%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n016.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 11:23:04 AM UTC 2026 % Result : Theorem 99.65s 100.88s % Output : Proof 78.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL550+1 : TPTP v9.3.1. Bugfixed v9.2.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.10/0.37 % Computer : n016.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.37 % CPULimit : 300 % 0.10/0.37 % WCLimit : 300 % 0.10/0.37 % DateTime : Sat Sep 5 18:22:00 UTC 2026 % 0.10/0.37 % CPUTime : % 0.10/0.46 %----Proving TF0_NAR, FOF, or CNF % 99.65/100.88 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 99.65/100.88 --- Run --no-e-matching --full-saturate-quant at 6... % 99.65/100.88 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 99.65/100.88 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 99.65/100.88 --- Run --multi-trigger-when-single --full-saturate-quant at 30... % 99.65/100.88 --- Run --trigger-sel=max --full-saturate-quant at 15... % 99.65/100.88 --- Run --multi-trigger-when-single --multi-trigger-priority --full-saturate-quant at 33... % 99.65/100.88 % SZS status Theorem % 99.65/100.88 % SZS output start Proof % 99.65/100.88 ( % 99.65/100.88 (declare-sort $$unsorted 0) % 99.65/100.88 (declare-const tptp.op_strict_implies Bool) % 99.65/100.88 (declare-const tptp.op_possibly Bool) % 99.65/100.88 (declare-const tptp.axiom_m10 Bool) % 99.65/100.88 (declare-const tptp.axiom_m9 Bool) % 99.65/100.88 (declare-const tptp.axiom_m7 Bool) % 99.65/100.88 (declare-const tptp.axiom_m6 Bool) % 99.65/100.88 (declare-const tptp.r2 Bool) % 99.65/100.88 (declare-const tptp.r1 Bool) % 99.65/100.88 (declare-const tptp.is_a_theorem (-> $$unsorted Bool)) % 99.65/100.88 (declare-const tptp.op_necessarily Bool) % 99.65/100.88 (declare-const tptp.kn3 Bool) % 99.65/100.88 (declare-const tptp.strict_equiv (-> $$unsorted $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.cn2 Bool) % 99.65/100.88 (declare-const tptp.axiom_m3 Bool) % 99.65/100.88 (declare-const tptp.kn2 Bool) % 99.65/100.88 (declare-const tptp.cn1 Bool) % 99.65/100.88 (declare-const tptp.or_2 Bool) % 99.65/100.88 (declare-const tptp.and_3 Bool) % 99.65/100.88 (declare-const tptp.r5 Bool) % 99.65/100.88 (declare-const tptp.necessitation Bool) % 99.65/100.88 (declare-const tptp.equivalence_1 Bool) % 99.65/100.88 (declare-const tptp.implies_1 Bool) % 99.65/100.88 (declare-const tptp.equivalence_2 Bool) % 99.65/100.88 (declare-const tptp.or_3 Bool) % 99.65/100.88 (declare-const tptp.and (-> $$unsorted $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.implies (-> $$unsorted $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.or (-> $$unsorted $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.substitution_of_equivalents Bool) % 99.65/100.88 (declare-const tptp.implies_3 Bool) % 99.65/100.88 (declare-const tptp.equiv (-> $$unsorted $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.axiom_m1 Bool) % 99.65/100.88 (declare-const tptp.and_1 Bool) % 99.65/100.88 (declare-const tptp.equivalence_3 Bool) % 99.65/100.88 (declare-const tptp.necessarily (-> $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.or_1 Bool) % 99.65/100.88 (declare-const tptp.op_or Bool) % 99.65/100.88 (declare-const tptp.cn3 Bool) % 99.65/100.88 (declare-const tptp.not (-> $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.op_strict_equiv Bool) % 99.65/100.88 (declare-const tptp.axiom_4 Bool) % 99.65/100.88 (declare-const tptp.modus_tollens Bool) % 99.65/100.88 (declare-const tptp.and_2 Bool) % 99.65/100.88 (declare-const tptp.implies_2 Bool) % 99.65/100.88 (declare-const tptp.axiom_5 Bool) % 99.65/100.88 (declare-const tptp.axiom_s2 Bool) % 99.65/100.88 (declare-const tptp.r4 Bool) % 99.65/100.88 (declare-const tptp.kn1 Bool) % 99.65/100.88 (declare-const tptp.adjunction Bool) % 99.65/100.88 (declare-const tptp.modus_ponens Bool) % 99.65/100.88 (declare-const tptp.op_and Bool) % 99.65/100.88 (declare-const tptp.axiom_M Bool) % 99.65/100.88 (declare-const tptp.possibly (-> $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.op_equiv