%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM690^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n013.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:40:23 AM UTC 2026 % Result : Theorem 166.40s 166.61s % Output : Proof 166.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM690^1 : TPTP v9.2.1. Released v3.7.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n013.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 11:54:30 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TH0 % 166.40/166.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 166.40/166.61 --- 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... % 166.40/166.61 --- 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... % 166.40/166.61 --- Run --ho-elim --full-saturate-quant at 18s... % 166.40/166.61 % SZS status Theorem % 166.40/166.61 % SZS output start Proof % 166.40/166.61 ( % 166.40/166.61 (declare-sort tptp.nat 0) % 166.40/166.61 (declare-const tptp.moreis (-> tptp.nat tptp.nat Bool)) % 166.40/166.61 (declare-const tptp.lessis (-> tptp.nat tptp.nat Bool)) % 166.40/166.61 (declare-const tptp.z tptp.nat) % 166.40/166.61 (declare-const tptp.pl (-> tptp.nat tptp.nat tptp.nat)) % 166.40/166.61 (declare-const tptp.u tptp.nat) % 166.40/166.61 (declare-const tptp.some (-> (-> tptp.nat Bool) Bool)) % 166.40/166.61 (declare-const tptp.diffprop (-> tptp.nat tptp.nat tptp.nat Bool)) % 166.40/166.61 (declare-const tptp.y tptp.nat) % 166.40/166.61 (declare-const tptp.x tptp.nat) % 166.40/166.61 (define @t1 () (@var "Xv" tptp.nat)) % 166.40/166.61 (define @t2 () (@list @t1)) % 166.40/166.61 (define @t3 () (_ tptp.some (lambda @t2 (_ (_ (_ tptp.diffprop tptp.y) tptp.x) @t1)))) % 166.40/166.61 (define @t4 () (_ (_ tptp.lessis tptp.z) tptp.u)) % 166.40/166.61 (define @t5 () (@var "Xu_0" tptp.nat)) % 166.40/166.61 (define @t6 () (@var "Xu" tptp.nat)) % 166.40/166.61 (define @t7 () (@var "Xy" tptp.nat)) % 166.40/166.61 (define @t8 () (_ (_ tptp.pl @t7) @t6)) % 166.40/166.61 (define @t9 () (@var "Xz" tptp.nat)) % 166.40/166.61 (define @t10 () (@var "Xx" tptp.nat)) % 166.40/166.61 (define @t11 () (_ (_ tptp.pl @t10) @t9)) % 166.40/166.61 (define @t12 () (_ (_ (_ tptp.diffprop @t11) @t8) @t5)) % 166.40/166.61 (define @t13 () (@list @t5)) % 166.40/166.61 (define @t14 () (lambda @t13 @t12)) % 166.40/166.61 (define @t15 () (_ tptp.some @t14)) % 166.40/166.61 (define @t16 () (_ (_ tptp.moreis @t9) @t6)) % 166.40/166.61 (define @t17 () (=> @t16 @t15)) % 166.40/166.61 (define @t18 () (_ (_ tptp.diffprop @t10) @t7)) % 166.40/166.61 (define @t19 () (lambda (@list @t6) (_ @t18 @t6))) % 166.40/166.61 (define @t20 () (=> (_ tptp.some @t19) @t17)) % 166.40/166.61 (define @t21 () (@list @t10 @t7 @t9 @t6)) % 166.40/166.61 (define @t22 () (forall @t21 @t20)) % 166.40/166.61 (define @t23 () (_ (_ tptp.moreis @t7) @t10)) % 166.40/166.61 (define @t24 () (_ (_ tptp.lessis @t10) @t7)) % 166.40/166.61 (define @t25 () (@list @t10 @t7)) % 166.40/166.61 (define @t26 () (forall @t25 (=> @t24 @t23))) % 166.40/166.61 (define @t27 () (not (_ tptp.some (lambda @t2 (_ (_ (_ tptp.diffprop (_ (_ tptp.pl tptp.y) tptp.u)) (_ (_ tptp.pl tptp.x) tptp.z)) @t1))))) % 166.40/166.61 (define @t28 () (@const 0 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat Bool)))) % 166.40/166.61 (define @t29 () (@const 1 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat Bool))))) % 166.40/166.61 (define @t30 () (@const 2 (-> (@ho-elim-sort (-> tptp.nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat Bool))))) % 166.40/166.61 (define @t31 () (_ @t30 (_ @t29 @t28 tptp.y) tptp.x)) % 166.40/166.61 (define @t32 () (@purify @t31)) % 166.40/166.61 (define @t33 () (@var "y" (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t34 () (@var "x" (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t35 () (@var "z" tptp.nat)) % 166.40/166.61 (define @t36 () (@const 3 (-> (@ho-elim-sort (-> tptp.nat Bool)) tptp.nat Bool))) % 166.40/166.61 (define @t37 () (@list @t35)) % 166.40/166.61 (define @t38 () (@const 4 (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t39 () (_ @t36 @t38 @t35)) % 166.40/166.61 (define @t40 () (forall @t37 (= @t39 (_ @t36 @t32 @t35)))) % 166.40/166.61 (define @t41 () (@quantifiers_skolemize @t40 0)) % 166.40/166.61 (define @t42 () (_ @t36 @t32 @t41)) % 166.40/166.61 (define @t43 () (_ @t36 @t38 @t41)) % 166.40/166.61 (define @t44 () (= @t43 @t42)) % 166.40/166.61 (define @t45 () (@var "BOUND_VARIABLE_7557" tptp.nat)) % 166.40/166.61 (define @t46 () (_ @t36 @t38 @t45)) % 166.40/166.61 (define @t47 () (_ @t36 @t31 @t45)) % 166.40/166.61 (define @t48 () (@list @t45)) % 166.40/166.61 (define @t49 () (forall @t48 (= @t46 @t47))) % 166.40/166.61 (define @t50 () (@const 5 (-> tptp.nat Bool))) % 166.40/166.61 (define @t51 () (forall @t48 (= (_ @t50 @t45) (tptp.diffprop tptp.y tptp.x @t45)))) % 166.40/166.61 (define @t52 () (_ @t36 @t31 @t41)) % 166.40/166.61 (define @t53 () (forall @t48 (= @t47 @t46))) % 166.40/166.61 (define @t54 () (= @t52 @t43)) % 166.40/166.61 (define @t55 () (= @t43 @t52)) % 166.40/166.61 (define @t56 () (@list false)) % 166.40/166.61 (define @t57 () (not @t55)) % 166.40/166.61 (define @t58 () (not @t43)) % 166.40/166.61 (define @t59 () (not @t52)) % 166.40/166.61 (define @t60 () (= @t31 @t32)) % 166.40/166.61 (define @t61 () (not @t60)) % 166.40/166.61 (define @t62 () (not @t42)) % 166.40/166.61 (define @t63 () (and @t60 @t62)) % 166.40/166.61 (define @t64 () (@list false false false true)) % 166.40/166.61 (define @t65 () (and @t60 @t42)) % 166.40/166.61 (define @t66 () (@list false true false false true)) % 166.40/166.61 (define @t67 () (not @t44)) % 166.40/166.61 (define @t68 () (not @t40)) % 166.40/166.61 (define @t69 () (= @t38 @t32)) % 166.40/166.61 (define @t70 () (or @t68 @t69)) % 166.40/166.61 (define @t71 () (@list false false)) % 166.40/166.61 (define @t72 () (@const 6 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat Bool)))) % 166.40/166.61 (define @t73 () (_ @t30 (_ @t29 @t72 tptp.y) tptp.x)) % 166.40/166.61 (define @t74 () (@var "ii" (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t75 () (@var "u" (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) Bool)))) % 166.40/166.61 (define @t76 () (@const 7 (-> (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) Bool)) (@ho-elim-sort (-> tptp.nat Bool)) Bool))) % 166.40/166.61 (define @t77 () (@var "e" Bool)) % 166.40/166.61 (define @t78 () (@var "i" (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t79 () (@var "v" (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) Bool)))) % 166.40/166.61 (define @t80 () (_ @t76 @t79 @t74)) % 166.40/166.61 (define @t81 () (@list @t74)) % 166.40/166.61 (define @t82 () (@list @t79)) % 166.40/166.61 (define @t83 () (@const 8 (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) Bool)))) % 166.40/166.61 (define @t84 () (_ @t76 @t83 @t38)) % 166.40/166.61 (define @t85 () (ite (= @t38 @t74) @t84 (_ @t76 @t83 @t74))) % 166.40/166.61 (define @t86 () (forall @t82 (not (forall @t81 (= @t80 @t85))))) % 166.40/166.61 (define @t87 () (@quantifiers_skolemize @t86 0)) % 166.40/166.61 (define @t88 () (_ @t76 @t87 @t74)) % 166.40/166.61 (define @t89 () (forall @t81 (= @t85 @t88))) % 166.40/166.61 (define @t90 () (not @t86)) % 166.40/166.61 (define @t91 () (forall @t81 (= @t88 @t85))) % 166.40/166.61 (define @t92 () (not (not @t91))) % 166.40/166.61 (define @t93 () (@list true)) % 166.40/166.61 (define @t94 () (@const 9 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat Bool)))) % 166.40/166.61 (define @t95 () (@const 10 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat tptp.nat Bool))))) % 166.40/166.61 (define @t96 () (@const 11 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat tptp.nat Bool)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat Bool))))) % 166.40/166.61 (define @t97 () (@const 12 (@ho-elim-sort (-> tptp.nat tptp.nat Bool)))) % 166.40/166.61 (define @t98 () (@const 13 (-> tptp.nat