%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG271^5 : TPTP v9.2.1. Bugfixed v5.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n022.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 08:05:43 AM UTC 2026 % Result : Theorem 175.61s 175.93s % Output : Proof 175.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG271^5 : TPTP v9.2.1. Bugfixed v5.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n022.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 : Wed Jun 3 01:56:53 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 175.61/175.93 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 175.61/175.93 --- 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... % 175.61/175.93 --- 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... % 175.61/175.93 --- Run --ho-elim --full-saturate-quant at 18s... % 175.61/175.93 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 175.61/175.93 % SZS status Theorem % 175.61/175.93 % SZS output start Proof % 175.61/175.93 ( % 175.61/175.93 (declare-sort tptp.g 0) % 175.61/175.93 (define tptp.cGRP_ASSOC () (let ((_let_1 (@var "Xc" tptp.g))) (let ((_let_2 (@var "Xb" tptp.g))) (let ((_let_3 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (let ((_let_4 (@var "Xa" tptp.g))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (= (_ (_ _let_3 (_ _let_5 _let_2)) _let_1) (_ _let_5 (_ (_ _let_3 _let_2) _let_1))))))))))) % 175.61/175.93 (define tptp.cGRP_INVERSE () (let ((_let_1 (@var "Xe" tptp.g))) (let ((_let_2 (@var "Xa" tptp.g))) (let ((_let_3 (@var "Xb" tptp.g))) (let ((_let_4 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (exists (@list _let_3) (and (= (_ (_ _let_4 _let_2) _let_3) _let_1) (= (_ (_ _let_4 _let_3) _let_2) _let_1)))))))))) % 175.61/175.93 (define tptp.cGRP_RIGHT_INVERSE () (let ((_let_1 (@var "Xe" tptp.g))) (let ((_let_2 (@var "Xb" tptp.g))) (let ((_let_3 (@var "Xa" tptp.g))) (let ((_let_4 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (lambda (@list _let_4 _let_1) (forall (@list _let_3) (exists (@list _let_2) (= (_ (_ _let_4 _let_3) _let_2) _let_1))))))))) % 175.61/175.93 (define tptp.cGRP_RIGHT_UNIT () (let ((_let_1 (@var "Xa" tptp.g))) (let ((_let_2 (@var "Xe" tptp.g))) (let ((_let_3 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (= (_ (_ _let_3 _let_1) _let_2) _let_1))))))) % 175.61/175.93 (define tptp.cGRP_UNIT () (let ((_let_1 (@var "Xa" tptp.g))) (let ((_let_2 (@var "Xe" tptp.g))) (let ((_let_3 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (and (= (_ (_ _let_3 _let_2) _let_1) _let_1) (= (_ (_ _let_3 _let_1) _let_2) _let_1)))))))) % 175.61/175.93 (define tptp.cGROUP1 () (let ((_let_1 (@var "Xe" tptp.g))) (let ((_let_2 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (lambda (@list _let_2 _let_1) (and (_ tptp.cGRP_ASSOC _let_2) (_ (_ tptp.cGRP_UNIT _let_2) _let_1) (_ (_ tptp.cGRP_INVERSE _let_2) _let_1)))))) % 175.61/175.93 (define tptp.cGROUP3 () (let ((_let_1 (@var "Xe" tptp.g))) (let ((_let_2 (@var "Xf" (-> tptp.g tptp.g tptp.g)))) (lambda (@list _let_2 _let_1) (and (_ tptp.cGRP_ASSOC _let_2) (_ (_ tptp.cGRP_RIGHT_UNIT _let_2) _let_1) (_ (_ tptp.cGRP_RIGHT_INVERSE _let_2) _let_1)))))) % 175.61/175.93 (define @t1 () (@var "Xe" tptp.g)) % 175.61/175.93 (define @t2 () (@var "Xf" (-> tptp.g tptp.g tptp.g))) % 175.61/175.93 (define @t3 () (= (_ (_ tptp.cGROUP1 @t2) @t1) (_ (_ tptp.cGROUP3 @t2) @t1))) % 175.61/175.93 (define @t4 () (@list @t2 @t1)) % 175.61/175.93 (define @t5 () (forall @t4 @t3)) % 175.61/175.93 (define @t6 () (not @t5)) % 175.61/175.93 (define @t7 () (@var "Xc" tptp.g)) % 175.61/175.93 (define @t8 () (@var "Xb" tptp.g)) % 175.61/175.93 (define @t9 () (_ @t2 @t8)) % 175.61/175.93 (define @t10 () (_ @t9 @t7)) % 175.61/175.93 (define @t11 () (@var "Xa" tptp.g)) % 175.61/175.93 (define @t12 () (_ @t2 @t11)) % 175.61/175.93 (define @t13 () (_ @t12 @t10)) % 175.61/175.93 (define @t14 () (_ @t12 @t8)) % 175.61/175.93 (define @t15 () (_ (_ @t2 @t14) @t7)) % 175.61/175.93 (define @t16 () (= @t15 @t13)) % 175.61/175.93 (define @t17 () (@list @t11 @t8 @t7)) % 175.61/175.93 (define @t18 () (forall @t17 @t16)) % 175.61/175.93 (define @t19 () (@list @t2)) % 175.61/175.93 (define @t20 () (lambda @t19 @t18)) % 175.61/175.93 (define @t21 () (_ @t9 @t11)) % 175.61/175.93 (define @t22 () (= @t14 @t1)) % 175.61/175.93 (define @t23 () (and @t22 (= @t21 @t1))) % 175.61/175.93 (define @t24 () (@list @t8)) % 175.61/175.93 (define @t25 () (exists @t24 @t23)) % 175.61/175.93 (define @t26 () (@list @t11)) % 175.61/175.93 (define @t27 () (forall @t26 @t25)) % 175.61/175.93 (define @t28 () (lambda @t4 @t27)) % 175.61/175.93 (define @t29 () (exists @t24 @t22)) % 175.61/175.93 (define @t30 () (forall @t26 @t29)) % 175.61/175.93 (define @t31 () (lambda @t4 @t30)) % 175.61/175.93 (define @t32 () (_ @t12 @t1)) % 175.61/175.93 (define @t33 () (= @t32 @t11)) % 175.61/175.93 (define @t34 () (forall @t26 @t33)) % 175.61/175.93 (define @t35 () (lambda @t4 @t34)) % 175.61/175.93 (define @t36 () (_ @t2 @t1)) % 175.61/175.93 (define @t37 () (_ @t36 @t11)) % 175.61/175.93 (define @t38 () (and (= @t37 @t11) @t33)) % 175.61/175.93 (define @t39 () (forall @t26 @t38)) % 175.61/175.93 (define @t40 () (lambda @t4 @t39)) % 175.61/175.93 (define @t41 () (_ tptp.cGRP_ASSOC @t2)) % 175.61/175.93 (define @t42 () (and @t41 (_ (_ tptp.cGRP_UNIT @t2) @t1) (_ (_ tptp.cGRP_INVERSE @t2) @t1))) % 175.61/175.93 (define @t43 () (lambda @t4 @t42)) % 175.61/175.93 (define @t44 () (and @t41 (_ (_ tptp.cGRP_RIGHT_UNIT @t2) @t1) (_ (_ tptp.cGRP_RIGHT_INVERSE @t2) @t1))) % 175.61/175.93 (define @t45 () (lambda @t4 @t44)) % 175.61/175.93 (define @t46 () (@var "BOUND_VARIABLE_7542" tptp.g)) % 175.61/175.93 (define @t47 () (@var "BOUND_VARIABLE_7665" (@ho-elim-sort (-> tptp.g tptp.g tptp.g)))) % 175.61/175.93 (define @t48 () (@const 0 (-> (@ho-elim-sort (-> tptp.g tptp.g tptp.g)) tptp.g (@ho-elim-sort (-> tptp.g tptp.g))))) % 175.61/175.93 (define @t49 () (@const 1 (-> (@ho-elim-sort (-> tptp.g tptp.g)) tptp.g tptp.g))) % 175.61/175.93 (define @t50 () (@list @t46)) % 175.61/175.93 (define @t51 () (forall @t50 (= @t46 (_ @t49 (_ @t48 @t47 @t46) @t1)))) % 175.61/175.93 (define @t52 () (@var "BOUND_VARIABLE_7536" tptp.g)) % 175.61/175.93 (define @t53 () (@list @t52)) % 175.61/175.93 (define @t54 () (forall @t53 (= @t52 (_ @t49 (_ @t48 @t47 @t1) @t52)))) % 175.61/175.93 (define @t55 () (_ @t48 @t47 @t8)) % 175.61/175.93 (define @t56 () (not (= @t1 (_ @t49 @t55 @t11)))) % 175.61/175.93 (define @t57 () (_ @t48 @t47 @t11)) % 175.61/175.93 (define @t58 () (_ @t49 @t57 @t8)) % 175.61/175.93 (define @t59 () (not (= @t1 @t58))) % 175.61/175.93 (define @t60 () (_ @t49 (_ @t48 @t47 @t58) @t7)) % 175.61/175.93 (define @t61 () (_ @t49 @t57 (_ @t49 @t55 @t7))) % 175.61/175.93 (define @t62 () (forall @t17 (= @t61 @t60))) % 175.61/175.93 (define @t63 () (forall @t26 (= @t11 (_ @t49 @t57 @t1)))) % 175.61/175.93 (define @t64 () (@list @t47 @t1)) % 175.61/175.93 (define @t65 () (forall @t64 (= (and @t62 @t63 (forall @t26 (not (forall @t24 @t59)))) (and @t62 (forall @t26 (not (forall @t24 (or @t59 @t56)))) @t54 @t51)))) % 175.61/175.93 (define @t66 () (@quantifiers_skolemize @t65 1)) % 175.61/175.93 (define @t67 () (@quantifiers_skolemize @t65 0)) % 175.61/175.93 (define @t68 () (_ @t48 @t67 @t11)) % 175.61/175.93 (define @t69 () (forall @t26 (= @t11 (_ @t49 @t68 @t66)))) % 175.61/175.93 (define @t70 () (_ @t48 @t67 @t8)) % 175.61/175.93 (define @t71 () (_ @t49 @t68 @t8)) % 175.61/175.93 (define @t72 () (not (= @t66 @t71))) % 175.61/175.93 (define @t73 () (forall @t26 (not (forall @t24 (or @t72 (not (= @t66 (_ @t49 @t70 @t11)))))))) % 175.61/175.93 (define @t74 () (@quantifiers_skolemize @t73 0)) % 175.61/175.93 (define @t75 () (@list @t74)) % 175.61/175.93 (define @t76 () (_ @t48 @t67 @t74)) % 175.61/175.93 (define @t77 () (= @t74 (_ @t49 @t76 @t66))) % 175.61/175.93 (define @t78 () (not (= @t66 (_ @t49 @t76 @t8)))) % 175.61/175.93 (define @t79 () (forall @t24 @t78)) % 175.61/175.93 (define @t80 () (@quantifiers_skolemize @t79 0)) % 175.61/175.93 (define @t81 () (@list @t80)) % 175.61/175.93 (define @t82 () (_ @t48 @t67 @t80)) % 175.61/175.93 (define @t83 () (_ @t49 @t82 @t66)) % 175.61/175.93 (define @t84 () (= @t80 @t83)) % 175.61/175.93 (define @t85 () (_ @t48 @t67 @t66)) % 175.61/175.93 (define @t86 () (forall @t53 (= @t52 (_ @t49 @t85 @t52)))) % 175.61/175.93 (define @t87 () (@quantifiers_skolemize @t86 0)) % 175.61/175.93 (define @t88 () (@list @t87)) % 175.61/175.93 (define @t89 () (_ @t48 @t67 @t87)) % 175.61/175.93 (define @t90 () (_ @t49 @t89 @t66)) % 175.61/175.93 (define @t91 () (= @t87 @t90)) % 175.61/175.93 (define @t92 () (forall @t26 (not (forall @t24 @t72)))) % 175.61/175.93 (define @t93 () (@quantifiers_skolemize @t92 0)) % 175.61/175.93 (define @t94 () (_ @t48 @t67 @t93)) % 175.61/175.93 (define @t95 () (not (= @t66 (_ @t49 @t94 @t8)))) % 175.61/175.93 (define @t96 () (forall @t24 (or @t95 (not (= @t66 (_ @t49 @t70 @t93)))))) % 175.61/175.93 (define @t97 () (not @t96)) % 175.61/175.93 (define @t98 () (forall @t24 (or (not (= @t66 (_ @t49 @t89 @t8))) (not (= @t66 (_ @t49 @t70 @t87)))))) % 175.61/175.93 (define @t99 () (not @t98)) % 175.61/175.93 (define @t100 () (@quantifiers_skolemize @t96 0)) % 175.61/175.93 (define @t101 () (= @t66 (_ @t49 @t94 @t100))) % 175.61/175.93 (define @t102 () (not @t101)) % 175.61/175.93 (define @t103 () (or @t102 (not (= @t66 (_ @t49 (_ @t48 @t67 @t100) @t93))))) % 175.61/175.93 (define @t104 () (not @t103)) % 175.61/175.93 (define @t105 () (@quantifiers_skolemize @t98 0)) % 175.61/175.93 (define @t106 () (_ @t49 (_ @t48 @t67 @t105) @t87)) % 175.61/175.93 (define @t107 () (= @t66 @t106)) % 175.61/175.93 (define @t108 () (not @t107)) % 175.61/175.93 (define @t109 () (_ @t49 @t89 @t105)) % 175.61/175.93 (define @t110 () (= @t66 @t109)) % 175.61/175.93 (define @t111 () (not @t110)) % 175.61/175.93 (define @t112 () (or @t111 @t108)) % 175.61/175.93 (define @t113 () (not @t112)) % 175.61/175.93 (define @t114 () (forall @t24 @t95)) % 175.61/175.93 (define @t115 () (not @t92)) % 175.61/175.93 (define @t116 () (not (not @t114))) % 175.61/175.93 (define @t117 () (forall @t17 (= (_ @t49 @t68 (_ @t49 @t70 @t7)) (_ @t49 (_ @t48 @t67 @t71) @t7)))) % 175.61/175.93 (define @t118 () (and @t117 @t69 @t92)) % 175.61/175.93 (define @t119 () (not @t118)) % 175.61/175.93 (define @t120 () (forall @t50 (= @t46 (_ @t49 (_ @t48 @t67 @t46) @t66)))) % 175.61/175.93 (define @t121 () (and @t117 @t73 @t86 @t120)) % 175.61/175.93 (define @t122 () (not @t121)) % 175.61/175.93 (define @t123 () (not (= @t58 @t1))) % 175.61/175.93 (define @t124 () (or @t123 @t56)) % 175.61/175.93 (define @t125 () (forall @t24 @t124)) % 175.61/175.93 (define @t126 () (not @t125)) % 175.61/175.93 (define @t127 () (forall @t26 @t126)) % 175.61/175.93 (define @t128 () (forall @t17 (= @t60 @t61))) % 175.61/175.93 (define @t129 () (and @t128 @t127 @t54 @t51)) % 175.61/175.93 (define @t130 () (forall @t24 @t123)) % 175.61/175.93 (define @t131 () (not @t130)) % 175.61/175.93 (define @t132 () (forall @t26 @t131)) % 175.61/175.93 (define @t133 () (and @t128 @t63 @t132)) % 175.61/175.93 (define @t134 () (forall @t64 (= @t129 @t133))) % 175.61/175.93 (define @t135 () (not @t134)) % 175.61/175.93 (define @t136 () (_ @t2 @t11 @t8)) % 175.61/175.93 (define @t137 () (not (= @t136 @t1))) % 175.61/175.93 (define @t138 () (forall @t26 (not (forall @t24 @t137)))) % 175.61/175.93 (define @t139 () (_ @t2 @t11 @t1)) % 175.61/175.93 (define @t140 () (forall @t26 (= @t11 @t139))) % 175.61/175.93 (define @t141 () (_ @t2 @t8 @t7)) % 175.61/175.93 (define @t142 () (_ @t2 @t11 @t141)) % 175.61/175.93 (define @t143 () (_ @t2 @t136 @t7)) % 175.61/175.93 (define @t144 () (forall @t17 (= @t143 @t142))) % 175.61/175.93 (define @t145 () (and @t144 @t140 @t138)) % 175.61/175.93 (define @t146 () (_ @t2 @t46 @t1)) % 175.61/175.93 (define @t147 () (forall @t50 (= @t46 @t146))) % 175.61/175.93 (define @t148 () (_ @t2 @t1 @t52)) % 175.61/175.93 (define @t149 () (forall @t53 (= @t52 @t148))) % 175.61/175.93 (define @t150 () (_ @t2 @t8 @t11)) % 175.61/175.93 (define @t151 () (forall @t26 (not (forall @t24 (or @t137 (not (= @t1 @t150))))))) % 175.61/175.93 (define @t152 () (and @t144 @t151 @t149 @t147)) % 175.61/175.93 (define @t153 () (@list @t1)) % 175.61/175.93 (define @t154 () (lambda @t153 @t152)) % 175.61/175.93 (define @t155 () (_ (lambda @t4 @t152) @t2)) % 175.61/175.93 (define @t156 () (lambda @t153 @t145)) % 175.61/175.93 (define @t157 () (_ (lambda @t4 @t145) @t2)) % 175.61/175.93 (define @t158 () (_ @t155 @t1)) % 175.61/175.93 (define @t159 () (_ @t157 @t1)) % 175.61/175.93 (define @t160 () (forall @t4 (= @t158 @t159))) % 175.61/175.93 (define @t161 () (lambda @t153 @t138)) % 175.61/175.93 (define @t162 () (_ (lambda @t4 @t138) @t2)) % 175.61/175.93 (define @t163 () (lambda @t153 @t140)) % 175.61/175.93 (define @t164 () (_ (lambda @t4 @t140) @t2)) % 175.61/175.93 (define @t165 () (_ (lambda @t19 @t144) @t2)) % 175.61/175.93 (define @t166 () (not @t22)) % 175.61/175.93 (define @t167 () (forall @t24 @t166)) % 175.61/175.93 (define @t168 () (not @t167)) % 175.61/175.93 (define @t169 () (= @t11 @t32)) % 175.61/175.93 (define @t170 () (forall @t26 @t169)) % 175.61/175.93 (define @t171 () (and @t149 @t147)) % 175.61/175.93 (define @t172 () (lambda @t153 @t151)) % 175.61/175.93 (define @t173 () (_ (lambda @t4 @t151) @t2)) % 175.61/175.93 (define @t174 () (lambda @t153 @t171)) % 175.61/175.93 (define @t175 () (_ (lambda @t4 @t171) @t2)) % 175.61/175.93 (define @t176 () (= @t1 @t21)) % 175.61/175.93 (define @t177 () (not @t176)) % 175.61/175.93 (define @t178 () (or @t166 @t177)) % 175.61/175.93 (define @t179 () (and @t22 @t176)) % 175.61/175.93 (define @t180 () (forall @t24 (not @t179))) % 175.61/175.93 (define @t181 () (not @t180)) % 175.61/175.93 (define @t182 () (_ (_ @t2 @t46) @t1)) % 175.61/175.93 (define @t183 () (= @t46 @t182)) % 175.61/175.93 (define @t184 () (forall @t50 @t183)) % 175.61/175.93 (define @t185 () (_ @t36 @t52)) % 175.61/175.93 (define @t186 () (= @t52 @t185)) % 175.61/175.93 (define @t187 () (forall @t53 @t186)) % 175.61/175.93 (define @t188 () (@list @t11)) % 175.61/175.93 (define @t189 () (@list @t46)) % 175.61/175.93 (define @t190 () (= @t11 @t37)) % 175.61/175.93 (define @t191 () (forall @t26 @t190)) % 175.61/175.93 (define @t192 () (and @t191 @t170)) % 175.61/175.93 (define @t193 () (= @t118 @t121)) % 175.61/175.93 (define @t194 () (not @t69)) % 175.61/175.93 (define @t195 () (not @t86)) % 175.61/175.93 (define @t196 () (not @t73)) % 175.61/175.93 (define @t197 () (= @t87 (_ @t49 @t85 @t87))) % 175.61/175.93 (define @t198 () (not @t197)) % 175.61/175.93 (define @t199 () (_ @t48 @t67 @t109)) % 175.61/175.93 (define @t200 () (_ @t49 @t199 @t87)) % 175.61/175.93 (define @t201 () (= (_ @t49 @t89 @t106) @t200)) % 175.61/175.93 (define @t202 () (and @t91 @t110 @t107 @t201)) % 175.61/175.93 (define @t203 () (forall @t24 (or @t78 (not (= @t66 (_ @t49 @t70 @t74)))))) % 175.61/175.93 (define @t204 () (not (not @t203))) % 175.61/175.93 (define @t205 () (= @t66 (_ @t49 @t82 @t74))) % 175.61/175.93 (define @t206 () (not @t205)) % 175.61/175.93 (define @t207 () (_ @t49 @t76 @t80)) % 175.61/175.93 (define @t208 () (= @t66 @t207)) % 175.61/175.93 (define @t209 () (not @t208)) % 175.61/175.93 (define @t210 () (or @t209 @t206)) % 175.61/175.93 (define @t211 () (not @t79)) % 175.61/175.93 (define @t212 () (forall @t24 (not (= @t66 (_ @t49 @t82 @t8))))) % 175.61/175.93 (define @t213 () (not @t212)) % 175.61/175.93 (define @t214 () (not @t209)) % 175.61/175.93 (define @t215 () (@quantifiers_skolemize @t212 0)) % 175.61/175.93 (define @t216 () (_ @t49 @t82 @t215)) % 175.61/175.93 (define @t217 () (= @t66 @t216)) % 175.61/175.93 (define @t218 () (not @t217)) % 175.61/175.93 (define @t219 () (not @t218)) % 175.61/175.93 (define @t220 () (_ @t49 @t76 @t216)) % 175.61/175.93 (define @t221 () (= @t220 (_ @t49 (_ @t48 @t67 @t207) @t215))) % 175.61/175.93 (define @t222 () (_ @t49 @t85 @t215)) % 175.61/175.93 (define @t223 () (_ @t49 @t82 @t222)) % 175.61/175.93 (define @t224 () (= @t223 (_ @t49 (_ @t48 @t67 @t83) @t215))) % 175.61/175.93 (define @t225 () (and @t77 @t208 @t84 @t217 @t221 @t224)) % 175.61/175.93 (define @t226 () (@list true)) % 175.61/175.93 (define @t227 () (@list @t69)) % 175.61/175.93 (assume @p1 @t6) % 175.61/175.93 (assume @p2 true) % 175.61/175.93 (step @p3 (= tptp.cGRP_ASSOC @t20) :rule refl :args (@t20)) % 175.61/175.93 (step @p4 (= tptp.cGRP_INVERSE @t28) :rule refl :args (@t28)) % 175.61/175.93 (step @p5 (= tptp.cGRP_RIGHT_INVERSE @t31) :rule refl :args (@t31)) % 175.61/175.93 (step @p6 (= tptp.cGRP_RIGHT_UNIT @t35) :rule refl :args (@t35)) % 175.61/175.93 (step @p7 (= tptp.cGRP_UNIT @t40) :rule refl :args (@t40)) % 175.61/175.93 (step @p8 (= tptp.cGROUP1 @t43) :rule refl :args (@t43)) % 175.61/175.93 (step @p9 (= tptp.cGROUP3 @t45) :rule refl :args (@t45)) % 175.61/175.93 (assume-push @p467 @t69) % 175.61/175.93 (step @p11 :rule instantiate :premises (@p467) :args (@t75)) % 175.61/175.93 (step-pop @p468 :rule scope :premises (@p11)) % 175.61/175.93 (step @p12 :rule process_scope :premises (@p468) :args (@t77)) % 175.61/175.93 (step @p14 :rule implies_elim :premises (@p12)) % 175.61/175.93 (assume-push @p469 @t69) % 175.61/175.93 (step @p16 :rule instantiate :premises (@p469) :args (@t81)) % 175.61/175.93 (step-pop @p470 :rule scope :premises (@p16)) % 175.61/175.93 (step @p17 :rule process_scope :premises (@p470) :args (@t84)) % 175.61/175.93 (step @p19 :rule implies_elim :premises (@p17)) % 175.61/175.93 (assume-push @p471 @t69) % 175.61/175.93 (step @p21 :rule instantiate :premises (@p471) :args (@t88)) % 175.61/175.93 (step-pop @p472 :rule scope :premises (@p21)) % 175.61/175.93 (step @p22 :rule process_scope :premises (@p472) :args (@t91)) % 175.61/175.93 (step @p24 :rule implies_elim :premises (@p22)) % 175.61/175.93 (assume-push @p473 @t73) % 175.61/175.93 (step @p26 :rule instantiate :premises (@p473) :args ((@list @t93))) % 175.61/175.93 (step-pop @p474 :rule scope :premises (@p26)) % 175.61/175.93 (step @p27 :rule process_scope :premises (@p474) :args (@t97)) % 175.61/175.93 (step @p29 :rule implies_elim :premises (@p27)) % 175.61/175.93 (assume-push @p475 @t73) % 175.61/175.93 (step @p31 :rule instantiate :premises (@p475) :args (@t88)) % 175.61/175.93 (step-pop @p476 :rule scope :premises (@p31)) % 175.61/175.93 (step @p32 :rule process_scope :premises (@p476) :args (@t99)) % 175.61/175.93 (step @p34 :rule implies_elim :premises (@p32)) % 175.61/175.93 (step @p35 :rule refl :args (@t104)) % 175.61/175.93 (step @p36 :rule bool-double-not-elim :args (@t96)) % 175.61/175.93 (step @p37 :rule nary_cong :premises (@p36 @p35) :args ((or (not @t97) @t104))) % 175.61/175.93 (assume-push @p477 @t97) % 175.61/175.93 (step @p39 :rule skolemize :premises (@p477)) % 175.61/175.93 (step-pop @p478 :rule scope :premises (@p39)) % 175.61/175.93 (step @p40 :rule process_scope :premises (@p478) :args (@t104)) % 175.61/175.93 (step @p42 :rule implies_elim :premises (@p40)) % 175.61/175.93 (step @p43 :rule eq_resolve :premises (@p42 @p37)) % 175.61/175.93 (step @p44 :rule refl :args (@t113)) % 175.61/175.93 (step @p45 :rule bool-double-not-elim :args (@t98)) % 175.61/175.93 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((or (not @t99) @t113))) % 175.61/175.93 (assume-push @p479 @t99) % 175.61/175.93 (step @p48 :rule skolemize :premises (@p479)) % 175.61/175.93 (step-pop @p480 :rule scope :premises (@p48)) % 175.61/175.93 (step @p49 :rule process_scope :premises (@p480) :args (@t113)) % 175.61/175.93 (step @p51 :rule implies_elim :premises (@p49)) % 175.61/175.93 (step @p52 :rule eq_resolve :premises (@p51 @p46)) % 175.61/175.93 (step @p53 :rule bool-double-not-elim :args (@t101)) % 175.61/175.93 (step @p54 :rule refl :args (@t103)) % 175.61/175.93 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t103 (not @t102)))) % 175.61/175.93 (step @p56 :rule cnf_or_neg :args (@t103 0)) % 175.61/175.93 (step @p57 :rule eq_resolve :premises (@p56 @p55)) % 175.61/175.93 (step @p58 :rule reordering :premises (@p57) :args ((or @t101 @t103))) % 175.61/175.93 (step @p59 :rule bool-double-not-elim :args (@t110)) % 175.61/175.93 (step @p60 :rule refl :args (@t112)) % 175.61/175.93 (step @p61 :rule nary_cong :premises (@p60 @p59) :args ((or @t112 (not @t111)))) % 175.61/175.93 (step @p62 :rule cnf_or_neg :args (@t112 0)) % 175.61/175.93 (step @p63 :rule eq_resolve :premises (@p62 @p61)) % 175.61/175.93 (step @p64 :rule reordering :premises (@p63) :args ((or @t110 @t112))) % 175.61/175.93 (step @p65 :rule bool-double-not-elim :args (@t107)) % 175.61/175.93 (step @p66 :rule nary_cong :premises (@p60 @p65) :args ((or @t112 (not @t108)))) % 175.61/175.93 (step @p67 :rule cnf_or_neg :args (@t112 1)) % 175.61/175.93 (step @p68 :rule eq_resolve :premises (@p67 @p66)) % 175.61/175.93 (step @p69 :rule reordering :premises (@p68) :args ((or @t107 @t112))) % 175.61/175.93 (assume-push @p481 @t114) % 175.61/175.93 (step @p71 :rule instantiate :premises (@p481) :args ((@list @t100))) % 175.61/175.93 (step-pop @p482 :rule scope :premises (@p71)) % 175.61/175.93 (step @p72 :rule process_scope :premises (@p482) :args (@t102)) % 175.61/175.93 (step @p74 :rule implies_elim :premises (@p72)) % 175.61/175.93 (step @p75 :rule refl :args (@t114)) % 175.61/175.93 (step @p76 :rule bool-double-not-elim :args (@t92)) % 175.61/175.93 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or (not @t115) @t114))) % 175.61/175.93 (step @p78 :rule bool-double-not-elim :args (@t114)) % 175.61/175.93 (step @p79 :rule refl :args (@t115)) % 175.61/175.93 (step @p80 :rule cong :premises (@p79 @p78) :args ((=> @t115 @t116))) % 175.61/175.93 (assume-push @p483 @t115) % 175.61/175.93 (step @p82 :rule skolemize :premises (@p483)) % 175.61/175.93 (step-pop @p484 :rule scope :premises (@p82)) % 175.61/175.93 (step @p83 :rule process_scope :premises (@p484) :args (@t116)) % 175.61/175.93 (step @p85 :rule eq_resolve :premises (@p83 @p80)) % 175.61/175.93 (step @p86 :rule implies_elim :premises (@p85)) % 175.61/175.93 (step @p87 :rule eq_resolve :premises (@p86 @p77)) % 175.61/175.93 (step @p88 :rule cnf_and_pos :args (@t118 0)) % 175.61/175.93 (step @p89 :rule reordering :premises (@p88) :args ((or @t117 @t119))) % 175.61/175.93 (step @p90 :rule cnf_and_pos :args (@t121 0)) % 175.61/175.93 (step @p91 :rule reordering :premises (@p90) :args ((or @t117 @t122))) % 175.61/175.93 (step @p92 :rule refl :args (@t51)) % 175.61/175.93 (step @p93 :rule refl :args (@t54)) % 175.61/175.93 (step @p94 :rule refl :args (@t56)) % 175.61/175.93 (step @p95 :rule eq-symm :args (@t58 @t1)) % 175.61/175.93 (step @p96 :rule cong :premises (@p95) :args (@t123)) % 175.61/175.93 (step @p97 :rule nary_cong :premises (@p96 @p94) :args (@t124)) % 175.61/175.93 (step @p98 :rule cong :premises (@p97) :args (@t125)) % 175.61/175.93 (step @p99 :rule cong :premises (@p98) :args (@t126)) % 175.61/175.93 (step @p100 :rule cong :premises (@p99) :args (@t127)) % 175.61/175.93 (step @p101 :rule eq-symm :args (@t60 @t61)) % 175.61/175.93 (step @p102 :rule cong :premises (@p101) :args (@t128)) % 175.61/175.93 (step @p103 :rule nary_cong :premises (@p102 @p100 @p93 @p92) :args (@t129)) % 175.61/175.93 (step @p104 :rule cong :premises (@p96) :args (@t130)) % 175.61/175.93 (step @p105 :rule cong :premises (@p104) :args (@t131)) % 175.61/175.93 (step @p106 :rule cong :premises (@p105) :args (@t132)) % 175.61/175.93 (step @p107 :rule refl :args (@t63)) % 175.61/175.93 (step @p108 :rule nary_cong :premises (@p102 @p107 @p106) :args (@t133)) % 175.61/175.93 (step @p109 :rule cong :premises (@p108 @p103) :args ((= @t133 @t129))) % 175.61/175.93 (step @p110 :rule eq-symm :args (@t129 @t133)) % 175.61/175.93 (step @p111 :rule trans :premises (@p110 @p109)) % 175.61/175.93 (step @p112 :rule cong :premises (@p111) :args (@t134)) % 175.61/175.93 (step @p113 :rule cong :premises (@p112) :args (@t135)) % 175.61/175.93 ; WARNING: add trust step for TRUST % 175.61/175.93 ; trust TRUST PREPROCESS_HO_ELIM % 175.61/175.93 (step @p114 :rule trust :premises () :args ((= (not (forall @t4 (= @t152 @t145))) @t135))) % 175.61/175.93 (step @p115 :rule eq-symm :args (@t145 @t152)) % 175.61/175.93 (step @p116 :rule beta-reduce :args ((= (_ @t154 @t1) @t152))) % 175.61/175.93 (step @p117 :rule refl :args (@t1)) % 175.61/175.93 (step @p118 :rule beta-reduce :args ((= @t155 @t154))) % 175.61/175.93 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 175.61/175.93 (step @p120 :rule trans :premises (@p119 @p116)) % 175.61/175.93 (step @p121 :rule beta-reduce :args ((= (_ @t156 @t1) @t145))) % 175.61/175.93 (step @p122 :rule beta-reduce :args ((= @t157 @t156))) % 175.61/175.93 (step @p123 :rule ho_cong :premises (@p122 @p117)) % 175.61/175.93 (step @p124 :rule trans :premises (@p123 @p121)) % 175.61/175.93 (step @p125 :rule cong :premises (@p124 @p120) :args ((= @t159 @t158))) % 175.61/175.93 (step @p126 :rule trans :premises (@p125 @p115)) % 175.61/175.93 (step @p127 :rule eq-symm :args (@t158 @t159)) % 175.61/175.93 (step @p128 :rule trans :premises (@p127 @p126)) % 175.61/175.93 (step @p129 :rule cong :premises (@p128) :args (@t160)) % 175.61/175.93 (step @p130 :rule cong :premises (@p129) :args ((not @t160))) % 175.61/175.93 (step @p131 :rule refl :args (@t2)) % 175.61/175.93 (step @p132 :rule beta-reduce :args ((= (_ @t161 @t1) @t138))) % 175.61/175.93 (step @p133 :rule beta-reduce :args ((= @t162 @t161))) % 175.61/175.93 (step @p134 :rule ho_cong :premises (@p133 @p117)) % 175.61/175.93 (step @p135 :rule trans :premises (@p134 @p132)) % 175.61/175.93 (step @p136 :rule beta-reduce :args ((= (_ @t163 @t1) @t140))) % 175.61/175.93 (step @p137 :rule beta-reduce :args ((= @t164 @t163))) % 175.61/175.93 (step @p138 :rule ho_cong :premises (@p137 @p117)) % 175.61/175.93 (step @p139 :rule trans :premises (@p138 @p136)) % 175.61/175.93 (step @p140 :rule beta-reduce :args ((= @t165 @t144))) % 175.61/175.93 (step @p141 :rule nary_cong :premises (@p140 @p139 @p135) :args ((and @t165 (_ @t164 @t1) (_ @t162 @t1)))) % 175.61/175.93 (step @p142 :rule refl :args (@t1)) % 175.61/175.93 (step @p143 :rule refl :args (@t136)) % 175.61/175.93 (step @p144 :rule refl :args (@t14)) % 175.61/175.93 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t14 @t136))) % 175.61/175.93 (step @p146 :rule symm :premises (@p145)) % 175.61/175.93 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 175.61/175.93 (step @p148 :rule cong :premises (@p147 @p142) :args (@t22)) % 175.61/175.93 (step @p149 :rule cong :premises (@p148) :args (@t166)) % 175.61/175.93 (step @p150 :rule cong :premises (@p149) :args (@t167)) % 175.61/175.93 (step @p151 :rule cong :premises (@p150) :args (@t168)) % 175.61/175.93 (step @p152 :rule exists-elim :args ((= @t29 @t168))) % 175.61/175.93 (step @p153 :rule trans :premises (@p152 @p151)) % 175.61/175.93 (step @p154 :rule cong :premises (@p153) :args (@t30)) % 175.61/175.93 (step @p155 :rule cong :premises (@p154) :args (@t31)) % 175.61/175.93 (step @p156 :rule trans :premises (@p5 @p155)) % 175.61/175.93 (step @p157 :rule ho_cong :premises (@p156 @p131)) % 175.61/175.93 (step @p158 :rule ho_cong :premises (@p157 @p117)) % 175.61/175.93 (step @p159 :rule refl :args (@t139)) % 175.61/175.93 (step @p160 :rule refl :args (@t32)) % 175.61/175.93 (step @p161 :rule cong :premises (@p160 @p159) :args ((= @t32 @t139))) % 175.61/175.93 (step @p162 :rule symm :premises (@p161)) % 175.61/175.93 (step @p163 :rule eq_resolve :premises (@p160 @p162)) % 175.61/175.93 (step @p164 :rule refl :args (@t11)) % 175.61/175.93 (step @p165 :rule cong :premises (@p164 @p163) :args (@t169)) % 175.61/175.93 (step @p166 :rule cong :premises (@p165) :args (@t170)) % 175.61/175.93 (step @p167 :rule eq-symm :args (@t32 @t11)) % 175.61/175.93 (step @p168 :rule cong :premises (@p167) :args (@t34)) % 175.61/175.93 (step @p169 :rule trans :premises (@p168 @p166)) % 175.61/175.93 (step @p170 :rule cong :premises (@p169) :args (@t35)) % 175.61/175.93 (step @p171 :rule trans :premises (@p6 @p170)) % 175.61/175.93 (step @p172 :rule ho_cong :premises (@p171 @p131)) % 175.61/175.93 (step @p173 :rule ho_cong :premises (@p172 @p117)) % 175.61/175.93 (step @p174 :rule refl :args ((_ @t2 @t11 @t10))) % 175.61/175.93 (step @p175 :rule refl :args (@t141)) % 175.61/175.93 (step @p176 :rule cong :premises (@p164 @p175) :args (@t142)) % 175.61/175.93 (step @p177 :rule trans :premises (@p176 @p174)) % 175.61/175.93 (step @p178 :rule refl :args (@t12)) % 175.61/175.93 (step @p179 :rule ho_cong :premises (@p178 @p175)) % 175.61/175.93 (step @p180 :rule cong :premises (@p179 @p177) :args ((= (_ @t12 @t141) @t142))) % 175.61/175.93 (step @p181 :rule symm :premises (@p180)) % 175.61/175.93 (step @p182 :rule refl :args (@t13)) % 175.61/175.93 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 175.61/175.93 (step @p184 :rule refl :args (@t10)) % 175.61/175.93 (step @p185 :rule cong :premises (@p184 @p175) :args ((= @t10 @t141))) % 175.61/175.93 (step @p186 :rule symm :premises (@p185)) % 175.61/175.93 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 175.61/175.93 (step @p188 :rule ho_cong :premises (@p178 @p187)) % 175.61/175.93 (step @p189 :rule trans :premises (@p188 @p183)) % 175.61/175.93 (step @p190 :rule refl :args ((_ @t2 @t14 @t7))) % 175.61/175.93 (step @p191 :rule refl :args (@t7)) % 175.61/175.93 (step @p192 :rule cong :premises (@p143 @p191) :args (@t143)) % 175.61/175.93 (step @p193 :rule trans :premises (@p192 @p190)) % 175.61/175.93 (step @p194 :rule refl :args (@t2)) % 175.61/175.93 (step @p195 :rule ho_cong :premises (@p194 @p143)) % 175.61/175.93 (step @p196 :rule ho_cong :premises (@p195 @p191)) % 175.61/175.93 (step @p197 :rule cong :premises (@p196 @p193) :args ((= (_ (_ @t2 @t136) @t7) @t143))) % 175.61/175.93 (step @p198 :rule symm :premises (@p197)) % 175.61/175.93 (step @p199 :rule refl :args (@t15)) % 175.61/175.93 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 175.61/175.93 (step @p201 :rule ho_cong :premises (@p194 @p147)) % 175.61/175.93 (step @p202 :rule ho_cong :premises (@p201 @p191)) % 175.61/175.93 (step @p203 :rule trans :premises (@p202 @p200)) % 175.61/175.93 (step @p204 :rule cong :premises (@p203 @p189) :args (@t16)) % 175.61/175.93 (step @p205 :rule cong :premises (@p204) :args (@t18)) % 175.61/175.93 (step @p206 :rule cong :premises (@p205) :args (@t20)) % 175.61/175.93 (step @p207 :rule trans :premises (@p3 @p206)) % 175.61/175.93 (step @p208 :rule ho_cong :premises (@p207 @p131)) % 175.61/175.93 (step @p209 :rule nary_cong :premises (@p208 @p173 @p158) :args (@t44)) % 175.61/175.93 (step @p210 :rule trans :premises (@p209 @p141)) % 175.61/175.93 (step @p211 :rule cong :premises (@p210) :args (@t45)) % 175.61/175.93 (step @p212 :rule trans :premises (@p9 @p211)) % 