%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV245^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n026.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:55:40 AM UTC 2026 % Result : Theorem 0.38s 0.61s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEV245^5 : TPTP v9.2.1. Released v4.0.0. % 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 : n026.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 18:22:25 EDT 2026 % 0.17/0.36 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.38/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.61 % SZS status Theorem % 0.38/0.61 % SZS output start Proof % 0.38/0.61 ( % 0.38/0.61 (declare-sort $$unsorted 0) % 0.38/0.61 (define @t1 () (@var "Xx" $$unsorted)) % 0.38/0.61 (define @t2 () (@var "Xx0" $$unsorted)) % 0.38/0.61 (define @t3 () (@var "S" (-> $$unsorted Bool))) % 0.38/0.61 (define @t4 () (_ @t3 @t2)) % 0.38/0.61 (define @t5 () (@var "Xx1" $$unsorted)) % 0.38/0.61 (define @t6 () (@var "K" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.38/0.61 (define @t7 () (_ @t6 @t3)) % 0.38/0.61 (define @t8 () (_ @t7 @t5)) % 0.38/0.61 (define @t9 () (_ @t3 @t5)) % 0.38/0.61 (define @t10 () (@list @t5)) % 0.38/0.61 (define @t11 () (forall @t10 (=> @t9 @t8))) % 0.38/0.61 (define @t12 () (and @t11 @t4)) % 0.38/0.61 (define @t13 () (@list @t3)) % 0.38/0.61 (define @t14 () (exists @t13 @t12)) % 0.38/0.61 (define @t15 () (@list @t2)) % 0.38/0.61 (define @t16 () (lambda @t15 @t14)) % 0.38/0.61 (define @t17 () (_ @t3 @t1)) % 0.38/0.61 (define @t18 () (_ @t7 @t2)) % 0.38/0.61 (define @t19 () (forall @t15 (=> @t4 @t18))) % 0.38/0.61 (define @t20 () (and @t19 @t17)) % 0.38/0.61 (define @t21 () (exists @t13 @t20)) % 0.38/0.61 (define @t22 () (=> @t21 (_ (_ @t6 @t16) @t1))) % 0.38/0.61 (define @t23 () (@list @t1)) % 0.38/0.61 (define @t24 () (forall @t23 @t22)) % 0.38/0.61 (define @t25 () (@var "Xy" (-> $$unsorted Bool))) % 0.38/0.61 (define @t26 () (_ (_ @t6 @t25) @t2)) % 0.38/0.61 (define @t27 () (@var "Xx" (-> $$unsorted Bool))) % 0.38/0.61 (define @t28 () (_ (_ @t6 @t27) @t2)) % 0.38/0.61 (define @t29 () (forall @t15 (=> @t28 @t26))) % 0.38/0.61 (define @t30 () (_ @t25 @t2)) % 0.38/0.61 (define @t31 () (_ @t27 @t2)) % 0.38/0.61 (define @t32 () (forall @t15 (=> @t31 @t30))) % 0.38/0.61 (define @t33 () (=> @t32 @t29)) % 0.38/0.61 (define @t34 () (@list @t27 @t25)) % 0.38/0.61 (define @t35 () (forall @t34 @t33)) % 0.38/0.61 (define @t36 () (=> @t35 @t24)) % 0.38/0.61 (define @t37 () (@list @t6)) % 0.38/0.61 (define @t38 () (forall @t37 @t36)) % 0.38/0.61 (define @t39 () (not @t38)) % 0.38/0.61 (define @t40 () (_ @t3 @t2)) % 0.38/0.61 (define @t41 () (not @t40)) % 0.38/0.61 (define @t42 () (@var "BOUND_VARIABLE_7559" $$unsorted)) % 0.38/0.61 (define @t43 () (@var "BOUND_VARIABLE_7561" (-> $$unsorted Bool))) % 0.38/0.61 (define @t44 () (not (_ @t43 @t42))) % 0.38/0.61 (define @t45 () (not (forall @t15 (or (not (_ @t43 @t2)) (_ @t6 @t43 @t2))))) % 0.38/0.61 (define @t46 () (_ @t6 @t3 @t5)) % 0.38/0.61 (define @t47 () (_ @t3 @t5)) % 0.38/0.61 (define @t48 () (not @t47)) % 0.38/0.61 (define @t49 () (or @t48 @t46)) % 0.38/0.61 (define @t50 () (forall @t10 @t49)) % 0.38/0.61 (define @t51 () (not @t50)) % 0.38/0.61 (define @t52 () (or @t51 @t41)) % 0.38/0.61 (define @t53 () (forall @t13 @t52)) % 0.38/0.61 (define @t54 () (not @t53)) % 0.38/0.61 (define @t55 () (lambda @t15 @t54)) % 0.38/0.61 (define @t56 () (_ @t6 @t55 @t42)) % 0.38/0.61 (define @t57 () (@var "BOUND_VARIABLE_7476" $$unsorted)) % 0.38/0.61 (define @t58 () (_ @t6 @t25 @t57)) % 0.38/0.61 (define @t59 () (not (_ @t6 @t27 @t57))) % 0.38/0.61 (define @t60 () (_ @t25 @t2)) % 0.38/0.61 (define @t61 () (_ @t27 @t2)) % 0.38/0.61 (define @t62 () (forall @t15 (or (not @t61) @t60))) % 0.38/0.61 (define @t63 () (not @t62)) % 0.38/0.61 (define @t64 () (or @t63 @t59 @t58)) % 0.38/0.61 (define @t65 () (@list @t27 @t25 @t57)) % 0.38/0.61 (define @t66 () (forall @t65 @t64)) % 0.38/0.61 (define @t67 () (not @t66)) % 0.38/0.61 (define @t68 () (or @t67 @t56 @t45 @t44)) % 0.38/0.61 (define @t69 () (@list @t6 @t42 @t43)) % 0.38/0.61 (define @t70 () (forall @t69 @t68)) % 0.38/0.61 (define @t71 () (@quantifiers_skolemize @t70 0)) % 0.38/0.61 (define @t72 () (not (forall @t10 (or @t48 (_ @t71 @t3 @t5))))) % 0.38/0.61 (define @t73 () (not (forall @t13 (or @t72 @t41)))) % 0.38/0.61 (define @t74 () (lambda @t15 @t73)) % 0.38/0.61 (define @t75 () (@purify @t74)) % 0.38/0.61 (define @t76 () (_ @t75 @t2)) % 0.38/0.61 (define @t77 () (_ @t74 @t2)) % 0.38/0.61 (define @t78 () (= @t76 @t77)) % 0.38/0.61 (define @t79 () (forall @t15 @t78)) % 0.38/0.61 (define @t80 () (@quantifiers_skolemize @t70 2)) % 0.38/0.61 (define @t81 () (not (_ @t80 @t2))) % 0.38/0.61 (define @t82 () (forall @t15 (or @t81 @t76))) % 0.38/0.61 (define @t83 () (@quantifiers_skolemize @t82 0)) % 0.38/0.61 (define @t84 () (forall @t13 (or @t72 (not (_ @t3 @t83))))) % 0.38/0.61 (define @t85 () (not @t84)) % 0.38/0.61 (define @t86 () (_ @t75 @t83)) % 0.38/0.61 (define @t87 () (forall @t15 (= @t73 @t76))) % 0.38/0.61 (define @t88 () (= @t85 @t86)) % 0.38/0.61 (define @t89 () (= @t86 @t85)) % 0.38/0.61 (define @t90 () (@list false)) % 0.38/0.61 (define @t91 () (or @t56 @t45 @t44)) % 0.38/0.61 (define @t92 () (or @t67 @t91)) % 0.38/0.61 (define @t93 () (forall @t69 @t92)) % 0.38/0.61 (define @t94 () (@list @t42 @t43)) % 0.38/0.61 (define @t95 () (forall @t94 @t92)) % 0.38/0.61 (define @t96 () (forall @t94 @t91)) % 0.38/0.61 (define @t97 () (@var "BOUND_VARIABLE_7538" (-> $$unsorted Bool))) % 0.38/0.61 (define @t98 () (or @t67 @t96)) % 0.38/0.61 (define @t99 () (not (_ @t97 @t1))) % 0.38/0.61 (define @t100 () (not (forall @t15 (or (not (_ @t97 @t2)) (_ @t6 @t97 @t2))))) % 0.38/0.61 (define @t101 () (_ @t6 @t55 @t1)) % 0.38/0.61 (define @t102 () (or @t101 @t100 @t99)) % 0.38/0.61 (define @t103 () (@list @t1 @t97)) % 0.38/0.61 (define @t104 () (forall @t103 @t102)) % 0.38/0.61 (define @t105 () (or @t100 @t99)) % 0.38/0.61 (define @t106 () (or @t105 @t101)) % 0.38/0.61 (define @t107 () (forall @t103 @t106)) % 0.38/0.61 (define @t108 () (@list @t97)) % 0.38/0.61 (define @t109 () (forall @t108 @t106)) % 0.38/0.61 (define @t110 () (forall @t108 @t105)) % 0.38/0.61 (define @t111 () (or @t110 @t101)) % 0.38/0.61 (define @t112 () (_ @t3 @t1)) % 0.38/0.61 (define @t113 () (_ @t6 @t3 @t2)) % 0.38/0.61 (define @t114 () (forall @t15 (or @t41 @t113))) % 0.38/0.61 (define @t115 () (not @t114)) % 0.38/0.61 (define @t116 () (forall @t13 (or @t115 (not @t112)))) % 0.38/0.61 (define @t117 () (not @t4)) % 0.38/0.61 (define @t118 () (not @t9)) % 0.38/0.61 (define @t119 () (or @t118 @t8)) % 0.38/0.61 (define @t120 () (forall @t10 @t119)) % 0.38/0.61 (define @t121 () (lambda @t15 (not (forall @t13 (or (not @t120) @t117))))) % 0.38/0.61 (define @t122 () (_ (_ @t6 @t55) @t1)) % 0.38/0.61 (define @t123 () (or @t116 @t122)) % 0.38/0.61 (define @t124 () (not @t116)) % 0.38/0.61 (define @t125 () (or @t51 @t117)) % 0.38/0.61 (define @t126 () (and @t50 @t4)) % 0.38/0.61 (define @t127 () (forall @t13 (not @t126))) % 0.38/0.61 (define @t128 () (not @t127)) % 0.38/0.61 (define @t129 () (not @t17)) % 0.38/0.61 (define @t130 () (or @t115 @t129)) % 0.38/0.61 (define @t131 () (and @t114 @t17)) % 0.38/0.61 (define @t132 () (forall @t13 (not @t131))) % 0.38/0.61 (define @t133 () (not @t132)) % 0.38/0.61 (define @t134 () (or @t117 @t18)) % 0.38/0.61 (define @t135 () (or @t59 @t58)) % 0.38/0.61 (define @t136 () (or @t63 @t135)) % 0.38/0.61 (define @t137 () (forall @t65 @t136)) % 0.38/0.61 (define @t138 () (@list @t57)) % 0.38/0.61 (define @t139 () (forall @t138 @t136)) % 0.38/0.61 (define @t140 () (forall @t138 @t135)) % 0.38/0.61 (define @t141 () (@list @t2)) % 0.38/0.61 (define @t142 () (or @t63 @t140)) % 0.38/0.61 (define @t143 () (_ @t6 @t25 @t2)) % 0.38/0.61 (define @t144 () (_ @t6 @t27 @t2)) % 0.38/0.61 (define @t145 () (forall @t15 (or (not @t144) @t143))) % 0.38/0.61 (define @t146 () (not @t28)) % 0.38/0.61 (define @t147 () (or @t146 @t26)) % 0.38/0.61 (define @t148 () (not @t31)) % 0.38/0.61 (define @t149 () (or @t148 @t30)) % 0.38/0.61 (define @t150 () (@quantifiers_skolemize @t70 1)) % 0.38/0.61 (define @t151 () (_ @t80 @t150)) % 0.38/0.61 (define @t152 () (not @t151)) % 0.38/0.61 (define @t153 () (forall @t15 (or @t81 (_ @t71 @t80 @t2)))) % 0.38/0.61 (define @t154 () (not @t153)) % 0.38/0.61 (define @t155 () (_ @t71 @t75 @t150)) % 0.38/0.61 (define @t156 () (forall @t65 (or @t63 (not (_ @t71 @t27 @t57)) (_ @t71 @t25 @t57)))) % 0.38/0.61 (define @t157 () (not @t156)) % 0.38/0.61 (define @t158 () (or @t157 @t155 @t154 @t152)) % 0.38/0.61 (define @t159 () (not @t158)) % 0.38/0.61 (define @t160 () (not @t70)) % 0.38/0.61 (define @t161 () (_ @t71 @t74 @t150)) % 0.38/0.61 (define @t162 () (or @t157 @t161 @t154 @t152)) % 0.38/0.61 (define @t163 () (not @t162)) % 0.38/0.61 (define @t164 () (@list true)) % 0.38/0.61 (define @t165 () (@list @t158)) % 0.38/0.61 (define @t166 () (_ @t71 @t80 @t150)) % 0.38/0.61 (define @t167 () (or @t152 @t166)) % 0.38/0.61 (define @t168 () (@list false false)) % 