % 0.40/0.61 (define @t122 () (forall @t10 (or (not (tptp.eiw_di @t7 @t121)) (not (tptp.f @t7 @t121))))) % 0.40/0.61 (define @t123 () (not @t122)) % 0.40/0.61 (define @t124 () (tptp.mrel tptp.mactual @t121)) % 0.40/0.61 (define @t125 () (not @t124)) % 0.40/0.61 (define @t126 () (or @t125 @t123)) % 0.40/0.61 (define @t127 () (@list true)) % 0.40/0.61 (define @t128 () (@list @t126)) % 0.40/0.61 (define @t129 () (@quantifiers_skolemize @t54 0)) % 0.40/0.61 (define @t130 () (forall @t35 (or @t50 (and (tptp.e @t129 @t5) (tptp.f @t129 @t5))))) % 0.40/0.61 (define @t131 () (not @t130)) % 0.40/0.61 (define @t132 () (tptp.eiw_di @t129 tptp.mactual)) % 0.40/0.61 (define @t133 () (not @t132)) % 0.40/0.61 (define @t134 () (or @t133 @t131)) % 0.40/0.61 (define @t135 () (@list @t134)) % 0.40/0.61 (define @t136 () (tptp.f @t129 @t121)) % 0.40/0.61 (define @t137 () (and (tptp.e @t129 @t121) @t136)) % 0.40/0.61 (define @t138 () (or @t125 @t137)) % 0.40/0.61 (define @t139 () (@list false false)) % 0.40/0.61 (define @t140 () (or @t115 @t119 @t11)) % 0.40/0.61 (define @t141 () (tptp.eiw_di @t129 @t121)) % 0.40/0.61 (define @t142 () (or @t133 @t125 @t141)) % 0.40/0.61 (define @t143 () (not @t136)) % 0.40/0.61 (define @t144 () (not @t141)) % 0.40/0.61 (define @t145 () (or @t144 @t143)) % 0.40/0.61 (define @t146 () (not @t145)) % 0.40/0.61 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.40/0.61 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and @t6 (_ (_ tptp.mrel @t5) @t4)) (_ @t2 @t4)))) % 0.40/0.61 (assume @p3 (forall @t3 (exists @t10 @t9))) % 0.40/0.61 (assume @p4 @t14) % 0.40/0.61 (assume @p5 @t21) % 0.40/0.61 (assume @p6 true) % 0.40/0.61 (step @p7 (= tptp.mlocal @t23) :rule refl :args (@t23)) % 0.40/0.61 (step @p8 (= tptp.mnot @t26) :rule refl :args (@t26)) % 0.40/0.61 (step @p9 (= tptp.mand @t30) :rule refl :args (@t30)) % 0.40/0.61 (step @p10 (= tptp.mor @t31) :rule refl :args (@t31)) % 0.40/0.61 (step @p11 (= tptp.mimplies @t32) :rule refl :args (@t32)) % 0.40/0.61 (step @p12 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 0.40/0.61 (step @p13 (= tptp.mbox @t38) :rule refl :args (@t38)) % 0.40/0.61 (step @p14 (= tptp.mdia @t39) :rule refl :args (@t39)) % 0.40/0.61 (step @p15 (= tptp.mforall_di @t43) :rule refl :args (@t43)) % 0.40/0.61 (step @p16 (= tptp.mexists_di @t46) :rule refl :args (@t46)) % 0.40/0.61 (step @p17 :rule beta-reduce :args ((= @t63 (=> (not @t54) @t51)))) % 0.40/0.61 (step @p18 :rule beta-reduce :args ((= (_ @t23 @t62) @t63))) % 0.40/0.61 (step @p19 :rule trans :premises (@p18 @p17)) % 0.40/0.61 (step @p20 :rule beta-reduce :args ((= @t65 @t57))) % 0.40/0.61 (step @p21 :rule refl :args (@t61)) % 0.40/0.61 (step @p22 :rule cong :premises (@p21 @p20) :args (@t66)) % 0.40/0.61 (step @p23 :rule cong :premises (@p22) :args (@t67)) % 0.40/0.61 (step @p24 :rule beta-reduce :args ((= (_ (lambda @t68 (=> @t61 @t28)) @t64) @t67))) % 0.40/0.61 (step @p25 :rule trans :premises (@p24 @p23)) % 0.40/0.61 (step @p26 :rule beta-reduce :args ((= @t71 @t49))) % 0.40/0.61 (step @p27 :rule refl :args (@t56)) % 0.40/0.61 (step @p28 :rule nary_cong :premises (@p27 @p26) :args (@t72)) % 0.40/0.61 (step @p29 :rule cong :premises (@p28) :args (@t73)) % 0.40/0.61 (step @p30 :rule cong :premises (@p29) :args (@t74)) % 0.40/0.61 (step @p31 :rule beta-reduce :args ((= (_ @t76 @t70) @t74))) % 0.40/0.61 (step @p32 :rule trans :premises (@p31 @p30)) % 0.40/0.61 (step @p33 :rule refl :args (@t69)) % 0.40/0.61 (step @p34 :rule refl :args (@t77)) % 0.40/0.61 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t77 @t69))) % 0.40/0.61 (step @p36 :rule symm :premises (@p35)) % 0.40/0.61 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.40/0.61 (step @p38 :rule cong :premises (@p37) :args (@t78)) % 0.40/0.61 (step @p39 :rule refl :args (@t60)) % 0.40/0.61 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t79)) % 0.40/0.61 (step @p41 :rule cong :premises (@p40) :args ((forall @t10 @t79))) % 0.40/0.61 (step @p42 :rule beta-reduce :args ((= @t80 @t77))) % 0.40/0.61 (step @p43 :rule cong :premises (@p42) :args (@t81)) % 0.40/0.61 (step @p44 :rule refl :args (@t60)) % 0.40/0.61 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t82)) % 0.40/0.61 (step @p46 :rule cong :premises (@p45) :args (@t83)) % 0.40/0.61 (step @p47 :rule trans :premises (@p46 @p41)) % 0.40/0.61 (step @p48 :rule cong :premises (@p47) :args (@t84)) % 0.40/0.61 (step @p49 :rule cong :premises (@p48) :args (@t85)) % 0.40/0.61 (step @p50 :rule beta-reduce :args ((= @t88 @t85))) % 0.40/0.61 (step @p51 :rule trans :premises (@p50 @p49)) % 0.40/0.61 (step @p52 :rule refl :args (@t76)) % 0.40/0.61 (step @p53 :rule ho_cong :premises (@p52 @p51)) % 0.40/0.61 (step @p54 :rule trans :premises (@p53 @p32)) % 0.40/0.61 (step @p55 :rule refl :args (@t28)) % 0.40/0.61 (step @p56 :rule beta-reduce :args ((= @t90 @t61))) % 0.40/0.61 (step @p57 :rule cong :premises (@p56 @p55) :args (@t91)) % 0.40/0.61 (step @p58 :rule cong :premises (@p57) :args (@t92)) % 0.40/0.61 (step @p59 :rule beta-reduce :args ((= (_ @t32 @t89) @t92))) % 0.40/0.61 (step @p60 :rule trans :premises (@p59 @p58)) % 0.40/0.61 (step @p61 :rule beta-reduce :args ((= @t95 @t58))) % 0.40/0.61 (step @p62 :rule cong :premises (@p61) :args (@t96)) % 0.40/0.61 (step @p63 :rule nary_cong :premises (@p44 @p62) :args (@t97)) % 0.40/0.61 (step @p64 :rule cong :premises (@p63) :args (@t98)) % 0.40/0.61 (step @p65 :rule cong :premises (@p64) :args (@t99)) % 0.40/0.61 (step @p66 :rule cong :premises (@p65) :args (@t100)) % 0.40/0.61 (step @p67 :rule beta-reduce :args ((= (_ @t87 @t94) @t100))) % 0.40/0.61 (step @p68 :rule trans :premises (@p67 @p66)) % 0.40/0.61 (step @p69 :rule beta-reduce :args ((= (_ (lambda @t3 @t58) @t15) @t93))) % 