%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ANA125^1 : TPTP v9.2.1. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:06:43 AM UTC 2026 % Result : Theorem 170.28s 170.52s % Output : Proof 170.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : ANA125^1 : TPTP v9.2.1. Released v7.0.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n011.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Wed Jun 3 02:22:05 EDT 2026 % 0.19/0.35 % CPUTime : % 0.33/0.50 %----Proving TH0 % 170.28/170.52 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 170.28/170.52 --- 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... % 170.28/170.52 --- 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... % 170.28/170.52 --- Run --ho-elim --full-saturate-quant at 18s... % 170.28/170.52 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 170.28/170.52 % SZS status Theorem % 170.28/170.52 % SZS output start Proof % 170.28/170.52 ( % 170.28/170.52 (declare-sort |tptp.'type/realax/real'| 0) % 170.28/170.52 (declare-const |tptp.'const/iterate/polynomial_function'| (-> (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|) Bool)) % 170.28/170.52 (declare-const |tptp.'const/realax/real_mul'| (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t1 () (@var "A1" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t2 () (@var "A" (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|))) % 170.28/170.52 (define @t3 () (_ @t2 @t1)) % 170.28/170.52 (define @t4 () (@var "A0" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t5 () (_ |tptp.'const/realax/real_mul'| @t4)) % 170.28/170.52 (define @t6 () (_ @t5 @t3)) % 170.28/170.52 (define @t7 () (@list @t1)) % 170.28/170.52 (define @t8 () (lambda @t7 @t6)) % 170.28/170.52 (define @t9 () (_ |tptp.'const/iterate/polynomial_function'| @t8)) % 170.28/170.52 (define @t10 () (_ |tptp.'const/iterate/polynomial_function'| @t2)) % 170.28/170.52 (define @t11 () (@list @t2 @t4)) % 170.28/170.52 (define @t12 () (forall @t11 (=> @t10 @t9))) % 170.28/170.52 (define @t13 () (@var "A" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t14 () (_ @t5 @t13)) % 170.28/170.52 (define @t15 () (_ (_ |tptp.'const/realax/real_mul'| @t13) @t4)) % 170.28/170.52 (define @t16 () (= @t15 @t14)) % 170.28/170.52 (define @t17 () (@list @t13 @t4)) % 170.28/170.52 (define @t18 () (forall @t17 @t16)) % 170.28/170.52 (define @t19 () (_ (_ |tptp.'const/realax/real_mul'| @t3) @t4)) % 170.28/170.52 (define @t20 () (lambda @t7 @t19)) % 170.28/170.52 (define @t21 () (_ |tptp.'const/iterate/polynomial_function'| @t20)) % 170.28/170.52 (define @t22 () (forall @t11 (=> @t10 @t21))) % 170.28/170.52 (define @t23 () (not @t22)) % 170.28/170.52 (define @t24 () (@var "y" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t25 () (@var "x" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t26 () (@var "z" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t27 () (@const 0 (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'|))) % 170.28/170.52 (define @t28 () (@list @t26)) % 170.28/170.52 (define @t29 () (@var "BOUND_VARIABLE_7528" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t30 () (@const 1 (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t31 () (@const 2 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|))))) % 170.28/170.52 (define @t32 () (@const 3 (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|))))) % 170.28/170.52 (define @t33 () (@const 4 (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool)))) % 170.28/170.52 (define @t34 () (@const 5 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool)) (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool))) % 170.28/170.52 (define @t35 () (not (_ @t34 @t33 @t29))) % 170.28/170.52 (define @t36 () (@list @t29 @t4)) % 170.28/170.52 (define @t37 () (forall @t36 (or @t35 (_ @t34 @t33 (_ @t32 (_ @t31 @t30 @t29) @t4))))) % 170.28/170.52 (define @t38 () (@quantifiers_skolemize @t37 0)) % 170.28/170.52 (define @t39 () (@quantifiers_skolemize @t37 1)) % 170.28/170.52 (define @t40 () (@const 6 (@ho-elim-sort (-> |tptp.'type/realax/real'| (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t41 () (@const 7 (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'|))))) % 170.28/170.52 (define @t42 () (@const 8 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|))))) % 170.28/170.52 (define @t43 () (_ @t42 (_ @t41 @t40 @t39) @t38)) % 170.28/170.52 (define @t44 () (_ @t32 (_ @t31 @t30 @t38) @t39)) % 170.28/170.52 (define @t45 () (@var "ii" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t46 () (@var "u" (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool)))) % 170.28/170.52 (define @t47 () (@var "e" Bool)) % 170.28/170.52 (define @t48 () (@var "i" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t49 () (@var "v" (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool)))) % 170.28/170.52 (define @t50 () (_ @t34 @t49 @t45)) % 170.28/170.52 (define @t51 () (@list @t45)) % 170.28/170.52 (define @t52 () (@list @t49)) % 170.28/170.52 (define @t53 () (forall (@list @t46 @t47 @t48) (not (forall @t52 (not (forall @t51 (= @t50 (ite (= @t48 @t45) @t47 (_ @t34 @t46 @t45))))))))) % 170.28/170.52 (define @t54 () (_ @t34 @t33 @t45)) % 170.28/170.52 (define @t55 () (_ @t34 @t33 @t44)) % 170.28/170.52 (define @t56 () (ite (= @t44 @t45) @t55 @t54)) % 170.28/170.52 (define @t57 () (= @t50 @t56)) % 170.28/170.52 (define @t58 () (forall @t51 @t57)) % 170.28/170.52 (define @t59 () (not @t58)) % 170.28/170.52 (define @t60 () (forall @t52 @t59)) % 170.28/170.52 (define @t61 () (not @t60)) % 170.28/170.52 (define @t62 () (ite (= @t45 @t44) @t55 @t54)) % 170.28/170.52 (define @t63 () (forall @t52 (not (forall @t51 (= @t50 @t62))))) % 170.28/170.52 (define @t64 () (not @t63)) % 170.28/170.52 (define @t65 () (@list false)) % 170.28/170.52 (define @t66 () (@quantifiers_skolemize @t63 0)) % 170.28/170.52 (define @t67 () (_ @t34 @t66 @t45)) % 170.28/170.52 (define @t68 () (forall @t51 (= @t62 @t67))) % 170.28/170.52 (define @t69 () (forall @t51 (= @t67 @t62))) % 170.28/170.52 (define @t70 () (not (not @t69))) % 170.28/170.52 (define @t71 () (@list true)) % 170.28/170.52 (define @t72 () (_ @t34 @t33 @t43)) % 170.28/170.52 (define @t73 () (= @t44 @t43)) % 