%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:07:17 AM UTC 2026 % Result : Theorem 0.36s 0.63s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n017.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 23:02:46 EDT 2026 % 0.17/0.34 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.36/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.63 % SZS status Theorem % 0.36/0.63 % SZS output start Proof % 0.36/0.63 ( % 0.36/0.63 (declare-sort tptp.d_unsorted 0) % 0.36/0.63 (declare-sort $$unsorted 0) % 0.36/0.63 (declare-const tptp.d_unsorted_0 tptp.d_unsorted) % 0.36/0.63 (declare-const tptp.d2unsorted (-> tptp.d_unsorted $$unsorted)) % 0.36/0.63 (declare-const tptp.so (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.total (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.term (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.ind (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.innf (-> (-> $$unsorted $$unsorted Bool) $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.nfof (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.norm (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.join (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.lconfl (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.subrel (-> (-> $$unsorted $$unsorted Bool) (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.sconfl (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.confl (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.inv (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.po (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.cr (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.trsc (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.trc (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.tc (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.trans (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.sc (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.asymm (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.antisymm (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.symm (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.rc (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.36/0.63 (declare-const tptp.irrefl (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.refl (-> (-> $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.mono (-> (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.infl (-> (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (declare-const tptp.idem (-> (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool) Bool)) % 0.36/0.63 (define @t1 () (@var "Y" $$unsorted)) % 0.36/0.63 (define @t2 () (@var "X" $$unsorted)) % 0.36/0.63 (define @t3 () (@var "Bound_variable_1538" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t4 () (@var "Bound_variable_663" $$unsorted)) % 0.36/0.63 (define @t5 () (@var "Bound_variable_661" $$unsorted)) % 0.36/0.63 (define @t6 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t7 () (_ (_ @t6 @t5) @t4)) % 0.36/0.63 (define @t8 () (not @t7)) % 0.36/0.63 (define @t9 () (@list @t5 @t4)) % 0.36/0.63 (define @t10 () (@var "Bound_variable_1106" $$unsorted)) % 0.36/0.63 (define @t11 () (@var "Bound_variable_672" $$unsorted)) % 0.36/0.63 (define @t12 () (_ @t3 @t11)) % 0.36/0.63 (define @t13 () (@var "Bound_variable_674" $$unsorted)) % 0.36/0.63 (define @t14 () (@list @t11 @t13 @t10)) % 0.36/0.63 (define @t15 () (@var "Bound_variable_1522" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t16 () (@var "Bound_variable_1125" $$unsorted)) % 0.36/0.63 (define @t17 () (_ @t15 @t11)) % 0.36/0.63 (define @t18 () (@list @t11 @t13 @t16)) % 0.36/0.63 (define @t19 () (@var "Bound_variable_1218" $$unsorted)) % 0.36/0.63 (define @t20 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t21 () (_ @t20 @t2)) % 0.36/0.63 (define @t22 () (_ (_ @t20 @t5) @t4)) % 0.36/0.63 (define @t23 () (or @t8 @t22)) % 0.36/0.63 (define @t24 () (forall @t9 @t23)) % 0.36/0.63 (define @t25 () (not @t24)) % 0.36/0.63 (define @t26 () (_ @t20 @t11)) % 0.36/0.63 (define @t27 () (_ @t20 @t13)) % 0.36/0.63 (define @t28 () (_ @t26 @t13)) % 0.36/0.63 (define @t29 () (not @t28)) % 0.36/0.63 (define @t30 () (not (forall @t14 (or @t29 (not (_ @t27 @t10)) (_ @t26 @t10))))) % 0.36/0.63 (define @t31 () (@list @t20)) % 0.36/0.63 (define @t32 () (_ @t20 @t1)) % 0.36/0.63 (define @t33 () (not (forall @t18 (or @t29 (not (_ @t27 @t16)) (_ @t26 @t16))))) % 0.36/0.63 (define @t34 () (not (forall @t31 (or @t33 @t25 (_ @t32 @t19))))) % 0.36/0.63 (define @t35 () (@list @t19)) % 0.36/0.63 (define @t36 () (forall @t35 (or @t34 (not (forall @t31 (or @t30 @t25 (_ @t21 @t19))))))) % 0.36/0.63 (define @t37 () (= @t2 @t1)) % 0.36/0.63 (define @t38 () (_ @t21 @t1)) % 0.36/0.63 (define @t39 () (@var "Z" $$unsorted)) % 0.36/0.63 (define @t40 () (_ @t26 @t39)) % 0.36/0.63 (define @t41 () (_ @t27 @t39)) % 0.36/0.63 (define @t42 () (not @t41)) % 0.36/0.63 (define @t43 () (or @t29 @t42 @t40)) % 0.36/0.63 (define @t44 () (@list @t11 @t13 @t39)) % 0.36/0.63 (define @t45 () (forall @t44 @t43)) % 0.36/0.63 (define @t46 () (not @t45)) % 0.36/0.63 (define @t47 () (or @t46 @t25 @t38)) % 0.36/0.63 (define @t48 () (forall @t31 @t47)) % 0.36/0.63 (define @t49 () (not @t48)) % 0.36/0.63 (define @t50 () (_ @t32 @t2)) % 0.36/0.63 (define @t51 () (forall @t31 (or @t46 @t25 @t50))) % 0.36/0.63 (define @t52 () (not @t37)) % 0.36/0.63 (define @t53 () (@list @t6)) % 0.36/0.63 (define @t54 () (@var "Bound_variable_1460" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t55 () (_ @t54 @t11)) % 0.36/0.63 (define @t56 () (@var "Bound_variable_1444" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t57 () (_ @t56 @t11)) % 0.36/0.63 (define @t58 () (not (forall @t35 (or @t34 (not (forall @t31 (or @t30 @t25 (_ (_ @t20 @t39) @t19)))))))) % 0.36/0.63 (define @t59 () (= @t1 @t39)) % 0.36/0.63 (define @t60 () (@var "Bound_variable_1422" $$unsorted)) % 0.36/0.63 (define @t61 () (@var "Bound_variable_1387" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t62 () (_ @t61 @t11)) % 0.36/0.63 (define @t63 () (@var "Bound_variable_1371" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t64 () (_ @t63 @t11)) % 0.36/0.63 (define @t65 () (@var "Bound_variable_1347" $$unsorted)) % 0.36/0.63 (define @t66 () (_ @t6 @t2)) % 0.36/0.63 (define @t67 () (_ @t66 @t39)) % 0.36/0.63 (define @t68 () (not @t67)) % 0.36/0.63 (define @t69 () (@var "Bound_variable_1309" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t70 () (_ @t69 @t11)) % 0.36/0.63 (define @t71 () (@var "Bound_variable_1293" (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t72 () (_ @t71 @t11)) % 0.36/0.63 (define @t73 () (_ @t66 @t1)) % 0.36/0.63 (define @t74 () (not @t73)) % 0.36/0.63 (define @t75 () (@list @t6 @t2 @t1)) % 0.36/0.63 (define @t76 () (@var "Bound_variable_985" $$unsorted)) % 0.36/0.63 (define @t77 () (@var "Bound_variable_1049" $$unsorted)) % 0.36/0.63 (define @t78 () (@list @t76)) % 0.36/0.63 (define @t79 () (@var "Bound_variable_1075" $$unsorted)) % 0.36/0.63 (define @t80 () (@list @t1)) % 0.36/0.63 (define @t81 () (@var "Bound_variable_917" $$unsorted)) % 0.36/0.63 (define @t82 () (@var "P" (-> $$unsorted Bool))) % 0.36/0.63 (define @t83 () (@list @t2)) % 0.36/0.63 (define @t84 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.63 (define @t85 () (@var "Bound_variable_862" $$unsorted)) % 0.36/0.63 (define @t86 () (_ @t6 @t1)) % 0.36/0.63 (define @t87 () (_ @t86 @t2)) % 0.36/0.63 (define @t88 () (@list @t2 @t1)) % 0.36/0.63 (define @t89 () (forall (@list @t2 @t1 @t39) (or @t74 (not (_ @t86 @t39)) @t67))) % 0.36/0.63 (define @t90 () (not @t87)) % 0.36/0.63 (define @t91 () (forall @t88 (or @t74 @t90))) % 0.36/0.63 (define @t92 () (forall @t88 (or @t74 @t90 @t37))) % 0.36/0.63 (define @t93 () (_ @t66 @t2)) % 0.36/0.63 (define @t94 () (forall @t83 @t93)) % 0.36/0.63 (define @t95 () (@var "Flatten_var_1" $$unsorted)) % 0.36/0.63 (define @t96 () (@var "Flatten_var_0" $$unsorted)) % 0.36/0.63 (define @t97 () (_ (_ @t20 @t96) @t95)) % 0.36/0.63 (define @t98 () (or @t46 @t25 @t97)) % 0.36/0.63 (define @t99 () (forall @t31 @t98)) % 0.36/0.63 (define @t100 () (_ (_ @t20 @t95) @t96)) % 0.36/0.63 (define @t101 () (or @t46 @t25 @t100)) % 0.36/0.63 (define @t102 () (forall @t31 @t101)) % 0.36/0.63 (define @t103 () (= @t96 @t95)) % 0.36/0.63 (define @t104 () (or @t103 @t102 @t99)) % 0.36/0.63 (define @t105 () (@list @t6 @t96 @t95)) % 0.36/0.63 (define @t106 () (lambda @t105 @t104)) % 0.36/0.63 (define @t107 () (= tptp.trsc @t106)) % 0.36/0.63 (define @t108 () (lambda @t75 @t48)) % 0.36/0.63 (define @t109 () (= tptp.tc @t108)) % 0.36/0.63 (define @t110 () (lambda @t75 (or @t87 @t73))) % 0.36/0.63 (define @t111 () (lambda @t75 (or @t37 @t73))) % 0.36/0.63 (define @t112 () (@var "Bound_variable_512" $$unsorted)) % 0.36/0.63 (define @t113 () (@var "Bound_variable_510" $$unsorted)) % 0.36/0.63 (define @t114 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t115 () (_ @t114 @t6)) % 0.36/0.63 (define @t116 () (forall @t88 (or @t74 @t38))) % 0.36/0.63 (define @t117 () (@list @t114)) % 0.36/0.63 (define @t118 () (@var "DU2" tptp.d_unsorted)) % 0.36/0.63 (define @t119 () (@var "DU1" tptp.d_unsorted)) % 0.36/0.63 (define @t120 () (@var "DU" tptp.d_unsorted)) % 0.36/0.63 (define @t121 () (@list @t120)) % 0.36/0.63 (define @t122 () (@var "U" $$unsorted)) % 0.36/0.63 (define @t123 () (@var "__flatten_var_1" $$unsorted)) % 0.36/0.63 (define @t124 () (@var "__flatten_var_0" $$unsorted)) % 0.36/0.63 (define @t125 () (@list @t6 @t124 @t123)) % 0.36/0.63 (define @t126 () (lambda @t125 (_ (_ (_ tptp.sc (_ tptp.rc (_ tptp.tc @t6))) @t124) @t123))) % 0.36/0.63 (define @t127 () (= tptp.trsc @t126)) % 0.36/0.63 (define @t128 () (not @t127)) % 0.36/0.63 (define @t129 () (_ @t20 @t96 @t95)) % 0.36/0.63 (define @t130 () (_ @t20 @t5 @t4)) % 0.36/0.63 (define @t131 () (_ @t6 @t5 @t4)) % 0.36/0.63 (define @t132 () (not (forall @t9 (or (not @t131) @t130)))) % 0.36/0.63 (define @t133 () (_ @t20 @t11 @t39)) % 0.36/0.63 (define @t134 () (_ @t20 @t13 @t39)) % 0.36/0.63 (define @t135 () (_ @t20 @t11 @t13)) % 0.36/0.63 (define @t136 () (not (forall @t44 (or (not @t135) (not @t134) @t133)))) % 0.36/0.63 (define @t137 () (_ @t20 @t95 @t96)) % 0.36/0.63 (define @t138 () (lambda @t105 (or @t103 (forall @t31 (or @t136 @t132 @t137)) (forall @t31 (or @t136 @t132 @t129))))) % 0.36/0.63 (define @t139 () (@purify @t138)) % 0.36/0.63 (define @t140 () (forall @t31 (or @t136 @t132 (_ @t20 @t124 @t123)))) % 0.36/0.63 (define @t141 () (forall @t31 (or @t136 @t132 (_ @t20 @t123 @t124)))) % 0.36/0.63 (define @t142 () (lambda @t125 (or (= @t124 @t123) @t141 @t140))) % 0.36/0.63 (define @t143 () (@purify @t142)) % 0.36/0.63 (define @t144 () (= @t138 @t142)) % 0.36/0.63 (define @t145 () (or (= @t123 @t124) @t141 @t140)) % 0.36/0.63 (define @t146 () (forall @t31 (or @t136 @t132 (_ @t20 @t124 @t1)))) % 0.36/0.63 (define @t147 () (forall @t31 (or @t136 @t132 (_ @t20 @t1 @t124)))) % 0.36/0.63 (define @t148 () (or (= @t124 @t1) @t147 @t146)) % 0.36/0.63 (define @t149 () (lambda @t80 @t148)) % 0.36/0.63 (define @t150 () (_ @t20 @t2 @t1)) % 0.36/0.63 (define @t151 () (forall @t31 (or @t136 @t132 @t150))) % 0.36/0.63 (define @t152 () (forall @t31 (or @t136 @t132 (_ @t20 @t1 @t2)))) % 0.36/0.63 (define @t153 () (or @t37 @t152 @t151)) % 0.36/0.63 (define @t154 () (or @t37 @t151)) % 0.36/0.63 (define @t155 () (lambda @t80 @t154)) % 0.36/0.63 (define @t156 () (lambda @t88 @t154)) % 0.36/0.63 (define @t157 () (_ @t156 @t2)) % 0.36/0.63 (define @t158 () (or (= @t1 @t2) @t152)) % 0.36/0.63 (define @t159 () (@var "BOUND_VARIABLE_8479" $$unsorted)) % 0.36/0.63 (define @t160 () (lambda (@list @t159) (or (= @t1 @t159) (forall @t31 (or @t136 @t132 (_ @t20 @t1 @t159)))))) % 0.36/0.63 (define @t161 () (or (_ (_ @t156 @t1) @t2) (_ @t157 @t1))) % 0.36/0.63 (define @t162 () (lambda @t88 @t161)) % 0.36/0.63 (define @t163 () (lambda @t80 @t151)) % 0.36/0.63 (define @t164 () (lambda @t88 @t151)) % 0.36/0.63 (define @t165 () (_ @t164 @t2)) % 0.36/0.63 (define @t166 () (or @t37 (_ @t165 @t1))) % 0.36/0.63 (define @t167 () (lambda @t88 @t166)) % 0.36/0.63 (define @t168 () (_ (lambda @t75 @t151) @t6)) % 0.36/0.63 (define @t169 () (lambda @t125 (_ (_ (_ @t110 (_ @t111 @t168)) @t124) @t123))) % 0.36/0.63 (define @t170 () (= @t138 @t169)) % 0.36/0.63 (define @t171 () (or @t136 @t132 @t38)) % 0.36/0.63 (define @t172 () (or @t136 @t132 @t97)) % 0.36/0.63 (define @t173 () (or @t136 @t132 @t100)) % 0.36/0.63 (define @t174 () (= @t143 @t139)) % 0.36/0.63 (define @t175 () (@const 0 $$unsorted)) % 0.36/0.63 (define @t176 () (@const 1 $$unsorted)) % 0.36/0.63 (define @t177 () (@const 2 (-> $$unsorted $$unsorted Bool))) % 0.36/0.63 (define @t178 () (not (forall @t9 (or (not (_ @t177 @t5 @t4)) @t130)))) % 0.36/0.63 (define @t179 () (or (= @t176 @t175) (forall @t31 (or @t136 @t178 (_ @t20 @t175 @t176))) (forall @t31 (or @t136 @t178 (_ @t20 @t176 @t175))))) % 0.36/0.63 (define @t180 () (= (_ @t138 @t177 @t176 @t175) @t179)) % 0.36/0.63 (define @t181 () (_ @t139 @t177 @t176 @t175)) % 0.36/0.63 (define @t182 () (_ @t142 @t177 @t176 @t175)) % 0.36/0.63 (define @t183 () (_ @t143 @t177 @t176 @t175)) % 0.36/0.63 (define @t184 () (= @t183 @t181)) % 0.36/0.63 (define @t185 () (not @t184)) % 0.36/0.63 (define @t186 () (or @t174 @t185)) % 0.36/0.63 (assume @p1 (and (forall (@list @t122) (exists @t121 (= @t122 (_ tptp.d2unsorted @t120)))) (forall @t121 (= @t120 tptp.d_unsorted_0)) (forall (@list @t119 @t118) (=> (= (_ tptp.d2unsorted @t119) (_ tptp.d2unsorted @t118)) (= @t119 @t118))) (= tptp.subrel (lambda (@list @t6 @t20) @t116)) (= tptp.inv (lambda @t75 @t87)) (= tptp.idem (lambda @t117 (forall @t53 (= @t115 (_ @t114 @t115))))) (= tptp.infl (lambda @t117 (forall @t75 (or @t74 (_ (_ @t115 @t2) @t1))))) (= tptp.mono (lambda @t117 (forall (@list @t6 @t20 @t113 @t112) (or (not @t116) (not (_ (_ @t115 @t113) @t112)) (_ (_ (_ @t114 @t20) @t113) @t112))))) (= tptp.refl (lambda @t53 @t94)) (= tptp.irrefl (lambda @t53 (forall @t83 (not @t93)))) (= tptp.rc @t111) (= tptp.symm (lambda @t53 (forall @t88 (or @t74 @t87)))) (= tptp.antisymm (lambda @t53 @t92)) (= tptp.asymm (lambda @t53 @t91)) (= tptp.sc @t110) (= tptp.trans (lambda @t53 @t89)) @t109 (= tptp.trc (lambda @t105 (or @t103 @t99))) @t107 (= tptp.po (lambda @t53 (and @t94 @t92 @t89))) (= tptp.so (lambda @t53 (and @t91 @t89))) (= tptp.total (lambda @t53 (forall @t88 (or @t37 @t73 @t87)))) (= tptp.term (lambda @t53 (forall (@list @t84 @t85) (or (not (_ @t84 @t85)) (not (forall @t83 (or (not (_ @t84 @t2)) (not (forall @t80 (or (not (_ @t84 @t1)) @t74)))))))))) (= tptp.ind (lambda @t53 (forall (@list @t82 @t81) (or (not (forall @t83 (or (not (forall @t80 (or @t49 (_ @t82 @t1)))) (_ @t82 @t2)))) (_ @t82 @t81))))) (= tptp.innf (lambda (@list @t6 @t2) (forall @t80 @t74))) (= tptp.nfof (lambda @t75 (and (or @t37 @t51) (forall @t78 (not (_ @t66 @t76)))))) (= tptp.norm (lambda @t53 (forall (@list @t2 @t79) (or (not (_ @t66 @t79)) (not (forall (@list @t77) (or (not (forall @t31 (or @t46 @t25 (_ @t21 @t77)))) (not (forall @t78 (not (_ (_ @t6 @t77) @t76))))))))))) (= tptp.join (lambda @t75 (not (and @t52 (not (forall @t31 (or @t33 @t25 @t50))) (not (forall @t31 (or @t30 @t25 @t38))) @t36)))) (= tptp.lconfl (lambda @t53 (forall (@list @t2 @t1 @t39 @t71 @t69) (or @t68 @t74 @t59 @t58 (not (forall @t18 (or (not (_ @t72 @t13)) (not (_ (_ @t71 @t13) @t16)) (_ @t72 @t16)))) (not (forall @t9 (or @t8 (_ (_ @t71 @t5) @t4)))) (_ (_ @t71 @t1) @t39) (not (forall @t14 (or (not (_ @t70 @t13)) (not (_ (_ @t69 @t13) @t10)) (_ @t70 @t10)))) (not (forall @t9 (or @t8 (_ (_ @t69 @t5) @t4)))) (_ (_ @t69 @t39) @t1))))) (= tptp.sconfl (lambda @t53 (forall (@list @t2 @t1 @t39 @t63 @t61) (or @t68 (and @t52 (not (forall @t31 (or (not (forall (@list @t11 @t13 @t65) (or @t29 (not (_ @t27 @t65)) (_ @t26 @t65)))) @t25 @t38)))) @t59 @t58 (not (forall @t18 (or (not (_ @t64 @t13)) (not (_ (_ @t63 @t13) @t16)) (_ @t64 @t16)))) (not (forall @t9 (or @t8 (_ (_ @t63 @t5) @t4)))) (_ (_ @t63 @t1) @t39) (not (forall @t14 (or (not (_ @t62 @t13)) (not (_ (_ @t61 @t13) @t10)) (_ @t62 @t10)))) (not (forall @t9 (or @t8 (_ (_ @t61 @t5) @t4)))) (_ (_ @t61 @t39) @t1))))) (= tptp.confl (lambda @t53 (forall (@list @t2 @t1 @t39 @t56 @t54) (or (and (not (= @t2 @t39)) (not (forall @t31 (or @t30 @t25 (_ @t21 @t39))))) (and @t52 (not (forall @t31 (or (not (forall (@list @t11 @t13 @t60) (or @t29 (not (_ @t27 @t60)) (_ @t26 @t60)))) @t25 @t38)))) @t59 @t58 (not (forall @t18 (or (not (_ @t57 @t13)) (not (_ (_ @t56 @t13) @t16)) (_ @t57 @t16)))) (not (forall @t9 (or @t8 (_ (_ @t56 @t5) @t4)))) (_ (_ @t56 @t1) @t39) (not (forall @t14 (or (not (_ @t55 @t13)) (not (_ (_ @t54 @t13) @t10)) (_ @t55 @t10)))) (not (forall @t9 (or @t8 (_ (_ @t54 @t5) @t4)))) (_ (_ @t54 @t39) @t1))))) (= tptp.cr (lambda @t53 (forall (@list @t2 @t1 @t15 @t3) (or (and @t52 (not @t51) @t49) @t37 (not @t36) (not (forall @t18 (or (not (_ @t17 @t13)) (not (_ (_ @t15 @t13) @t16)) (_ @t17 @t16)))) (not (forall @t9 (or @t8 (_ (_ @t15 @t5) @t4)))) (_ (_ @t15 @t1) @t2) (not (forall @t14 (or (not (_ @t12 @t13)) (not (_ (_ @t3 @t13) @t10)) (_ @t12 @t10)))) (not (forall @t9 (or @t8 (_ (_ @t3 @t5) @t4)))) (_ (_ @t3 @t2) @t1))))))) % 0.36/0.63 (assume @p2 @t128) % 0.36/0.63 (assume @p3 true) % 0.36/0.63 (step @p4 :rule eq-symm :args (@t139 @t143)) % 0.36/0.63 (step @p5 :rule eq-refl :args (@t142)) % 0.36/0.63 (step @p6 :rule