tptp.nat tptp.nat tptp.nat tptp.nat Bool))) % 166.40/166.61 (define @t99 () (tptp.moreis @t9 @t6)) % 166.40/166.61 (define @t100 () (not @t99)) % 166.40/166.61 (define @t101 () (@const 14 (-> tptp.nat tptp.nat tptp.nat Bool))) % 166.40/166.61 (define @t102 () (forall @t21 (or (not (tptp.some (_ (_ @t101 @t10) @t7))) @t100 (tptp.some (_ (_ (_ (_ @t98 @t10) @t9) @t7) @t6))))) % 166.40/166.61 (define @t103 () (tptp.pl @t7 @t6)) % 166.40/166.61 (define @t104 () (tptp.pl @t10 @t9)) % 166.40/166.61 (define @t105 () (tptp.diffprop @t104 @t103 @t5)) % 166.40/166.61 (define @t106 () (lambda @t13 @t105)) % 166.40/166.61 (define @t107 () (tptp.some @t106)) % 166.40/166.61 (define @t108 () (@var "BOUND_VARIABLE_7476" tptp.nat)) % 166.40/166.61 (define @t109 () (tptp.diffprop @t10 @t7 @t108)) % 166.40/166.61 (define @t110 () (@list @t108)) % 166.40/166.61 (define @t111 () (lambda @t110 @t109)) % 166.40/166.61 (define @t112 () (tptp.some @t111)) % 166.40/166.61 (define @t113 () (not @t16)) % 166.40/166.61 (define @t114 () (_ @t18 @t108)) % 166.40/166.61 (define @t115 () (lambda @t110 @t114)) % 166.40/166.61 (define @t116 () (_ tptp.some @t115)) % 166.40/166.61 (define @t117 () (not @t116)) % 166.40/166.61 (define @t118 () (or @t117 @t113 @t15)) % 166.40/166.61 (define @t119 () (_ @t30 (_ @t29 (_ @t96 (_ @t95 @t94 tptp.y) tptp.u) tptp.x) tptp.z)) % 166.40/166.61 (define @t120 () (@const 15 (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t121 () (@const 16 (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)))) % 166.40/166.61 (define @t122 () (@const 17 (-> (@ho-elim-sort (-> tptp.nat tptp.nat tptp.nat)) tptp.nat (@ho-elim-sort (-> tptp.nat tptp.nat))))) % 166.40/166.61 (define @t123 () (@const 18 (-> (@ho-elim-sort (-> tptp.nat tptp.nat)) tptp.nat tptp.nat))) % 166.40/166.61 (define @t124 () (_ @t30 (_ @t29 @t28 (_ @t123 (_ @t122 @t121 tptp.y) tptp.u)) (_ @t123 (_ @t122 @t121 tptp.x) tptp.z))) % 166.40/166.61 (define @t125 () (@purify @t124)) % 166.40/166.61 (define @t126 () (_ @t36 @t120 @t35)) % 166.40/166.61 (define @t127 () (forall @t37 (= @t126 (_ @t36 @t125 @t35)))) % 166.40/166.61 (define @t128 () (@quantifiers_skolemize @t127 0)) % 166.40/166.61 (define @t129 () (_ @t36 @t125 @t128)) % 166.40/166.61 (define @t130 () (_ @t36 @t120 @t128)) % 166.40/166.61 (define @t131 () (= @t130 @t129)) % 166.40/166.61 (define @t132 () (@var "BOUND_VARIABLE_7583" tptp.nat)) % 166.40/166.61 (define @t133 () (_ @t36 @t120 @t132)) % 166.40/166.61 (define @t134 () (_ @t36 @t124 @t132)) % 166.40/166.61 (define @t135 () (@list @t132)) % 166.40/166.61 (define @t136 () (forall @t135 (= @t133 @t134))) % 166.40/166.61 (define @t137 () (@const 19 (-> tptp.nat Bool))) % 166.40/166.61 (define @t138 () (forall @t135 (= (_ @t137 @t132) (tptp.diffprop (tptp.pl tptp.y tptp.u) (tptp.pl tptp.x tptp.z) @t132)))) % 166.40/166.61 (define @t139 () (_ @t36 @t124 @t128)) % 166.40/166.61 (define @t140 () (forall @t135 (= @t134 @t133))) % 166.40/166.61 (define @t141 () (= @t139 @t130)) % 166.40/166.61 (define @t142 () (= @t130 @t139)) % 166.40/166.61 (define @t143 () (not @t142)) % 166.40/166.61 (define @t144 () (not @t130)) % 166.40/166.61 (define @t145 () (not @t139)) % 166.40/166.61 (define @t146 () (= @t124 @t125)) % 166.40/166.61 (define @t147 () (not @t146)) % 166.40/166.61 (define @t148 () (not @t129)) % 166.40/166.61 (define @t149 () (and @t146 @t148)) % 166.40/166.61 (define @t150 () (and @t146 @t129)) % 166.40/166.61 (define @t151 () (not @t131)) % 166.40/166.61 (define @t152 () (not @t127)) % 166.40/166.61 (define @t153 () (= @t120 @t125)) % 166.40/166.61 (define @t154 () (or @t152 @t153)) % 166.40/166.61 (define @t155 () (forall @t37 (= @t126 (_ @t36 @t119 @t35)))) % 166.40/166.61 (define @t156 () (@quantifiers_skolemize @t155 0)) % 166.40/166.61 (define @t157 () (_ @t36 @t119 @t156)) % 166.40/166.61 (define @t158 () (_ @t36 @t120 @t156)) % 166.40/166.61 (define @t159 () (= @t158 @t157)) % 166.40/166.61 (define @t160 () (@var "BOUND_VARIABLE_7567" tptp.nat)) % 166.40/166.61 (define @t161 () (@var "BOUND_VARIABLE_7566" tptp.nat)) % 166.40/166.61 (define @t162 () (@var "BOUND_VARIABLE_7565" tptp.nat)) % 166.40/166.61 (define @t163 () (@var "BOUND_VARIABLE_7564" tptp.nat)) % 166.40/166.61 (define @t164 () (@var "BOUND_VARIABLE_7563" tptp.nat)) % 166.40/166.61 (define @t165 () (_ @t36 (_ @t30 (_ @t29 @t28 (_ @t123 (_ @t122 @t121 @t164) @t163)) (_ @t123 (_ @t122 @t121 @t162) @t161)) @t160)) % 166.40/166.61 (define @t166 () (_ @t36 (_ @t30 (_ @t29 (_ @t96 (_ @t95 @t94 @t164) @t163) @t162) @t161) @t160)) % 166.40/166.61 (define @t167 () (@list @t164 @t163 @t162 @t161 @t160)) % 166.40/166.61 (define @t168 () (forall @t167 (= @t165 @t166))) % 166.40/166.61 (define @t169 () (forall @t167 (= (tptp.diffprop (tptp.pl @t164 @t163) (tptp.pl @t162 @t161) @t160) (_ @t98 @t164 @t163 @t162 @t161 @t160)))) % 166.40/166.61 (define @t170 () (_ @t36 @t124 @t156)) % 166.40/166.61 (define @t171 () (= @t157 @t170)) % 166.40/166.61 (define @t172 () (not @t171)) % 166.40/166.61 (define @t173 () (not @t170)) % 166.40/166.61 (define @t174 () (and @t146 @t153 @t158)) % 166.40/166.61 (define @t175 () (not @t158)) % 166.40/166.61 (define @t176 () (not @t153)) % 166.40/166.61 (define @t177 () (and @t146 @t153 @t175)) % 166.40/166.61 (define @t178 () (not @t159)) % 166.40/166.61 (define @t179 () (not @t155)) % 166.40/166.61 (define @t180 () (= @t120 @t119)) % 166.40/166.61 (define @t181 () (or @t179 @t180)) % 166.40/166.61 (define @t182 () (_ @t76 @t83 @t120)) % 166.40/166.61 (define @t183 () (not @t182)) % 166.40/166.61 (define @t184 () (not (_ tptp.some @t137))) % 166.40/166.61 (define @t185 () (_ @t76 @t83 @t119)) % 166.40/166.61 (define @t186 () (not @t185)) % 166.40/166.61 (define @t187 () (not @t180)) % 166.40/166.61 (define @t188 () (and @t183 @t180)) % 166.40/166.61 (define @t189 () (@list true false)) % 166.40/166.61 (define @t190 () (@const 20 (@ho-elim-sort (-> tptp.nat tptp.nat Bool)))) % 166.40/166.61 (define @t191 () (tptp.moreis @t7 @t10)) % 166.40/166.61 (define @t192 () (tptp.lessis @t10 @t7)) % 166.40/166.61 (define @t193 () (not @t24)) % 166.40/166.61 (define @t194 () (or @t193 @t23)) % 166.40/166.61 (define @t195 () (_ @t36 (_ @t30 @t190 tptp.z) tptp.u)) % 166.40/166.61 (define @t196 () (_ @t36 (_ @t30 @t97 tptp.u) tptp.z)) % 166.40/166.61 (define @t197 () (not @t195)) % 166.40/166.61 (define @t198 () (or @t197 @t196)) % 166.40/166.61 (define @t199 () (not @t196)) % 166.40/166.61 (define @t200 () (_ @t76 @t83 @t73)) % 166.40/166.61 (define @t201 () (not @t200)) % 166.40/166.61 (define @t202 () (or @t201 @t199 @t185)) % 166.40/166.61 (define @t203 () (@var "y" (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) Bool)))) % 166.40/166.61 (define @t204 () (@var "x" (@ho-elim-sort (-> (@ho-elim-sort (-> tptp.nat Bool)) Bool)))) % 166.40/166.61 (define @t205 () (@var "z" (@ho-elim-sort (-> tptp.nat Bool)))) % 166.40/166.61 (define @t206 () (@list @t205)) % 166.40/166.61 (define @t207 () (forall @t206 (= (_ @t76 @t83 @t205) (_ @t76 @t87 @t205)))) % 166.40/166.61 (define @t208 () (@quantifiers_skolemize @t207 0)) % 166.40/166.61 (define @t209 () (_ @t76 @t87 @t208)) % 166.40/166.61 (define @t210 () (_ @t76 @t83 @t208)) % 166.40/166.61 (define @t211 () (= @t210 @t209)) % 166.40/166.61 (define @t212 () (_ tptp.some @t50)) % 166.40/166.61 (define @t213 () (= @t38 @t208)) % 166.40/166.61 (define @t214 () (ite @t213 @t84 @t210)) % 166.40/166.61 (define @t215 () (not @t210)) % 166.40/166.61 (define @t216 () (not @t84)) % 166.40/166.61 (define @t217 () (= @t214 @t209)) % 166.40/166.61 (define @t218 () (= @t209 @t214)) % 166.40/166.61 (define @t219 () (not @t218)) % 166.40/166.61 (define @t220 () (not @t214)) % 166.40/166.61 (define @t221 () (not @t213)) % 166.40/166.61 (define @t222 () (and @t84 @t213 @t215)) % 166.40/166.61 (define @t223 () (not @t211)) % 166.40/166.61 (define @t224 () (not @t207)) % 166.40/166.61 (define @t225 () (= @t83 @t87)) % 