Bool) % 99.65/100.88 (declare-const tptp.strict_implies (-> $$unsorted $$unsorted $$unsorted)) % 99.65/100.88 (declare-const tptp.axiom_m8 Bool) % 99.65/100.88 (declare-const tptp.modus_ponens_strict_implies Bool) % 99.65/100.88 (declare-const tptp.substitution_strict_equiv Bool) % 99.65/100.88 (declare-const tptp.axiom_K Bool) % 99.65/100.88 (declare-const tptp.op_implies Bool) % 99.65/100.88 (declare-const tptp.axiom_B Bool) % 99.65/100.88 (declare-const tptp.axiom_s1 Bool) % 99.65/100.88 (declare-const tptp.r3 Bool) % 99.65/100.88 (declare-const tptp.axiom_s3 Bool) % 99.65/100.88 (declare-const tptp.axiom_s4 Bool) % 99.65/100.88 (declare-const tptp.axiom_m2 Bool) % 99.65/100.88 (declare-const tptp.op_implies_and Bool) % 99.65/100.88 (declare-const tptp.axiom_m4 Bool) % 99.65/100.88 (declare-const tptp.op_implies_or Bool) % 99.65/100.88 (declare-const tptp.axiom_m5 Bool) % 99.65/100.88 (define @t1 () (@var "Y" $$unsorted)) % 99.65/100.88 (define @t2 () (tptp.is_a_theorem @t1)) % 99.65/100.88 (define @t3 () (@var "X" $$unsorted)) % 99.65/100.88 (define @t4 () (tptp.implies @t3 @t1)) % 99.65/100.88 (define @t5 () (tptp.is_a_theorem @t4)) % 99.65/100.88 (define @t6 () (tptp.is_a_theorem @t3)) % 99.65/100.88 (define @t7 () (and @t6 @t5)) % 99.65/100.88 (define @t8 () (@list @t3 @t1)) % 99.65/100.88 (define @t9 () (forall @t8 (=> @t7 @t2))) % 99.65/100.88 (define @t10 () (= tptp.modus_ponens @t9)) % 99.65/100.88 (define @t11 () (= @t3 @t1)) % 99.65/100.88 (define @t12 () (tptp.equiv @t3 @t1)) % 99.65/100.88 (define @t13 () (tptp.not @t3)) % 99.65/100.88 (define @t14 () (tptp.not @t1)) % 99.65/100.88 (define @t15 () (tptp.implies @t1 @t3)) % 99.65/100.88 (define @t16 () (@var "Z" $$unsorted)) % 99.65/100.88 (define @t17 () (tptp.implies @t3 @t16)) % 99.65/100.88 (define @t18 () (tptp.implies @t1 @t16)) % 99.65/100.88 (define @t19 () (@list @t3 @t1 @t16)) % 99.65/100.88 (define @t20 () (tptp.and @t3 @t1)) % 99.65/100.88 (define @t21 () (tptp.or @t3 @t1)) % 99.65/100.88 (define @t22 () (@var "P" $$unsorted)) % 99.65/100.88 (define @t23 () (@list @t22)) % 99.65/100.88 (define @t24 () (@var "Q" $$unsorted)) % 99.65/100.88 (define @t25 () (tptp.and @t22 @t24)) % 99.65/100.88 (define @t26 () (@list @t22 @t24)) % 99.65/100.88 (define @t27 () (@var "R" $$unsorted)) % 99.65/100.88 (define @t28 () (tptp.implies @t22 @t24)) % 99.65/100.88 (define @t29 () (@list @t22 @t24 @t27)) % 99.65/100.88 (define @t30 () (tptp.implies @t24 @t27)) % 99.65/100.88 (define @t31 () (tptp.not @t22)) % 99.65/100.88 (define @t32 () (tptp.or @t22 @t24)) % 99.65/100.88 (define @t33 () (tptp.or @t22 @t27)) % 99.65/100.88 (define @t34 () (forall @t8 (= @t4 (tptp.not (tptp.and @t3 @t14))))) % 99.65/100.88 (define @t35 () (=> tptp.op_implies_and @t34)) % 99.65/100.88 (define @t36 () (tptp.necessarily @t3)) % 99.65/100.88 (define @t37 () (@list @t3)) % 99.65/100.88 (define @t38 () (tptp.strict_implies @t3 @t1)) % 99.65/100.88 (define @t39 () (tptp.is_a_theorem @t38)) % 99.65/100.88 (define @t40 () (and @t6 @t39)) % 99.65/100.88 (define @t41 () (forall @t8 (=> @t40 @t2))) % 99.65/100.88 (define @t42 () (= tptp.modus_ponens_strict_implies @t41)) % 99.65/100.88 (define @t43 () (tptp.is_a_theorem @t20)) % 99.65/100.88 (define @t44 () (and @t6 @t2)) % 99.65/100.88 (define @t45 () (forall @t8 (=> @t44 @t43))) % 99.65/100.88 (define @t46 () (= tptp.adjunction @t45)) % 99.65/100.88 (define @t47 () (tptp.strict_equiv @t3 @t1)) % 99.65/100.88 (define @t48 () (tptp.is_a_theorem @t47)) % 99.65/100.88 (define @t49 () (forall @t8 (=> @t48 @t11))) % 99.65/100.88 (define @t50 () (= tptp.substitution_strict_equiv @t49)) % 99.65/100.88 (define @t51 () (tptp.necessarily @t4)) % 99.65/100.88 (define @t52 () (tptp.necessarily @t36)) % 99.65/100.88 (define @t53 () (tptp.possibly @t3)) % 99.65/100.88 (define @t54 () (tptp.necessarily @t53)) % 99.65/100.88 (define @t55 () (tptp.possibly @t24)) % 99.65/100.88 (define @t56 () (tptp.possibly @t22)) % 99.65/100.88 (define @t57 () (tptp.possibly @t25)) % 99.65/100.88 (define @t58 () (forall @t8 (= @t38 @t51))) % 99.65/100.88 (define @t59 () (=> tptp.op_strict_implies @t58)) % 99.65/100.88 (define @t60 () (forall @t8 (= @t47 (tptp.and @t38 (tptp.strict_implies @t1 @t3))))) % 99.65/100.88 (define @t61 () (=> tptp.op_strict_equiv @t60)) % 99.65/100.88 (define @t62 () (not tptp.modus_ponens)) % 99.65/100.88 (define @t63 () (not @t5)) % 99.65/100.88 (define @t64 () (not @t6)) % 99.65/100.88 (define @t65 () (or @t64 @t63 @t2)) % 99.65/100.88 (define @t66 () (forall @t8 @t65)) % 99.65/100.88 (define @t67 () (@quantifiers_skolemize @t66 0)) % 99.65/100.88 (define @t68 () (@quantifiers_skolemize @t66 1)) % 99.65/100.88 (define @t69 () (tptp.not @t68)) % 99.65/100.88 (define @t70 () (tptp.and @t67 @t69)) % 99.65/100.88 (define @t71 () (tptp.and @t69 @t67)) % 99.65/100.88 (define @t72 () (@list @t71 @t70)) % 99.65/100.88 (define @t73 () (tptp.not @t70)) % 99.65/100.88 (define @t74 () (tptp.and @t73 @t71)) % 99.65/100.88 (define @t75 () (tptp.and @t71 @t73)) % 99.65/100.88 (define @t76 () (@list @t75 @t74)) % 99.65/100.88 (define @t77 () (not @t2)) % 99.65/100.88 (define @t78 () (tptp.strict_implies @t74 @t75)) % 99.65/100.88 (define @t79 () (tptp.strict_implies @t75 @t74)) % 99.65/100.88 (define @t80 () (tptp.is_a_theorem (tptp.and @t79 @t78))) % 99.65/100.88 (define @t81 () (tptp.is_a_theorem @t78)) % 99.65/100.88 (define @t82 () (not @t81)) % 99.65/100.88 (define @t83 () (tptp.is_a_theorem @t79)) % 99.65/100.88 (define @t84 () (not @t83)) % 99.65/100.88 (define @t85 () (or @t84 @t82 @t80)) % 99.65/100.88 (define @t86 () (@list false false false)) % 99.65/100.88 (define @t87 () (tptp.is_a_theorem (tptp.strict_equiv @t75 @t74))) % 99.65/100.88 (define @t88 () (= @t75 @t74)) % 99.65/100.88 (define @t89 () (not @t87)) % 99.65/100.88 (define @t90 () (or @t89 @t88)) % 99.65/100.88 (define @t91 () (@list false false)) % 99.65/100.88 (define @t92 () (@list @t70 @t71)) % 99.65/100.88 (define @t93 () (tptp.strict_implies @t71 @t70)) % 99.65/100.88 (define @t94 () (tptp.strict_implies @t70 @t71)) % 99.65/100.88 (define @t95 () (tptp.is_a_theorem (tptp.and @t94 @t93))) % 99.65/100.88 (define @t96 () (tptp.is_a_theorem @t93)) % 99.65/100.88 (define @t97 () (not @t96)) % 99.65/100.88 (define @t98 () (tptp.is_a_theorem @t94)) % 99.65/100.88 (define @t99 () (not @t98)) % 99.65/100.88 (define @t100 () (or @t99 @t97 @t95)) % 99.65/100.88 (define @t101 () (tptp.is_a_theorem (tptp.strict_equiv @t70 @t71))) % 99.65/100.88 (define @t102 () (= @t70 @t71)) % 99.65/100.88 (define @t103 () (not @t101)) % 99.65/100.88 (define @t104 () (or @t103 @t102)) % 99.65/100.88 (define @t105 () (tptp.and @t73 @t70)) % 99.65/100.88 (define @t106 () (tptp.and @t73 @t67)) % 99.65/100.88 (define @t107 () (tptp.and @t106 @t69)) % 99.65/100.88 (define @t108 () (@list @t107 @t105)) % 99.65/100.88 (define @t109 () (tptp.strict_implies @t105 @t107)) % 99.65/100.88 (define @t110 () (tptp.strict_implies @t107 @t105)) % 99.65/100.88 (define @t111 () (tptp.and @t67 @t73)) % 99.65/100.88 (define @t112 () (@list @t111 @t106)) % 99.65/100.88 (define @t113 () (tptp.strict_implies @t106 @t111)) % 99.65/100.88 (define @t114 () (tptp.strict_implies @t111 @t106)) % 99.65/100.88 (define @t115 () (@list @t67 @t73)) % 99.65/100.88 (define @t116 () (tptp.is_a_theorem (tptp.and @t114 @t113))) % 99.65/100.88 (define @t117 () (tptp.is_a_theorem @t113)) % 99.65/100.88 (define @t118 () (not @t117)) % 99.65/100.88 (define @t119 () (tptp.is_a_theorem @t114)) % 99.65/100.88 (define @t120 () (not @t119)) % 99.65/100.88 (define @t121 () (or @t120 @t118 @t116)) % 99.65/100.88 (define @t122 () (tptp.is_a_theorem (tptp.strict_equiv @t111 @t106))) % 99.65/100.88 (define @t123 () (= @t111 @t106)) % 99.65/100.88 (define @t124 () (not @t122)) % 99.65/100.88 (define @t125 () (or @t124 @t123)) % 99.65/100.88 (define @t126 () (tptp.and @t69 @t111)) % 99.65/100.88 (define @t127 () (tptp.and @t69 @t73)) % 99.65/100.88 (define @t128 () (tptp.and @t127 @t67)) % 99.65/100.88 (define @t129 () (tptp.and @t67 @t127)) % 99.65/100.88 (define @t130 () (@list @t129 @t128)) % 99.65/100.88 (define @t131 () (tptp.strict_implies @t128 @t129)) % 99.65/100.88 (define @t132 () (tptp.strict_implies @t129 @t128)) % 99.65/100.88 (define @t133 () (tptp.is_a_theorem (tptp.and @t132 @t131))) % 99.65/100.88 (define @t134 () (tptp.is_a_theorem @t131)) % 99.65/100.88 (define @t135 () (not @t134)) % 99.65/100.88 (define @t136 () (tptp.is_a_theorem @t132)) % 99.65/100.88 (define @t137 () (not @t136)) % 99.65/100.88 (define @t138 () (or @t137 @t135 @t133)) % 99.65/100.88 (define @t139 () (tptp.is_a_theorem (tptp.strict_equiv @t129 @t128))) % 99.65/100.88 (define @t140 () (= @t129 @t128)) % 99.65/100.88 (define @t141 () (not @t139)) % 99.65/100.88 (define @t142 () (or @t141 @t140)) % 99.65/100.88 (define @t143 () (tptp.and @t70 @t73)) % 99.65/100.88 (define @t144 () (@list @t143 @t129)) % 99.65/100.88 (define @t145 () (tptp.strict_implies @t129 @t143)) % 99.65/100.88 (define @t146 () (tptp.strict_implies @t143 @t129)) % 99.65/100.88 (define @t147 () (tptp.not @t71)) % 99.65/100.88 (define @t148 () (tptp.and @t70 @t147)) % 99.65/100.88 (define @t149 () (tptp.and @t73 @t69)) % 99.65/100.88 (define @t150 () (@list @t127 @t149)) % 99.65/100.88 (define @t151 () (tptp.strict_implies @t149 @t127)) % 99.65/100.88 (define @t152 () (tptp.strict_implies @t127 @t149)) % 99.65/100.88 (define @t153 () (tptp.is_a_theorem (tptp.and @t152 @t151))) % 99.65/100.88 (define @t154 () (tptp.is_a_theorem @t151)) % 99.65/100.88 (define @t155 () (not @t154)) % 99.65/100.88 (define @t156 () (tptp.is_a_theorem @t152)) % 99.65/100.88 (define @t157 () (not @t156)) % 99.65/100.88 (define @t158 () (or @t157 @t155 @t153)) % 99.65/100.88 (define @t159 () (tptp.is_a_theorem (tptp.strict_equiv @t127 @t149))) % 99.65/100.88 (define @t160 () (= @t127 @t149)) % 99.65/100.88 (define @t161 () (not @t159)) % 99.65/100.88 (define @t162 () (or @t161 @t160)) % 99.65/100.88 (define @t163 () (tptp.is_a_theorem @t145)) % 99.65/100.88 (define @t164 () (tptp.is_a_theorem (tptp.and @t146 @t145))) % 99.65/100.88 (define @t165 () (not @t163)) % 99.65/100.88 (define @t166 () (tptp.is_a_theorem @t146)) % 99.65/100.88 (define @t167 () (not @t166)) % 99.65/100.88 (define @t168 () (or @t167 @t165 @t164)) % 99.65/100.88 (define @t169 () (tptp.is_a_theorem (tptp.strict_equiv @t143 @t129))) % 99.65/100.88 (define @t170 () (= @t143 @t129)) % 99.65/100.88 (define @t171 () (not @t169)) % 99.65/100.88 (define @t172 () (or @t171 @t170)) % 99.65/100.88 (define @t173 () (tptp.and @t111 @t69)) % 99.65/100.88 (define @t174 () (tptp.is_a_theorem (tptp.strict_equiv @t173 @t126))) % 99.65/100.88 (define @t175 () (not @t174)) % 99.65/100.88 (define @t176 () (or @t175 (= @t173 @t126))) % 99.65/100.88 (define @t177 () (forall @t8 (or (not @t48) @t11))) % 99.65/100.88 (define @t178 () (@list @t173 @t126)) % 99.65/100.88 (define @t179 () (= @t126 @t173)) % 99.65/100.88 (define @t180 () (or @t175 @t179)) % 99.65/100.88 (define @t181 () (tptp.strict_implies @t126 @t173)) % 99.65/100.88 (define @t182 () (tptp.strict_implies @t173 @t126)) % 99.65/100.88 (define @t183 () (tptp.is_a_theorem (tptp.and @t182 @t181))) % 99.65/100.88 (define @t184 () (tptp.is_a_theorem @t181)) % 99.65/100.88 (define @t185 () (not @t184)) % 99.65/100.88 (define @t186 () (tptp.is_a_theorem @t182)) % 99.65/100.88 (define @t187 () (not @t186)) % 99.65/100.88 (define @t188 () (or @t187 @t185 @t183)) % 99.65/100.88 (define @t189 () (tptp.is_a_theorem @t109)) % 99.65/100.88 (define @t190 () (tptp.is_a_theorem (tptp.and @t110 @t109))) % 99.65/100.88 (define @t191 () (not @t189)) % 99.65/100.88 (define @t192 () (tptp.is_a_theorem @t110)) % 99.65/100.88 (define @t193 () (not @t192)) % 99.65/100.88 (define @t194 () (or @t193 @t191 @t190)) % 99.65/100.88 (define @t195 () (tptp.is_a_theorem (tptp.strict_equiv @t107 @t105))) % 99.65/100.88 (define @t196 () (= @t107 @t105)) % 99.65/100.88 (define @t197 () (not @t195)) % 99.65/100.88 (define @t198 () (or @t197 @t196)) % 99.65/100.88 (define @t199 () (tptp.implies @t106 @t68)) % 99.65/100.88 (define @t200 () (@list @t106 @t68)) % 99.65/100.88 (define @t201 () (tptp.is_a_theorem (tptp.strict_implies @t106 @t68))) % 99.65/100.88 (define @t202 () (not @t39)) % 99.65/100.88 (define @t203 () (tptp.is_a_theorem (tptp.implies @t67 @t68))) % 99.65/100.88 (define @t204 () (tptp.is_a_theorem @t68)) % 99.65/100.88 (define @t205 () (not @t203)) % 99.65/100.88 (define @t206 () (tptp.is_a_theorem @t67)) % 99.65/100.88 (define @t207 () (not @t206)) % 99.65/100.88 (define @t208 () (or @t207 @t205 @t204)) % 99.65/100.88 (define @t209 () (@list true)) % 99.65/100.88 (define @t210 () (@list @t208)) % 99.65/100.88 (define @t211 () (tptp.is_a_theorem @t73)) % 99.65/100.88 (define @t212 () (tptp.is_a_theorem @t111)) % 99.65/100.88 (define @t213 () (not @t211)) % 99.65/100.88 (define @t214 () (or @t207 @t213 @t212)) % 99.65/100.88 (define @t215 () (tptp.is_a_theorem @t106)) % 99.65/100.88 (define @t216 () (not @t212)) % 99.65/100.88 (define @t217 () (or @t216 @t120 @t215)) % 99.65/100.88 (define @t218 () (not @t201)) % 99.65/100.88 (define @t219 () (not @t215)) % 99.65/100.88 (define @t220 () (or @t219 @t218 @t204)) % 99.65/100.88 (assume @p1 @t10) % 99.65/100.88 (assume @p2 (= tptp.substitution_of_equivalents (forall @t8 (=> (tptp.is_a_theorem @t12) @t11)))) % 99.65/100.88 (assume @p3 (= tptp.modus_tollens (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t14 @t13) @t4))))) % 99.65/100.88 (assume @p4 (= tptp.implies_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t15))))) % 99.65/100.88 (assume @p5 (= tptp.implies_2 (forall @t8 (tptp.is_a_theorem (tptp.implies (tptp.implies @t3 @t4) @t4))))) % 99.65/100.88 (assume @p6 (= tptp.implies_3 (forall @t19 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t18 @t17)))))) % 99.65/100.88 (assume @p7 (= tptp.and_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t3))))) % 99.65/100.88 (assume @p8 (= tptp.and_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t20 @t1))))) % 99.65/100.88 (assume @p9 (= tptp.and_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 (tptp.implies @t1 @t20)))))) % 99.65/100.88 (assume @p10 (= tptp.or_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t3 @t21))))) % 99.65/100.88 (assume @p11 (= tptp.or_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t1 @t21))))) % 99.65/100.88 (assume @p12 (= tptp.or_3 (forall @t19 (tptp.is_a_theorem (tptp.implies @t17 (tptp.implies @t18 (tptp.implies @t21 @t16))))))) % 99.65/100.88 (assume @p13 (= tptp.equivalence_1 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t4))))) % 99.65/100.88 (assume @p14 (= tptp.equivalence_2 (forall @t8 (tptp.is_a_theorem (tptp.implies @t12 @t15))))) % 99.65/100.88 (assume @p15 (= tptp.equivalence_3 (forall @t8 (tptp.is_a_theorem (tptp.implies @t4 (tptp.implies @t15 @t12)))))) % 99.65/100.88 (assume @p16 (= tptp.kn1 (forall @t23 (tptp.is_a_theorem (tptp.implies @t22 (tptp.and @t22 @t22)))))) % 99.65/100.88 (assume @p17 (= tptp.kn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t25 @t22))))) % 99.65/100.88 (assume @p18 (= tptp.kn3 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies (tptp.not (tptp.and @t24 @t27)) (tptp.not (tptp.and @t27 @t22)))))))) % 99.65/100.88 (assume @p19 (= tptp.cn1 (forall @t29 (tptp.is_a_theorem (tptp.implies @t28 (tptp.implies @t30 (tptp.implies @t22 @t27))))))) % 99.65/100.88 (assume @p20 (= tptp.cn2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t22 (tptp.implies @t31 @t24)))))) % 99.65/100.88 (assume @p21 (= tptp.cn3 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.implies @t31 @t22) @t22))))) % 99.65/100.88 (assume @p22 (= tptp.r1 (forall @t23 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 @t22) @t22))))) % 99.65/100.88 (assume @p23 (= tptp.r2 (forall @t26 (tptp.is_a_theorem (tptp.implies @t24 @t32))))) % 99.65/100.88 (assume @p24 (= tptp.r3 (forall @t26 (tptp.is_a_theorem (tptp.implies @t32 (tptp.or @t24 @t22)))))) % 99.65/100.88 (assume @p25 (= tptp.r4 (forall @t29 (tptp.is_a_theorem (tptp.implies (tptp.or @t22 (tptp.or @t24 @t27)) (tptp.or @t24 @t33)))))) % 99.65/100.88 (assume @p26 (= tptp.r5 (forall @t29 (tptp.is_a_theorem (tptp.implies @t30 (tptp.implies @t32 @t33)))))) % 