skolem_intro :args (@t143)) % 0.36/0.63 (step @p7 :rule refl :args (@t142)) % 0.36/0.63 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t142 @t143))) % 0.36/0.63 (step @p9 :rule trans :premises (@p8 @p5)) % 0.36/0.63 (step @p10 :rule true_elim :premises (@p9)) % 0.36/0.63 (step @p11 :rule eq-refl :args (@t138)) % 0.36/0.63 (step @p12 :rule skolem_intro :args (@t139)) % 0.36/0.63 (step @p13 :rule refl :args (@t138)) % 0.36/0.63 (step @p14 :rule cong :premises (@p13 @p12) :args ((= @t138 @t139))) % 0.36/0.63 (step @p15 :rule trans :premises (@p14 @p11)) % 0.36/0.63 (step @p16 :rule true_elim :premises (@p15)) % 0.36/0.63 (step @p17 :rule cong :premises (@p16 @p10) :args (@t144)) % 0.36/0.63 (step @p18 :rule trans :premises (@p17 @p4)) % 0.36/0.63 (step @p19 :rule cong :premises (@p18) :args ((not @t144))) % 0.36/0.63 (step @p20 :rule refl :args (@t140)) % 0.36/0.63 (step @p21 :rule refl :args (@t141)) % 0.36/0.63 (step @p22 :rule eq-symm :args (@t123 @t124)) % 0.36/0.63 (step @p23 :rule nary_cong :premises (@p22 @p21 @p20) :args (@t145)) % 0.36/0.63 (step @p24 :rule beta-reduce :args ((= (_ (lambda @t80 (or (= @t1 @t124) @t147 @t146)) @t123) @t145))) % 0.36/0.63 (step @p25 :rule trans :premises (@p24 @p23)) % 0.36/0.63 (step @p26 :rule refl :args (@t123)) % 0.36/0.63 (step @p27 :rule refl :args (@t146)) % 0.36/0.63 (step @p28 :rule refl :args (@t147)) % 0.36/0.63 (step @p29 :rule eq-symm :args (@t124 @t1)) % 0.36/0.63 (step @p30 :rule nary_cong :premises (@p29 @p28 @p27) :args (@t148)) % 0.36/0.63 (step @p31 :rule cong :premises (@p30) :args (@t149)) % 0.36/0.63 (step @p32 :rule beta-reduce :args ((= (_ (lambda @t88 @t153) @t124) @t149))) % 0.36/0.63 (step @p33 :rule trans :premises (@p32 @p31)) % 0.36/0.63 (step @p34 :rule refl :args (@t124)) % 0.36/0.63 (step @p35 :rule aci_norm :args ((= (or (or @t37 @t152) @t154) @t153))) % 0.36/0.63 (step @p36 :rule beta-reduce :args ((= (_ @t155 @t1) @t154))) % 0.36/0.63 (step @p37 :rule refl :args (@t1)) % 0.36/0.63 (step @p38 :rule beta-reduce :args ((= @t157 @t155))) % 0.36/0.63 (step @p39 :rule ho_cong :premises (@p38 @p37)) % 0.36/0.63 (step @p40 :rule trans :premises (@p39 @p36)) % 0.36/0.63 (step @p41 :rule refl :args (@t152)) % 0.36/0.63 (step @p42 :rule eq-symm :args (@t1 @t2)) % 0.36/0.63 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t158)) % 0.36/0.63 (step @p44 :rule beta-reduce :args ((= (_ @t160 @t2) @t158))) % 0.36/0.63 (step @p45 :rule trans :premises (@p44 @p43)) % 0.36/0.63 (step @p46 :rule refl :args (@t2)) % 0.36/0.63 (step @p47 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t159) (or (= @t2 @t159) (forall @t31 (or @t136 @t132 (_ @t20 @t2 @t159))))) @t1) @t160))) % 0.36/0.63 (step @p48 :rule refl :args (@t1)) % 0.36/0.63 (step @p49 :rule alpha_equiv :args (@t156 (@list @t1) (@list @t159))) % 0.36/0.63 (step @p50 :rule ho_cong :premises (@p49 @p48)) % 0.36/0.63 (step @p51 :rule trans :premises (@p50 @p47)) % 0.36/0.63 (step @p52 :rule ho_cong :premises (@p51 @p46)) % 0.36/0.63 (step @p53 :rule trans :premises (@p52 @p45)) % 0.36/0.63 (step @p54 :rule nary_cong :premises (@p53 @p40) :args (@t161)) % 0.36/0.63 (step @p55 :rule trans :premises (@p54 @p35)) % 0.36/0.63 (step @p56 :rule cong :premises (@p55) :args (@t162)) % 0.36/0.63 (step @p57 :rule beta-reduce :args ((= (_ @t110 @t156) @t162))) % 0.36/0.63 (step @p58 :rule trans :premises (@p57 @p56)) % 0.36/0.63 (step @p59 :rule beta-reduce :args ((= (_ @t163 @t1) @t151))) % 0.36/0.63 (step @p60 :rule beta-reduce :args ((= @t165 @t163))) % 0.36/0.63 (step @p61 :rule ho_cong :premises (@p60 @p37)) % 0.36/0.63 (step @p62 :rule trans :premises (@p61 @p59)) % 0.36/0.63 (step @p63 :rule refl :args (@t37)) % 0.36/0.63 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t166)) % 0.36/0.63 (step @p65 :rule cong :premises (@p64) :args (@t167)) % 0.36/0.63 (step @p66 :rule beta-reduce :args ((= (_ @t111 @t164) @t167))) % 0.36/0.63 (step @p67 :rule trans :premises (@p66 @p65)) % 0.36/0.63 (step @p68 :rule beta-reduce :args ((= @t168 @t164))) % 0.36/0.63 (step @p69 :rule refl :args (@t111)) % 0.36/0.63 (step @p70 :rule ho_cong :premises (@p69 @p68)) % 0.36/0.63 (step @p71 :rule trans :premises (@p70 @p67)) % 0.36/0.63 (step @p72 :rule refl :args (@t110)) % 0.36/0.63 (step @p73 :rule ho_cong :premises (@p72 @p71)) % 0.36/0.63 (step @p74 :rule trans :premises (@p73 @p58)) % 0.36/0.63 (step @p75 :rule ho_cong :premises (@p74 @p34)) % 0.36/0.63 (step @p76 :rule trans :premises (@p75 @p33)) % 0.36/0.63 (step @p77 :rule ho_cong :premises (@p76 @p26)) % 0.36/0.63 (step @p78 :rule trans :premises (@p77 @p25)) % 0.36/0.63 (step @p79 :rule cong :premises (@p78) :args (@t169)) % 0.36/0.63 (step @p80 :rule cong :premises (@p13 @p79) :args (@t170)) % 0.36/0.63 (step @p81 :rule cong :premises (@p80) :args ((not @t170))) % 0.36/0.63 (step @p82 :rule refl :args (@t6)) % 0.36/0.63 (step @p83 :rule refl :args (@t150)) % 0.36/0.63 (step @p84 :rule refl :args (@t38)) % 0.36/0.63 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t38 @t150))) % 0.36/0.63 (step @p86 :rule symm :premises (@p85)) % 0.36/0.63 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 0.36/0.63 (step @p88 :rule refl :args (@t132)) % 0.36/0.63 (step @p89 :rule refl :args (@t136)) % 0.36/0.63 (step @p90 :rule nary_cong :premises (@p89 @p88 @p87) :args (@t171)) % 0.36/0.63 (step @p91 :rule cong :premises (@p90) :args ((forall @t31 @t171))) % 0.36/0.63 (step @p92 :rule refl :args (@t38)) % 0.36/0.63 (step @p93 :rule refl :args (@t130)) % 0.36/0.63 (step @p94 :rule refl :args (@t22)) % 0.36/0.63 (step @p95 :rule cong :premises (@p94 @p93) :args ((= @t22 @t130))) % 0.36/0.63 (step @p96 :rule symm :premises (@p95)) % 0.36/0.63 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.36/0.63 (step @p98 :rule refl :args (@t131)) % 0.36/0.63 (step @p99 :rule refl :args (@t7)) % 0.36/0.63 (step @p100 :rule cong :premises (@p99 @p98) :args ((= @t7 @t131))) % 0.36/0.63 (step @p101 :rule symm :premises (@p100)) % 0.36/0.63 (step @p102 :rule eq_resolve :premises (@p99 @p101)) % 0.36/0.63 (step @p103 :rule cong :premises (@p102) :args (@t8)) % 0.36/0.63 (step @p104 :rule nary_cong :premises (@p103 @p97) :args (@t23)) % 0.36/0.63 (step @p105 :rule cong :premises (@p104) :args (@t24)) % 0.36/0.63 (step @p106 :rule cong :premises (@p105) :args (@t25)) % 0.36/0.63 (step @p107 :rule refl :args (@t133)) % 0.36/0.63 (step @p108 :rule refl :args 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(@p123 @p117 @p111) :args (@t43)) % 0.36/0.63 (step @p125 :rule cong :premises (@p124) :args (@t45)) % 0.36/0.63 (step @p126 :rule cong :premises (@p125) :args (@t46)) % 0.36/0.63 (step @p127 :rule nary_cong :premises (@p126 @p106 @p92) :args (@t47)) % 0.36/0.63 (step @p128 :rule cong :premises (@p127) :args (@t48)) % 0.36/0.63 (step @p129 :rule trans :premises (@p128 @p91)) % 0.36/0.63 (step @p130 :rule cong :premises (@p129) :args (@t108)) % 0.36/0.63 (step @p131 :rule refl :args (tptp.tc)) % 