%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG272^5 : 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 : n014.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 169.81s 170.85s % Output : Proof 169.81s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG272^5 : TPTP v9.2.1. Bugfixed v5.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n014.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Wed Jun 3 01:57:13 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 169.81/170.85 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 169.81/170.85 --- 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... % 169.81/170.85 --- 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... % 169.81/170.85 --- Run --ho-elim --full-saturate-quant at 18s... % 169.81/170.85 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 169.81/170.85 % SZS status Theorem % 169.81/170.85 % SZS output start Proof % 169.81/170.85 ( % 169.81/170.85 (declare-sort tptp.g 0) % 169.81/170.85 (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))))))))))) % 169.81/170.85 (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)))))))))) % 169.81/170.85 (define tptp.cGRP_LEFT_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) (= (_ (_ _let_4 _let_3) _let_2) _let_1))))))))) % 169.81/170.85 (define tptp.cGRP_LEFT_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_2) _let_1) _let_1))))))) % 169.81/170.85 (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)))))))) % 169.81/170.85 (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)))))) % 169.81/170.85 (define tptp.cGROUP2 () (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_LEFT_UNIT _let_2) _let_1) (_ (_ tptp.cGRP_LEFT_INVERSE _let_2) _let_1)))))) % 169.81/170.85 (define @t1 () (@var "Xe" tptp.g)) % 169.81/170.85 (define @t2 () (@var "Xf" (-> tptp.g tptp.g tptp.g))) % 169.81/170.85 (define @t3 () (= (_ (_ tptp.cGROUP1 @t2) @t1) (_ (_ tptp.cGROUP2 @t2) @t1))) % 169.81/170.85 (define @t4 () (@list @t2 @t1)) % 169.81/170.85 (define @t5 () (forall @t4 @t3)) % 169.81/170.85 (define @t6 () (not @t5)) % 169.81/170.85 (define @t7 () (@var "Xc" tptp.g)) % 169.81/170.85 (define @t8 () (@var "Xb" tptp.g)) % 169.81/170.85 (define @t9 () (_ @t2 @t8)) % 169.81/170.85 (define @t10 () (_ @t9 @t7)) % 169.81/170.85 (define @t11 () (@var "Xa" tptp.g)) % 169.81/170.85 (define @t12 () (_ @t2 @t11)) % 169.81/170.85 (define @t13 () (_ @t12 @t10)) % 169.81/170.85 (define @t14 () (_ @t12 @t8)) % 169.81/170.85 (define @t15 () (_ (_ @t2 @t14) @t7)) % 169.81/170.85 (define @t16 () (= @t15 @t13)) % 169.81/170.85 (define @t17 () (@list @t11 @t8 @t7)) % 169.81/170.85 (define @t18 () (forall @t17 @t16)) % 169.81/170.85 (define @t19 () (@list @t2)) % 169.81/170.85 (define @t20 () (lambda @t19 @t18)) % 169.81/170.85 (define @t21 () (_ @t9 @t11)) % 169.81/170.85 (define @t22 () (= @t21 @t1)) % 169.81/170.85 (define @t23 () (= @t14 @t1)) % 169.81/170.85 (define @t24 () (and @t23 @t22)) % 169.81/170.85 (define @t25 () (@list @t8)) % 169.81/170.85 (define @t26 () (exists @t25 @t24)) % 169.81/170.85 (define @t27 () (@list @t11)) % 169.81/170.85 (define @t28 () (forall @t27 @t26)) % 169.81/170.85 (define @t29 () (lambda @t4 @t28)) % 169.81/170.85 (define @t30 () (exists @t25 @t22)) % 169.81/170.85 (define @t31 () (forall @t27 @t30)) % 169.81/170.85 (define @t32 () (lambda @t4 @t31)) % 169.81/170.85 (define @t33 () (_ @t2 @t1)) % 169.81/170.85 (define @t34 () (_ @t33 @t11)) % 169.81/170.85 (define @t35 () (= @t34 @t11)) % 169.81/170.85 (define @t36 () (forall @t27 @t35)) % 169.81/170.85 (define @t37 () (lambda @t4 @t36)) % 169.81/170.85 (define @t38 () (_ @t12 @t1)) % 169.81/170.85 (define @t39 () (and @t35 (= @t38 @t11))) % 169.81/170.85 (define @t40 () (forall @t27 @t39)) % 169.81/170.85 (define @t41 () (lambda @t4 @t40)) % 169.81/170.85 (define @t42 () (_ tptp.cGRP_ASSOC @t2)) % 169.81/170.85 (define @t43 () (and @t42 (_ (_ tptp.cGRP_UNIT @t2) @t1) (_ (_ tptp.cGRP_INVERSE @t2) @t1))) % 169.81/170.85 (define @t44 () (lambda @t4 @t43)) % 169.81/170.85 (define @t45 () (and @t42 (_ (_ tptp.cGRP_LEFT_UNIT @t2) @t1) (_ (_ tptp.cGRP_LEFT_INVERSE @t2) @t1))) % 169.81/170.85 (define @t46 () (lambda @t4 @t45)) % 169.81/170.85 (define @t47 () (@var "BOUND_VARIABLE_7543" tptp.g)) % 169.81/170.85 (define @t48 () (@var "BOUND_VARIABLE_7666" (@ho-elim-sort (-> tptp.g tptp.g tptp.g)))) % 169.81/170.85 (define @t49 () (@const 0 (-> (@ho-elim-sort (-> tptp.g tptp.g tptp.g)) tptp.g (@ho-elim-sort (-> tptp.g tptp.g))))) % 169.81/170.85 (define @t50 () (@const 1 (-> (@ho-elim-sort (-> tptp.g tptp.g)) tptp.g tptp.g))) % 169.81/170.85 (define @t51 () (@list @t47)) % 169.81/170.85 (define @t52 () (forall @t51 (= @t47 (_ @t50 (_ @t49 @t48 @t47) @t1)))) % 169.81/170.85 (define @t53 () (@var "BOUND_VARIABLE_7537" tptp.g)) % 169.81/170.85 (define @t54 () (_ @t49 @t48 @t1)) % 169.81/170.85 (define @t55 () (@list @t53)) % 169.81/170.85 (define @t56 () (forall @t55 (= @t53 (_ @t50 @t54 @t53)))) % 169.81/170.85 (define @t57 () (_ @t49 @t48 @t8)) % 169.81/170.85 (define @t58 () (not (= @t1 (_ @t50 @t57 @t11)))) % 169.81/170.85 (define @t59 () (_ @t49 @t48 @t11)) % 169.81/170.85 (define @t60 () (_ @t50 @t59 @t8)) % 169.81/170.85 (define @t61 () (_ @t50 (_ @t49 @t48 @t60) @t7)) % 169.81/170.85 (define @t62 () (_ @t50 @t59 (_ @t50 @t57 @t7))) % 169.81/170.85 (define @t63 () (forall @t17 (= @t62 @t61))) % 169.81/170.85 (define @t64 () (forall @t27 (not (forall @t25 @t58)))) % 169.81/170.85 (define @t65 () (forall @t27 (= @t11 (_ @t50 @t54 @t11)))) % 169.81/170.85 (define @t66 () (@list @t48 @t1)) % 169.81/170.85 (define @t67 () (forall @t66 (= (and @t63 @t65 @t64) (and @t63 (forall @t27 (not (forall @t25 (or (not (= @t1 @t60)) @t58)))) @t56 @t52)))) % 169.81/170.85 (define @t68 () (@quantifiers_skolemize @t67 1)) % 169.81/170.85 (define @t69 () (@quantifiers_skolemize @t67 0)) % 169.81/170.85 (define @t70 () (_ @t49 @t69 @t68)) % 169.81/170.85 (define @t71 () (forall @t27 (= @t11 (_ @t50 @t70 @t11)))) % 169.81/170.85 (define @t72 () (_ @t49 @t69 @t8)) % 169.81/170.85 (define @t73 () (not (= @t68 (_ @t50 @t72 @t11)))) % 169.81/170.85 (define @t74 () (_ @t49 @t69 @t11)) % 169.81/170.85 (define @t75 () (_ @t50 @t74 @t8)) % 169.81/170.85 (define @t76 () (forall @t27 (not (forall @t25 (or (not (= @t68 @t75)) @t73))))) % 169.81/170.85 (define @t77 () (@quantifiers_skolemize @t76 0)) % 169.81/170.85 (define @t78 () (not (= @t68 (_ @t50 @t72 @t77)))) % 169.81/170.85 (define @t79 () (forall @t25 @t78)) % 169.81/170.85 (define @t80 () (@quantifiers_skolemize @t79 0)) % 169.81/170.85 (define @t81 () (@list @t80)) % 169.81/170.85 (define @t82 () (_ @t50 @t70 @t80)) % 169.81/170.85 (define @t83 () (= @t80 @t82)) % 169.81/170.85 (define @t84 () (forall @t51 (= @t47 (_ @t50 (_ @t49 @t69 @t47) @t68)))) % 169.81/170.85 (define @t85 () (@quantifiers_skolemize @t84 0)) % 169.81/170.85 (define @t86 () (@list @t85)) % 169.81/170.85 (define @t87 () (_ @t50 @t70 @t85)) % 169.81/170.85 (define @t88 () (= @t85 @t87)) % 169.81/170.85 (define @t89 () (forall @t27 (not (forall @t25 @t73)))) % 169.81/170.85 (define @t90 () (forall @t17 (= (_ @t50 @t74 (_ @t50 @t72 @t7)) (_ @t50 (_ @t49 @t69 @t75) @t7)))) % 169.81/170.85 (define @t91 () (and @t90 @t71 @t89)) % 169.81/170.85 (define @t92 () (not @t91)) % 169.81/170.85 (define @t93 () (forall @t55 (= @t53 (_ @t50 @t70 @t53)))) % 169.81/170.85 (define @t94 () (and @t90 @t76 @t93 @t84)) % 169.81/170.85 (define @t95 () (not @t94)) % 169.81/170.85 (define @t96 () (not (= @t60 @t1))) % 169.81/170.85 (define @t97 () (or @t96 @t58)) % 169.81/170.85 (define @t98 () (forall @t25 @t97)) % 169.81/170.85 (define @t99 () (not @t98)) % 169.81/170.85 (define @t100 () (forall @t27 @t99)) % 169.81/170.85 (define @t101 () (forall @t17 (= @t61 @t62))) % 169.81/170.85 (define @t102 () (and @t101 @t100 @t56 @t52)) % 169.81/170.85 (define @t103 () (and @t101 @t65 @t64)) % 169.81/170.85 (define @t104 () (forall @t66 (= @t102 @t103))) % 169.81/170.85 (define @t105 () (not @t104)) % 169.81/170.85 (define @t106 () (_ @t2 @t8 @t11)) % 169.81/170.85 (define @t107 () (not (= @t1 @t106))) % 169.81/170.85 (define @t108 () (forall @t27 (not (forall @t25 @t107)))) % 169.81/170.85 (define @t109 () (_ @t2 @t1 @t11)) % 169.81/170.85 (define @t110 () (forall @t27 (= @t11 @t109))) % 169.81/170.85 (define @t111 () (_ @t2 @t8 @t7)) % 169.81/170.85 (define @t112 () (_ @t2 @t11 @t111)) % 169.81/170.85 (define @t113 () (_ @t2 @t11 @t8)) % 169.81/170.85 (define @t114 () (_ @t2 @t113 @t7)) % 169.81/170.85 (define @t115 () (forall @t17 (= @t114 @t112))) % 169.81/170.85 (define @t116 () (and @t115 @t110 @t108)) % 169.81/170.85 (define @t117 () (_ @t2 @t47 @t1)) % 169.81/170.85 (define @t118 () (forall @t51 (= @t47 @t117))) % 169.81/170.85 (define @t119 () (_ @t2 @t1 @t53)) % 169.81/170.85 (define @t120 () (forall @t55 (= @t53 @t119))) % 169.81/170.85 (define @t121 () (forall @t27 (not (forall @t25 (or (not (= @t113 @t1)) @t107))))) % 169.81/170.85 (define @t122 () (and @t115 @t121 @t120 @t118)) % 169.81/170.85 (define @t123 () (@list @t1)) % 169.81/170.85 (define @t124 () (lambda @t123 @t122)) % 169.81/170.85 (define @t125 () (_ (lambda @t4 @t122) @t2)) % 169.81/170.85 (define @t126 () (lambda @t123 @t116)) % 169.81/170.85 (define @t127 () (_ (lambda @t4 @t116) @t2)) % 169.81/170.85 (define @t128 () (_ @t125 @t1)) % 169.81/170.85 (define @t129 () (_ @t127 @t1)) % 169.81/170.85 (define @t130 () (forall @t4 (= @t128 @t129))) % 169.81/170.85 (define @t131 () (lambda @t123 @t108)) % 169.81/170.85 (define @t132 () (_ (lambda @t4 @t108) @t2)) % 169.81/170.85 (define @t133 () (lambda @t123 @t110)) % 169.81/170.85 (define @t134 () (_ (lambda @t4 @t110) @t2)) % 169.81/170.85 (define @t135 () (_ (lambda @t19 @t115) @t2)) % 169.81/170.85 (define @t136 () (= @t1 @t21)) % 169.81/170.85 (define @t137 () (not @t136)) % 169.81/170.85 (define @t138 () (forall @t25 @t137)) % 169.81/170.85 (define @t139 () (not @t138)) % 169.81/170.85 (define @t140 () (= @t11 @t34)) % 169.81/170.85 (define @t141 () (forall @t27 @t140)) % 169.81/170.85 (define @t142 () (and @t120 @t118)) % 169.81/170.85 (define @t143 () (lambda @t123 @t121)) % 169.81/170.85 (define @t144 () (_ (lambda @t4 @t121) @t2)) % 169.81/170.85 (define @t145 () (lambda @t123 @t142)) % 169.81/170.85 (define @t146 () (_ (lambda @t4 @t142) @t2)) % 169.81/170.85 (define @t147 () (not @t23)) % 169.81/170.85 (define @t148 () (or @t147 @t137)) % 169.81/170.85 (define @t149 () (and @t23 @t136)) % 169.81/170.85 (define @t150 () (forall @t25 (not @t149))) % 169.81/170.85 (define @t151 () (not @t150)) % 169.81/170.85 (define @t152 () (_ (_ @t2 @t47) @t1)) % 169.81/170.85 (define @t153 () (= @t47 @t152)) % 169.81/170.85 (define @t154 () (forall @t51 @t153)) % 169.81/170.85 (define @t155 () (_ @t33 @t53)) % 169.81/170.85 (define @t156 () (= @t53 @t155)) % 169.81/170.85 (define @t157 () (forall @t55 @t156)) % 169.81/170.85 (define @t158 () (= @t11 @t38)) % 169.81/170.85 (define @t159 () (forall @t27 @t158)) % 169.81/170.85 (define @t160 () (@list @t11)) % 169.81/170.85 (define @t161 () (@list @t53)) % 169.81/170.85 (define @t162 () (and @t141 @t159)) % 169.81/170.85 (define @t163 () (= @t91 @t94)) % 169.81/170.85 (define @t164 () (@quantifiers_skolemize @t89 0)) % 169.81/170.85 (define @t165 () (not (= @t68 (_ @t50 @t72 @t164)))) % 169.81/170.85 (define @t166 () (_ @t49 @t69 @t164)) % 169.81/170.85 (define @t167 () (forall @t25 (or (not (= @t68 (_ @t50 @t166 @t8))) @t165))) % 169.81/170.85 (define @t168 () (not @t167)) % 169.81/170.85 (define @t169 () (@quantifiers_skolemize @t167 0)) % 169.81/170.85 (define @t170 () (= @t68 (_ @t50 (_ @t49 @t69 @t169) @t164))) % 169.81/170.85 (define @t171 () (not @t170)) % 169.81/170.85 (define @t172 () (or (not (= @t68 (_ @t50 @t166 @t169))) @t171)) % 169.81/170.85 (define @t173 () (not @t172)) % 169.81/170.85 (define @t174 () (forall @t25 @t165)) % 169.81/170.85 (define @t175 () (not @t89)) % 