%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO536^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:13:05 AM UTC 2026 % Result : Theorem 1.62s 1.89s % Output : Proof 1.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO536^1 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n028.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 00:19:50 EDT 2026 % 0.16/0.34 % CPUTime : % 0.26/0.49 %----Proving TH0 % 1.62/1.89 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.62/1.89 % SZS status Theorem % 1.62/1.89 % SZS output start Proof % 1.62/1.89 ( % 1.62/1.89 (declare-sort $$unsorted 0) % 1.62/1.89 (declare-const tptp.epsii (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted $$unsorted)) % 1.62/1.89 (declare-const tptp.eps (-> (-> $$unsorted Bool) $$unsorted)) % 1.62/1.89 (define tptp.epsa () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "X" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "R" (-> (-> $$unsorted $$unsorted) $$unsorted Bool)))) (lambda (@list _let_4 _let_1) (_ (_ tptp.epsii (lambda (@list _let_3) (exists (@list _let_2) (_ (_ _let_4 _let_3) _let_2)))) _let_1))))))) % 1.62/1.89 (define tptp.epsb () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "R" (-> (-> $$unsorted $$unsorted) $$unsorted Bool)))) (lambda (@list _let_2) (_ tptp.eps (lambda (@list _let_1) (_ (_ _let_2 (_ tptp.epsa _let_2)) _let_1))))))) % 1.62/1.89 (define @t1 () (@var "P" (-> $$unsorted Bool))) % 1.62/1.89 (define @t2 () (_ tptp.eps @t1)) % 1.62/1.89 (define @t3 () (_ @t1 @t2)) % 1.62/1.89 (define @t4 () (@var "X" $$unsorted)) % 1.62/1.89 (define @t5 () (_ @t1 @t4)) % 1.62/1.89 (define @t6 () (@list @t4)) % 1.62/1.89 (define @t7 () (exists @t6 @t5)) % 1.62/1.89 (define @t8 () (=> @t7 @t3)) % 1.62/1.89 (define @t9 () (@list @t1)) % 1.62/1.89 (define @t10 () (forall @t9 @t8)) % 1.62/1.89 (define @t11 () (@var "P" (-> (-> $$unsorted $$unsorted) Bool))) % 1.62/1.89 (define @t12 () (_ tptp.epsii @t11)) % 1.62/1.89 (define @t13 () (_ @t11 @t12)) % 1.62/1.89 (define @t14 () (@var "X" (-> $$unsorted $$unsorted))) % 1.62/1.89 (define @t15 () (_ @t11 @t14)) % 1.62/1.89 (define @t16 () (@list @t14)) % 1.62/1.89 (define @t17 () (exists @t16 @t15)) % 1.62/1.89 (define @t18 () (=> @t17 @t13)) % 1.62/1.89 (define @t19 () (@list @t11)) % 1.62/1.89 (define @t20 () (forall @t19 @t18)) % 1.62/1.89 (define @t21 () (@var "R" (-> (-> $$unsorted $$unsorted) $$unsorted Bool))) % 1.62/1.89 (define @t22 () (_ @t21 (_ tptp.epsa @t21))) % 1.62/1.89 (define @t23 () (@var "Y" $$unsorted)) % 1.62/1.89 (define @t24 () (_ @t21 @t14)) % 1.62/1.89 (define @t25 () (_ @t24 @t23)) % 1.62/1.89 (define @t26 () (@list @t14 @t23)) % 1.62/1.89 (define @t27 () (exists @t26 @t25)) % 1.62/1.89 (define @t28 () (=> @t27 (_ @t22 (_ tptp.epsb @t21)))) % 1.62/1.89 (define @t29 () (@list @t21)) % 1.62/1.89 (define @t30 () (forall @t29 @t28)) % 1.62/1.89 (define @t31 () (not @t30)) % 1.62/1.89 (define @t32 () (@var "__flatten_var_0" $$unsorted)) % 1.62/1.89 (define @t33 () (@list @t23)) % 1.62/1.89 (define @t34 () (exists @t33 @t25)) % 1.62/1.89 (define @t35 () (lambda @t16 @t34)) % 1.62/1.89 (define @t36 () (@list @t21 @t32)) % 1.62/1.89 (define @t37 () (lambda @t36 (_ (_ tptp.epsii @t35) @t32))) % 1.62/1.89 (define @t38 () (lambda @t33 (_ @t22 @t23))) % 1.62/1.89 (define @t39 () (lambda @t29 (_ tptp.eps @t38))) % 1.62/1.89 (define @t40 () (@var "BOUND_VARIABLE_7486" $$unsorted)) % 1.62/1.89 (define @t41 () (_ @t21 @t14 @t40)) % 1.62/1.89 (define @t42 () (not @t41)) % 1.62/1.89 (define @t43 () (@list @t40)) % 1.62/1.89 (define @t44 () (forall @t43 @t42)) % 1.62/1.89 (define @t45 () (not @t44)) % 1.62/1.89 (define @t46 () (lambda @t16 @t45)) % 1.62/1.89 (define @t47 () (tptp.epsii @t46 @t32)) % 1.62/1.89 (define @t48 () (@list @t32)) % 1.62/1.89 (define @t49 () (lambda @t48 @t47)) % 1.62/1.89 (define @t50 () (_ @t21 @t49 @t23)) % 1.62/1.89 (define @t51 () (lambda @t33 @t50)) % 1.62/1.89 (define @t52 () (tptp.eps @t51)) % 1.62/1.89 (define @t53 () (_ @t21 @t14 @t23)) % 1.62/1.89 (define @t54 () (not @t53)) % 1.62/1.89 (define @t55 () (forall @t33 @t54)) % 1.62/1.89 (define @t56 () (not @t55)) % 1.62/1.89 (define @t57 () (lambda @t16 @t56)) % 1.62/1.89 (define @t58 () (tptp.epsii @t57 @t32)) % 1.62/1.89 (define @t59 () (lambda @t48 @t58)) % 1.62/1.89 (define @t60 () (_ @t21 @t59 @t52)) % 1.62/1.89 (define @t61 () (@var "BOUND_VARIABLE_7600" $$unsorted)) % 1.62/1.89 (define @t62 () (@var "BOUND_VARIABLE_7598" (-> $$unsorted $$unsorted))) % 1.62/1.89 (define @t63 () (not (_ @t21 @t62 @t61))) % 1.62/1.89 (define @t64 () (or @t63 @t60)) % 1.62/1.89 (define @t65 () (forall (@list @t21 @t62 @t61) @t64)) % 1.62/1.89 (define @t66 () (@list @t62 @t61)) % 1.62/1.89 (define @t67 () (forall @t66 @t64)) % 1.62/1.89 (define @t68 () (forall @t66 @t63)) % 1.62/1.89 (define @t69 () (or @t68 @t60)) % 1.62/1.89 (define @t70 () (forall @t26 @t54)) % 1.62/1.89 (define @t71 () (lambda @t16 (not (forall @t43 (not (_ @t24 @t40)))))) % 1.62/1.89 (define @t72 () (_ (_ tptp.epsii @t71) @t32)) % 1.62/1.89 (define @t73 () (lambda @t48 @t72)) % 1.62/1.89 (define @t74 () (_ (_ @t21 @t73) @t23)) % 1.62/1.89 (define @t75 () (lambda @t33 @t74)) % 1.62/1.89 (define @t76 () (_ tptp.eps @t75)) % 1.62/1.89 (define @t77 () (not @t25)) % 1.62/1.89 (define @t78 () (forall @t33 @t77)) % 1.62/1.89 (define @t79 () (not @t78)) % 1.62/1.89 (define @t80 () (lambda @t16 @t79)) % 1.62/1.89 (define @t81 () (_ (_ tptp.epsii @t80) @t32)) % 1.62/1.89 (define @t82 () (lambda @t48 @t81)) % 1.62/1.89 (define @t83 () (_ (_ tptp.epsii @t46) @t32)) % 1.62/1.89 (define @t84 () (lambda @t48 @t83)) % 1.62/1.89 (define @t85 () (lambda @t33 (_ (_ @t21 @t84) @t23))) % 1.62/1.89 (define @t86 () (_ (_ tptp.epsii @t57) @t32)) % 1.62/1.89 (define @t87 () (lambda @t48 @t86)) % 1.62/1.89 (define @t88 () (_ tptp.eps @t85)) % 1.62/1.89 (define @t89 () (_ @t21 @t87)) % 1.62/1.89 (define @t90 () (_ @t89 @t88)) % 1.62/1.89 (define @t91 () (or @t70 @t90)) % 1.62/1.89 (define @t92 () (not @t70)) % 1.62/1.89 (define @t93 () (_ (lambda @t29 @t88) @t21)) % 1.62/1.89 (define @t94 () (_ (lambda @t36 @t86) @t21)) % 1.62/1.89 (define @t95 () (forall @t26 @t77)) % 1.62/1.89 (define @t96 () (not @t95)) % 1.62/1.89 (define @t97 () (_ @t21 @t94)) % 1.62/1.89 (define @t98 () (=> @t27 (_ @t97 @t93))) % 1.62/1.89 (define @t99 () (forall @t29 @t98)) % 1.62/1.89 (define @t100 () (@quantifiers_skolemize @t65 0)) % 1.62/1.89 (define @t101 () (not (forall @t43 (not (_ @t100 @t14 @t40))))) % 1.62/1.89 (define @t102 () (lambda @t16 @t101)) % 1.62/1.89 (define @t103 () (@purify @t102)) % 1.62/1.89 (define @t104 () (_ tptp.epsii @t103)) % 1.62/1.89 (define @t105 () (_ @t100 @t104)) % 1.62/1.89 (define @t106 () (tptp.eps @t105)) % 1.62/1.89 (define @t107 () (lambda @t16 (not (forall @t33 (not (_ @t100 @t14 @t23)))))) % 1.62/1.89 (define @t108 () (@purify @t107)) % 1.62/1.89 (define @t109 () (_ @t100 (_ tptp.epsii @t108) @t106)) % 1.62/1.89 (define @t110 () (@quantifiers_skolemize @t65 2)) % 1.62/1.89 (define @t111 () (@quantifiers_skolemize @t65 1)) % 1.62/1.89 (define @t112 () (_ @t100 @t111 @t110)) % 1.62/1.89 (define @t113 () (not @t112)) % 1.62/1.89 (define @t114 () (or @t113 @t109)) % 1.62/1.89 (define @t115 () (not @t114)) % 1.62/1.89 (define @t116 () (not @t65)) % 1.62/1.89 (define @t117 () (lambda @t48 (tptp.epsii @t102 @t32))) % 1.62/1.89 (define @t118 () (lambda @t33 (_ @t100 @t117 @t23))) % 1.62/1.89 (define @t119 () (tptp.eps @t118)) % 1.62/1.89 (define @t120 () (lambda @t48 (tptp.epsii @t107 @t32))) % 1.62/1.89 (define @t121 () (_ @t100 @t120 @t119)) % 1.62/1.89 (define @t122 () (or @t113 @t121)) % 1.62/1.89 (define @t123 () (not @t122)) % 1.62/1.89 (define @t124 () (@list true)) % 1.62/1.89 (define @t125 () (not @t109)) % 1.62/1.89 (define @t126 () (@list @t114)) % 1.62/1.89 (define @t127 () (tptp.eps @t1)) % 1.62/1.89 (define @t128 () (_ @t1 @t127)) % 1.62/1.89 (define @t129 () (@var "BOUND_VARIABLE_7533" $$unsorted)) % 1.62/1.89 (define @t130 () (not (_ @t1 @t129))) % 1.62/1.89 (define @t131 () (or @t130 @t128)) % 1.62/1.89 (define @t132 () (forall (@list @t1 @t129) @t131)) % 1.62/1.89 (define @t133 () (@list @t129)) % 1.62/1.89 (define @t134 () (forall @t133 @t131)) % 1.62/1.89 (define @t135 () (forall @t133 @t130)) % 1.62/1.89 (define @t136 () (or @t135 @t128)) % 1.62/1.89 (define @t137 () (_ @t1 @t4)) % 1.62/1.89 (define @t138 () (forall @t6 (not @t137))) % 1.62/1.89 (define @t139 () (or @t138 @t3)) % 1.62/1.89 (define @t140 () (not @t138)) % 1.62/1.89 (define @t141 () (not @t5)) % 1.62/1.89 (define @t142 () (forall @t6 @t141)) % 1.62/1.89 (define @t143 () (not @t142)) % 1.62/1.89 (define @t144 () (_ tptp.eps @t105)) % 1.62/1.89 (define @t145 () (_ @t100 @t104 @t106)) % 1.62/1.89 (define @t146 () (_ @t105 @t106)) % 1.62/1.89 (define @t147 () (forall @t33 (not (_ @t100 @t104 @t23)))) % 1.62/1.89 (define @t148 () (@quantifiers_skolemize @t147 0)) % 1.62/1.89 (define @t149 () (_ @t100 @t104 @t148)) % 1.62/1.89 (define @t150 () (_ @t105 @t148)) % 1.62/1.89 (define @t151 () (not @t150)) % 1.62/1.89 (define @t152 () (or @t151 @t146)) % 1.62/1.89 (define @t153 () (_ @t105 @t106)) % 1.62/1.89 (define @t154 () (_ @t105 @t148)) % 1.62/1.89 (define @t155 () (not @t154)) % 1.62/1.89 (define @t156 () (or @t155 @t153)) % 1.62/1.89 (define @t157 () (not @t149)) % 1.62/1.89 (define @t158 () (or @t157 @t145)) % 1.62/1.89 (define @t159 () (@list false)) % 1.62/1.89 (define @t160 () (_ @t103 @t14)) % 1.62/1.89 (define @t161 () (_ @t102 @t14)) % 1.62/1.89 (define @t162 () (= @t160 @t161)) % 1.62/1.89 (define @t163 () (forall @t16 @t162)) % 1.62/1.89 (define @t164 () (forall @t43 (not (_ @t100 @t104 @t40)))) % 1.62/1.89 (define @t165 () (not @t164)) % 1.62/1.89 (define @t166 () (_ @t103 @t104)) % 1.62/1.89 (define @t167 () (forall @t16 (= @t101 @t160))) % 1.62/1.89 (define @t168 () (= @t165 @t166)) % 1.62/1.89 (define @t169 () (= @t166 @t165)) % 1.62/1.89 (define @t170 () (@list @t167)) % 1.62/1.89 (define @t171 () (_ @t11 @t12)) % 1.62/1.89 (define @t172 () (@var "BOUND_VARIABLE_7555" (-> $$unsorted $$unsorted))) % 1.62/1.89 (define @t173 () (not (_ @t11 @t172))) % 1.62/1.89 (define @t174 () (or @t173 @t171)) % 1.62/1.89 (define @t175 () (@list @t172)) % 1.62/1.89 (define @t176 () (forall @t175 @t174)) % 1.62/1.89 (define @t177 () (forall @t175 @t173)) % 1.62/1.89 (define @t178 () (or @t177 @t171)) % 1.62/1.89 (define @t179 () (_ @t11 @t14)) % 1.62/1.89 (define @t180 () (forall @t16 (not @t179))) % 1.62/1.89 (define @t181 () (or @t180 @t13)) % 1.62/1.89 (define @t182 () (not @t180)) % 1.62/1.89 (define @t183 () (not @t15)) % 1.62/1.89 (define @t184 () (forall @t16 @t183)) % 1.62/1.89 (define @t185 () (not @t184)) % 1.62/1.89 (define @t186 () (@var "BOUND_VARIABLE_306995" $$unsorted)) % 1.62/1.89 (define @t187 () (lambda (@list @t186) (_ @t111 @t186))) % 1.62/1.89 (define @t188 () (_ @t103 @t187)) % 1.62/1.89 (define @t189 () (_ @t100 @t187 @t40)) % 1.62/1.89 (define @t190 () (not @t189)) % 1.62/1.89 (define @t191 () (forall @t43 @t190)) % 1.62/1.89 (define @t192 () (not @t191)) % 1.62/1.89 (define @t193 () (= @t192 @t188)) % 1.62/1.89 (define @t194 () (_ @t103 @t111)) % 1.62/1.89 (define @t195 () (forall @t43 (not (_ @t100 @t111 @t40)))) % 1.62/1.89 (define @t196 () (not @t195)) % 1.62/1.89 (define @t197 () (= @t196 @t194)) % 1.62/1.89 (define @t198 () (forall @t33 (not (_ @t100 @t111 @t23)))) % 1.62/1.89 (define @t199 () (not @t198)) % 1.62/1.89 (define @t200 () (@list @t23)) % 1.62/1.89 (define @t201 () (@list @t40)) % 1.62/1.89 (define @t202 () (not @t197)) % 1.62/1.89 (define @t203 () (@list true false)) % 1.62/1.89 (define @t204 () (not @t194)) % 1.62/1.89 (define @t205 () (or @t204 @t166)) % 1.62/1.89 (define @t206 () (@list false false)) % 1.62/1.89 (define @t207 () (not @t147)) % 1.62/1.89 (define @t208 () (not @t157)) % 1.62/1.89 (define @t209 () (not @t145)) % 1.62/1.89 (define @t210 () (= @t103 @t108)) % 1.62/1.89 (define @t211 () (not @t210)) % 1.62/1.89 (define @t212 () (and @t125 @t210)) % 1.62/1.89 (define @t213 () (@const 0 (-> $$unsorted $$unsorted))) % 1.62/1.89 (define @t214 () (forall @t43 (not (_ @t100 @t213 @t40)))) % 1.62/1.89 (define @t215 () (not @t214)) % 1.62/1.89 (define @t216 () (forall @t33 (not (_ @t100 @t213 @t23)))) % 1.62/1.89 (define @t217 () (not @t216)) % 1.62/1.89 (define @t218 () (_ @t107 @t213)) % 1.62/1.89 (define @t219 () (_ @t108 @t213)) % 1.62/1.89 (define @t220 () (_ @t102 @t213)) % 1.62/1.89 (define @t221 () (_ @t103 @t213)) % 1.62/1.89 (define @t222 () (= @t221 @t219)) % 1.62/1.89 (define @t223 () (not @t222)) % 1.62/1.89 (define @t224 () (or @t210 @t223)) % 1.62/1.89 (define @t225 () (= @t217 @t215)) % 1.62/1.89 (assume @p1 @t10) % 1.62/1.89 (assume @p2 @t20) % 1.62/1.89 (assume @p3 @t31) % 1.62/1.89 (assume @p4 true) % 1.62/1.89 (step @p5 (= tptp.epsa @t37) :rule refl :args (@t37)) % 1.62/1.89 (step @p6 (= tptp.epsb @t39) :rule refl :args (@t39)) % 1.62/1.89 (step @p7 :rule quant-merge-prenex :args ((= (forall @t29 @t67) @t65))) % 1.62/1.89 (step @p8 :rule refl :args (@t60)) % 1.62/1.89 (step @p9 :rule alpha_equiv :args (@t68 (@list @t62 @t61) (@list @t14 @t23))) % 1.62/1.89 (step @p10 :rule nary_cong :premises (@p9 @p8) :args (@t69)) % 1.62/1.89 (step @p11 :rule quant-miniscope-or :args ((= @t67 @t69))) % 1.62/1.89 (step @p12 :rule trans :premises (@p11 @p10)) % 1.62/1.89 (step @p13 :rule symm :premises (@p12)) % 1.62/1.89 (step @p14 :rule cong :premises (@p13) :args ((forall @t29 (or @t70 @t60)))) % 1.62/1.89 (step @p15 :rule trans :premises (@p14 @p7)) % 1.62/1.89 (step @p16 :rule refl :args ((_ @t21 @t82 @t76))) % 1.62/1.89 (step @p17 :rule refl :args ((tptp.eps @t75))) % 1.62/1.89 (step @p18 :rule refl :args ((_ @t21 @t73 @t23))) % 1.62/1.89 (step @p19 :rule refl :args (@t23)) % 1.62/1.89 (step @p20 :rule refl :args ((tptp.epsii @t71 @t32))) % 1.62/1.89 (step @p21 :rule refl :args (@t32)) % 1.62/1.89 (step @p22 :rule refl :args (@t41)) % 1.62/1.89 (step @p23 :rule cong :premises (@p22) :args (@t42)) % 1.62/1.89 (step @p24 :rule cong :premises (@p23) :args (@t44)) % 1.62/1.89 (step @p25 :rule cong :premises (@p24) :args (@t45)) % 1.62/1.89 (step @p26 :rule cong :premises (@p25) :args (@t46)) % 1.62/1.89 (step @p27 :rule cong :premises (@p26 @p21) :args (@t47)) % 1.62/1.89 (step @p28 :rule trans :premises (@p27 @p20)) % 1.62/1.89 (step @p29 :rule cong :premises (@p28) :args (@t49)) % 1.62/1.89 (step @p30 :rule cong :premises (@p29 @p19) :args (@t50)) % 1.62/1.89 (step @p31 :rule trans :premises (@p30 @p18)) % 1.62/1.89 (step @p32 :rule cong :premises (@p31) :args (@t51)) % 1.62/1.89 (step @p33 :rule cong :premises (@p32) :args (@t52)) % 1.62/1.89 (step @p34 :rule trans :premises (@p33 @p17)) % 1.62/1.89 (step @p35 :rule refl :args ((tptp.epsii @t80 @t32))) % 1.62/1.89 (step @p36 :rule refl :args (@t53)) % 1.62/1.89 (step @p37 :rule cong :premises (@p36) :args (@t54)) % 1.62/1.89 (step @p38 :rule cong :premises (@p37) :args (@t55)) % 1.62/1.89 (step @p39 :rule cong :premises (@p38) :args (@t56)) % 1.62/1.89 (step @p40 :rule cong :premises (@p39) :args (@t57)) % 1.62/1.89 (step @p41 :rule cong :premises (@p40 @p21) :args (@t58)) % 1.62/1.89 (step @p42 :rule trans :premises (@p41 @p35)) % 1.62/1.89 (step @p43 :rule cong :premises (@p42) :args (@t59)) % 1.62/1.89 (step @p44 :rule cong :premises (@p43 @p34) :args (@t60)) % 1.62/1.89 (step @p45 :rule trans :premises (@p44 @p16)) % 1.62/1.89 (step @p46 :rule refl :args (@t21)) % 1.62/1.89 (step @p47 :rule ho_cong :premises (@p46 @p43)) % 1.62/1.89 (step @p48 :rule ho_cong :premises (@p47 @p34)) % 1.62/1.89 (step @p49 :rule cong :premises (@p48 @p45) :args ((= (_ (_ @t21 @t59) @t52) @t60))) % 1.62/1.89 (step @p50 :rule symm :premises (@p49)) % 1.62/1.89 (step @p51 :rule refl :args ((_ (_ @t21 @t82) @t76))) % 1.62/1.89 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 1.62/1.89 (step @p53 :rule refl :args (tptp.eps)) % 1.62/1.89 (step @p54 :rule ho_cong :premises (@p53 @p32)) % 1.62/1.89 (step @p55 :rule cong :premises (@p54 @p34) :args ((= (_ tptp.eps @t51) @t52))) % 1.62/1.89 (step @p56 :rule symm :premises (@p55)) % 1.62/1.89 (step @p57 :rule refl :args (@t76)) % 1.62/1.89 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 1.62/1.89 (step @p59 :rule ho_cong :premises (@p46 @p29)) % 1.62/1.89 (step @p60 :rule ho_cong :premises (@p59 @p19)) % 1.62/1.89 (step @p61 :rule cong :premises (@p60 @p31) :args ((= (_ (_ @t21 @t49) @t23) @t50))) % 1.62/1.89 (step @p62 :rule symm :premises (@p61)) % 1.62/1.89 (step @p63 :rule refl :args (@t74)) % 1.62/1.89 (step @p64 :rule eq_resolve :premises (@p63 @p62)) % 1.62/1.89 (step @p65 :rule refl :args (tptp.epsii)) % 1.62/1.89 (step @p66 :rule ho_cong :premises (@p65 @p26)) % 1.62/1.89 (step @p67 :rule ho_cong :premises (@p66 @p21)) % 1.62/1.89 (step @p68 :rule cong :premises (@p67 @p28) :args ((= @t83 @t47))) % 1.62/1.89 (step @p69 :rule symm :premises (@p68)) % 1.62/1.89 (step @p70 :rule refl :args (@t72)) % 1.62/1.89 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 1.62/1.89 (step @p72 :rule cong :premises (@p71) :args (@t84)) % 1.62/1.89 (step @p73 :rule