%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO541^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:13:05 AM UTC 2026 % Result : Theorem 151.07s 151.33s % Output : Proof 151.07s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO541^1 : TPTP v9.2.1. Released v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n005.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Wed Jun 3 00:19:48 EDT 2026 % 0.16/0.35 % CPUTime : % 0.32/0.50 %----Proving TH0 % 151.07/151.33 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 151.07/151.33 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 151.07/151.33 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 151.07/151.33 --- Run --ho-elim --full-saturate-quant at 18s... % 151.07/151.33 % SZS status Theorem % 151.07/151.33 % SZS output start Proof % 151.07/151.33 ( % 151.07/151.33 (declare-sort $$unsorted 0) % 151.07/151.33 (declare-const tptp.epsii (-> (-> (-> $$unsorted $$unsorted) Bool) $$unsorted $$unsorted)) % 151.07/151.33 (define tptp.if () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Z" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "B" Bool))) (let ((_let_5 (@var "X" (-> $$unsorted $$unsorted)))) (lambda (@list _let_4 _let_5 _let_2 _let_1) (_ (_ tptp.epsii (lambda (@list _let_3) (or (and _let_4 (= _let_3 _let_5)) (and (not _let_4) (= _let_3 _let_2))))) _let_1)))))))) % 151.07/151.33 (define @t1 () (@var "P" (-> (-> $$unsorted $$unsorted) Bool))) % 151.07/151.33 (define @t2 () (_ tptp.epsii @t1)) % 151.07/151.33 (define @t3 () (_ @t1 @t2)) % 151.07/151.33 (define @t4 () (@var "X" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t5 () (_ @t1 @t4)) % 151.07/151.33 (define @t6 () (@list @t4)) % 151.07/151.33 (define @t7 () (exists @t6 @t5)) % 151.07/151.33 (define @t8 () (=> @t7 @t3)) % 151.07/151.33 (define @t9 () (@list @t1)) % 151.07/151.33 (define @t10 () (forall @t9 @t8)) % 151.07/151.33 (define @t11 () (@var "Y" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t12 () (= (_ (_ (_ tptp.if false) @t4) @t11) @t11)) % 151.07/151.33 (define @t13 () (= (_ (_ (_ tptp.if true) @t4) @t11) @t4)) % 151.07/151.33 (define @t14 () (and @t13 @t12)) % 151.07/151.33 (define @t15 () (@list @t4 @t11)) % 151.07/151.33 (define @t16 () (forall @t15 @t14)) % 151.07/151.33 (define @t17 () (not @t16)) % 151.07/151.33 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 151.07/151.33 (define @t19 () (@var "Z" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t20 () (@var "B" Bool)) % 151.07/151.33 (define @t21 () (not @t20)) % 151.07/151.33 (define @t22 () (and @t21 (= @t19 @t11))) % 151.07/151.33 (define @t23 () (and @t20 (= @t19 @t4))) % 151.07/151.33 (define @t24 () (or @t23 @t22)) % 151.07/151.33 (define @t25 () (@list @t19)) % 151.07/151.33 (define @t26 () (lambda @t25 @t24)) % 151.07/151.33 (define @t27 () (@list @t20 @t4 @t11 @t18)) % 151.07/151.33 (define @t28 () (lambda @t27 (_ (_ tptp.epsii @t26) @t18))) % 151.07/151.33 (define @t29 () (@var "y" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t30 () (@var "x" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t31 () (@var "z" $$unsorted)) % 151.07/151.33 (define @t32 () (@const 0 (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted))) % 151.07/151.33 (define @t33 () (@list @t31)) % 151.07/151.33 (define @t34 () (@var "BOUND_VARIABLE_7715" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t35 () (@const 1 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted)))) % 151.07/151.33 (define @t36 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 151.07/151.33 (define @t37 () (forall (@list @t34) (= @t34 (_ @t36 @t35 @t34)))) % 151.07/151.33 (define @t38 () (@quantifiers_skolemize @t37 0)) % 151.07/151.33 (define @t39 () (_ @t36 @t35 @t38)) % 151.07/151.33 (define @t40 () (@var "BOUND_VARIABLE_7724" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t41 () (@const 3 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) $$unsorted $$unsorted)))) % 151.07/151.33 (define @t42 () (forall (@list @t40) (= @t40 (_ @t36 @t41 @t40)))) % 151.07/151.33 (define @t43 () (@quantifiers_skolemize @t42 0)) % 151.07/151.33 (define @t44 () (_ @t36 @t41 @t43)) % 151.07/151.33 (define @t45 () (@var "BOUND_VARIABLE_7649" $$unsorted)) % 151.07/151.33 (define @t46 () (@var "BOUND_VARIABLE_7759" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t47 () (_ @t32 (_ @t36 @t41 @t46) @t45)) % 151.07/151.33 (define @t48 () (@const 4 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)))) % 151.07/151.33 (define @t49 () (@const 5 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool))))) % 151.07/151.33 (define @t50 () (@const 6 (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) $$unsorted $$unsorted)))) % 151.07/151.33 (define @t51 () (@const 7 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) $$unsorted $$unsorted)) (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) (@ho-elim-sort (-> $$unsorted $$unsorted))))) % 151.07/151.33 (define @t52 () (_ @t32 (_ @t51 @t50 (_ @t49 @t48 @t46)) @t45)) % 151.07/151.33 (define @t53 () (forall (@list @t46 @t45) (= @t47 @t52))) % 151.07/151.33 (define @t54 () (@var "BOUND_VARIABLE_7648" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t55 () (@const 8 (-> (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) Bool))) % 151.07/151.33 (define @t56 () (@const 9 (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 151.07/151.33 (define @t57 () (forall (@list @t54 @t45) (= (_ @t56 @t54 @t45) (tptp.epsii (_ @t55 @t54) @t45)))) % 151.07/151.33 (define @t58 () (forall @t33 (= (_ @t32 @t43 @t31) (_ @t32 @t44 @t31)))) % 151.07/151.33 (define @t59 () (@quantifiers_skolemize @t58 0)) % 151.07/151.33 (define @t60 () (@var "BOUND_VARIABLE_7795" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t61 () (@var "BOUND_VARIABLE_7794" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t62 () (= @t61 @t60)) % 151.07/151.33 (define @t63 () (@const 10 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool))) % 151.07/151.33 (define @t64 () (_ @t63 (_ @t49 @t48 @t60) @t61)) % 151.07/151.33 (define @t65 () (= @t60 @t61)) % 151.07/151.33 (define @t66 () (@list @t60 @t61)) % 151.07/151.33 (define @t67 () (forall @t66 (= @t64 @t65))) % 151.07/151.33 (define @t68 () (@var "BOUND_VARIABLE_7674" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t69 () (@var "BOUND_VARIABLE_7673" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t70 () (forall (@list @t69 @t68) (= (_ @t55 @t69 @t68) (= @t69 @t68)))) % 151.07/151.33 (define @t71 () (_ @t49 @t48 @t43)) % 151.07/151.33 (define @t72 () (_ @t51 @t50 @t71)) % 151.07/151.33 (define @t73 () (_ @t63 @t71 @t72)) % 151.07/151.33 (define @t74 () (= @t73 (= @t72 @t43))) % 151.07/151.33 (define @t75 () (forall @t66 (= @t64 @t62))) % 151.07/151.33 (define @t76 () (= @t43 @t72)) % 151.07/151.33 (define @t77 () (= @t73 @t76)) % 151.07/151.33 (define @t78 () (@list false)) % 151.07/151.33 (define @t79 () (@list @t75)) % 151.07/151.33 (define @t80 () (@var "BOUND_VARIABLE_7694" (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)))) % 151.07/151.33 (define @t81 () (@var "BOUND_VARIABLE_7705" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t82 () (_ @t1 @t2)) % 151.07/151.33 (define @t83 () (@var "BOUND_VARIABLE_7484" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t84 () (not (_ @t1 @t83))) % 151.07/151.33 (define @t85 () (or @t84 @t82)) % 151.07/151.33 (define @t86 () (forall (@list @t1 @t83) @t85)) % 151.07/151.33 (define @t87 () (@list @t83)) % 151.07/151.33 (define @t88 () (forall @t87 @t85)) % 151.07/151.33 (define @t89 () (forall @t87 @t84)) % 151.07/151.33 (define @t90 () (or @t89 @t82)) % 151.07/151.33 (define @t91 () (_ @t1 @t4)) % 151.07/151.33 (define @t92 () (forall @t6 (not @t91))) % 151.07/151.33 (define @t93 () (or @t92 @t3)) % 151.07/151.33 (define @t94 () (not @t92)) % 151.07/151.33 (define @t95 () (not @t5)) % 151.07/151.33 (define @t96 () (forall @t6 @t95)) % 151.07/151.33 (define @t97 () (not @t96)) % 151.07/151.33 (define @t98 () (_ @t63 @t71 @t43)) % 151.07/151.33 (define @t99 () (= @t43 @t43)) % 151.07/151.33 (define @t100 () (= @t98 @t99)) % 151.07/151.33 (define @t101 () (not @t98)) % 151.07/151.33 (define @t102 () (or @t101 @t73)) % 151.07/151.33 (define @t103 () (@list false false)) % 151.07/151.33 (define @t104 () (_ @t32 @t43 @t59)) % 151.07/151.33 (define @t105 () (= @t104 (_ @t32 @t44 @t59))) % 151.07/151.33 (define @t106 () (not @t105)) % 151.07/151.33 (define @t107 () (not @t58)) % 151.07/151.33 (define @t108 () (= @t43 @t44)) % 151.07/151.33 (define @t109 () (or @t107 @t108)) % 151.07/151.33 (define @t110 () (not @t108)) % 151.07/151.33 (define @t111 () (not @t42)) % 151.07/151.33 (define @t112 () (@var "BOUND_VARIABLE_7565" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t113 () (@const 11 (-> (-> $$unsorted $$unsorted) $$unsorted $$unsorted))) % 151.07/151.33 (define @t114 () (@list @t112)) % 151.07/151.33 (define @t115 () (@var "BOUND_VARIABLE_7551" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t116 () (@list @t115)) % 151.07/151.33 (define @t117 () (not (and (forall @t116 (= @t115 (_ @t56 @t115))) (forall @t114 (= @t112 (_ @t113 @t112)))))) % 151.07/151.33 (define @t118 () (lambda @t25 (= @t19 @t112))) % 151.07/151.33 (define @t119 () (tptp.epsii @t118 @t18)) % 151.07/151.33 (define @t120 () (@list @t18)) % 151.07/151.33 (define @t121 () (lambda @t25 (= @t19 @t115))) % 151.07/151.33 (define @t122 () (tptp.epsii @t121 @t18)) % 151.07/151.33 (define @t123 () (_ (_ tptp.epsii @t118) @t18)) % 151.07/151.33 (define @t124 () (lambda @t120 @t123)) % 151.07/151.33 (define @t125 () (= @t112 @t124)) % 151.07/151.33 (define @t126 () (forall @t114 @t125)) % 151.07/151.33 (define @t127 () (@var "BOUND_VARIABLE_7563" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t128 () (@list @t127 @t112)) % 151.07/151.33 (define @t129 () (lambda @t25 (= @t112 @t19))) % 151.07/151.33 (define @t130 () (lambda @t120 (_ (_ tptp.epsii @t129) @t18))) % 151.07/151.33 (define @t131 () (= @t112 @t130)) % 151.07/151.33 (define @t132 () (forall @t128 @t131)) % 151.07/151.33 (define @t133 () (_ (_ tptp.epsii @t121) @t18)) % 151.07/151.33 (define @t134 () (lambda @t120 @t133)) % 151.07/151.33 (define @t135 () (= @t115 @t134)) % 151.07/151.33 (define @t136 () (forall @t116 @t135)) % 151.07/151.33 (define @t137 () (@var "BOUND_VARIABLE_7553" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t138 () (@list @t115 @t137)) % 151.07/151.33 (define @t139 () (lambda @t25 (= @t115 @t19))) % 151.07/151.33 (define @t140 () (lambda @t120 (_ (_ tptp.epsii @t139) @t18))) % 151.07/151.33 (define @t141 () (= @t115 @t140)) % 151.07/151.33 (define @t142 () (forall @t138 @t141)) % 151.07/151.33 (define @t143 () (= @t11 @t19)) % 151.07/151.33 (define @t144 () (_ (_ tptp.epsii (lambda @t25 @t143)) @t18)) % 151.07/151.33 (define @t145 () (lambda @t120 @t144)) % 151.07/151.33 (define @t146 () (= @t11 @t145)) % 151.07/151.33 (define @t147 () (forall @t15 @t146)) % 151.07/151.33 (define @t148 () (@list @t4 @t11)) % 151.07/151.33 (define @t149 () (= @t4 @t19)) % 151.07/151.33 (define @t150 () (_ (_ tptp.epsii (lambda @t25 @t149)) @t18)) % 151.07/151.33 (define @t151 () (lambda @t120 @t150)) % 151.07/151.33 (define @t152 () (= @t4 @t151)) % 151.07/151.33 (define @t153 () (forall @t15 @t152)) % 151.07/151.33 (define @t154 () (and @t153 @t147)) % 151.07/151.33 (define @t155 () (@list @t11 @t18)) % 151.07/151.33 (define @t156 () (lambda @t155 @t144)) % 151.07/151.33 (define @t157 () (@list @t4 @t11 @t18)) % 151.07/151.33 (define @t158 () (not false)) % 151.07/151.33 (define @t159 () (and @t158 @t143)) % 151.07/151.33 (define @t160 () (and false @t149)) % 151.07/151.33 (define @t161 () (or @t160 @t159)) % 151.07/151.33 (define @t162 () (lambda @t25 @t161)) % 151.07/151.33 (define @t163 () (lambda @t157 (_ (_ tptp.epsii @t162) @t18))) % 151.07/151.33 (define @t164 () (lambda @t27 (_ (_ tptp.epsii (lambda @t25 (or (and @t20 @t149) (and @t21 @t143)))) @t18))) % 151.07/151.33 (define @t165 () (_ @t164 false)) % 151.07/151.33 (define @t166 () (= (_ (_ @t165 @t4) @t11) @t11)) % 151.07/151.33 (define @t167 () (lambda @t155 @t150)) % 151.07/151.33 (define @t168 () (not true)) % 151.07/151.33 (define @t169 () (and @t168 @t143)) % 151.07/151.33 (define @t170 () (and true @t149)) % 151.07/151.33 (define @t171 () (or @t170 @t169)) % 151.07/151.33 (define @t172 () (lambda @t25 @t171)) % 151.07/151.33 (define @t173 () (lambda @t157 (_ (_ tptp.epsii @t172) @t18))) % 151.07/151.33 (define @t174 () (_ @t164 true)) % 151.07/151.33 (define @t175 () (= (_ (_ @t174 @t4) @t11) @t4)) % 151.07/151.33 (define @t176 () (and @t175 @t166)) % 151.07/151.33 (define @t177 () (forall @t15 @t176)) % 151.07/151.33 (define @t178 () (not @t37)) % 151.07/151.33 (define @t179 () (= @t38 @t39)) % 151.07/151.33 (define @t180 () (not @t179)) % 151.07/151.33 (define @t181 () (@list true)) % 151.07/151.33 (define @t182 () (forall @t33 (= (_ @t32 @t38 @t31) (_ @t32 @t39 @t31)))) % 151.07/151.33 (define @t183 () (not @t182)) % 151.07/151.33 (define @t184 () (or @t183 @t179)) % 151.07/151.33 (define @t185 () (@quantifiers_skolemize @t182 0)) % 151.07/151.33 (define @t186 () (_ @t32 @t39 @t185)) % 151.07/151.33 (define @t187 () (_ @t32 @t38 @t185)) % 151.07/151.33 (define @t188 () (= @t187 @t186)) % 151.07/151.33 (define @t189 () (not @t188)) % 151.07/151.33 (define @t190 () (@var "BOUND_VARIABLE_7630" $$unsorted)) % 151.07/151.33 (define @t191 () (@var "BOUND_VARIABLE_7736" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t192 () (_ @t32 (_ @t36 @t35 @t191) @t190)) % 151.07/151.33 (define @t193 () (@const 12 (@ho-elim-sort (-> (@ho-elim-sort (-> $$unsorted $$unsorted)) (@ho-elim-sort (-> $$unsorted $$unsorted)) Bool)))) % 151.07/151.33 (define @t194 () (_ @t32 (_ @t51 @t50 (_ @t49 @t193 @t191)) @t190)) % 151.07/151.33 (define @t195 () (@list @t191 @t190)) % 151.07/151.33 (define @t196 () (forall @t195 (= @t192 @t194))) % 151.07/151.33 (define @t197 () (@var "BOUND_VARIABLE_7629" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t198 () (@const 13 (-> (-> $$unsorted $$unsorted) (-> $$unsorted $$unsorted) Bool))) % 151.07/151.33 (define @t199 () (forall (@list @t197 @t190) (= (_ @t113 @t197 @t190) (tptp.epsii (_ @t198 @t197) @t190)))) % 151.07/151.33 (define @t200 () (_ @t49 @t193 @t38)) % 151.07/151.33 (define @t201 () (_ @t51 @t50 @t200)) % 151.07/151.33 (define @t202 () (_ @t32 @t201 @t185)) % 151.07/151.33 (define @t203 () (forall @t195 (= @t194 @t192))) % 151.07/151.33 (define @t204 () (= @t202 @t186)) % 151.07/151.33 (define @t205 () (@list @t38 @t185)) % 151.07/151.33 (define @t206 () (= @t186 @t202)) % 151.07/151.33 (define @t207 () (@var "BOUND_VARIABLE_7777" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t208 () (@var "BOUND_VARIABLE_7776" (@ho-elim-sort (-> $$unsorted $$unsorted)))) % 151.07/151.33 (define @t209 () (= @t208 @t207)) % 151.07/151.33 (define @t210 () (_ @t63 (_ @t49 @t193 @t207) @t208)) % 151.07/151.33 (define @t211 () (= @t207 @t208)) % 151.07/151.33 (define @t212 () (@list @t207 @t208)) % 151.07/151.33 (define @t213 () (forall @t212 (= @t210 @t211))) % 151.07/151.33 (define @t214 () (@var "BOUND_VARIABLE_7667" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t215 () (@var "BOUND_VARIABLE_7666" (-> $$unsorted $$unsorted))) % 151.07/151.33 (define @t216 () (forall (@list @t215 @t214) (= (_ @t198 @t215 @t214) (= @t215 @t214)))) % 151.07/151.33 (define @t217 () (_ @t63 @t200 @t201)) % 151.07/151.33 (define @t218 () (= @t201 @t38)) % 151.07/151.33 (define @t219 () (forall @t212 (= @t210 @t209))) % 151.07/151.33 (define @t220 () (= @t217 @t218)) % 151.07/151.33 (define @t221 () (= @t38 @t201)) % 151.07/151.33 (define @t222 () (= @t221 @t217)) % 151.07/151.33 (define @t223 () (@list @t219)) % 151.07/151.33 (define @t224 () (_ @t49 @t48 @t38)) % 151.07/151.33 (define @t225 () (_ @t51 @t50 @t224)) % 151.07/151.33 (define @t226 () (_ @t63 @t200 @t225)) % 151.07/151.33 (define @t227 () (= @t225 @t38)) % 151.07/151.33 (define @t228 () (= @t226 @t227)) % 151.07/151.33 (define @t229 () (@list @t38 @t225)) % 151.07/151.33 (define @t230 () (= @t38 @t225)) % 151.07/151.33 (define @t231 () (= @t230 @t226)) % 151.07/151.33 (define @t232 () (_ @t63 @t224 @t225)) % 151.07/151.33 (define @t233 () (= @t232 @t227)) % 151.07/151.33 (define @t234 () (= @t232 @t230)) % 151.07/151.33 (define @t235 () (_ @t63 @t224 @t38)) % 151.07/151.33 (define @t236 () (= @t38 @t38)) % 151.07/151.33 (define @t237 () (= @t235 @t236)) % 151.07/151.33 (define @t238 () (not @t235)) % 151.07/151.33 (define @t239 () (or @t238 @t232)) % 151.07/151.33 (define @t240 () (not @t226)) % 151.07/151.33 (define @t241 () (or @t240 @t217)) % 151.07/151.33 (define @t242 () (and @t221 @t206)) % 151.07/151.33 (assume @p1 @t10) % 151.07/151.33 (assume @p2 @t17) % 151.07/151.33 (assume @p3 true) % 151.07/151.33 (step @p4 (= tptp.if @t28) :rule refl :args (@t28)) % 151.07/151.33 ; WARNING: add trust step for TRUST % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.07/151.33 (step @p5 :rule trust :premises () :args ((forall (@list @t30 @t29) (or (not (forall @t33 (= (_ @t32 @t30 @t31) (_ @t32 @t29 @t31)))) (= @t30 @t29))))) % 151.07/151.33 (step @p6 :rule instantiate :premises (@p5) :args ((@list @t38 @t39))) % 151.07/151.33 (step @p7 :rule instantiate :premises (@p5) :args ((@list @t43 @t44))) % 151.07/151.33 (step @p8 :rule eq-symm :args (@t47 @t52)) % 151.07/151.33 (step @p9 :rule cong :premises (@p8) :args (@t53)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p10 :rule trust :premises () :args ((= @t57 @t53))) % 151.07/151.33 (step @p11 :rule trans :premises (@p10 @p9)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.07/151.33 (step @p12 :rule trust :premises () :args (@t57)) % 151.07/151.33 (step @p13 :rule eq_resolve :premises (@p12 @p11)) % 151.07/151.33 (step @p14 :rule instantiate :premises (@p13) :args ((@list @t43 @t59))) % 151.07/151.33 (step @p15 :rule refl :args (@t59)) % 151.07/151.33 (step @p16 :rule eq-symm :args (@t62 @t64)) % 151.07/151.33 (step @p17 :rule refl :args (@t64)) % 151.07/151.33 (step @p18 :rule eq-symm :args (@t60 @t61)) % 151.07/151.33 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t65 @t64))) % 151.07/151.33 (step @p20 :rule trans :premises (@p19 @p16)) % 151.07/151.33 (step @p21 :rule eq-symm :args (@t64 @t65)) % 151.07/151.33 (step @p22 :rule trans :premises (@p21 @p20)) % 151.07/151.33 (step @p23 :rule cong :premises (@p22) :args (@t67)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p24 :rule trust :premises () :args ((= @t70 @t67))) % 151.07/151.33 (step @p25 :rule trans :premises (@p24 @p23)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.07/151.33 (step @p26 :rule trust :premises () :args (@t70)) % 151.07/151.33 (step @p27 :rule eq_resolve :premises (@p26 @p25)) % 151.07/151.33 (step @p28 :rule eq-symm :args (@t72 @t43)) % 151.07/151.33 (step @p29 :rule refl :args (@t73)) % 151.07/151.33 (step @p30 :rule cong :premises (@p29 @p28) :args (@t74)) % 151.07/151.33 (step @p31 :rule refl :args (@t75)) % 151.07/151.33 (step @p32 :rule cong :premises (@p31 @p30) :args ((=> @t75 @t74))) % 151.07/151.33 (assume-push @p399 @t75) % 151.07/151.33 (step @p34 :rule instantiate :premises (@p27) :args ((@list @t43 @t72))) % 151.07/151.33 (step-pop @p400 :rule scope :premises (@p34)) % 151.07/151.33 (step @p35 :rule process_scope :premises (@p400) :args (@t74)) % 151.07/151.33 (step @p37 :rule eq_resolve :premises (@p35 @p32)) % 151.07/151.33 (step @p38 :rule implies_elim :premises (@p37)) % 151.07/151.33 (step @p39 :rule chain_m_resolution :premises (@p38 @p27) :args (@t77 @t78 @t79)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p40 :rule trust :premises () :args ((= @t86 (forall (@list @t80 @t81) (or (not (_ @t63 @t80 @t81)) (_ @t63 @t80 (_ @t51 @t50 @t80))))))) % 151.07/151.33 (step @p41 :rule quant-merge-prenex :args ((= (forall @t9 @t88) @t86))) % 151.07/151.33 (step @p42 :rule refl :args (@t82)) % 151.07/151.33 (step @p43 :rule alpha_equiv :args (@t89 (@list @t83) (@list @t4))) % 151.07/151.33 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t90)) % 151.07/151.33 (step @p45 :rule quant-miniscope-or :args ((= @t88 @t90))) % 151.07/151.33 (step @p46 :rule trans :premises (@p45 @p44)) % 151.07/151.33 (step @p47 :rule symm :premises (@p46)) % 151.07/151.33 (step @p48 :rule cong :premises (@p47) :args ((forall @t9 (or @t92 @t82)))) % 151.07/151.33 (step @p49 :rule trans :premises (@p48 @p41)) % 151.07/151.33 (step @p50 :rule refl :args (@t82)) % 151.07/151.33 (step @p51 :rule refl :args (@t3)) % 151.07/151.33 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t3 @t82))) % 151.07/151.33 (step @p53 :rule symm :premises (@p52)) % 151.07/151.33 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 151.07/151.33 (step @p55 :rule refl :args (@t92)) % 151.07/151.33 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t93)) % 151.07/151.33 (step @p57 :rule cong :premises (@p56) :args ((forall @t9 @t93))) % 151.07/151.33 (step @p58 :rule trans :premises (@p57 @p49)) % 151.07/151.33 (step @p59 :rule bool-double-not-elim :args (@t92)) % 151.07/151.33 (step @p60 :rule nary_cong :premises (@p59 @p51) :args ((or (not @t94) @t3))) % 151.07/151.33 (step @p61 :rule bool-impl-elim :args (@t94 @t3)) % 151.07/151.33 (step @p62 :rule trans :premises (@p61 @p60)) % 151.07/151.33 (step @p63 :rule cong :premises (@p62) :args ((forall @t9 (=> @t94 @t3)))) % 151.07/151.33 (step @p64 :rule trans :premises (@p63 @p58)) % 151.07/151.33 (step @p65 :rule refl :args (@t3)) % 151.07/151.33 (step @p66 :rule refl :args (@t91)) % 151.07/151.33 (step @p67 :rule refl :args (@t5)) % 151.07/151.33 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t5 @t91))) % 151.07/151.33 (step @p69 :rule symm :premises (@p68)) % 151.07/151.33 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 151.07/151.33 (step @p71 :rule cong :premises (@p70) :args (@t95)) % 151.07/151.33 (step @p72 :rule cong :premises (@p71) :args (@t96)) % 151.07/151.33 (step @p73 :rule cong :premises (@p72) :args (@t97)) % 151.07/151.33 (step @p74 :rule exists-elim :args ((= @t7 @t97))) % 151.07/151.33 (step @p75 :rule trans :premises (@p74 @p73)) % 151.07/151.33 (step @p76 :rule cong :premises (@p75 @p65) :args (@t8)) % 151.07/151.33 (step @p77 :rule cong :premises (@p76) :args (@t10)) % 151.07/151.33 (step @p78 :rule trans :premises (@p77 @p64)) % 151.07/151.33 (step @p79 :rule trans :premises (@p78 @p40)) % 151.07/151.33 (step @p80 :rule eq_resolve :premises (@p1 @p79)) % 151.07/151.33 (step @p81 :rule instantiate :premises (@p80) :args ((@list @t71 @t43))) % 151.07/151.33 (step @p82 :rule bool-eq-true :args (@t98)) % 151.07/151.33 (step @p83 :rule eq-symm :args (true @t98)) % 151.07/151.33 (step @p84 :rule trans :premises (@p83 @p82)) % 151.07/151.33 (step @p85 :rule refl :args (@t98)) % 151.07/151.33 (step @p86 :rule eq-refl :args (@t43)) % 151.07/151.33 (step @p87 :rule cong :premises (@p86 @p85) :args ((= @t99 @t98))) % 151.07/151.33 (step @p88 :rule trans :premises (@p87 @p84)) % 151.07/151.33 (step @p89 :rule eq-symm :args (@t98 @t99)) % 151.07/151.33 (step @p90 :rule trans :premises (@p89 @p88)) % 151.07/151.33 (step @p91 :rule cong :premises (@p31 @p90) :args ((=> @t75 @t100))) % 151.07/151.33 (assume-push @p401 @t75) % 151.07/151.33 (step @p93 :rule instantiate :premises (@p27) :args ((@list @t43 @t43))) % 151.07/151.33 (step-pop @p402 :rule scope :premises (@p93)) % 151.07/151.33 (step @p94 :rule process_scope :premises (@p402) :args (@t100)) % 151.07/151.33 (step @p96 :rule eq_resolve :premises (@p94 @p91)) % 151.07/151.33 (step @p97 :rule implies_elim :premises (@p96)) % 151.07/151.33 (step @p98 :rule chain_m_resolution :premises (@p97 @p27) :args (@t98 @t78 @t79)) % 151.07/151.33 (step @p99 :rule cnf_or_pos :args (@t102)) % 151.07/151.33 (step @p100 :rule reordering :premises (@p99) :args ((or @t101 @t73 (not @t102)))) % 151.07/151.33 (step @p101 :rule chain_m_resolution :premises (@p100 @p98 @p81) :args (@t73 @t103 (@list @t98 @t102))) % 151.07/151.33 (step @p102 :rule cnf_equiv_pos1 :args (@t77)) % 151.07/151.33 (step @p103 :rule reordering :premises (@p102) :args ((or (not @t73) @t76 (not @t77)))) % 151.07/151.33 (step @p104 :rule chain_m_resolution :premises (@p103 @p101 @p39) :args (@t76 @t103 (@list @t73 @t77))) % 151.07/151.33 (step @p105 :rule cong :premises (@p104 @p15) :args (@t104)) % 151.07/151.33 (step @p106 :rule trans :premises (@p105 @p14)) % 151.07/151.33 (step @p107 :rule refl :args (@t106)) % 151.07/151.33 (step @p108 :rule bool-double-not-elim :args (@t58)) % 151.07/151.33 (step @p109 :rule nary_cong :premises (@p108 @p107) :args ((or (not @t107) @t106))) % 151.07/151.33 (assume-push @p403 @t107) % 151.07/151.33 (step @p111 :rule skolemize :premises (@p403)) % 151.07/151.33 (step-pop @p404 :rule scope :premises (@p111)) % 151.07/151.33 (step @p112 :rule process_scope :premises (@p404) :args (@t106)) % 151.07/151.33 (step @p114 :rule implies_elim :premises (@p112)) % 151.07/151.33 (step @p115 :rule eq_resolve :premises (@p114 @p109)) % 151.07/151.33 (step @p116 :rule chain_m_resolution :premises (@p115 @p106) :args (@t58 @t78 (@list @t105))) % 151.07/151.33 (step @p117 :rule cnf_or_pos :args (@t109)) % 151.07/151.33 (step @p118 :rule reordering :premises (@p117) :args ((or @t108 @t107 (not @t109)))) % 151.07/151.33 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p7) :args (@t108 @t103 (@list @t58 @t109))) % 151.07/151.33 (step @p120 :rule refl :args (@t110)) % 151.07/151.33 (step @p121 :rule bool-double-not-elim :args (@t42)) % 151.07/151.33 (step @p122 :rule nary_cong :premises (@p121 @p120) :args ((or (not @t111) @t110))) % 151.07/151.33 (assume-push @p405 @t111) % 151.07/151.33 (step @p124 :rule skolemize :premises (@p405)) % 151.07/151.33 (step-pop @p406 :rule scope :premises (@p124)) % 151.07/151.33 (step @p125 :rule process_scope :premises (@p406) :args (@t110)) % 151.07/151.33 (step @p127 :rule implies_elim :premises (@p125)) % 151.07/151.33 (step @p128 :rule eq_resolve :premises (@p127 @p122)) % 151.07/151.33 (step @p129 :rule chain_m_resolution :premises (@p128 @p119) :args (@t42 @t78 (@list @t108))) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p130 :rule trust :premises () :args ((= @t117 (not (and @t42 @t37))))) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p131 :rule trust :premises () :args ((= (not (and (forall @t116 (= @t115 (lambda @t120 @t122))) (forall @t114 (= @t112 (lambda @t120 @t119))))) @t117))) % 151.07/151.33 (step @p132 :rule refl :args (@t119)) % 151.07/151.33 (step @p133 :rule refl :args (@t123)) % 151.07/151.33 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t123 @t119))) % 151.07/151.33 (step @p135 :rule symm :premises (@p134)) % 151.07/151.33 (step @p136 :rule eq_resolve :premises (@p133 @p135)) % 151.07/151.33 (step @p137 :rule cong :premises (@p136) :args (@t124)) % 151.07/151.33 (step @p138 :rule refl :args (@t112)) % 151.07/151.33 (step @p139 :rule cong :premises (@p138 @p137) :args (@t125)) % 151.07/151.33 (step @p140 :rule cong :premises (@p139) :args (@t126)) % 151.07/151.33 (step @p141 :rule quant-unused-vars :args ((= (forall @t128 @t125) @t126))) % 151.07/151.33 (step @p142 :rule trans :premises (@p141 @p140)) % 151.07/151.33 (step @p143 :rule refl :args (@t18)) % 151.07/151.33 (step @p144 :rule eq-symm :args (@t112 @t19)) % 151.07/151.33 (step @p145 :rule cong :premises (@p144) :args (@t129)) % 151.07/151.33 (step @p146 :rule refl :args (tptp.epsii)) % 151.07/151.33 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 151.07/151.33 (step @p148 :rule ho_cong :premises (@p147 @p143)) % 151.07/151.33 (step @p149 :rule cong :premises (@p148) :args (@t130)) % 151.07/151.33 (step @p150 :rule refl :args (@t112)) % 151.07/151.33 (step @p151 :rule cong :premises (@p150 @p149) :args (@t131)) % 151.07/151.33 (step @p152 :rule cong :premises (@p151) :args (@t132)) % 151.07/151.33 (step @p153 :rule trans :premises (@p152 @p142)) % 151.07/151.33 (step @p154 :rule refl :args (@t122)) % 151.07/151.33 (step @p155 :rule refl :args (@t133)) % 151.07/151.33 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t133 @t122))) % 151.07/151.33 (step @p157 :rule symm :premises (@p156)) % 151.07/151.33 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 151.07/151.33 (step @p159 :rule cong :premises (@p158) :args (@t134)) % 151.07/151.33 (step @p160 :rule refl :args (@t115)) % 151.07/151.33 (step @p161 :rule cong :premises (@p160 @p159) :args (@t135)) % 151.07/151.33 (step @p162 :rule cong :premises (@p161) :args (@t136)) % 151.07/151.33 (step @p163 :rule quant-unused-vars :args ((= (forall @t138 @t135) @t136))) % 151.07/151.33 (step @p164 :rule trans :premises (@p163 @p162)) % 151.07/151.33 (step @p165 :rule eq-symm :args (@t115 @t19)) % 151.07/151.33 (step @p166 :rule cong :premises (@p165) :args (@t139)) % 151.07/151.33 (step @p167 :rule ho_cong :premises (@p146 @p166)) % 