0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM 0.13/0.33 % Computer : n031.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1920 0.13/0.33 % WCLimit : 240 0.13/0.33 % DateTime : Fri Sep 5 22:34:37 EDT 2025 0.13/0.33 % CPUTime : 0.18/0.48 %----Proving TH0 0.36/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 72s... 0.36/0.59 % SZS status Theorem 0.36/0.59 % SZS output start Proof 0.36/0.59 ( 0.36/0.59 (declare-type tptp.nat ()) 0.36/0.59 (declare-const tptp.some (-> (-> tptp.nat Bool) Bool)) 0.36/0.59 (declare-const tptp.p (-> tptp.nat Bool)) 0.36/0.59 (declare-const tptp.lessis (-> tptp.nat tptp.nat Bool)) 0.36/0.59 (declare-const tptp.more (-> tptp.nat tptp.nat Bool)) 0.36/0.59 (define @t1 () (@var "Xx" tptp.nat)) 0.36/0.59 (define @t2 () (@var "Xy" tptp.nat)) 0.36/0.59 (define @t3 () (_ (_ tptp.more @t2) @t1)) 0.36/0.59 (define @t4 () (not @t3)) 0.36/0.59 (define @t5 () (=> @t4 (= @t2 @t1))) 0.36/0.59 (define @t6 () (_ tptp.lessis @t1)) 0.36/0.59 (define @t7 () (_ @t6 @t2)) 0.36/0.59 (define @t8 () (=> @t7 @t5)) 0.36/0.59 (define @t9 () (@list @t1 @t2)) 0.36/0.59 (define @t10 () (forall @t9 @t8)) 0.36/0.59 (define @t11 () (_ tptp.some tptp.p)) 0.36/0.59 (define @t12 () (@var "Xa" Bool)) 0.36/0.59 (define @t13 () (_ tptp.p @t1)) 0.36/0.59 (define @t14 () (not @t13)) 0.36/0.59 (define @t15 () (@var "Xx_0" tptp.nat)) 0.36/0.59 (define @t16 () (_ @t6 @t15)) 0.36/0.59 (define @t17 () (_ tptp.p @t15)) 0.36/0.59 (define @t18 () (@list @t15)) 0.36/0.60 (define @t19 () (forall @t18 (=> @t17 @t16))) 0.36/0.60 (define @t20 () (=> @t19 @t14)) 0.36/0.60 (define @t21 () (not @t20)) 0.36/0.60 (define @t22 () (@list @t1)) 0.36/0.60 (define @t23 () (lambda @t22 @t21)) 0.36/0.60 (define @t24 () (not (_ tptp.some @t23))) 0.36/0.60 (define @t25 () (= @t1 @t2)) 0.36/0.60 (define @t26 () (_ tptp.p @t2)) 0.36/0.60 (define @t27 () (not @t26)) 0.36/0.60 (define @t28 () (_ (_ tptp.lessis @t2) @t15)) 0.36/0.60 (define @t29 () (forall @t18 (=> @t17 @t28))) 0.36/0.60 (define @t30 () (=> @t29 @t27)) 0.36/0.60 (define @t31 () (not @t30)) 0.36/0.60 (define @t32 () (=> @t31 @t25)) 0.36/0.60 (define @t33 () (=> @t21 @t32)) 0.36/0.60 (define @t34 () (forall @t9 @t33)) 0.36/0.60 (define @t35 () (=> @t34 @t24)) 0.36/0.60 (define @t36 () (_ (_ tptp.more @t1) @t2)) 0.36/0.60 (define @t37 () (not @t36)) 0.36/0.60 (define @t38 () (forall @t9 (=> @t7 @t37))) 0.36/0.60 (define @t39 () (@var "Xp" (-> tptp.nat Bool))) 0.36/0.60 (define @t40 () (_ @t39 @t1)) 0.36/0.60 (define @t41 () (not @t40)) 0.36/0.60 (define @t42 () (_ @t39 @t15)) 0.36/0.60 (define @t43 () (forall @t18 (=> @t42 @t16))) 0.36/0.60 (define @t44 () (=> @t43 @t41)) 0.36/0.60 (define @t45 () (not @t44)) 0.36/0.60 (define @t46 () (lambda @t22 @t45)) 0.36/0.60 (define @t47 () (_ tptp.some @t39)) 0.36/0.60 (define @t48 () (=> @t47 (_ tptp.some @t46))) 0.36/0.60 (define @t49 () (@list @t39)) 0.36/0.60 (define @t50 () (forall @t49 @t48)) 0.36/0.60 (define @t51 () (tptp.p @t1)) 0.36/0.60 (define @t52 () (not @t51)) 0.36/0.60 (define @t53 () (tptp.lessis @t1 @t15)) 0.36/0.60 (define @t54 () (tptp.p @t15)) 0.36/0.60 (define @t55 () (not @t54)) 0.36/0.60 (define @t56 () (forall @t18 (or @t55 @t53))) 0.36/0.60 (define @t57 () (not (=> @t56 @t52))) 0.36/0.60 (define @t58 () (lambda @t22 @t57)) 0.36/0.60 (define @t59 () (@purify @t58)) 0.36/0.60 (define @t60 () (_ @t59 @t1)) 0.36/0.60 (define @t61 () (= @t57 @t60)) 0.36/0.60 (define @t62 () (_ @t58 @t1)) 0.36/0.60 (define @t63 () (= @t60 @t62)) 0.36/0.60 (define @t64 () (forall @t22 @t63)) 0.36/0.60 (define @t65 () (@const 0 tptp.nat)) 0.36/0.60 (define @t66 () (and (forall @t18 (or @t55 (tptp.lessis @t65 @t15))) (tptp.p @t65))) 0.36/0.60 (define @t67 () (_ @t59 @t65)) 0.36/0.60 (define @t68 () (forall @t22 (= (and @t56 @t51) @t60))) 0.36/0.60 (define @t69 () (= @t66 @t67)) 0.36/0.60 (define @t70 () (@list @t65)) 0.36/0.60 (define @t71 () (@list false)) 0.36/0.60 (define @t72 () (not @t42)) 0.36/0.60 (define @t73 () (or @t72 @t16)) 0.36/0.60 (define @t74 () (forall @t18 @t73)) 0.36/0.60 (define @t75 () (lambda @t22 (not (=> @t74 @t41)))) 0.36/0.60 (define @t76 () (_ @t39 @t1)) 0.36/0.60 (define @t77 () (not @t76)) 0.36/0.60 (define @t78 () (_ @t39 @t15)) 0.36/0.60 (define @t79 () (not @t78)) 0.36/0.60 (define @t80 () (or @t79 @t53)) 0.36/0.60 (define @t81 () (forall @t18 @t80)) 0.36/0.60 (define @t82 () (=> @t81 @t77)) 0.36/0.60 (define @t83 () (not @t82)) 0.36/0.60 (define @t84 () (lambda @t22 @t83)) 0.36/0.60 (define @t85 () (tptp.some @t84)) 0.36/0.60 (define @t86 () (=> @t81 @t41)) 0.36/0.60 (define @t87 () (not @t86)) 0.36/0.60 (define @t88 () (lambda @t22 @t87)) 0.36/0.60 (define @t89 () (tptp.some @t39)) 0.36/0.60 (define @t90 () (not @t47)) 0.36/0.60 (define @t91 () (_ tptp.some @t88)) 0.36/0.60 (define @t92 () (or @t90 @t91)) 0.36/0.60 (define @t93 () (tptp.some @t58)) 0.36/0.60 (define @t94 () (tptp.some tptp.p)) 0.36/0.60 (define @t95 () (not @t94)) 0.36/0.60 (define @t96 () (or @t95 @t93)) 0.36/0.60 (define @t97 () (forall @t49 (or (not @t89) @t85))) 0.36/0.60 (define @t98 () (tptp.some @t59)) 0.36/0.60 (define @t99 () (or @t95 @t98)) 0.36/0.60 (define @t100 () (@list false false)) 0.36/0.60 (define @t101 () (tptp.p @t2)) 0.36/0.60 (define @t102 () (tptp.lessis @t2 @t15)) 0.36/0.60 (define @t103 () (forall @t18 (or @t55 @t102))) 0.36/0.60 (define @t104 () (not @t103)) 0.36/0.60 (define @t105 () (not @t56)) 0.36/0.60 (define @t106 () (forall @t9 (or @t105 @t52 @t104 (not @t101) @t25))) 0.36/0.60 (define @t107 () (@quantifiers_skolemize @t106 0)) 0.36/0.60 (define @t108 () (forall @t18 (or @t55 (tptp.lessis @t107 @t15)))) 0.36/0.60 (define @t109 () (@quantifiers_skolemize @t106 1)) 0.36/0.60 (define @t110 () (= @t107 @t109)) 0.36/0.60 (define @t111 () (tptp.p @t109)) 0.36/0.60 (define @t112 () (not @t111)) 0.36/0.60 (define @t113 () (forall @t18 (or @t55 (tptp.lessis @t109 @t15)))) 0.36/0.60 (define @t114 () (not @t113)) 0.36/0.60 (define @t115 () (tptp.p @t107)) 0.36/0.60 (define @t116 () (not @t115)) 0.36/0.60 (define @t117 () (not @t108)) 0.36/0.60 (define @t118 () (or @t117 @t116 @t114 @t112 @t110)) 0.36/0.60 (define @t119 () (tptp.lessis @t107 @t109)) 0.36/0.60 (define @t120 () (or @t112 @t119)) 0.36/0.60 (define @t121 () (tptp.lessis @t109 @t107)) 0.36/0.60 (define @t122 () (or @t116 @t121)) 0.36/0.60 (define @t123 () (tptp.more @t1 @t2)) 0.36/0.60 (define @t124 () (tptp.lessis @t1 @t2)) 0.36/0.60 (define @t125 () (not @t7)) 0.36/0.60 (define @t126 () (or @t125 @t37)) 0.36/0.60 (define @t127 () (tptp.more @t107 @t109)) 0.36/0.60 (define @t128 () (not @t127)) 0.36/0.60 (define @t129 () (not @t119)) 0.36/0.60 (define @t130 () (or @t129 @t128)) 0.36/0.60 (define @t131 () (tptp.more @t2 @t1)) 0.36/0.60 (define @t132 () (or @t125 @t3 @t25)) 0.36/0.60 (define @t133 () (=> @t4 @t25)) 0.36/0.60 (define @t134 () (not @t121)) 0.36/0.60 (define @t135 () (or @t134 @t127 (= @t109 @t107))) 0.36/0.60 (define @t136 () (forall @t9 (or (not @t124) @t131 @t25))) 0.36/0.60 (define @t137 () (or @t134 @t127 @t110)) 0.36/0.60 (define @t138 () (not @t118)) 0.36/0.60 (define @t139 () (not @t106)) 0.36/0.60 (define @t140 () (=> @t56 @t14)) 0.36/0.60 (define @t141 () (not @t140)) 0.36/0.60 (define @t142 () (lambda @t22 @t141)) 0.36/0.60 (define @t143 () (@purify @t142)) 0.36/0.60 (define @t144 () (tptp.some @t143)) 0.36/0.60 (define @t145 () (_ tptp.some @t143)) 0.36/0.60 (define @t146 () (not (_ tptp.some @t142))) 0.36/0.60 (define @t147 () (not @t17)) 0.36/0.60 (define @t148 () (or @t147 @t16)) 0.36/0.60 (define @t149 () (or @t105 @t14 @t104 @t27 @t25)) 0.36/0.60 (define @t150 () (or @t104 @t27 @t25)) 0.36/0.60 (define @t151 () (=> @t103 @t27)) 0.36/0.60 (define @t152 () (not @t151)) 0.36/0.60 (define @t153 () (=> @t152 @t25)) 0.36/0.60 (define @t154 () (or @t147 @t28)) 0.36/0.60 (define @t155 () (not @t144)) 0.36/0.60 (define @t156 () (= @t143 @t59)) 0.36/0.60 (define @t157 () (not @t156)) 0.36/0.60 (define @t158 () (not @t98)) 0.36/0.60 (define @t159 () (and @t155 @t156 @t98)) 0.36/0.60 (define @t160 () (@list true false)) 0.36/0.60 (define @t161 () (_ @t143 @t65)) 0.36/0.60 (define @t162 () (= @t161 @t67)) 0.36/0.60 (define @t163 () (and @t56 @t13)) 0.36/0.60 (define @t164 () (_ @t143 @t1)) 0.36/0.60 (define @t165 () (= @t164 @t163)) 0.36/0.60 (define @t166 () (= @t141 @t164)) 0.36/0.60 (define @t167 () (_ @t142 @t1)) 0.36/0.60 (define @t168 () (= @t164 @t167)) 0.36/0.60 (define @t169 () (forall @t22 @t168)) 0.36/0.60 (define @t170 () (= @t161 @t66)) 0.36/0.60 (define @t171 () (not @t170)) 0.36/0.60 (define @t172 () (not @t66)) 0.36/0.60 (define @t173 () (= @t67 @t66)) 0.36/0.60 (define @t174 () (not @t173)) 0.36/0.60 (assume @p1 @t10) 0.36/0.60 (assume @p2 @t11) 0.36/0.60 (assume @p3 (forall (@list @t12) (=> (not (not @t12)) @t12))) 0.36/0.60 (assume @p4 (not (not @t35))) 0.36/0.60 (assume @p5 @t38) 0.36/0.60 (assume @p6 @t50) 0.36/0.60 (assume @p7 true) 0.36/0.60 (step @p8 :rule refl :args (@t60)) 0.36/0.60 (step @p9 :rule bool-double-not-elim :args (@t51)) 0.36/0.60 (step @p10 :rule refl :args (@t56)) 0.36/0.60 (step @p11 :rule nary_cong :premises (@p10 @p9) :args ((and @t56 (not @t52)))) 0.36/0.60 (step @p12 :rule bool-implies-de-morgan :args (@t56 @t52)) 0.36/0.60 (step @p13 :rule trans :premises (@p12 @p11)) 0.36/0.60 (step @p14 :rule cong :premises (@p13 @p8) :args (@t61)) 0.36/0.60 (step @p15 :rule cong :premises (@p14) :args ((forall @t22 @t61))) 0.36/0.60 (step @p16 :rule eq-symm :args (@t60 @t57)) 0.36/0.60 (step @p17 :rule beta-reduce :args ((= @t62 @t57))) 0.36/0.60 (step @p18 :rule refl :args (@t60)) 0.36/0.60 (step @p19 :rule cong :premises (@p18 @p17) :args (@t63)) 0.36/0.60 (step @p20 :rule trans :premises (@p19 @p16)) 0.36/0.60 (step @p21 :rule cong :premises (@p20) :args (@t64)) 0.36/0.60 (step @p22 :rule trans :premises (@p21 @p15)) 0.36/0.60 (step @p23 :rule quant-unused-vars :args ((= (forall @t22 true) true))) 0.36/0.60 (step @p24 :rule eq-refl :args (@t62)) 0.36/0.60 (step @p25 :rule cong :premises (@p24) :args ((forall @t22 (= @t62 @t62)))) 0.36/0.60 (step @p26 :rule trans :premises (@p25 @p23)) 0.36/0.60 (step @p27 :rule refl :args (@t62)) 0.36/0.60 (step @p28 :rule refl :args (@t1)) 0.36/0.60 (step @p29 :rule skolem_intro :args (@t59)) 0.36/0.60 (step @p30 :rule ho_cong :premises (@p29 @p28)) 0.36/0.60 (step @p31 :rule cong :premises (@p30 @p27) :args (@t63)) 0.36/0.60 (step @p32 :rule cong :premises (@p31) :args (@t64)) 0.36/0.60 (step @p33 :rule trans :premises (@p32 @p26)) 0.36/0.60 (step @p34 :rule true_elim :premises (@p33)) 0.36/0.60 (step @p35 :rule eq_resolve :premises (@p34 @p22)) 0.36/0.60 (step @p36 :rule eq-symm :args (@t66 @t67)) 0.36/0.60 (step @p37 :rule refl :args (@t68)) 0.36/0.60 (step @p38 :rule cong :premises (@p37 @p36) :args ((=> @t68 @t69))) 0.36/0.60 (assume-push @p428 @t68) 0.36/0.60 (step @p40 :rule instantiate :premises (@p35) :args (@t70)) 0.36/0.60 (step-pop @p428 :rule scope :premises (@p40)) 0.36/0.60 (step @p41 :rule process_scope :premises (@p428) :args (@t69)) 0.36/0.60 (step @p43 :rule eq_resolve :premises (@p41 @p38)) 0.36/0.60 (step @p44 :rule implies_elim :premises (@p43)) 0.36/0.60 (step @p45 :rule chain_resolution :premises (@p44 @p35) :args (@t71 (@list @t68))) 0.36/0.60 (step @p46 :rule refl :args ((tptp.some @t75))) 0.36/0.60 (step @p47 :rule refl :args (@t76)) 0.36/0.60 (step @p48 :rule cong :premises (@p47) :args (@t77)) 0.36/0.60 (step @p49 :rule refl :args (@t53)) 0.36/0.60 (step @p50 :rule refl :args (@t78)) 0.36/0.60 (step @p51 :rule cong :premises (@p50) :args (@t79)) 0.36/0.60 (step @p52 :rule nary_cong :premises (@p51 @p49) :args (@t80)) 0.36/0.60 (step @p53 :rule cong :premises (@p52) :args (@t81)) 0.36/0.60 (step @p54 :rule cong :premises (@p53 @p48) :args (@t82)) 0.36/0.60 (step @p55 :rule cong :premises (@p54) :args (@t83)) 0.36/0.60 (step @p56 :rule cong :premises (@p55) :args (@t84)) 0.36/0.60 (step @p57 :rule cong :premises (@p56) :args (@t85)) 0.36/0.60 (step @p58 :rule trans :premises (@p57 @p46)) 0.36/0.60 (step @p59 :rule refl :args (tptp.some)) 0.36/0.60 (step @p60 :rule ho_cong :premises (@p59 @p56)) 0.36/0.60 (step @p61 :rule cong :premises (@p60 @p58) :args ((= (_ tptp.some @t84) @t85))) 0.36/0.60 (step @p62 :rule symm :premises (@p61)) 0.36/0.60 (step @p63 :rule refl :args ((_ tptp.some @t75))) 0.36/0.60 (step @p64 :rule eq_resolve :premises (@p63 @p62)) 0.36/0.60 (step @p65 :rule refl :args (@t40)) 0.36/0.60 (step @p66 :rule cong :premises (@p65 @p47) :args ((= @t40 @t76))) 0.36/0.60 (step @p67 :rule symm :premises (@p66)) 0.36/0.60 (step @p68 :rule eq_resolve :premises (@p65 @p67)) 0.36/0.60 (step @p69 :rule cong :premises (@p68) :args (@t41)) 0.36/0.60 (step @p70 :rule refl :args (@t81)) 0.36/0.60 (step @p71 :rule cong :premises (@p70 @p69) :args (@t86)) 0.36/0.60 (step @p72 :rule cong :premises (@p71) :args (@t87)) 0.36/0.60 (step @p73 :rule cong :premises (@p72) :args (@t88)) 0.36/0.60 (step @p74 :rule ho_cong :premises (@p59 @p73)) 0.36/0.60 (step @p75 :rule trans :premises (@p74 @p64)) 0.36/0.60 (step @p76 :rule refl :args (@t89)) 0.36/0.60 (step @p77 :rule refl :args (@t47)) 0.36/0.60 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t47 @t89))) 0.36/0.60 (step @p79 :rule symm :premises (@p78)) 0.36/0.60 (step @p80 :rule eq_resolve :premises (@p77 @p79)) 0.36/0.60 (step @p81 :rule cong :premises (@p80) :args (@t90)) 0.36/0.60 (step @p82 :rule nary_cong :premises (@p81 @p75) :args (@t92)) 0.36/0.60 (step @p83 :rule cong :premises (@p82) :args ((forall @t49 @t92))) 0.36/0.60 (step @p84 :rule bool-impl-elim :args (@t47 @t91)) 0.36/0.60 (step @p85 :rule cong :premises (@p84) :args ((forall @t49 (=> @t47 @t91)))) 0.36/0.60 (step @p86 :rule trans :premises (@p85 @p83)) 0.36/0.60 (step @p87 :rule refl :args (@t41)) 0.36/0.60 (step @p88 :rule refl :args (@t16)) 0.36/0.60 (step @p89 :rule cong :premises (@p88 @p49) :args ((= @t16 @t53))) 0.36/0.60 (step @p90 :rule symm :premises (@p89)) 0.36/0.60 (step @p91 :rule eq_resolve :premises (@p88 @p90)) 0.36/0.60 (step @p92 :rule refl :args (@t42)) 0.36/0.60 (step @p93 :rule