0.36/0.63 (step @p132 :rule cong :premises (@p131 @p130) :args (@t109)) % 0.36/0.63 (step @p133 :rule and_elim :premises (@p1) :args (16)) % 0.36/0.63 (step @p134 :rule eq_resolve :premises (@p133 @p132)) % 0.36/0.63 (step @p135 :rule ho_cong :premises (@p134 @p82)) % 0.36/0.63 (step @p136 :rule and_elim :premises (@p1) :args (10)) % 0.36/0.63 (step @p137 :rule ho_cong :premises (@p136 @p135)) % 0.36/0.63 (step @p138 :rule and_elim :premises (@p1) :args (14)) % 0.36/0.63 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.36/0.63 (step @p140 :rule ho_cong :premises (@p139 @p34)) % 0.36/0.63 (step @p141 :rule ho_cong :premises (@p140 @p26)) % 0.36/0.63 (step @p142 :rule cong :premises (@p141) :args (@t126)) % 0.36/0.63 (step @p143 :rule refl :args (@t129)) % 0.36/0.63 (step @p144 :rule refl :args (@t97)) % 0.36/0.63 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t97 @t129))) % 0.36/0.63 (step @p146 :rule symm :premises (@p145)) % 0.36/0.63 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.36/0.63 (step @p148 :rule nary_cong :premises (@p89 @p88 @p147) :args (@t172)) % 0.36/0.63 (step @p149 :rule cong :premises (@p148) :args ((forall @t31 @t172))) % 0.36/0.63 (step @p150 :rule refl :args (@t97)) % 0.36/0.63 (step @p151 :rule nary_cong :premises (@p126 @p106 @p150) :args (@t98)) % 0.36/0.63 (step @p152 :rule cong :premises (@p151) :args (@t99)) % 0.36/0.63 (step @p153 :rule trans :premises (@p152 @p149)) % 0.36/0.63 (step @p154 :rule refl :args 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@p167) :args (@t107)) % 0.36/0.63 (step @p170 :rule and_elim :premises (@p1) :args (18)) % 0.36/0.63 (step @p171 :rule eq_resolve :premises (@p170 @p169)) % 0.36/0.63 (step @p172 :rule cong :premises (@p171 @p142) :args (@t127)) % 0.36/0.63 (step @p173 :rule cong :premises (@p172) :args (@t128)) % 0.36/0.63 (step @p174 :rule trans :premises (@p173 @p81)) % 0.36/0.63 (step @p175 :rule trans :premises (@p174 @p19)) % 0.36/0.63 (step @p176 :rule eq_resolve :premises (@p2 @p175)) % 0.36/0.63 (step @p177 :rule aci_norm :args ((= (or @t174 false) @t174))) % 0.36/0.63 (step @p178 :rule evaluate :args ((not true))) % 0.36/0.63 (step @p179 :rule eq-refl :args (@t179)) % 0.36/0.63 (step @p180 :rule refl :args (@t179)) % 0.36/0.63 (step @p181 :rule beta-reduce :args (@t180)) % 0.36/0.63 (step @p182 :rule cong :premises (@p181 @p180) :args (@t180)) % 0.36/0.63 (step @p183 :rule trans :premises (@p182 @p179)) % 0.36/0.63 (step @p184 :rule refl :args (@t175)) % 0.36/0.63 (step @p185 :rule refl :args 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@p190) :args (@t184)) % 0.36/0.64 (step @p201 :rule trans :premises (@p200 @p179)) % 0.36/0.64 (step @p202 :rule cong :premises (@p201) :args (@t185)) % 0.36/0.64 (step @p203 :rule trans :premises (@p202 @p178)) % 0.36/0.64 (step @p204 :rule refl :args (@t174)) % 0.36/0.64 (step @p205 :rule nary_cong :premises (@p204 @p203) :args (@t186)) % 0.36/0.64 (step @p206 :rule trans :premises (@p205 @p177)) % 0.36/0.64 ; WARNING: add trust step for TRUST % 0.36/0.64 ; trust TRUST THEORY_LEMMA % 0.36/0.64 (step @p207 :rule trust :premises () :args (@t186)) % 0.36/0.64 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 0.36/0.64 (step @p209 false :rule chain_m_resolution :premises (@p208 @p176) :args (false (@list true) (@list @t174))) % 0.36/0.64 ) % 0.36/0.64 % SZS output end Proof % 0.36/0.64 % cvc5 exiting %------------------------------------------------------------------------------