169.81/170.85 (define @t176 () (not (not @t174))) % 169.81/170.85 (define @t177 () (not @t71)) % 169.81/170.85 (define @t178 () (not @t84)) % 169.81/170.85 (define @t179 () (not @t76)) % 169.81/170.85 (define @t180 () (_ @t49 @t69 @t85)) % 169.81/170.85 (define @t181 () (forall @t25 (or (not (= @t68 (_ @t50 @t180 @t8))) (not (= @t68 (_ @t50 @t72 @t85)))))) % 169.81/170.85 (define @t182 () (not @t181)) % 169.81/170.85 (define @t183 () (= @t85 (_ @t50 @t180 @t68))) % 169.81/170.85 (define @t184 () (not @t183)) % 169.81/170.85 (define @t185 () (@quantifiers_skolemize @t181 0)) % 169.81/170.85 (define @t186 () (_ @t50 (_ @t49 @t69 @t185) @t85)) % 169.81/170.85 (define @t187 () (= @t68 @t186)) % 169.81/170.85 (define @t188 () (not @t187)) % 169.81/170.85 (define @t189 () (_ @t50 @t180 @t185)) % 169.81/170.85 (define @t190 () (= @t68 @t189)) % 169.81/170.85 (define @t191 () (not @t190)) % 169.81/170.85 (define @t192 () (or @t191 @t188)) % 169.81/170.85 (define @t193 () (not @t192)) % 169.81/170.85 (define @t194 () (_ @t50 @t180 @t186)) % 169.81/170.85 (define @t195 () (= @t194 (_ @t50 (_ @t49 @t69 @t189) @t85))) % 169.81/170.85 (define @t196 () (and @t88 @t190 @t187 @t195)) % 169.81/170.85 (define @t197 () (_ @t49 @t69 @t77)) % 169.81/170.85 (define @t198 () (_ @t50 @t197 @t80)) % 169.81/170.85 (define @t199 () (= @t198 (_ @t50 @t70 @t198))) % 169.81/170.85 (define @t200 () (forall @t25 (or (not (= @t68 (_ @t50 @t197 @t8))) @t78))) % 169.81/170.85 (define @t201 () (not (not @t200))) % 169.81/170.85 (define @t202 () (_ @t49 @t69 @t80)) % 169.81/170.85 (define @t203 () (_ @t50 @t202 @t77)) % 169.81/170.85 (define @t204 () (= @t68 @t203)) % 169.81/170.85 (define @t205 () (not @t204)) % 169.81/170.85 (define @t206 () (= @t68 @t198)) % 169.81/170.85 (define @t207 () (not @t206)) % 169.81/170.85 (define @t208 () (or @t207 @t205)) % 169.81/170.85 (define @t209 () (not @t79)) % 169.81/170.85 (define @t210 () (forall @t25 (not (= @t68 (_ @t50 @t72 @t80))))) % 169.81/170.85 (define @t211 () (not @t210)) % 169.81/170.85 (define @t212 () (not @t205)) % 169.81/170.85 (define @t213 () (@quantifiers_skolemize @t210 0)) % 169.81/170.85 (define @t214 () (_ @t49 @t69 @t213)) % 169.81/170.85 (define @t215 () (_ @t50 @t214 @t80)) % 169.81/170.85 (define @t216 () (= @t68 @t215)) % 169.81/170.85 (define @t217 () (not @t216)) % 169.81/170.85 (define @t218 () (not @t217)) % 169.81/170.85 (define @t219 () (_ @t50 @t202 @t198)) % 169.81/170.85 (define @t220 () (= @t219 (_ @t50 (_ @t49 @t69 @t203) @t80))) % 169.81/170.85 (define @t221 () (_ @t49 @t69 @t215)) % 169.81/170.85 (define @t222 () (_ @t50 @t221 @t198)) % 169.81/170.85 (define @t223 () (= (_ @t50 @t214 @t219) @t222)) % 169.81/170.85 (define @t224 () (and @t204 @t83 @t216 @t199 @t220 @t223)) % 169.81/170.85 (define @t225 () (@list true)) % 169.81/170.85 (define @t226 () (@list @t71)) % 169.81/170.85 (assume @p1 @t6) % 169.81/170.85 (assume @p2 true) % 169.81/170.85 (step @p3 (= tptp.cGRP_ASSOC @t20) :rule refl :args (@t20)) % 169.81/170.85 (step @p4 (= tptp.cGRP_INVERSE @t29) :rule refl :args (@t29)) % 169.81/170.85 (step @p5 (= tptp.cGRP_LEFT_INVERSE @t32) :rule refl :args (@t32)) % 169.81/170.85 (step @p6 (= tptp.cGRP_LEFT_UNIT @t37) :rule refl :args (@t37)) % 169.81/170.85 (step @p7 (= tptp.cGRP_UNIT @t41) :rule refl :args (@t41)) % 169.81/170.85 (step @p8 (= tptp.cGROUP1 @t44) :rule refl :args (@t44)) % 169.81/170.85 (step @p9 (= tptp.cGROUP2 @t46) :rule refl :args (@t46)) % 169.81/170.85 (assume-push @p466 @t71) % 169.81/170.85 (step @p11 :rule instantiate :premises (@p466) :args (@t81)) % 169.81/170.85 (step-pop @p467 :rule scope :premises (@p11)) % 169.81/170.85 (step @p12 :rule process_scope :premises (@p467) :args (@t83)) % 169.81/170.85 (step @p14 :rule implies_elim :premises (@p12)) % 169.81/170.85 (assume-push @p468 @t71) % 169.81/170.85 (step @p16 :rule instantiate :premises (@p468) :args (@t86)) % 169.81/170.85 (step-pop @p469 :rule scope :premises (@p16)) % 169.81/170.85 (step @p17 :rule process_scope :premises (@p469) :args (@t88)) % 169.81/170.85 (step @p19 :rule implies_elim :premises (@p17)) % 169.81/170.85 (step @p20 :rule cnf_and_pos :args (@t91 0)) % 169.81/170.85 (step @p21 :rule reordering :premises (@p20) :args ((or @t90 @t92))) % 169.81/170.85 (step @p22 :rule cnf_and_pos :args (@t94 0)) % 169.81/170.85 (step @p23 :rule reordering :premises (@p22) :args ((or @t90 @t95))) % 169.81/170.85 (step @p24 :rule refl :args (@t52)) % 169.81/170.85 (step @p25 :rule refl :args (@t56)) % 169.81/170.85 (step @p26 :rule refl :args (@t58)) % 169.81/170.85 (step @p27 :rule eq-symm :args (@t60 @t1)) % 169.81/170.85 (step @p28 :rule cong :premises (@p27) :args (@t96)) % 169.81/170.85 (step @p29 :rule nary_cong :premises (@p28 @p26) :args (@t97)) % 169.81/170.85 (step @p30 :rule cong :premises (@p29) :args (@t98)) % 169.81/170.85 (step @p31 :rule cong :premises (@p30) :args (@t99)) % 169.81/170.85 (step @p32 :rule cong :premises (@p31) :args (@t100)) % 169.81/170.85 (step @p33 :rule eq-symm :args (@t61 @t62)) % 169.81/170.85 (step @p34 :rule cong :premises (@p33) :args (@t101)) % 169.81/170.85 (step @p35 :rule nary_cong :premises (@p34 @p32 @p25 @p24) :args (@t102)) % 169.81/170.85 (step @p36 :rule refl :args (@t64)) % 169.81/170.85 (step @p37 :rule refl :args (@t65)) % 169.81/170.85 (step @p38 :rule nary_cong :premises (@p34 @p37 @p36) :args (@t103)) % 169.81/170.85 (step @p39 :rule cong :premises (@p38 @p35) :args ((= @t103 @t102))) % 169.81/170.85 (step @p40 :rule eq-symm :args (@t102 @t103)) % 169.81/170.85 (step @p41 :rule trans :premises (@p40 @p39)) % 169.81/170.85 (step @p42 :rule cong :premises (@p41) :args (@t104)) % 169.81/170.85 (step @p43 :rule cong :premises (@p42) :args (@t105)) % 169.81/170.85 ; WARNING: add trust step for TRUST % 169.81/170.85 ; trust TRUST PREPROCESS_HO_ELIM % 169.81/170.85 (step @p44 :rule trust :premises () :args ((= (not (forall @t4 (= @t122 @t116))) @t105))) % 169.81/170.85 (step @p45 :rule eq-symm :args (@t116 @t122)) % 169.81/170.85 (step @p46 :rule beta-reduce :args ((= (_ @t124 @t1) @t122))) % 169.81/170.85 (step @p47 :rule refl :args (@t1)) % 169.81/170.85 (step @p48 :rule beta-reduce :args ((= @t125 @t124))) % 169.81/170.85 (step @p49 :rule ho_cong :premises (@p48 @p47)) % 169.81/170.85 (step @p50 :rule trans :premises (@p49 @p46)) % 169.81/170.85 (step @p51 :rule beta-reduce :args ((= (_ @t126 @t1) @t116))) % 169.81/170.85 (step @p52 :rule beta-reduce :args ((= @t127 @t126))) % 169.81/170.85 (step @p53 :rule ho_cong :premises (@p52 @p47)) % 169.81/170.85 (step @p54 :rule trans :premises (@p53 @p51)) % 169.81/170.85 (step @p55 :rule cong :premises (@p54 @p50) :args ((= @t129 @t128))) % 169.81/170.85 (step @p56 :rule trans :premises (@p55 @p45)) % 169.81/170.85 (step @p57 :rule eq-symm :args (@t128 @t129)) % 169.81/170.85 (step @p58 :rule trans :premises (@p57 @p56)) % 169.81/170.85 (step @p59 :rule cong :premises (@p58) :args (@t130)) % 169.81/170.85 (step @p60 :rule cong :premises (@p59) :args ((not @t130))) % 169.81/170.85 (step @p61 :rule refl :args (@t2)) % 169.81/170.85 (step @p62 :rule beta-reduce :args ((= (_ @t131 @t1) @t108))) % 169.81/170.85 (step @p63 :rule beta-reduce :args ((= @t132 @t131))) % 169.81/170.85 (step @p64 :rule ho_cong :premises (@p63 @p47)) % 169.81/170.85 (step @p65 :rule trans :premises (@p64 @p62)) % 169.81/170.85 (step @p66 :rule beta-reduce :args ((= (_ @t133 @t1) @t110))) % 169.81/170.85 (step @p67 :rule beta-reduce :args ((= @t134 @t133))) % 169.81/170.85 (step @p68 :rule ho_cong :premises (@p67 @p47)) % 169.81/170.85 (step @p69 :rule trans :premises (@p68 @p66)) % 169.81/170.85 (step @p70 :rule beta-reduce :args ((= @t135 @t115))) % 169.81/170.85 (step @p71 :rule nary_cong :premises (@p70 @p69 @p65) :args ((and @t135 (_ @t134 @t1) (_ @t132 @t1)))) % 169.81/170.85 (step @p72 :rule refl :args (@t106)) % 169.81/170.85 (step @p73 :rule refl :args (@t21)) % 169.81/170.85 (step @p74 :rule cong :premises (@p73 @p72) :args ((= @t21 @t106))) % 169.81/170.85 (step @p75 :rule symm :premises (@p74)) % 169.81/170.85 (step @p76 :rule eq_resolve :premises (@p73 @p75)) % 169.81/170.85 (step @p77 :rule refl :args (@t1)) % 169.81/170.85 (step @p78 :rule cong :premises (@p77 @p76) :args (@t136)) % 169.81/170.85 (step @p79 :rule cong :premises (@p78) :args (@t137)) % 169.81/170.85 (step @p80 :rule cong :premises (@p79) :args (@t138)) % 169.81/170.85 (step @p81 :rule cong :premises (@p80) :args (@t139)) % 169.81/170.85 (step @p82 :rule exists-elim :args ((= (exists @t25 @t136) @t139))) % 169.81/170.85 (step @p83 :rule trans :premises (@p82 @p81)) % 169.81/170.85 (step @p84 :rule eq-symm :args (@t21 @t1)) % 169.81/170.85 (step @p85 :rule cong :premises (@p84) :args (@t30)) % 169.81/170.85 (step @p86 :rule trans :premises (@p85 @p83)) % 169.81/170.85 (step @p87 :rule cong :premises (@p86) :args (@t31)) % 169.81/170.85 (step @p88 :rule cong :premises (@p87) :args (@t32)) % 169.81/170.85 (step @p89 :rule trans :premises (@p5 @p88)) % 169.81/170.85 (step @p90 :rule ho_cong :premises (@p89 @p61)) % 169.81/170.85 (step @p91 :rule ho_cong :premises (@p90 @p47)) % 169.81/170.85 (step @p92 :rule refl :args (@t109)) % 169.81/170.85 (step @p93 :rule refl :args (@t34)) % 169.81/170.85 (step @p94 :rule cong :premises (@p93 @p92) :args ((= @t34 @t109))) % 169.81/170.85 (step @p95 :rule symm :premises (@p94)) % 169.81/170.85 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 169.81/170.85 (step @p97 :rule refl :args (@t11)) % 169.81/170.85 (step @p98 :rule cong :premises (@p97 @p96) :args (@t140)) % 169.81/170.85 (step @p99 :rule cong :premises (@p98) :args (@t141)) % 169.81/170.85 (step @p100 :rule eq-symm :args (@t34 @t11)) % 169.81/170.85 (step @p101 :rule cong :premises (@p100) :args (@t36)) % 169.81/170.85 (step @p102 :rule trans :premises (@p101 @p99)) % 169.81/170.85 (step @p103 :rule cong :premises (@p102) :args (@t37)) % 169.81/170.85 (step @p104 :rule trans :premises (@p6 @p103)) % 169.81/170.85 (step @p105 :rule ho_cong :premises (@p104 @p61)) % 169.81/170.85 (step @p106 :rule ho_cong :premises (@p105 @p47)) % 169.81/170.85 (step @p107 :rule refl :args ((_ @t2 @t11 @t10))) % 169.81/170.85 (step @p108 :rule refl :args (@t111)) % 169.81/170.85 (step @p109 :rule cong :premises (@p97 @p108) :args (@t112)) % 169.81/170.85 (step @p110 :rule trans :premises (@p109 @p107)) % 169.81/170.85 (step @p111 :rule refl :args (@t12)) % 169.81/170.85 (step @p112 :rule ho_cong :premises (@p111 @p108)) % 169.81/170.85 (step @p113 :rule cong :premises (@p112 @p110) :args ((= (_ @t12 @t111) @t112))) % 169.81/170.85 (step @p114 :rule symm :premises (@p113)) % 169.81/170.85 (step @p115 :rule refl :args (@t13)) % 169.81/170.85 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 169.81/170.85 (step @p117 :rule refl :args (@t10)) % 169.81/170.85 (step @p118 :rule cong :premises (@p117 @p108) :args ((= @t10 @t111))) % 169.81/170.85 (step @p119 :rule symm :premises (@p118)) % 169.81/170.85 (step @p120 :rule eq_resolve :premises (@p117 @p119)) % 169.81/170.85 (step @p121 :rule ho_cong :premises (@p111 @p120)) % 169.81/170.85 (step @p122 :rule trans :premises (@p121 @p116)) % 169.81/170.85 (step @p123 :rule refl :args ((_ @t2 @t14 @t7))) % 169.81/170.85 (step @p124 :rule refl :args (@t7)) % 169.81/170.85 (step @p125 :rule refl :args (@t113)) % 169.81/170.85 (step @p126 :rule cong :premises (@p125 @p124) :args (@t114)) % 169.81/170.85 (step @p127 :rule trans :premises (@p126 @p123)) % 169.81/170.85 (step @p128 :rule refl :args (@t2)) % 169.81/170.85 (step @p129 :rule ho_cong :premises (@p128 @p125)) % 169.81/170.85 (step @p130 :rule ho_cong :premises (@p129 @p124)) % 169.81/170.85 (step @p131 :rule cong :premises (@p130 @p127) :args ((= (_ (_ @t2 @t113) @t7) @t114))) % 169.81/170.85 (step @p132 :rule symm :premises (@p131)) % 169.81/170.85 (step @p133 :rule refl :args (@t15)) % 169.81/170.85 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 