99.65/100.88 (assume @p27 (=> tptp.op_or (forall @t8 (= @t21 (tptp.not (tptp.and @t13 @t14)))))) % 99.65/100.88 (assume @p28 (=> tptp.op_and (forall @t8 (= @t20 (tptp.not (tptp.or @t13 @t14)))))) % 99.65/100.88 (assume @p29 @t35) % 99.65/100.88 (assume @p30 (=> tptp.op_implies_or (forall @t8 (= @t4 (tptp.or @t13 @t1))))) % 99.65/100.88 (assume @p31 (=> tptp.op_equiv (forall @t8 (= @t12 (tptp.and @t4 @t15))))) % 99.65/100.88 (assume @p32 (= tptp.necessitation (forall @t37 (=> @t6 (tptp.is_a_theorem @t36))))) % 99.65/100.88 (assume @p33 @t42) % 99.65/100.88 (assume @p34 @t46) % 99.65/100.88 (assume @p35 @t50) % 99.65/100.88 (assume @p36 (= tptp.axiom_K (forall @t8 (tptp.is_a_theorem (tptp.implies @t51 (tptp.implies @t36 (tptp.necessarily @t1))))))) % 99.65/100.88 (assume @p37 (= tptp.axiom_M (forall @t37 (tptp.is_a_theorem (tptp.implies @t36 @t3))))) % 99.65/100.88 (assume @p38 (= tptp.axiom_4 (forall @t37 (tptp.is_a_theorem (tptp.implies @t36 @t52))))) % 99.65/100.88 (assume @p39 (= tptp.axiom_B (forall @t37 (tptp.is_a_theorem (tptp.implies @t3 @t54))))) % 99.65/100.88 (assume @p40 (= tptp.axiom_5 (forall @t37 (tptp.is_a_theorem (tptp.implies @t53 @t54))))) % 99.65/100.88 (assume @p41 (= tptp.axiom_s1 (forall @t19 (tptp.is_a_theorem (tptp.implies (tptp.and @t51 (tptp.necessarily @t18)) (tptp.necessarily @t17)))))) % 99.65/100.88 (assume @p42 (= tptp.axiom_s2 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies @t57 (tptp.and @t56 @t55)))))) % 99.65/100.88 (assume @p43 (= tptp.axiom_s3 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t38 (tptp.strict_implies (tptp.not (tptp.possibly @t1)) (tptp.not @t53))))))) % 99.65/100.88 (assume @p44 (= tptp.axiom_s4 (forall @t37 (tptp.is_a_theorem (tptp.strict_implies @t36 @t52))))) % 99.65/100.88 (assume @p45 (= tptp.axiom_m1 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t20 (tptp.and @t1 @t3)))))) % 99.65/100.88 (assume @p46 (= tptp.axiom_m2 (forall @t8 (tptp.is_a_theorem (tptp.strict_implies @t20 @t3))))) % 99.65/100.88 (assume @p47 (= tptp.axiom_m3 (forall @t19 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t20 @t16) (tptp.and @t3 (tptp.and @t1 @t16))))))) % 99.65/100.88 (assume @p48 (= tptp.axiom_m4 (forall @t37 (tptp.is_a_theorem (tptp.strict_implies @t3 (tptp.and @t3 @t3)))))) % 99.65/100.88 (assume @p49 (= tptp.axiom_m5 (forall @t19 (tptp.is_a_theorem (tptp.strict_implies (tptp.and @t38 (tptp.strict_implies @t1 @t16)) (tptp.strict_implies @t3 @t16)))))) % 99.65/100.88 (assume @p50 (= tptp.axiom_m6 (forall @t37 (tptp.is_a_theorem (tptp.strict_implies @t3 @t53))))) % 99.65/100.88 (assume @p51 (= tptp.axiom_m7 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies @t57 @t22))))) % 99.65/100.88 (assume @p52 (= tptp.axiom_m8 (forall @t26 (tptp.is_a_theorem (tptp.strict_implies (tptp.strict_implies @t22 @t24) (tptp.strict_implies @t56 @t55)))))) % 99.65/100.88 (assume @p53 (= tptp.axiom_m9 (forall @t37 (tptp.is_a_theorem (tptp.strict_implies (tptp.possibly @t53) @t53))))) % 99.65/100.88 (assume @p54 (= tptp.axiom_m10 (forall @t37 (tptp.is_a_theorem (tptp.strict_implies @t53 @t54))))) % 99.65/100.88 (assume @p55 (=> tptp.op_possibly (forall @t37 (= @t53 (tptp.not (tptp.necessarily @t13)))))) % 99.65/100.88 (assume @p56 (=> tptp.op_necessarily (forall @t37 (= @t36 (tptp.not (tptp.possibly @t13)))))) % 99.65/100.88 (assume @p57 @t59) % 99.65/100.88 (assume @p58 @t61) % 99.65/100.88 (assume @p59 tptp.op_possibly) % 99.65/100.88 (assume @p60 tptp.op_or) % 99.65/100.88 (assume @p61 tptp.op_implies) % 99.65/100.88 (assume @p62 tptp.op_strict_implies) % 99.65/100.88 (assume @p63 tptp.op_equiv) % 99.65/100.88 (assume @p64 tptp.op_strict_equiv) % 99.65/100.88 (assume @p65 tptp.modus_ponens_strict_implies) % 99.65/100.88 (assume @p66 tptp.substitution_strict_equiv) % 99.65/100.88 (assume @p67 tptp.adjunction) % 99.65/100.88 (assume @p68 tptp.axiom_m1) % 99.65/100.88 (assume @p69 tptp.axiom_m2) % 99.65/100.88 (assume @p70 tptp.axiom_m3) % 99.65/100.88 (assume @p71 tptp.axiom_m4) % 99.65/100.88 (assume @p72 tptp.axiom_m5) % 99.65/100.88 (assume @p73 