0.40/0.61 (step @p70 :rule refl :args (@t15)) % 0.40/0.61 (step @p71 :rule refl :args (@t47)) % 0.40/0.61 (step @p72 :rule refl :args (@t101)) % 0.40/0.61 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t101 @t47))) % 0.40/0.61 (step @p74 :rule symm :premises (@p73)) % 0.40/0.61 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 0.40/0.61 (step @p76 :rule refl :args (@t52)) % 0.40/0.61 (step @p77 :rule refl :args (@t102)) % 0.40/0.61 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t102 @t52))) % 0.40/0.61 (step @p79 :rule symm :premises (@p78)) % 0.40/0.61 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.40/0.61 (step @p81 :rule nary_cong :premises (@p80 @p75) :args (@t103)) % 0.40/0.61 (step @p82 :rule refl :args (@t56)) % 0.40/0.61 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t104)) % 0.40/0.61 (step @p84 :rule cong :premises (@p83) :args ((forall @t35 @t104))) % 0.40/0.61 (step @p85 :rule beta-reduce :args ((= @t107 @t103))) % 0.40/0.61 (step @p86 :rule nary_cong :premises (@p27 @p85) :args (@t108)) % 0.40/0.61 (step @p87 :rule cong :premises (@p86) :args (@t109)) % 0.40/0.61 (step @p88 :rule trans :premises (@p87 @p84)) % 0.40/0.61 (step @p89 :rule cong :premises (@p88) :args (@t110)) % 0.40/0.61 (step @p90 :rule beta-reduce :args ((= (_ @t76 @t106) @t110))) % 0.40/0.61 (step @p91 :rule trans :premises (@p90 @p89)) % 0.40/0.61 (step @p92 :rule beta-reduce :args ((= (_ @t111 @t16) @t106))) % 0.40/0.61 (step @p93 :rule refl :args (@t16)) % 0.40/0.61 (step @p94 :rule beta-reduce :args ((= @t112 @t111))) % 0.40/0.61 (step @p95 :rule ho_cong :premises (@p94 @p93)) % 0.40/0.61 (step @p96 :rule trans :premises (@p95 @p92)) % 0.40/0.61 (step @p97 :rule ho_cong :premises (@p52 @p96)) % 0.40/0.61 (step @p98 :rule trans :premises (@p97 @p91)) % 0.40/0.61 (step @p99 :rule ho_cong :premises (@p98 @p70)) % 0.40/0.61 (step @p100 :rule trans :premises (@p99 @p69)) % 0.40/0.61 (step @p101 :rule cong :premises (@p100) :args (@t113)) % 0.40/0.61 (step @p102 :rule refl :args (@t87)) % 0.40/0.61 (step @p103 :rule ho_cong :premises (@p102 @p101)) % 0.40/0.61 (step @p104 :rule trans :premises (@p103 @p68)) % 0.40/0.61 (step @p105 :rule refl :args (@t32)) % 0.40/0.61 (step @p106 :rule ho_cong :premises (@p105 @p104)) % 0.40/0.61 (step @p107 :rule trans :premises (@p106 @p60)) % 0.40/0.61 (step @p108 :rule ho_cong :premises (@p107 @p54)) % 0.40/0.61 (step @p109 :rule trans :premises (@p108 @p25)) % 0.40/0.61 (step @p110 :rule refl :args (@t23)) % 0.40/0.61 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 0.40/0.61 (step @p112 :rule trans :premises (@p111 @p19)) % 0.40/0.61 (step @p113 :rule cong :premises (@p112) :args ((not (_ @t23 (_ (_ @t32 (_ @t87 @t113)) (_ @t76 @t88)))))) % 0.40/0.61 (step @p114 :rule refl :args (@t18)) % 0.40/0.61 (step @p115 :rule refl :args (@t86)) % 0.40/0.61 (step @p116 :rule