%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO325^5 : 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 : n013.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 09:12:26 AM UTC 2026 % Result : Theorem 0.38s 0.62s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO325^5 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n013.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Wed Jun 3 00:03:15 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.38/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.62 % SZS status Theorem % 0.38/0.62 % SZS output start Proof % 0.38/0.62 ( % 0.38/0.62 (declare-sort tptp.a 0) % 0.38/0.62 (declare-const tptp.cK (-> (-> tptp.a Bool) tptp.a Bool)) % 0.38/0.62 (define @t1 () (@var "Xx" tptp.a)) % 0.38/0.62 (define @t2 () (@var "Xx0" tptp.a)) % 0.38/0.62 (define @t3 () (@var "S" (-> tptp.a Bool))) % 0.38/0.62 (define @t4 () (_ @t3 @t2)) % 0.38/0.62 (define @t5 () (@var "Xx1" tptp.a)) % 0.38/0.62 (define @t6 () (_ (_ tptp.cK @t3) @t5)) % 0.38/0.62 (define @t7 () (_ @t3 @t5)) % 0.38/0.62 (define @t8 () (@list @t5)) % 0.38/0.62 (define @t9 () (forall @t8 (=> @t7 @t6))) % 0.38/0.62 (define @t10 () (and @t9 @t4)) % 0.38/0.62 (define @t11 () (@list @t3)) % 0.38/0.62 (define @t12 () (exists @t11 @t10)) % 0.38/0.62 (define @t13 () (@list @t2)) % 0.38/0.62 (define @t14 () (lambda @t13 @t12)) % 0.38/0.62 (define @t15 () (_ tptp.cK @t14)) % 0.38/0.62 (define @t16 () (=> (_ @t15 @t1) (_ (_ tptp.cK @t15) @t1))) % 0.38/0.62 (define @t17 () (@list @t1)) % 0.38/0.62 (define @t18 () (forall @t17 @t16)) % 0.38/0.62 (define @t19 () (@var "Y" (-> tptp.a Bool))) % 0.38/0.62 (define @t20 () (_ (_ tptp.cK @t19) @t1)) % 0.38/0.62 (define @t21 () (@var "X" (-> tptp.a Bool))) % 0.38/0.62 (define @t22 () (_ (_ tptp.cK @t21) @t1)) % 0.38/0.62 (define @t23 () (forall @t17 (=> @t22 @t20))) % 0.38/0.62 (define @t24 () (_ @t19 @t1)) % 0.38/0.62 (define @t25 () (_ @t21 @t1)) % 0.38/0.62 (define @t26 () (forall @t17 (=> @t25 @t24))) % 0.38/0.62 (define @t27 () (=> @t26 @t23)) % 0.38/0.62 (define @t28 () (@list @t21 @t19)) % 0.38/0.62 (define @t29 () (forall @t28 @t27)) % 0.38/0.62 (define @t30 () (=> @t29 @t18)) % 0.38/0.62 (define @t31 () (not @t30)) % 0.38/0.62 (define @t32 () (_ @t3 @t2)) % 0.38/0.62 (define @t33 () (not @t32)) % 0.38/0.62 (define @t34 () (tptp.cK @t3 @t5)) % 0.38/0.62 (define @t35 () (_ @t3 @t5)) % 0.38/0.62 (define @t36 () (not @t35)) % 0.38/0.62 (define @t37 () (or @t36 @t34)) % 0.38/0.62 (define @t38 () (forall @t8 @t37)) % 0.38/0.62 (define @t39 () (not @t38)) % 0.38/0.62 (define @t40 () (or @t39 @t33)) % 0.38/0.62 (define @t41 () (forall @t11 @t40)) % 0.38/0.62 (define @t42 () (not @t41)) % 0.38/0.62 (define @t43 () (lambda @t13 @t42)) % 0.38/0.62 (define @t44 () (@purify @t43)) % 0.38/0.62 (define @t45 () (_ @t44 @t2)) % 0.38/0.62 (define @t46 () (_ @t43 @t2)) % 0.38/0.62 (define @t47 () (= @t45 @t46)) % 0.38/0.62 (define @t48 () (forall @t13 @t47)) % 0.38/0.62 (define @t49 () (_ @t44 @t1)) % 0.38/0.62 (define @t50 () (tptp.cK @t44 @t1)) % 0.38/0.62 (define @t51 () (not @t49)) % 0.38/0.62 (define @t52 () (forall @t17 (or @t51 @t50))) % 0.38/0.62 (define @t53 () (@quantifiers_skolemize @t52 0)) % 0.38/0.62 (define @t54 () (forall @t11 (or @t39 (not (_ @t3 @t53))))) % 0.38/0.62 (define @t55 () (@quantifiers_skolemize @t54 0)) % 0.38/0.62 (define @t56 () (forall @t17 (or (not (_ @t55 @t1)) @t49))) % 0.38/0.62 (define @t57 () (@quantifiers_skolemize @t56 0)) % 0.38/0.62 (define @t58 () (forall @t11 (or @t39 (not (_ @t3 @t57))))) % 0.38/0.62 (define @t59 () (not @t58)) % 0.38/0.62 (define @t60 () (_ @t44 @t57)) % 0.38/0.62 (define @t61 () (forall @t13 (= @t42 @t45))) % 0.38/0.62 (define @t62 () (= @t59 @t60)) % 0.38/0.62 (define @t63 () (= @t60 @t59)) % 0.38/0.62 (define @t64 () (@list false)) % 0.38/0.62 (define @t65 () (@list @t61)) % 0.38/0.62 (define @t66 () (not @t4)) % 0.38/0.62 (define @t67 () (not @t7)) % 0.38/0.62 (define @t68 () (or @t67 @t6)) % 0.38/0.62 (define @t69 () (forall @t8 @t68)) % 0.38/0.62 (define @t70 () (lambda @t13 (not (forall @t11 (or (not @t69) @t66))))) % 0.38/0.62 (define @t71 () (_ tptp.cK @t70)) % 0.38/0.62 (define @t72 () (_ tptp.cK @t43)) % 0.38/0.62 (define @t73 () (tptp.cK @t72 @t1)) % 0.38/0.62 (define @t74 () (_ (_ tptp.cK @t72) @t1)) % 0.38/0.62 (define @t75 () (tptp.cK @t43 @t1)) % 0.38/0.62 (define @t76 () (_ @t72 @t1)) % 0.38/0.62 (define @t77 () (not @t76)) % 0.38/0.62 (define @t78 () (or @t77 @t74)) % 0.38/0.62 (define @t79 () (or @t39 @t66)) % 0.38/0.62 (define @t80 () (and @t38 @t4)) % 0.38/0.62 (define @t81 () (forall @t11 (not @t80))) % 0.38/0.62 (define @t82 () (not @t81)) % 0.38/0.62 (define @t83 () (@var "BOUND_VARIABLE_7471" tptp.a)) % 0.38/0.62 (define @t84 () (tptp.cK @t19 @t83)) % 0.38/0.62 (define @t85 () (not (tptp.cK @t21 @t83))) % 0.38/0.62 (define @t86 () (_ @t19 @t1)) % 0.38/0.62 (define @t87 () (_ @t21 @t1)) % 0.38/0.62 (define @t88 () (forall @t17 (or (not @t87) @t86))) % 0.38/0.62 (define @t89 () (not @t88)) % 0.38/0.62 (define @t90 () (or @t89 @t85 @t84)) % 0.38/0.62 (define @t91 () (or @t85 @t84)) % 0.38/0.62 (define @t92 () (or @t89 @t91)) % 0.38/0.62 (define @t93 () (@list @t21 @t19 @t83)) % 0.38/0.62 (define @t94 () (forall @t93 @t92)) % 0.38/0.62 (define @t95 () (@list @t83)) % 0.38/0.62 (define @t96 () (forall @t95 @t92)) % 0.38/0.62 (define @t97 () (forall @t95 @t91)) % 0.38/0.62 (define @t98 () (or @t89 @t97)) % 0.38/0.62 (define @t99 () (tptp.cK @t19 @t1)) % 0.38/0.62 (define @t100 () (tptp.cK @t21 @t1)) % 0.38/0.62 (define @t101 () (forall @t17 (or (not @t100) @t99))) % 0.38/0.62 (define @t102 () (not @t22)) % 0.38/0.62 (define @t103 () (or @t102 @t20)) % 0.38/0.62 (define @t104 () (not @t25)) % 0.38/0.62 (define @t105 () (or @t104 @t24)) % 0.38/0.62 (define @t106 () (not @t54)) % 0.38/0.62 (define @t107 () (_ @t44 @t53)) % 0.38/0.62 (define @t108 () (= @t106 @t107)) % 0.38/0.62 (define @t109 () (@list @t53)) % 0.38/0.62 (define @t110 () (= @t107 @t106)) % 0.38/0.62 (define @t111 () (forall @t17 (or (not @t75) @t73))) % 0.38/0.62 (define @t112 () (@quantifiers_skolemize @t111 0)) % 0.38/0.62 (define @t113 () (_ tptp.cK @t44)) % 0.38/0.62 (define @t114 () (tptp.cK @t113 @t112)) % 0.38/0.62 (define @t115 () (tptp.cK @t44 @t112)) % 0.38/0.62 (define @t116 () (not @t115)) % 0.38/0.62 (define @t117 () (_ @t113 @t1)) % 0.38/0.62 (define @t118 () (or @t51 @t117)) % 0.38/0.62 (define @t119 () (_ @t113 @t1)) % 0.38/0.62 (define @t120 () (or @t51 @t119)) % 0.38/0.62 (define @t121 () (forall @t17 @t120)) % 0.38/0.62 (define @t122 () (not @t121)) % 0.38/0.62 (define @t123 () (or @t122 @t116 @t114)) % 0.38/0.62 (define @t124 () (forall @t93 @t90)) % 0.38/0.62 (define @t125 () (not @t52)) % 0.38/0.62 (define @t126 () (or @t125 @t116 @t114)) % 0.38/0.62 (define @t127 () (or @t116 @t114)) % 0.38/0.62 (define @t128 () (not @t127)) % 0.38/0.62 (define @t129 () (not @t111)) % 0.38/0.62 (define @t130 () (tptp.cK @t72 @t112)) % 0.38/0.62 (define @t131 () (tptp.cK @t43 @t112)) % 0.38/0.62 (define @t132 () (not @t131)) % 0.38/0.62 (define @t133 () (or @t132 @t130)) % 0.38/0.62 (define @t134 () (not @t133)) % 0.38/0.62 (define @t135 () (@list true)) % 0.38/0.62 (define @t136 () (@list @t127)) % 0.38/0.62 (define @t137 () (@list true false false)) % 0.38/0.62 (define @t138 () (tptp.cK @t44 @t53)) % 0.38/0.62 (define @t139 () (not @t107)) % 0.38/0.62 (define @t140 () (or @t139 @t138)) % 0.38/0.62 (define @t141 () (@list @t140)) % 0.38/0.62 (define @t142 () (@list false false)) % 0.38/0.62 (define @t143 () (forall @t8 (or (not (_ @t55 @t5)) (tptp.cK @t55 @t5)))) % 0.38/0.62 (define @t144 () (_ @t55 @t53)) % 0.38/0.62 (define @t145 () (not @t144)) % 0.38/0.62 (define @t146 () (not @t143)) % 0.38/0.62 (define @t147 () (or @t146 @t145)) % 0.38/0.62 (define @t148 () (@list @t147)) % 0.38/0.62 (define @t149 () (tptp.cK @t55 @t53)) % 0.38/0.62 (define @t150 () (or @t145 @t149)) % 0.38/0.62 (define @t151 () (not @t149)) % 0.38/0.62 (define @t152 () (not @t56)) % 0.38/0.62 (define @t153 () (or @t152 @t151 @t138)) % 0.38/0.62 (define @t154 () (_ @t55 @t57)) % 0.38/0.62 (define @t155 () (not @t154)) % 0.38/0.62 (define @t156 () (or @t155 @t60)) % 0.38/0.62 (define @t157 () (@list @t156)) % 0.38/0.62 (define @t158 () (not @t63)) % 0.38/0.62 (define @t159 () (@list true false)) % 0.38/0.62 (define @t160 () (or @t146 @t155)) % 0.38/0.62 (define @t161 () (not @t160)) % 0.38/0.62 (assume @p1 @t31) % 0.38/0.62 (assume @p2 true) % 0.38/0.62 (step @p3 :rule eq-symm :args (@t45 @t42)) % 0.38/0.62 (step @p4 :rule beta-reduce :args ((= @t46 @t42))) % 0.38/0.62 (step @p5 :rule refl :args (@t45)) % 0.38/0.62 (step @p6 :rule cong :premises (@p5 @p4) :args (@t47)) % 0.38/0.62 (step @p7 :rule trans :premises (@p6 @p3)) % 0.38/0.62 (step @p8 :rule cong :premises (@p7) :args (@t48)) % 0.38/0.62 (step @p9 :rule quant-unused-vars :args ((= (forall @t13 true) true))) % 0.38/0.62 (step @p10 :rule eq-refl :args (@t46)) % 0.38/0.62 (step @p11 :rule cong :premises (@p10) :args ((forall @t13 (= @t46 @t46)))) % 0.38/0.62 (step @p12 :rule trans :premises (@p11 @p9)) % 0.38/0.62 (step @p13 :rule refl :args (@t46)) % 0.38/0.62 (step @p14 :rule refl :args (@t2)) % 0.38/0.62 (step @p15 :rule skolem_intro :args (@t44)) % 0.38/0.62 (step @p16 :rule ho_cong :premises (@p15 @p14)) % 0.38/0.62 (step @p17 :rule cong :premises (@p16 @p13) :args (@t47)) % 