tptp.op_implies_and) % 99.65/100.88 (assume @p74 tptp.substitution_of_equivalents) % 99.65/100.88 (assume @p75 @t62) % 99.65/100.88 (assume @p76 true) % 99.65/100.88 (step @p77 :rule evaluate :args ((= false true))) % 99.65/100.88 (step @p78 :rule eq_resolve :premises (@p68 @p45)) % 99.65/100.88 (step @p79 :rule instantiate :premises (@p78) :args ((@list @t69 @t67))) % 99.65/100.88 (step @p80 :rule true_intro :premises (@p79)) % 99.65/100.88 (step @p81 :rule bool-impl-true2 :args (@t58)) % 99.65/100.88 (step @p82 :rule refl :args (@t58)) % 99.65/100.88 (step @p83 :rule bool-eq-true :args (tptp.op_strict_implies)) % 99.65/100.88 (step @p84 :rule symm :premises (@p83)) % 99.65/100.88 (step @p85 :rule eq_resolve :premises (@p62 @p84)) % 99.65/100.88 (step @p86 :rule cong :premises (@p85 @p82) :args (@t59)) % 99.65/100.88 (step @p87 :rule trans :premises (@p86 @p81)) % 99.65/100.88 (step @p88 :rule eq_resolve :premises (@p57 @p87)) % 99.65/100.88 (step @p89 :rule instantiate :premises (@p88) :args (@t72)) % 99.65/100.88 (step @p90 :rule symm :premises (@p89)) % 99.65/100.88 (step @p91 :rule bool-impl-true2 :args (@t34)) % 99.65/100.88 (step @p92 :rule refl :args (@t34)) % 99.65/100.88 (step @p93 :rule bool-eq-true :args (tptp.op_implies_and)) % 99.65/100.88 (step @p94 :rule symm :premises (@p93)) % 99.65/100.88 (step @p95 :rule eq_resolve :premises (@p73 @p94)) % 99.65/100.88 (step @p96 :rule cong :premises (@p95 @p92) :args (@t35)) % 99.65/100.88 (step @p97 :rule trans :premises (@p96 @p91)) % 99.65/100.88 (step @p98 :rule eq_resolve :premises (@p29 @p97)) % 99.65/100.88 (step @p99 :rule instantiate :premises (@p98) :args (@t72)) % 99.65/100.88 (step @p100 :rule symm :premises (@p99)) % 99.65/100.88 (step @p101 :rule bool-impl-elim :args (@t48 @t11)) % 99.65/100.88 (step @p102 :rule cong :premises (@p101) :args (@t49)) % 99.65/100.88 (step @p103 :rule refl :args (tptp.substitution_strict_equiv)) % 99.65/100.88 (step @p104 :rule cong :premises (@p103 @p102) :args (@t50)) % 99.65/100.88 (step @p105 :rule eq_resolve :premises (@p35 @p104)) % 99.65/100.88 (step @p106 :rule eq_resolve :premises (@p66 @p105)) % 99.65/100.88 (step @p107 :rule instantiate :premises (@p106) :args (@t76)) % 99.65/100.88 (step @p108 :rule aci_norm :args ((= (or (or @t64 @t77) @t43) (or @t64 @t77 @t43)))) % 99.65/100.88 (step @p109 :rule refl :args (@t43)) % 99.65/100.88 (step @p110 :rule bool-and-de-morgan :args (@t6 @t2 true)) % 99.65/100.88 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or (not @t44) @t43))) % 99.65/100.88 (step @p112 :rule trans :premises (@p111 @p108)) % 99.65/100.88 (step @p113 :rule bool-impl-elim :args (@t44 @t43)) % 99.65/100.88 (step @p114 :rule trans :premises (@p113 @p112)) % 99.65/100.88 (step @p115 :rule cong :premises (@p114) :args (@t45)) % 99.65/100.88 (step @p116 :rule refl :args (tptp.adjunction)) % 99.65/100.88 (step @p117 :rule cong :premises (@p116 @p115) :args (@t46)) % 99.65/100.88 (step @p118 :rule eq_resolve :premises (@p34 @p117)) % 99.65/100.88 (step @p119 :rule eq_resolve :premises (@p67 @p118)) % 99.65/100.88 (step @p120 :rule instantiate :premises (@p119) :args ((@list @t79 @t78))) % 99.65/100.88 (step @p121 :rule instantiate :premises (@p78) :args ((@list @t73 @t71))) % 99.65/100.88 (step @p122 :rule instantiate :premises (@p78) :args ((@list @t71 @t73))) % 99.65/100.88 (step @p123 :rule cnf_or_pos :args (@t85)) % 99.65/100.88 (step @p124 :rule reordering :premises (@p123) :args ((or @t84 @t82 @t80 (not @t85)))) % 99.65/100.88 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p121 @p120) :args (@t80 @t86 (@list @t83 @t81 @t85))) % 99.65/100.88 (step @p126 :rule true_intro :premises (@p125)) % 99.65/100.88 (step @p127 :rule bool-impl-true2 :args (@t60)) % 99.65/100.88 (step @p128 :rule refl :args (@t60)) % 99.65/100.88 (step @p129 :rule bool-eq-true :args (tptp.op_strict_equiv)) % 99.65/100.88 (step @p130 :rule symm :premises (@p129)) % 99.65/100.88 (step @p131 :rule eq_resolve :premises (@p64 @p130)) % 99.65/100.88 (step @p132 :rule cong :premises (@p131 @p128) :args (@t61)) % 