%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYN390^4 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n017.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 09:08:46 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYN390^4 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n017.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 23:24:31 EDT 2026 % 0.15/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.p (-> $$unsorted Bool)) % 0.37/0.58 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.37/0.58 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.58 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.58 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.irel _let_3) _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.58 (define tptp.iatom () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ _let_2 _let_1))))) % 0.37/0.58 (define tptp.inot () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 _let_2)) _let_1))))) % 0.37/0.58 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.58 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mand _let_3) _let_2) _let_1)))))) % 0.37/0.58 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.37/0.58 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mimplies (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.37/0.58 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.37/0.58 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iand (_ (_ tptp.iimplies _let_2) _let_3)) (_ (_ tptp.iimplies _let_3) _let_2)) _let_1)))))) % 0.37/0.58 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.37/0.58 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.58 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.58 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.58 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.58 (define @t1 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t2 () (_ tptp.irel @t1)) % 0.37/0.58 (define @t3 () (@list @t1)) % 0.37/0.58 (define @t4 () (@var "Z" $$unsorted)) % 0.37/0.58 (define @t5 () (@var "Y" $$unsorted)) % 0.37/0.58 (define @t6 () (_ @t2 @t5)) % 0.37/0.58 (define @t7 () (_ tptp.iatom tptp.p)) % 0.37/0.58 (define @t8 () (not (_ tptp.ivalid (_ (_ tptp.iequiv @t7) @t7)))) % 0.37/0.58 (define @t9 () (@var "U" $$unsorted)) % 0.37/0.58 (define @t10 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.58 (define @t11 () (_ @t10 @t9)) % 0.37/0.58 (define @t12 () (lambda (@list @t10 @t9) (not @t11))) % 0.37/0.58 (define @t13 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.58 (define @t14 () (_ @t13 @t9)) % 0.37/0.58 (define @t15 () (@list @t10 @t13 @t9)) % 0.37/0.58 (define @t16 () (lambda @t15 (or @t11 @t14))) % 0.37/0.58 (define @t17 () (lambda @t15 (and @t11 @t14))) % 0.37/0.58 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.58 (define @t19 () (@var "V" (-> $$unsorted Bool))) % 0.37/0.58 (define @t20 () (@var "U" (-> $$unsorted Bool))) % 0.37/0.58 (define @t21 () (@list @t20 @t19 @t18)) % 0.37/0.58 (define @t22 () (lambda @t21 (_ (_ (_ tptp.mor (_ tptp.mnot @t20)) @t19) @t18))) % 0.37/0.58 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.58 (define @t24 () (_ @t23 @t5)) % 0.37/0.58 (define @t25 () (@list @t5)) % 0.37/0.58 (define @t26 () (forall @t25 (=> @t6 @t24))) % 0.37/0.58 (define @t27 () (@list @t23 @t1)) % 0.37/0.58 (define @t28 () (lambda @t27 @t26)) % 0.37/0.58 (define @t29 () (_ @t23 @t18)) % 0.37/0.58 (define @t30 () (@list @t23 @t18)) % 0.37/0.58 (define @t31 () (lambda @t30 @t29)) % 0.37/0.58 (define @t32 () (_ tptp.mbox_s4 @t23)) % 0.37/0.58 (define @t33 () (lambda @t30 (_ (_ tptp.mnot @t32) @t18))) % 0.37/0.58 (define @t34 () (@var "W" $$unsorted)) % 0.37/0.58 (define @t35 () (@list @t34)) % 0.37/0.58 (define @t36 () (lambda @t35 true)) % 0.37/0.58 (define @t37 () (@var "Q" (-> $$unsorted Bool))) % 0.37/0.58 (define @t38 () (@list @t23 @t37 @t18)) % 0.37/0.58 (define @t39 () (lambda @t38 (_ (_ (_ tptp.mand @t23) @t37) @t18))) % 0.37/0.58 (define @t40 () (_ tptp.mbox_s4 @t37)) % 0.37/0.58 (define @t41 () (lambda @t38 (_ (_ (_ tptp.mor @t32) @t40) @t18))) % 0.37/0.58 (define @t42 () (lambda @t38 (_ (_ (_ tptp.mimplies @t32) @t40) @t18))) % 0.37/0.58 (define @t43 () (_ (_ tptp.iimplies @t37) @t23)) % 0.37/0.58 (define @t44 () (lambda @t38 (_ @t43 @t18))) % 0.37/0.58 (define @t45 () (lambda @t38 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t23) @t37)) @t43) @t18))) % 0.37/0.58 (define @t46 () (lambda @t38 (_ (_ tptp.inot (_ (_ tptp.iequiv @t23) @t37)) @t18))) % 0.37/0.58 (define @t47 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.58 (define @t48 () (_ @t47 @t34)) % 0.37/0.58 (define @t49 () (forall @t35 @t48)) % 0.37/0.58 (define @t50 () (@list @t47)) % 0.37/0.58 (define @t51 () (lambda @t50 @t49)) % 0.37/0.58 (define @t52 () (lambda @t50 (exists @t35 @t48))) % 0.37/0.58 (define @t53 () (not @t48)) % 0.37/0.58 (define @t54 () (lambda @t50 (exists @t35 @t53))) % 0.37/0.58 (define @t55 () (lambda @t50 (forall @t35 @t53))) % 0.37/0.58 (define @t56 () (tptp.p @t5)) % 0.37/0.58 (define @t57 () (forall @t25 (or (not (tptp.irel @t34 @t5)) @t56))) % 0.37/0.58 (define @t58 () (or (not @t57) @t57)) % 0.37/0.58 (define @t59 () (not (tptp.irel @t18 @t5))) % 0.37/0.58 (define @t60 () (forall @t25 (or @t59 @t56))) % 0.37/0.58 (define @t61 () (not @t60)) % 0.37/0.58 (define @t62 () (or @t61 @t60)) % 0.37/0.58 (define @t63 () (@list @t18)) % 0.37/0.58 (define @t64 () (lambda @t63 @t62)) % 0.37/0.58 (define @t65 () (_ @t64 @t34)) % 0.37/0.58 (define @t66 () (forall @t35 @t65)) % 0.37/0.58 (define @t67 () (_ @t47 @t34)) % 0.37/0.58 (define @t68 () (lambda @t50 (forall @t35 @t67))) % 0.37/0.58 (define @t69 () (_ tptp.p @t5)) % 0.37/0.58 (define @t70 () (or @t59 @t69)) % 0.37/0.58 (define @t71 () (lambda @t63 (_ tptp.p @t18))) % 0.37/0.58 (define @t72 () (_ @t71 @t5)) % 0.37/0.58 (define @t73 () (or @t59 @t72)) % 0.37/0.58 (define @t74 () (forall @t25 @t73)) % 0.37/0.58 (define @t75 () (not @t74)) % 0.37/0.58 (define @t76 () (or @t75 @t60)) % 0.37/0.58 (define @t77 () (or @t61 @t74)) % 0.37/0.58 (define @t78 () (and @t77 @t76)) % 0.37/0.58 (define @t79 () (lambda @t63 @t78)) % 0.37/0.58 (define @t80 () (_ @t37 @t5)) % 0.37/0.58 (define @t81 () (forall @t25 (or @t59 @t80))) % 0.37/0.58 (define @t82 () (not @t81)) % 0.37/0.58 (define @t83 () (@list @t37 @t18)) % 0.37/0.58 (define @t84 () (_ @t31 tptp.p)) % 0.37/0.58 (define @t85 () (or @t82 @t74)) % 0.37/0.58 (define @t86 () (or @t75 @t81)) % 0.37/0.58 (define @t87 () (and @t86 @t85)) % 0.37/0.58 (define @t88 () (lambda @t83 @t87)) % 0.37/0.58 (define @t89 () (_ @t23 @t5)) % 0.37/0.58 (define @t90 () (forall @t25 (or @t59 @t89))) % 0.37/0.58 (define @t91 () (or @t82 @t90)) % 0.37/0.58 (define @t92 () (not @t90)) % 0.37/0.58 (define @t93 () (or @t92 @t81)) % 0.37/0.58 (define @t94 () (and @t93 @t91)) % 0.37/0.58 (define @t95 () (lambda @t38 @t94)) % 0.37/0.58 (define @t96 () (lambda @t63 @t91)) % 0.37/0.58 (define @t97 () (_ @t96 @t18)) % 0.37/0.58 (define @t98 () (and @t93 @t97)) % 0.37/0.58 (define @t99 () (lambda @t63 @t98)) % 0.37/0.58 (define @t100 () (@var "BOUND_VARIABLE_7728" (-> $$unsorted Bool))) % 0.37/0.58 (define @t101 () (_ @t100 @t18)) % 0.37/0.58 (define @t102 () (@list @t100 @t18)) % 0.37/0.58 (define @t103 () (@var "BOUND_VARIABLE_7685" (-> $$unsorted Bool))) % 0.37/0.58 (define @t104 () (forall @t25 (or @t59 (_ @t103 @t5)))) % 0.37/0.58 (define @t105 () (lambda (@list @t103 @t18) (or @t82 @t104))) % 0.37/0.58 (define @t106 () (lambda @t38 @t93)) % 0.37/0.58 (define @t107 () (@list @t37)) % 0.37/0.58 (define @t108 () (lambda @t63 @t93)) % 0.37/0.58 (define @t109 () (_ @t108 @t18)) % 0.37/0.58 (define @t110 () (and @t109 @t101)) % 0.37/0.58 (define @t111 () (lambda @t102 @t110)) % 0.37/0.58 (define @t112 () (and @t29 (_ @t37 @t18))) % 0.37/0.58 (define @t113 () (lambda @t38 @t112)) % 0.37/0.58 (define @t114 () (lambda @t83 @t93)) % 0.37/0.58 (define @t115 () (tptp.irel @t1 @t5)) % 0.37/0.58 (define @t116 () (not @t115)) % 0.37/0.58 (define @t117 () (lambda @t3 (forall @t25 (or @t116 @t80)))) % 0.37/0.58 (define @t118 () (_ @t117 @t18)) % 0.37/0.58 (define @t119 () (or @t92 @t118)) % 0.37/0.58 (define @t120 () (lambda @t63 @t119)) % 0.37/0.58 (define @t121 () (_ @t19 @t18)) % 0.37/0.58 (define @t122 () (@list @t19 @t18)) % 0.37/0.58 (define @t123 () (forall @t25 (or @t116 @t89))) % 0.37/0.58 (define @t124 () (lambda @t27 @t123)) % 0.37/0.58 (define @t125 () (lambda @t3 @t123)) % 0.37/0.58 (define @t126 () (_ @t125 @t18)) % 0.37/0.58 (define @t127 () (not @t126)) % 0.37/0.58 (define @t128 () (or @t127 @t121)) % 0.37/0.58 (define @t129 () (lambda @t122 @t128)) % 0.37/0.58 (define @t130 () (or (not (_ @t20 @t18)) @t121)) % 0.37/0.58 (define @t131 () (lambda @t21 @t130)) % 0.37/0.58 (define @t132 () (not @t6)) % 0.37/0.58 (define @t133 () (or @t132 @t24)) % 0.37/0.58 (define @t134 () (not (_ @t20 @t9))) % 0.37/0.58 (define @t135 () (@list @t9)) % 0.37/0.58 (define @t136 () (lambda @t135 (or @t134 (_ @t19 @t9)))) % 0.37/0.58 (define @t137 () (@list @t13 @t9)) % 0.37/0.58 (define @t138 () (lambda @t135 @t134)) % 0.37/0.58 (define @t139 () (_ @t138 @t9)) % 0.37/0.58 (define @t140 () (or @t139 @t14)) % 0.37/0.58 (define @t141 () (lambda @t137 @t140)) % 0.37/0.58 (define @t142 () (_ @t23 @t9)) % 0.37/0.58 (define @t143 () (lambda @t135 (and @t142 (_ @t37 @t9)))) % 0.37/0.58 (define @t144 () (lambda @t137 (and @t142 @t14))) % 0.37/0.58 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.37/0.58 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and @t6 (_ (_ tptp.irel @t5) @t4)) (_ @t2 @t4)))) % 0.37/0.58 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.37/0.58 (assume @p4 @t8) % 0.37/0.58 (assume @p5 true) % 0.37/0.58 (step @p6 (= tptp.mnot @t12) :rule refl :args (@t12)) % 0.37/0.58 (step @p7 (= tptp.mor @t16) :rule refl :args (@t16)) % 0.37/0.58 (step @p8 (= tptp.mand @t17) :rule refl :args (@t17)) % 0.37/0.58 (step @p9 (= tptp.mimplies @t22) :rule refl :args (@t22)) % 0.37/0.58 (step @p10 (= tptp.mbox_s4 @t28) :rule refl :args (@t28)) % 0.37/0.58 (step @p11 (= tptp.iatom @t31) :rule refl :args (@t31)) % 0.37/0.58 (step @p12 (= tptp.inot @t33) :rule refl :args (@t33)) % 0.37/0.58 (step @p13 (= tptp.itrue @t36) :rule refl :args (@t36)) % 0.37/0.58 (step @p14 (= tptp.iand @t39) :rule refl :args (@t39)) % 0.37/0.58 (step @p15 (= tptp.ior @t41) :rule refl :args (@t41)) % 0.37/0.58 (step @p16 (= tptp.iimplies @t42) :rule refl :args (@t42)) % 0.37/0.58 (step @p17 (= tptp.iimplied @t44) :rule refl :args (@t44)) % 0.37/0.58 (step @p18 (= tptp.iequiv @t45) :rule refl :args (@t45)) % 0.37/0.58 (step @p19 (= tptp.ixor @t46) :rule refl :args (@t46)) % 0.37/0.58 (step @p20 (= tptp.ivalid @t51) :rule refl :args (@t51)) % 0.37/0.58 (step @p21 (= tptp.isatisfiable @t52) :rule refl :args (@t52)) % 0.37/0.58 (step @p22 (= tptp.icountersatisfiable @t54) :rule refl :args (@t54)) % 0.37/0.58 (step @p23 (= tptp.iinvalid @t55) :rule refl :args (@t55)) % 0.37/0.58 (step @p24 :rule evaluate :args ((not true))) % 0.37/0.58 (step @p25 :rule quant-unused-vars :args ((= (forall @t35 true) true))) % 0.37/0.58 (step @p26 :rule bool-or-taut2 :args (false @t57 false false)) % 0.37/0.58 (step @p27 :rule cong :premises (@p26) :args ((forall @t35 @t58))) % 0.37/0.58 (step @p28 :rule trans :premises (@p27 @p25)) % 0.37/0.58 (step @p29 :rule beta-reduce :args ((= @t65 @t58))) % 0.37/0.58 (step @p30 :rule cong :premises (@p29) :args (@t66)) % 0.37/0.58 (step @p31 :rule trans :premises (@p30 @p28)) % 0.37/0.58 (step @p32 :rule beta-reduce :args ((= (_ @t68 @t64) @t66))) % 0.37/0.58 (step @p33 :rule trans :premises (@p32 @p31)) % 0.37/0.58 (step @p34 :rule aci_norm :args ((= (and @t62 @t62) @t62))) % 0.37/0.58 (step @p35 :rule refl :args (@t60)) % 0.37/0.58 (step @p36 :rule refl :args (@t56)) % 0.37/0.58 (step @p37 :rule refl :args (@t69)) % 0.37/0.58 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t69 @t56))) % 0.37/0.58 (step @p39 :rule symm :premises (@p38)) % 0.37/0.58 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.37/0.58 (step @p41 :rule refl :args (@t59)) % 0.37/0.58 (step @p42 :rule nary_cong :premises (@p41 @p40) :args (@t70)) % 0.37/0.58 (step @p43 :rule cong :premises (@p42) :args ((forall @t25 @t70))) % 0.37/0.58 (step @p44 :rule beta-reduce :args ((= @t72 @t69))) % 0.37/0.58 (step @p45 :rule refl :args (@t59)) % 0.37/0.58 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t73)) % 0.37/0.58 (step @p47 :rule cong :premises (@p46) :args (@t74)) % 0.37/0.58 (step @p48 :rule trans :premises (@p47 @p43)) % 0.37/0.58 (step @p49 :rule cong :premises (@p48) :args (@t75)) % 0.37/0.58 (step @p50 :rule nary_cong :premises (@p49 @p35) :args (@t76)) % 0.37/0.58 (step @p51 :rule refl :args (@t61)) % 0.37/0.58 (step @p52 :rule nary_cong :premises (@p51 @p48) :args (@t77)) % 0.37/0.58 (step @p53 :rule nary_cong :premises (@p52 @p50) :args (@t78)) % 0.37/0.58 (step @p54 :rule trans :premises (@p53 @p34)) % 0.37/0.58 (step @p55 :rule cong :premises (@p54) :args (@t79)) % 0.37/0.58 (step @p56 :rule beta-reduce :args ((= (_ (lambda @t83 (and (or @t61 @t81) (or @t82 @t60))) @t71) @t79))) % 0.37/0.58 (step @p57 :rule trans :premises (@p56 @p55)) % 0.37/0.58 (step @p58 :rule beta-reduce :args ((= @t84 @t71))) % 0.37/0.58 (step @p59 :rule refl :args (@t82)) % 0.37/0.58 (step @p60 :rule nary_cong :premises (@p59 @p48) :args (@t85)) % 0.37/0.58 (step @p61 :rule refl :args (@t81)) % 0.37/0.58 (step @p62 :rule nary_cong :premises (@p49 @p61) :args (@t86)) % 0.37/0.58 (step @p63 :rule nary_cong :premises (@p62 @p60) :args (@t87)) % 0.37/0.58 (step @p64 :rule cong :premises (@p63) :args (@t88)) % 0.37/0.58 (step @p65 :rule beta-reduce :args ((= (_ @t95 @t71) @t88))) % 0.37/0.58 (step @p66 :rule trans :premises (@p65 @p64)) % 0.37/0.58 (step @p67 :rule refl :args (@t95)) % 0.37/0.58 (step @p68 :rule ho_cong :premises (@p67 @p58)) % 0.37/0.58 (step @p69 :rule trans :premises (@p68 @p66)) % 0.37/0.58 (step @p70 :rule ho_cong :premises (@p69 @p58)) % 0.37/0.58 (step @p71 :rule trans :premises (@p70 @p57)) % 0.37/0.58 (step @p72 :rule refl :args (@t68)) % 0.37/0.58 (step @p73 :rule ho_cong :premises (@p72 @p71)) % 0.37/0.58 (step @p74 :rule trans :premises (@p73 @p33)) % 0.37/0.58 (step @p75 :rule cong :premises (@p74) :args ((not (_ @t68 (_ (_ @t95 @t84) @t84))))) % 0.37/0.58 (step @p76 :rule trans :premises (@p75 @p24)) % 0.37/0.58 (step @p77 :rule refl :args (tptp.p)) % 0.37/0.58 (step @p78 :rule ho_cong :premises (@p11 @p77)) % 0.37/0.58 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t63 @t94) @t18) @t94))) % 0.37/0.58 (step @p80 :rule refl :args (@t18)) % 0.37/0.58 (step @p81 :rule beta-reduce :args ((= @t97 @t91))) % 0.37/0.58 (step @p82 :rule refl :args (@t93)) % 0.37/0.58 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t98)) % 0.37/0.58 (step @p84 :rule cong :premises (@p83) :args (@t99)) % 0.37/0.58 (step @p85 :rule beta-reduce :args ((= (_ (lambda @t102 (and @t93 @t101)) @t96) @t99))) % 0.37/0.58 (step @p86 :rule trans :premises (@p85 @p84)) % 0.37/0.58 (step @p87 :rule beta-reduce :args ((= (_ @t105 @t23) @t96))) % 