ho_cong :premises (@p46 @p72)) % 1.62/1.89 (step @p74 :rule ho_cong :premises (@p73 @p19)) % 1.62/1.89 (step @p75 :rule trans :premises (@p74 @p64)) % 1.62/1.89 (step @p76 :rule cong :premises (@p75) :args (@t85)) % 1.62/1.89 (step @p77 :rule ho_cong :premises (@p53 @p76)) % 1.62/1.89 (step @p78 :rule trans :premises (@p77 @p58)) % 1.62/1.89 (step @p79 :rule ho_cong :premises (@p65 @p40)) % 1.62/1.89 (step @p80 :rule ho_cong :premises (@p79 @p21)) % 1.62/1.89 (step @p81 :rule cong :premises (@p80 @p42) :args ((= @t86 @t58))) % 1.62/1.89 (step @p82 :rule symm :premises (@p81)) % 1.62/1.89 (step @p83 :rule refl :args (@t81)) % 1.62/1.89 (step @p84 :rule eq_resolve :premises (@p83 @p82)) % 1.62/1.89 (step @p85 :rule cong :premises (@p84) :args (@t87)) % 1.62/1.89 (step @p86 :rule ho_cong :premises (@p46 @p85)) % 1.62/1.89 (step @p87 :rule ho_cong :premises (@p86 @p78)) % 1.62/1.89 (step @p88 :rule trans :premises (@p87 @p52)) % 1.62/1.89 (step @p89 :rule refl :args (@t70)) % 1.62/1.89 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t91)) % 1.62/1.89 (step @p91 :rule cong :premises (@p90) :args ((forall @t29 @t91))) % 1.62/1.89 (step @p92 :rule trans :premises (@p91 @p15)) % 1.62/1.89 (step @p93 :rule refl :args (@t90)) % 1.62/1.89 (step @p94 :rule bool-double-not-elim :args (@t70)) % 1.62/1.89 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or (not @t92) @t90))) % 1.62/1.89 (step @p96 :rule bool-impl-elim :args (@t92 @t90)) % 1.62/1.89 (step @p97 :rule trans :premises (@p96 @p95)) % 1.62/1.89 (step @p98 :rule cong :premises (@p97) :args ((forall @t29 (=> @t92 @t90)))) % 1.62/1.89 (step @p99 :rule trans :premises (@p98 @p92)) % 1.62/1.89 (step @p100 :rule beta-reduce :args ((= @t93 @t88))) % 1.62/1.89 (step @p101 :rule beta-reduce :args ((= @t94 @t87))) % 1.62/1.89 (step @p102 :rule refl :args (@t21)) % 1.62/1.89 (step @p103 :rule ho_cong :premises (@p102 @p101)) % 1.62/1.89 (step @p104 :rule ho_cong :premises (@p103 @p100)) % 1.62/1.89 (step @p105 :rule refl :args (@t25)) % 1.62/1.89 (step @p106 :rule cong :premises (@p105 @p36) :args ((= @t25 @t53))) % 1.62/1.89 (step @p107 :rule symm :premises (@p106)) % 1.62/1.89 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 1.62/1.89 (step @p109 :rule cong :premises (@p108) :args (@t77)) % 1.62/1.89 (step @p110 :rule cong :premises (@p109) :args (@t95)) % 1.62/1.89 (step @p111 :rule cong :premises (@p110) :args (@t96)) % 1.62/1.89 (step @p112 :rule exists-elim :args ((= @t27 @t96))) % 1.62/1.89 (step @p113 :rule trans :premises (@p112 @p111)) % 1.62/1.89 (step @p114 :rule cong :premises (@p113 @p104) :args (@t98)) % 1.62/1.89 (step @p115 :rule cong :premises (@p114) :args (@t99)) % 1.62/1.89 (step @p116 :rule trans :premises (@p115 @p99)) % 1.62/1.89 (step @p117 :rule cong :premises (@p116) :args ((not @t99))) % 1.62/1.89 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 1.62/1.89 ; trust TRUST_THEORY_REWRITE % 1.62/1.89 (step @p118 :rule trust :premises () :args ((= (lambda @t33 (_ @t89 @t23)) @t85))) % 1.62/1.89 (step @p119 :rule refl :args (@t23)) % 1.62/1.89 (step @p120 :rule ho_cong :premises (@p103 @p119)) % 1.62/1.89 (step @p121 :rule cong :premises (@p120) :args ((lambda @t33 (_ @t97 @t23)))) % 1.62/1.89 (step @p122 :rule trans :premises (@p121 @p118)) % 1.62/1.89 (step @p123 :rule refl :args (tptp.eps)) % 1.62/1.89 (step @p124 :rule ho_cong :premises (@p123 @p122)) % 1.62/1.89 (step @p125 :rule refl :args (@t32)) % 1.62/1.89 (step @p126 :rule cong :premises (@p109) :args (@t78)) % 1.62/1.89 (step @p127 :rule cong :premises (@p126) :args (@t79)) % 1.62/1.89 (step @p128 :rule exists-elim :args ((= @t34 @t79))) % 1.62/1.89 (step @p129 :rule trans :premises (@p128 @p127)) % 1.62/1.89 (step @p130 :rule cong :premises (@p129) :args (@t35)) % 1.62/1.89 (step @p131 :rule refl :args (tptp.epsii)) % 1.62/1.89 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 1.62/1.89 (step @p133 :rule ho_cong :premises (@p132 @p125)) % 1.62/1.89 (step @p134 :rule cong :premises (@p133) :args (@t37)) % 1.62/1.89 (step @p135 :rule trans :premises (@p5 @p134)) % 1.62/1.89 (step @p136 :rule ho_cong :premises (@p135 @p102)) % 1.62/1.89 (step @p137 :rule ho_cong :premises (@p102 @p136)) % 1.62/1.89 (step @p138 :rule ho_cong :premises (@p137 @p119)) % 1.62/1.89 (step @p139 :rule cong :premises (@p138) :args (@t38)) % 1.62/1.89 (step @p140 :rule ho_cong :premises (@p123 @p139)) % 1.62/1.89 (step @p141 :rule trans :premises (@p140 @p124)) % 1.62/1.89 (step @p142 :rule cong :premises (@p141) :args (@t39)) % 1.62/1.89 (step @p143 :rule trans :premises (@p6 @p142)) % 1.62/1.89 (step @p144 :rule ho_cong :premises (@p143 @p102)) % 1.62/1.89 (step @p145 :rule ho_cong :premises (@p137 @p144)) % 1.62/1.89 (step @p146 :rule refl :args (@t27)) % 1.62/1.89 (step @p147 :rule cong :premises (@p146 @p145) :args (@t28)) % 1.62/1.89 (step @p148 :rule cong :premises (@p147) :args (@t30)) % 1.62/1.89 (step @p149 :rule cong :premises (@p148) :args (@t31)) % 1.62/1.89 (step @p150 :rule trans :premises (@p149 @p117)) % 1.62/1.89 (step @p151 :rule eq_resolve :premises (@p3 @p150)) % 1.62/1.89 (step @p152 :rule refl :args (@t115)) % 1.62/1.89 (step @p153 :rule bool-double-not-elim :args (@t65)) % 1.62/1.89 (step @p154 :rule nary_cong :premises (@p153 @p152) :args ((or (not @t116) @t115))) % 1.62/1.89 (step @p155 :rule eq-refl :args (@t102)) % 1.62/1.89 (step @p156 :rule skolem_intro :args (@t103)) % 1.62/1.89 (step @p157 :rule refl :args (@t102)) % 1.62/1.89 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t102 @t103))) % 1.62/1.89 (step @p159 :rule trans :premises (@p158 @p155)) % 1.62/1.89 (step @p160 :rule true_elim :premises (@p159)) % 1.62/1.89 (step @p161 :rule ho_cong :premises (@p131 @p160)) % 1.62/1.89 (step @p162 :rule lambda-elim :args ((= @t117 (_ tptp.epsii @t102)))) % 1.62/1.89 (step @p163 :rule trans :premises (@p162 @p161)) % 1.62/1.89 (step @p164 :rule refl :args (@t100)) % 1.62/1.89 (step @p165 :rule ho_cong :premises (@p164 @p163)) % 1.62/1.89 (step @p166 :rule lambda-elim :args ((= @t118 (_ @t100 @t117)))) % 1.62/1.89 (step @p167 :rule trans :premises (@p166 @p165)) % 1.62/1.89 (step @p168 :rule cong :premises (@p167) :args (@t119)) % 1.62/1.89 (step @p169 :rule eq-refl :args (@t107)) % 1.62/1.89 (step @p170 :rule skolem_intro :args (@t108)) % 1.62/1.89 (step @p171 :rule refl :args (@t107)) % 1.62/1.89 (step @p172 :rule cong :premises (@p171 @p170) :args ((= @t107 @t108))) % 1.62/1.89 (step @p173 :rule trans :premises (@p172 @p169)) % 1.62/1.89 (step @p174 :rule true_elim :premises (@p173)) % 1.62/1.89 (step @p175 :rule ho_cong :premises (@p131 @p174)) % 1.62/1.89 (step @p176 :rule lambda-elim :args ((= @t120 (_ tptp.epsii @t107)))) % 1.62/1.89 (step @p177 :rule trans :premises (@p176 @p175)) % 1.62/1.89 (step @p178 :rule cong :premises (@p177 @p168) :args (@t121)) % 1.62/1.89 (step @p179 :rule refl :args (@t113)) % 1.62/1.89 (step @p180 :rule nary_cong :premises (@p179 @p178) :args (@t122)) % 1.62/1.89 (step @p181 :rule cong :premises (@p180) :args (@t123)) % 1.62/1.89 (step @p182 :rule refl :args (@t116)) % 1.62/1.89 (step @p183 :rule cong :premises (@p182 @p181) :args ((=> @t116 @t123))) % 1.62/1.89 (assume-push @p491 @t116) % 1.62/1.89 (step @p185 :rule skolemize :premises (@p151)) % 1.62/1.89 (step-pop @p492 :rule scope :premises (@p185)) % 1.62/1.89 (step @p186 :rule process_scope :premises (@p492) :args (@t123)) % 1.62/1.89 (step @p188 :rule eq_resolve :premises (@p186 @p183)) % 1.62/1.89 (step @p189 :rule implies_elim :premises (@p188)) % 1.62/1.89 (step @p190 :rule eq_resolve :premises (@p189 @p154)) % 1.62/1.89 (step @p191 :rule chain_m_resolution :premises (@p190 @p151) :args (@t115 @t124 (@list @t65))) % 1.62/1.89 (step @p192 :rule cnf_or_neg :args (@t114 1)) % 1.62/1.89 (step @p193 :rule chain_m_resolution :premises (@p192 @p191) :args (@t125 @t124 @t126)) % 1.62/1.89 (step @p194 :rule quant-merge-prenex :args ((= (forall @t9 @t134) @t132))) % 1.62/1.89 (step @p195 :rule refl :args (@t128)) % 1.62/1.89 (step @p196 :rule alpha_equiv :args (@t135 (@list @t129) (@list @t4))) % 1.62/1.89 (step @p197 :rule nary_cong :premises (@p196 @p195) :args (@t136)) % 1.62/1.89 (step @p198 :rule quant-miniscope-or :args ((= @t134 @t136))) % 1.62/1.89 (step @p199 :rule trans :premises (@p198 @p197)) % 1.62/1.89 (step @p200 :rule symm :premises (@p199)) % 1.62/1.89 (step @p201 :rule cong :premises (@p200) :args ((forall @t9 (or @t138 @t128)))) % 1.62/1.89 (step @p202 :rule trans :premises (@p201 @p194)) % 1.62/1.89 (step @p203 :rule refl :args ((_ @t1 @t2))) % 1.62/1.89 (step @p204 :rule refl :args (@t127)) % 1.62/1.89 (step @p205 :rule cong :premises (@p204) :args (@t128)) % 1.62/1.89 (step @p206 :rule trans :premises (@p205 @p203)) % 1.62/1.89 (step @p207 :rule refl :args (@t1)) % 1.62/1.89 (step @p208 :rule ho_cong :premises (@p207 @p204)) % 1.62/1.89 (step @p209 :rule cong :premises (@p208 @p206) :args ((= (_ @t1 @t127) @t128))) % 1.62/1.89 (step @p210 :rule symm :premises (@p209)) % 1.62/1.89 (step @p211 :rule refl :args (@t3)) % 1.62/1.89 (step @p212 :rule eq_resolve :premises (@p211 @p210)) % 1.62/1.89 (step @p213 :rule refl :args (@t2)) % 1.62/1.89 (step @p214 :rule cong :premises (@p213 @p204) :args ((= @t2 @t127))) % 1.62/1.89 (step @p215 :rule symm :premises (@p214)) % 1.62/1.89 (step @p216 :rule eq_resolve :premises (@p213 @p215)) % 1.62/1.89 (step @p217 :rule ho_cong :premises (@p207 @p216)) % 1.62/1.89 (step @p218 :rule trans :premises (@p217 @p212)) % 1.62/1.89 (step @p219 :rule refl :args (@t138)) % 1.62/1.89 (step @p220 :rule nary_cong :premises (@p219 @p218) :args (@t139)) % 1.62/1.89 (step @p221 :rule cong :premises (@p220) :args ((forall @t9 @t139))) % 1.62/1.89 (step @p222 :rule trans :premises (@p221 @p202)) % 1.62/1.89 (step @p223 :rule bool-double-not-elim :args (@t138)) % 1.62/1.89 (step @p224 :rule nary_cong :premises (@p223 @p211) :args ((or (not @t140) @t3))) % 1.62/1.89 (step @p225 :rule bool-impl-elim :args (@t140 @t3)) % 1.62/1.89 (step @p226 :rule trans :premises (@p225 @p224)) % 1.62/1.89 (step @p227 :rule cong :premises (@p226) :args ((forall @t9 (=> @t140 @t3)))) % 1.62/1.89 (step @p228 :rule trans :premises (@p227 @p222)) % 1.62/1.89 (step @p229 :rule refl :args (@t3)) % 1.62/1.89 (step @p230 :rule refl :args (@t137)) % 1.62/1.89 (step @p231 :rule refl :args (@t5)) % 1.62/1.89 (step @p232 :rule cong :premises (@p231 @p230) :args ((= @t5 @t137))) % 1.62/1.89 (step @p233 :rule symm :premises (@p232)) % 1.62/1.89 (step @p234 :rule eq_resolve :premises (@p231 @p233)) % 1.62/1.89 (step @p235 :rule cong :premises (@p234) :args (@t141)) % 1.62/1.89 (step @p236 :rule cong :premises (@p235) :args (@t142)) % 1.62/1.89 (step @p237 :rule cong :premises (@p236) :args (@t143)) % 1.62/1.89 (step @p238 :rule exists-elim :args ((= @t7 @t143))) % 1.62/1.89 (step @p239 :rule trans :premises (@p238 @p237)) % 1.62/1.89 (step @p240 :rule cong :premises (@p239 @p229) :args (@t8)) % 1.62/1.89 (step @p241 :rule cong :premises (@p240) :args (@t10)) % 1.62/1.89 (step @p242 :rule trans :premises (@p241 @p228)) % 1.62/1.89 (step @p243 :rule eq_resolve :premises (@p1 @p242)) % 1.62/1.89 (step @p244 :rule refl :args ((_ @t100 @t104 @t144))) % 1.62/1.89 (step @p245 :rule refl :args (@t106)) % 1.62/1.89 (step @p246 :rule refl :args (@t104)) % 1.62/1.89 (step @p247 :rule cong :premises (@p246 @p245) :args (@t145)) % 1.62/1.89 (step @p248 :rule