175.61/175.93 (step @p213 :rule ho_cong :premises (@p212 @p131)) % 175.61/175.93 (step @p214 :rule ho_cong :premises (@p213 @p117)) % 175.61/175.93 (step @p215 :rule aci_norm :args ((= (and @t144 @t171 @t151) @t152))) % 175.61/175.93 (step @p216 :rule beta-reduce :args ((= (_ @t172 @t1) @t151))) % 175.61/175.93 (step @p217 :rule beta-reduce :args ((= @t173 @t172))) % 175.61/175.93 (step @p218 :rule ho_cong :premises (@p217 @p117)) % 175.61/175.93 (step @p219 :rule trans :premises (@p218 @p216)) % 175.61/175.93 (step @p220 :rule beta-reduce :args ((= (_ @t174 @t1) @t171))) % 175.61/175.93 (step @p221 :rule beta-reduce :args ((= @t175 @t174))) % 175.61/175.93 (step @p222 :rule ho_cong :premises (@p221 @p117)) % 175.61/175.93 (step @p223 :rule trans :premises (@p222 @p220)) % 175.61/175.93 (step @p224 :rule nary_cong :premises (@p140 @p223 @p219) :args ((and @t165 (_ @t175 @t1) (_ @t173 @t1)))) % 175.61/175.93 (step @p225 :rule trans :premises (@p224 @p215)) % 175.61/175.93 (step @p226 :rule refl :args (@t150)) % 175.61/175.93 (step @p227 :rule refl :args (@t21)) % 175.61/175.93 (step @p228 :rule cong :premises (@p227 @p226) :args ((= @t21 @t150))) % 175.61/175.93 (step @p229 :rule symm :premises (@p228)) % 175.61/175.93 (step @p230 :rule eq_resolve :premises (@p227 @p229)) % 175.61/175.93 (step @p231 :rule cong :premises (@p142 @p230) :args (@t176)) % 175.61/175.93 (step @p232 :rule cong :premises (@p231) :args (@t177)) % 175.61/175.93 (step @p233 :rule nary_cong :premises (@p149 @p232) :args (@t178)) % 175.61/175.93 (step @p234 :rule cong :premises (@p233) :args ((forall @t24 @t178))) % 175.61/175.93 (step @p235 :rule bool-and-de-morgan :args (@t22 @t176 true)) % 175.61/175.93 (step @p236 :rule cong :premises (@p235) :args (@t180)) % 175.61/175.93 (step @p237 :rule trans :premises (@p236 @p234)) % 175.61/175.93 (step @p238 :rule cong :premises (@p237) :args (@t181)) % 175.61/175.93 (step @p239 :rule exists-elim :args ((= (exists @t24 @t179) @t181))) % 175.61/175.93 (step @p240 :rule trans :premises (@p239 @p238)) % 175.61/175.93 (step @p241 :rule eq-symm :args (@t21 @t1)) % 175.61/175.93 (step @p242 :rule refl :args (@t22)) % 175.61/175.93 (step @p243 :rule nary_cong :premises (@p242 @p241) :args (@t23)) % 175.61/175.93 (step @p244 :rule cong :premises (@p243) :args (@t25)) % 175.61/175.93 (step @p245 :rule trans :premises (@p244 @p240)) % 175.61/175.93 (step @p246 :rule cong :premises (@p245) :args (@t27)) % 175.61/175.93 (step @p247 :rule cong :premises (@p246) :args (@t28)) % 175.61/175.93 (step @p248 :rule trans :premises (@p4 @p247)) % 175.61/175.93 (step @p249 :rule ho_cong :premises (@p248 @p131)) % 175.61/175.93 (step @p250 :rule ho_cong :premises (@p249 @p117)) % 175.61/175.93 (step @p251 :rule refl :args (@t146)) % 175.61/175.93 (step @p252 :rule refl :args (@t182)) % 175.61/175.93 (step @p253 :rule cong :premises (@p252 @p251) :args ((= @t182 @t146))) % 175.61/175.93 (step @p254 :rule symm :premises (@p253)) % 175.61/175.93 (step @p255 :rule eq_resolve :premises (@p252 @p254)) % 175.61/175.93 (step @p256 :rule refl :args (@t46)) % 175.61/175.93 (step @p257 :rule cong :premises (@p256 @p255) :args (@t183)) % 175.61/175.93 (step @p258 :rule cong :premises (@p257) :args (@t184)) % 175.61/175.93 (step @p259 :rule refl :args (@t148)) % 175.61/175.93 (step @p260 :rule refl :args (@t185)) % 175.61/175.93 (step @p261 :rule cong :premises (@p260 @p259) :args ((= @t185 @t148))) % 175.61/175.93 (step @p262 :rule symm :premises (@p261)) % 175.61/175.93 (step @p263 :rule eq_resolve :premises (@p260 @p262)) % 175.61/175.93 (step @p264 :rule refl :args (@t52)) % 175.61/175.93 (step @p265 :rule cong :premises (@p264 @p263) :args (@t186)) % 175.61/175.93 (step @p266 :rule cong :premises (@p265) :args (@t187)) % 175.61/175.93 (step @p267 :rule nary_cong :premises (@p266 @p258) :args ((and @t187 @t184))) % 175.61/175.93 (step @p268 :rule alpha_equiv :args (@t170 @t188 @t189)) % 175.61/175.93 (step @p269 :rule alpha_equiv :args (@t191 @t188 (@list @t52))) % 175.61/175.93 (step @p270 :rule nary_cong :premises (@p269 @p268) :args (@t192)) % 175.61/175.93 (step @p271 :rule quant-miniscope-and :args ((= (forall @t26 (and @t190 @t169)) @t192))) % 175.61/175.93 (step @p272 :rule trans :premises (@p271 @p270)) % 175.61/175.93 (step @p273 :rule trans :premises (@p272 @p267)) % 175.61/175.93 (step @p274 :rule eq-symm :args (@t37 @t11)) % 175.61/175.93 (step @p275 :rule nary_cong :premises (@p274 @p167) :args (@t38)) % 175.61/175.93 (step @p276 :rule cong :premises (@p275) :args (@t39)) % 175.61/175.93 (step @p277 :rule trans :premises (@p276 @p273)) % 175.61/175.93 (step @p278 :rule cong :premises (@p277) :args (@t40)) % 175.61/175.93 (step @p279 :rule trans :premises (@p7 @p278)) % 175.61/175.93 (step @p280 :rule ho_cong :premises (@p279 @p131)) % 175.61/175.93 (step @p281 :rule ho_cong :premises (@p280 @p117)) % 175.61/175.93 (step @p282 :rule nary_cong :premises (@p208 @p281 @p250) :args (@t42)) % 175.61/175.93 (step @p283 :rule trans :premises (@p282 @p225)) % 175.61/175.93 (step @p284 :rule cong :premises (@p283) :args (@t43)) % 175.61/175.93 (step @p285 :rule trans :premises (@p8 @p284)) % 175.61/175.93 (step @p286 :rule ho_cong :premises (@p285 @p131)) % 175.61/175.93 (step @p287 :rule ho_cong :premises (@p286 @p117)) % 175.61/175.93 (step @p288 :rule cong :premises (@p287 @p214) :args (@t3)) % 175.61/175.93 (step @p289 :rule cong :premises (@p288) :args (@t5)) % 175.61/175.93 (step @p290 :rule cong :premises (@p289) :args (@t6)) % 175.61/175.93 (step @p291 :rule trans :premises (@p290 @p130)) % 175.61/175.93 (step @p292 :rule trans :premises (@p291 @p114 @p113)) % 175.61/175.93 (step @p293 :rule eq_resolve :premises (@p1 @p292)) % 175.61/175.93 (step @p294 :rule skolemize :premises (@p293)) % 175.61/175.93 (step @p295 :rule cnf_equiv_neg1 :args (@t193)) % 175.61/175.93 (step @p296 :rule reordering :premises (@p295) :args ((or @t118 @t121 @t193))) % 175.61/175.93 (step @p297 :rule chain_m_resolution :premises (@p296 @p294 @p91 @p89) :args (@t117 (@list true true true) (@list @t193 @t121 @t118))) % 175.61/175.93 (step @p298 :rule alpha_equiv :args (@t69 @t188 @t189)) % 