0.37/0.58 (step @p88 :rule refl :args (@t23)) % 0.37/0.58 (step @p89 :rule beta-reduce :args ((= (_ (lambda (@list @t23 @t103 @t18) (or @t92 @t104)) @t37) @t105))) % 0.37/0.58 (step @p90 :rule refl :args (@t37)) % 0.37/0.58 (step @p91 :rule alpha_equiv :args (@t106 @t107 (@list @t103))) % 0.37/0.58 (step @p92 :rule ho_cong :premises (@p91 @p90)) % 0.37/0.58 (step @p93 :rule trans :premises (@p92 @p89)) % 0.37/0.58 (step @p94 :rule ho_cong :premises (@p93 @p88)) % 0.37/0.58 (step @p95 :rule trans :premises (@p94 @p87)) % 0.37/0.58 (step @p96 :rule refl :args (@t101)) % 0.37/0.58 (step @p97 :rule beta-reduce :args ((= @t109 @t93))) % 0.37/0.58 (step @p98 :rule nary_cong :premises (@p97 @p96) :args (@t110)) % 0.37/0.58 (step @p99 :rule cong :premises (@p98) :args (@t111)) % 0.37/0.58 (step @p100 :rule beta-reduce :args ((= (_ (lambda (@list @t23 @t100 @t18) (and @t29 @t101)) @t108) @t111))) % 0.37/0.58 (step @p101 :rule trans :premises (@p100 @p99)) % 0.37/0.58 (step @p102 :rule refl :args (@t108)) % 0.37/0.58 (step @p103 :rule alpha_equiv :args (@t113 @t107 (@list @t100))) % 0.37/0.58 (step @p104 :rule ho_cong :premises (@p103 @p102)) % 0.37/0.58 (step @p105 :rule trans :premises (@p104 @p101)) % 0.37/0.58 (step @p106 :rule beta-reduce :args ((= (_ @t114 @t37) @t108))) % 0.37/0.58 (step @p107 :rule refl :args (@t37)) % 0.37/0.58 (step @p108 :rule beta-reduce :args ((= (_ @t106 @t23) @t114))) % 0.37/0.58 (step @p109 :rule ho_cong :premises (@p108 @p107)) % 0.37/0.58 (step @p110 :rule trans :premises (@p109 @p106)) % 0.37/0.58 (step @p111 :rule refl :args (@t113)) % 0.37/0.58 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.37/0.58 (step @p113 :rule trans :premises (@p112 @p105)) % 0.37/0.58 (step @p114 :rule ho_cong :premises (@p113 @p95)) % 0.37/0.58 (step @p115 :rule trans :premises (@p114 @p86)) % 0.37/0.58 (step @p116 :rule ho_cong :premises (@p115 @p80)) % 0.37/0.58 (step @p117 :rule trans :premises (@p116 @p79)) % 0.37/0.58 (step @p118 :rule beta-reduce :args ((= @t118 @t81))) % 0.37/0.58 (step @p119 :rule refl :args (@t92)) % 0.37/0.58 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t119)) % 0.37/0.58 (step @p121 :rule cong :premises (@p120) :args (@t120)) % 0.37/0.58 (step @p122 :rule beta-reduce :args ((= (_ (lambda @t122 (or @t92 @t121)) @t117) @t120))) % 0.37/0.58 (step @p123 :rule trans :premises (@p122 @p121)) % 0.37/0.58 (step @p124 :rule beta-reduce :args ((= (_ @t124 @t37) @t117))) % 0.37/0.58 (step @p125 :rule refl :args (@t121)) % 0.37/0.58 (step @p126 :rule beta-reduce :args ((= @t126 @t90))) % 0.37/0.58 (step @p127 :rule cong :premises (@p126) :args (@t127)) % 0.37/0.58 (step @p128 :rule nary_cong :premises (@p127 @p125) :args (@t128)) % 0.37/0.58 (step @p129 :rule cong :premises (@p128) :args (@t129)) % 0.37/0.58 (step @p130 :rule beta-reduce :args ((= (_ @t131 @t125) @t129))) % 0.37/0.58 (step @p131 :rule trans :premises (@p130 @p129)) % 0.37/0.58 (step @p132 :rule beta-reduce :args ((= (_ @t124 @t23) @t125))) % 0.37/0.58 (step @p133 :rule refl :args (@t131)) % 0.37/0.58 (step @p134 :rule ho_cong :premises (@p133 @p132)) % 0.37/0.58 (step @p135 :rule trans :premises (@p134 @p131)) % 0.37/0.58 (step @p136 :rule ho_cong :premises (@p135 @p124)) % 0.37/0.58 (step @p137 :rule trans :premises (@p136 @p123)) % 0.37/0.58 (step @p138 :rule ho_cong :premises (@p137 @p80)) % 0.37/0.58 (step @p139 :rule trans :premises (@p138 @p97)) % 0.37/0.58 (step @p140 :rule refl :args (@t89)) % 0.37/0.58 (step @p141 :rule refl :args (@t24)) % 0.37/0.58 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t24 @t89))) % 0.37/0.58 (step @p143 :rule symm :premises (@p142)) % 0.37/0.58 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.37/0.58 (step @p145 :rule refl :args (@t115)) % 0.37/0.58 (step @p146 :rule refl :args (@t6)) % 0.37/0.58 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t6 @t115))) % 0.37/0.58 (step @p148 :rule symm :premises (@p147)) % 0.37/0.58 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.37/0.58 (step @p150 :rule cong :premises (@p149) :args (@t132)) % 0.37/0.58 (step @p151 :rule nary_cong :premises (@p150 @p144) :args (@t133)) % 0.37/0.58 (step @p152 :rule cong :premises (@p151) :args ((forall @t25 @t133))) % 0.37/0.58 (step @p153 :rule bool-impl-elim :args (@t6 @t24)) % 0.37/0.58 (step @p154 :rule cong :premises (@p153) :args (@t26)) % 0.37/0.58 (step @p155 :rule trans :premises (@p154 @p152)) % 0.37/0.58 (step @p156 :rule cong :premises (@p155) :args (@t28)) % 0.37/0.58 (step @p157 :rule trans :premises (@p10 @p156)) % 0.37/0.58 (step @p158 :rule ho_cong :premises (@p157 @p107)) % 0.37/0.58 (step @p159 :rule ho_cong :premises (@p157 @p88)) % 0.37/0.58 (step @p160 :rule beta-reduce :args ((= (_ @t136 @t18) @t130))) % 0.37/0.58 (step @p161 :rule beta-reduce :args ((= (_ (lambda @t137 (or @t134 @t14)) @t19) @t136))) % 0.37/0.58 (step @p162 :rule refl :args (@t19)) % 0.37/0.58 (step @p163 :rule refl :args (@t14)) % 0.37/0.58 (step @p164 :rule beta-reduce :args ((= @t139 @t134))) % 0.37/0.58 (step @p165 :rule nary_cong :premises (@p164 @p163) :args (@t140)) % 0.37/0.58 (step @p166 :rule cong :premises (@p165) :args (@t141)) % 0.37/0.58 (step @p167 :rule beta-reduce :args ((= (_ @t16 @t138) @t141))) % 0.37/0.58 (step @p168 :rule trans :premises (@p167 @p166)) % 0.37/0.58 (step @p169 :rule beta-reduce :args ((= (_ @t12 @t20) @t138))) % 0.37/0.58 (step @p170 :rule refl :args (@t16)) % 0.37/0.58 (step @p171 :rule ho_cong :premises (@p170 @p169)) % 0.37/0.58 (step @p172 :rule trans :premises (@p171 @p168)) % 0.37/0.58 (step @p173 :rule ho_cong :premises (@p172 @p162)) % 0.37/0.58 (step @p174 :rule trans :premises (@p173 @p161)) % 0.37/0.58 (step @p175 :rule ho_cong :premises (@p174 @p80)) % 0.37/0.58 (step @p176 :rule trans :premises (@p175 @p160)) % 0.37/0.58 (step @p177 :rule refl :args (@t20)) % 0.37/0.58 (step @p178 :rule ho_cong :premises (@p6 @p177)) % 0.37/0.58 (step @p179 :rule ho_cong :premises (@p7 @p178)) % 0.37/0.58 (step @p180 :rule ho_cong :premises (@p179 @p162)) % 0.37/0.58 (step @p181 :rule ho_cong :premises (@p180 @p80)) % 0.37/0.58 (step @p182 :rule trans :premises (@p181 @p176)) % 0.37/0.58 (step @p183 :rule cong :premises (@p182) :args (@t22)) % 0.37/0.58 (step @p184 :rule trans :premises (@p9 @p183)) % 0.37/0.58 (step @p185 :rule ho_cong :premises (@p184 @p159)) % 0.37/0.58 (step @p186 :rule ho_cong :premises (@p185 @p158)) % 0.37/0.58 (step @p187 :rule ho_cong :premises (@p186 @p80)) % 0.37/0.58 (step @p188 :rule trans :premises (@p187 @p139)) % 0.37/0.58 (step @p189 :rule cong :premises (@p188) :args (@t42)) % 0.37/0.58 (step @p190 :rule trans :premises (@p16 @p189)) % 0.37/0.58 (step @p191 :rule ho_cong :premises (@p190 @p107)) % 0.37/0.58 (step @p192 :rule ho_cong :premises (@p191 @p88)) % 0.37/0.58 (step @p193 :rule ho_cong :premises (@p190 @p88)) % 0.37/0.58 (step @p194 :rule ho_cong :premises (@p193 @p107)) % 0.37/0.58 (step @p195 :rule beta-reduce :args ((= (_ @t143 @t18) @t112))) % 0.37/0.58 (step @p196 :rule beta-reduce :args ((= (_ @t144 @t37) @t143))) % 0.37/0.58 (step @p197 :rule beta-reduce :args ((= (_ @t17 @t23) @t144))) % 0.37/0.58 (step @p198 :rule ho_cong :premises (@p197 @p107)) % 0.37/0.58 (step @p199 :rule trans :premises (@p198 @p196)) % 0.37/0.58 (step @p200 :rule ho_cong :premises (@p199 @p80)) % 0.37/0.58 (step @p201 :rule trans :premises (@p200 @p195)) % 0.37/0.58 (step @p202 :rule ho_cong :premises (@p8 @p88)) % 0.37/0.58 (step @p203 :rule ho_cong :premises (@p202 @p107)) % 0.37/0.58 (step @p204 :rule ho_cong :premises (@p203 @p80)) % 0.37/0.58 (step @p205 :rule trans :premises (@p204 @p201)) % 0.37/0.58 (step @p206 :rule cong :premises (@p205) :args (@t39)) % 0.37/0.58 (step @p207 :rule trans :premises (@p14 @p206)) % 0.37/0.58 (step @p208 :rule ho_cong :premises (@p207 @p194)) % 0.37/0.58 (step @p209 :rule ho_cong :premises (@p208 @p192)) % 0.37/0.58 (step @p210 :rule ho_cong :premises (@p209 @p80)) % 0.37/0.58 (step @p211 :rule trans :premises (@p210 @p117)) % 0.37/0.58 (step @p212 :rule cong :premises (@p211) :args (@t45)) % 0.37/0.58 (step @p213 :rule trans :premises (@p18 @p212)) % 0.37/0.58 (step @p214 :rule ho_cong :premises (@p213 @p78)) % 0.37/0.58 (step @p215 :rule ho_cong :premises (@p214 @p78)) % 0.37/0.58 (step @p216 :rule refl :args (@t67)) % 0.37/0.58 (step @p217 :rule refl :args (@t48)) % 0.37/0.58 (step @p218 :rule cong :premises (@p217 @p216) :args ((= @t48 @t67))) % 0.37/0.58 (step @p219 :rule symm :premises (@p218)) % 0.37/0.58 (step @p220 :rule eq_resolve :premises (@p217 @p219)) % 0.37/0.58 (step @p221 :rule cong :premises (@p220) :args (@t49)) % 0.37/0.58 (step @p222 :rule cong :premises (@p221) :args (@t51)) % 0.37/0.58 (step @p223 :rule trans :premises (@p20 @p222)) % 0.37/0.58 (step @p224 :rule ho_cong :premises (@p223 @p215)) % 0.37/0.58 (step @p225 :rule cong :premises (@p224) :args (@t8)) % 0.37/0.58 (step @p226 :rule trans :premises (@p225 @p76)) % 0.37/0.58 (step @p227 false :rule eq_resolve :premises (@p4 @p226)) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------