%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO066^4.001 : 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 : n005.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 09:11:55 AM UTC 2026 % Result : Theorem 0.41s 0.59s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SYO066^4.001 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n005.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 : Tue Jun 2 23:53:03 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.51 %----Proving TH0 % 0.41/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.41/0.59 % SZS status Theorem % 0.41/0.59 % SZS output start Proof % 0.41/0.59 ( % 0.41/0.59 (declare-sort $$unsorted 0) % 0.41/0.59 (declare-const tptp.irel (-> $$unsorted $$unsorted Bool)) % 0.41/0.59 (declare-const tptp.o21 (-> $$unsorted Bool)) % 0.41/0.59 (declare-const tptp.o11 (-> $$unsorted Bool)) % 0.41/0.59 (declare-const tptp.ifalse (-> $$unsorted Bool)) % 0.41/0.59 (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)))))) % 0.41/0.59 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.41/0.59 (define tptp.mand () (let ((_let_1 (@var "U" $$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))))))) % 0.41/0.59 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.41/0.59 (define tptp.mbox_s4 () (let ((_let_1 (@var "Y" $$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)))))))) % 0.41/0.59 (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))))) % 0.41/0.59 (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))))) % 0.41/0.59 (define tptp.itrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.41/0.59 (define tptp.iand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.59 (define tptp.ior () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mbox_s4 _let_3)) (_ tptp.mbox_s4 _let_2)) _let_1)))))) % 0.41/0.59 (define tptp.iimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.59 (define tptp.iimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Q" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.iimplies _let_3) _let_2) _let_1)))))) % 0.41/0.59 (define tptp.iequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.41/0.59 (define tptp.ixor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Q" (-> $$unsorted Bool)))) (let ((_let_3 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.inot (_ (_ tptp.iequiv _let_3) _let_2)) _let_1)))))) % 0.41/0.59 (define tptp.ivalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.41/0.59 (define tptp.isatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.41/0.59 (define tptp.icountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.41/0.59 (define tptp.iinvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.41/0.59 (define @t1 () (@var "X" $$unsorted)) % 0.41/0.59 (define @t2 () (_ tptp.irel @t1)) % 0.41/0.59 (define @t3 () (@list @t1)) % 0.41/0.59 (define @t4 () (@var "Z" $$unsorted)) % 0.41/0.59 (define @t5 () (@var "Y" $$unsorted)) % 0.41/0.59 (define @t6 () (_ @t2 @t5)) % 0.41/0.59 (define @t7 () (_ tptp.iatom tptp.o11)) % 0.41/0.59 (define @t8 () (_ tptp.iatom tptp.o21)) % 0.41/0.59 (define @t9 () (not (_ tptp.ivalid (_ (_ tptp.ior @t7) @t8)))) % 