trans :premises (@p247 @p244)) % 1.62/1.89 (step @p249 :rule refl :args (@t105)) % 1.62/1.89 (step @p250 :rule ho_cong :premises (@p249 @p245)) % 1.62/1.89 (step @p251 :rule cong :premises (@p250 @p248) :args ((= @t146 @t145))) % 1.62/1.89 (step @p252 :rule symm :premises (@p251)) % 1.62/1.89 (step @p253 :rule refl :args ((_ @t105 @t144))) % 1.62/1.89 (step @p254 :rule eq_resolve :premises (@p253 @p252)) % 1.62/1.89 (step @p255 :rule refl :args (@t149)) % 1.62/1.89 (step @p256 :rule refl :args (@t150)) % 1.62/1.89 (step @p257 :rule cong :premises (@p256 @p255) :args ((= @t150 @t149))) % 1.62/1.89 (step @p258 :rule symm :premises (@p257)) % 1.62/1.89 (step @p259 :rule eq_resolve :premises (@p256 @p258)) % 1.62/1.89 (step @p260 :rule cong :premises (@p259) :args (@t151)) % 1.62/1.89 (step @p261 :rule nary_cong :premises (@p260 @p254) :args (@t152)) % 1.62/1.89 (step @p262 :rule refl :args (@t132)) % 1.62/1.89 (step @p263 :rule cong :premises (@p262 @p261) :args ((=> @t132 @t152))) % 1.62/1.89 (step @p264 :rule refl :args ((_ @t105 @t144))) % 1.62/1.89 (step @p265 :rule cong :premises (@p245) :args (@t153)) % 1.62/1.89 (step @p266 :rule trans :premises (@p265 @p264)) % 1.62/1.89 (step @p267 :rule cong :premises (@p266 @p250) :args ((= @t153 @t146))) % 1.62/1.89 (step @p268 :rule symm :premises (@p267)) % 1.62/1.89 (step @p269 :rule eq_resolve :premises (@p253 @p268)) % 1.62/1.89 (step @p270 :rule refl :args (@t154)) % 1.62/1.89 (step @p271 :rule cong :premises (@p270) :args (@t155)) % 1.62/1.89 (step @p272 :rule nary_cong :premises (@p271 @p269) :args (@t156)) % 1.62/1.89 (step @p273 :rule cong :premises (@p262 @p272) :args ((=> @t132 @t156))) % 1.62/1.89 (assume-push @p493 @t132) % 1.62/1.89 (step @p275 :rule instantiate :premises (@p243) :args ((@list @t105 @t148))) % 1.62/1.89 (step-pop @p494 :rule scope :premises (@p275)) % 1.62/1.89 (step @p276 :rule process_scope :premises (@p494) :args (@t156)) % 1.62/1.89 (step @p278 :rule eq_resolve :premises (@p276 @p273)) % 1.62/1.89 (step @p279 :rule eq_resolve :premises (@p278 @p263)) % 1.62/1.89 (step @p280 :rule implies_elim :premises (@p279)) % 1.62/1.89 (step @p281 :rule chain_m_resolution :premises (@p280 @p243) :args (@t158 @t159 (@list @t132))) % 1.62/1.89 (step @p282 :rule eq-symm :args (@t160 @t101)) % 1.62/1.89 (step @p283 :rule beta-reduce :args ((= @t161 @t101))) % 1.62/1.89 (step @p284 :rule refl :args (@t160)) % 1.62/1.89 (step @p285 :rule cong :premises (@p284 @p283) :args (@t162)) % 1.62/1.89 (step @p286 :rule trans :premises (@p285 @p282)) % 1.62/1.89 (step @p287 :rule cong :premises (@p286) :args (@t163)) % 1.62/1.89 (step @p288 :rule quant-unused-vars :args ((= (forall @t16 true) true))) % 1.62/1.89 (step @p289 :rule eq-refl :args (@t161)) % 1.62/1.89 (step @p290 :rule cong :premises (@p289) :args ((forall @t16 (= @t161 @t161)))) % 1.62/1.89 (step @p291 :rule trans :premises (@p290 @p288)) % 1.62/1.89 (step @p292 :rule refl :args (@t161)) % 1.62/1.89 (step @p293 :rule refl :args (@t14)) % 1.62/1.89 (step @p294 :rule ho_cong :premises (@p156 @p293)) % 1.62/1.89 (step @p295 :rule cong :premises (@p294 @p292) :args (@t162)) % 1.62/1.89 (step @p296 :rule cong :premises (@p295) :args (@t163)) % 1.62/1.89 (step @p297 :rule trans :premises (@p296 @p291)) % 1.62/1.89 (step @p298 :rule true_elim :premises (@p297)) % 1.62/1.89 (step @p299 :rule eq_resolve :premises (@p298 @p287)) % 1.62/1.89 (step @p300 :rule eq-symm :args (@t165 @t166)) % 1.62/1.89 (step @p301 :rule refl :args (@t167)) % 1.62/1.89 (step @p302 :rule cong :premises (@p301 @p300) :args ((=> @t167 @t168))) % 1.62/1.89 (assume-push @p495 @t167) % 1.62/1.89 (step @p304 :rule instantiate :premises (@p299) :args ((@list @t104))) % 1.62/1.89 (step-pop @p496 :rule scope :premises (@p304)) % 1.62/1.89 (step @p305 :rule process_scope :premises (@p496) :args (@t168)) % 1.62/1.89 (step @p307 :rule eq_resolve :premises (@p305 @p302)) % 1.62/1.89 (step @p308 :rule implies_elim :premises (@p307)) % 1.62/1.89 (step @p309 :rule chain_m_resolution :premises (@p308 @p299) :args (@t169 @t159 @t170)) % 1.62/1.89 (step @p310 :rule quant-merge-prenex :args ((= (forall @t19 @t176) (forall (@list @t11 @t172) @t174)))) % 1.62/1.89 (step @p311 :rule refl :args (@t171)) % 1.62/1.89 (step @p312 :rule alpha_equiv :args (@t177 (@list @t172) (@list @t14))) % 1.62/1.89 (step @p313 :rule nary_cong :premises (@p312 @p311) :args (@t178)) % 1.62/1.89 (step @p314 :rule quant-miniscope-or :args ((= @t176 @t178))) % 1.62/1.89 (step @p315 :rule trans :premises (@p314 @p313)) % 1.62/1.89 (step @p316 :rule symm :premises (@p315)) % 1.62/1.89 (step @p317 :rule cong :premises (@p316) :args ((forall @t19 (or @t180 @t171)))) % 1.62/1.89 (step @p318 :rule trans :premises (@p317 @p310)) % 1.62/1.89 (step @p319 :rule refl :args (@t171)) % 1.62/1.89 (step @p320 :rule refl :args (@t13)) % 1.62/1.89 (step @p321 :rule cong :premises (@p320 @p319) :args ((= @t13 @t171))) % 1.62/1.89 (step @p322 :rule symm :premises (@p321)) % 1.62/1.89 (step @p323 :rule eq_resolve :premises (@p320 @p322)) % 1.62/1.89 (step @p324 :rule refl :args (@t180)) % 1.62/1.89 (step @p325 :rule nary_cong :premises (@p324 @p323) :args (@t181)) % 1.62/1.89 (step @p326 :rule cong :premises (@p325) :args ((forall @t19 @t181))) % 1.62/1.89 (step @p327 :rule trans :premises (@p326 @p318)) % 1.62/1.89 (step @p328 :rule bool-double-not-elim :args (@t180)) % 1.62/1.89 (step @p329 :rule nary_cong :premises (@p328 @p320) :args ((or (not @t182) @t13))) % 1.62/1.89 (step @p330 :rule bool-impl-elim :args (@t182 @t13)) % 1.62/1.89 (step @p331 :rule trans :premises (@p330 @p329)) % 1.62/1.89 (step @p332 :rule cong :premises (@p331) :args ((forall @t19 (=> @t182 @t13)))) % 