%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL624^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:11 AM UTC 2026 % Result : Theorem 0.19s 0.55s % Output : Proof 0.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL624^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.11/0.38 % Computer : n011.cluster.edu % 0.11/0.38 % Model : x86_64 x86_64 % 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.38 % Memory : 8046.5625MB % 0.11/0.38 % OS : Linux 6.8.0-71-generic % 0.11/0.38 % CPULimit : 300 % 0.11/0.38 % WCLimit : 300 % 0.11/0.38 % DateTime : Sat Sep 5 14:14:44 UTC 2026 % 0.11/0.39 % CPUTime : % 0.11/0.45 %----Proving TH0 % 0.19/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.19/0.55 % SZS status Theorem % 0.19/0.55 % SZS output start Proof % 0.19/0.55 ( % 0.19/0.55 (declare-sort $$unsorted 0) % 0.19/0.55 (declare-sort tptp.individuals 0) % 0.19/0.55 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.19/0.55 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.19/0.55 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.19/0.55 (define tptp.mor () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.55 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.19/0.55 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.19/0.55 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.19/0.55 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.55 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.19/0.55 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.55 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.19/0.55 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.55 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.19/0.55 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.55 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.19/0.55 (define @t1 () (@var "Q" (-> $$unsorted Bool))) % 0.19/0.55 (define @t2 () (@var "P" (-> $$unsorted Bool))) % 0.19/0.55 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.19/0.55 (define @t4 () (_ tptp.mdia @t3)) % 0.19/0.55 (define @t5 () (_ tptp.mbox @t3)) % 0.19/0.55 (define @t6 () (@list @t3 @t2 @t1)) % 0.19/0.55 (define @t7 () (forall @t6 (_ tptp.mvalid (_ (_ tptp.mimpl (_ (_ tptp.mand (_ @t4 (_ @t5 @t2))) (_ @t5 (_ @t4 @t1)))) (_ @t4 (_ @t4 (_ (_ tptp.mand @t2) @t1))))))) % 0.19/0.55 (define @t8 () (not @t7)) % 0.19/0.55 (define @t9 () (@var "X" $$unsorted)) % 0.19/0.55 (define @t10 () (@list @t9)) % 0.19/0.55 (define @t11 () (lambda @t10 false)) % 0.19/0.55 (define @t12 () (lambda @t10 true)) % 0.19/0.55 (define @t13 () (@var "U" $$unsorted)) % 0.19/0.55 (define @t14 () (@var "X" (-> $$unsorted Bool))) % 0.19/0.55 (define @t15 () (_ @t14 @t13)) % 0.19/0.55 (define @t16 () (lambda (@list @t14 @t13) (not @t15))) % 0.19/0.55 (define @t17 () (@var "Y" (-> $$unsorted Bool))) % 0.19/0.55 (define @t18 () (_ @t17 @t13)) % 0.19/0.55 (define @t19 () (@list @t14 @t17 @t13)) % 0.19/0.55 (define @t20 () (lambda @t19 (or @t15 @t18))) % 0.19/0.55 (define @t21 () (lambda @t19 (and @t15 @t18))) % 0.19/0.55 (define @t22 () (@var "__flatten_var_0" $$unsorted)) % 0.19/0.55 (define @t23 () (@var "V" (-> $$unsorted Bool))) % 0.19/0.55 (define @t24 () (@var "U" (-> $$unsorted Bool))) % 0.19/0.55 (define @t25 () (@list @t24 @t23 @t22)) % 0.19/0.55 (define @t26 () (lambda @t25 (_ (_ (_ tptp.mor (_ tptp.mnot @t24)) @t23) @t22))) % 0.19/0.55 (define @t27 () (lambda @t25 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t24) @t23)) (_ (_ tptp.mimpl @t23) @t24)) @t22))) % 0.19/0.55 (define @t28 () (@var "Y" $$unsorted)) % 0.19/0.55 (define @t29 () (_ @t2 @t28)) % 0.19/0.55 (define @t30 () (_ (_ @t3 @t9) @t28)) % 0.19/0.55 (define @t31 () (@list @t28)) % 0.19/0.55 (define @t32 () (forall @t31 (=> @t30 @t29))) % 0.19/0.55 (define @t33 () (@list @t3 @t2 @t9)) % 0.19/0.55 (define @t34 () (lambda @t33 @t32)) % 0.19/0.55 (define @t35 () (and @t30 @t29)) % 0.19/0.55 (define @t36 () (exists @t31 @t35)) % 0.19/0.55 (define @t37 () (lambda @t33 @t36)) % 0.19/0.55 (define @t38 () (@var "W" $$unsorted)) % 0.19/0.55 (define @t39 () (@var "X" tptp.individuals)) % 0.19/0.55 (define @t40 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.19/0.55 (define @t41 () (_ (_ @t40 @t39) @t38)) % 0.19/0.55 (define @t42 () (@list @t39)) % 0.19/0.55 (define @t43 () (@list @t40 @t38)) % 0.19/0.55 (define @t44 () (lambda @t43 (forall @t42 @t41))) % 0.19/0.55 (define @t45 () (lambda @t43 (exists @t42 @t41))) % 0.19/0.55 (define @t46 () (_ @t2 @t38)) % 0.19/0.55 (define @t47 () (@list @t38)) % 0.19/0.55 (define @t48 () (forall @t47 @t46)) % 0.19/0.55 (define @t49 () (@list @t2)) % 0.19/0.55 (define @t50 () (lambda @t49 @t48)) % 0.19/0.55 (define @t51 () (lambda @t49 (exists @t47 @t46))) % 0.19/0.55 (define @t52 () (not @t46)) % 0.19/0.55 (define @t53 () (lambda @t49 (exists @t47 @t52))) % 0.19/0.55 (define @t54 () (lambda @t49 (forall @t47 @t52))) % 0.19/0.55 (define @t55 () (@var "BOUND_VARIABLE_7798" $$unsorted)) % 0.19/0.55 (define @t56 () (_ @t2 @t55)) % 0.19/0.55 (define @t57 () (@var "BOUND_VARIABLE_7989" $$unsorted)) % 0.19/0.55 (define @t58 () (@list @t55)) % 0.19/0.55 (define @t59 () (not (forall @t58 (or (not (_ @t3 @t57 @t55)) @t56)))) % 0.19/0.55 (define @t60 () (not (_ @t3 @t38 @t57))) % 0.19/0.55 (define @t61 () (@var "BOUND_VARIABLE_7942" $$unsorted)) % 0.19/0.55 (define @t62 () (not (_ @t1 @t61))) % 0.19/0.55 (define @t63 () (not (_ @t2 @t61))) % 0.19/0.55 (define @t64 () (not (_ @t3 @t28 @t61))) % 0.19/0.55 (define @t65 () (not (_ @t3 @t38 @t28))) % 0.19/0.55 (define @t66 () (@list @t28 @t61)) % 0.19/0.55 (define @t67 () (not (forall @t66 (or @t65 @t64 @t63 @t62)))) % 0.19/0.55 (define @t68 () (@var "BOUND_VARIABLE_7840" $$unsorted)) % 0.19/0.55 (define @t69 () (not (_ @t1 @t68))) % 0.19/0.55 (define @t70 () (@list @t68)) % 0.19/0.55 (define @t71 () (not (forall @t70 (or (not (_ @t3 @t28 @t68)) @t69)))) % 0.19/0.55 (define @t72 () (forall @t31 (or @t65 @t71))) % 0.19/0.55 (define @t73 () (not @t72)) % 0.19/0.55 (define @t74 () (or @t73 @t67 @t60 @t59)) % 0.19/0.55 (define @t75 () (forall (@list @t3 @t2 @t1 @t38 @t57) @t74)) % 0.19/0.55 (define @t76 () (@list @t38 @t57)) % 0.19/0.55 (define @t77 () (or @t60 @t59)) % 0.19/0.55 (define @t78 () (or @t77 @t73 @t67)) % 0.19/0.55 (define @t79 () (forall @t76 @t78)) % 0.19/0.55 (define @t80 () (@list @t57)) % 0.19/0.55 (define @t81 () (forall @t80 @t78)) % 0.19/0.55 (define @t82 () (forall @t80 @t77)) % 0.19/0.55 (define @t83 () (@list @t28)) % 0.19/0.55 (define @t84 () (or @t82 @t73 @t67)) % 0.19/0.55 (define @t85 () (forall @t58 (or (not (_ @t3 @t28 @t55)) @t56))) % 0.19/0.55 (define @t86 () (not @t85)) % 0.19/0.55 (define @t87 () (forall @t31 (or @t65 @t86))) % 0.19/0.55 (define @t88 () (or @t87 @t73 @t67)) % 0.19/0.55 (define @t89 () (not @t87)) % 0.19/0.55 (define @t90 () (or (not (and @t89 @t72)) @t67)) % 0.19/0.55 (define @t91 () (not (_ @t3 @t22 @t28))) % 0.19/0.55 (define @t92 () (not (forall @t66 (or @t91 @t64 @t63 @t62)))) % 0.19/0.55 (define @t93 () (and (not (forall @t31 (or @t91 @t86))) (forall @t31 (or @t91 @t71)))) % 0.19/0.55 (define @t94 () (not @t93)) % 0.19/0.55 (define @t95 () (@list @t22)) % 0.19/0.55 (define @t96 () (lambda @t95 (or @t94 @t92))) % 0.19/0.55 (define @t97 () (_ @t96 @t38)) % 0.19/0.55 (define @t98 () (forall @t47 @t97)) % 0.19/0.55 (define @t99 () (_ @t2 @t38)) % 0.19/0.55 (define @t100 () (lambda @t49 (forall @t47 @t99))) % 0.19/0.55 (define @t101 () (_ @t3 @t9 @t28)) % 0.19/0.55 (define @t102 () (not @t101)) % 0.19/0.55 (define @t103 () (or @t102 @t64 @t63 @t62)) % 0.19/0.55 (define @t104 () (lambda @t10 (not (forall @t66 @t103)))) % 0.19/0.55 (define @t105 () (_ @t104 @t22)) % 0.19/0.55 (define @t106 () (or @t94 @t105)) % 0.19/0.55 (define @t107 () (lambda @t95 @t106)) % 0.19/0.55 (define @t108 () (_ @t23 @t22)) % 0.19/0.55 (define @t109 () (@list @t23 @t22)) % 0.19/0.55 (define @t110 () (or @t64 @t63 @t62)) % 0.19/0.55 (define @t111 () (or @t102 @t110)) % 0.19/0.55 (define @t112 () (forall @t66 @t111)) % 0.19/0.55 (define @t113 () (@list @t61)) % 0.19/0.55 (define @t114 () (forall @t113 @t111)) % 0.19/0.55 (define @t115 () (forall @t113 @t110)) % 0.19/0.55 (define @t116 () (@var "BOUND_VARIABLE_7920" $$unsorted)) % 0.19/0.55 (define @t117 () (@list @t116)) % 0.19/0.55 (define @t118 () (or @t102 @t115)) % 0.19/0.55 (define @t119 () (not (_ @t1 @t116))) % 0.19/0.55 (define @t120 () (not (_ @t2 @t116))) % 0.19/0.55 (define @t121 () (@list @t116)) % 0.19/0.55 (define @t122 () (forall @t121 (or (not (_ @t3 @t28 @t116)) @t120 @t119))) % 0.19/0.55 (define @t123 () (_ @t1 @t28)) % 0.19/0.55 (define @t124 () (not @t123)) % 0.19/0.55 (define @t125 () (_ @t2 @t28)) % 0.19/0.55 (define @t126 () (not @t125)) % 0.19/0.55 (define @t127 () (forall @t31 (or @t102 @t126 @t124))) % 0.19/0.55 (define @t128 () (not @t127)) % 0.19/0.55 (define @t129 () (lambda @t10 @t128)) % 0.19/0.55 (define @t130 () (not (_ @t129 @t28))) % 0.19/0.55 (define @t131 () (or @t102 @t130)) % 0.19/0.55 (define @t132 () (forall @t31 @t131)) % 0.19/0.55 (define @t133 () (not @t132)) % 0.19/0.55 (define @t134 () (lambda @t10 @t133)) % 0.19/0.55 (define @t135 () (not (forall @t31 (or @t102 @t126)))) % 0.19/0.55 (define @t136 () (@list @t2 @t9)) % 0.19/0.55 (define @t137 () (lambda @t136 @t135)) % 0.19/0.55 (define @t138 () (_ @t1 @t28)) % 0.19/0.55 (define @t139 () (not @t138)) % 0.19/0.55 (define @t140 () (not @t29)) % 0.19/0.55 (define @t141 () (or @t102 @t140 @t139)) % 0.19/0.55 (define @t142 () (and @t29 @t138)) % 0.19/0.55 (define @t143 () (or @t102 (not @t142))) % 0.19/0.55 (define @t144 () (_ @t2 @t13)) % 0.19/0.55 (define @t145 () (@list @t13)) % 0.19/0.55 (define @t146 () (lambda @t145 (and @t144 (_ @t1 @t13)))) % 0.19/0.55 (define @t147 () (_ @t146 @t28)) % 0.19/0.55 (define @t148 () (not @t147)) % 0.19/0.55 (define @t149 () (or @t102 @t148)) % 0.19/0.55 (define @t150 () (forall @t31 @t149)) % 0.19/0.55 (define @t151 () (not @t150)) % 0.19/0.55 (define @t152 () (lambda @t10 @t151)) % 0.19/0.55 (define @t153 () (@list @t17 @t13)) % 0.19/0.55 (define @t154 () (lambda @t153 (and @t144 @t18))) % 0.19/0.55 (define @t155 () (_ @t21 @t2)) % 0.19/0.55 (define @t156 () (_ (lambda @t33 @t135) @t3)) % 0.19/0.55 (define @t157 () (not (_ @t3 @t13 @t28))) % 0.19/0.55 (define @t158 () (forall @t31 (or @t157 @t71))) % 0.19/0.55 (define @t159 () (not (forall @t31 (or @t157 @t86)))) % 0.19/0.55 (define @t160 () (lambda @t145 (and @t159 @t158))) % 0.19/0.55 (define @t161 () (_ @t160 @t22)) % 0.19/0.55 (define @t162 () (not @t161)) % 0.19/0.55 (define @t163 () (or @t162 @t108)) % 0.19/0.55 (define @t164 () (lambda @t109 @t163)) % 0.19/0.55 (define @t165 () (or (not (_ @t24 @t22)) @t108)) % 0.19/0.55 (define @t166 () (lambda @t25 @t165)) % 0.19/0.55 (define @t167 () (lambda @t10 (forall @t31 (or @t102 @t71)))) % 0.19/0.55 (define @t168 () (_ @t167 @t13)) % 0.19/0.55 (define @t169 () (and @t159 @t168)) % 0.19/0.55 (define @t170 () (lambda @t145 @t169)) % 0.19/0.55 (define @t171 () (forall @t31 (or @t102 @t124))) % 0.19/0.55 (define @t172 () (not @t171)) % 0.19/0.55 (define @t173 () (lambda @t10 @t172)) % 0.19/0.55 (define @t174 () (or @t102 (_ @t173 @t28))) % 0.19/0.55 (define @t175 () (forall @t31 @t174)) % 0.19/0.55 (define @t176 () (lambda @t10 @t175)) % 0.19/0.55 (define @t177 () (forall @t31 (or @t102 @t125))) % 0.19/0.55 (define @t178 () (lambda @t136 @t177)) % 0.19/0.55 (define @t179 () (_ (lambda @t33 @t177) @t3)) % 0.19/0.55 (define @t180 () (lambda @t10 (not (forall @t31 (or @t102 @t86))))) % 0.19/0.55 (define @t181 () (_ @t180 @t13)) % 0.19/0.55 (define @t182 () (and @t181 @t18)) % 0.19/0.55 (define @t183 () (lambda @t153 @t182)) % 0.19/0.55 (define @t184 () (lambda @t10 @t177)) % 0.19/0.55 (define @t185 () (not (_ @t184 @t28))) % 0.19/0.55 (define @t186 () (or @t102 @t185)) % 0.19/0.55 (define @t187 () (forall @t31 @t186)) % 0.19/0.55 (define @t188 () (not @t187)) % 0.19/0.55 (define @t189 () (lambda @t10 @t188)) % 0.19/0.55 (define @t190 () (forall @t6 (_ @t100 (_ (_ @t166 (_ (_ @t21 (_ @t156 (_ @t179 @t2))) (_ @t179 (_ @t156 @t1)))) (_ @t156 (_ @t156 (_ @t155 @t1))))))) % 0.19/0.55 (define @t191 () (not @t30)) % 0.19/0.55 (define @t192 () (or @t191 @t140)) % 0.19/0.55 (define @t193 () (forall @t31 (not @t35))) % 0.19/0.55 (define @t194 () (not @t193)) % 0.19/0.55 (define @t195 () (or @t191 @t29)) % 0.19/0.55 (define @t196 () (not (_ @t24 @t13))) % 0.19/0.55 (define @t197 () (lambda @t145 (or @t196 (_ @t23 @t13)))) % 0.19/0.55 (define @t198 () (lambda @t145 @t196)) % 0.19/0.55 (define @t199 () (_ @t198 @t13)) % 0.19/0.55 (define @t200 () (or @t199 @t18)) % 0.19/0.55 (define @t201 () (lambda @t153 @t200)) % 0.19/0.55 (define @t202 () (@quantifiers_skolemize @t75 2)) % 0.19/0.55 (define @t203 () (not (_ @t202 @t68))) % 0.19/0.55 (define @t204 () (@quantifiers_skolemize @t75 0)) % 0.19/0.55 (define @t205 () (@quantifiers_skolemize @t75 3)) % 0.19/0.55 (define @t206 () (not (_ @t204 @t205 @t28))) % 0.19/0.55 (define @t207 () (forall @t31 (or @t206 (not (forall @t70 (or (not (_ @t204 @t28 @t68)) @t203)))))) % 0.19/0.55 (define @t208 () (@quantifiers_skolemize @t75 1)) % 0.19/0.55 (define @t209 () (@quantifiers_skolemize @t75 4)) % 0.19/0.55 (define @t210 () (forall @t58 (or (not (_ @t204 @t209 @t55)) (_ @t208 @t55)))) % 0.19/0.55 (define @t211 () (not @t210)) % 0.19/0.55 (define @t212 () (_ @t204 @t205 @t209)) % 0.19/0.55 (define @t213 () (not @t212)) % 0.19/0.55 (define @t214 () (forall @t66 (or @t206 (not (_ @t204 @t28 @t61)) (not (_ @t208 @t61)) (not (_ @t202 @t61))))) % 0.19/0.55 (define @t215 () (not @t214)) % 0.19/0.55 (define @t216 () (not @t207)) % 0.19/0.55 (define @t217 () (or @t216 @t215 @t213 @t211)) % 0.19/0.55 (define @t218 () (@list true)) % 0.19/0.55 (define @t219 () (@list @t217)) % 0.19/0.55 (define @t220 () (forall @t70 (or (not (_ @t204 @t209 @t68)) @t203))) % 0.19/0.55 (define @t221 () (not @t220)) % 0.19/0.55 (define @t222 () (or @t213 @t221)) % 0.19/0.55 (define @t223 () (@quantifiers_skolemize @t220 0)) % 0.19/0.55 (define @t224 () (_ @t204 @t209 @t223)) % 0.19/0.55 (define @t225 () (_ @t202 @t223)) % 0.19/0.55 (define @t226 () (not @t225)) % 0.19/0.55 (define @t227 () (not @t224)) % 0.19/0.55 (define @t228 () (or @t227 @t226)) % 0.19/0.55 (define @t229 () (@list @t228)) % 0.19/0.55 (define @t230 () (_ @t208 @t223)) % 0.19/0.55 (define @t231 () (not @t230)) % 0.19/0.55 (define @t232 () (or @t213 @t227 @t231 @t226)) % 0.19/0.55 (define @t233 () (or @t227 @t230)) % 0.19/0.55 (assume @p1 @t8) % 0.19/0.55 (assume @p2 true) % 0.19/0.55 (step @p3 (= tptp.mfalse @t11) :rule refl :args (@t11)) % 0.19/0.55 (step @p4 (= tptp.mtrue @t12) :rule refl :args (@t12)) % 0.19/0.55 (step @p5 (= tptp.mnot @t16) :rule refl :args (@t16)) % 0.19/0.55 (step @p6 (= tptp.mor @t20) :rule refl :args (@t20)) % 0.19/0.55 (step @p7 (= tptp.mand @t21) :rule refl :args (@t21)) % 0.19/0.55 (step @p8 (= tptp.mimpl @t26) :rule refl :args (@t26)) % 0.19/0.55 (step @p9 (= tptp.miff @t27) :rule refl :args (@t27)) % 0.19/0.55 (step @p10 (= tptp.mbox @t34) :rule refl :args (@t34)) % 0.19/0.55 (step @p11 (= tptp.mdia @t37) :rule refl :args (@t37)) % 0.19/0.55 (step @p12 (= tptp.mall @t44) :rule refl :args (@t44)) % 0.19/0.55 (step @p13 (= tptp.mexists @t45) :rule refl :args (@t45)) % 0.19/0.55 (step @p14 (= tptp.mvalid @t50) :rule refl :args (@t50)) % 0.19/0.55 (step @p15 (= tptp.msatisfiable @t51) :rule refl :args (@t51)) % 0.19/0.55 (step @p16 (= tptp.mcountersatisfiable @t53) :rule refl :args (@t53)) % 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(step @p61 :rule cong :premises (@p60) :args ((forall @t31 (or @t102 @t122)))) % 0.19/0.55 (step @p62 :rule trans :premises (@p61 @p54)) % 0.19/0.55 (step @p63 :rule trans :premises (@p62 @p53)) % 0.19/0.55 (step @p64 :rule bool-double-not-elim :args (@t122)) % 0.19/0.55 (step @p65 :rule beta-reduce :args ((= (_ (lambda @t10 (not (forall @t121 (or (not (_ @t3 @t9 @t116)) @t120 @t119)))) @t28) (not @t122)))) % 0.19/0.55 (step @p66 :rule refl :args (@t28)) % 0.19/0.55 (step @p67 :rule alpha_equiv :args (@t127 @t83 @t117)) % 0.19/0.55 (step @p68 :rule cong :premises (@p67) :args (@t128)) % 0.19/0.55 (step @p69 :rule cong :premises (@p68) :args (@t129)) % 0.19/0.55 (step @p70 :rule ho_cong :premises (@p69 @p66)) % 0.19/0.55 (step @p71 :rule trans :premises (@p70 @p65)) % 0.19/0.55 (step @p72 :rule cong :premises (@p71) :args (@t130)) % 0.19/0.55 (step @p73 :rule trans :premises (@p72 @p64)) % 0.19/0.55 (step @p74 :rule refl :args (@t102)) % 0.19/0.55 (step @p75 :rule nary_cong :premises 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:args (@t150)) % 0.19/0.55 (step @p106 :rule trans :premises (@p105 @p101)) % 0.19/0.55 (step @p107 :rule cong :premises (@p106) :args (@t151)) % 0.19/0.55 (step @p108 :rule cong :premises (@p107) :args (@t152)) % 0.19/0.55 (step @p109 :rule beta-reduce :args ((= (_ @t137 @t146) @t152))) % 0.19/0.55 (step @p110 :rule trans :premises (@p109 @p108)) % 0.19/0.55 (step @p111 :rule beta-reduce :args ((= (_ @t154 @t1) @t146))) % 0.19/0.55 (step @p112 :rule refl :args (@t1)) % 0.19/0.55 (step @p113 :rule beta-reduce :args ((= @t155 @t154))) % 0.19/0.55 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 0.19/0.55 (step @p115 :rule trans :premises (@p114 @p111)) % 0.19/0.55 (step @p116 :rule beta-reduce :args ((= @t156 @t137))) % 0.19/0.55 (step @p117 :rule ho_cong :premises (@p116 @p115)) % 0.19/0.55 (step @p118 :rule trans :premises (@p117 @p110)) % 0.19/0.55 (step @p119 :rule ho_cong :premises (@p116 @p118)) % 0.19/0.55 (step @p120 :rule trans :premises (@p119 @p81)) % 0.19/0.55 (step 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(step @p179 :rule trans :premises (@p178 @p133)) % 0.19/0.55 (step @p180 :rule refl :args (@t166)) % 0.19/0.55 (step @p181 :rule ho_cong :premises (@p180 @p179)) % 0.19/0.55 (step @p182 :rule trans :premises (@p181 @p127)) % 0.19/0.55 (step @p183 :rule ho_cong :premises (@p182 @p120)) % 0.19/0.55 (step @p184 :rule trans :premises (@p183 @p51)) % 0.19/0.55 (step @p185 :rule refl :args (@t100)) % 0.19/0.55 (step @p186 :rule ho_cong :premises (@p185 @p184)) % 0.19/0.55 (step @p187 :rule trans :premises (@p186 @p45)) % 0.19/0.55 (step @p188 :rule cong :premises (@p187) :args (@t190)) % 0.19/0.55 (step @p189 :rule trans :premises (@p188 @p18)) % 0.19/0.55 (step @p190 :rule cong :premises (@p189) :args ((not @t190))) % 0.19/0.55 (step @p191 :rule ho_cong :premises (@p7 @p170)) % 0.19/0.55 (step @p192 :rule ho_cong :premises (@p191 @p112)) % 0.19/0.55 (step @p193 :rule refl :args (@t3)) % 0.19/0.55 (step @p194 :rule refl :args (@t101)) % 0.19/0.55 (step @p195 :rule refl :args (@t30)) % 0.19/0.55 (step @p196 :rule cong :premises (@p195 @p194) :args ((= @t30 @t101))) % 0.19/0.55 (step @p197 :rule symm :premises (@p196)) % 0.19/0.55 (step @p198 :rule eq_resolve :premises (@p195 @p197)) % 0.19/0.55 (step @p199 :rule cong :premises (@p198) :args (@t191)) % 0.19/0.55 (step @p200 :rule nary_cong :premises (@p199 @p93) :args (@t192)) % 0.19/0.55 (step @p201 :rule cong :premises (@p200) :args ((forall @t31 @t192))) % 0.19/0.55 (step @p202 :rule bool-and-de-morgan :args (@t30 @t29 true)) % 0.19/0.55 (step @p203 :rule cong :premises (@p202) :args (@t193)) % 0.19/0.55 (step @p204 :rule trans :premises (@p203 @p201)) % 0.19/0.55 (step @p205 :rule cong :premises (@p204) :args (@t194)) % 0.19/0.55 (step @p206 :rule exists-elim :args ((= @t36 @t194))) % 0.19/0.55 (step @p207 :rule trans :premises (@p206 @p205)) % 0.19/0.55 (step @p208 :rule cong :premises (@p207) :args (@t37)) % 0.19/0.55 (step @p209 :rule trans :premises (@p11 @p208)) % 0.19/0.55 (step @p210 :rule ho_cong :premises (@p209 @p193)) % 0.19/0.55 (step @p211 :rule ho_cong :premises (@p210 @p192)) % 0.19/0.55 (step @p212 :rule ho_cong :premises (@p210 @p211)) % 0.19/0.55 (step @p213 :rule ho_cong :premises (@p210 @p112)) % 0.19/0.55 (step @p214 :rule nary_cong :premises (@p199 @p92) :args (@t195)) % 0.19/0.55 (step @p215 :rule cong :premises (@p214) :args ((forall @t31 @t195))) % 0.19/0.55 (step @p216 :rule bool-impl-elim :args (@t30 @t29)) % 0.19/0.55 (step @p217 :rule cong :premises (@p216) :args (@t32)) % 0.19/0.55 (step @p218 :rule trans :premises (@p217 @p215)) % 0.19/0.55 (step @p219 :rule cong :premises (@p218) :args (@t34)) % 0.19/0.55 (step @p220 :rule trans :premises (@p10 @p219)) % 0.19/0.55 (step @p221 :rule ho_cong :premises (@p220 @p193)) % 0.19/0.55 (step @p222 :rule ho_cong :premises (@p221 @p213)) % 0.19/0.55 (step @p223 :rule ho_cong :premises (@p221 @p170)) % 0.19/0.55 (step @p224 :rule ho_cong :premises (@p210 @p223)) % 0.19/0.55 (step @p225 :rule ho_cong :premises (@p7 @p224)) % 0.19/0.55 (step @p226 :rule ho_cong :premises (@p225 @p222)) % 0.19/0.55 (step @p227 :rule