refl :args (@t41)) % 0.40/0.61 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t41 @t86))) % 0.40/0.61 (step @p118 :rule symm :premises (@p117)) % 0.40/0.61 (step @p119 :rule eq_resolve :premises (@p116 @p118)) % 0.40/0.61 (step @p120 :rule cong :premises (@p119) :args (@t114)) % 0.40/0.61 (step @p121 :rule refl :args (@t59)) % 0.40/0.61 (step @p122 :rule refl :args (@t9)) % 0.40/0.61 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t9 @t59))) % 0.40/0.61 (step @p124 :rule symm :premises (@p123)) % 0.40/0.61 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.40/0.61 (step @p126 :rule cong :premises (@p125) :args (@t115)) % 0.40/0.61 (step @p127 :rule nary_cong :premises (@p126 @p120) :args (@t116)) % 0.40/0.61 (step @p128 :rule cong :premises (@p127) :args ((forall @t10 @t116))) % 0.40/0.61 (step @p129 :rule bool-and-de-morgan :args (@t9 @t41 true)) % 0.40/0.61 (step @p130 :rule cong :premises (@p129) :args (@t117)) % 0.40/0.61 (step @p131 :rule trans :premises (@p130 @p128)) % 0.40/0.61 (step @p132 :rule cong :premises (@p131) :args (@t118)) % 0.40/0.61 (step @p133 :rule exists-elim :args ((= @t45 @t118))) % 0.40/0.61 (step @p134 :rule trans :premises (@p133 @p132)) % 0.40/0.61 (step @p135 :rule cong :premises (@p134) :args (@t46)) % 0.40/0.61 (step @p136 :rule trans :premises (@p16 @p135)) % 0.40/0.61 (step @p137 :rule ho_cong :premises (@p136 @p114)) % 0.40/0.61 (step @p138 :rule refl :args (@t75)) % 0.40/0.61 (step @p139 :rule refl :args (@t34)) % 0.40/0.61 (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t34 @t75))) % 0.40/0.61 (step @p141 :rule symm :premises (@p140)) % 0.40/0.61 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.40/0.61 (step @p143 :rule refl :args (@t55)) % 0.40/0.61 (step @p144 :rule refl :args (@t6)) % 0.40/0.61 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t6 @t55))) % 0.40/0.61 (step @p146 :rule symm :premises (@p145)) % 0.40/0.61 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.40/0.61 (step @p148 :rule cong :premises (@p147) :args (@t119)) % 0.40/0.61 (step @p149 :rule nary_cong :premises (@p148 @p142) :args (@t120)) % 0.40/0.61 (step @p150 :rule cong :premises (@p149) :args ((forall @t35 @t120))) % 0.40/0.61 (step @p151 :rule bool-impl-elim :args (@t6 @t34)) % 0.40/0.61 (step @p152 :rule cong :premises (@p151) :args (@t36)) % 0.40/0.61 (step @p153 :rule trans :premises (@p152 @p150)) % 0.40/0.61 (step @p154 :rule cong :premises (@p153) :args (@t38)) % 0.40/0.61 (step @p155 :rule trans :premises (@p13 @p154)) % 0.40/0.61 (step @p156 :rule ho_cong :premises (@p155 @p137)) % 0.40/0.61 (step @p157 :rule refl :args (@t19)) % 0.40/0.61 (step @p158 :rule ho_cong :premises (@p9 @p157)) % 0.40/0.61 (step @p159 :rule ho_cong :premises (@p158 @p93)) % 0.40/0.61 (step @p160 :rule ho_cong :premises (@p155 @p159)) % 0.40/0.61 (step @p161 :rule ho_cong :premises (@p160 @p70)) % 0.40/0.61 (step @p162 :rule cong :premises (@p161) :args (@t20)) % 0.40/0.61 (step @p163 :rule ho_cong :premises (@p136 @p162)) % 0.40/0.61 (step @p164 :rule ho_cong :premises (@p11 @p163)) % 0.40/0.61 (step @p165 :rule ho_cong :premises (@p164 @p156)) % 0.40/0.61 (step @p166 :rule ho_cong :premises (@p7 @p165)) % 0.40/0.61 (step @p167 :rule cong :premises (@p166) :args (@t21)) % 0.40/0.61 (step @p168 :rule trans :premises (@p167 @p113)) % 0.40/0.61 (step @p169 :rule eq_resolve :premises (@p5 @p168)) % 0.40/0.61 (step @p170 :rule not_implies_elim2 :premises (@p169)) % 0.40/0.61 (step @p171 :rule skolemize :premises (@p170)) % 0.40/0.61 (step @p172 :rule bool-double-not-elim :args (@t122)) % 0.40/0.61 (step @p173 :rule refl :args (@t126)) % 0.40/0.61 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or @t126 (not @t123)))) % 0.40/0.61 (step @p175 :rule cnf_or_neg :args (@t126 1)) % 0.40/0.61 (step @p176 :rule eq_resolve :premises (@p175 @p174)) % 0.40/0.61 (step @p177 :rule reordering :premises (@p176) :args ((or @t122 @t126))) % 0.40/0.61 (step @p178 :rule chain_m_resolution :premises (@p177 @p171) :args (@t122 @t127 @t128)) % 0.40/0.61 (step @p179 :rule not_implies_elim1 :premises (@p169)) % 0.40/0.61 (step @p180 :rule skolemize :premises (@p179)) % 0.40/0.61 (step @p181 :rule bool-double-not-elim :args (@t130)) % 0.40/0.61 (step @p182 :rule refl :args (@t134)) % 0.40/0.61 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or @t134 (not @t131)))) % 0.40/0.61 (step @p184 :rule cnf_or_neg :args (@t134 1)) % 0.40/0.61 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.40/0.61 (step @p186 :rule reordering :premises (@p185) :args ((or @t130 @t134))) % 0.40/0.61 (step @p187 :rule chain_m_resolution :premises (@p186 @p180) :args (@t130 @t127 @t135)) % 0.40/0.61 (step @p188 :rule instantiate :premises (@p187) :args ((@list @t121))) % 0.40/0.61 (step @p189 :rule bool-double-not-elim :args (@t124)) % 0.40/0.61 (step @p190 :rule nary_cong :premises (@p173 @p189) :args ((or @t126 (not @t125)))) % 0.40/0.61 (step @p191 :rule cnf_or_neg :args (@t126 0)) % 0.40/0.61 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.40/0.61 (step @p193 :rule reordering :premises (@p192) :args ((or @t124 @t126))) % 0.40/0.61 (step @p194 :rule chain_m_resolution :premises (@p193 @p171) :args (@t124 @t127 @t128)) % 0.40/0.61 (step @p195 :rule cnf_or_pos :args (@t138)) % 0.40/0.61 (step @p196 :rule reordering :premises (@p195) :args ((or @t125 @t137 (not @t138)))) % 0.40/0.61 (step @p197 :rule chain_m_resolution :premises (@p196 @p194 @p188) :args (@t137 @t139 (@list @t124 @t138))) % 0.40/0.61 (step @p198 :rule cnf_and_pos :args (@t137 1)) % 0.40/0.61 (step @p199 :rule reordering :premises (@p198) :args ((or @t136 (not @t137)))) % 0.40/0.61 (step @p200 :rule chain_m_resolution :premises (@p199 @p197) :args (@t136 (@list false) (@list @t137))) % 0.40/0.61 (step @p201 :rule refl :args (@t48)) % 0.40/0.61 (step @p202 :rule refl :args (@t11)) % 0.40/0.61 (step @p203 :rule cong :premises (@p202 @p201) :args ((= @t11 @t48))) % 0.40/0.61 (step @p204 :rule symm :premises (@p203)) % 0.40/0.61 (step @p205 :rule eq_resolve :premises (@p202 @p204)) % 0.40/0.61 (step @p206 :rule nary_cong :premises (@p126 @p148 @p205) :args (@t140)) % 0.40/0.61 (step @p207 :rule cong :premises (@p206) :args ((forall @t13 @t140))) % 0.40/0.61 (step @p208 :rule aci_norm :args ((= (or (or @t115 @t119) @t11) @t140))) % 0.40/0.61 (step @p209 :rule bool-and-de-morgan :args (@t9 @t6 true)) % 0.40/0.61 (step @p210 :rule nary_cong :premises (@p209 @p202) :args ((or (not @t12) @t11))) % 0.40/0.61 (step @p211 :rule trans :premises (@p210 @p208)) % 0.40/0.61 (step @p212 :rule bool-impl-elim :args (@t12 @t11)) % 0.40/0.61 (step @p213 :rule trans :premises (@p212 @p211)) % 0.40/0.61 (step @p214 :rule cong :premises (@p213) :args (@t14)) % 0.40/0.61 (step @p215 :rule trans :premises (@p214 @p207)) % 0.40/0.61 (step @p216 :rule eq_resolve :premises (@p4 @p215)) % 0.40/0.61 (step @p217 :rule instantiate :premises (@p216) :args ((@list tptp.mactual @t121 @t129))) % 0.40/0.61 (step @p218 :rule bool-double-not-elim :args (@t132)) % 0.40/0.61 (step @p219 :rule nary_cong :premises (@p182 @p218) :args ((or @t134 (not @t133)))) % 0.40/0.61 (step @p220 :rule cnf_or_neg :args (@t134 0)) % 0.40/0.61 (step @p221 :rule eq_resolve :premises (@p220 @p219)) % 0.40/0.61 (step @p222 :rule reordering :premises (@p221) :args ((or @t132 @t134))) % 0.40/0.61 (step @p223 :rule chain_m_resolution :premises (@p222 @p180) :args (@t132 @t127 @t135)) % 0.40/0.61 (step @p224 :rule cnf_or_pos :args (@t142)) % 0.40/0.61 (step @p225 :rule reordering :premises (@p224) :args ((or @t133 @t125 @t141 (not @t142)))) % 0.40/0.61 (step @p226 :rule chain_m_resolution :premises (@p225 @p223 @p194 @p217) :args (@t141 (@list false false false) (@list @t132 @t124 @t142))) % 0.40/0.61 (step @p227 :rule cnf_or_pos :args (@t145)) % 0.40/0.61 (step @p228 :rule reordering :premises (@p227) :args ((or @t144 @t143 @t146))) % 0.40/0.61 (step @p229 :rule chain_m_resolution :premises (@p228 @p226 @p200) :args (@t146 @t139 (@list @t141 @t136))) % 0.40/0.61 (assume-push @p236 @t122) % 0.40/0.61 (step @p231 :rule instantiate :premises (@p178) :args ((@list @t129))) % 0.40/0.61 (step-pop @p237 :rule scope :premises (@p231)) % 0.40/0.61 (step @p232 :rule process_scope :premises (@p237) :args (@t145)) % 0.40/0.61 (step @p234 :rule implies_elim :premises (@p232)) % 0.40/0.61 (step @p235 false :rule chain_m_resolution :premises (@p234 @p229 @p178) :args (false (@list true false) (@list @t145 @t122))) % 0.40/0.61 ) % 0.40/0.61 % SZS output end Proof % 0.40/0.61 % cvc5 exiting %------------------------------------------------------------------------------