151.07/151.33 (step @p168 :rule ho_cong :premises (@p167 @p143)) % 151.07/151.33 (step @p169 :rule cong :premises (@p168) :args (@t140)) % 151.07/151.33 (step @p170 :rule refl :args (@t115)) % 151.07/151.33 (step @p171 :rule cong :premises (@p170 @p169) :args (@t141)) % 151.07/151.33 (step @p172 :rule cong :premises (@p171) :args (@t142)) % 151.07/151.33 (step @p173 :rule trans :premises (@p172 @p164)) % 151.07/151.33 (step @p174 :rule nary_cong :premises (@p173 @p153) :args ((and @t142 @t132))) % 151.07/151.33 (step @p175 :rule alpha_equiv :args (@t147 @t148 (@list @t127 @t112))) % 151.07/151.33 (step @p176 :rule alpha_equiv :args (@t153 @t148 (@list @t115 @t137))) % 151.07/151.33 (step @p177 :rule nary_cong :premises (@p176 @p175) :args (@t154)) % 151.07/151.33 (step @p178 :rule quant-miniscope-and :args ((= (forall @t15 (and @t152 @t146)) @t154))) % 151.07/151.33 (step @p179 :rule trans :premises (@p178 @p177)) % 151.07/151.33 (step @p180 :rule trans :premises (@p179 @p174)) % 151.07/151.33 (step @p181 :rule eq-symm :args (@t145 @t11)) % 151.07/151.33 (step @p182 :rule refl :args (@t11)) % 151.07/151.33 (step @p183 :rule beta-reduce :args ((= (_ @t156 @t11) @t145))) % 151.07/151.33 (step @p184 :rule beta-reduce :args ((= (_ (lambda @t157 @t144) @t4) @t156))) % 151.07/151.33 (step @p185 :rule refl :args (@t4)) % 151.07/151.33 (step @p186 :rule aci_norm :args ((= (or false @t143) @t143))) % 151.07/151.33 (step @p187 :rule aci_norm :args ((= (and true @t143) @t143))) % 151.07/151.33 (step @p188 :rule refl :args (@t143)) % 151.07/151.33 (step @p189 :rule evaluate :args (@t158)) % 151.07/151.33 (step @p190 :rule nary_cong :premises (@p189 @p188) :args (@t159)) % 151.07/151.33 (step @p191 :rule trans :premises (@p190 @p187)) % 151.07/151.33 (step @p192 :rule absorb :args ((= @t160 false))) % 151.07/151.33 (step @p193 :rule nary_cong :premises (@p192 @p191) :args (@t161)) % 151.07/151.33 (step @p194 :rule trans :premises (@p193 @p186)) % 151.07/151.33 (step @p195 :rule cong :premises (@p194) :args (@t162)) % 151.07/151.33 (step @p196 :rule ho_cong :premises (@p146 @p195)) % 151.07/151.33 (step @p197 :rule ho_cong :premises (@p196 @p143)) % 151.07/151.33 (step @p198 :rule cong :premises (@p197) :args (@t163)) % 151.07/151.33 (step @p199 :rule beta-reduce :args ((= @t165 @t163))) % 151.07/151.33 (step @p200 :rule trans :premises (@p199 @p198)) % 151.07/151.33 (step @p201 :rule ho_cong :premises (@p200 @p185)) % 151.07/151.33 (step @p202 :rule trans :premises (@p201 @p184)) % 151.07/151.33 (step @p203 :rule ho_cong :premises (@p202 @p182)) % 151.07/151.33 (step @p204 :rule trans :premises (@p203 @p183)) % 151.07/151.33 (step @p205 :rule cong :premises (@p204 @p182) :args (@t166)) % 151.07/151.33 (step @p206 :rule trans :premises (@p205 @p181)) % 151.07/151.33 (step @p207 :rule eq-symm :args (@t151 @t4)) % 151.07/151.33 (step @p208 :rule beta-reduce :args ((= (_ @t167 @t11) @t151))) % 151.07/151.33 (step @p209 :rule beta-reduce :args ((= (_ (lambda @t157 @t150) @t4) @t167))) % 151.07/151.33 (step @p210 :rule aci_norm :args ((= (or @t149 false) @t149))) % 151.07/151.33 (step @p211 :rule absorb :args ((= (and false @t143) false))) % 151.07/151.33 (step @p212 :rule evaluate :args (@t168)) % 151.07/151.33 (step @p213 :rule nary_cong :premises (@p212 @p188) :args (@t169)) % 151.07/151.33 (step @p214 :rule trans :premises (@p213 @p211)) % 151.07/151.33 (step @p215 :rule aci_norm :args ((= @t170 @t149))) % 151.07/151.33 (step @p216 :rule nary_cong :premises (@p215 @p214) :args (@t171)) % 151.07/151.33 (step @p217 :rule trans :premises (@p216 @p210)) % 151.07/151.33 (step @p218 :rule cong :premises (@p217) :args (@t172)) % 151.07/151.33 (step @p219 :rule ho_cong :premises (@p146 @p218)) % 151.07/151.33 (step @p220 :rule ho_cong :premises (@p219 @p143)) % 151.07/151.33 (step @p221 :rule cong :premises (@p220) :args (@t173)) % 151.07/151.33 (step @p222 :rule beta-reduce :args ((= @t174 @t173))) % 151.07/151.33 (step @p223 :rule trans :premises (@p222 @p221)) % 151.07/151.33 (step @p224 :rule ho_cong :premises (@p223 @p185)) % 151.07/151.33 (step @p225 :rule trans :premises (@p224 @p209)) % 151.07/151.33 (step @p226 :rule ho_cong :premises (@p225 @p182)) % 151.07/151.33 (step @p227 :rule trans :premises (@p226 @p208)) % 151.07/151.33 (step @p228 :rule cong :premises (@p227 @p185) :args (@t175)) % 151.07/151.33 (step @p229 :rule trans :premises (@p228 @p207)) % 151.07/151.33 (step @p230 :rule nary_cong :premises (@p229 @p206) :args (@t176)) % 151.07/151.33 (step @p231 :rule cong :premises (@p230) :args (@t177)) % 151.07/151.33 (step @p232 :rule trans :premises (@p231 @p180)) % 151.07/151.33 (step @p233 :rule cong :premises (@p232) :args ((not @t177))) % 151.07/151.33 (step @p234 :rule refl :args (false)) % 151.07/151.33 (step @p235 :rule eq-symm :args (@t19 @t11)) % 151.07/151.33 (step @p236 :rule refl :args (@t21)) % 151.07/151.33 (step @p237 :rule nary_cong :premises (@p236 @p235) :args (@t22)) % 151.07/151.33 (step @p238 :rule eq-symm :args (@t19 @t4)) % 151.07/151.33 (step @p239 :rule refl :args (@t20)) % 151.07/151.33 (step @p240 :rule nary_cong :premises (@p239 @p238) :args (@t23)) % 151.07/151.33 (step @p241 :rule nary_cong :premises (@p240 @p237) :args (@t24)) % 151.07/151.33 (step @p242 :rule cong :premises (@p241) :args (@t26)) % 151.07/151.33 (step @p243 :rule ho_cong :premises (@p146 @p242)) % 151.07/151.33 (step @p244 :rule ho_cong :premises (@p243 @p143)) % 151.07/151.33 (step @p245 :rule cong :premises (@p244) :args (@t28)) % 151.07/151.33 (step @p246 :rule trans :premises (@p4 @p245)) % 151.07/151.33 (step @p247 :rule ho_cong :premises (@p246 @p234)) % 151.07/151.33 (step @p248 :rule ho_cong :premises (@p247 @p185)) % 151.07/151.33 (step @p249 :rule ho_cong :premises (@p248 @p182)) % 