beta-reduce :args ((= (_ @t197 @t22) @t165))) % 0.19/0.55 (step @p228 :rule refl :args (@t22)) % 0.19/0.55 (step @p229 :rule beta-reduce :args ((= (_ (lambda @t153 (or @t196 @t18)) @t23) @t197))) % 0.19/0.55 (step @p230 :rule refl :args (@t23)) % 0.19/0.55 (step @p231 :rule beta-reduce :args ((= @t199 @t196))) % 0.19/0.55 (step @p232 :rule nary_cong :premises (@p231 @p151) :args (@t200)) % 0.19/0.55 (step @p233 :rule cong :premises (@p232) :args (@t201)) % 0.19/0.55 (step @p234 :rule beta-reduce :args ((= (_ @t20 @t198) @t201))) % 0.19/0.55 (step @p235 :rule trans :premises (@p234 @p233)) % 0.19/0.55 (step @p236 :rule beta-reduce :args ((= (_ @t16 @t24) @t198))) % 0.19/0.55 (step @p237 :rule refl :args (@t20)) % 0.19/0.55 (step @p238 :rule ho_cong :premises (@p237 @p236)) % 0.19/0.55 (step @p239 :rule trans :premises (@p238 @p235)) % 0.19/0.55 (step @p240 :rule ho_cong :premises (@p239 @p230)) % 0.19/0.55 (step @p241 :rule trans :premises (@p240 @p229)) % 0.19/0.55 (step @p242 :rule ho_cong :premises (@p241 @p228)) % 0.19/0.55 (step @p243 :rule trans :premises (@p242 @p227)) % 0.19/0.55 (step @p244 :rule refl :args (@t24)) % 0.19/0.55 (step @p245 :rule ho_cong :premises (@p5 @p244)) % 0.19/0.55 (step @p246 :rule ho_cong :premises (@p6 @p245)) % 0.19/0.55 (step @p247 :rule ho_cong :premises (@p246 @p230)) % 0.19/0.55 (step @p248 :rule ho_cong :premises (@p247 @p228)) % 0.19/0.55 (step @p249 :rule trans :premises (@p248 @p243)) % 0.19/0.55 (step @p250 :rule cong :premises (@p249) :args (@t26)) % 0.19/0.55 (step @p251 :rule trans :premises (@p8 @p250)) % 0.19/0.55 (step @p252 :rule ho_cong :premises (@p251 @p226)) % 0.19/0.55 (step @p253 :rule ho_cong :premises (@p252 @p212)) % 0.19/0.55 (step @p254 :rule refl :args (@t99)) % 0.19/0.55 (step @p255 :rule refl :args (@t46)) % 0.19/0.55 (step @p256 :rule cong :premises (@p255 @p254) :args ((= @t46 @t99))) % 0.19/0.55 (step @p257 :rule symm :premises (@p256)) % 0.19/0.55 (step @p258 :rule eq_resolve :premises (@p255 @p257)) % 0.19/0.55 (step @p259 :rule cong :premises (@p258) :args (@t48)) % 0.19/0.55 (step @p260 :rule cong :premises (@p259) :args (@t50)) % 0.19/0.55 (step @p261 :rule trans :premises (@p14 @p260)) % 0.19/0.55 (step @p262 :rule ho_cong :premises (@p261 @p253)) % 0.19/0.55 (step @p263 :rule cong :premises (@p262) :args (@t7)) % 0.19/0.55 (step @p264 :rule cong :premises (@p263) :args (@t8)) % 0.19/0.55 (step @p265 :rule trans :premises (@p264 @p190)) % 0.19/0.55 (step @p266 :rule eq_resolve :premises (@p1 @p265)) % 0.19/0.55 (step @p267 :rule skolemize :premises (@p266)) % 0.19/0.55 (step @p268 :rule bool-double-not-elim :args (@t207)) % 0.19/0.55 (step @p269 :rule refl :args (@t217)) % 0.19/0.55 (step @p270 :rule nary_cong :premises (@p269 @p268) :args ((or @t217 (not @t216)))) % 0.19/0.55 (step @p271 :rule cnf_or_neg :args (@t217 0)) % 0.19/0.55 (step @p272 :rule eq_resolve :premises (@p271 @p270)) % 0.19/0.55 (step @p273 :rule reordering :premises (@p272) :args ((or @t207 @t217))) % 0.19/0.55 (step @p274 :rule chain_m_resolution :premises (@p273 @p267) :args (@t207 @t218 @t219)) % 0.19/0.55 (step @p275 :rule instantiate :premises (@p274) :args ((@list @t209))) % 0.19/0.55 (step @p276 :rule bool-double-not-elim :args (@t212)) % 0.19/0.55 (step @p277 :rule nary_cong :premises (@p269 @p276) :args ((or @t217 (not @t213)))) % 0.19/0.55 (step @p278 :rule cnf_or_neg :args (@t217 2)) % 0.19/0.55 (step @p279 :rule eq_resolve :premises (@p278 @p277)) % 0.19/0.55 (step @p280 :rule reordering :premises (@p279) :args ((or @t212 @t217))) % 0.19/0.55 (step @p281 :rule chain_m_resolution :premises (@p280 @p267) :args (@t212 @t218 @t219)) % 0.19/0.55 (step @p282 :rule cnf_or_pos :args (@t222)) % 0.19/0.55 (step @p283 :rule reordering :premises (@p282) :args ((or @t213 @t221 (not @t222)))) % 0.19/0.55 (step @p284 :rule chain_m_resolution :premises (@p283 @p281 @p275) :args (@t221 (@list false false) (@list @t212 @t222))) % 0.19/0.55 (step @p285 :rule skolemize :premises (@p284)) % 0.19/0.55 (step @p286 :rule bool-double-not-elim :args (@t224)) % 0.19/0.55 (step @p287 :rule refl :args (@t228)) % 0.19/0.55 (step @p288 :rule nary_cong :premises (@p287 @p286) :args ((or @t228 (not @t227)))) % 0.19/0.55 (step @p289 :rule cnf_or_neg :args (@t228 0)) % 0.19/0.55 (step @p290 :rule eq_resolve :premises (@p289 @p288)) % 0.19/0.55 (step @p291 :rule reordering :premises (@p290) :args ((or @t224 @t228))) % 0.19/0.55 (step @p292 :rule chain_m_resolution :premises (@p291 @p285) :args (@t224 @t218 @t229)) % 0.19/0.55 (step @p293 :rule bool-double-not-elim :args (@t210)) % 0.19/0.55 (step @p294 :rule nary_cong :premises (@p269 @p293) :args ((or @t217 (not @t211)))) % 0.19/0.55 (step @p295 :rule cnf_or_neg :args (@t217 3)) % 0.19/0.55 (step @p296 :rule eq_resolve :premises (@p295 @p294)) % 0.19/0.55 (step @p297 :rule reordering :premises (@p296) :args ((or @t210 @t217))) % 0.19/0.55 (step @p298 :rule chain_m_resolution :premises (@p297 @p267) :args (@t210 @t218 @t219)) % 0.19/0.55 (step @p299 :rule instantiate :premises (@p298) :args ((@list @t223))) % 0.19/0.55 (step @p300 :rule bool-double-not-elim :args (@t214)) % 0.19/0.55 (step @p301 :rule nary_cong :premises (@p269 @p300) :args ((or @t217 (not @t215)))) % 0.19/0.55 (step @p302 :rule cnf_or_neg :args (@t217 1)) % 0.19/0.55 (step @p303 :rule eq_resolve :premises (@p302 @p301)) % 0.19/0.55 (step @p304 :rule reordering :premises (@p303) :args ((or @t214 @t217))) % 0.19/0.55 (step @p305 :rule chain_m_resolution :premises (@p304 @p267) :args (@t214 @t218 @t219)) % 0.19/0.55 (step @p306 :rule instantiate :premises (@p305) :args ((@list @t209 @t223))) % 0.19/0.55 (step @p307 :rule bool-double-not-elim :args (@t225)) % 0.19/0.55 (step @p308 :rule nary_cong :premises (@p287 @p307) :args ((or @t228 (not @t226)))) % 0.19/0.55 (step @p309 :rule cnf_or_neg :args (@t228 1)) % 0.19/0.55 (step @p310 :rule eq_resolve :premises (@p309 @p308)) % 0.19/0.55 (step @p311 :rule reordering :premises (@p310) :args ((or @t225 @t228))) % 0.19/0.55 (step @p312 :rule chain_m_resolution :premises (@p311 @p285) :args (@t225 @t218 @t229)) % 0.19/0.55 (step @p313 :rule cnf_or_pos :args (@t232)) % 0.19/0.55 (step @p314 :rule reordering :premises (@p313) :args ((or @t213 @t227 @t226 @t231 (not @t232)))) % 0.19/0.55 (step @p315 :rule chain_m_resolution :premises (@p314 @p281 @p292 @p312 @p306) :args (@t231 (@list false false false false) (@list @t212 @t224 @t225 @t232))) % 0.19/0.55 (step @p316 :rule cnf_or_pos :args (@t233)) % 0.19/0.55 (step @p317 :rule reordering :premises (@p316) :args ((or @t227 @t230 (not @t233)))) % 0.19/0.55 (step @p318 false :rule chain_m_resolution :premises (@p317 @p315 @p299 @p292) :args (false (@list true false false) (@list @t230 @t233 @t224))) % 0.19/0.55 ) % 0.19/0.55 % SZS output end Proof % 0.19/0.55 % cvc5 exiting %------------------------------------------------------------------------------