0.38/0.61 (define @t169 () (not @t166)) % 0.38/0.61 (define @t170 () (not @t82)) % 0.38/0.61 (define @t171 () (or @t170 @t169 @t155)) % 0.38/0.61 (define @t172 () (_ @t80 @t83)) % 0.38/0.61 (define @t173 () (not @t172)) % 0.38/0.61 (define @t174 () (or @t173 @t86)) % 0.38/0.61 (define @t175 () (@list @t174)) % 0.38/0.61 (define @t176 () (not @t89)) % 0.38/0.61 (define @t177 () (@list true false)) % 0.38/0.61 (define @t178 () (forall @t10 (or (not (_ @t80 @t5)) (_ @t71 @t80 @t5)))) % 0.38/0.61 (define @t179 () (not @t178)) % 0.38/0.61 (define @t180 () (or @t179 @t173)) % 0.38/0.61 (define @t181 () (not @t180)) % 0.38/0.61 (assume @p1 @t39) % 0.38/0.61 (assume @p2 true) % 0.38/0.61 (step @p3 :rule eq-symm :args (@t76 @t73)) % 0.38/0.61 (step @p4 :rule beta-reduce :args ((= @t77 @t73))) % 0.38/0.61 (step @p5 :rule refl :args (@t76)) % 0.38/0.61 (step @p6 :rule cong :premises (@p5 @p4) :args (@t78)) % 0.38/0.61 (step @p7 :rule trans :premises (@p6 @p3)) % 0.38/0.61 (step @p8 :rule cong :premises (@p7) :args (@t79)) % 0.38/0.61 (step @p9 :rule quant-unused-vars :args ((= (forall @t15 true) true))) % 0.38/0.61 (step @p10 :rule eq-refl :args (@t77)) % 0.38/0.61 (step @p11 :rule cong :premises (@p10) :args ((forall @t15 (= @t77 @t77)))) % 0.38/0.61 (step @p12 :rule trans :premises (@p11 @p9)) % 0.38/0.61 (step @p13 :rule refl :args (@t77)) % 0.38/0.61 (step @p14 :rule refl :args (@t2)) % 0.38/0.61 (step @p15 :rule skolem_intro :args (@t75)) % 0.38/0.61 (step @p16 :rule ho_cong :premises (@p15 @p14)) % 0.38/0.61 (step @p17 :rule cong :premises (@p16 @p13) :args (@t78)) % 0.38/0.61 (step @p18 :rule cong :premises (@p17) :args (@t79)) % 0.38/0.61 (step @p19 :rule trans :premises (@p18 @p12)) % 0.38/0.61 (step @p20 :rule true_elim :premises (@p19)) % 0.38/0.61 (step @p21 :rule eq_resolve :premises (@p20 @p8)) % 0.38/0.61 (step @p22 :rule eq-symm :args (@t85 @t86)) % 0.38/0.61 (step @p23 :rule refl :args (@t87)) % 0.38/0.61 (step @p24 :rule cong :premises (@p23 @p22) :args ((=> @t87 @t88))) % 0.38/0.61 (assume-push @p301 @t87) % 0.38/0.61 (step @p26 :rule instantiate :premises (@p21) :args ((@list @t83))) % 0.38/0.61 (step-pop @p302 :rule scope :premises (@p26)) % 0.38/0.61 (step @p27 :rule process_scope :premises (@p302) :args (@t88)) % 0.38/0.61 (step @p29 :rule eq_resolve :premises (@p27 @p24)) % 0.38/0.61 (step @p30 :rule implies_elim :premises (@p29)) % 0.38/0.61 (step @p31 :rule chain_m_resolution :premises (@p30 @p21) :args (@t89 @t90 (@list @t87))) % 0.38/0.61 (step @p32 :rule aci_norm :args ((= @t92 @t68))) % 0.38/0.61 (step @p33 :rule cong :premises (@p32) :args (@t93)) % 0.38/0.61 (step @p34 :rule quant-merge-prenex :args ((= (forall @t37 @t95) @t93))) % 0.38/0.61 (step @p35 :rule alpha_equiv :args (@t96 (@list @t42 @t43) (@list @t1 @t97))) % 0.38/0.61 (step @p36 :rule refl :args (@t67)) % 0.38/0.61 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t98)) % 0.38/0.61 (step @p38 :rule quant-miniscope-or :args ((= @t95 @t98))) % 0.38/0.61 (step @p39 :rule trans :premises (@p38 @p37)) % 0.38/0.61 (step @p40 :rule symm :premises (@p39)) % 0.38/0.61 (step @p41 :rule cong :premises (@p40) :args ((forall @t37 (or @t67 @t104)))) % 0.38/0.61 (step @p42 :rule trans :premises (@p41 @p34)) % 0.38/0.61 (step @p43 :rule trans :premises (@p42 @p33)) % 0.38/0.61 (step @p44 :rule bool-impl-elim :args (@t66 @t104)) % 0.38/0.61 (step @p45 :rule cong :premises (@p44) :args ((forall @t37 (=> @t66 @t104)))) % 0.38/0.61 (step @p46 :rule trans :premises (@p45 @p43)) % 0.38/0.61 (step @p47 :rule aci_norm :args ((= @t106 @t102))) % 0.38/0.61 (step @p48 :rule cong :premises (@p47) :args (@t107)) % 0.38/0.61 (step @p49 :rule quant-merge-prenex :args ((= (forall @t23 @t109) @t107))) % 0.38/0.61 (step @p50 :rule refl :args (@t101)) % 0.38/0.61 (step @p51 :rule alpha_equiv :args (@t110 (@list @t97) (@list @t3))) % 0.38/0.61 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t111)) % 0.38/0.61 (step @p53 :rule quant-miniscope-or :args ((= @t109 @t111))) % 0.38/0.61 (step @p54 :rule trans :premises (@p53 @p52)) % 0.38/0.61 (step @p55 :rule symm :premises (@p54)) % 0.38/0.61 (step @p56 :rule cong :premises (@p55) :args ((forall @t23 (or @t116 @t101)))) % 0.38/0.61 (step @p57 :rule trans :premises (@p56 @p49)) % 0.38/0.61 (step @p58 :rule trans :premises (@p57 @p48)) % 0.38/0.61 (step @p59 :rule refl :args ((_ @t6 @t121 @t1))) % 0.38/0.61 (step @p60 :rule refl :args (@t1)) % 0.38/0.61 (step @p61 :rule refl :args (@t40)) % 0.38/0.61 (step @p62 :rule cong :premises (@p61) :args (@t41)) % 0.38/0.61 (step @p63 :rule refl :args (@t46)) % 0.38/0.61 (step @p64 :rule refl :args (@t47)) % 0.38/0.61 (step @p65 :rule cong :premises (@p64) :args (@t48)) % 0.38/0.61 (step @p66 :rule nary_cong :premises (@p65 @p63) :args (@t49)) % 0.38/0.61 (step @p67 :rule cong :premises (@p66) :args (@t50)) % 0.38/0.61 (step @p68 :rule cong :premises (@p67) :args (@t51)) % 0.38/0.61 (step @p69 :rule nary_cong :premises (@p68 @p62) :args (@t52)) % 0.38/0.61 (step @p70 :rule cong :premises (@p69) :args (@t53)) % 0.38/0.61 (step @p71 :rule cong :premises (@p70) :args (@t54)) % 0.38/0.61 (step @p72 :rule cong :premises (@p71) :args (@t55)) % 0.38/0.61 (step @p73 :rule cong :premises (@p72 @p60) :args (@t101)) % 0.38/0.61 (step @p74 :rule trans :premises (@p73 @p59)) % 0.38/0.61 (step @p75 :rule refl :args (@t6)) % 0.38/0.61 (step @p76 :rule ho_cong :premises (@p75 @p72)) % 0.38/0.61 (step @p77 :rule ho_cong :premises (@p76 @p60)) % 0.38/0.61 (step @p78 :rule cong :premises (@p77 @p74) :args ((= @t122 @t101))) % 0.38/0.61 (step @p79 :rule symm :premises (@p78)) % 0.38/0.61 (step @p80 :rule refl :args ((_ (_ @t6 @t121) @t1))) % 0.38/0.61 (step @p81 :rule eq_resolve :premises (@p80 @p79)) % 0.38/0.61 (step @p82 :rule refl :args (@t116)) % 0.38/0.61 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t123)) % 0.38/0.61 (step @p84 :rule cong :premises (@p83) :args ((forall @t23 @t123))) % 0.38/0.61 (step @p85 :rule trans :premises (@p84 @p58)) % 0.38/0.61 (step @p86 :rule refl :args (@t122)) % 0.38/0.61 (step @p87 :rule bool-double-not-elim :args (@t116)) % 0.38/0.61 (step @p88 :rule nary_cong :premises (@p87 @p86) :args ((or (not @t124) @t122))) % 0.38/0.61 (step @p89 :rule bool-impl-elim :args (@t124 @t122)) % 0.38/0.61 (step @p90 :rule trans :premises (@p89 @p88)) % 0.38/0.61 (step @p91 :rule cong :premises (@p90) :args ((forall @t23 (=> @t124 @t122)))) % 0.38/0.61 (step @p92 :rule trans :premises (@p91 @p85)) % 0.38/0.61 (step @p93 :rule refl :args (@t1)) % 0.38/0.61 (step @p94 :rule refl :args (@t4)) % 0.38/0.61 (step @p95 :rule cong :premises (@p94 @p61) :args ((= @t4 @t40))) % 0.38/0.61 (step @p96 :rule symm :premises (@p95)) % 0.38/0.61 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 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0.38/0.61 (step @p159 :rule cong :premises (@p158 @p129) :args (@t22)) % 0.38/0.61 (step @p160 :rule cong :premises (@p159) :args (@t24)) % 0.38/0.61 (step @p161 :rule trans :premises (@p160 @p92)) % 0.38/0.61 (step @p162 :rule aci_norm :args ((= @t136 @t64))) % 0.38/0.61 (step @p163 :rule cong :premises (@p162) :args (@t137)) % 0.38/0.61 (step @p164 :rule quant-merge-prenex :args ((= (forall @t34 @t139) @t137))) % 0.38/0.61 (step @p165 :rule alpha_equiv :args (@t140 (@list @t57) @t141)) % 0.38/0.61 (step @p166 :rule refl :args (@t63)) % 0.38/0.61 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t142)) % 0.38/0.61 (step @p168 :rule quant-miniscope-or :args ((= @t139 @t142))) % 0.38/0.61 (step @p169 :rule trans :premises (@p168 @p167)) % 0.38/0.61 (step @p170 :rule symm :premises (@p169)) % 0.38/0.61 (step @p171 :rule cong :premises (@p170) :args ((forall @t34 (or @t63 @t145)))) % 0.38/0.61 (step @p172 :rule trans :premises (@p171 @p164)) % 0.38/0.61 (step @p173 :rule trans 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@p197) :args (@t149)) % 0.38/0.61 (step @p205 :rule cong :premises (@p204) :args ((forall @t15 @t149))) % 0.38/0.61 (step @p206 :rule bool-impl-elim :args (@t31 @t30)) % 0.38/0.61 (step @p207 :rule cong :premises (@p206) :args (@t32)) % 0.38/0.61 (step @p208 :rule trans :premises (@p207 @p205)) % 0.38/0.61 (step @p209 :rule cong :premises (@p208 @p192) :args (@t33)) % 0.38/0.61 (step @p210 :rule cong :premises (@p209) :args (@t35)) % 0.38/0.61 (step @p211 :rule trans :premises (@p210 @p176)) % 0.38/0.61 (step @p212 :rule cong :premises (@p211 @p161) :args (@t36)) % 0.38/0.61 (step @p213 :rule cong :premises (@p212) :args (@t38)) % 0.38/0.61 (step @p214 :rule trans :premises (@p213 @p46)) % 0.38/0.61 (step @p215 :rule cong :premises (@p214) :args (@t39)) % 0.38/0.61 (step @p216 :rule eq_resolve :premises (@p1 @p215)) % 0.38/0.61 (step @p217 :rule refl :args (@t159)) % 0.38/0.61 (step @p218 :rule bool-double-not-elim :args (@t70)) % 0.38/0.61 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or (not @t160) @t159))) % 0.38/0.61 (step @p220 :rule refl :args (@t152)) % 0.38/0.61 (step @p221 :rule refl :args (@t154)) % 0.38/0.61 (step @p222 :rule refl :args (@t150)) % 0.38/0.61 (step @p223 :rule eq-refl :args (@t74)) % 0.38/0.61 (step @p224 :rule refl :args (@t74)) % 0.38/0.61 (step @p225 :rule cong :premises (@p224 @p15) :args ((= @t74 @t75))) % 0.38/0.61 (step @p226 :rule trans :premises (@p225 @p223)) % 0.38/0.61 (step @p227 :rule true_elim :premises (@p226)) % 0.38/0.61 (step @p228 :rule cong :premises (@p227 @p222) :args (@t161)) % 0.38/0.61 (step @p229 :rule refl :args (@t157)) % 0.38/0.61 (step @p230 :rule nary_cong :premises (@p229 @p228 @p221 @p220) :args (@t162)) % 0.38/0.61 (step @p231 :rule cong :premises (@p230) :args (@t163)) % 0.38/0.61 (step @p232 :rule refl :args (@t160)) % 0.38/0.61 (step @p233 :rule cong :premises (@p232 @p231) :args ((=> @t160 @t163))) % 0.38/0.61 (assume-push @p303 @t160) % 0.38/0.61 (step @p235 :rule skolemize :premises (@p216)) % 0.38/0.61 (step-pop @p304 :rule scope :premises (@p235)) % 0.38/0.61 (step @p236 :rule process_scope :premises (@p304) :args (@t163)) % 0.38/0.61 (step @p238 :rule eq_resolve :premises (@p236 @p233)) % 0.38/0.61 (step @p239 :rule implies_elim :premises (@p238)) % 0.38/0.61 (step @p240 :rule eq_resolve :premises (@p239 @p219)) % 0.38/0.61 (step @p241 :rule chain_m_resolution :premises (@p240 @p216) :args (@t159 @t164 (@list @t70))) % 0.38/0.61 (step @p242 :rule bool-double-not-elim :args (@t156)) % 0.38/0.61 (step @p243 :rule refl :args (@t158)) % 0.38/0.61 (step @p244 :rule nary_cong :premises (@p243 @p242) :args ((or @t158 (not @t157)))) % 0.38/0.61 (step @p245 :rule cnf_or_neg :args (@t158 0)) % 0.38/0.61 (step @p246 :rule eq_resolve :premises (@p245 @p244)) % 0.38/0.61 (step @p247 :rule reordering :premises (@p246) :args ((or @t156 @t158))) % 0.38/0.61 (step @p248 :rule chain_m_resolution :premises (@p247 @p241) :args (@t156 @t164 @t165)) % 0.38/0.61 (step @p249 :rule instantiate :premises (@p248) :args ((@list @t80 @t75 @t150))) % 0.38/0.61 (step @p250 :rule bool-double-not-elim :args (@t153)) % 0.38/0.61 (step @p251 :rule nary_cong :premises (@p243 @p250) :args ((or @t158 (not @t154)))) % 0.38/0.61 (step @p252 :rule cnf_or_neg :args (@t158 2)) % 0.38/0.61 (step @p253 :rule eq_resolve :premises (@p252 @p251)) % 0.38/0.61 (step @p254 :rule reordering :premises (@p253) :args ((or @t153 @t158))) % 0.38/0.61 (step @p255 :rule chain_m_resolution :premises (@p254 @p241) :args (@t153 @t164 @t165)) % 0.38/0.61 (step @p256 :rule instantiate :premises (@p255) :args ((@list @t150))) % 0.38/0.61 (step @p257 :rule bool-double-not-elim :args (@t151)) % 0.38/0.61 (step @p258 :rule nary_cong :premises (@p243 @p257) :args ((or @t158 (not @t152)))) % 0.38/0.61 (step @p259 :rule cnf_or_neg :args (@t158 3)) % 0.38/0.61 (step @p260 :rule eq_resolve :premises (@p259 @p258)) % 0.38/0.61 (step @p261 :rule reordering :premises (@p260) :args ((or @t151 @t158))) % 0.38/0.61 (step @p262 :rule chain_m_resolution :premises (@p261 @p241) :args (@t151 @t164 @t165)) % 0.38/0.61 (step @p263 :rule cnf_or_pos :args (@t167)) % 0.38/0.61 (step @p264 :rule reordering :premises (@p263) :args ((or @t152 @t166 (not @t167)))) % 0.38/0.61 (step @p265 :rule chain_m_resolution :premises (@p264 @p262 @p256) :args (@t166 @t168 (@list @t151 @t167))) % 0.38/0.61 (step @p266 :rule cnf_or_neg :args (@t158 1)) % 0.38/0.61 (step @p267 :rule chain_m_resolution :premises (@p266 @p241) :args ((not @t155) @t164 @t165)) % 0.38/0.61 (step @p268 :rule cnf_or_pos :args (@t171)) % 0.38/0.61 (step @p269 :rule reordering :premises (@p268) :args ((or @t155 @t169 @t170 (not @t171)))) % 0.38/0.61 (step @p270 :rule chain_m_resolution :premises (@p269 @p267 @p265 @p249) :args (@t170 (@list true false false) (@list @t155 @t166 @t171))) % 0.38/0.61 (step @p271 :rule skolemize :premises (@p270)) % 0.38/0.61 (step @p272 :rule cnf_or_neg :args (@t174 1)) % 0.38/0.61 (step @p273 :rule chain_m_resolution :premises (@p272 @p271) :args ((not @t86) @t164 @t175)) % 0.38/0.61 (step @p274 :rule bool-double-not-elim :args (@t84)) % 0.38/0.61 (step @p275 :rule refl :args (@t86)) % 0.38/0.61 (step @p276 :rule refl :args (@t176)) % 0.38/0.61 (step @p277 :rule nary_cong :premises (@p276 @p275 @p274) :args ((or @t176 @t86 (not @t85)))) % 0.38/0.61 (step @p278 :rule cnf_equiv_pos2 :args (@t89)) % 0.38/0.61 (step @p279 :rule eq_resolve :premises (@p278 @p277)) % 0.38/0.61 (step @p280 :rule reordering :premises (@p279) :args ((or @t86 @t84 @t176))) % 0.38/0.61 (step @p281 :rule chain_m_resolution :premises (@p280 @p273 @p31) :args (@t84 @t177 (@list @t86 @t89))) % 0.38/0.61 (step @p282 :rule alpha_equiv :args (@t153 @t141 (@list @t5))) % 0.38/0.61 (step @p283 :rule equiv_elim1 :premises (@p282)) % 0.38/0.61 (step @p284 :rule chain_m_resolution :premises (@p283 @p255) :args (@t178 @t90 (@list @t153))) % 0.38/0.61 (step @p285 :rule bool-double-not-elim :args (@t172)) % 0.38/0.61 (step @p286 :rule refl :args (@t174)) % 0.38/0.61 (step @p287 :rule nary_cong :premises (@p286 @p285) :args ((or @t174 (not @t173)))) % 0.38/0.61 (step @p288 :rule cnf_or_neg :args (@t174 0)) % 0.38/0.61 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 0.38/0.61 (step @p290 :rule reordering :premises (@p289) :args ((or @t172 @t174))) % 0.38/0.61 (step @p291 :rule chain_m_resolution :premises (@p290 @p271) :args (@t172 @t164 @t175)) % 0.38/0.61 (step @p292 :rule cnf_or_pos :args (@t180)) % 0.38/0.61 (step @p293 :rule reordering :premises (@p292) :args ((or @t173 @t179 @t181))) % 0.38/0.61 (step @p294 :rule chain_m_resolution :premises (@p293 @p291 @p284) :args (@t181 @t168 (@list @t172 @t178))) % 0.38/0.61 (assume-push @p305 @t84) % 0.38/0.61 (step @p296 :rule instantiate :premises (@p281) :args ((@list @t80))) % 0.38/0.61 (step-pop @p306 :rule scope :premises (@p296)) % 0.38/0.61 (step @p297 :rule process_scope :premises (@p306) :args (@t180)) % 0.38/0.61 (step @p299 :rule implies_elim :premises (@p297)) % 0.38/0.61 (step @p300 false :rule chain_m_resolution :premises (@p299 @p294 @p281) :args (false @t177 (@list @t180 @t84))) % 0.38/0.61 ) % 0.38/0.61 % SZS output end Proof % 0.38/0.61 % cvc5 exiting %------------------------------------------------------------------------------