0.38/0.62 (step @p18 :rule cong :premises (@p17) :args (@t48)) % 0.38/0.62 (step @p19 :rule trans :premises (@p18 @p12)) % 0.38/0.62 (step @p20 :rule true_elim :premises (@p19)) % 0.38/0.62 (step @p21 :rule eq_resolve :premises (@p20 @p8)) % 0.38/0.62 (step @p22 :rule eq-symm :args (@t59 @t60)) % 0.38/0.62 (step @p23 :rule refl :args (@t61)) % 0.38/0.62 (step @p24 :rule cong :premises (@p23 @p22) :args ((=> @t61 @t62))) % 0.38/0.62 (assume-push @p301 @t61) % 0.38/0.62 (step @p26 :rule instantiate :premises (@p21) :args ((@list @t57))) % 0.38/0.62 (step-pop @p302 :rule scope :premises (@p26)) % 0.38/0.62 (step @p27 :rule process_scope :premises (@p302) :args (@t62)) % 0.38/0.62 (step @p29 :rule eq_resolve :premises (@p27 @p24)) % 0.38/0.62 (step @p30 :rule implies_elim :premises (@p29)) % 0.38/0.62 (step @p31 :rule chain_m_resolution :premises (@p30 @p21) :args (@t63 @t64 @t65)) % 0.38/0.62 (step @p32 :rule refl :args ((tptp.cK @t71 @t1))) % 0.38/0.62 (step @p33 :rule refl :args (@t1)) % 0.38/0.62 (step @p34 :rule refl :args (@t32)) % 0.38/0.62 (step @p35 :rule cong :premises (@p34) :args (@t33)) % 0.38/0.62 (step @p36 :rule refl :args (@t34)) % 0.38/0.62 (step @p37 :rule refl :args (@t35)) % 0.38/0.62 (step @p38 :rule cong :premises (@p37) :args (@t36)) % 0.38/0.62 (step @p39 :rule nary_cong :premises (@p38 @p36) :args (@t37)) % 0.38/0.62 (step @p40 :rule cong :premises (@p39) :args (@t38)) % 0.38/0.62 (step @p41 :rule cong :premises (@p40) :args (@t39)) % 0.38/0.62 (step @p42 :rule nary_cong :premises (@p41 @p35) :args (@t40)) % 0.38/0.62 (step @p43 :rule cong :premises (@p42) :args (@t41)) % 0.38/0.62 (step @p44 :rule cong :premises (@p43) :args (@t42)) % 0.38/0.62 (step @p45 :rule cong :premises (@p44) :args (@t43)) % 0.38/0.62 (step @p46 :rule refl :args (tptp.cK)) % 0.38/0.62 (step @p47 :rule ho_cong :premises (@p46 @p45)) % 0.38/0.62 (step @p48 :rule cong :premises (@p47 @p33) :args (@t73)) % 0.38/0.62 (step @p49 :rule trans :premises (@p48 @p32)) % 0.38/0.62 (step @p50 :rule ho_cong :premises (@p46 @p47)) % 0.38/0.62 (step @p51 :rule ho_cong :premises (@p50 @p33)) % 0.38/0.62 (step @p52 :rule cong :premises (@p51 @p49) :args ((= @t74 @t73))) % 0.38/0.62 (step @p53 :rule symm :premises (@p52)) % 0.38/0.62 (step @p54 :rule refl :args ((_ (_ tptp.cK @t71) @t1))) % 0.38/0.62 (step @p55 :rule eq_resolve :premises (@p54 @p53)) % 0.38/0.62 (step @p56 :rule refl :args ((tptp.cK @t70 @t1))) % 0.38/0.62 (step @p57 :rule cong :premises (@p45 @p33) :args (@t75)) % 0.38/0.62 (step @p58 :rule trans :premises (@p57 @p56)) % 0.38/0.62 (step @p59 :rule ho_cong :premises (@p47 @p33)) % 0.38/0.62 (step @p60 :rule cong :premises (@p59 @p58) :args ((= @t76 @t75))) % 0.38/0.62 (step @p61 :rule symm :premises (@p60)) % 0.38/0.62 (step @p62 :rule refl :args ((_ @t71 @t1))) % 0.38/0.62 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 0.38/0.62 (step @p64 :rule cong :premises (@p63) :args (@t77)) % 0.38/0.62 (step @p65 :rule nary_cong :premises (@p64 @p55) :args (@t78)) % 0.38/0.62 (step @p66 :rule cong :premises (@p65) :args ((forall @t17 @t78))) % 0.38/0.62 (step @p67 :rule bool-impl-elim :args (@t76 @t74)) % 0.38/0.62 (step @p68 :rule cong :premises (@p67) :args ((forall @t17 (=> @t76 @t74)))) % 0.38/0.62 (step @p69 :rule trans :premises (@p68 @p66)) % 0.38/0.62 (step @p70 :rule refl :args (@t1)) % 0.38/0.62 (step @p71 :rule refl :args (@t4)) % 0.38/0.62 (step @p72 :rule cong :premises (@p71 @p34) :args ((= @t4 @t32))) % 0.38/0.62 (step @p73 :rule symm :premises (@p72)) % 0.38/0.62 (step @p74 :rule eq_resolve :premises (@p71 @p73)) % 0.38/0.62 (step @p75 :rule cong :premises (@p74) :args (@t66)) % 0.38/0.62 (step @p76 :rule refl :args (@t39)) % 0.38/0.62 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t79)) % 0.38/0.62 (step @p78 :rule cong :premises (@p77) :args ((forall @t11 @t79))) % 0.38/0.62 (step @p79 :rule bool-and-de-morgan :args (@t38 @t4 true)) % 0.38/0.62 (step @p80 :rule cong :premises (@p79) :args (@t81)) % 0.38/0.62 (step @p81 :rule trans :premises (@p80 @p78)) % 0.38/0.62 (step @p82 :rule cong :premises (@p81) :args (@t82)) % 0.38/0.62 (step @p83 :rule exists-elim :args ((= (exists @t11 @t80) @t82))) % 0.38/0.62 (step @p84 :rule trans :premises (@p83 @p82)) % 0.38/0.62 (step @p85 :rule refl :args (@t4)) % 0.38/0.62 (step @p86 :rule refl :args (@t6)) % 0.38/0.62 (step @p87 :rule cong :premises (@p86 @p36) :args ((= @t6 @t34))) % 0.38/0.62 (step @p88 :rule symm :premises (@p87)) % 0.38/0.62 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.38/0.62 (step @p90 :rule refl :args (@t7)) % 0.38/0.62 (step @p91 :rule cong :premises (@p90 @p37) :args ((= @t7 @t35))) % 0.38/0.62 (step @p92 :rule symm :premises (@p91)) % 0.38/0.62 (step @p93 :rule eq_resolve :premises (@p90 @p92)) % 0.38/0.62 (step @p94 :rule cong :premises (@p93) :args (@t67)) % 0.38/0.62 (step @p95 :rule nary_cong :premises (@p94 @p89) :args (@t68)) % 0.38/0.62 (step @p96 :rule cong :premises (@p95) :args (@t69)) % 0.38/0.62 (step @p97 :rule bool-impl-elim :args (@t7 @t6)) % 0.38/0.62 (step @p98 :rule cong :premises (@p97) :args (@t9)) % 0.38/0.62 (step @p99 :rule trans :premises (@p98 @p96)) % 0.38/0.62 (step @p100 :rule nary_cong :premises (@p99 @p85) :args (@t10)) % 0.38/0.62 (step @p101 :rule cong :premises (@p100) :args (@t12)) % 0.38/0.62 (step @p102 :rule trans :premises (@p101 @p84)) % 0.38/0.62 (step @p103 :rule cong :premises (@p102) :args (@t14)) % 0.38/0.62 (step @p104 :rule refl :args (tptp.cK)) % 0.38/0.62 (step @p105 :rule ho_cong :premises (@p104 @p103)) % 0.38/0.62 (step @p106 :rule ho_cong :premises (@p104 @p105)) % 0.38/0.62 (step @p107 :rule ho_cong :premises (@p106 @p70)) % 0.38/0.62 (step @p108 :rule ho_cong :premises (@p105 @p70)) % 0.38/0.62 (step @p109 :rule cong :premises (@p108 @p107) :args (@t16)) % 0.38/0.62 (step @p110 :rule cong :premises (@p109) :args (@t18)) % 0.38/0.62 (step @p111 :rule trans :premises (@p110 @p69)) % 0.38/0.62 (step @p112 :rule aci_norm :args ((= @t92 @t90))) % 0.38/0.62 (step @p113 :rule cong :premises (@p112) :args (@t94)) % 0.38/0.62 (step @p114 :rule quant-merge-prenex :args ((= (forall @t28 @t96) @t94))) % 0.38/0.62 (step @p115 :rule alpha_equiv :args (@t97 (@list @t83) (@list @t1))) % 0.38/0.62 (step @p116 :rule