0.41/0.59 (define @t10 () (@var "U" $$unsorted)) % 0.41/0.59 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.41/0.59 (define @t12 () (_ @t11 @t10)) % 0.41/0.59 (define @t13 () (lambda (@list @t11 @t10) (not @t12))) % 0.41/0.59 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.41/0.59 (define @t15 () (_ @t14 @t10)) % 0.41/0.59 (define @t16 () (@list @t11 @t14 @t10)) % 0.41/0.59 (define @t17 () (lambda @t16 (or @t12 @t15))) % 0.41/0.59 (define @t18 () (lambda @t16 (and @t12 @t15))) % 0.41/0.59 (define @t19 () (@var "__flatten_var_0" $$unsorted)) % 0.41/0.59 (define @t20 () (@var "V" (-> $$unsorted Bool))) % 0.41/0.59 (define @t21 () (@var "U" (-> $$unsorted Bool))) % 0.41/0.59 (define @t22 () (lambda (@list @t21 @t20 @t19) (_ (_ (_ tptp.mor (_ tptp.mnot @t21)) @t20) @t19))) % 0.41/0.59 (define @t23 () (@var "P" (-> $$unsorted Bool))) % 0.41/0.59 (define @t24 () (_ @t23 @t5)) % 0.41/0.59 (define @t25 () (@list @t5)) % 0.41/0.59 (define @t26 () (forall @t25 (=> @t6 @t24))) % 0.41/0.59 (define @t27 () (@list @t23 @t1)) % 0.41/0.59 (define @t28 () (lambda @t27 @t26)) % 0.41/0.59 (define @t29 () (@list @t23 @t19)) % 0.41/0.59 (define @t30 () (lambda @t29 (_ @t23 @t19))) % 0.41/0.59 (define @t31 () (_ tptp.mbox_s4 @t23)) % 0.41/0.59 (define @t32 () (lambda @t29 (_ (_ tptp.mnot @t31) @t19))) % 0.41/0.59 (define @t33 () (@var "W" $$unsorted)) % 0.41/0.59 (define @t34 () (@list @t33)) % 0.41/0.59 (define @t35 () (lambda @t34 true)) % 0.41/0.59 (define @t36 () (@var "Q" (-> $$unsorted Bool))) % 0.41/0.59 (define @t37 () (@list @t23 @t36 @t19)) % 0.41/0.59 (define @t38 () (lambda @t37 (_ (_ (_ tptp.mand @t23) @t36) @t19))) % 0.41/0.59 (define @t39 () (_ tptp.mbox_s4 @t36)) % 0.41/0.59 (define @t40 () (lambda @t37 (_ (_ (_ tptp.mor @t31) @t39) @t19))) % 0.41/0.59 (define @t41 () (lambda @t37 (_ (_ (_ tptp.mimplies @t31) @t39) @t19))) % 0.41/0.59 (define @t42 () (_ (_ tptp.iimplies @t36) @t23)) % 0.41/0.59 (define @t43 () (lambda @t37 (_ @t42 @t19))) % 0.41/0.59 (define @t44 () (lambda @t37 (_ (_ (_ tptp.iand (_ (_ tptp.iimplies @t23) @t36)) @t42) @t19))) % 0.41/0.59 (define @t45 () (lambda @t37 (_ (_ tptp.inot (_ (_ tptp.iequiv @t23) @t36)) @t19))) % 0.41/0.59 (define @t46 () (@var "Phi" (-> $$unsorted Bool))) % 0.41/0.59 (define @t47 () (_ @t46 @t33)) % 0.41/0.59 (define @t48 () (forall @t34 @t47)) % 0.41/0.59 (define @t49 () (@list @t46)) % 0.41/0.59 (define @t50 () (lambda @t49 @t48)) % 0.41/0.59 (define @t51 () (lambda @t49 (exists @t34 @t47))) % 0.41/0.59 (define @t52 () (not @t47)) % 0.41/0.59 (define @t53 () (lambda @t49 (exists @t34 @t52))) % 0.41/0.59 (define @t54 () (lambda @t49 (forall @t34 @t52))) % 0.41/0.59 (define @t55 () (tptp.o11 @t33)) % 0.41/0.59 (define @t56 () (_ tptp.o11 @t33)) % 0.41/0.59 (define @t57 () (@list @t19)) % 0.41/0.59 (define @t58 () (lambda @t57 (_ tptp.o11 @t19))) % 0.41/0.59 (define @t59 () (_ @t58 @t33)) % 0.41/0.59 (define @t60 () (forall @t34 @t59)) % 0.41/0.59 (define @t61 () (_ @t46 @t33)) % 0.41/0.59 (define @t62 () (lambda @t49 (forall @t34 @t61))) % 0.41/0.59 (define @t63 () (_ @t30 tptp.o11)) % 0.41/0.59 (define @t64 () (@var "BOUND_VARIABLE_8086" $$unsorted)) % 0.41/0.59 (define @t65 () (tptp.o21 @t64)) % 0.41/0.59 (define @t66 () (not (tptp.irel @t33 @t64))) % 0.41/0.59 (define @t67 () (@var "BOUND_VARIABLE_8080" $$unsorted)) % 0.41/0.59 (define @t68 () (tptp.o11 @t67)) % 0.41/0.59 (define @t69 () (not (tptp.irel @t33 @t67))) % 0.41/0.59 (define @t70 () (or @t69 @t68 @t66 @t65)) % 0.41/0.59 (define @t71 () (or @t66 @t65)) % 0.41/0.59 (define @t72 () (or @t69 @t68)) % 0.41/0.59 (define @t73 () (or @t72 @t71)) % 0.41/0.59 (define @t74 () (@list @t33 @t67 @t64)) % 0.41/0.59 (define @t75 () (forall @t74 @t73)) % 0.41/0.59 (define @t76 () (forall (@list @t67 @t64) @t73)) % 0.41/0.59 (define @t77 () (forall (@list @t64) @t71)) % 0.41/0.59 (define @t78 () (@list @t5)) % 0.41/0.59 (define @t79 () (forall (@list @t67) @t72)) % 0.41/0.59 (define @t80 () (or @t79 @t77)) % 0.41/0.59 (define @t81 () (tptp.o21 @t5)) % 0.41/0.59 (define @t82 () (not (tptp.irel @t33 @t5))) % 0.41/0.59 (define @t83 () (tptp.o11 @t5)) % 0.41/0.59 (define @t84 () (or (forall @t25 (or @t82 @t83)) (forall @t25 (or @t82 @t81)))) % 0.41/0.59 (define @t85 () (not (tptp.irel @t19 @t5))) % 0.41/0.59 (define @t86 () (forall @t25 (or @t85 @t83))) % 0.41/0.59 (define @t87 () (lambda @t57 (or @t86 (forall @t25 (or @t85 @t81))))) % 0.41/0.59 (define @t88 () (_ @t87 @t33)) % 0.41/0.59 (define @t89 () (forall @t34 @t88)) % 0.41/0.59 (define @t90 () (_ tptp.o21 @t5)) % 0.41/0.59 (define @t91 () (or @t85 @t90)) % 0.41/0.59 (define @t92 () (lambda @t57 (_ tptp.o21 @t19))) % 0.41/0.59 (define @t93 () (_ @t92 @t5)) % 0.41/0.59 (define @t94 () (or @t85 @t93)) % 0.41/0.59 (define @t95 () (forall @t25 @t94)) % 0.41/0.59 (define @t96 () (or @t86 @t95)) % 0.41/0.59 (define @t97 () (lambda @t57 @t96)) % 0.41/0.59 (define @t98 () (_ @t36 @t5)) % 0.41/0.59 (define @t99 () (forall @t25 (or @t85 @t98))) % 0.41/0.59 (define @t100 () (@list @t36 @t19)) % 0.41/0.59 (define @t101 () (_ @t30 tptp.o21)) % 0.41/0.59 (define @t102 () (_ tptp.o11 @t5)) % 0.41/0.59 (define @t103 () (or @t85 @t102)) % 0.41/0.59 (define @t104 () (_ @t58 @t5)) % 0.41/0.59 (define @t105 () (or @t85 @t104)) % 0.41/0.59 (define @t106 () (forall @t25 @t105)) % 0.41/0.59 (define @t107 () (or @t106 @t99)) % 0.41/0.59 (define @t108 () (lambda @t100 @t107)) % 0.41/0.59 (define @t109 () (_ @t23 @t5)) % 0.41/0.59 (define @t110 () (or (forall @t25 (or @t85 @t109)) @t99)) % 0.41/0.59 (define @t111 () (lambda @t37 @t110)) % 0.41/0.59 (define @t112 () (not (tptp.irel @t10 @t5))) % 0.41/0.59 (define @t113 () (forall @t25 (or @t112 @t98))) % 0.41/0.59 (define @t114 () (forall @t25 (or @t112 @t109))) % 0.41/0.59 (define @t115 () (@list @t10)) % 0.41/0.59 (define @t116 () (tptp.irel @t1 @t5)) % 0.41/0.59 (define @t117 () (not @t116)) % 0.41/0.59 (define @t118 () (lambda @t3 (forall @t25 (or @t117 @t98)))) % 0.41/0.59 (define @t119 () (_ @t118 @t10)) % 0.41/0.59 (define @t120 () (or @t114 @t119)) % 0.41/0.59 (define @t121 () (lambda @t115 @t120)) % 0.41/0.59 (define @t122 () (@list @t14 @t10)) % 0.41/0.59 (define @t123 () (forall @t25 (or @t117 @t109))) % 0.41/0.59 (define @t124 () (lambda @t27 @t123)) % 0.41/0.59 (define @t125 () (lambda @t3 @t123)) % 0.41/0.59 (define @t126 () (_ @t125 @t10)) % 0.41/0.59 (define @t127 () (or @t126 @t15)) % 0.41/0.59 (define @t128 () (lambda @t122 @t127)) % 0.41/0.59 (define @t129 () (not @t6)) % 0.41/0.59 (define @t130 () (or @t129 @t24)) % 0.41/0.59 (define @t131 () (forall @t74 @t70)) % 0.41/0.59 (define @t132 () (@quantifiers_skolemize @t131 2)) % 0.41/0.59 (define @t133 () (@quantifiers_skolemize @t131 0)) % 0.41/0.59 (define @t134 () (@quantifiers_skolemize @t131 1)) % 0.41/0.59 (define @t135 () (tptp.o11 @t134)) % 0.41/0.59 (define @t136 () (or (not (tptp.irel @t133 @t134)) @t135 (not (tptp.irel @t133 @t132)) (tptp.o21 @t132))) % 0.41/0.59 (define @t137 () (forall @t34 @t55)) % 0.41/0.59 (assume @p1 (forall @t3 (_ @t2 @t1))) % 0.41/0.59 (assume @p2 (forall (@list @t1 @t5 @t4) (=> (and @t6 (_ (_ tptp.irel @t5) @t4)) (_ @t2 @t4)))) % 0.41/0.59 (assume @p3 (= tptp.ifalse (_ tptp.inot tptp.itrue))) % 0.41/0.59 (assume @p4 (_ tptp.ivalid @t7)) % 0.41/0.59 (assume @p5 (_ tptp.ivalid @t8)) % 0.41/0.59 (assume @p6 @t9) % 0.41/0.59 (assume @p7 true) % 0.41/0.59 (step @p8 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.41/0.59 (step @p9 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.41/0.59 (step @p10 (= tptp.mand @t18) :rule refl :args (@t18)) % 0.41/0.59 (step @p11 (= tptp.mimplies @t22) :rule refl :args (@t22)) % 0.41/0.59 (step @p12 (= tptp.mbox_s4 @t28) :rule refl :args (@t28)) % 0.41/0.59 (step @p13 (= tptp.iatom @t30) :rule refl :args (@t30)) % 0.41/0.59 (step @p14 (= tptp.inot @t32) :rule refl :args (@t32)) % 0.41/0.59 (step @p15 (= tptp.itrue @t35) :rule refl :args (@t35)) % 0.41/0.59 (step @p16 (= tptp.iand @t38) :rule refl :args (@t38)) % 0.41/0.59 (step @p17 (= tptp.ior @t40) :rule refl :args (@t40)) % 0.41/0.59 (step @p18 (= tptp.iimplies @t41) :rule refl :args (@t41)) % 0.41/0.59 (step @p19 (= tptp.iimplied @t43) :rule refl :args (@t43)) % 0.41/0.59 (step @p20 (= tptp.iequiv @t44) :rule refl :args (@t44)) % 0.41/0.59 (step @p21 (= tptp.ixor @t45) :rule refl :args (@t45)) % 0.41/0.59 (step @p22 (= tptp.ivalid @t50) :rule refl :args (@t50)) % 0.41/0.59 (step @p23 (= tptp.isatisfiable @t51) :rule refl :args (@t51)) % 0.41/0.59 (step @p24 (= tptp.icountersatisfiable @t53) :rule refl :args (@t53)) % 0.41/0.59 (step @p25 (= tptp.iinvalid @t54) :rule refl :args (@t54)) % 0.41/0.59 (step @p26 :rule refl :args (@t55)) % 0.41/0.59 (step @p27 :rule refl :args (@t56)) % 0.41/0.59 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t56 @t55))) % 0.41/0.59 (step @p29 :rule symm :premises (@p28)) % 0.41/0.59 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.41/0.59 (step @p31 :rule cong :premises (@p30) :args ((forall @t34 @t56))) % 0.41/0.59 (step @p32 :rule beta-reduce :args ((= @t59 @t56))) % 0.41/0.59 (step @p33 :rule cong :premises (@p32) :args (@t60)) % 0.41/0.59 (step @p34 :rule trans :premises (@p33 @p31)) % 0.41/0.59 (step @p35 :rule beta-reduce :args ((= (_ @t62 @t58) @t60))) % 0.41/0.59 (step @p36 :rule trans :premises (@p35 @p34)) % 0.41/0.59 (step @p37 :rule beta-reduce :args ((= @t63 @t58))) % 0.41/0.59 (step @p38 :rule refl :args (@t62)) % 0.41/0.59 (step @p39 :rule ho_cong :premises (@p38 @p37)) % 0.41/0.59 (step @p40 :rule trans :premises (@p39 @p36)) % 0.41/0.59 (step @p41 :rule refl :args (tptp.o11)) % 0.41/0.59 (step @p42 :rule ho_cong :premises (@p13 @p41)) % 0.41/0.59 (step @p43 :rule refl :args (@t61)) % 0.41/0.59 (step @p44 :rule refl :args (@t47)) % 0.41/0.59 (step @p45 :rule cong :premises (@p44 @p43) :args ((= @t47 @t61))) % 0.41/0.59 (step @p46 :rule symm :premises (@p45)) % 0.41/0.59 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.41/0.59 (step @p48 :rule cong :premises (@p47) :args (@t48)) % 0.41/0.59 (step @p49 :rule cong :premises (@p48) :args (@t50)) % 0.41/0.59 (step @p50 :rule trans :premises (@p22 @p49)) % 0.41/0.59 (step @p51 :rule ho_cong :premises (@p50 @p42)) % 0.41/0.59 (step @p52 :rule trans :premises (@p51 @p40)) % 0.41/0.59 (step @p53 :rule eq_resolve :premises (@p4 @p52)) % 0.41/0.59 (step @p54 :rule aci_norm :args ((= @t73 @t70))) % 0.41/0.59 (step @p55 :rule cong :premises (@p54) :args (@t75)) % 0.41/0.59 (step @p56 :rule quant-merge-prenex :args ((= (forall @t34 @t76) @t75))) % 0.41/0.59 (step @p57 :rule alpha_equiv :args (@t77 (@list @t64) @t78)) % 0.41/0.59 (step @p58 :rule alpha_equiv :args (@t79 (@list @t67) @t78)) % 0.41/0.59 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t80)) % 0.41/0.59 (step @p60 :rule quant-miniscope-or :args ((= @t76 @t80))) % 0.41/0.59 (step @p61 :rule trans :premises (@p60 @p59)) % 0.41/0.59 (step @p62 :rule symm :premises (@p61)) % 0.41/0.59 (step @p63 :rule cong :premises (@p62) :args ((forall @t34 @t84))) % 0.41/0.59 (step @p64 :rule trans :premises (@p63 @p56)) % 0.41/0.59 (step @p65 :rule trans :premises (@p64 @p55)) % 0.41/0.59 (step @p66 :rule beta-reduce :args ((= @t88 @t84))) % 0.41/0.59 (step @p67 :rule cong :premises (@p66) :args (@t89)) % 0.41/0.59 (step @p68 :rule trans :premises (@p67 @p65)) % 0.41/0.59 (step @p69 :rule beta-reduce :args ((= (_ @t62 @t87) @t89))) % 0.41/0.59 (step @p70 :rule trans :premises (@p69 @p68)) % 0.41/0.59 (step @p71 :rule refl :args (@t81)) % 0.41/0.59 (step @p72 :rule refl :args (@t90)) % 0.41/0.59 (step @p73 :rule cong :premises (@p72 @p71) :args ((= @t90 @t81))) % 0.41/0.59 (step @p74 :rule symm :premises (@p73)) % 0.41/0.59 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 0.41/0.59 (step @p76 :rule refl :args (@t85)) % 0.41/0.59 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t91)) % 0.41/0.59 (step @p78 :rule cong :premises (@p77) :args ((forall @t25 @t91))) % 0.41/0.59 (step @p79 :rule beta-reduce :args ((= @t93 @t90))) % 0.41/0.59 (step @p80 :rule refl :args (@t85)) % 0.41/0.59 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t94)) % 0.41/0.59 (step @p82 :rule cong :premises (@p81) :args (@t95)) % 0.41/0.59 (step @p83 :rule trans :premises (@p82 @p78)) % 0.41/0.59 (step @p84 :rule refl :args (@t86)) % 0.41/0.59 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t96)) % 0.41/0.59 (step @p86 :rule cong :premises (@p85) :args (@t97)) % 0.41/0.59 (step @p87 :rule beta-reduce :args ((= (_ (lambda @t100 (or @t86 @t99)) @t92) @t97))) % 0.41/0.59 (step @p88 :rule trans :premises (@p87 @p86)) % 0.41/0.59 (step @p89 :rule beta-reduce :args ((= @t101 @t92))) % 0.41/0.59 (step @p90 :rule refl :args (@t99)) % 0.41/0.59 (step @p91 :rule refl :args (@t83)) % 0.41/0.59 (step @p92 :rule refl :args (@t102)) % 0.41/0.59 (step @p93 :rule cong :premises (@p92 @p91) :args ((= @t102 @t83))) % 0.41/0.59 (step @p94 :rule symm :premises (@p93)) % 0.41/0.59 (step @p95 :rule eq_resolve :premises (@p92 @p94)) % 0.41/0.59 (step @p96 :rule nary_cong :premises (@p76 @p95) :args (@t103)) % 0.41/0.59 (step @p97 :rule cong :premises (@p96) :args ((forall @t25 @t103))) % 0.41/0.59 (step @p98 :rule beta-reduce :args ((= @t104 @t102))) % 0.41/0.59 (step @p99 :rule nary_cong :premises (@p80 @p98) :args (@t105)) % 0.41/0.59 (step @p100 :rule cong :premises (@p99) :args (@t106)) % 0.41/0.59 (step @p101 :rule trans :premises (@p100 @p97)) % 0.41/0.59 (step @p102 :rule nary_cong :premises (@p101 @p90) :args (@t107)) % 0.41/0.59 (step @p103 :rule cong :premises (@p102) :args (@t108)) % 0.41/0.59 (step @p104 :rule beta-reduce :args ((= (_ @t111 @t58) @t108))) % 0.41/0.59 (step @p105 :rule trans :premises (@p104 @p103)) % 0.41/0.59 (step @p106 :rule refl :args (@t111)) % 0.41/0.59 (step @p107 :rule ho_cong :premises (@p106 @p37)) % 0.41/0.59 (step @p108 :rule trans :premises (@p107 @p105)) % 0.41/0.59 (step @p109 :rule ho_cong :premises (@p108 @p89)) % 0.41/0.59 (step @p110 :rule trans :premises (@p109 @p88)) % 0.41/0.59 (step @p111 :rule ho_cong :premises (@p38 @p110)) % 0.41/0.59 (step @p112 :rule trans :premises (@p111 @p70)) % 0.41/0.59 (step @p113 :rule cong :premises (@p112) :args ((not (_ @t62 (_ (_ @t111 @t63) @t101))))) % 0.41/0.59 (step @p114 :rule refl :args (tptp.o21)) % 0.41/0.59 (step @p115 :rule ho_cong :premises (@p13 @p114)) % 0.41/0.59 (step @p116 :rule beta-reduce :args ((= (_ (lambda @t115 (or @t114 @t113)) @t19) @t110))) % 0.41/0.59 (step @p117 :rule refl :args (@t19)) % 0.41/0.59 (step @p118 :rule beta-reduce :args ((= @t119 @t113))) % 0.41/0.59 (step @p119 :rule refl :args (@t114)) % 0.41/0.59 (step @p120 :rule nary_cong :premises (@p119 @p118) :args (@t120)) % 0.41/0.59 (step @p121 :rule cong :premises (@p120) :args (@t121)) % 0.41/0.59 (step @p122 :rule beta-reduce :args ((= (_ (lambda @t122 (or @t114 @t15)) @t118) @t121))) % 0.41/0.59 (step @p123 :rule trans :premises (@p122 @p121)) % 0.41/0.59 (step @p124 :rule beta-reduce :args ((= (_ @t124 @t36) @t118))) % 0.41/0.59 (step @p125 :rule refl :args (@t15)) % 0.41/0.59 (step @p126 :rule beta-reduce :args ((= @t126 @t114))) % 0.41/0.59 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t127)) % 0.41/0.59 (step @p128 :rule cong :premises (@p127) :args (@t128)) % 0.41/0.59 (step @p129 :rule beta-reduce :args ((= (_ @t17 @t125) @t128))) % 0.41/0.59 (step @p130 :rule trans :premises (@p129 @p128)) % 0.41/0.59 (step @p131 :rule beta-reduce :args ((= (_ @t124 @t23) @t125))) % 0.41/0.59 (step @p132 :rule refl :args (@t17)) % 0.41/0.59 (step @p133 :rule ho_cong :premises (@p132 @p131)) % 0.41/0.59 (step @p134 :rule trans :premises (@p133 @p130)) % 0.41/0.59 (step @p135 :rule ho_cong :premises (@p134 @p124)) % 