151.07/151.33 (step @p250 :rule cong :premises (@p249 @p182) :args (@t12)) % 151.07/151.33 (step @p251 :rule refl :args (true)) % 151.07/151.33 (step @p252 :rule ho_cong :premises (@p246 @p251)) % 151.07/151.33 (step @p253 :rule ho_cong :premises (@p252 @p185)) % 151.07/151.33 (step @p254 :rule ho_cong :premises (@p253 @p182)) % 151.07/151.33 (step @p255 :rule cong :premises (@p254 @p185) :args (@t13)) % 151.07/151.33 (step @p256 :rule nary_cong :premises (@p255 @p250) :args (@t14)) % 151.07/151.33 (step @p257 :rule cong :premises (@p256) :args (@t16)) % 151.07/151.33 (step @p258 :rule cong :premises (@p257) :args (@t17)) % 151.07/151.33 (step @p259 :rule trans :premises (@p258 @p233)) % 151.07/151.33 (step @p260 :rule trans :premises (@p259 @p131 @p130)) % 151.07/151.33 (step @p261 :rule eq_resolve :premises (@p2 @p260)) % 151.07/151.33 (step @p262 :rule not_and :premises (@p261)) % 151.07/151.33 (step @p263 :rule chain_m_resolution :premises (@p262 @p129) :args (@t178 @t78 (@list @t42))) % 151.07/151.33 (step @p264 :rule refl :args (@t180)) % 151.07/151.33 (step @p265 :rule bool-double-not-elim :args (@t37)) % 151.07/151.33 (step @p266 :rule nary_cong :premises (@p265 @p264) :args ((or (not @t178) @t180))) % 151.07/151.33 (assume-push @p407 @t178) % 151.07/151.33 (step @p268 :rule skolemize :premises (@p407)) % 151.07/151.33 (step-pop @p408 :rule scope :premises (@p268)) % 151.07/151.33 (step @p269 :rule process_scope :premises (@p408) :args (@t180)) % 151.07/151.33 (step @p271 :rule implies_elim :premises (@p269)) % 151.07/151.33 (step @p272 :rule eq_resolve :premises (@p271 @p266)) % 151.07/151.33 (step @p273 :rule chain_m_resolution :premises (@p272 @p263) :args (@t180 @t181 (@list @t37))) % 151.07/151.33 (step @p274 :rule cnf_or_pos :args (@t184)) % 151.07/151.33 (step @p275 :rule reordering :premises (@p274) :args ((or @t179 @t183 (not @t184)))) % 151.07/151.33 (step @p276 :rule chain_m_resolution :premises (@p275 @p273 @p6) :args (@t183 (@list true false) (@list @t179 @t184))) % 151.07/151.33 (step @p277 :rule refl :args (@t189)) % 151.07/151.33 (step @p278 :rule bool-double-not-elim :args (@t182)) % 151.07/151.33 (step @p279 :rule nary_cong :premises (@p278 @p277) :args ((or (not @t183) @t189))) % 151.07/151.33 (assume-push @p409 @t183) % 151.07/151.33 (step @p281 :rule skolemize :premises (@p409)) % 151.07/151.33 (step-pop @p410 :rule scope :premises (@p281)) % 151.07/151.33 (step @p282 :rule process_scope :premises (@p410) :args (@t189)) % 151.07/151.33 (step @p284 :rule implies_elim :premises (@p282)) % 151.07/151.33 (step @p285 :rule eq_resolve :premises (@p284 @p279)) % 151.07/151.33 (step @p286 :rule chain_m_resolution :premises (@p285 @p276) :args (@t189 @t181 (@list @t182))) % 151.07/151.33 (step @p287 :rule eq-symm :args (@t192 @t194)) % 151.07/151.33 (step @p288 :rule cong :premises (@p287) :args (@t196)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p289 :rule trust :premises () :args ((= @t199 @t196))) % 151.07/151.33 (step @p290 :rule trans :premises (@p289 @p288)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.07/151.33 (step @p291 :rule trust :premises () :args (@t199)) % 151.07/151.33 (step @p292 :rule eq_resolve :premises (@p291 @p290)) % 151.07/151.33 (step @p293 :rule eq-symm :args (@t202 @t186)) % 151.07/151.33 (step @p294 :rule refl :args (@t203)) % 151.07/151.33 (step @p295 :rule cong :premises (@p294 @p293) :args ((=> @t203 @t204))) % 151.07/151.33 (assume-push @p411 @t203) % 151.07/151.33 (step @p297 :rule instantiate :premises (@p292) :args (@t205)) % 151.07/151.33 (step-pop @p412 :rule scope :premises (@p297)) % 151.07/151.33 (step @p298 :rule process_scope :premises (@p412) :args (@t204)) % 151.07/151.33 (step @p300 :rule eq_resolve :premises (@p298 @p295)) % 151.07/151.33 (step @p301 :rule implies_elim :premises (@p300)) % 151.07/151.33 (step @p302 :rule chain_m_resolution :premises (@p301 @p292) :args (@t206 @t78 (@list @t203))) % 151.07/151.33 (step @p303 :rule eq-symm :args (@t209 @t210)) % 151.07/151.33 (step @p304 :rule refl :args (@t210)) % 151.07/151.33 (step @p305 :rule eq-symm :args (@t207 @t208)) % 151.07/151.33 (step @p306 :rule cong :premises (@p305 @p304) :args ((= @t211 @t210))) % 151.07/151.33 (step @p307 :rule trans :premises (@p306 @p303)) % 151.07/151.33 (step @p308 :rule eq-symm :args (@t210 @t211)) % 151.07/151.33 (step @p309 :rule trans :premises (@p308 @p307)) % 151.07/151.33 (step @p310 :rule cong :premises (@p309) :args (@t213)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM % 151.07/151.33 (step @p311 :rule trust :premises () :args ((= @t216 @t213))) % 151.07/151.33 (step @p312 :rule trans :premises (@p311 @p310)) % 151.07/151.33 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 151.07/151.33 (step @p313 :rule trust :premises () :args (@t216)) % 151.07/151.33 (step @p314 :rule eq_resolve :premises (@p313 @p312)) % 151.07/151.33 (step @p315 :rule refl :args (@t217)) % 151.07/151.33 (step @p316 :rule eq-symm :args (@t201 @t38)) % 151.07/151.33 (step @p317 :rule cong :premises (@p316 @p315) :args ((= @t218 @t217))) % 151.07/151.33 (step @p318 :rule eq-symm :args (@t217 @t218)) % 151.07/151.33 (step @p319 :rule trans :premises (@p318 @p317)) % 151.07/151.33 (step @p320 :rule refl :args (@t219)) % 151.07/151.33 (step @p321 :rule cong :premises (@p320 @p319) :args ((=> @t219 @t220))) % 151.07/151.33 (assume-push @p413 @t219) % 151.07/151.33 (step @p323 :rule instantiate :premises (@p314) :args ((@list @t38 @t201))) % 151.07/151.33 (step-pop @p414 :rule scope :premises (@p323)) % 151.07/151.33 (step @p324 :rule process_scope :premises (@p414) :args (@t220)) % 151.07/151.33 (step @p326 :rule eq_resolve :premises (@p324 @p321)) % 151.07/151.33 (step @p327 :rule implies_elim :premises (@p326)) % 