166.40/166.61 (define @t226 () (or @t224 @t225)) % 166.40/166.61 (define @t227 () (_ @t76 @t87 @t73)) % 166.40/166.61 (define @t228 () (not @t227)) % 166.40/166.61 (define @t229 () (not @t225)) % 166.40/166.61 (define @t230 () (and @t225 @t201)) % 166.40/166.61 (define @t231 () (@list false true)) % 166.40/166.61 (define @t232 () (= @t38 @t73)) % 166.40/166.61 (define @t233 () (ite @t232 @t84 @t200)) % 166.40/166.61 (define @t234 () (= @t233 @t227)) % 166.40/166.61 (define @t235 () (not @t233)) % 166.40/166.61 (define @t236 () (not @t232)) % 166.40/166.61 (define @t237 () (forall @t37 (= @t39 (_ @t36 @t73 @t35)))) % 166.40/166.61 (define @t238 () (not @t237)) % 166.40/166.61 (define @t239 () (or @t238 @t232)) % 166.40/166.61 (define @t240 () (@quantifiers_skolemize @t237 0)) % 166.40/166.61 (define @t241 () (_ @t36 @t73 @t240)) % 166.40/166.61 (define @t242 () (_ @t36 @t38 @t240)) % 166.40/166.61 (define @t243 () (= @t242 @t241)) % 166.40/166.61 (define @t244 () (not @t243)) % 166.40/166.61 (define @t245 () (@var "BOUND_VARIABLE_7577" tptp.nat)) % 166.40/166.61 (define @t246 () (@var "BOUND_VARIABLE_7576" tptp.nat)) % 166.40/166.61 (define @t247 () (@var "BOUND_VARIABLE_7575" tptp.nat)) % 166.40/166.61 (define @t248 () (_ @t36 (_ @t30 (_ @t29 @t28 @t247) @t246) @t245)) % 166.40/166.61 (define @t249 () (_ @t36 (_ @t30 (_ @t29 @t72 @t247) @t246) @t245)) % 166.40/166.61 (define @t250 () (@list @t247 @t246 @t245)) % 166.40/166.61 (define @t251 () (forall @t250 (= @t248 @t249))) % 166.40/166.61 (define @t252 () (forall @t250 (= (tptp.diffprop @t247 @t246 @t245) (_ @t101 @t247 @t246 @t245)))) % 166.40/166.61 (define @t253 () (_ @t36 @t31 @t240)) % 166.40/166.61 (define @t254 () (= @t241 @t253)) % 166.40/166.61 (define @t255 () (not @t254)) % 166.40/166.61 (define @t256 () (not @t253)) % 166.40/166.61 (define @t257 () (and @t60 @t69 @t242)) % 166.40/166.61 (define @t258 () (not @t242)) % 166.40/166.61 (define @t259 () (not @t69)) % 166.40/166.61 (define @t260 () (and @t60 @t69 @t258)) % 166.40/166.61 (assume @p1 @t3) % 166.40/166.61 (assume @p2 @t4) % 166.40/166.61 (assume @p3 @t22) % 166.40/166.61 (assume @p4 @t26) % 166.40/166.61 (assume @p5 @t27) % 166.40/166.61 (assume @p6 true) % 166.40/166.61 (step @p7 :rule skolem_intro :args (@t32)) % 166.40/166.61 (step @p8 :rule symm :premises (@p7)) % 166.40/166.61 ; WARNING: add trust step for TRUST % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.61 (step @p9 :rule trust :premises () :args ((forall (@list @t34 @t33) (or (not (forall @t37 (= (_ @t36 @t34 @t35) (_ @t36 @t33 @t35)))) (= @t34 @t33))))) % 166.40/166.61 (step @p10 :rule instantiate :premises (@p9) :args ((@list @t38 @t32))) % 166.40/166.61 (step @p11 :rule cnf_equiv_neg2 :args (@t44)) % 166.40/166.61 (step @p12 :rule eq-symm :args (@t46 @t47)) % 166.40/166.61 (step @p13 :rule cong :premises (@p12) :args (@t49)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p14 :rule trust :premises () :args ((= @t51 @t49))) % 166.40/166.61 (step @p15 :rule trans :premises (@p14 @p13)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.61 (step @p16 :rule trust :premises () :args (@t51)) % 166.40/166.61 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 166.40/166.61 (step @p18 :rule eq-symm :args (@t52 @t43)) % 166.40/166.61 (step @p19 :rule refl :args (@t53)) % 166.40/166.61 (step @p20 :rule cong :premises (@p19 @p18) :args ((=> @t53 @t54))) % 166.40/166.61 (assume-push @p620 @t53) % 166.40/166.61 (step @p22 :rule instantiate :premises (@p17) :args ((@list @t41))) % 166.40/166.61 (step-pop @p621 :rule scope :premises (@p22)) % 166.40/166.61 (step @p23 :rule process_scope :premises (@p621) :args (@t54)) % 166.40/166.61 (step @p25 :rule eq_resolve :premises (@p23 @p20)) % 166.40/166.61 (step @p26 :rule implies_elim :premises (@p25)) % 166.40/166.61 (step @p27 :rule chain_m_resolution :premises (@p26 @p17) :args (@t55 @t56 (@list @t53))) % 166.40/166.61 (step @p28 :rule cnf_equiv_pos1 :args (@t55)) % 166.40/166.61 (step @p29 :rule reordering :premises (@p28) :args ((or @t58 @t52 @t57))) % 166.40/166.61 (step @p30 :rule refl :args (@t59)) % 166.40/166.61 (step @p31 :rule bool-double-not-elim :args (@t42)) % 166.40/166.61 (step @p32 :rule refl :args (@t61)) % 166.40/166.61 (step @p33 :rule nary_cong :premises (@p32 @p31 @p30) :args ((or @t61 (not @t62) @t59))) % 166.40/166.61 (assume-push @p622 @t60) % 166.40/166.61 (assume-push @p623 @t62) % 166.40/166.61 (assume-push @p624 @t62) % 166.40/166.61 (assume-push @p625 @t60) % 166.40/166.61 (step @p38 :rule false_intro :premises (@p623)) % 166.40/166.61 (step @p39 :rule refl :args (@t41)) % 166.40/166.61 (step @p40 :rule cong :premises (@p8 @p39) :args (@t52)) % 166.40/166.61 (step @p41 :rule trans :premises (@p40 @p38)) % 166.40/166.61 (step @p42 :rule false_elim :premises (@p41)) % 166.40/166.61 (step-pop @p626 :rule scope :premises (@p42)) % 166.40/166.61 (step-pop @p627 :rule scope :premises (@p626)) % 166.40/166.61 (step @p43 :rule process_scope :premises (@p627) :args (@t59)) % 166.40/166.61 (step @p46 :rule and_intro :premises (@p623 @p8)) % 166.40/166.61 (step @p47 :rule modus_ponens :premises (@p46 @p43)) % 166.40/166.61 (step-pop @p628 :rule scope :premises (@p47)) % 166.40/166.61 (step-pop @p629 :rule scope :premises (@p628)) % 166.40/166.61 (step @p48 :rule process_scope :premises (@p629) :args (@t59)) % 166.40/166.61 (step @p51 :rule implies_elim :premises (@p48)) % 166.40/166.61 (step @p52 :rule cnf_and_neg :args (@t63)) % 166.40/166.61 (step @p53 :rule resolution :premises (@p52 @p51) :args (true @t63)) % 166.40/166.61 (step @p54 :rule eq_resolve :premises (@p53 @p33)) % 166.40/166.61 (step @p55 :rule chain_m_resolution :premises (@p54 @p8 @p29 @p27 @p11) :args ((or @t44 @t58) @t64 (@list @t60 @t52 @t55 @t42))) % 166.40/166.61 (step @p56 :rule cnf_equiv_neg1 :args (@t44)) % 166.40/166.61 (step @p57 :rule reordering :premises (@p56) :args ((or @t43 @t42 @t44))) % 166.40/166.61 (step @p58 :rule cnf_equiv_pos2 :args (@t55)) % 166.40/166.61 (step @p59 :rule reordering :premises (@p58) :args ((or @t43 @t59 @t57))) % 166.40/166.61 (assume-push @p630 @t60) % 166.40/166.61 (assume-push @p631 @t42) % 166.40/166.61 (assume-push @p632 @t42) % 166.40/166.61 (assume-push @p633 @t60) % 166.40/166.61 (step @p64 :rule true_intro :premises (@p631)) % 166.40/166.61 (step @p39 :rule refl :args (@t41)) % 166.40/166.61 (step @p40 :rule cong :premises (@p8 @p39) :args (@t52)) % 166.40/166.61 (step @p65 :rule trans :premises (@p40 @p64)) % 166.40/166.61 (step @p66 :rule true_elim :premises (@p65)) % 166.40/166.61 (step-pop @p634 :rule scope :premises (@p66)) % 166.40/166.61 (step-pop @p635 :rule scope :premises (@p634)) % 166.40/166.61 (step @p67 :rule process_scope :premises (@p635) :args (@t52)) % 166.40/166.61 (step @p70 :rule and_intro :premises (@p631 @p8)) % 166.40/166.61 (step @p71 :rule modus_ponens :premises (@p70 @p67)) % 166.40/166.61 (step-pop @p636 :rule scope :premises (@p71)) % 166.40/166.61 (step-pop @p637 :rule scope :premises (@p636)) % 166.40/166.61 (step @p72 :rule process_scope :premises (@p637) :args (@t52)) % 166.40/166.61 (step @p75 :rule implies_elim :premises (@p72)) % 166.40/166.61 (step @p76 :rule cnf_and_neg :args (@t65)) % 166.40/166.61 (step @p77 :rule resolution :premises (@p76 @p75) :args (true @t65)) % 166.40/166.61 (step @p78 :rule chain_m_resolution :premises (@p77 @p8 @p59 @p27 @p57 @p55) :args (@t44 @t66 (@list @t60 @t52 @t55 @t42 @t43))) % 166.40/166.61 (step @p79 :rule refl :args (@t67)) % 166.40/166.61 (step @p80 :rule bool-double-not-elim :args (@t40)) % 166.40/166.61 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or (not @t68) @t67))) % 166.40/166.61 (assume-push @p638 @t68) % 166.40/166.61 (step @p83 :rule skolemize :premises (@p638)) % 166.40/166.61 (step-pop @p639 :rule scope :premises (@p83)) % 166.40/166.61 (step @p84 :rule process_scope :premises (@p639) :args (@t67)) % 166.40/166.61 (step @p86 :rule implies_elim :premises (@p84)) % 166.40/166.61 (step @p87 :rule eq_resolve :premises (@p86 @p81)) % 166.40/166.61 (step @p88 :rule chain_m_resolution :premises (@p87 @p78) :args (@t40 @t56 (@list @t44))) % 166.40/166.61 (step @p89 :rule cnf_or_pos :args (@t70)) % 166.40/166.61 (step @p90 :rule reordering :premises (@p89) :args ((or @t68 @t69 (not @t70)))) % 166.40/166.61 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p10) :args (@t69 @t71 (@list @t40 @t70))) % 166.40/166.61 (step @p92 :rule instantiate :premises (@p9) :args ((@list @t38 @t73))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.61 (step @p93 :rule trust :premises () :args ((forall (@list @t75 @t77 @t78) (not (forall @t82 (not (forall @t81 (= @t80 (ite (= @t78 @t74) @t77 (_ @t76 @t75 @t74)))))))))) % 166.40/166.61 (step @p94 :rule instantiate :premises (@p93) :args ((@list @t83 @t84 @t38))) % 166.40/166.61 (step @p95 :rule refl :args (@t89)) % 166.40/166.61 (step @p96 :rule bool-double-not-elim :args (@t86)) % 166.40/166.61 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t90) @t89))) % 166.40/166.61 (step @p98 :rule eq-symm :args (@t88 @t85)) % 166.40/166.61 (step @p99 :rule cong :premises (@p98) :args (@t91)) % 166.40/166.61 (step @p100 :rule bool-double-not-elim :args (@t91)) % 166.40/166.61 (step @p101 :rule trans :premises (@p100 @p99)) % 166.40/166.61 (step @p102 :rule refl :args (@t90)) % 166.40/166.61 (step @p103 :rule cong :premises (@p102 @p101) :args ((=> @t90 @t92))) % 166.40/166.61 (assume-push @p640 @t90) % 166.40/166.61 (step @p105 :rule skolemize :premises (@p94)) % 166.40/166.61 (step-pop @p641 :rule scope :premises (@p105)) % 166.40/166.61 (step @p106 :rule process_scope :premises (@p641) :args (@t92)) % 166.40/166.61 (step @p108 :rule eq_resolve :premises (@p106 @p103)) % 166.40/166.61 (step @p109 :rule implies_elim :premises (@p108)) % 166.40/166.61 (step @p110 :rule eq_resolve :premises (@p109 @p97)) % 166.40/166.61 (step @p111 :rule chain_m_resolution :premises (@p110 @p94) :args (@t89 @t93 (@list @t86))) % 166.40/166.61 (step @p112 :rule instantiate :premises (@p111) :args ((@list @t73))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p113 :rule trust :premises () :args ((= @t102 (forall @t21 (or (not (_ @t76 @t83 (_ @t30 (_ @t29 @t72 @t10) @t7))) (not (_ @t36 (_ @t30 @t97 @t9) @t6)) (_ @t76 @t83 (_ @t30 (_ @t29 (_ @t96 (_ @t95 @t94 @t10) @t9) @t7) @t6))))))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p114 :rule trust :premises () :args ((= (forall @t21 (or (not @t112) @t100 @t107)) @t102))) % 166.40/166.61 (step @p115 :rule refl :args ((tptp.some @t14))) % 166.40/166.61 (step @p116 :rule refl :args ((tptp.diffprop @t11 @t8 @t5))) % 166.40/166.61 (step @p117 :rule refl :args (@t5)) % 166.40/166.61 (step @p118 :rule refl :args (@t103)) % 166.40/166.61 (step @p119 :rule refl :args (@t104)) % 166.40/166.61 (step @p120 :rule cong :premises (@p119 @p118 @p117) :args (@t105)) % 166.40/166.61 (step @p121 :rule trans :premises (@p120 @p116)) % 166.40/166.61 (step @p122 :rule cong :premises (@p121) :args (@t106)) % 166.40/166.61 (step @p123 :rule cong :premises (@p122) :args (@t107)) % 166.40/166.61 (step @p124 :rule trans :premises (@p123 @p115)) % 166.40/166.61 (step @p125 :rule refl :args (tptp.some)) % 166.40/166.61 (step @p126 :rule ho_cong :premises (@p125 @p122)) % 166.40/166.61 (step @p127 :rule cong :premises (@p126 @p124) :args ((= (_ tptp.some @t106) @t107))) % 166.40/166.61 (step @p128 :rule symm :premises (@p127)) % 166.40/166.61 (step @p129 :rule refl :args (@t15)) % 166.40/166.61 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 166.40/166.61 (step @p131 :rule refl :args (tptp.diffprop)) % 166.40/166.61 (step @p132 :rule ho_cong :premises (@p131 @p119)) % 166.40/166.61 (step @p133 :rule ho_cong :premises (@p132 @p118)) % 166.40/166.61 (step @p134 :rule ho_cong :premises (@p133 @p117)) % 166.40/166.61 (step @p135 :rule cong :premises (@p134 @p121) :args ((= (_ (_ (_ tptp.diffprop @t104) @t103) @t5) @t105))) % 166.40/166.61 (step @p136 :rule symm :premises (@p135)) % 166.40/166.61 (step @p137 :rule refl :args (@t12)) % 166.40/166.61 (step @p138 :rule eq_resolve :premises (@p137 @p136)) % 166.40/166.61 (step @p139 :rule refl :args (@t8)) % 166.40/166.61 (step @p140 :rule cong :premises (@p139 @p118) :args ((= @t8 @t103))) % 166.40/166.61 (step @p141 :rule symm :premises (@p140)) % 166.40/166.61 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 166.40/166.61 (step @p143 :rule refl :args (@t11)) % 166.40/166.61 (step @p144 :rule cong :premises (@p143 @p119) :args ((= @t11 @t104))) % 166.40/166.61 (step @p145 :rule symm :premises (@p144)) % 166.40/166.61 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 166.40/166.61 (step @p147 :rule ho_cong :premises (@p131 @p146)) % 166.40/166.61 (step @p148 :rule ho_cong :premises (@p147 @p142)) % 166.40/166.61 (step @p149 :rule ho_cong :premises (@p148 @p117)) % 166.40/166.61 (step @p150 :rule trans :premises (@p149 @p138)) % 166.40/166.61 (step @p151 :rule cong :premises (@p150) :args (@t14)) % 166.40/166.61 (step @p152 :rule ho_cong :premises (@p125 @p151)) % 166.40/166.61 (step @p153 :rule trans :premises (@p152 @p130)) % 166.40/166.61 (step @p154 :rule refl :args (@t99)) % 166.40/166.61 (step @p155 :rule refl :args (@t16)) % 166.40/166.61 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t16 @t99))) % 166.40/166.61 (step @p157 :rule symm :premises (@p156)) % 166.40/166.61 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 166.40/166.61 (step @p159 :rule cong :premises (@p158) :args (@t113)) % 166.40/166.61 (step @p160 :rule refl :args ((tptp.some @t115))) % 166.40/166.61 (step @p161 :rule refl :args (@t109)) % 166.40/166.61 (step @p162 :rule cong :premises (@p161) :args (@t111)) % 166.40/166.61 (step @p163 :rule cong :premises (@p162) :args (@t112)) % 166.40/166.61 (step @p164 :rule trans :premises (@p163 @p160)) % 166.40/166.61 (step @p165 :rule ho_cong :premises (@p125 @p162)) % 166.40/166.61 (step @p166 :rule cong :premises (@p165 @p164) :args ((= (_ tptp.some @t111) @t112))) % 166.40/166.61 (step @p167 :rule symm :premises (@p166)) % 166.40/166.61 (step @p168 :rule refl :args (@t116)) % 166.40/166.61 (step @p169 :rule eq_resolve :premises (@p168 @p167)) % 166.40/166.61 (step @p170 :rule refl :args (@t114)) % 166.40/166.61 (step @p171 :rule cong :premises (@p170 @p161) :args ((= @t114 @t109))) % 166.40/166.61 (step @p172 :rule symm :premises (@p171)) % 166.40/166.61 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 166.40/166.61 (step @p174 :rule cong :premises (@p173) :args (@t115)) % 166.40/166.61 (step @p175 :rule ho_cong :premises (@p125 @p174)) % 166.40/166.61 (step @p176 :rule trans :premises (@p175 @p169)) % 166.40/166.61 (step @p177 :rule cong :premises (@p176) :args (@t117)) % 166.40/166.61 (step @p178 :rule nary_cong :premises (@p177 @p159 @p153) :args (@t118)) % 166.40/166.61 (step @p179 :rule cong :premises (@p178) :args ((forall @t21 @t118))) % 166.40/166.61 (step @p180 :rule aci_norm :args ((= (or @t117 (or @t113 @t15)) @t118))) % 166.40/166.61 (step @p181 :rule bool-impl-elim :args (@t16 @t15)) % 166.40/166.61 (step @p182 :rule refl :args (@t117)) % 166.40/166.61 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or @t117 @t17))) % 166.40/166.61 (step @p184 :rule trans :premises (@p183 @p180)) % 166.40/166.61 (step @p185 :rule bool-impl-elim :args (@t116 @t17)) % 166.40/166.61 (step @p186 :rule trans :premises (@p185 @p184)) % 166.40/166.61 (step @p187 :rule cong :premises (@p186) :args ((forall @t21 (=> @t116 @t17)))) % 166.40/166.61 (step @p188 :rule trans :premises (@p187 @p179)) % 166.40/166.61 (step @p189 :rule refl :args (@t17)) % 166.40/166.61 (step @p190 :rule alpha_equiv :args (@t19 (@list @t6) (@list @t108))) % 166.40/166.61 (step @p191 :rule ho_cong :premises (@p125 @p190)) % 166.40/166.61 (step @p192 :rule cong :premises (@p191 @p189) :args (@t20)) % 166.40/166.61 (step @p193 :rule cong :premises (@p192) :args (@t22)) % 166.40/166.61 (step @p194 :rule trans :premises (@p193 @p188)) % 166.40/166.61 (step @p195 :rule trans :premises (@p194 @p114 @p113)) % 166.40/166.61 (step @p196 :rule eq_resolve :premises (@p3 @p195)) % 166.40/166.61 (step @p197 :rule instantiate :premises (@p196) :args ((@list tptp.y tptp.x tptp.u tptp.z))) % 166.40/166.61 (step @p198 :rule instantiate :premises (@p9) :args ((@list @t120 @t119))) % 166.40/166.61 (step @p199 :rule instantiate :premises (@p9) :args ((@list @t120 @t125))) % 166.40/166.61 (step @p200 :rule cnf_equiv_neg2 :args (@t131)) % 166.40/166.61 (step @p201 :rule eq-symm :args (@t133 @t134)) % 166.40/166.61 (step @p202 :rule cong :premises (@p201) :args (@t136)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p203 :rule trust :premises () :args ((= @t138 @t136))) % 166.40/166.61 (step @p204 :rule trans :premises (@p203 @p202)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.61 (step @p205 :rule trust :premises () :args (@t138)) % 166.40/166.61 (step @p206 :rule eq_resolve :premises (@p205 @p204)) % 166.40/166.61 (step @p207 :rule eq-symm :args (@t139 @t130)) % 166.40/166.61 (step @p208 :rule refl :args (@t140)) % 166.40/166.61 (step @p209 :rule cong :premises (@p208 @p207) :args ((=> @t140 @t141))) % 166.40/166.61 (assume-push @p642 @t140) % 166.40/166.61 (step @p211 :rule instantiate :premises (@p206) :args ((@list @t128))) % 166.40/166.61 (step-pop @p643 :rule scope :premises (@p211)) % 166.40/166.61 (step @p212 :rule process_scope :premises (@p643) :args (@t141)) % 166.40/166.61 (step @p214 :rule eq_resolve :premises (@p212 @p209)) % 166.40/166.61 (step @p215 :rule implies_elim :premises (@p214)) % 166.40/166.61 (step @p216 :rule chain_m_resolution :premises (@p215 @p206) :args (@t142 @t56 (@list @t140))) % 166.40/166.61 (step @p217 :rule cnf_equiv_pos1 :args (@t142)) % 166.40/166.61 (step @p218 :rule reordering :premises (@p217) :args ((or @t144 @t139 @t143))) % 166.40/166.61 (step @p219 :rule skolem_intro :args (@t125)) % 166.40/166.61 (step @p220 :rule symm :premises (@p219)) % 166.40/166.61 (step @p221 :rule refl :args (@t145)) % 166.40/166.61 (step @p222 :rule bool-double-not-elim :args (@t129)) % 166.40/166.61 (step @p223 :rule refl :args (@t147)) % 166.40/166.61 (step @p224 :rule nary_cong :premises (@p223 @p222 @p221) :args ((or @t147 (not @t148) @t145))) % 166.40/166.61 (assume-push @p644 @t146) % 166.40/166.61 (assume-push @p645 @t148) % 166.40/166.61 (assume-push @p646 @t148) % 166.40/166.61 (assume-push @p647 @t146) % 166.40/166.61 (step @p229 :rule false_intro :premises (@p645)) % 166.40/166.61 (step @p230 :rule refl :args (@t128)) % 166.40/166.61 (step @p231 :rule cong :premises (@p220 @p230) :args (@t139)) % 166.40/166.61 (step @p232 :rule trans :premises (@p231 @p229)) % 166.40/166.61 (step @p233 :rule false_elim :premises (@p232)) % 166.40/166.61 (step-pop @p648 :rule scope :premises (@p233)) % 166.40/166.61 (step-pop @p649 :rule scope :premises (@p648)) % 166.40/166.61 (step @p234 :rule process_scope :premises (@p649) :args (@t145)) % 166.40/166.61 (step @p237 :rule and_intro :premises (@p645 @p220)) % 166.40/166.61 (step @p238 :rule modus_ponens :premises (@p237 @p234)) % 166.40/166.61 (step-pop @p650 :rule scope :premises (@p238)) % 166.40/166.61 (step-pop @p651 :rule scope :premises (@p650)) % 166.40/166.61 (step @p239 :rule process_scope :premises (@p651) :args (@t145)) % 166.40/166.61 (step @p242 :rule implies_elim :premises (@p239)) % 166.40/166.61 (step @p243 :rule cnf_and_neg :args (@t149)) % 166.40/166.61 (step @p244 :rule resolution :premises (@p243 @p242) :args (true @t149)) % 166.40/166.61 (step @p245 :rule eq_resolve :premises (@p244 @p224)) % 166.40/166.61 (step @p246 :rule chain_m_resolution :premises (@p245 @p220 @p218 @p216 @p200) :args ((or @t131 @t144) @t64 (@list @t146 @t139 @t142 @t129))) % 166.40/166.61 (step @p247 :rule cnf_equiv_neg1 :args (@t131)) % 166.40/166.61 (step @p248 :rule reordering :premises (@p247) :args ((or @t130 @t129 @t131))) % 166.40/166.61 (step @p249 :rule cnf_equiv_pos2 :args (@t142)) % 166.40/166.61 (step @p250 :rule reordering :premises (@p249) :args ((or @t130 @t145 @t143))) % 166.40/166.61 (assume-push @p652 @t146) % 166.40/166.61 (assume-push @p653 @t129) % 166.40/166.61 (assume-push @p654 @t129) % 166.40/166.61 (assume-push @p655 @t146) % 166.40/166.61 (step @p255 :rule true_intro :premises (@p653)) % 166.40/166.61 (step @p230 :rule refl :args (@t128)) % 166.40/166.61 (step @p231 :rule cong :premises (@p220 @p230) :args (@t139)) % 166.40/166.61 (step @p256 :rule trans :premises (@p231 @p255)) % 166.40/166.61 (step @p257 :rule true_elim :premises (@p256)) % 166.40/166.61 (step-pop @p656 :rule scope :premises (@p257)) % 166.40/166.61 (step-pop @p657 :rule scope :premises (@p656)) % 166.40/166.61 (step @p258 :rule process_scope :premises (@p657) :args (@t139)) % 166.40/166.61 (step @p261 :rule and_intro :premises (@p653 @p220)) % 166.40/166.61 (step @p262 :rule modus_ponens :premises (@p261 @p258)) % 166.40/166.61 (step-pop @p658 :rule scope :premises (@p262)) % 166.40/166.61 (step-pop @p659 :rule scope :premises (@p658)) % 166.40/166.61 (step @p263 :rule process_scope :premises (@p659) :args (@t139)) % 166.40/166.61 (step @p266 :rule implies_elim :premises (@p263)) % 166.40/166.61 (step @p267 :rule cnf_and_neg :args (@t150)) % 166.40/166.61 (step @p268 :rule resolution :premises (@p267 @p266) :args (true @t150)) % 166.40/166.61 (step @p269 :rule chain_m_resolution :premises (@p268 @p220 @p250 @p216 @p248 @p246) :args (@t131 @t66 (@list @t146 @t139 @t142 @t129 @t130))) % 166.40/166.61 (step @p270 :rule refl :args (@t151)) % 166.40/166.61 (step @p271 :rule bool-double-not-elim :args (@t127)) % 166.40/166.61 (step @p272 :rule nary_cong :premises (@p271 @p270) :args ((or (not @t152) @t151))) % 166.40/166.61 (assume-push @p660 @t152) % 166.40/166.61 (step @p274 :rule skolemize :premises (@p660)) % 166.40/166.61 (step-pop @p661 :rule scope :premises (@p274)) % 166.40/166.61 (step @p275 :rule process_scope :premises (@p661) :args (@t151)) % 166.40/166.61 (step @p277 :rule implies_elim :premises (@p275)) % 166.40/166.61 (step @p278 :rule eq_resolve :premises (@p277 @p272)) % 166.40/166.61 (step @p279 :rule chain_m_resolution :premises (@p278 @p269) :args (@t127 @t56 (@list @t131))) % 166.40/166.61 (step @p280 :rule cnf_or_pos :args (@t154)) % 166.40/166.61 (step @p281 :rule reordering :premises (@p280) :args ((or @t153 @t152 (not @t154)))) % 166.40/166.61 (step @p282 :rule chain_m_resolution :premises (@p281 @p279 @p199) :args (@t153 @t71 (@list @t127 @t154))) % 166.40/166.61 (step @p283 :rule cnf_equiv_neg2 :args (@t159)) % 166.40/166.61 (step @p284 :rule eq-symm :args (@t165 @t166)) % 166.40/166.61 (step @p285 :rule cong :premises (@p284) :args (@t168)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p286 :rule trust :premises () :args ((= @t169 @t168))) % 166.40/166.61 (step @p287 :rule trans :premises (@p286 @p285)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.61 (step @p288 :rule trust :premises () :args (@t169)) % 166.40/166.61 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 166.40/166.61 (step @p290 :rule instantiate :premises (@p289) :args ((@list tptp.y tptp.u tptp.x tptp.z @t156))) % 166.40/166.61 (step @p291 :rule cnf_equiv_pos2 :args (@t171)) % 166.40/166.61 (step @p292 :rule reordering :premises (@p291) :args ((or @t157 @t173 @t172))) % 166.40/166.61 (assume-push @p662 @t146) % 166.40/166.61 (assume-push @p663 @t153) % 166.40/166.61 (assume-push @p664 @t158) % 166.40/166.61 (assume-push @p665 @t158) % 166.40/166.61 (assume-push @p666 @t153) % 166.40/166.61 (assume-push @p667 @t146) % 166.40/166.61 (step @p299 :rule true_intro :premises (@p664)) % 166.40/166.61 (step @p300 :rule refl :args (@t156)) % 166.40/166.61 (step @p301 :rule symm :premises (@p663)) % 166.40/166.61 (step @p302 :rule trans :premises (@p220 @p301)) % 166.40/166.61 (step @p303 :rule cong :premises (@p302 @p300) :args (@t170)) % 166.40/166.61 (step @p304 :rule trans :premises (@p303 @p299)) % 166.40/166.61 (step @p305 :rule true_elim :premises (@p304)) % 166.40/166.61 (step-pop @p668 :rule scope :premises (@p305)) % 166.40/166.61 (step-pop @p669 :rule scope :premises (@p668)) % 166.40/166.61 (step-pop @p670 :rule scope :premises (@p669)) % 166.40/166.61 (step @p306 :rule process_scope :premises (@p670) :args (@t170)) % 166.40/166.61 (step @p310 :rule and_intro :premises (@p664 @p663 @p220)) % 166.40/166.61 (step @p311 :rule modus_ponens :premises (@p310 @p306)) % 166.40/166.61 (step-pop @p671 :rule scope :premises (@p311)) % 166.40/166.61 (step-pop @p672 :rule scope :premises (@p671)) % 166.40/166.61 (step-pop @p673 :rule scope :premises (@p672)) % 166.40/166.61 (step @p312 :rule process_scope :premises (@p673) :args (@t170)) % 166.40/166.61 (step @p316 :rule implies_elim :premises (@p312)) % 166.40/166.61 (step @p317 :rule cnf_and_neg :args (@t174)) % 166.40/166.61 (step @p318 :rule resolution :premises (@p317 @p316) :args (true @t174)) % 166.40/166.61 (step @p319 :rule chain_m_resolution :premises (@p318 @p220 @p292 @p290 @p283) :args ((or @t176 @t159 @t175) (@list false true false true) (@list @t146 @t170 @t171 @t157))) % 166.40/166.61 (step @p320 :rule cnf_equiv_neg1 :args (@t159)) % 166.40/166.61 (step @p321 :rule reordering :premises (@p320) :args ((or @t158 @t157 @t159))) % 166.40/166.61 (step @p322 :rule refl :args (@t173)) % 166.40/166.61 (step @p323 :rule bool-double-not-elim :args (@t158)) % 166.40/166.61 (step @p324 :rule refl :args (@t176)) % 166.40/166.61 (step @p325 :rule nary_cong :premises (@p223 @p324 @p323 @p322) :args ((or @t147 @t176 (not @t175) @t173))) % 166.40/166.61 (assume-push @p674 @t146) % 166.40/166.61 (assume-push @p675 @t153) % 166.40/166.61 (assume-push @p676 @t175) % 166.40/166.61 (assume-push @p677 @t175) % 166.40/166.61 (assume-push @p678 @t153) % 166.40/166.61 (assume-push @p679 @t146) % 166.40/166.61 (step @p332 :rule false_intro :premises (@p676)) % 166.40/166.61 (step @p300 :rule refl :args (@t156)) % 166.40/166.61 (step @p333 :rule symm :premises (@p675)) % 166.40/166.61 (step @p334 :rule trans :premises (@p220 @p333)) % 166.40/166.61 (step @p335 :rule cong :premises (@p334 @p300) :args (@t170)) % 166.40/166.61 (step @p336 :rule trans :premises (@p335 @p332)) % 166.40/166.61 (step @p337 :rule false_elim :premises (@p336)) % 166.40/166.61 (step-pop @p680 :rule scope :premises (@p337)) % 166.40/166.61 (step-pop @p681 :rule scope :premises (@p680)) % 166.40/166.61 (step-pop @p682 :rule scope :premises (@p681)) % 166.40/166.61 (step @p338 :rule process_scope :premises (@p682) :args (@t173)) % 166.40/166.61 (step @p342 :rule and_intro :premises (@p676 @p675 @p220)) % 166.40/166.61 (step @p343 :rule modus_ponens :premises (@p342 @p338)) % 166.40/166.61 (step-pop @p683 :rule scope :premises (@p343)) % 166.40/166.61 (step-pop @p684 :rule scope :premises (@p683)) % 166.40/166.61 (step-pop @p685 :rule scope :premises (@p684)) % 166.40/166.61 (step @p344 :rule process_scope :premises (@p685) :args (@t173)) % 166.40/166.61 (step @p348 :rule implies_elim :premises (@p344)) % 166.40/166.61 (step @p349 :rule cnf_and_neg :args (@t177)) % 166.40/166.61 (step @p350 :rule resolution :premises (@p349 @p348) :args (true @t177)) % 166.40/166.61 (step @p351 :rule eq_resolve :premises (@p350 @p325)) % 166.40/166.61 (step @p352 :rule cnf_equiv_pos1 :args (@t171)) % 166.40/166.61 (step @p353 :rule reordering :premises (@p352) :args ((or (not @t157) @t170 @t172))) % 166.40/166.61 (step @p354 :rule chain_m_resolution :premises (@p353 @p290 @p351 @p282 @p220 @p321 @p319 @p282) :args (@t159 (@list false true false false false true false) (@list @t171 @t170 @t153 @t146 @t157 @t158 @t153))) % 166.40/166.61 (step @p355 :rule refl :args (@t178)) % 166.40/166.61 (step @p356 :rule bool-double-not-elim :args (@t155)) % 166.40/166.61 (step @p357 :rule nary_cong :premises (@p356 @p355) :args ((or (not @t179) @t178))) % 166.40/166.61 (assume-push @p686 @t179) % 166.40/166.61 (step @p359 :rule skolemize :premises (@p686)) % 166.40/166.61 (step-pop @p687 :rule scope :premises (@p359)) % 166.40/166.61 (step @p360 :rule process_scope :premises (@p687) :args (@t178)) % 166.40/166.61 (step @p362 :rule implies_elim :premises (@p360)) % 166.40/166.61 (step @p363 :rule eq_resolve :premises (@p362 @p357)) % 166.40/166.61 (step @p364 :rule chain_m_resolution :premises (@p363 @p354) :args (@t155 @t56 (@list @t159))) % 166.40/166.61 (step @p365 :rule cnf_or_pos :args (@t181)) % 166.40/166.61 (step @p366 :rule reordering :premises (@p365) :args ((or @t180 @t179 (not @t181)))) % 166.40/166.61 (step @p367 :rule chain_m_resolution :premises (@p366 @p364 @p198) :args (@t180 @t71 (@list @t155 @t181))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p368 :rule trust :premises () :args ((= @t184 @t183))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p369 :rule trust :premises () :args ((= @t27 @t184))) % 166.40/166.61 (step @p370 :rule trans :premises (@p369 @p368)) % 166.40/166.61 (step @p371 :rule eq_resolve :premises (@p5 @p370)) % 166.40/166.61 (step @p372 :rule refl :args (@t186)) % 166.40/166.61 (step @p373 :rule refl :args (@t187)) % 166.40/166.61 (step @p374 :rule bool-double-not-elim :args (@t182)) % 166.40/166.61 (step @p375 :rule nary_cong :premises (@p374 @p373 @p372) :args ((or (not @t183) @t187 @t186))) % 166.40/166.61 (assume-push @p688 @t183) % 166.40/166.61 (assume-push @p689 @t180) % 166.40/166.61 (assume-push @p690 @t183) % 166.40/166.61 (assume-push @p691 @t180) % 166.40/166.61 (step @p380 :rule false_intro :premises (@p371)) % 166.40/166.61 (step @p381 :rule symm :premises (@p689)) % 166.40/166.61 (step @p382 :rule refl :args (@t83)) % 166.40/166.61 (step @p383 :rule cong :premises (@p382 @p381) :args (@t185)) % 166.40/166.61 (step @p384 :rule trans :premises (@p383 @p380)) % 166.40/166.61 (step @p385 :rule false_elim :premises (@p384)) % 166.40/166.61 (step-pop @p692 :rule scope :premises (@p385)) % 166.40/166.61 (step-pop @p693 :rule scope :premises (@p692)) % 166.40/166.61 (step @p386 :rule process_scope :premises (@p693) :args (@t186)) % 166.40/166.61 (step @p389 :rule and_intro :premises (@p371 @p689)) % 166.40/166.61 (step @p390 :rule modus_ponens :premises (@p389 @p386)) % 166.40/166.61 (step-pop @p694 :rule scope :premises (@p390)) % 166.40/166.61 (step-pop @p695 :rule scope :premises (@p694)) % 166.40/166.61 (step @p391 :rule process_scope :premises (@p695) :args (@t186)) % 166.40/166.61 (step @p394 :rule implies_elim :premises (@p391)) % 166.40/166.61 (step @p395 :rule cnf_and_neg :args (@t188)) % 166.40/166.61 (step @p396 :rule resolution :premises (@p395 @p394) :args (true @t188)) % 166.40/166.61 (step @p397 :rule eq_resolve :premises (@p396 @p375)) % 166.40/166.61 (step @p398 :rule reordering :premises (@p397) :args ((or @t182 @t186 @t187))) % 166.40/166.61 (step @p399 :rule chain_m_resolution :premises (@p398 @p371 @p367) :args (@t186 @t189 (@list @t182 @t180))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p400 :rule trust :premises () :args ((= (forall @t25 (or (not @t192) @t191)) (forall @t25 (or (not (_ @t36 (_ @t30 @t190 @t10) @t7)) (_ @t36 (_ @t30 @t97 @t7) @t10)))))) % 166.40/166.61 (step @p401 :rule refl :args (@t191)) % 166.40/166.61 (step @p402 :rule refl :args (@t23)) % 166.40/166.61 (step @p403 :rule cong :premises (@p402 @p401) :args ((= @t23 @t191))) % 166.40/166.61 (step @p404 :rule symm :premises (@p403)) % 166.40/166.61 (step @p405 :rule eq_resolve :premises (@p402 @p404)) % 166.40/166.61 (step @p406 :rule refl :args (@t192)) % 166.40/166.61 (step @p407 :rule refl :args (@t24)) % 166.40/166.61 (step @p408 :rule cong :premises (@p407 @p406) :args ((= @t24 @t192))) % 166.40/166.61 (step @p409 :rule symm :premises (@p408)) % 166.40/166.61 (step @p410 :rule eq_resolve :premises (@p407 @p409)) % 166.40/166.61 (step @p411 :rule cong :premises (@p410) :args (@t193)) % 166.40/166.61 (step @p412 :rule nary_cong :premises (@p411 @p405) :args (@t194)) % 166.40/166.61 (step @p413 :rule cong :premises (@p412) :args ((forall @t25 @t194))) % 166.40/166.61 (step @p414 :rule bool-impl-elim :args (@t24 @t23)) % 166.40/166.61 (step @p415 :rule cong :premises (@p414) :args (@t26)) % 166.40/166.61 (step @p416 :rule trans :premises (@p415 @p413)) % 166.40/166.61 (step @p417 :rule trans :premises (@p416 @p400)) % 166.40/166.61 (step @p418 :rule eq_resolve :premises (@p4 @p417)) % 166.40/166.61 (step @p419 :rule instantiate :premises (@p418) :args ((@list tptp.z tptp.u))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p420 :rule trust :premises () :args ((= @t4 @t195))) % 166.40/166.61 (step @p421 :rule eq_resolve :premises (@p2 @p420)) % 166.40/166.61 (step @p422 :rule cnf_or_pos :args (@t198)) % 166.40/166.61 (step @p423 :rule reordering :premises (@p422) :args ((or @t197 @t196 (not @t198)))) % 166.40/166.61 (step @p424 :rule chain_m_resolution :premises (@p423 @p421 @p419) :args (@t196 @t71 (@list @t195 @t198))) % 166.40/166.61 (step @p425 :rule cnf_or_pos :args (@t202)) % 166.40/166.61 (step @p426 :rule reordering :premises (@p425) :args ((or @t199 @t201 @t185 (not @t202)))) % 166.40/166.61 (step @p427 :rule chain_m_resolution :premises (@p426 @p424 @p399 @p197) :args (@t201 (@list false true false) (@list @t196 @t185 @t202))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.61 (step @p428 :rule trust :premises () :args ((forall (@list @t204 @t203) (or (not (forall @t206 (= (_ @t76 @t204 @t205) (_ @t76 @t203 @t205)))) (= @t204 @t203))))) % 166.40/166.61 (step @p429 :rule instantiate :premises (@p428) :args ((@list @t83 @t87))) % 166.40/166.61 (step @p430 :rule cnf_equiv_neg2 :args (@t211)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p431 :rule trust :premises () :args ((= @t212 @t84))) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p432 :rule trust :premises () :args ((= @t3 @t212))) % 166.40/166.61 (step @p433 :rule trans :premises (@p432 @p431)) % 166.40/166.61 (step @p434 :rule eq_resolve :premises (@p1 @p433)) % 166.40/166.61 (step @p435 :rule cnf_ite_neg3 :args (@t214)) % 166.40/166.61 (step @p436 :rule reordering :premises (@p435) :args ((or @t216 @t215 @t214))) % 166.40/166.61 (step @p437 :rule eq-symm :args (@t214 @t209)) % 166.40/166.61 (step @p438 :rule cong :premises (@p95 @p437) :args ((=> @t89 @t217))) % 166.40/166.61 (assume-push @p696 @t89) % 166.40/166.61 (step @p440 :rule instantiate :premises (@p111) :args ((@list @t208))) % 166.40/166.61 (step-pop @p697 :rule scope :premises (@p440)) % 166.40/166.61 (step @p441 :rule process_scope :premises (@p697) :args (@t217)) % 166.40/166.61 (step @p443 :rule eq_resolve :premises (@p441 @p438)) % 166.40/166.61 (step @p444 :rule implies_elim :premises (@p443)) % 166.40/166.61 (step @p445 :rule chain_m_resolution :premises (@p444 @p111) :args (@t218 @t56 (@list @t89))) % 166.40/166.61 (step @p446 :rule cnf_equiv_pos2 :args (@t218)) % 166.40/166.61 (step @p447 :rule reordering :premises (@p446) :args ((or @t209 @t220 @t219))) % 166.40/166.61 (step @p448 :rule chain_m_resolution :premises (@p447 @p445 @p436 @p434 @p430) :args ((or @t211 @t215) @t64 (@list @t218 @t214 @t84 @t209))) % 166.40/166.61 (step @p449 :rule cnf_equiv_neg1 :args (@t211)) % 166.40/166.61 (step @p450 :rule reordering :premises (@p449) :args ((or @t210 @t209 @t211))) % 166.40/166.61 (step @p451 :rule cnf_equiv_pos1 :args (@t218)) % 166.40/166.61 (step @p452 :rule reordering :premises (@p451) :args ((or (not @t209) @t214 @t219))) % 166.40/166.61 (step @p453 :rule cnf_ite_pos2 :args (@t214)) % 166.40/166.61 (step @p454 :rule reordering :premises (@p453) :args ((or @t210 @t213 @t220))) % 166.40/166.61 (step @p455 :rule refl :args (@t221)) % 166.40/166.61 (step @p456 :rule bool-double-not-elim :args (@t210)) % 166.40/166.61 (step @p457 :rule refl :args (@t216)) % 166.40/166.61 (step @p458 :rule nary_cong :premises (@p457 @p456 @p455) :args ((or @t216 (not @t215) @t221))) % 166.40/166.61 (assume-push @p698 @t84) % 166.40/166.61 (assume-push @p699 @t213) % 166.40/166.61 (assume-push @p700 @t215) % 166.40/166.61 (step @p462 :rule evaluate :args ((= false true))) % 166.40/166.61 (step @p463 :rule true_intro :premises (@p434)) % 166.40/166.61 (step @p464 :rule symm :premises (@p699)) % 166.40/166.61 (step @p382 :rule refl :args (@t83)) % 166.40/166.61 (step @p465 :rule cong :premises (@p382 @p464) :args (@t210)) % 166.40/166.61 (step @p466 :rule false_intro :premises (@p700)) % 166.40/166.61 (step @p467 :rule symm :premises (@p466)) % 166.40/166.61 (step @p468 :rule trans :premises (@p467 @p465 @p463)) % 166.40/166.61 (step @p469 false :rule eq_resolve :premises (@p468 @p462)) % 166.40/166.61 (step-pop @p701 :rule scope :premises (@p469)) % 166.40/166.61 (step-pop @p702 :rule scope :premises (@p701)) % 166.40/166.61 (step-pop @p703 :rule scope :premises (@p702)) % 166.40/166.61 (step @p470 :rule process_scope :premises (@p703) :args (false)) % 166.40/166.61 (assume-push @p704 @t84) % 166.40/166.61 (assume-push @p705 @t215) % 166.40/166.61 (assume-push @p706 @t213) % 166.40/166.61 (step @p477 :rule and_intro :premises (@p434 @p706 @p705)) % 166.40/166.61 (step-pop @p707 :rule scope :premises (@p477)) % 166.40/166.61 (step-pop @p708 :rule scope :premises (@p707)) % 166.40/166.61 (step-pop @p709 :rule scope :premises (@p708)) % 166.40/166.61 (step @p478 :rule process_scope :premises (@p709) :args (@t222)) % 166.40/166.61 (step @p482 :rule implies_elim :premises (@p478)) % 166.40/166.61 (step @p483 :rule resolution :premises (@p482 @p470) :args (true @t222)) % 166.40/166.61 (step @p484 :rule not_and :premises (@p483)) % 166.40/166.61 (step @p485 :rule eq_resolve :premises (@p484 @p458)) % 166.40/166.61 (step @p486 :rule chain_m_resolution :premises (@p485 @p434 @p454 @p452 @p445 @p450 @p448) :args (@t211 (@list false false false false false true) (@list @t84 @t213 @t214 @t218 @t209 @t210))) % 166.40/166.61 (step @p487 :rule refl :args (@t223)) % 166.40/166.61 (step @p488 :rule bool-double-not-elim :args (@t207)) % 166.40/166.61 (step @p489 :rule nary_cong :premises (@p488 @p487) :args ((or (not @t224) @t223))) % 166.40/166.61 (assume-push @p710 @t224) % 166.40/166.61 (step @p491 :rule skolemize :premises (@p710)) % 166.40/166.61 (step-pop @p711 :rule scope :premises (@p491)) % 166.40/166.61 (step @p492 :rule process_scope :premises (@p711) :args (@t223)) % 166.40/166.61 (step @p494 :rule implies_elim :premises (@p492)) % 166.40/166.61 (step @p495 :rule eq_resolve :premises (@p494 @p489)) % 166.40/166.61 (step @p496 :rule chain_m_resolution :premises (@p495 @p486) :args (@t207 @t56 (@list @t211))) % 166.40/166.61 (step @p497 :rule cnf_or_pos :args (@t226)) % 166.40/166.61 (step @p498 :rule reordering :premises (@p497) :args ((or @t224 @t225 (not @t226)))) % 166.40/166.61 (step @p499 :rule chain_m_resolution :premises (@p498 @p496 @p429) :args (@t225 @t71 (@list @t207 @t226))) % 166.40/166.61 (step @p500 :rule refl :args (@t228)) % 166.40/166.61 (step @p501 :rule bool-double-not-elim :args (@t200)) % 166.40/166.61 (step @p502 :rule refl :args (@t229)) % 166.40/166.61 (step @p503 :rule nary_cong :premises (@p502 @p501 @p500) :args ((or @t229 (not @t201) @t228))) % 166.40/166.61 (assume-push @p712 @t225) % 166.40/166.61 (assume-push @p713 @t201) % 166.40/166.61 (assume-push @p714 @t201) % 166.40/166.61 (assume-push @p715 @t225) % 166.40/166.61 (step @p508 :rule false_intro :premises (@p713)) % 166.40/166.61 (step @p509 :rule refl :args (@t73)) % 166.40/166.61 (step @p510 :rule symm :premises (@p712)) % 166.40/166.61 (step @p511 :rule cong :premises (@p510 @p509) :args (@t227)) % 166.40/166.61 (step @p512 :rule trans :premises (@p511 @p508)) % 166.40/166.61 (step @p513 :rule false_elim :premises (@p512)) % 166.40/166.61 (step-pop @p716 :rule scope :premises (@p513)) % 166.40/166.61 (step-pop @p717 :rule scope :premises (@p716)) % 166.40/166.61 (step @p514 :rule process_scope :premises (@p717) :args (@t228)) % 166.40/166.61 (step @p517 :rule and_intro :premises (@p713 @p712)) % 166.40/166.61 (step @p518 :rule modus_ponens :premises (@p517 @p514)) % 166.40/166.61 (step-pop @p718 :rule scope :premises (@p518)) % 166.40/166.61 (step-pop @p719 :rule scope :premises (@p718)) % 166.40/166.61 (step @p519 :rule process_scope :premises (@p719) :args (@t228)) % 166.40/166.61 (step @p522 :rule implies_elim :premises (@p519)) % 166.40/166.61 (step @p523 :rule cnf_and_neg :args (@t230)) % 166.40/166.61 (step @p524 :rule resolution :premises (@p523 @p522) :args (true @t230)) % 166.40/166.61 (step @p525 :rule eq_resolve :premises (@p524 @p503)) % 166.40/166.61 (step @p526 :rule chain_m_resolution :premises (@p525 @p499 @p427) :args (@t228 @t231 (@list @t225 @t200))) % 166.40/166.61 (step @p527 :rule cnf_equiv_pos1 :args (@t234)) % 166.40/166.61 (step @p528 :rule reordering :premises (@p527) :args ((or @t227 @t235 (not @t234)))) % 166.40/166.61 (step @p529 :rule chain_m_resolution :premises (@p528 @p526 @p112) :args (@t235 @t189 (@list @t227 @t234))) % 166.40/166.61 (step @p530 :rule cnf_ite_neg1 :args (@t233)) % 166.40/166.61 (step @p531 :rule reordering :premises (@p530) :args ((or @t216 @t233 @t236))) % 166.40/166.61 (step @p532 :rule chain_m_resolution :premises (@p531 @p434 @p529) :args (@t236 @t231 (@list @t84 @t233))) % 166.40/166.61 (step @p533 :rule cnf_or_pos :args (@t239)) % 166.40/166.61 (step @p534 :rule reordering :premises (@p533) :args ((or @t232 @t238 (not @t239)))) % 166.40/166.61 (step @p535 :rule chain_m_resolution :premises (@p534 @p532 @p92) :args (@t238 @t189 (@list @t232 @t239))) % 166.40/166.61 (step @p536 :rule refl :args (@t244)) % 166.40/166.61 (step @p537 :rule bool-double-not-elim :args (@t237)) % 166.40/166.61 (step @p538 :rule nary_cong :premises (@p537 @p536) :args ((or (not @t238) @t244))) % 166.40/166.61 (assume-push @p720 @t238) % 166.40/166.61 (step @p540 :rule skolemize :premises (@p720)) % 166.40/166.61 (step-pop @p721 :rule scope :premises (@p540)) % 166.40/166.61 (step @p541 :rule process_scope :premises (@p721) :args (@t244)) % 166.40/166.61 (step @p543 :rule implies_elim :premises (@p541)) % 166.40/166.61 (step @p544 :rule eq_resolve :premises (@p543 @p538)) % 166.40/166.61 (step @p545 :rule chain_m_resolution :premises (@p544 @p535) :args (@t244 @t93 (@list @t237))) % 166.40/166.61 (step @p546 :rule cnf_equiv_neg2 :args (@t243)) % 166.40/166.61 (step @p547 :rule eq-symm :args (@t248 @t249)) % 166.40/166.61 (step @p548 :rule cong :premises (@p547) :args (@t251)) % 166.40/166.61 ; trust TRUST PREPROCESS_HO_ELIM % 166.40/166.61 (step @p549 :rule trust :premises () :args ((= @t252 @t251))) % 166.40/166.62 (step @p550 :rule trans :premises (@p549 @p548)) % 166.40/166.62 ; trust TRUST PREPROCESS_HO_ELIM_LEMMA % 166.40/166.62 (step @p551 :rule trust :premises () :args (@t252)) % 166.40/166.62 (step @p552 :rule eq_resolve :premises (@p551 @p550)) % 166.40/166.62 (step @p553 :rule instantiate :premises (@p552) :args ((@list tptp.y tptp.x @t240))) % 166.40/166.62 (step @p554 :rule cnf_equiv_pos2 :args (@t254)) % 166.40/166.62 (step @p555 :rule reordering :premises (@p554) :args ((or @t241 @t256 @t255))) % 166.40/166.62 (assume-push @p722 @t60) % 166.40/166.62 (assume-push @p723 @t69) % 166.40/166.62 (assume-push @p724 @t242) % 166.40/166.62 (assume-push @p725 @t242) % 166.40/166.62 (assume-push @p726 @t69) % 166.40/166.62 (assume-push @p727 @t60) % 166.40/166.62 (step @p562 :rule true_intro :premises (@p724)) % 166.40/166.62 (step @p563 :rule refl :args (@t240)) % 166.40/166.62 (step @p564 :rule symm :premises (@p723)) % 166.40/166.62 (step @p565 :rule trans :premises (@p8 @p564)) % 166.40/166.62 (step @p566 :rule cong :premises (@p565 @p563) :args (@t253)) % 166.40/166.62 (step @p567 :rule trans :premises (@p566 @p562)) % 166.40/166.62 (step @p568 :rule true_elim :premises (@p567)) % 166.40/166.62 (step-pop @p728 :rule scope :premises (@p568)) % 166.40/166.62 (step-pop @p729 :rule scope :premises (@p728)) % 166.40/166.62 (step-pop @p730 :rule scope :premises (@p729)) % 166.40/166.62 (step @p569 :rule process_scope :premises (@p730) :args (@t253)) % 166.40/166.62 (step @p573 :rule and_intro :premises (@p724 @p723 @p8)) % 166.40/166.62 (step @p574 :rule modus_ponens :premises (@p573 @p569)) % 166.40/166.62 (step-pop @p731 :rule scope :premises (@p574)) % 166.40/166.62 (step-pop @p732 :rule scope :premises (@p731)) % 166.40/166.62 (step-pop @p733 :rule scope :premises (@p732)) % 166.40/166.62 (step @p575 :rule process_scope :premises (@p733) :args (@t253)) % 166.40/166.62 (step @p579 :rule implies_elim :premises (@p575)) % 166.40/166.62 (step @p580 :rule cnf_and_neg :args (@t257)) % 166.40/166.62 (step @p581 :rule resolution :premises (@p580 @p579) :args (true @t257)) % 166.40/166.62 (step @p582 :rule chain_m_resolution :premises (@p581 @p91 @p8 @p555 @p553 @p546 @p545) :args (@t258 (@list false false true false true true) (@list @t69 @t60 @t253 @t254 @t241 @t243))) % 166.40/166.62 (step @p583 :rule cnf_equiv_neg1 :args (@t243)) % 166.40/166.62 (step @p584 :rule reordering :premises (@p583) :args ((or @t242 @t241 @t243))) % 166.40/166.62 (step @p585 :rule chain_m_resolution :premises (@p584 @p582 @p545) :args (@t241 (@list true true) (@list @t242 @t243))) % 166.40/166.62 (step @p586 :rule cnf_equiv_pos1 :args (@t254)) % 166.40/166.62 (step @p587 :rule reordering :premises (@p586) :args ((or (not @t241) @t253 @t255))) % 166.40/166.62 (step @p588 :rule chain_m_resolution :premises (@p587 @p585 @p553) :args (@t253 @t71 (@list @t241 @t254))) % 166.40/166.62 (step @p589 :rule refl :args (@t256)) % 166.40/166.62 (step @p590 :rule bool-double-not-elim :args (@t242)) % 166.40/166.62 (step @p591 :rule refl :args (@t259)) % 166.40/166.62 (step @p592 :rule nary_cong :premises (@p32 @p591 @p590 @p589) :args ((or @t61 @t259 (not @t258) @t256))) % 166.40/166.62 (assume-push @p734 @t60) % 166.40/166.62 (assume-push @p735 @t69) % 166.40/166.62 (assume-push @p736 @t258) % 166.40/166.62 (assume-push @p737 @t258) % 166.40/166.62 (assume-push @p738 @t69) % 166.40/166.62 (assume-push @p739 @t60) % 166.40/166.62 (step @p599 :rule false_intro :premises (@p736)) % 166.40/166.62 (step @p563 :rule refl :args (@t240)) % 166.40/166.62 (step @p600 :rule symm :premises (@p735)) % 166.40/166.62 (step @p601 :rule trans :premises (@p8 @p600)) % 166.40/166.62 (step @p602 :rule cong :premises (@p601 @p563) :args (@t253)) % 166.40/166.62 (step @p603 :rule trans :premises (@p602 @p599)) % 166.40/166.62 (step @p604 :rule false_elim :premises (@p603)) % 166.40/166.62 (step-pop @p740 :rule scope :premises (@p604)) % 166.40/166.62 (step-pop @p741 :rule scope :premises (@p740)) % 166.40/166.62 (step-pop @p742 :rule scope :premises (@p741)) % 166.40/166.62 (step @p605 :rule process_scope :premises (@p742) :args (@t256)) % 166.40/166.62 (step @p609 :rule and_intro :premises (@p736 @p735 @p8)) % 166.40/166.62 (step @p610 :rule modus_ponens :premises (@p609 @p605)) % 166.40/166.62 (step-pop @p743 :rule scope :premises (@p610)) % 166.40/166.62 (step-pop @p744 :rule scope :premises (@p743)) % 166.40/166.62 (step-pop @p745 :rule scope :premises (@p744)) % 166.40/166.62 (step @p611 :rule process_scope :premises (@p745) :args (@t256)) % 166.40/166.62 (step @p615 :rule implies_elim :premises (@p611)) % 166.40/166.62 (step @p616 :rule cnf_and_neg :args (@t260)) % 166.40/166.62 (step @p617 :rule resolution :premises (@p616 @p615) :args (true @t260)) % 166.40/166.62 (step @p618 :rule eq_resolve :premises (@p617 @p592)) % 166.40/166.62 (step @p619 false :rule chain_m_resolution :premises (@p618 @p588 @p582 @p91 @p8) :args (false (@list false true false false) (@list @t253 @t242 @t69 @t60))) % 166.40/166.62 ) % 166.40/166.62 % SZS output end Proof % 166.40/166.62 % cvc5 exiting %------------------------------------------------------------------------------