170.28/170.52 (define @t74 () (ite @t73 @t55 @t72)) % 170.28/170.52 (define @t75 () (_ @t34 @t66 @t43)) % 170.28/170.52 (define @t76 () (ite (= @t43 @t44) @t55 @t72)) % 170.28/170.52 (define @t77 () (= @t76 @t75)) % 170.28/170.52 (define @t78 () (= @t75 @t74)) % 170.28/170.52 (define @t79 () (@list @t68)) % 170.28/170.52 (define @t80 () (@var "y" (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool)))) % 170.28/170.52 (define @t81 () (@var "x" (@ho-elim-sort (-> (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)) Bool)))) % 170.28/170.52 (define @t82 () (@var "z" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t83 () (@list @t82)) % 170.28/170.52 (define @t84 () (forall @t83 (= (_ @t34 @t33 @t82) (_ @t34 @t66 @t82)))) % 170.28/170.52 (define @t85 () (@quantifiers_skolemize @t84 0)) % 170.28/170.52 (define @t86 () (_ @t34 @t66 @t85)) % 170.28/170.52 (define @t87 () (_ @t34 @t33 @t85)) % 170.28/170.52 (define @t88 () (= @t87 @t86)) % 170.28/170.52 (define @t89 () (ite (= @t85 @t44) @t55 @t87)) % 170.28/170.52 (define @t90 () (= @t89 @t86)) % 170.28/170.52 (define @t91 () (= @t44 @t85)) % 170.28/170.52 (define @t92 () (ite @t91 @t55 @t87)) % 170.28/170.52 (define @t93 () (= @t86 @t92)) % 170.28/170.52 (define @t94 () (not @t93)) % 170.28/170.52 (define @t95 () (not @t92)) % 170.28/170.52 (define @t96 () (not @t87)) % 170.28/170.52 (define @t97 () (@const 9 (-> (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|) |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|))) % 170.28/170.52 (define @t98 () (|tptp.'const/iterate/polynomial_function'| @t2)) % 170.28/170.52 (define @t99 () (not @t98)) % 170.28/170.52 (define @t100 () (not (forall @t11 (or @t99 (|tptp.'const/iterate/polynomial_function'| (_ (_ @t97 @t2) @t4)))))) % 170.28/170.52 (define @t101 () (_ @t2 @t1)) % 170.28/170.52 (define @t102 () (|tptp.'const/realax/real_mul'| @t101 @t4)) % 170.28/170.52 (define @t103 () (lambda @t7 @t102)) % 170.28/170.52 (define @t104 () (|tptp.'const/iterate/polynomial_function'| @t103)) % 170.28/170.52 (define @t105 () (not @t10)) % 170.28/170.52 (define @t106 () (or @t105 @t21)) % 170.28/170.52 (define @t107 () (_ @t34 @t33 @t38)) % 170.28/170.52 (define @t108 () (not @t107)) % 170.28/170.52 (define @t109 () (or @t108 @t55)) % 170.28/170.52 (define @t110 () (not @t55)) % 170.28/170.52 (define @t111 () (@list @t109)) % 170.28/170.52 (define @t112 () (not @t91)) % 170.28/170.52 (define @t113 () (and @t110 @t91 @t87)) % 170.28/170.52 (define @t114 () (not @t88)) % 170.28/170.52 (define @t115 () (not @t84)) % 170.28/170.52 (define @t116 () (= @t33 @t66)) % 170.28/170.52 (define @t117 () (or @t115 @t116)) % 170.28/170.52 (define @t118 () (@list false false)) % 170.28/170.52 (define @t119 () (@const 10 (-> |tptp.'type/realax/real'| (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|) |tptp.'type/realax/real'| |tptp.'type/realax/real'|))) % 170.28/170.52 (define @t120 () (forall @t11 (or @t99 (|tptp.'const/iterate/polynomial_function'| (_ (_ @t119 @t4) @t2))))) % 170.28/170.52 (define @t121 () (|tptp.'const/realax/real_mul'| @t4 @t101)) % 170.28/170.52 (define @t122 () (lambda @t7 @t121)) % 170.28/170.52 (define @t123 () (|tptp.'const/iterate/polynomial_function'| @t122)) % 170.28/170.52 (define @t124 () (or @t105 @t9)) % 170.28/170.52 (define @t125 () (or @t108 @t72)) % 170.28/170.52 (define @t126 () (and @t72 @t116)) % 170.28/170.52 (define @t127 () (not @t73)) % 170.28/170.52 (define @t128 () (@list true false)) % 170.28/170.52 (define @t129 () (forall @t28 (= (_ @t27 @t44 @t26) (_ @t27 @t43 @t26)))) % 170.28/170.52 (define @t130 () (not @t129)) % 170.28/170.52 (define @t131 () (or @t130 @t73)) % 170.28/170.52 (define @t132 () (@quantifiers_skolemize @t129 0)) % 170.28/170.52 (define @t133 () (_ @t27 @t43 @t132)) % 170.28/170.52 (define @t134 () (_ @t27 @t44 @t132)) % 170.28/170.52 (define @t135 () (= @t134 @t133)) % 170.28/170.52 (define @t136 () (not @t135)) % 170.28/170.52 (define @t137 () (@var "ii" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t138 () (@var "u" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t139 () (@var "e" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t140 () (@var "i" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t141 () (@var "v" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t142 () (_ @t27 @t141 @t137)) % 170.28/170.52 (define @t143 () (@list @t137)) % 170.28/170.52 (define @t144 () (@list @t141)) % 170.28/170.52 (define @t145 () (forall (@list @t138 @t139 @t140) (not (forall @t144 (not (forall @t143 (= @t142 (ite (= @t140 @t137) @t139 (_ @t27 @t138 @t137))))))))) % 170.28/170.52 (define @t146 () (_ @t27 @t44 @t137)) % 170.28/170.52 (define @t147 () (ite (= @t39 @t137) @t39 @t146)) % 170.28/170.52 (define @t148 () (= @t142 @t147)) % 170.28/170.52 (define @t149 () (forall @t143 @t148)) % 170.28/170.52 (define @t150 () (not @t149)) % 170.28/170.52 (define @t151 () (forall @t144 @t150)) % 170.28/170.52 (define @t152 () (not @t151)) % 170.28/170.52 (define @t153 () (ite (= @t137 @t39) @t39 @t146)) % 170.28/170.52 (define @t154 () (forall @t144 (not (forall @t143 (= @t142 @t153))))) % 170.28/170.52 (define @t155 () (not @t154)) % 170.28/170.52 (define @t156 () (@quantifiers_skolemize @t154 0)) % 170.28/170.52 (define @t157 () (_ @t27 @t156 @t137)) % 170.28/170.52 (define @t158 () (forall @t143 (= @t153 @t157))) % 170.28/170.52 (define @t159 () (forall @t143 (= @t157 @t153))) % 170.28/170.52 (define @t160 () (not (not @t159))) % 170.28/170.52 (define @t161 () (= @t39 @t132)) % 170.28/170.52 (define @t162 () (ite @t161 @t39 @t134)) % 170.28/170.52 (define @t163 () (@purify @t162)) % 170.28/170.52 (define @t164 () (_ @t27 @t156 @t132)) % 170.28/170.52 (define @t165 () (= @t164 @t162)) % 170.28/170.52 (define @t166 () (ite (= @t132 @t39) @t39 @t134)) % 170.28/170.52 (define @t167 () (= @t166 @t164)) % 170.28/170.52 (define @t168 () (= @t164 @t163)) % 170.28/170.52 (define @t169 () (@var "BOUND_VARIABLE_7505" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t170 () (@var "BOUND_VARIABLE_7586" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t171 () (@var "BOUND_VARIABLE_7503" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t172 () (@const 11 (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t173 () (_ @t27 (_ @t32 @t172 @t171) (_ @t27 @t170 @t169))) % 170.28/170.52 (define @t174 () (_ @t27 (_ @t42 (_ @t41 @t40 @t171) @t170) @t169)) % 170.28/170.52 (define @t175 () (forall (@list @t171 @t170 @t169) (= @t173 @t174))) % 170.28/170.52 (define @t176 () (@var "BOUND_VARIABLE_7504" (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|))) % 170.28/170.52 (define @t177 () (forall (@list @t171 @t176 @t169) (= (|tptp.'const/realax/real_mul'| @t171 (_ @t176 @t169)) (_ @t119 @t171 @t176 @t169)))) % 170.28/170.52 (define @t178 () (@var "BOUND_VARIABLE_7513" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t179 () (@var "BOUND_VARIABLE_7514" |tptp.'type/realax/real'|)) % 170.28/170.52 (define @t180 () (@var "BOUND_VARIABLE_7607" (@ho-elim-sort (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|)))) % 170.28/170.52 (define @t181 () (_ @t27 (_ @t32 @t172 (_ @t27 @t180 @t179)) @t178)) % 170.28/170.52 (define @t182 () (_ @t27 (_ @t32 (_ @t31 @t30 @t180) @t178) @t179)) % 170.28/170.52 (define @t183 () (forall (@list @t180 @t178 @t179) (= @t181 @t182))) % 170.28/170.52 (define @t184 () (@var "BOUND_VARIABLE_7512" (-> |tptp.'type/realax/real'| |tptp.'type/realax/real'|))) % 170.28/170.52 (define @t185 () (forall (@list @t184 @t178 @t179) (= (|tptp.'const/realax/real_mul'| (_ @t184 @t179) @t178) (_ @t97 @t184 @t178 @t179)))) % 170.28/170.52 (define @t186 () (_ @t27 (_ @t32 @t172 @t13) @t4)) % 170.28/170.52 (define @t187 () (_ @t27 (_ @t32 @t172 @t4) @t13)) % 170.28/170.52 (define @t188 () (forall @t17 (= @t186 @t187))) % 170.28/170.52 (define @t189 () (|tptp.'const/realax/real_mul'| @t4 @t13)) % 170.28/170.52 (define @t190 () (|tptp.'const/realax/real_mul'| @t13 @t4)) % 170.28/170.52 (define @t191 () (_ @t27 @t38 @t39)) % 170.28/170.52 (define @t192 () (_ @t32 @t172 @t39)) % 170.28/170.52 (define @t193 () (_ @t27 @t192 @t191)) % 170.28/170.52 (define @t194 () (_ @t27 @t43 @t39)) % 170.28/170.52 (define @t195 () (= @t194 @t193)) % 170.28/170.52 (define @t196 () (_ @t27 (_ @t32 @t172 @t191) @t39)) % 170.28/170.52 (define @t197 () (= (_ @t27 @t44 @t39) @t196)) % 170.28/170.52 (define @t198 () (= @t193 @t196)) % 170.28/170.52 (define @t199 () (and @t195 @t197 @t198 @t161)) % 170.28/170.52 (define @t200 () (not @t161)) % 170.28/170.52 (define @t201 () (= @t162 @t134)) % 170.28/170.52 (define @t202 () (= @t162 @t39)) % 170.28/170.52 (define @t203 () (= @t134 @t163)) % 170.28/170.52 (define @t204 () (_ @t27 @t38 @t132)) % 170.28/170.52 (define @t205 () (_ @t27 @t192 @t204)) % 170.28/170.52 (define @t206 () (_ @t27 (_ @t32 @t172 @t204) @t39)) % 170.28/170.52 (define @t207 () (forall @t17 (= @t187 @t186))) % 170.28/170.52 (define @t208 () (= @t205 @t206)) % 170.28/170.52 (define @t209 () (@list @t204 @t39)) % 170.28/170.52 (define @t210 () (= @t206 @t205)) % 170.28/170.52 (define @t211 () (not @t210)) % 170.28/170.52 (define @t212 () (= @t133 @t205)) % 170.28/170.52 (define @t213 () (not @t212)) % 170.28/170.52 (define @t214 () (= @t134 @t206)) % 170.28/170.52 (define @t215 () (not @t214)) % 170.28/170.52 (define @t216 () (not @t203)) % 170.28/170.52 (define @t217 () (not @t168)) % 170.28/170.52 (define @t218 () (and @t168 @t203 @t214 @t210 @t212 @t136)) % 170.28/170.52 (assume @p1 @t12) % 170.28/170.52 (assume @p2 @t18) % 170.28/170.52 (assume @p3 @t23) % 170.28/170.52 (assume @p4 true) % 170.28/170.52 ; WARNING: add trust step for TRUST % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.28/170.52 (step @p5 :rule trust :premises () :args ((forall (@list @t25 @t24) (or (not (forall @t28 (= (_ @t27 @t25 @t26) (_ @t27 @t24 @t26)))) (= @t25 @t24))))) % 170.28/170.52 (step @p6 :rule instantiate :premises (@p5) :args ((@list @t44 @t43))) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.28/170.52 (step @p7 :rule trust :premises () :args (@t53)) % 170.28/170.52 (step @p8 :rule refl :args (@t54)) % 170.28/170.52 (step @p9 :rule refl :args (@t55)) % 170.28/170.52 (step @p10 :rule eq-symm :args (@t44 @t45)) % 170.28/170.52 (step @p11 :rule cong :premises (@p10 @p9 @p8) :args (@t56)) % 170.28/170.52 (step @p12 :rule refl :args (@t50)) % 170.28/170.52 (step @p13 :rule cong :premises (@p12 @p11) :args (@t57)) % 170.28/170.52 (step @p14 :rule cong :premises (@p13) :args (@t58)) % 170.28/170.52 (step @p15 :rule cong :premises (@p14) :args (@t59)) % 170.28/170.52 (step @p16 :rule cong :premises (@p15) :args (@t60)) % 170.28/170.52 (step @p17 :rule cong :premises (@p16) :args (@t61)) % 170.28/170.52 (step @p18 :rule refl :args (@t53)) % 170.28/170.52 (step @p19 :rule cong :premises (@p18 @p17) :args ((=> @t53 @t61))) % 170.28/170.52 (assume-push @p469 @t53) % 170.28/170.52 (step @p21 :rule instantiate :premises (@p7) :args ((@list @t33 @t55 @t44))) % 170.28/170.52 (step-pop @p470 :rule scope :premises (@p21)) % 170.28/170.52 (step @p22 :rule process_scope :premises (@p470) :args (@t61)) % 170.28/170.52 (step @p24 :rule eq_resolve :premises (@p22 @p19)) % 170.28/170.52 (step @p25 :rule implies_elim :premises (@p24)) % 170.28/170.52 (step @p26 :rule chain_m_resolution :premises (@p25 @p7) :args (@t64 @t65 (@list @t53))) % 170.28/170.52 (step @p27 :rule refl :args (@t68)) % 170.28/170.52 (step @p28 :rule bool-double-not-elim :args (@t63)) % 170.28/170.52 (step @p29 :rule nary_cong :premises (@p28 @p27) :args ((or (not @t64) @t68))) % 170.28/170.52 (step @p30 :rule eq-symm :args (@t67 @t62)) % 170.28/170.52 (step @p31 :rule cong :premises (@p30) :args (@t69)) % 170.28/170.52 (step @p32 :rule bool-double-not-elim :args (@t69)) % 170.28/170.52 (step @p33 :rule trans :premises (@p32 @p31)) % 170.28/170.52 (step @p34 :rule refl :args (@t64)) % 170.28/170.52 (step @p35 :rule cong :premises (@p34 @p33) :args ((=> @t64 @t70))) % 170.28/170.52 (assume-push @p471 @t64) % 170.28/170.52 (step @p37 :rule skolemize :premises (@p26)) % 170.28/170.52 (step-pop @p472 :rule scope :premises (@p37)) % 170.28/170.52 (step @p38 :rule process_scope :premises (@p472) :args (@t70)) % 170.28/170.52 (step @p40 :rule eq_resolve :premises (@p38 @p35)) % 170.28/170.52 (step @p41 :rule implies_elim :premises (@p40)) % 170.28/170.52 (step @p42 :rule eq_resolve :premises (@p41 @p29)) % 170.28/170.52 (step @p43 :rule