175.61/175.93 (step @p299 :rule equiv_elim1 :premises (@p298)) % 175.61/175.93 (step @p300 :rule reordering :premises (@p299) :args ((or @t120 @t194))) % 175.61/175.93 (step @p301 :rule cnf_and_neg :args (@t121)) % 175.61/175.93 (step @p302 :rule cnf_and_neg :args (@t118)) % 175.61/175.93 (step @p303 :rule cnf_equiv_neg2 :args (@t193)) % 175.61/175.93 (step @p304 :rule chain_m_resolution :premises (@p303 @p294 @p302 @p301 @p300) :args ((or (not @t117) @t194 @t115 @t196 @t195) (@list true false false false) (@list @t193 @t118 @t121 @t120))) % 175.61/175.93 (step @p305 :rule refl :args (@t198)) % 175.61/175.93 (step @p306 :rule bool-double-not-elim :args (@t86)) % 175.61/175.93 (step @p307 :rule nary_cong :premises (@p306 @p305) :args ((or (not @t195) @t198))) % 175.61/175.93 (assume-push @p485 @t195) % 175.61/175.93 (step @p309 :rule skolemize :premises (@p485)) % 175.61/175.93 (step-pop @p486 :rule scope :premises (@p309)) % 175.61/175.93 (step @p310 :rule process_scope :premises (@p486) :args (@t198)) % 175.61/175.93 (step @p312 :rule implies_elim :premises (@p310)) % 175.61/175.93 (step @p313 :rule eq_resolve :premises (@p312 @p307)) % 175.61/175.93 (step @p314 :rule instantiate :premises (@p297) :args ((@list @t87 @t105 @t87))) % 175.61/175.93 (assume-push @p487 @t91) % 175.61/175.93 (assume-push @p488 @t110) % 175.61/175.93 (assume-push @p489 @t107) % 175.61/175.93 (assume-push @p490 @t201) % 175.61/175.93 (assume-push @p491 @t91) % 175.61/175.93 (assume-push @p492 @t107) % 175.61/175.93 (assume-push @p493 @t201) % 175.61/175.93 (assume-push @p494 @t110) % 175.61/175.93 (step @p323 :rule refl :args (@t87)) % 175.61/175.93 (step @p324 :rule symm :premises (@p488)) % 175.61/175.93 (step @p325 :rule refl :args (@t67)) % 175.61/175.93 (step @p326 :rule cong :premises (@p325 @p324) :args (@t199)) % 175.61/175.93 (step @p327 :rule cong :premises (@p326 @p323) :args (@t200)) % 175.61/175.93 (step @p328 :rule refl :args (@t89)) % 175.61/175.93 (step @p329 :rule cong :premises (@p328 @p489) :args (@t90)) % 175.61/175.93 (step @p330 :rule trans :premises (@p487 @p329 @p314 @p327)) % 175.61/175.93 (step-pop @p495 :rule scope :premises (@p330)) % 175.61/175.93 (step-pop @p496 :rule scope :premises (@p495)) % 175.61/175.93 (step-pop @p497 :rule scope :premises (@p496)) % 175.61/175.93 (step-pop @p498 :rule scope :premises (@p497)) % 175.61/175.93 (step @p331 :rule process_scope :premises (@p498) :args (@t197)) % 175.61/175.93 (step @p336 :rule and_intro :premises (@p487 @p489 @p314 @p488)) % 175.61/175.93 (step @p337 :rule modus_ponens :premises (@p336 @p331)) % 175.61/175.93 (step-pop @p499 :rule scope :premises (@p337)) % 175.61/175.93 (step-pop @p500 :rule scope :premises (@p499)) % 175.61/175.93 (step-pop @p501 :rule scope :premises (@p500)) % 175.61/175.93 (step-pop @p502 :rule scope :premises (@p501)) % 175.61/175.93 (step @p338 :rule process_scope :premises (@p502) :args (@t197)) % 175.61/175.93 (step @p343 :rule implies_elim :premises (@p338)) % 175.61/175.93 (step @p344 :rule cnf_and_neg :args (@t202)) % 175.61/175.93 (step @p345 :rule resolution :premises (@p344 @p343) :args (true @t202)) % 175.61/175.93 (step @p346 :rule reordering :premises (@p345) :args ((or @t197 (not @t91) @t111 @t108 (not @t201)))) % 175.61/175.93 (step @p347 :rule chain_m_resolution :premises (@p346 @p314 @p313 @p304 @p297 @p87 @p74 @p69 @p64 @p58 @p52 @p43 @p34 @p29 @p24) :args ((or @t194 @t196) (@list false true true false false true false false false true true true true false) (@list @t201 @t197 @t86 @t117 @t92 @t114 @t107 @t110 @t101 @t112 @t103 @t98 @t96 @t91))) % 175.61/175.93 (step @p348 :rule cnf_and_pos :args (@t121 1)) % 175.61/175.93 (step @p349 :rule reordering :premises (@p348) :args ((or @t73 @t122))) % 175.61/175.93 (step @p350 :rule refl :args (@t203)) % 175.61/175.93 (step @p351 :rule bool-double-not-elim :args (@t73)) % 175.61/175.93 (step @p352 :rule nary_cong :premises (@p351 @p350) :args ((or (not @t196) @t203))) % 175.61/175.93 (step @p353 :rule bool-double-not-elim :args (@t203)) % 175.61/175.93 (step @p354 :rule refl :args (@t196)) % 175.61/175.93 (step @p355 :rule cong :premises (@p354 @p353) :args ((=> @t196 @t204))) % 175.61/175.93 (assume-push @p503 @t196) % 175.61/175.93 (step @p357 :rule skolemize :premises (@p503)) % 175.61/175.93 (step-pop @p504 :rule scope :premises (@p357)) % 175.61/175.93 (step @p358 :rule process_scope :premises (@p504) :args (@t204)) % 175.61/175.93 (step @p360 :rule eq_resolve :premises (@p358 @p355)) % 175.61/175.93 (step @p361 :rule implies_elim :premises (@p360)) % 175.61/175.93 (step @p362 :rule eq_resolve :premises (@p361 @p352)) % 175.61/175.93 (assume-push @p505 @t203) % 175.61/175.93 (step @p364 :rule instantiate :premises (@p505) :args (@t81)) % 175.61/175.93 (step-pop @p506 :rule scope :premises (@p364)) % 175.61/175.93 (step @p365 :rule process_scope :premises (@p506) :args (@t210)) % 175.61/175.93 (step @p367 :rule implies_elim :premises (@p365)) % 175.61/175.93 (step @p368 :rule cnf_and_pos :args (@t118 2)) % 175.61/175.93 (step @p369 :rule reordering :premises (@p368) :args ((or @t92 @t119))) % 175.61/175.93 (assume-push @p507 @t92) % 175.61/175.93 (step @p371 :rule instantiate :premises (@p507) :args (@t75)) % 175.61/175.93 (step-pop @p508 :rule scope :premises (@p371)) % 175.61/175.93 (step @p372 :rule process_scope :premises (@p508) :args (@t211)) % 175.61/175.93 (step @p374 :rule implies_elim :premises (@p372)) % 175.61/175.93 (assume-push @p509 @t92) % 175.61/175.93 (step @p376 :rule instantiate :premises (@p509) :args (@t81)) % 175.61/175.93 (step-pop @p510 :rule scope :premises (@p376)) % 175.61/175.93 (step @p377 :rule process_scope :premises (@p510) :args (@t213)) % 175.61/175.93 (step @p379 :rule implies_elim :premises (@p377)) % 175.61/175.93 (step @p380 :rule refl :args (@t208)) % 175.61/175.93 (step @p381 :rule bool-double-not-elim :args (@t79)) % 175.61/175.93 (step @p382 :rule nary_cong :premises (@p381 @p380) :args ((or (not @t211) @t208))) % 175.61/175.93 (step @p383 :rule bool-double-not-elim :args (@t208)) % 175.61/175.93 (step @p384 :rule refl :args (@t211)) % 175.61/175.93 (step @p385 :rule