151.07/151.33 (step @p328 :rule chain_m_resolution :premises (@p327 @p314) :args (@t222 @t78 @t223)) % 151.07/151.33 (step @p329 :rule instantiate :premises (@p80) :args ((@list @t200 @t225))) % 151.07/151.33 (step @p330 :rule refl :args (@t226)) % 151.07/151.33 (step @p331 :rule eq-symm :args (@t225 @t38)) % 151.07/151.33 (step @p332 :rule cong :premises (@p331 @p330) :args ((= @t227 @t226))) % 151.07/151.33 (step @p333 :rule eq-symm :args (@t226 @t227)) % 151.07/151.33 (step @p334 :rule trans :premises (@p333 @p332)) % 151.07/151.33 (step @p335 :rule cong :premises (@p320 @p334) :args ((=> @t219 @t228))) % 151.07/151.33 (assume-push @p415 @t219) % 151.07/151.33 (step @p337 :rule instantiate :premises (@p314) :args (@t229)) % 151.07/151.33 (step-pop @p416 :rule scope :premises (@p337)) % 151.07/151.33 (step @p338 :rule process_scope :premises (@p416) :args (@t228)) % 151.07/151.33 (step @p340 :rule eq_resolve :premises (@p338 @p335)) % 151.07/151.33 (step @p341 :rule implies_elim :premises (@p340)) % 151.07/151.33 (step @p342 :rule chain_m_resolution :premises (@p341 @p314) :args (@t231 @t78 @t223)) % 151.07/151.33 (step @p343 :rule refl :args (@t232)) % 151.07/151.33 (step @p344 :rule cong :premises (@p343 @p331) :args (@t233)) % 151.07/151.33 (step @p345 :rule cong :premises (@p31 @p344) :args ((=> @t75 @t233))) % 151.07/151.33 (assume-push @p417 @t75) % 151.07/151.33 (step @p347 :rule instantiate :premises (@p27) :args (@t229)) % 151.07/151.33 (step-pop @p418 :rule scope :premises (@p347)) % 151.07/151.33 (step @p348 :rule process_scope :premises (@p418) :args (@t233)) % 151.07/151.33 (step @p350 :rule eq_resolve :premises (@p348 @p345)) % 151.07/151.33 (step @p351 :rule implies_elim :premises (@p350)) % 151.07/151.33 (step @p352 :rule chain_m_resolution :premises (@p351 @p27) :args (@t234 @t78 @t79)) % 151.07/151.33 (step @p353 :rule instantiate :premises (@p80) :args ((@list @t224 @t38))) % 151.07/151.33 (step @p354 :rule bool-eq-true :args (@t235)) % 151.07/151.33 (step @p355 :rule eq-symm :args (true @t235)) % 151.07/151.33 (step @p356 :rule trans :premises (@p355 @p354)) % 151.07/151.33 (step @p357 :rule refl :args (@t235)) % 151.07/151.33 (step @p358 :rule eq-refl :args (@t38)) % 151.07/151.33 (step @p359 :rule cong :premises (@p358 @p357) :args ((= @t236 @t235))) % 151.07/151.33 (step @p360 :rule trans :premises (@p359 @p356)) % 151.07/151.33 (step @p361 :rule eq-symm :args (@t235 @t236)) % 151.07/151.33 (step @p362 :rule trans :premises (@p361 @p360)) % 151.07/151.33 (step @p363 :rule cong :premises (@p31 @p362) :args ((=> @t75 @t237))) % 151.07/151.33 (assume-push @p419 @t75) % 151.07/151.33 (step @p365 :rule instantiate :premises (@p27) :args ((@list @t38 @t38))) % 151.07/151.33 (step-pop @p420 :rule scope :premises (@p365)) % 151.07/151.33 (step @p366 :rule process_scope :premises (@p420) :args (@t237)) % 151.07/151.33 (step @p368 :rule eq_resolve :premises (@p366 @p363)) % 151.07/151.33 (step @p369 :rule implies_elim :premises (@p368)) % 151.07/151.33 (step @p370 :rule chain_m_resolution :premises (@p369 @p27) :args (@t235 @t78 @t79)) % 151.07/151.33 (step @p371 :rule cnf_or_pos :args (@t239)) % 151.07/151.33 (step @p372 :rule reordering :premises (@p371) :args ((or @t238 @t232 (not @t239)))) % 151.07/151.33 (step @p373 :rule chain_m_resolution :premises (@p372 @p370 @p353) :args (@t232 @t103 (@list @t235 @t239))) % 151.07/151.33 (step @p374 :rule cnf_equiv_pos1 :args (@t234)) % 151.07/151.33 (step @p375 :rule reordering :premises (@p374) :args ((or (not @t232) @t230 (not @t234)))) % 151.07/151.33 (step @p376 :rule chain_m_resolution :premises (@p375 @p373 @p352) :args (@t230 @t103 (@list @t232 @t234))) % 151.07/151.33 (step @p377 :rule cnf_equiv_pos1 :args (@t231)) % 151.07/151.33 (step @p378 :rule reordering :premises (@p377) :args ((or @t226 (not @t230) (not @t231)))) % 151.07/151.33 (step @p379 :rule chain_m_resolution :premises (@p378 @p376 @p342) :args (@t226 @t103 (@list @t230 @t231))) % 151.07/151.33 (step @p380 :rule cnf_or_pos :args (@t241)) % 151.07/151.33 (step @p381 :rule reordering :premises (@p380) :args ((or @t240 @t217 (not @t241)))) % 151.07/151.33 (step @p382 :rule chain_m_resolution :premises (@p381 @p379 @p329) :args (@t217 @t103 (@list @t226 @t241))) % 151.07/151.33 (step @p383 :rule cnf_equiv_pos2 :args (@t222)) % 151.07/151.33 (step @p384 :rule reordering :premises (@p383) :args ((or @t221 (not @t217) (not @t222)))) % 151.07/151.33 (step @p385 :rule chain_m_resolution :premises (@p384 @p382 @p328) :args (@t221 @t103 (@list @t217 @t222))) % 151.07/151.33 (assume-push @p421 @t221) % 151.07/151.33 (assume-push @p422 @t206) % 151.07/151.33 (step @p297 :rule instantiate :premises (@p292) :args (@t205)) % 151.07/151.33 (step @p388 :rule refl :args (@t185)) % 151.07/151.33 (step @p389 :rule cong :premises (@p385 @p388) :args (@t187)) % 151.07/151.33 (step @p390 :rule trans :premises (@p389 @p297)) % 151.07/151.33 (step-pop @p423 :rule scope :premises (@p390)) % 151.07/151.33 (step-pop @p424 :rule scope :premises (@p423)) % 151.07/151.33 (step @p391 :rule process_scope :premises (@p424) :args (@t188)) % 151.07/151.33 (step @p394 :rule implies_elim :premises (@p391)) % 151.07/151.33 (step @p395 :rule cnf_and_neg :args (@t242)) % 151.07/151.33 (step @p396 :rule resolution :premises (@p395 @p394) :args (true @t242)) % 151.07/151.33 (step @p397 :rule reordering :premises (@p396) :args ((or @t188 (not @t206) (not @t221)))) % 151.07/151.33 (step @p398 false :rule chain_m_resolution :premises (@p397 @p385 @p302 @p286) :args (false (@list false false true) (@list @t221 @t206 @t188))) % 151.07/151.33 ) % 151.07/151.33 % SZS output end Proof % 151.07/151.33 % cvc5 exiting %------------------------------------------------------------------------------