0.41/0.59 (step @p136 :rule trans :premises (@p135 @p123)) % 0.41/0.59 (step @p137 :rule ho_cong :premises (@p136 @p117)) % 0.41/0.59 (step @p138 :rule trans :premises (@p137 @p116)) % 0.41/0.59 (step @p139 :rule refl :args (@t36)) % 0.41/0.59 (step @p140 :rule refl :args (@t109)) % 0.41/0.59 (step @p141 :rule refl :args (@t24)) % 0.41/0.59 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t24 @t109))) % 0.41/0.59 (step @p143 :rule symm :premises (@p142)) % 0.41/0.59 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.41/0.59 (step @p145 :rule refl :args (@t116)) % 0.41/0.59 (step @p146 :rule refl :args (@t6)) % 0.41/0.59 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t6 @t116))) % 0.41/0.59 (step @p148 :rule symm :premises (@p147)) % 0.41/0.59 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.41/0.59 (step @p150 :rule cong :premises (@p149) :args (@t129)) % 0.41/0.59 (step @p151 :rule nary_cong :premises (@p150 @p144) :args (@t130)) % 0.41/0.59 (step @p152 :rule cong :premises (@p151) :args ((forall @t25 @t130))) % 0.41/0.59 (step @p153 :rule bool-impl-elim :args (@t6 @t24)) % 0.41/0.59 (step @p154 :rule cong :premises (@p153) :args (@t26)) % 0.41/0.59 (step @p155 :rule trans :premises (@p154 @p152)) % 0.41/0.59 (step @p156 :rule cong :premises (@p155) :args (@t28)) % 0.41/0.59 (step @p157 :rule trans :premises (@p12 @p156)) % 0.41/0.59 (step @p158 :rule ho_cong :premises (@p157 @p139)) % 0.41/0.59 (step @p159 :rule refl :args (@t23)) % 0.41/0.59 (step @p160 :rule ho_cong :premises (@p157 @p159)) % 0.41/0.59 (step @p161 :rule ho_cong :premises (@p9 @p160)) % 0.41/0.59 (step @p162 :rule ho_cong :premises (@p161 @p158)) % 0.41/0.59 (step @p163 :rule ho_cong :premises (@p162 @p117)) % 0.41/0.59 (step @p164 :rule trans :premises (@p163 @p138)) % 0.41/0.59 (step @p165 :rule cong :premises (@p164) :args (@t40)) % 0.41/0.59 (step @p166 :rule trans :premises (@p17 @p165)) % 0.41/0.59 (step @p167 :rule ho_cong :premises (@p166 @p42)) % 0.41/0.59 (step @p168 :rule ho_cong :premises (@p167 @p115)) % 0.41/0.59 (step @p169 :rule ho_cong :premises (@p50 @p168)) % 0.41/0.59 (step @p170 :rule cong :premises (@p169) :args (@t9)) % 0.41/0.59 (step @p171 :rule trans :premises (@p170 @p113)) % 0.41/0.59 (step @p172 :rule eq_resolve :premises (@p6 @p171)) % 0.41/0.59 (step @p173 :rule skolemize :premises (@p172)) % 0.41/0.59 (step @p174 :rule cnf_or_neg :args (@t136 1)) % 0.41/0.59 (step @p175 :rule chain_m_resolution :premises (@p174 @p173) :args ((not @t135) (@list true) (@list @t136))) % 0.41/0.59 (assume-push @p182 @t137) % 0.41/0.59 (step @p177 :rule instantiate :premises (@p53) :args ((@list @t134))) % 0.41/0.59 (step-pop @p183 :rule scope :premises (@p177)) % 0.41/0.59 (step @p178 :rule process_scope :premises (@p183) :args (@t135)) % 0.41/0.59 (step @p180 :rule implies_elim :premises (@p178)) % 0.41/0.59 (step @p181 false :rule chain_m_resolution :premises (@p180 @p175 @p53) :args (false (@list true false) (@list @t135 @t137))) % 0.41/0.59 ) % 0.41/0.59 % SZS output end Proof % 0.41/0.59 % cvc5 exiting %------------------------------------------------------------------------------