169.81/170.85 (step @p135 :rule refl :args (@t14)) % 169.81/170.85 (step @p136 :rule cong :premises (@p135 @p125) :args ((= @t14 @t113))) % 169.81/170.85 (step @p137 :rule symm :premises (@p136)) % 169.81/170.85 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 169.81/170.85 (step @p139 :rule ho_cong :premises (@p128 @p138)) % 169.81/170.85 (step @p140 :rule ho_cong :premises (@p139 @p124)) % 169.81/170.85 (step @p141 :rule trans :premises (@p140 @p134)) % 169.81/170.85 (step @p142 :rule cong :premises (@p141 @p122) :args (@t16)) % 169.81/170.85 (step @p143 :rule cong :premises (@p142) :args (@t18)) % 169.81/170.85 (step @p144 :rule cong :premises (@p143) :args (@t20)) % 169.81/170.85 (step @p145 :rule trans :premises (@p3 @p144)) % 169.81/170.85 (step @p146 :rule ho_cong :premises (@p145 @p61)) % 169.81/170.85 (step @p147 :rule nary_cong :premises (@p146 @p106 @p91) :args (@t45)) % 169.81/170.85 (step @p148 :rule trans :premises (@p147 @p71)) % 169.81/170.85 (step @p149 :rule cong :premises (@p148) :args (@t46)) % 169.81/170.85 (step @p150 :rule trans :premises (@p9 @p149)) % 169.81/170.85 (step @p151 :rule ho_cong :premises (@p150 @p61)) % 169.81/170.85 (step @p152 :rule ho_cong :premises (@p151 @p47)) % 169.81/170.85 (step @p153 :rule aci_norm :args ((= (and @t115 @t142 @t121) @t122))) % 169.81/170.85 (step @p154 :rule beta-reduce :args ((= (_ @t143 @t1) @t121))) % 169.81/170.85 (step @p155 :rule beta-reduce :args ((= @t144 @t143))) % 169.81/170.85 (step @p156 :rule ho_cong :premises (@p155 @p47)) % 169.81/170.85 (step @p157 :rule trans :premises (@p156 @p154)) % 169.81/170.85 (step @p158 :rule beta-reduce :args ((= (_ @t145 @t1) @t142))) % 169.81/170.85 (step @p159 :rule beta-reduce :args ((= @t146 @t145))) % 169.81/170.85 (step @p160 :rule ho_cong :premises (@p159 @p47)) % 169.81/170.85 (step @p161 :rule trans :premises (@p160 @p158)) % 169.81/170.85 (step @p162 :rule nary_cong :premises (@p70 @p161 @p157) :args ((and @t135 (_ @t146 @t1) (_ @t144 @t1)))) % 169.81/170.85 (step @p163 :rule trans :premises (@p162 @p153)) % 169.81/170.85 (step @p164 :rule cong :premises (@p138 @p77) :args (@t23)) % 169.81/170.85 (step @p165 :rule cong :premises (@p164) :args (@t147)) % 169.81/170.85 (step @p166 :rule nary_cong :premises (@p165 @p79) :args (@t148)) % 169.81/170.85 (step @p167 :rule cong :premises (@p166) :args ((forall @t25 @t148))) % 169.81/170.85 (step @p168 :rule bool-and-de-morgan :args (@t23 @t136 true)) % 169.81/170.85 (step @p169 :rule cong :premises (@p168) :args (@t150)) % 169.81/170.85 (step @p170 :rule trans :premises (@p169 @p167)) % 169.81/170.85 (step @p171 :rule cong :premises (@p170) :args (@t151)) % 169.81/170.85 (step @p172 :rule exists-elim :args ((= (exists @t25 @t149) @t151))) % 169.81/170.85 (step @p173 :rule trans :premises (@p172 @p171)) % 169.81/170.85 (step @p174 :rule refl :args (@t23)) % 169.81/170.85 (step @p175 :rule nary_cong :premises (@p174 @p84) :args (@t24)) % 169.81/170.85 (step @p176 :rule cong :premises (@p175) :args (@t26)) % 169.81/170.85 (step @p177 :rule trans :premises (@p176 @p173)) % 169.81/170.85 (step @p178 :rule cong :premises (@p177) :args (@t28)) % 169.81/170.85 (step @p179 :rule cong :premises (@p178) :args (@t29)) % 169.81/170.85 (step @p180 :rule trans :premises (@p4 @p179)) % 169.81/170.85 (step @p181 :rule ho_cong :premises (@p180 @p61)) % 169.81/170.85 (step @p182 :rule ho_cong :premises (@p181 @p47)) % 169.81/170.85 (step @p183 :rule refl :args (@t117)) % 169.81/170.85 (step @p184 :rule refl :args (@t152)) % 169.81/170.85 (step @p185 :rule cong :premises (@p184 @p183) :args ((= @t152 @t117))) % 169.81/170.85 (step @p186 :rule symm :premises (@p185)) % 169.81/170.85 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 169.81/170.85 (step @p188 :rule refl :args (@t47)) % 169.81/170.85 (step @p189 :rule cong :premises (@p188 @p187) :args (@t153)) % 169.81/170.85 (step @p190 :rule cong :premises (@p189) :args (@t154)) % 169.81/170.85 (step @p191 :rule refl :args (@t119)) % 169.81/170.85 (step @p192 :rule refl :args (@t155)) % 169.81/170.85 (step @p193 :rule cong :premises (@p192 @p191) :args ((= @t155 @t119))) % 169.81/170.85 (step @p194 :rule symm :premises (@p193)) % 169.81/170.85 (step @p195 :rule eq_resolve :premises (@p192 @p194)) % 169.81/170.85 (step @p196 :rule refl :args (@t53)) % 169.81/170.85 (step @p197 :rule cong :premises (@p196 @p195) :args (@t156)) % 169.81/170.85 (step @p198 :rule cong :premises (@p197) :args (@t157)) % 169.81/170.85 (step @p199 :rule nary_cong :premises (@p198 @p190) :args ((and @t157 @t154))) % 169.81/170.85 (step @p200 :rule alpha_equiv :args (@t159 @t160 (@list @t47))) % 169.81/170.85 (step @p201 :rule alpha_equiv :args (@t141 @t160 @t161)) % 169.81/170.85 (step @p202 :rule nary_cong :premises (@p201 @p200) :args (@t162)) % 169.81/170.85 (step @p203 :rule quant-miniscope-and :args ((= (forall @t27 (and @t140 @t158)) @t162))) % 169.81/170.85 (step @p204 :rule trans :premises (@p203 @p202)) % 169.81/170.85 (step @p205 :rule trans :premises (@p204 @p199)) % 169.81/170.85 (step @p206 :rule eq-symm :args (@t38 @t11)) % 169.81/170.85 (step @p207 :rule nary_cong :premises (@p100 @p206) :args (@t39)) % 169.81/170.85 (step @p208 :rule cong :premises (@p207) :args (@t40)) % 169.81/170.85 (step @p209 :rule trans :premises (@p208 @p205)) % 169.81/170.85 (step @p210 :rule cong :premises (@p209) :args (@t41)) % 169.81/170.85 (step @p211 :rule trans :premises (@p7 @p210)) % 169.81/170.85 (step @p212 :rule ho_cong :premises (@p211 @p61)) % 169.81/170.85 (step @p213 :rule ho_cong :premises (@p212 @p47)) % 169.81/170.85 (step @p214 :rule nary_cong :premises (@p146 @p213 @p182) :args (@t43)) % 169.81/170.85 (step @p215 :rule trans :premises (@p214 @p163)) % 169.81/170.85 (step @p216 :rule cong :premises (@p215) :args (@t44)) % 169.81/170.85 (step @p217 :rule trans :premises (@p8 @p216)) % 169.81/170.85 (step @p218 :rule ho_cong :premises (@p217 @p61)) % 169.81/170.85 (step @p219 :rule ho_cong :premises (@p218 @p47)) % 169.81/170.85 (step @p220 :rule cong :premises (@p219 @p152) :args (@t3)) % 169.81/170.85 (step @p221 :rule cong :premises (@p220) :args (@t5)) % 169.81/170.85 (step @p222 :rule cong :premises (@p221) :args (@t6)) % 169.81/170.85 (step @p223 :rule trans :premises (@p222 @p60)) % 169.81/170.85 (step @p224 :rule trans :premises (@p223 @p44 @p43)) % 169.81/170.85 (step @p225 :rule eq_resolve :premises (@p1 @p224)) % 169.81/170.85 (step @p226 :rule skolemize :premises (@p225)) % 169.81/170.85 (step @p227 :rule cnf_equiv_neg1 :args (@t163)) % 169.81/170.85 (step @p228 :rule reordering :premises (@p227) :args ((or @t91 @t94 @t163))) % 169.81/170.85 (step @p229 :rule chain_m_resolution :premises (@p228 @p226 @p23 @p21) :args (@t90 (@list true true true) (@list @t163 @t94 @t91))) % 169.81/170.85 (assume-push @p470 @t76) % 169.81/170.85 (step @p231 :rule instantiate :premises (@p470) :args ((@list @t164))) % 169.81/170.85 (step-pop @p471 :rule scope :premises (@p231)) % 169.81/170.85 (step @p232 :rule process_scope :premises (@p471) :args (@t168)) % 169.81/170.85 (step @p234 :rule implies_elim :premises (@p232)) % 169.81/170.85 (step @p235 :rule refl :args (@t173)) % 169.81/170.85 (step @p236 :rule bool-double-not-elim :args (@t167)) % 169.81/170.85 (step @p237 :rule nary_cong :premises (@p236 @p235) :args ((or (not @t168) @t173))) % 169.81/170.85 (assume-push @p472 @t168) % 169.81/170.85 (step @p239 :rule skolemize :premises (@p472)) % 169.81/170.85 (step-pop @p473 :rule scope :premises (@p239)) % 169.81/170.85 (step @p240 :rule process_scope :premises (@p473) :args (@t173)) % 169.81/170.85 (step @p242 :rule implies_elim :premises (@p240)) % 169.81/170.85 (step @p243 :rule eq_resolve :premises (@p242 @p237)) % 169.81/170.85 (step @p244 :rule bool-double-not-elim :args (@t170)) % 169.81/170.85 (step @p245 :rule refl :args (@t172)) % 169.81/170.85 (step @p246 :rule nary_cong :premises (@p245 @p244) :args ((or @t172 (not @t171)))) % 169.81/170.85 (step @p247 :rule cnf_or_neg :args (@t172 1)) % 169.81/170.85 (step @p248 :rule eq_resolve :premises (@p247 @p246)) % 169.81/170.85 (step @p249 :rule reordering :premises (@p248) :args ((or @t170 @t172))) % 169.81/170.85 (assume-push @p474 @t174) % 169.81/170.85 (step @p251 :rule instantiate :premises (@p474) :args ((@list @t169))) % 169.81/170.85 (step-pop @p475 :rule scope :premises (@p251)) % 169.81/170.85 (step @p252 :rule process_scope :premises (@p475) :args (@t171)) % 169.81/170.85 (step @p254 :rule implies_elim :premises (@p252)) % 169.81/170.85 (step @p255 :rule refl :args (@t174)) % 169.81/170.85 (step @p256 :rule bool-double-not-elim :args (@t89)) % 169.81/170.85 (step @p257 :rule nary_cong :premises (@p256 @p255) :args ((or (not @t175) @t174))) % 169.81/170.85 (step @p258 :rule bool-double-not-elim :args (@t174)) % 169.81/170.85 (step @p259 :rule refl :args (@t175)) % 169.81/170.85 (step @p260 :rule cong :premises (@p259 @p258) :args ((=> @t175 @t176))) % 169.81/170.85 (assume-push @p476 @t175) % 169.81/170.85 (step @p262 :rule skolemize :premises (@p476)) % 169.81/170.85 (step-pop @p477 :rule scope :premises (@p262)) % 169.81/170.85 (step @p263 :rule process_scope :premises (@p477) :args (@t176)) % 169.81/170.85 (step @p265 :rule eq_resolve :premises (@p263 @p260)) % 169.81/170.85 (step @p266 :rule implies_elim :premises (@p265)) % 169.81/170.85 (step @p267 :rule eq_resolve :premises (@p266 @p257)) % 169.81/170.85 (step @p268 :rule alpha_equiv :args (@t71 @t160 @t161)) % 169.81/170.85 (step @p269 :rule equiv_elim1 :premises (@p268)) % 169.81/170.85 (step @p270 :rule reordering :premises (@p269) :args ((or @t93 @t177))) % 169.81/170.85 (step @p271 :rule cnf_and_neg :args (@t94)) % 169.81/170.85 (step @p272 :rule cnf_and_neg :args (@t91)) % 169.81/170.85 (step @p273 :rule cnf_equiv_neg2 :args (@t163)) % 169.81/170.85 (step @p274 :rule chain_m_resolution :premises (@p273 @p226 @p272 @p271 @p270 @p267 @p254 @p249 @p243 @p234) :args ((or (not @t90) @t177 @t179 @t178) (@list true false false false false true false true true) (@list @t163 @t91 @t94 @t93 @t89 @t174 @t170 @t172 @t167))) % 169.81/170.85 (assume-push @p478 @t76) % 169.81/170.85 (step @p276 :rule instantiate :premises (@p478) :args (@t86)) % 169.81/170.85 (step-pop @p479 :rule scope :premises (@p276)) % 169.81/170.85 (step @p277 :rule process_scope :premises (@p479) :args (@t182)) % 169.81/170.85 (step @p279 :rule implies_elim :premises (@p277)) % 169.81/170.85 (step @p280 :rule refl :args (@t184)) % 169.81/170.85 (step @p281 :rule bool-double-not-elim :args (@t84)) % 169.81/170.85 (step @p282 :rule nary_cong :premises (@p281 @p280) :args ((or (not @t178) @t184))) % 169.81/170.85 (assume-push @p480 @t178) % 169.81/170.85 (step @p284 :rule skolemize :premises (@p480)) % 169.81/170.85 (step-pop @p481 :rule scope :premises (@p284)) % 169.81/170.85 (step @p285 :rule process_scope :premises (@p481) :args (@t184)) % 169.81/170.85 (step @p287 :rule implies_elim :premises (@p285)) % 169.81/170.85 (step @p288 :rule eq_resolve :premises (@p287 @p282)) % 169.81/170.85 (step @p289 :rule refl :args (@t193)) % 169.81/170.85 (step @p290 :rule bool-double-not-elim :args (@t181)) % 169.81/170.85 (step @p291 :rule nary_cong :premises (@p290 @p289) :args ((or (not @t182) @t193))) % 169.81/170.85 (assume-push @p482 @t182) % 169.81/170.85 (step @p293 :rule skolemize :premises (@p482)) % 169.81/170.85 (step-pop @p483 :rule scope :premises (@p293)) % 169.81/170.85 (step @p294 :rule process_scope :premises (@p483) :args (@t193)) % 169.81/170.85 (step @p296 :rule implies_elim :premises (@p294)) % 169.81/170.85 (step @p297 :rule eq_resolve :premises (@p296 @p291)) % 169.81/170.85 (step @p298 :rule bool-double-not-elim :args (@t190)) % 169.81/170.85 (step @p299 :rule refl :args (@t192)) % 169.81/170.85 (step @p300 :rule nary_cong :premises (@p299 @p298) :args ((or @t192 (not @t191)))) % 169.81/170.85 (step @p301 :rule cnf_or_neg :args (@t192 0)) % 169.81/170.85 (step @p302 :rule eq_resolve :premises (@p301 @p300)) % 169.81/170.85 (step @p303 :rule reordering :premises (@p302) :args ((or @t190 @t192))) % 169.81/170.85 (step @p304 :rule bool-double-not-elim :args (@t187)) % 169.81/170.85 (step @p305 :rule nary_cong :premises (@p299 @p304) :args ((or @t192 (not @t188)))) % 169.81/170.85 (step @p306 :rule cnf_or_neg :args (@t192 1)) % 169.81/170.85 (step @p307 :rule eq_resolve :premises (@p306 @p305)) % 169.81/170.85 (step @p308 :rule reordering :premises (@p307) :args ((or @t187 @t192))) % 169.81/170.85 (step @p309 :rule instantiate :premises (@p229) :args ((@list @t85 @t185 @t85))) % 169.81/170.85 (assume-push @p484 @t88) % 169.81/170.85 (assume-push @p485 @t190) % 169.81/170.85 (assume-push @p486 @t187) % 169.81/170.85 (assume-push @p487 @t195) % 169.81/170.85 (assume-push @p488 @t88) % 169.81/170.85 (assume-push @p489 @t190) % 169.81/170.85 (assume-push @p490 @t195) % 169.81/170.85 (assume-push @p491 @t187) % 169.81/170.85 (step @p318 :rule symm :premises (@p486)) % 169.81/170.85 (step @p319 :rule refl :args (@t180)) % 169.81/170.85 (step @p320 :rule cong :premises (@p319 @p318) :args (@t194)) % 169.81/170.85 (step @p321 :rule symm :premises (@p309)) % 169.81/170.85 (step @p322 :rule refl :args (@t85)) % 169.81/170.85 (step @p323 :rule refl :args (@t69)) % 169.81/170.85 (step @p324 :rule cong :premises (@p323 @p485) :args (@t70)) % 169.81/170.85 (step @p325 :rule cong :premises (@p324 @p322) :args (@t87)) % 169.81/170.85 (step @p326 :rule trans :premises (@p484 @p325 @p321 @p320)) % 169.81/170.85 (step-pop @p492 :rule scope :premises (@p326)) % 169.81/170.85 (step-pop @p493 :rule scope :premises (@p492)) % 169.81/170.85 (step-pop @p494 :rule scope :premises (@p493)) % 169.81/170.85 (step-pop @p495 :rule scope :premises (@p494)) % 169.81/170.85 (step @p327 :rule process_scope :premises (@p495) :args (@t183)) % 169.81/170.85 (step @p332 :rule and_intro :premises (@p484 @p485 @p309 @p486)) % 169.81/170.85 (step @p333 :rule modus_ponens :premises (@p332 @p327)) % 169.81/170.85 (step-pop @p496 :rule scope :premises (@p333)) % 169.81/170.85 (step-pop @p497 :rule scope :premises (@p496)) % 169.81/170.85 (step-pop @p498 :rule scope :premises (@p497)) % 169.81/170.85 (step-pop @p499 :rule scope :premises (@p498)) % 169.81/170.85 (step @p334 :rule process_scope :premises (@p499) :args (@t183)) % 169.81/170.85 (step @p339 :rule implies_elim :premises (@p334)) % 169.81/170.85 (step @p340 :rule cnf_and_neg :args (@t196)) % 169.81/170.85 (step @p341 :rule resolution :premises (@p340 @p339) :args (true @t196)) % 169.81/170.85 (step @p342 :rule reordering :premises (@p341) :args ((or @t183 (not @t88) @t191 @t188 (not @t195)))) % 169.81/170.85 (step @p343 :rule chain_m_resolution :premises (@p342 @p309 @p308 @p303 @p297 @p288 @p279 @p274 @p229 @p19) :args ((or @t177 @t179) (@list false false false true true true true false false) (@list @t195 @t187 @t190 @t192 @t183 @t181 @t84 @t90 @t88))) % 169.81/170.85 (assume-push @p500 @t71) % 169.81/170.85 (step @p345 :rule instantiate :premises (@p500) :args ((@list @t198))) % 169.81/170.85 (step-pop @p501 :rule scope :premises (@p345)) % 169.81/170.85 (step @p346 :rule process_scope :premises (@p501) :args (@t199)) % 169.81/170.85 (step @p348 :rule implies_elim :premises (@p346)) % 169.81/170.85 (step @p349 :rule cnf_and_pos :args (@t94 1)) % 169.81/170.85 (step @p350 :rule reordering :premises (@p349) :args ((or @t76 @t95))) % 169.81/170.85 (step @p351 :rule refl :args (@t200)) % 169.81/170.85 (step @p352 :rule bool-double-not-elim :args (@t76)) % 169.81/170.85 (step @p353 :rule nary_cong :premises (@p352 @p351) :args ((or (not @t179) @t200))) % 169.81/170.85 (step @p354 :rule bool-double-not-elim :args (@t200)) % 169.81/170.85 (step @p355 :rule refl :args (@t179)) % 169.81/170.85 (step @p356 :rule cong :premises (@p355 @p354) :args ((=> @t179 @t201))) % 169.81/170.85 (assume-push @p502 @t179) % 169.81/170.85 (step @p358 :rule skolemize :premises (@p502)) % 169.81/170.85 (step-pop @p503 :rule scope :premises (@p358)) % 169.81/170.85 (step @p359 :rule process_scope :premises (@p503) :args (@t201)) % 169.81/170.85 (step @p361 :rule eq_resolve :premises (@p359 @p356)) % 169.81/170.85 (step @p362 :rule implies_elim :premises (@p361)) % 169.81/170.85 (step @p363 :rule eq_resolve :premises (@p362 @p353)) % 169.81/170.85 (assume-push @p504 @t200) % 169.81/170.85 (step @p365 :rule instantiate :premises (@p504) :args (@t81)) % 169.81/170.85 (step-pop @p505 :rule scope :premises (@p365)) % 169.81/170.85 (step @p366 :rule process_scope :premises (@p505) :args (@t208)) % 169.81/170.85 (step @p368 :rule implies_elim :premises (@p366)) % 169.81/170.85 (step @p369 :rule cnf_and_pos :args (@t91 2)) % 169.81/170.85 (step @p370 :rule reordering :premises (@p369) :args ((or @t89 @t92))) % 169.81/170.85 (assume-push @p506 @t89) % 169.81/170.85 (step @p372 :rule instantiate :premises (@p506) :args ((@list @t77))) % 169.81/170.85 (step-pop @p507 :rule scope :premises (@p372)) % 169.81/170.85 (step @p373 :rule process_scope :premises (@p507) :args (@t209)) % 169.81/170.85 (step @p375 :rule implies_elim :premises (@p373)) % 169.81/170.85 (assume-push @p508 @t89) % 169.81/170.85 (step @p377 :rule instantiate :premises (@p508) :args (@t81)) % 169.81/170.85 (step-pop @p509 :rule scope :premises (@p377)) % 169.81/170.85 (step @p378 :rule process_scope :premises (@p509) :args (@t211)) % 169.81/170.85 (step @p380 :rule implies_elim :premises (@p378)) % 169.81/170.85 (step @p381 :rule refl :args (@t204)) % 169.81/170.85 (step @p382 :rule bool-double-not-elim :args (@t79)) % 169.81/170.85 (step @p383 :rule nary_cong :premises (@p382 @p381) :args ((or (not @t209) @t204))) % 169.81/170.85 (step @p384 :rule bool-double-not-elim :args (@t204)) % 169.81/170.85 (step @p385 :rule refl :args (@t209)) % 169.81/170.85 (step @p386 :rule cong :premises (@p385 @p384) :args ((=> @t209 @t212))) % 