refl :args (@t89)) % 0.38/0.62 (step @p117 :rule nary_cong :premises (@p116 @p115) :args (@t98)) % 0.38/0.62 (step @p118 :rule quant-miniscope-or :args ((= 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(step @p150 :rule cong :premises (@p149 @p148) :args ((= @t25 @t87))) % 0.38/0.62 (step @p151 :rule symm :premises (@p150)) % 0.38/0.62 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 0.38/0.62 (step @p153 :rule cong :premises (@p152) :args (@t104)) % 0.38/0.62 (step @p154 :rule nary_cong :premises (@p153 @p147) :args (@t105)) % 0.38/0.62 (step @p155 :rule cong :premises (@p154) :args ((forall @t17 @t105))) % 0.38/0.62 (step @p156 :rule bool-impl-elim :args (@t25 @t24)) % 0.38/0.62 (step @p157 :rule cong :premises (@p156) :args (@t26)) % 0.38/0.62 (step @p158 :rule trans :premises (@p157 @p155)) % 0.38/0.62 (step @p159 :rule cong :premises (@p158 @p142) :args (@t27)) % 0.38/0.62 (step @p160 :rule cong :premises (@p159) :args (@t29)) % 0.38/0.62 (step @p161 :rule trans :premises (@p160 @p126)) % 0.38/0.62 (step @p162 :rule cong :premises (@p161 @p111) :args (@t30)) % 0.38/0.62 (step @p163 :rule cong :premises (@p162) :args (@t31)) % 0.38/0.62 (step @p164 :rule eq_resolve 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@t123))) % 0.38/0.62 (assume-push @p305 @t124) % 0.38/0.62 (step @p196 :rule instantiate :premises (@p165) :args ((@list @t44 @t113 @t112))) % 0.38/0.62 (step-pop @p306 :rule scope :premises (@p196)) % 0.38/0.62 (step @p197 :rule process_scope :premises (@p306) :args (@t123)) % 0.38/0.62 (step @p199 :rule eq_resolve :premises (@p197 @p194)) % 0.38/0.62 (step @p200 :rule implies_elim :premises (@p199)) % 0.38/0.62 (step @p201 :rule chain_m_resolution :premises (@p200 @p165) :args (@t126 @t64 (@list @t124))) % 0.38/0.62 (step @p202 :rule not_implies_elim2 :premises (@p164)) % 0.38/0.62 (step @p203 :rule refl :args (@t128)) % 0.38/0.62 (step @p204 :rule bool-double-not-elim :args (@t111)) % 0.38/0.62 (step @p205 :rule nary_cong :premises (@p204 @p203) :args ((or (not @t129) @t128))) % 0.38/0.62 (step @p206 :rule refl :args (@t112)) % 0.38/0.62 (step @p207 :rule eq-refl :args (@t43)) % 0.38/0.62 (step @p208 :rule refl :args (@t43)) % 0.38/0.62 (step @p209 :rule cong :premises (@p208 @p15) :args ((= @t43 @t44))) % 0.38/0.62 (step @p210 :rule trans :premises (@p209 @p207)) % 0.38/0.62 (step @p211 :rule true_elim :premises (@p210)) % 0.38/0.62 (step @p212 :rule ho_cong :premises (@p104 @p211)) % 0.38/0.62 (step @p213 :rule cong :premises (@p212 @p206) :args (@t130)) % 0.38/0.62 (step @p214 :rule cong :premises (@p211 @p206) :args (@t131)) % 0.38/0.62 (step @p215 :rule cong :premises (@p214) :args (@t132)) % 0.38/0.62 (step @p216 :rule nary_cong :premises (@p215 @p213) :args (@t133)) % 0.38/0.62 (step @p217 :rule cong :premises (@p216) :args (@t134)) % 0.38/0.62 (step @p218 :rule refl :args (@t129)) % 0.38/0.62 (step @p219 :rule cong :premises (@p218 @p217) :args ((=> @t129 @t134))) % 0.38/0.62 (assume-push @p307 @t129) % 0.38/0.62 (step @p221 :rule skolemize :premises (@p202)) % 0.38/0.62 (step-pop @p308 :rule scope :premises (@p221)) % 0.38/0.62 (step @p222 :rule process_scope :premises (@p308) :args (@t134)) % 0.38/0.62 (step @p224 :rule eq_resolve :premises (@p222 @p219)) % 0.38/0.62 (step @p225 :rule implies_elim :premises (@p224)) % 0.38/0.62 (step @p226 :rule eq_resolve :premises (@p225 @p205)) % 0.38/0.62 (step @p227 :rule chain_m_resolution :premises (@p226 @p202) :args (@t128 @t135 (@list @t111))) % 0.38/0.62 (step @p228 :rule bool-double-not-elim :args (@t115)) % 0.38/0.62 (step @p229 :rule refl :args (@t127)) % 0.38/0.62 (step @p230 :rule nary_cong :premises (@p229 @p228) :args ((or @t127 (not @t116)))) % 0.38/0.62 (step @p231 :rule cnf_or_neg :args (@t127 0)) % 0.38/0.62 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 0.38/0.62 (step @p233 :rule reordering :premises (@p232) :args ((or @t115 @t127))) % 0.38/0.62 (step @p234 :rule chain_m_resolution :premises (@p233 @p227) :args (@t115 @t135 @t136)) % 0.38/0.62 (step @p235 :rule cnf_or_neg :args (@t127 1)) % 0.38/0.62 (step @p236 :rule chain_m_resolution :premises (@p235 @p227) :args ((not @t114) @t135 @t136)) % 0.38/0.62 (step @p237 :rule cnf_or_pos :args (@t126)) % 0.38/0.62 (step @p238 :rule reordering :premises (@p237) :args ((or @t114 @t116 @t125 (not @t126)))) % 0.38/0.62 (step @p239 :rule chain_m_resolution :premises (@p238 @p236 @p234 @p201) :args (@t125 @t137 (@list @t114 @t115 @t126))) % 0.38/0.62 (step @p240 :rule skolemize :premises (@p239)) % 0.38/0.62 (step @p241 :rule bool-double-not-elim :args (@t107)) % 0.38/0.62 (step @p242 :rule refl :args (@t140)) % 0.38/0.62 (step @p243 :rule nary_cong :premises (@p242 @p241) :args ((or @t140 (not @t139)))) % 0.38/0.62 (step @p244 :rule cnf_or_neg :args (@t140 0)) % 0.38/0.62 (step @p245 :rule eq_resolve :premises (@p244 @p243)) % 0.38/0.62 (step @p246 :rule reordering :premises (@p245) :args ((or @t107 @t140))) % 0.38/0.62 (step @p247 :rule chain_m_resolution :premises (@p246 @p240) :args (@t107 @t135 @t141)) % 0.38/0.62 (step @p248 :rule cnf_equiv_pos1 :args (@t110)) % 0.38/0.62 (step @p249 :rule reordering :premises (@p248) :args ((or @t139 @t106 (not @t110)))) % 0.38/0.62 (step @p250 :rule chain_m_resolution :premises (@p249 @p247 @p175) :args (@t106 @t142 (@list @t107 @t110))) % 0.38/0.62 (step @p251 :rule skolemize :premises (@p250)) % 0.38/0.62 (step @p252 :rule bool-double-not-elim :args (@t143)) % 0.38/0.62 (step @p253 :rule refl :args (@t147)) % 0.38/0.62 (step @p254 :rule nary_cong :premises (@p253 @p252) :args ((or @t147 (not @t146)))) % 0.38/0.62 (step @p255 :rule cnf_or_neg :args (@t147 0)) % 0.38/0.62 (step @p256 :rule eq_resolve :premises (@p255 @p254)) % 0.38/0.62 (step @p257 :rule reordering :premises (@p256) :args ((or @t143 @t147))) % 0.38/0.62 (step @p258 :rule chain_m_resolution :premises (@p257 @p251) :args (@t143 @t135 @t148)) % 0.38/0.62 (step @p259 :rule instantiate :premises (@p258) :args (@t109)) % 0.38/0.62 (step @p260 :rule bool-double-not-elim :args (@t144)) % 0.38/0.62 (step @p261 :rule nary_cong :premises (@p253 @p260) :args ((or @t147 (not @t145)))) % 0.38/0.62 (step @p262 :rule cnf_or_neg :args (@t147 1)) % 0.38/0.62 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.38/0.62 (step @p264 :rule reordering :premises (@p263) :args ((or @t144 @t147))) % 0.38/0.62 (step @p265 :rule chain_m_resolution :premises (@p264 @p251) :args (@t144 @t135 @t148)) % 0.38/0.62 (step @p266 :rule cnf_or_pos :args (@t150)) % 0.38/0.62 (step @p267 :rule reordering :premises (@p266) :args ((or @t145 @t149 (not @t150)))) % 0.38/0.62 (step @p268 :rule chain_m_resolution :premises (@p267 @p265 @p259) :args (@t149 @t142 (@list @t144 @t150))) % 0.38/0.62 (step @p269 :rule cnf_or_neg :args (@t140 1)) % 0.38/0.62 (step @p270 :rule chain_m_resolution :premises (@p269 @p240) :args ((not @t138) @t135 @t141)) % 0.38/0.62 (step @p271 :rule cnf_or_pos :args (@t153)) % 0.38/0.62 (step @p272 :rule reordering :premises (@p271) :args ((or @t138 @t151 @t152 (not @t153)))) % 0.38/0.62 (step @p273 :rule chain_m_resolution :premises (@p272 @p270 @p268 @p166) :args (@t152 @t137 (@list @t138 @t149 @t153))) % 0.38/0.62 (step @p274 :rule skolemize :premises (@p273)) % 0.38/0.62 (step @p275 :rule cnf_or_neg :args (@t156 1)) % 0.38/0.62 (step @p276 :rule chain_m_resolution :premises (@p275 @p274) :args ((not @t60) @t135 @t157)) % 0.38/0.62 (step @p277 :rule bool-double-not-elim :args (@t58)) % 0.38/0.62 (step @p278 :rule refl :args (@t60)) % 0.38/0.62 (step @p279 :rule refl :args (@t158)) % 0.38/0.62 (step @p280 :rule nary_cong :premises (@p279 @p278 @p277) :args ((or @t158 @t60 (not @t59)))) % 0.38/0.62 (step @p281 :rule cnf_equiv_pos2 :args (@t63)) % 0.38/0.62 (step @p282 :rule eq_resolve :premises (@p281 @p280)) % 0.38/0.62 (step @p283 :rule reordering :premises (@p282) :args ((or @t60 @t58 @t158))) % 0.38/0.62 (step @p284 :rule chain_m_resolution :premises (@p283 @p276 @p31) :args (@t58 @t159 (@list @t60 @t63))) % 0.38/0.62 (step @p285 :rule bool-double-not-elim :args (@t154)) % 0.38/0.62 (step @p286 :rule refl :args (@t156)) % 0.38/0.62 (step @p287 :rule nary_cong :premises (@p286 @p285) :args ((or @t156 (not @t155)))) % 0.38/0.62 (step @p288 :rule cnf_or_neg :args (@t156 0)) % 0.38/0.62 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 0.38/0.62 (step @p290 :rule reordering :premises (@p289) :args ((or @t154 @t156))) % 0.38/0.62 (step @p291 :rule chain_m_resolution :premises (@p290 @p274) :args (@t154 @t135 @t157)) % 0.38/0.62 (step @p292 :rule cnf_or_pos :args (@t160)) % 0.38/0.62 (step @p293 :rule reordering :premises (@p292) :args ((or @t146 @t155 @t161))) % 0.38/0.62 (step @p294 :rule chain_m_resolution :premises (@p293 @p258 @p291) :args (@t161 @t142 (@list @t143 @t154))) % 0.38/0.62 (assume-push @p309 @t58) % 0.38/0.62 (step @p296 :rule instantiate :premises (@p284) :args ((@list @t55))) % 0.38/0.62 (step-pop @p310 :rule scope :premises (@p296)) % 0.38/0.62 (step @p297 :rule process_scope :premises (@p310) :args (@t160)) % 0.38/0.62 (step @p299 :rule implies_elim :premises (@p297)) % 0.38/0.62 (step @p300 false :rule chain_m_resolution :premises (@p299 @p294 @p284) :args (false @t159 (@list @t160 @t58))) % 0.38/0.62 ) % 0.38/0.62 % SZS output end Proof % 0.38/0.62 % cvc5 exiting %------------------------------------------------------------------------------