cong :premises (@p384 @p383) :args ((=> @t211 @t214))) % 175.61/175.93 (assume-push @p511 @t211) % 175.61/175.93 (step @p387 :rule skolemize :premises (@p511)) % 175.61/175.93 (step-pop @p512 :rule scope :premises (@p387)) % 175.61/175.93 (step @p388 :rule process_scope :premises (@p512) :args (@t214)) % 175.61/175.93 (step @p390 :rule eq_resolve :premises (@p388 @p385)) % 175.61/175.93 (step @p391 :rule implies_elim :premises (@p390)) % 175.61/175.93 (step @p392 :rule eq_resolve :premises (@p391 @p382)) % 175.61/175.93 (step @p393 :rule refl :args (@t217)) % 175.61/175.93 (step @p394 :rule bool-double-not-elim :args (@t212)) % 175.61/175.93 (step @p395 :rule nary_cong :premises (@p394 @p393) :args ((or (not @t213) @t217))) % 175.61/175.93 (step @p396 :rule bool-double-not-elim :args (@t217)) % 175.61/175.93 (step @p397 :rule refl :args (@t213)) % 175.61/175.93 (step @p398 :rule cong :premises (@p397 @p396) :args ((=> @t213 @t219))) % 175.61/175.93 (assume-push @p513 @t213) % 175.61/175.93 (step @p400 :rule skolemize :premises (@p513)) % 175.61/175.93 (step-pop @p514 :rule scope :premises (@p400)) % 175.61/175.93 (step @p401 :rule process_scope :premises (@p514) :args (@t219)) % 175.61/175.93 (step @p403 :rule eq_resolve :premises (@p401 @p398)) % 175.61/175.93 (step @p404 :rule implies_elim :premises (@p403)) % 175.61/175.93 (step @p405 :rule eq_resolve :premises (@p404 @p395)) % 175.61/175.93 (step @p406 :rule cnf_or_pos :args (@t210)) % 175.61/175.93 (step @p407 :rule reordering :premises (@p406) :args ((or @t209 @t206 (not @t210)))) % 175.61/175.93 (step @p408 :rule instantiate :premises (@p297) :args ((@list @t74 @t80 @t215))) % 175.61/175.93 (step @p409 :rule instantiate :premises (@p297) :args ((@list @t80 @t66 @t215))) % 175.61/175.93 (assume-push @p515 @t77) % 175.61/175.93 (assume-push @p516 @t208) % 175.61/175.93 (assume-push @p517 @t84) % 175.61/175.93 (assume-push @p518 @t217) % 175.61/175.93 (assume-push @p519 @t221) % 175.61/175.93 (assume-push @p520 @t224) % 175.61/175.93 (assume-push @p521 @t84) % 175.61/175.93 (assume-push @p522 @t224) % 175.61/175.93 (assume-push @p523 @t217) % 175.61/175.93 (assume-push @p524 @t221) % 175.61/175.93 (assume-push @p525 @t208) % 175.61/175.93 (assume-push @p526 @t77) % 175.61/175.93 (step @p422 :rule symm :premises (@p515)) % 175.61/175.93 (step @p423 :rule symm :premises (@p518)) % 175.61/175.93 (step @p424 :rule refl :args (@t76)) % 175.61/175.93 (step @p425 :rule cong :premises (@p424 @p423) :args (@t220)) % 175.61/175.93 (step @p426 :rule symm :premises (@p408)) % 175.61/175.93 (step @p427 :rule refl :args (@t215)) % 175.61/175.93 (step @p325 :rule refl :args (@t67)) % 175.61/175.93 (step @p428 :rule cong :premises (@p325 @p516) :args (@t85)) % 175.61/175.93 (step @p429 :rule cong :premises (@p428 @p427) :args (@t222)) % 175.61/175.93 (step @p430 :rule trans :premises (@p429 @p426 @p425 @p422)) % 175.61/175.93 (step @p431 :rule refl :args (@t82)) % 175.61/175.93 (step @p432 :rule cong :premises (@p431 @p430) :args (@t223)) % 175.61/175.93 (step @p433 :rule symm :premises (@p409)) % 175.61/175.93 (step @p434 :rule cong :premises (@p325 @p517) :args (@t82)) % 175.61/175.93 (step @p435 :rule cong :premises (@p434 @p427) :args (@t216)) % 175.61/175.93 (step @p436 :rule trans :premises (@p518 @p435 @p433 @p432)) % 175.61/175.93 (step-pop @p527 :rule scope :premises (@p436)) % 175.61/175.93 (step-pop @p528 :rule scope :premises (@p527)) % 175.61/175.93 (step-pop @p529 :rule scope :premises (@p528)) % 175.61/175.93 (step-pop @p530 :rule scope :premises (@p529)) % 175.61/175.93 (step-pop @p531 :rule scope :premises (@p530)) % 175.61/175.93 (step-pop @p532 :rule scope :premises (@p531)) % 175.61/175.93 (step @p437 :rule process_scope :premises (@p532) :args (@t205)) % 175.61/175.93 (step @p444 :rule and_intro :premises (@p517 @p409 @p518 @p408 @p516 @p515)) % 175.61/175.93 (step @p445 :rule modus_ponens :premises (@p444 @p437)) % 175.61/175.93 (step-pop @p533 :rule scope :premises (@p445)) % 175.61/175.93 (step-pop @p534 :rule scope :premises (@p533)) % 175.61/175.93 (step-pop @p535 :rule scope :premises (@p534)) % 175.61/175.93 (step-pop @p536 :rule scope :premises (@p535)) % 175.61/175.93 (step-pop @p537 :rule scope :premises (@p536)) % 175.61/175.93 (step-pop @p538 :rule scope :premises (@p537)) % 175.61/175.93 (step @p446 :rule process_scope :premises (@p538) :args (@t205)) % 175.61/175.93 (step @p453 :rule implies_elim :premises (@p446)) % 175.61/175.93 (step @p454 :rule cnf_and_neg :args (@t225)) % 175.61/175.93 (step @p455 :rule resolution :premises (@p454 @p453) :args (true @t225)) % 175.61/175.93 (step @p456 :rule reordering :premises (@p455) :args ((or (not @t77) @t209 (not @t84) @t205 @t218 (not @t221) (not @t224)))) % 175.61/175.93 (step @p457 :rule chain_m_resolution :premises (@p456 @p409 @p408 @p407 @p405 @p392 @p379 @p374 @p369 @p367 @p296 @p294 @p362 @p349 @p347 @p19 @p14) :args (@t194 (@list false false true false false true true false false false true false true true false false) (@list @t224 @t221 @t205 @t217 @t208 @t212 @t79 @t92 @t210 @t118 @t193 @t203 @t121 @t73 @t84 @t77))) % 175.61/175.94 (step @p458 :rule equiv_elim2 :premises (@p298)) % 175.61/175.94 (step @p459 :rule chain_m_resolution :premises (@p458 @p457) :args ((not @t120) @t226 @t227)) % 175.61/175.94 (step @p460 :rule cnf_and_pos :args (@t118 1)) % 175.61/175.94 (step @p461 :rule reordering :premises (@p460) :args ((or @t69 @t119))) % 175.61/175.94 (step @p462 :rule chain_m_resolution :premises (@p461 @p457) :args (@t119 @t226 @t227)) % 175.61/175.94 (step @p463 :rule chain_m_resolution :premises (@p296 @p462 @p294) :args (@t121 (@list true true) (@list @t118 @t193))) % 175.61/175.94 (step @p464 :rule cnf_and_pos :args (@t121 3)) % 175.61/175.94 (step @p465 :rule reordering :premises (@p464) :args ((or @t120 @t122))) % 175.61/175.94 (step @p466 false :rule chain_m_resolution :premises (@p465 @p463 @p459) :args (false (@list false true) (@list @t121 @t120))) % 175.61/175.94 ) % 175.61/175.94 % SZS output end Proof % 175.61/175.94 % cvc5 exiting %------------------------------------------------------------------------------