chain_m_resolution :premises (@p42 @p26) :args (@t68 @t71 (@list @t63))) % 170.28/170.52 (step @p44 :rule eq-symm :args (@t74 @t75)) % 170.28/170.52 (step @p45 :rule refl :args (@t75)) % 170.28/170.52 (step @p46 :rule refl :args (@t72)) % 170.28/170.52 (step @p47 :rule eq-symm :args (@t43 @t44)) % 170.28/170.52 (step @p48 :rule cong :premises (@p47 @p9 @p46) :args (@t76)) % 170.28/170.52 (step @p49 :rule cong :premises (@p48 @p45) :args (@t77)) % 170.28/170.52 (step @p50 :rule trans :premises (@p49 @p44)) % 170.28/170.52 (step @p51 :rule cong :premises (@p27 @p50) :args ((=> @t68 @t77))) % 170.28/170.52 (assume-push @p473 @t68) % 170.28/170.52 (step @p53 :rule instantiate :premises (@p43) :args ((@list @t43))) % 170.28/170.52 (step-pop @p474 :rule scope :premises (@p53)) % 170.28/170.52 (step @p54 :rule process_scope :premises (@p474) :args (@t77)) % 170.28/170.52 (step @p56 :rule eq_resolve :premises (@p54 @p51)) % 170.28/170.52 (step @p57 :rule implies_elim :premises (@p56)) % 170.28/170.52 (step @p58 :rule chain_m_resolution :premises (@p57 @p43) :args (@t78 @t65 @t79)) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.28/170.52 (step @p59 :rule trust :premises () :args ((forall (@list @t81 @t80) (or (not (forall @t83 (= (_ @t34 @t81 @t82) (_ @t34 @t80 @t82)))) (= @t81 @t80))))) % 170.28/170.52 (step @p60 :rule instantiate :premises (@p59) :args ((@list @t33 @t66))) % 170.28/170.52 (step @p61 :rule cnf_equiv_neg2 :args (@t88)) % 170.28/170.52 (step @p62 :rule refl :args (@t87)) % 170.28/170.52 (step @p63 :rule eq-symm :args (@t85 @t44)) % 170.28/170.52 (step @p64 :rule cong :premises (@p63 @p9 @p62) :args (@t89)) % 170.28/170.52 (step @p65 :rule refl :args (@t86)) % 170.28/170.52 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t86 @t89))) % 170.28/170.52 (step @p67 :rule eq-symm :args (@t89 @t86)) % 170.28/170.52 (step @p68 :rule trans :premises (@p67 @p66)) % 170.28/170.52 (step @p69 :rule cong :premises (@p27 @p68) :args ((=> @t68 @t90))) % 170.28/170.52 (assume-push @p475 @t68) % 170.28/170.52 (step @p71 :rule instantiate :premises (@p43) :args ((@list @t85))) % 170.28/170.52 (step-pop @p476 :rule scope :premises (@p71)) % 170.28/170.52 (step @p72 :rule process_scope :premises (@p476) :args (@t90)) % 170.28/170.52 (step @p74 :rule eq_resolve :premises (@p72 @p69)) % 170.28/170.52 (step @p75 :rule implies_elim :premises (@p74)) % 170.28/170.52 (step @p76 :rule chain_m_resolution :premises (@p75 @p43) :args (@t93 @t65 @t79)) % 170.28/170.52 (step @p77 :rule cnf_equiv_pos2 :args (@t93)) % 170.28/170.52 (step @p78 :rule reordering :premises (@p77) :args ((or @t86 @t95 @t94))) % 170.28/170.52 (step @p79 :rule cnf_ite_neg2 :args (@t92)) % 170.28/170.52 (step @p80 :rule reordering :premises (@p79) :args ((or @t96 @t91 @t92))) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p81 :rule trust :premises () :args ((= @t100 (not @t37)))) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p82 :rule trust :premises () :args ((= (not (forall @t11 (or @t99 @t104))) @t100))) % 170.28/170.52 (step @p83 :rule refl :args ((|tptp.'const/iterate/polynomial_function'| @t20))) % 170.28/170.52 (step @p84 :rule refl :args ((|tptp.'const/realax/real_mul'| @t3 @t4))) % 170.28/170.52 (step @p85 :rule refl :args (@t4)) % 170.28/170.52 (step @p86 :rule refl :args (@t101)) % 170.28/170.52 (step @p87 :rule cong :premises (@p86 @p85) :args (@t102)) % 170.28/170.52 (step @p88 :rule trans :premises (@p87 @p84)) % 170.28/170.52 (step @p89 :rule cong :premises (@p88) :args (@t103)) % 170.28/170.52 (step @p90 :rule cong :premises (@p89) :args (@t104)) % 170.28/170.52 (step @p91 :rule trans :premises (@p90 @p83)) % 170.28/170.52 (step @p92 :rule refl :args (|tptp.'const/iterate/polynomial_function'|)) % 170.28/170.52 (step @p93 :rule ho_cong :premises (@p92 @p89)) % 170.28/170.52 (step @p94 :rule cong :premises (@p93 @p91) :args ((= (_ |tptp.'const/iterate/polynomial_function'| @t103) @t104))) % 170.28/170.52 (step @p95 :rule symm :premises (@p94)) % 170.28/170.52 (step @p96 :rule refl :args (@t21)) % 170.28/170.52 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 170.28/170.52 (step @p98 :rule refl :args (|tptp.'const/realax/real_mul'|)) % 170.28/170.52 (step @p99 :rule ho_cong :premises (@p98 @p86)) % 170.28/170.52 (step @p100 :rule ho_cong :premises (@p99 @p85)) % 170.28/170.52 (step @p101 :rule cong :premises (@p100 @p88) :args ((= (_ (_ |tptp.'const/realax/real_mul'| @t101) @t4) @t102))) % 170.28/170.52 (step @p102 :rule symm :premises (@p101)) % 170.28/170.52 (step @p103 :rule refl :args (@t19)) % 170.28/170.52 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 170.28/170.52 (step @p105 :rule refl :args (@t3)) % 170.28/170.52 (step @p106 :rule cong :premises (@p105 @p86) :args ((= @t3 @t101))) % 170.28/170.52 (step @p107 :rule symm :premises (@p106)) % 170.28/170.52 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 170.28/170.52 (step @p109 :rule ho_cong :premises (@p98 @p108)) % 170.28/170.52 (step @p110 :rule ho_cong :premises (@p109 @p85)) % 170.28/170.52 (step @p111 :rule trans :premises (@p110 @p104)) % 170.28/170.52 (step @p112 :rule cong :premises (@p111) :args (@t20)) % 170.28/170.52 (step @p113 :rule ho_cong :premises (@p92 @p112)) % 170.28/170.52 (step @p114 :rule trans :premises (@p113 @p97)) % 170.28/170.52 (step @p115 :rule refl :args (@t98)) % 170.28/170.52 (step @p116 :rule refl :args (@t10)) % 170.28/170.52 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t10 @t98))) % 170.28/170.52 (step @p118 :rule symm :premises (@p117)) % 170.28/170.52 (step @p119 :rule eq_resolve :premises (@p116 @p118)) % 170.28/170.52 (step @p120 :rule cong :premises (@p119) :args (@t105)) % 170.28/170.52 (step @p121 :rule nary_cong :premises (@p120 @p114) :args (@t106)) % 170.28/170.52 (step @p122 :rule cong :premises (@p121) :args ((forall @t11 @t106))) % 170.28/170.52 (step @p123 :rule bool-impl-elim :args (@t10 @t21)) % 170.28/170.52 (step @p124 :rule cong :premises (@p123) :args (@t22)) % 170.28/170.52 (step @p125 :rule trans :premises (@p124 @p122)) % 170.28/170.52 (step @p126 :rule cong :premises (@p125) :args (@t23)) % 170.28/170.52 (step @p127 :rule trans :premises (@p126 @p82 @p81)) % 170.28/170.52 (step @p128 :rule eq_resolve :premises (@p3 @p127)) % 170.28/170.52 (step @p129 :rule skolemize :premises (@p128)) % 170.28/170.52 (step @p130 :rule cnf_or_neg :args (@t109 1)) % 170.28/170.52 (step @p131 :rule chain_m_resolution :premises (@p130 @p129) :args (@t110 @t71 @t111)) % 170.28/170.52 (step @p132 :rule refl :args (@t112)) % 170.28/170.52 (step @p133 :rule refl :args (@t96)) % 170.28/170.52 (step @p134 :rule bool-double-not-elim :args (@t55)) % 170.28/170.52 (step @p135 :rule nary_cong :premises (@p134 @p133 @p132) :args ((or (not @t110) @t96 @t112))) % 170.28/170.52 (assume-push @p477 @t110) % 170.28/170.52 (assume-push @p478 @t91) % 170.28/170.52 (assume-push @p479 @t87) % 170.28/170.52 (step @p139 :rule evaluate :args ((= true false))) % 170.28/170.52 (step @p140 :rule false_intro :premises (@p131)) % 170.28/170.52 (step @p141 :rule symm :premises (@p478)) % 170.28/170.52 (step @p142 :rule refl :args (@t33)) % 170.28/170.52 (step @p143 :rule cong :premises (@p142 @p141) :args (@t87)) % 170.28/170.52 (step @p144 :rule true_intro :premises (@p479)) % 170.28/170.52 (step @p145 :rule symm :premises (@p144)) % 170.28/170.52 (step @p146 :rule trans :premises (@p145 @p143 @p140)) % 170.28/170.52 (step @p147 false :rule eq_resolve :premises (@p146 @p139)) % 170.28/170.52 (step-pop @p480 :rule scope :premises (@p147)) % 170.28/170.52 (step-pop @p481 :rule scope :premises (@p480)) % 170.28/170.52 (step-pop @p482 :rule scope :premises (@p481)) % 170.28/170.52 (step @p148 :rule process_scope :premises (@p482) :args (false)) % 170.28/170.52 (assume-push @p483 @t110) % 170.28/170.52 (assume-push @p484 @t87) % 170.28/170.52 (assume-push @p485 @t91) % 170.28/170.52 (step @p155 :rule and_intro :premises (@p131 @p485 @p484)) % 170.28/170.52 (step-pop @p486 :rule scope :premises (@p155)) % 170.28/170.52 (step-pop @p487 :rule scope :premises (@p486)) % 170.28/170.52 (step-pop @p488 :rule scope :premises (@p487)) % 170.28/170.52 (step @p156 :rule process_scope :premises (@p488) :args (@t113)) % 170.28/170.52 (step @p160 :rule implies_elim :premises (@p156)) % 170.28/170.52 (step @p161 :rule resolution :premises (@p160 @p148) :args (true @t113)) % 170.28/170.52 (step @p162 :rule not_and :premises (@p161)) % 170.28/170.52 (step @p163 :rule eq_resolve :premises (@p162 @p135)) % 170.28/170.52 (step @p164 :rule chain_m_resolution :premises (@p163 @p131 @p80 @p78 @p76 @p61) :args ((or @t88 @t96) (@list true false true false true) (@list @t55 @t91 @t92 @t93 @t86))) % 170.28/170.52 (step @p165 :rule cnf_equiv_neg1 :args (@t88)) % 170.28/170.52 (step @p166 :rule reordering :premises (@p165) :args ((or @t87 @t86 @t88))) % 170.28/170.52 (step @p167 :rule cnf_ite_pos3 :args (@t92)) % 170.28/170.52 (step @p168 :rule reordering :premises (@p167) :args ((or @t55 @t87 @t95))) % 170.28/170.52 (step @p169 :rule cnf_equiv_pos1 :args (@t93)) % 170.28/170.52 (step @p170 :rule reordering :premises (@p169) :args ((or (not @t86) @t92 @t94))) % 170.28/170.52 (step @p171 :rule chain_m_resolution :premises (@p170 @p76 @p168 @p131 @p166 @p164) :args (@t88 (@list false true true false true) (@list @t93 @t92 @t55 @t86 @t87))) % 170.28/170.52 (step @p172 :rule refl :args (@t114)) % 170.28/170.52 (step @p173 :rule bool-double-not-elim :args (@t84)) % 170.28/170.52 (step @p174 :rule nary_cong :premises (@p173 @p172) :args ((or (not @t115) @t114))) % 170.28/170.52 (assume-push @p489 @t115) % 170.28/170.52 (step @p176 :rule skolemize :premises (@p489)) % 170.28/170.52 (step-pop @p490 :rule scope :premises (@p176)) % 170.28/170.52 (step @p177 :rule process_scope :premises (@p490) :args (@t114)) % 170.28/170.52 (step @p179 :rule implies_elim :premises (@p177)) % 170.28/170.52 (step @p180 :rule eq_resolve :premises (@p179 @p174)) % 170.28/170.52 (step @p181 :rule chain_m_resolution :premises (@p180 @p171) :args (@t84 @t65 (@list @t88))) % 170.28/170.52 (step @p182 :rule cnf_or_pos :args (@t117)) % 170.28/170.52 (step @p183 :rule reordering :premises (@p182) :args ((or @t115 @t116 (not @t117)))) % 170.28/170.52 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p60) :args (@t116 @t118 (@list @t84 @t117))) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p185 :rule trust :premises () :args ((= @t120 (forall @t36 (or @t35 (_ @t34 @t33 (_ @t42 (_ @t41 @t40 @t4) @t29))))))) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p186 :rule trust :premises () :args ((= (forall @t11 (or @t99 @t123)) @t120))) % 170.28/170.52 (step @p187 :rule refl :args ((|tptp.'const/iterate/polynomial_function'| @t8))) % 170.28/170.52 (step @p188 :rule refl :args ((|tptp.'const/realax/real_mul'| @t4 @t3))) % 170.28/170.52 (step @p189 :rule cong :premises (@p85 @p86) :args (@t121)) % 170.28/170.52 (step @p190 :rule trans :premises (@p189 @p188)) % 170.28/170.52 (step @p191 :rule cong :premises (@p190) :args (@t122)) % 170.28/170.52 (step @p192 :rule cong :premises (@p191) :args (@t123)) % 170.28/170.52 (step @p193 :rule trans :premises (@p192 @p187)) % 170.28/170.52 (step @p194 :rule ho_cong :premises (@p92 @p191)) % 170.28/170.52 (step @p195 :rule cong :premises (@p194 @p193) :args ((= (_ |tptp.'const/iterate/polynomial_function'| @t122) @t123))) % 170.28/170.52 (step @p196 :rule symm :premises (@p195)) % 170.28/170.52 (step @p197 :rule refl :args (@t9)) % 170.28/170.52 (step @p198 :rule eq_resolve :premises (@p197 @p196)) % 170.28/170.52 (step @p199 :rule refl :args (@t5)) % 170.28/170.52 (step @p200 :rule ho_cong :premises (@p199 @p86)) % 170.28/170.52 (step @p201 :rule cong :premises (@p200 @p190) :args ((= (_ @t5 @t101) @t121))) % 170.28/170.52 (step @p202 :rule symm :premises (@p201)) % 170.28/170.52 (step @p203 :rule refl :args (@t6)) % 170.28/170.52 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 170.28/170.52 (step @p205 :rule ho_cong :premises (@p199 @p108)) % 170.28/170.52 (step @p206 :rule trans :premises (@p205 @p204)) % 170.28/170.52 (step @p207 :rule cong :premises (@p206) :args (@t8)) % 170.28/170.52 (step @p208 :rule ho_cong :premises (@p92 @p207)) % 170.28/170.52 (step @p209 :rule trans :premises (@p208 @p198)) % 170.28/170.52 (step @p210 :rule nary_cong :premises (@p120 @p209) :args (@t124)) % 170.28/170.52 (step @p211 :rule cong :premises (@p210) :args ((forall @t11 @t124))) % 170.28/170.52 (step @p212 :rule bool-impl-elim :args (@t10 @t9)) % 170.28/170.52 (step @p213 :rule cong :premises (@p212) :args (@t12)) % 170.28/170.52 (step @p214 :rule trans :premises (@p213 @p211)) % 170.28/170.52 (step @p215 :rule trans :premises (@p214 @p186 @p185)) % 170.28/170.52 (step @p216 :rule eq_resolve :premises (@p1 @p215)) % 170.28/170.52 (step @p217 :rule instantiate :premises (@p216) :args ((@list @t38 @t39))) % 170.28/170.52 (step @p218 :rule bool-double-not-elim :args (@t107)) % 170.28/170.52 (step @p219 :rule refl :args (@t109)) % 170.28/170.52 (step @p220 :rule nary_cong :premises (@p219 @p218) :args ((or @t109 (not @t108)))) % 170.28/170.52 (step @p221 :rule cnf_or_neg :args (@t109 0)) % 170.28/170.52 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 170.28/170.52 (step @p223 :rule reordering :premises (@p222) :args ((or @t107 @t109))) % 170.28/170.52 (step @p224 :rule chain_m_resolution :premises (@p223 @p129) :args (@t107 @t71 @t111)) % 170.28/170.52 (step @p225 :rule cnf_or_pos :args (@t125)) % 170.28/170.52 (step @p226 :rule reordering :premises (@p225) :args ((or @t108 @t72 (not @t125)))) % 170.28/170.52 (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p217) :args (@t72 @t118 (@list @t107 @t125))) % 170.28/170.52 (assume-push @p491 @t72) % 170.28/170.52 (assume-push @p492 @t116) % 170.28/170.52 (assume-push @p493 @t72) % 170.28/170.52 (assume-push @p494 @t116) % 170.28/170.52 (step @p232 :rule true_intro :premises (@p227)) % 170.28/170.52 (step @p233 :rule refl :args (@t43)) % 170.28/170.52 (step @p234 :rule symm :premises (@p492)) % 170.28/170.52 (step @p235 :rule cong :premises (@p234 @p233) :args (@t75)) % 170.28/170.52 (step @p236 :rule trans :premises (@p235 @p232)) % 170.28/170.52 (step @p237 :rule true_elim :premises (@p236)) % 170.28/170.52 (step-pop @p495 :rule scope :premises (@p237)) % 170.28/170.52 (step-pop @p496 :rule scope :premises (@p495)) % 170.28/170.52 (step @p238 :rule process_scope :premises (@p496) :args (@t75)) % 170.28/170.52 (step @p241 :rule and_intro :premises (@p227 @p492)) % 170.28/170.52 (step @p242 :rule modus_ponens :premises (@p241 @p238)) % 170.28/170.52 (step-pop @p497 :rule scope :premises (@p242)) % 170.28/170.52 (step-pop @p498 :rule scope :premises (@p497)) % 170.28/170.52 (step @p243 :rule process_scope :premises (@p498) :args (@t75)) % 170.28/170.52 (step @p246 :rule implies_elim :premises (@p243)) % 170.28/170.52 (step @p247 :rule cnf_and_neg :args (@t126)) % 170.28/170.52 (step @p248 :rule resolution :premises (@p247 @p246) :args (true @t126)) % 170.28/170.52 (step @p249 :rule chain_m_resolution :premises (@p248 @p227 @p184) :args (@t75 @t118 (@list @t72 @t116))) % 170.28/170.52 (step @p250 :rule cnf_equiv_pos1 :args (@t78)) % 170.28/170.52 (step @p251 :rule reordering :premises (@p250) :args ((or @t74 (not @t75) (not @t78)))) % 170.28/170.52 (step @p252 :rule chain_m_resolution :premises (@p251 @p249 @p58) :args (@t74 @t118 (@list @t75 @t78))) % 170.28/170.52 (step @p253 :rule cnf_ite_pos1 :args (@t74)) % 170.28/170.52 (step @p254 :rule reordering :premises (@p253) :args ((or @t55 @t127 (not @t74)))) % 170.28/170.52 (step @p255 :rule chain_m_resolution :premises (@p254 @p131 @p252) :args (@t127 @t128 (@list @t55 @t74))) % 170.28/170.52 (step @p256 :rule cnf_or_pos :args (@t131)) % 170.28/170.52 (step @p257 :rule reordering :premises (@p256) :args ((or @t130 @t73 (not @t131)))) % 170.28/170.52 (step @p258 :rule chain_m_resolution :premises (@p257 @p255 @p6) :args (@t130 @t128 (@list @t73 @t131))) % 170.28/170.52 (step @p259 :rule refl :args (@t136)) % 170.28/170.52 (step @p260 :rule bool-double-not-elim :args (@t129)) % 170.28/170.52 (step @p261 :rule nary_cong :premises (@p260 @p259) :args ((or (not @t130) @t136))) % 170.28/170.52 (assume-push @p499 @t130) % 170.28/170.52 (step @p263 :rule skolemize :premises (@p499)) % 170.28/170.52 (step-pop @p500 :rule scope :premises (@p263)) % 170.28/170.52 (step @p264 :rule process_scope :premises (@p500) :args (@t136)) % 170.28/170.52 (step @p266 :rule implies_elim :premises (@p264)) % 170.28/170.52 (step @p267 :rule eq_resolve :premises (@p266 @p261)) % 170.28/170.52 (step @p268 :rule chain_m_resolution :premises (@p267 @p258) :args (@t136 @t71 (@list @t129))) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.28/170.52 (step @p269 :rule trust :premises () :args (@t145)) % 170.28/170.52 (step @p270 :rule refl :args (@t146)) % 170.28/170.52 (step @p271 :rule refl :args (@t39)) % 170.28/170.52 (step @p272 :rule eq-symm :args (@t39 @t137)) % 170.28/170.52 (step @p273 :rule cong :premises (@p272 @p271 @p270) :args (@t147)) % 170.28/170.52 (step @p274 :rule refl :args (@t142)) % 170.28/170.52 (step @p275 :rule cong :premises (@p274 @p273) :args (@t148)) % 170.28/170.52 (step @p276 :rule cong :premises (@p275) :args (@t149)) % 170.28/170.52 (step @p277 :rule cong :premises (@p276) :args (@t150)) % 170.28/170.52 (step @p278 :rule cong :premises (@p277) :args (@t151)) % 170.28/170.52 (step @p279 :rule cong :premises (@p278) :args (@t152)) % 170.28/170.52 (step @p280 :rule refl :args (@t145)) % 170.28/170.52 (step @p281 :rule cong :premises (@p280 @p279) :args ((=> @t145 @t152))) % 170.28/170.52 (assume-push @p501 @t145) % 170.28/170.52 (step @p283 :rule instantiate :premises (@p269) :args ((@list @t44 @t39 @t39))) % 170.28/170.52 (step-pop @p502 :rule scope :premises (@p283)) % 170.28/170.52 (step @p284 :rule process_scope :premises (@p502) :args (@t152)) % 170.28/170.52 (step @p286 :rule eq_resolve :premises (@p284 @p281)) % 170.28/170.52 (step @p287 :rule implies_elim :premises (@p286)) % 170.28/170.52 (step @p288 :rule chain_m_resolution :premises (@p287 @p269) :args (@t155 @t65 (@list @t145))) % 170.28/170.52 (step @p289 :rule refl :args (@t158)) % 170.28/170.52 (step @p290 :rule bool-double-not-elim :args (@t154)) % 170.28/170.52 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or (not @t155) @t158))) % 170.28/170.52 (step @p292 :rule eq-symm :args (@t157 @t153)) % 170.28/170.52 (step @p293 :rule cong :premises (@p292) :args (@t159)) % 170.28/170.52 (step @p294 :rule bool-double-not-elim :args (@t159)) % 170.28/170.52 (step @p295 :rule trans :premises (@p294 @p293)) % 