169.81/170.85 (assume-push @p510 @t209) % 169.81/170.85 (step @p388 :rule skolemize :premises (@p510)) % 169.81/170.85 (step-pop @p511 :rule scope :premises (@p388)) % 169.81/170.85 (step @p389 :rule process_scope :premises (@p511) :args (@t212)) % 169.81/170.85 (step @p391 :rule eq_resolve :premises (@p389 @p386)) % 169.81/170.85 (step @p392 :rule implies_elim :premises (@p391)) % 169.81/170.85 (step @p393 :rule eq_resolve :premises (@p392 @p383)) % 169.81/170.85 (step @p394 :rule refl :args (@t216)) % 169.81/170.85 (step @p395 :rule bool-double-not-elim :args (@t210)) % 169.81/170.85 (step @p396 :rule nary_cong :premises (@p395 @p394) :args ((or (not @t211) @t216))) % 169.81/170.85 (step @p397 :rule bool-double-not-elim :args (@t216)) % 169.81/170.85 (step @p398 :rule refl :args (@t211)) % 169.81/170.85 (step @p399 :rule cong :premises (@p398 @p397) :args ((=> @t211 @t218))) % 169.81/170.85 (assume-push @p512 @t211) % 169.81/170.85 (step @p401 :rule skolemize :premises (@p512)) % 169.81/170.85 (step-pop @p513 :rule scope :premises (@p401)) % 169.81/170.85 (step @p402 :rule process_scope :premises (@p513) :args (@t218)) % 169.81/170.85 (step @p404 :rule eq_resolve :premises (@p402 @p399)) % 169.81/170.85 (step @p405 :rule implies_elim :premises (@p404)) % 169.81/170.85 (step @p406 :rule eq_resolve :premises (@p405 @p396)) % 169.81/170.85 (step @p407 :rule cnf_or_pos :args (@t208)) % 169.81/170.85 (step @p408 :rule reordering :premises (@p407) :args ((or @t205 @t207 (not @t208)))) % 169.81/170.85 (step @p409 :rule instantiate :premises (@p229) :args ((@list @t80 @t77 @t80))) % 169.81/170.85 (step @p410 :rule instantiate :premises (@p229) :args ((@list @t213 @t80 @t198))) % 169.81/170.85 (assume-push @p514 @t204) % 169.81/170.85 (assume-push @p515 @t83) % 169.81/170.85 (assume-push @p516 @t216) % 169.81/170.85 (assume-push @p517 @t199) % 169.81/170.85 (assume-push @p518 @t220) % 169.81/170.85 (assume-push @p519 @t223) % 169.81/170.85 (assume-push @p520 @t199) % 169.81/170.85 (assume-push @p521 @t216) % 169.81/170.85 (assume-push @p522 @t223) % 169.81/170.85 (assume-push @p523 @t220) % 169.81/170.85 (assume-push @p524 @t204) % 169.81/170.85 (assume-push @p525 @t83) % 169.81/170.85 (step @p423 :rule symm :premises (@p517)) % 169.81/170.85 (step @p424 :rule refl :args (@t198)) % 169.81/170.85 (step @p425 :rule symm :premises (@p516)) % 169.81/170.85 (step @p323 :rule refl :args (@t69)) % 169.81/170.85 (step @p426 :rule cong :premises (@p323 @p425) :args (@t221)) % 169.81/170.85 (step @p427 :rule cong :premises (@p426 @p424) :args (@t222)) % 169.81/170.85 (step @p428 :rule symm :premises (@p409)) % 169.81/170.85 (step @p429 :rule refl :args (@t80)) % 169.81/170.85 (step @p430 :rule cong :premises (@p323 @p514) :args (@t70)) % 169.81/170.85 (step @p431 :rule cong :premises (@p430 @p429) :args (@t82)) % 169.81/170.85 (step @p432 :rule trans :premises (@p515 @p431 @p428)) % 169.81/170.85 (step @p433 :rule refl :args (@t214)) % 169.81/170.85 (step @p434 :rule cong :premises (@p433 @p432) :args (@t215)) % 169.81/170.85 (step @p435 :rule trans :premises (@p516 @p434 @p410 @p427 @p423)) % 169.81/170.85 (step-pop @p526 :rule scope :premises (@p435)) % 169.81/170.85 (step-pop @p527 :rule scope :premises (@p526)) % 169.81/170.85 (step-pop @p528 :rule scope :premises (@p527)) % 169.81/170.85 (step-pop @p529 :rule scope :premises (@p528)) % 169.81/170.85 (step-pop @p530 :rule scope :premises (@p529)) % 169.81/170.85 (step-pop @p531 :rule scope :premises (@p530)) % 169.81/170.85 (step @p436 :rule process_scope :premises (@p531) :args (@t206)) % 169.81/170.85 (step @p443 :rule and_intro :premises (@p517 @p516 @p410 @p409 @p514 @p515)) % 169.81/170.85 (step @p444 :rule modus_ponens :premises (@p443 @p436)) % 169.81/170.85 (step-pop @p532 :rule scope :premises (@p444)) % 169.81/170.85 (step-pop @p533 :rule scope :premises (@p532)) % 169.81/170.85 (step-pop @p534 :rule scope :premises (@p533)) % 169.81/170.85 (step-pop @p535 :rule scope :premises (@p534)) % 169.81/170.85 (step-pop @p536 :rule scope :premises (@p535)) % 169.81/170.85 (step-pop @p537 :rule scope :premises (@p536)) % 169.81/170.85 (step @p445 :rule process_scope :premises (@p537) :args (@t206)) % 169.81/170.85 (step @p452 :rule implies_elim :premises (@p445)) % 169.81/170.85 (step @p453 :rule cnf_and_neg :args (@t224)) % 169.81/170.85 (step @p454 :rule resolution :premises (@p453 @p452) :args (true @t224)) % 169.81/170.85 (step @p455 :rule reordering :premises (@p454) :args ((or @t205 (not @t83) @t206 @t217 (not @t199) (not @t220) (not @t223)))) % 169.81/170.85 (step @p456 :rule chain_m_resolution :premises (@p455 @p410 @p409 @p408 @p406 @p393 @p380 @p375 @p370 @p368 @p228 @p226 @p363 @p350 @p348 @p343 @p14) :args (@t177 (@list false false true false false true true false false false true false true false true false) (@list @t223 @t220 @t206 @t216 @t204 @t210 @t79 @t89 @t208 @t91 @t163 @t200 @t94 @t199 @t76 @t83))) % 169.81/170.85 (step @p457 :rule equiv_elim2 :premises (@p268)) % 169.81/170.86 (step @p458 :rule chain_m_resolution :premises (@p457 @p456) :args ((not @t93) @t225 @t226)) % 169.81/170.86 (step @p459 :rule cnf_and_pos :args (@t91 1)) % 169.81/170.86 (step @p460 :rule reordering :premises (@p459) :args ((or @t71 @t92))) % 169.81/170.86 (step @p461 :rule chain_m_resolution :premises (@p460 @p456) :args (@t92 @t225 @t226)) % 169.81/170.86 (step @p462 :rule chain_m_resolution :premises (@p228 @p461 @p226) :args (@t94 (@list true true) (@list @t91 @t163))) % 169.81/170.86 (step @p463 :rule cnf_and_pos :args (@t94 2)) % 169.81/170.86 (step @p464 :rule reordering :premises (@p463) :args ((or @t93 @t95))) % 169.81/170.86 (step @p465 false :rule chain_m_resolution :premises (@p464 @p462 @p458) :args (false (@list false true) (@list @t94 @t93))) % 169.81/170.86 ) % 169.81/170.86 % SZS output end Proof % 169.81/170.86 % cvc5 exiting %------------------------------------------------------------------------------