1.62/1.89 (step @p333 :rule trans :premises (@p332 @p327)) % 1.62/1.89 (step @p334 :rule refl :args (@t13)) % 1.62/1.89 (step @p335 :rule refl :args (@t179)) % 1.62/1.89 (step @p336 :rule refl :args (@t15)) % 1.62/1.89 (step @p337 :rule cong :premises (@p336 @p335) :args ((= @t15 @t179))) % 1.62/1.89 (step @p338 :rule symm :premises (@p337)) % 1.62/1.89 (step @p339 :rule eq_resolve :premises (@p336 @p338)) % 1.62/1.89 (step @p340 :rule cong :premises (@p339) :args (@t183)) % 1.62/1.89 (step @p341 :rule cong :premises (@p340) :args (@t184)) % 1.62/1.89 (step @p342 :rule cong :premises (@p341) :args (@t185)) % 1.62/1.89 (step @p343 :rule exists-elim :args ((= @t17 @t185))) % 1.62/1.89 (step @p344 :rule trans :premises (@p343 @p342)) % 1.62/1.89 (step @p345 :rule cong :premises (@p344 @p334) :args (@t18)) % 1.62/1.89 (step @p346 :rule cong :premises (@p345) :args (@t20)) % 1.62/1.89 (step @p347 :rule trans :premises (@p346 @p333)) % 1.62/1.89 (step @p348 :rule eq_resolve :premises (@p2 @p347)) % 1.62/1.89 (step @p349 :rule instantiate :premises (@p348) :args ((@list @t103 @t111))) % 1.62/1.89 (step @p350 :rule lambda-elim :args ((= @t187 @t111))) % 1.62/1.89 (step @p351 :rule cong :premises (@p350) :args (@t188)) % 1.62/1.89 (step @p352 :rule refl :args (@t40)) % 1.62/1.89 (step @p353 :rule cong :premises (@p350 @p352) :args (@t189)) % 1.62/1.89 (step @p354 :rule cong :premises (@p353) :args (@t190)) % 1.62/1.89 (step @p355 :rule cong :premises (@p354) :args (@t191)) % 1.62/1.89 (step @p356 :rule cong :premises (@p355) :args (@t192)) % 1.62/1.89 (step @p357 :rule cong :premises (@p356 @p351) :args (@t193)) % 1.62/1.89 (step @p358 :rule cong :premises (@p301 @p357) :args ((=> @t167 @t193))) % 1.62/1.89 (assume-push @p497 @t167) % 1.62/1.89 (step @p360 :rule instantiate :premises (@p299) :args ((@list @t187))) % 1.62/1.89 (step-pop @p498 :rule scope :premises (@p360)) % 1.62/1.89 (step @p361 :rule process_scope :premises (@p498) :args (@t193)) % 1.62/1.89 (step @p363 :rule eq_resolve :premises (@p361 @p358)) % 1.62/1.89 (step @p364 :rule implies_elim :premises (@p363)) % 1.62/1.89 (step @p365 :rule chain_m_resolution :premises (@p364 @p299) :args (@t197 @t159 @t170)) % 1.62/1.89 (step @p366 :rule bool-double-not-elim :args (@t112)) % 1.62/1.89 (step @p367 :rule refl :args (@t114)) % 1.62/1.89 (step @p368 :rule nary_cong :premises (@p367 @p366) :args ((or @t114 (not @t113)))) % 1.62/1.89 (step @p369 :rule cnf_or_neg :args (@t114 0)) % 1.62/1.89 (step @p370 :rule eq_resolve :premises (@p369 @p368)) % 1.62/1.89 (step @p371 :rule reordering :premises (@p370) :args ((or @t112 @t114))) % 1.62/1.89 (step @p372 :rule chain_m_resolution :premises (@p371 @p191) :args (@t112 @t124 @t126)) % 1.62/1.89 (assume-push @p499 @t198) % 1.62/1.89 (step @p374 :rule instantiate :premises (@p499) :args ((@list @t110))) % 1.62/1.89 (step-pop @p500 :rule scope :premises (@p374)) % 1.62/1.89 (step @p375 :rule process_scope :premises (@p500) :args (@t113)) % 1.62/1.89 (step @p377 :rule implies_elim :premises (@p375)) % 1.62/1.89 (step @p378 :rule reordering :premises (@p377) :args ((or @t113 @t199))) % 1.62/1.89 (step @p379 :rule chain_m_resolution :premises (@p378 @p372) :args (@t199 @t159 (@list @t112))) % 1.62/1.89 (step @p380 :rule alpha_equiv :args (@t198 @t200 @t201)) % 1.62/1.89 (step @p381 :rule equiv_elim2 :premises (@p380)) % 1.62/1.89 (step @p382 :rule chain_m_resolution :premises (@p381 @p379) :args (@t196 @t124 (@list @t198))) % 1.62/1.89 (step @p383 :rule refl :args (@t194)) % 1.62/1.89 (step @p384 :rule bool-double-not-elim :args (@t195)) % 1.62/1.89 (step @p385 :rule refl :args (@t202)) % 1.62/1.89 (step @p386 :rule nary_cong :premises (@p385 @p384 @p383) :args ((or @t202 (not @t196) @t194))) % 1.62/1.89 (step @p387 :rule cnf_equiv_pos1 :args (@t197)) % 1.62/1.89 (step @p388 :rule eq_resolve :premises (@p387 @p386)) % 1.62/1.89 (step @p389 :rule reordering :premises (@p388) :args ((or @t195 @t194 @t202))) % 1.62/1.89 (step @p390 :rule chain_m_resolution :premises (@p389 @p382 @p365) :args (@t194 @t203 (@list @t195 @t197))) % 1.62/1.89 (step @p391 :rule cnf_or_pos :args (@t205)) % 1.62/1.89 (step @p392 :rule reordering :premises (@p391) :args ((or @t204 @t166 (not @t205)))) % 1.62/1.89 (step @p393 :rule chain_m_resolution :premises (@p392 @p390 @p349) :args (@t166 @t206 (@list @t194 @t205))) % 1.62/1.89 (step @p394 :rule cnf_equiv_pos1 :args (@t169)) % 1.62/1.89 (step @p395 :rule reordering :premises (@p394) :args ((or (not @t166) @t165 (not @t169)))) % 1.62/1.89 (step @p396 :rule chain_m_resolution :premises (@p395 @p393 @p309) :args (@t165 @t206 (@list @t166 @t169))) % 1.62/1.89 (step @p397 :rule alpha_equiv :args (@t147 @t200 @t201)) % 1.62/1.89 (step @p398 :rule equiv_elim1 :premises (@p397)) % 1.62/1.89 (step @p399 :rule chain_m_resolution :premises (@p398 @p396) :args (@t207 @t124 (@list @t164))) % 1.62/1.89 (step @p400 :rule refl :args (@t149)) % 1.62/1.89 (step @p401 :rule bool-double-not-elim :args (@t147)) % 1.62/1.89 (step @p402 :rule nary_cong :premises (@p401 @p400) :args ((or (not @t207) @t149))) % 1.62/1.89 (step @p403 :rule bool-double-not-elim :args (@t149)) % 1.62/1.89 (step @p404 :rule refl :args (@t207)) % 1.62/1.89 (step @p405 :rule cong :premises (@p404 @p403) :args ((=> @t207 @t208))) % 1.62/1.89 (assume-push @p501 @t207) % 1.62/1.89 (step @p407 :rule skolemize :premises (@p501)) % 1.62/1.89 (step-pop @p502 :rule scope :premises (@p407)) % 1.62/1.89 (step @p408 :rule process_scope :premises (@p502) :args (@t208)) % 1.62/1.89 (step @p410 :rule eq_resolve :premises (@p408 @p405)) % 1.62/1.89 (step @p411 :rule implies_elim :premises (@p410)) % 1.62/1.89 (step @p412 :rule eq_resolve :premises (@p411 @p402)) % 1.62/1.89 (step @p413 :rule chain_m_resolution :premises (@p412 @p399) :args (@t149 @t124 (@list @t147))) % 1.62/1.89 (step @p414 :rule cnf_or_pos :args (@t158)) % 1.62/1.89 (step @p415 :rule reordering :premises (@p414) :args ((or @t157 @t145 (not @t158)))) % 1.62/1.89 (step @p416 :rule chain_m_resolution :premises (@p415 @p413 @p281) :args (@t145 @t206 (@list @t149 @t158))) % 1.62/1.89 (step @p417 :rule refl :args (@t209)) % 1.62/1.89 (step @p418 :rule refl :args (@t211)) % 1.62/1.89 (step @p419 :rule bool-double-not-elim :args (@t109)) % 1.62/1.89 (step @p420 :rule nary_cong :premises (@p419 @p418 @p417) :args ((or (not @t125) @t211 @t209))) % 1.62/1.89 (assume-push @p503 @t125) % 1.62/1.89 (assume-push @p504 @t210) % 1.62/1.89 (assume-push @p505 @t125) % 1.62/1.89 (assume-push @p506 @t210) % 1.62/1.89 (step @p425 :rule false_intro :premises (@p193)) % 1.62/1.89 (step @p426 :rule refl :args (@t106)) % 1.62/1.89 (step @p427 :rule ho_cong :premises (@p131 @p504)) % 1.62/1.89 (step @p428 :rule cong :premises (@p427 @p426) :args (@t145)) % 1.62/1.89 (step @p429 :rule trans :premises (@p428 @p425)) % 1.62/1.89 (step @p430 :rule false_elim :premises (@p429)) % 1.62/1.89 (step-pop @p507 :rule scope :premises (@p430)) % 1.62/1.89 (step-pop @p508 :rule scope :premises (@p507)) % 1.62/1.89 (step @p431 :rule process_scope :premises (@p508) :args (@t209)) % 1.62/1.89 (step @p434 :rule and_intro :premises (@p193 @p504)) % 1.62/1.89 (step @p435 :rule modus_ponens :premises (@p434 @p431)) % 1.62/1.89 (step-pop @p509 :rule scope :premises (@p435)) % 1.62/1.89 (step-pop @p510 :rule scope :premises (@p509)) % 1.62/1.89 (step @p436 :rule process_scope :premises (@p510) :args (@t209)) % 1.62/1.89 (step @p439 :rule implies_elim :premises (@p436)) % 1.62/1.89 (step @p440 :rule cnf_and_neg :args (@t212)) % 1.62/1.89 (step @p441 :rule resolution :premises (@p440 @p439) :args (true @t212)) % 1.62/1.89 (step @p442 :rule eq_resolve :premises (@p441 @p420)) % 1.62/1.89 (step @p443 :rule chain_m_resolution :premises (@p442 @p416 @p193) :args (@t211 (@list false true) (@list @t145 @t109))) % 1.62/1.89 (step @p444 :rule eq-symm :args (@t215 @t217)) % 1.62/1.89 (step @p445 :rule eq-refl :args (@t217)) % 1.62/1.89 (step @p446 :rule beta-reduce :args ((= @t218 @t217))) % 1.62/1.89 (step @p447 :rule refl :args (@t217)) % 1.62/1.89 (step @p448 :rule cong :premises (@p447 @p446) :args ((= @t217 @t218))) % 1.62/1.89 (step @p449 :rule trans :premises (@p448 @p445)) % 1.62/1.89 (step @p450 :rule eq-symm :args (@t218 @t217)) % 1.62/1.89 (step @p451 :rule trans :premises (@p450 @p449)) % 1.62/1.89 (step @p452 :rule refl :args (@t213)) % 1.62/1.89 (step @p453 :rule ho_cong :premises (@p170 @p452)) % 1.62/1.89 (step @p454 :rule cong :premises (@p453 @p447) :args ((= @t219 @t217))) % 1.62/1.89 (step @p455 :rule trans :premises (@p454 @p451)) % 1.62/1.89 (step @p456 :rule true_elim :premises (@p455)) % 1.62/1.89 (step @p457 :rule eq-refl :args (@t215)) % 1.62/1.89 (step @p458 :rule beta-reduce :args ((= @t220 @t215))) % 1.62/1.89 (step @p459 :rule refl :args (@t215)) % 1.62/1.89 (step @p460 :rule cong :premises (@p459 @p458) :args ((= @t215 @t220))) % 1.62/1.89 (step @p461 :rule trans :premises (@p460 @p457)) % 1.62/1.89 (step @p462 :rule eq-symm :args (@t220 @t215)) % 1.62/1.89 (step @p463 :rule trans :premises (@p462 @p461)) % 1.62/1.89 (step @p464 :rule ho_cong :premises (@p156 @p452)) % 1.62/1.89 (step @p465 :rule cong :premises (@p464 @p459) :args ((= @t221 @t215))) % 1.62/1.89 (step @p466 :rule trans :premises (@p465 @p463)) % 1.62/1.89 (step @p467 :rule true_elim :premises (@p466)) % 1.62/1.89 (step @p468 :rule cong :premises (@p467 @p456) :args (@t222)) % 1.62/1.89 (step @p469 :rule trans :premises (@p468 @p444)) % 1.62/1.89 (step @p470 :rule cong :premises (@p469) :args (@t223)) % 1.62/1.89 (step @p471 :rule refl :args (@t210)) % 1.62/1.89 (step @p472 :rule nary_cong :premises (@p471 @p470) :args (@t224)) % 1.62/1.89 ; WARNING: add trust step for TRUST % 1.62/1.89 ; trust TRUST THEORY_LEMMA % 1.62/1.89 (step @p473 :rule trust :premises () :args (@t224)) % 1.62/1.89 (step @p474 :rule eq_resolve :premises (@p473 @p472)) % 1.62/1.89 (step @p475 :rule chain_m_resolution :premises (@p474 @p443) :args ((not @t225) @t124 (@list @t210))) % 1.62/1.89 (step @p476 :rule alpha_equiv :args (@t216 @t200 @t201)) % 1.62/1.89 (step @p477 :rule equiv_elim1 :premises (@p476)) % 1.62/1.89 (step @p478 :rule cnf_equiv_neg1 :args (@t225)) % 1.62/1.89 (step @p479 :rule reordering :premises (@p478) :args ((or @t217 @t215 @t225))) % 1.62/1.89 (step @p480 :rule chain_m_resolution :premises (@p479 @p475 @p477) :args (@t217 @t203 (@list @t225 @t214))) % 1.62/1.89 (step @p481 :rule equiv_elim2 :premises (@p476)) % 1.62/1.89 (step @p482 :rule chain_m_resolution :premises (@p481 @p480) :args (@t215 @t124 (@list @t216))) % 1.62/1.89 (step @p483 :rule bool-double-not-elim :args (@t214)) % 1.62/1.89 (step @p484 :rule bool-double-not-elim :args (@t216)) % 1.62/1.89 (step @p485 :rule refl :args (@t225)) % 1.62/1.89 (step @p486 :rule nary_cong :premises (@p485 @p484 @p483) :args ((or @t225 (not @t217) (not @t215)))) % 1.62/1.89 (step @p487 :rule cnf_equiv_neg2 :args (@t225)) % 1.62/1.89 (step @p488 :rule eq_resolve :premises (@p487 @p486)) % 1.62/1.89 (step @p489 :rule reordering :premises (@p488) :args ((or @t216 @t214 @t225))) % 1.62/1.89 (step @p490 false :rule chain_m_resolution :premises (@p489 @p482 @p480 @p475) :args (false (@list true true true) (@list @t214 @t216 @t225))) % 1.62/1.89 ) % 1.62/1.89 % SZS output end Proof % 1.62/1.89 % cvc5 exiting %------------------------------------------------------------------------------