170.28/170.52 (step @p296 :rule refl :args (@t155)) % 170.28/170.52 (step @p297 :rule cong :premises (@p296 @p295) :args ((=> @t155 @t160))) % 170.28/170.52 (assume-push @p503 @t155) % 170.28/170.52 (step @p299 :rule skolemize :premises (@p288)) % 170.28/170.52 (step-pop @p504 :rule scope :premises (@p299)) % 170.28/170.52 (step @p300 :rule process_scope :premises (@p504) :args (@t160)) % 170.28/170.52 (step @p302 :rule eq_resolve :premises (@p300 @p297)) % 170.28/170.52 (step @p303 :rule implies_elim :premises (@p302)) % 170.28/170.52 (step @p304 :rule eq_resolve :premises (@p303 @p291)) % 170.28/170.52 (step @p305 :rule chain_m_resolution :premises (@p304 @p288) :args (@t158 @t71 (@list @t154))) % 170.28/170.52 (step @p306 :rule eq-refl :args (@t162)) % 170.28/170.52 (step @p307 :rule skolem_intro :args (@t163)) % 170.28/170.52 (step @p308 :rule refl :args (@t162)) % 170.28/170.52 (step @p309 :rule cong :premises (@p308 @p307) :args ((= @t162 @t163))) % 170.28/170.52 (step @p310 :rule trans :premises (@p309 @p306)) % 170.28/170.52 (step @p311 :rule true_elim :premises (@p310)) % 170.28/170.52 (step @p312 :rule refl :args (@t164)) % 170.28/170.52 (step @p313 :rule cong :premises (@p312 @p311) :args (@t165)) % 170.28/170.52 (step @p314 :rule cong :premises (@p289 @p313) :args ((=> @t158 @t165))) % 170.28/170.52 (step @p315 :rule eq-symm :args (@t162 @t164)) % 170.28/170.52 (step @p316 :rule refl :args (@t134)) % 170.28/170.52 (step @p317 :rule eq-symm :args (@t132 @t39)) % 170.28/170.52 (step @p318 :rule cong :premises (@p317 @p271 @p316) :args (@t166)) % 170.28/170.52 (step @p319 :rule cong :premises (@p318 @p312) :args (@t167)) % 170.28/170.52 (step @p320 :rule trans :premises (@p319 @p315)) % 170.28/170.52 (step @p321 :rule cong :premises (@p289 @p320) :args ((=> @t158 @t167))) % 170.28/170.52 (assume-push @p505 @t158) % 170.28/170.52 (step @p323 :rule instantiate :premises (@p305) :args ((@list @t132))) % 170.28/170.52 (step-pop @p506 :rule scope :premises (@p323)) % 170.28/170.52 (step @p324 :rule process_scope :premises (@p506) :args (@t167)) % 170.28/170.52 (step @p326 :rule eq_resolve :premises (@p324 @p321)) % 170.28/170.52 (step @p327 :rule eq_resolve :premises (@p326 @p314)) % 170.28/170.52 (step @p328 :rule implies_elim :premises (@p327)) % 170.28/170.52 (step @p329 :rule chain_m_resolution :premises (@p328 @p305) :args (@t168 @t65 (@list @t158))) % 170.28/170.52 (step @p330 :rule eq-symm :args (@t173 @t174)) % 170.28/170.52 (step @p331 :rule cong :premises (@p330) :args (@t175)) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p332 :rule trust :premises () :args ((= @t177 @t175))) % 170.28/170.52 (step @p333 :rule trans :premises (@p332 @p331)) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.28/170.52 (step @p334 :rule trust :premises () :args (@t177)) % 170.28/170.52 (step @p335 :rule eq_resolve :premises (@p334 @p333)) % 170.28/170.52 (step @p336 :rule instantiate :premises (@p335) :args ((@list @t39 @t38 @t39))) % 170.28/170.52 (step @p337 :rule eq-symm :args (@t181 @t182)) % 170.28/170.52 (step @p338 :rule cong :premises (@p337) :args (@t183)) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p339 :rule trust :premises () :args ((= @t185 @t183))) % 170.28/170.52 (step @p340 :rule trans :premises (@p339 @p338)) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 170.28/170.52 (step @p341 :rule trust :premises () :args (@t185)) % 170.28/170.52 (step @p342 :rule eq_resolve :premises (@p341 @p340)) % 170.28/170.52 (step @p343 :rule instantiate :premises (@p342) :args ((@list @t38 @t39 @t39))) % 170.28/170.52 (step @p344 :rule eq-symm :args (@t186 @t187)) % 170.28/170.52 (step @p345 :rule cong :premises (@p344) :args (@t188)) % 170.28/170.52 ; trust TRUST PREPROCESS_HO_ELIM % 170.28/170.52 (step @p346 :rule trust :premises () :args ((= (forall @t17 (= @t190 @t189)) @t188))) % 170.28/170.52 (step @p347 :rule refl :args (@t189)) % 170.28/170.52 (step @p348 :rule refl :args (@t14)) % 170.28/170.52 (step @p349 :rule cong :premises (@p348 @p347) :args ((= @t14 @t189))) % 170.28/170.52 (step @p350 :rule symm :premises (@p349)) % 170.28/170.52 (step @p351 :rule eq_resolve :premises (@p348 @p350)) % 170.28/170.52 (step @p352 :rule refl :args (@t190)) % 170.28/170.52 (step @p353 :rule refl :args (@t15)) % 170.28/170.52 (step @p354 :rule cong :premises (@p353 @p352) :args ((= @t15 @t190))) % 170.28/170.52 (step @p355 :rule symm :premises (@p354)) % 170.28/170.52 (step @p356 :rule eq_resolve :premises (@p353 @p355)) % 170.28/170.52 (step @p357 :rule cong :premises (@p356 @p351) :args (@t16)) % 170.28/170.52 (step @p358 :rule cong :premises (@p357) :args (@t18)) % 170.28/170.52 (step @p359 :rule trans :premises (@p358 @p346 @p345)) % 170.28/170.52 (step @p360 :rule eq_resolve :premises (@p2 @p359)) % 170.28/170.52 (step @p361 :rule instantiate :premises (@p360) :args ((@list @t191 @t39))) % 170.28/170.52 (assume-push @p507 @t195) % 170.28/170.52 (assume-push @p508 @t197) % 170.28/170.52 (assume-push @p509 @t198) % 170.28/170.52 (assume-push @p510 @t161) % 170.28/170.52 (assume-push @p511 @t161) % 170.28/170.52 (assume-push @p512 @t195) % 170.28/170.52 (assume-push @p513 @t198) % 170.28/170.52 (assume-push @p514 @t197) % 170.28/170.52 (step @p233 :rule refl :args (@t43)) % 170.28/170.52 (step @p370 :rule cong :premises (@p233 @p510) :args (@t194)) % 170.28/170.52 (step @p371 :rule symm :premises (@p336)) % 170.28/170.52 (step @p372 :rule symm :premises (@p361)) % 170.28/170.52 (step @p373 :rule symm :premises (@p510)) % 170.28/170.52 (step @p374 :rule refl :args (@t44)) % 170.28/170.52 (step @p375 :rule cong :premises (@p374 @p373) :args (@t134)) % 170.28/170.52 (step @p376 :rule trans :premises (@p375 @p343 @p372 @p371 @p370)) % 170.28/170.52 (step-pop @p515 :rule scope :premises (@p376)) % 170.28/170.52 (step-pop @p516 :rule scope :premises (@p515)) % 170.28/170.52 (step-pop @p517 :rule scope :premises (@p516)) % 170.28/170.52 (step-pop @p518 :rule scope :premises (@p517)) % 170.28/170.52 (step @p377 :rule process_scope :premises (@p518) :args (@t135)) % 170.28/170.52 (step @p382 :rule and_intro :premises (@p510 @p336 @p361 @p343)) % 170.28/170.52 (step @p383 :rule modus_ponens :premises (@p382 @p377)) % 170.28/170.52 (step-pop @p519 :rule scope :premises (@p383)) % 170.28/170.52 (step-pop @p520 :rule scope :premises (@p519)) % 170.28/170.52 (step-pop @p521 :rule scope :premises (@p520)) % 170.28/170.52 (step-pop @p522 :rule scope :premises (@p521)) % 170.28/170.52 (step @p384 :rule process_scope :premises (@p522) :args (@t135)) % 170.28/170.52 (step @p389 :rule implies_elim :premises (@p384)) % 170.28/170.52 (step @p390 :rule cnf_and_neg :args (@t199)) % 170.28/170.52 (step @p391 :rule resolution :premises (@p390 @p389) :args (true @t199)) % 170.28/170.52 (step @p392 :rule reordering :premises (@p391) :args ((or (not @t195) (not @t197) (not @t198) @t135 @t200))) % 170.28/170.52 (step @p393 :rule chain_m_resolution :premises (@p392 @p268 @p361 @p343 @p336) :args (@t200 (@list true false false false) (@list @t135 @t198 @t197 @t195))) % 170.28/170.52 (step @p394 :rule eq-symm :args (@t163 @t134)) % 170.28/170.52 (step @p395 :rule eq-symm :args (@t163 @t39)) % 170.28/170.52 (step @p396 :rule refl :args (@t161)) % 170.28/170.52 (step @p397 :rule cong :premises (@p396 @p395 @p394) :args ((ite @t161 (= @t163 @t39) (= @t163 @t134)))) % 170.28/170.52 (step @p398 :rule cong :premises (@p311 @p316) :args (@t201)) % 170.28/170.52 (step @p399 :rule cong :premises (@p311 @p271) :args (@t202)) % 170.28/170.52 (step @p400 :rule cong :premises (@p396 @p399 @p398) :args ((ite @t161 @t202 @t201))) % 170.28/170.52 (step @p401 :rule ite_eq :args (@t162)) % 170.28/170.52 (step @p402 :rule eq_resolve :premises (@p401 @p400)) % 170.28/170.52 (step @p403 :rule eq_resolve :premises (@p402 @p397)) % 170.28/170.52 (step @p404 :rule ite_elim2 :premises (@p403)) % 170.28/170.52 (step @p405 :rule chain_m_resolution :premises (@p404 @p393) :args (@t203 @t71 (@list @t161))) % 170.28/170.52 (step @p406 :rule instantiate :premises (@p342) :args ((@list @t38 @t39 @t132))) % 170.28/170.52 (step @p407 :rule instantiate :premises (@p335) :args ((@list @t39 @t38 @t132))) % 170.28/170.52 (step @p408 :rule eq-symm :args (@t205 @t206)) % 170.28/170.52 (step @p409 :rule refl :args (@t207)) % 170.28/170.52 (step @p410 :rule cong :premises (@p409 @p408) :args ((=> @t207 @t208))) % 170.28/170.52 (assume-push @p523 @t207) % 170.28/170.52 (step @p412 :rule instantiate :premises (@p360) :args (@t209)) % 170.28/170.52 (step-pop @p524 :rule scope :premises (@p412)) % 170.28/170.52 (step @p413 :rule process_scope :premises (@p524) :args (@t208)) % 170.28/170.52 (step @p415 :rule eq_resolve :premises (@p413 @p410)) % 170.28/170.52 (step @p416 :rule implies_elim :premises (@p415)) % 170.28/170.52 (step @p417 :rule chain_m_resolution :premises (@p416 @p360) :args (@t210 @t65 (@list @t207))) % 170.28/170.52 (step @p418 :rule refl :args (@t211)) % 170.28/170.52 (step @p419 :rule refl :args (@t213)) % 170.28/170.52 (step @p420 :rule refl :args (@t215)) % 170.28/170.52 (step @p421 :rule refl :args (@t216)) % 170.28/170.52 (step @p422 :rule refl :args (@t217)) % 170.28/170.52 (step @p423 :rule bool-double-not-elim :args (@t135)) % 170.28/170.52 (step @p424 :rule nary_cong :premises (@p423 @p422 @p421 @p420 @p419 @p418) :args ((or (not @t136) @t217 @t216 @t215 @t213 @t211))) % 170.28/170.52 (assume-push @p525 @t168) % 170.28/170.52 (assume-push @p526 @t203) % 170.28/170.52 (assume-push @p527 @t214) % 170.28/170.52 (assume-push @p528 @t210) % 170.28/170.52 (assume-push @p529 @t212) % 170.28/170.52 (assume-push @p530 @t136) % 170.28/170.52 (step @p431 :rule evaluate :args ((= false true))) % 170.28/170.52 (step @p432 :rule symm :premises (@p406)) % 170.28/170.52 (step @p412 :rule instantiate :premises (@p360) :args (@t209)) % 170.28/170.52 (step @p433 :rule trans :premises (@p407 @p412 @p432 @p526)) % 170.28/170.52 (step @p434 :rule symm :premises (@p433)) % 170.28/170.52 (step @p435 :rule symm :premises (@p329)) % 170.28/170.52 (step @p436 :rule trans :premises (@p526 @p435)) % 170.28/170.52 (step @p437 :rule trans :premises (@p436 @p329 @p434)) % 170.28/170.52 (step @p438 :rule true_intro :premises (@p437)) % 170.28/170.52 (step @p439 :rule false_intro :premises (@p530)) % 170.28/170.52 (step @p440 :rule symm :premises (@p439)) % 170.28/170.52 (step @p441 :rule trans :premises (@p440 @p438)) % 170.28/170.52 (step @p442 false :rule eq_resolve :premises (@p441 @p431)) % 170.28/170.52 (step-pop @p531 :rule scope :premises (@p442)) % 170.28/170.52 (step-pop @p532 :rule scope :premises (@p531)) % 170.28/170.52 (step-pop @p533 :rule scope :premises (@p532)) % 170.28/170.52 (step-pop @p534 :rule scope :premises (@p533)) % 170.28/170.52 (step-pop @p535 :rule scope :premises (@p534)) % 170.28/170.52 (step-pop @p536 :rule scope :premises (@p535)) % 170.28/170.52 (step @p443 :rule process_scope :premises (@p536) :args (false)) % 170.28/170.52 (assume-push @p537 @t136) % 170.28/170.52 (assume-push @p538 @t168) % 170.28/170.52 (assume-push @p539 @t203) % 170.28/170.52 (assume-push @p540 @t214) % 170.28/170.52 (assume-push @p541 @t212) % 170.28/170.52 (assume-push @p542 @t210) % 170.28/170.52 (step @p456 :rule and_intro :premises (@p329 @p539 @p406 @p417 @p407 @p537)) % 170.28/170.52 (step-pop @p543 :rule scope :premises (@p456)) % 170.28/170.52 (step-pop @p544 :rule scope :premises (@p543)) % 170.28/170.52 (step-pop @p545 :rule scope :premises (@p544)) % 170.28/170.52 (step-pop @p546 :rule scope :premises (@p545)) % 170.28/170.52 (step-pop @p547 :rule scope :premises (@p546)) % 170.28/170.52 (step-pop @p548 :rule scope :premises (@p547)) % 170.28/170.52 (step @p457 :rule process_scope :premises (@p548) :args (@t218)) % 170.28/170.52 (step @p464 :rule implies_elim :premises (@p457)) % 170.28/170.52 (step @p465 :rule resolution :premises (@p464 @p443) :args (true @t218)) % 170.28/170.52 (step @p466 :rule not_and :premises (@p465)) % 170.28/170.52 (step @p467 :rule eq_resolve :premises (@p466 @p424)) % 170.28/170.52 (step @p468 false :rule chain_m_resolution :premises (@p467 @p417 @p407 @p406 @p405 @p329 @p268) :args (false (@list false false false false false true) (@list @t210 @t212 @t214 @t203 @t168 @t135))) % 170.28/170.52 ) % 170.28/170.52 % SZS output end Proof % 170.28/170.52 % cvc5 exiting %------------------------------------------------------------------------------