cong :premises (@p92 @p50) :args ((= @t42 @t78))) 0.36/0.60 (step @p94 :rule symm :premises (@p93)) 0.36/0.60 (step @p95 :rule eq_resolve :premises (@p92 @p94)) 0.36/0.60 (step @p96 :rule cong :premises (@p95) :args (@t72)) 0.36/0.60 (step @p97 :rule nary_cong :premises (@p96 @p91) :args (@t73)) 0.36/0.60 (step @p98 :rule cong :premises (@p97) :args (@t74)) 0.36/0.60 (step @p99 :rule bool-impl-elim :args (@t42 @t16)) 0.36/0.60 (step @p100 :rule cong :premises (@p99) :args (@t43)) 0.36/0.60 (step @p101 :rule trans :premises (@p100 @p98)) 0.36/0.60 (step @p102 :rule cong :premises (@p101 @p87) :args (@t44)) 0.36/0.60 (step @p103 :rule cong :premises (@p102) :args (@t45)) 0.36/0.60 (step @p104 :rule cong :premises (@p103) :args (@t46)) 0.36/0.60 (step @p105 :rule refl :args (tptp.some)) 0.36/0.60 (step @p106 :rule ho_cong :premises (@p105 @p104)) 0.36/0.60 (step @p107 :rule refl :args (@t47)) 0.36/0.60 (step @p108 :rule cong :premises (@p107 @p106) :args (@t48)) 0.36/0.60 (step @p109 :rule cong :premises (@p108) :args (@t50)) 0.36/0.60 (step @p110 :rule trans :premises (@p109 @p86)) 0.36/0.60 (step @p111 :rule eq_resolve :premises (@p6 @p110)) 0.36/0.60 (step @p112 :rule eq-refl :args (@t58)) 0.36/0.60 (step @p113 :rule refl :args (@t58)) 0.36/0.60 (step @p114 :rule cong :premises (@p113 @p29) :args ((= @t58 @t59))) 0.36/0.60 (step @p115 :rule trans :premises (@p114 @p112)) 0.36/0.60 (step @p116 :rule true_elim :premises (@p115)) 0.36/0.60 (step @p117 :rule cong :premises (@p116) :args (@t93)) 0.36/0.60 (step @p118 :rule refl :args (@t95)) 0.36/0.60 (step @p119 :rule nary_cong :premises (@p118 @p117) :args (@t96)) 0.36/0.60 (step @p120 :rule refl :args (@t97)) 0.36/0.60 (step @p121 :rule cong :premises (@p120 @p119) :args ((=> @t97 @t96))) 0.36/0.60 (assume-push @p430 @t97) 0.36/0.60 (step @p123 :rule instantiate :premises (@p111) :args ((@list tptp.p))) 0.36/0.60 (step-pop @p430 :rule scope :premises (@p123)) 0.36/0.60 (step @p124 :rule process_scope :premises (@p430) :args (@t96)) 0.36/0.60 (step @p126 :rule eq_resolve :premises (@p124 @p121)) 0.36/0.60 (step @p127 :rule implies_elim :premises (@p126)) 0.36/0.60 (step @p128 :rule chain_resolution :premises (@p127 @p111) :args (@t71 (@list @t97))) 0.36/0.60 (step @p129 :rule refl :args (@t94)) 0.36/0.60 (step @p130 :rule refl :args (@t11)) 0.36/0.60 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t11 @t94))) 0.36/0.60 (step @p132 :rule symm :premises (@p131)) 0.36/0.60 (step @p133 :rule eq_resolve :premises (@p130 @p132)) 0.36/0.60 (step @p134 :rule eq_resolve 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(step @p345 :rule chain_resolution :premises (@p344 @p249) :args (@t71 (@list @t106))) 0.36/0.60 (step @p346 :rule refl :args (@t157)) 0.36/0.60 (step @p347 :rule refl :args (@t158)) 0.36/0.60 (step @p348 :rule bool-double-not-elim :args (@t144)) 0.36/0.60 (step @p349 :rule nary_cong :premises (@p348 @p347 @p346) :args ((or (not @t155) @t158 @t157))) 0.36/0.60 (assume-push @p440 @t155) 0.36/0.60 (assume-push @p441 @t156) 0.36/0.60 (assume-push @p442 @t98) 0.36/0.60 (step @p353 :rule evaluate :args ((= true false))) 0.36/0.60 (step @p354 :rule false_intro :premises (@p440)) 0.36/0.60 (step @p355 :rule symm :premises (@p441)) 0.36/0.60 (step @p356 :rule cong :premises (@p355) :args (@t98)) 0.36/0.60 (step @p357 :rule true_intro :premises (@p137)) 0.36/0.60 (step @p358 :rule symm :premises (@p357)) 0.36/0.60 (step @p359 :rule trans :premises (@p358 @p356 @p354)) 0.36/0.60 (step @p360 false :rule eq_resolve :premises (@p359 @p353)) 0.36/0.60 (step-pop @p442 :rule scope :premises (@p360)) 0.36/0.60 (step-pop @p443 :rule scope :premises (@p442)) 0.36/0.60 (step-pop @p444 :rule scope :premises (@p443)) 0.36/0.60 (step @p361 :rule process_scope :premises (@p444) :args (false)) 0.36/0.60 (assume-push @p446 @t155) 0.36/0.60 (assume-push @p447 @t98) 0.36/0.60 (assume-push @p448 @t156) 0.36/0.60 (step @p368 :rule and_intro :premises (@p446 @p448 @p137)) 0.36/0.60 (step-pop @p448 :rule scope :premises (@p368)) 0.36/0.60 (step-pop @p449 :rule scope :premises (@p448)) 0.36/0.60 (step-pop @p450 :rule scope :premises (@p449)) 0.36/0.60 (step @p369 :rule process_scope :premises (@p450) :args (@t159)) 0.36/0.60 (step @p373 :rule implies_elim :premises (@p369)) 0.36/0.60 (step @p374 :rule resolution :premises (@p373 @p361) :args (true @t159)) 0.36/0.60 (step @p375 :rule not_and :premises (@p374)) 0.36/0.60 (step @p376 :rule eq_resolve :premises (@p375 @p349)) 0.36/0.60 (step @p377 :rule chain_resolution :premises (@p376 @p345 @p137) :args (@t160 (@list @t144 @t98))) 0.36/0.60 ; WARNING: add trust step for TRUST 0.36/0.60 ; trust TRUST THEORY_LEMMA 0.36/0.60 (step @p378 :rule trust :premises () :args ((or @t156 (not @t162)))) 0.36/0.60 (step @p379 :rule chain_resolution :premises (@p378 @p377) :args ((@list true) (@list @t156))) 0.36/0.60 (step @p380 :rule cnf_equiv_neg1 :args (@t162)) 0.36/0.60 (step @p381 :rule reordering :premises (@p380) :args ((or @t161 @t67 @t162))) 0.36/0.60 (step @p382 :rule nary_cong :premises (@p10 @p294) :args (@t163)) 0.36/0.60 (step @p383 :rule refl :args (@t164)) 0.36/0.60 (step @p384 :rule cong :premises (@p383 @p382) :args (@t165)) 0.36/0.60 (step @p385 :rule cong :premises (@p384) :args ((forall @t22 @t165))) 0.36/0.60 (step @p386 :rule eq-symm :args (@t163 @t164)) 0.36/0.60 (step @p387 :rule cong :premises (@p386) :args ((forall @t22 (= @t163 @t164)))) 0.36/0.60 (step @p388 :rule trans :premises (@p387 @p385)) 0.36/0.60 (step @p389 :rule bool-double-not-elim :args (@t13)) 0.36/0.60 (step @p390 :rule nary_cong :premises (@p10 @p389) :args ((and @t56 (not @t14)))) 0.36/0.60 (step @p391 :rule bool-implies-de-morgan :args (@t56 @t14)) 0.36/0.60 (step @p392 :rule trans :premises (@p391 @p390)) 0.36/0.60 (step @p393 :rule cong :premises (@p392 @p383) :args (@t166)) 0.36/0.60 (step @p394 :rule cong :premises (@p393) :args ((forall @t22 @t166))) 0.36/0.60 (step @p395 :rule trans :premises (@p394 @p388)) 0.36/0.60 (step @p396 :rule eq-symm :args (@t164 @t141)) 0.36/0.60 (step @p397 :rule beta-reduce :args ((= @t167 @t141))) 0.36/0.60 (step @p398 :rule refl :args (@t164)) 0.36/0.60 (step @p399 :rule cong :premises (@p398 @p397) :args (@t168)) 0.36/0.60 (step @p400 :rule trans :premises (@p399 @p396)) 0.36/0.60 (step @p401 :rule cong :premises (@p400) :args (@t169)) 0.36/0.60 (step @p402 :rule trans :premises (@p401 @p395)) 0.36/0.60 (step @p403 :rule eq-refl :args (@t167)) 0.36/0.60 (step @p404 :rule cong :premises (@p403) :args ((forall @t22 (= @t167 @t167)))) 0.36/0.60 (step @p405 :rule trans :premises (@p404 @p23)) 0.36/0.60 (step @p406 :rule refl :args (@t167)) 0.36/0.60 (step @p407 :rule ho_cong :premises (@p256 @p28)) 0.36/0.60 (step @p408 :rule cong :premises (@p407 @p406) :args (@t168)) 0.36/0.60 (step @p409 :rule cong :premises (@p408) :args (@t169)) 0.36/0.60 (step @p410 :rule trans :premises (@p409 @p405)) 0.36/0.60 (step @p411 :rule true_elim :premises (@p410)) 0.36/0.60 (step @p412 :rule eq_resolve :premises (@p411 @p402)) 0.36/0.60 (step @p413 :rule instantiate :premises (@p412) :args (@t70)) 0.36/0.60 (step @p414 :rule cnf_equiv_pos2 :args (@t170)) 0.36/0.60 (step @p415 :rule reordering :premises (@p414) :args ((or @t161 @t172 @t171))) 0.36/0.60 (step @p416 :rule cnf_equiv_pos1 :args (@t173)) 0.36/0.60 (step @p417 :rule reordering :premises (@p416) :args ((or (not @t67) @t66 @t174))) 0.36/0.60 (step @p418 :rule chain_resolution :premises (@p417 @p45 @p415 @p413 @p381 @p379) :args ((@list false true false false true) (@list @t173 @t66 @t170 @t67 @t162))) 0.36/0.60 (step @p419 :rule factoring :premises (@p418)) 0.36/0.60 (step @p420 :rule cnf_equiv_neg2 :args (@t162)) 0.36/0.60 (step @p421 :rule chain_resolution :premises (@p420 @p379 @p419) :args (@t160 (@list @t162 @t161))) 0.36/0.60 (step @p422 :rule cnf_equiv_pos1 :args (@t170)) 0.36/0.60 (step @p423 :rule reordering :premises (@p422) :args ((or (not @t161) @t66 @t171))) 0.36/0.60 (step @p424 :rule chain_resolution :premises (@p423 @p419 @p413) :args (@t100 (@list @t161 @t170))) 0.36/0.60 (step @p425 :rule cnf_equiv_pos2 :args (@t173)) 0.36/0.60 (step @p426 :rule reordering :premises (@p425) :args ((or @t67 @t172 @t174))) 0.36/0.60 (step @p427 false :rule chain_resolution :premises (@p426 @p424 @p421 @p45) :args ((@list false true false) (@list @t66 @t67 @t173))) 0.36/0.60 ) 0.36/0.60 % SZS output end Proof 0.36/0.60 % cvc5 exiting 0.36/0.60 EOF