99.65/100.88 (step @p133 :rule trans :premises (@p132 @p127)) % 99.65/100.88 (step @p134 :rule eq_resolve :premises (@p58 @p133)) % 99.65/100.88 (step @p135 :rule instantiate :premises (@p134) :args (@t76)) % 99.65/100.88 (step @p136 :rule cong :premises (@p135) :args (@t87)) % 99.65/100.88 (step @p137 :rule trans :premises (@p136 @p126)) % 99.65/100.88 (step @p138 :rule true_elim :premises (@p137)) % 99.65/100.88 (step @p139 :rule cnf_or_pos :args (@t90)) % 99.65/100.88 (step @p140 :rule reordering :premises (@p139) :args ((or @t89 @t88 (not @t90)))) % 99.65/100.88 (step @p141 :rule chain_m_resolution :premises (@p140 @p138 @p107) :args (@t88 @t91 (@list @t87 @t90))) % 99.65/100.88 (step @p142 :rule symm :premises (@p141)) % 99.65/100.88 (step @p143 :rule instantiate :premises (@p106) :args (@t92)) % 99.65/100.88 (step @p144 :rule instantiate :premises (@p119) :args ((@list @t94 @t93))) % 99.65/100.88 (step @p145 :rule instantiate :premises (@p78) :args ((@list @t67 @t69))) % 99.65/100.88 (step @p146 :rule cnf_or_pos :args (@t100)) % 99.65/100.88 (step @p147 :rule reordering :premises (@p146) :args ((or @t99 @t97 @t95 (not @t100)))) % 99.65/100.88 (step @p148 :rule chain_m_resolution :premises (@p147 @p145 @p79 @p144) :args (@t95 @t86 (@list @t98 @t96 @t100))) % 99.65/100.88 (step @p149 :rule true_intro :premises (@p148)) % 99.65/100.88 (step @p150 :rule instantiate :premises (@p134) :args (@t92)) % 99.65/100.88 (step @p151 :rule cong :premises (@p150) :args (@t101)) % 99.65/100.88 (step @p152 :rule trans :premises (@p151 @p149)) % 99.65/100.88 (step @p153 :rule true_elim :premises (@p152)) % 99.65/100.88 (step @p154 :rule cnf_or_pos :args (@t104)) % 99.65/100.88 (step @p155 :rule reordering :premises (@p154) :args ((or @t103 @t102 (not @t104)))) % 99.65/100.88 (step @p156 :rule chain_m_resolution :premises (@p155 @p153 @p143) :args (@t102 @t91 (@list @t101 @t104))) % 99.65/100.88 (step @p157 :rule refl :args (@t73)) % 99.65/100.88 (step @p158 :rule cong :premises (@p157 @p156) :args (@t105)) % 99.65/100.88 (step @p159 :rule instantiate :premises (@p106) :args (@t108)) % 99.65/100.88 (step @p160 :rule instantiate :premises (@p119) :args ((@list @t110 @t109))) % 99.65/100.88 (step @p161 :rule eq_resolve :premises (@p70 @p47)) % 99.65/100.88 (step @p162 :rule instantiate :premises (@p161) :args ((@list @t69 @t73 @t67))) % 99.65/100.88 (step @p163 :rule true_intro :premises (@p162)) % 99.65/100.88 (step @p164 :rule instantiate :premises (@p106) :args (@t112)) % 99.65/100.88 (step @p165 :rule instantiate :premises (@p119) :args ((@list @t114 @t113))) % 99.65/100.88 (step @p166 :rule instantiate :premises (@p78) :args ((@list @t73 @t67))) % 99.65/100.88 (step @p167 :rule instantiate :premises (@p78) :args (@t115)) % 99.65/100.88 (step @p168 :rule cnf_or_pos :args (@t121)) % 99.65/100.88 (step @p169 :rule reordering :premises (@p168) :args ((or @t120 @t118 @t116 (not @t121)))) % 99.65/100.88 (step @p170 :rule chain_m_resolution :premises (@p169 @p167 @p166 @p165) :args (@t116 @t86 (@list @t119 @t117 @t121))) % 99.65/100.88 (step @p171 :rule true_intro :premises (@p170)) % 99.65/100.88 (step @p172 :rule instantiate :premises (@p134) :args (@t112)) % 99.65/100.88 (step @p173 :rule cong :premises (@p172) :args (@t122)) % 99.65/100.88 (step @p174 :rule trans :premises (@p173 @p171)) % 99.65/100.88 (step @p175 :rule true_elim :premises (@p174)) % 99.65/100.88 (step @p176 :rule cnf_or_pos :args (@t125)) % 99.65/100.88 (step @p177 :rule reordering :premises (@p176) :args ((or @t124 @t123 (not @t125)))) % 99.65/100.88 (step @p178 :rule chain_m_resolution :premises (@p177 @p175 @p164) :args (@t123 @t91 (@list @t122 @t125))) % 99.65/100.88 (step @p179 :rule refl :args (@t69)) % 99.65/100.88 (step @p180 :rule cong :premises (@p179 @p178) :args (@t126)) % 99.65/100.88 (step @p181 :rule instantiate :premises (@p106) :args (@t130)) % 99.65/100.88 (step @p182 :rule instantiate :premises (@p119) :args ((@list @t132 @t131))) % 99.65/100.88 (step @p183 :rule instantiate :premises (@p78) :args ((@list @t127 @t67))) % 99.65/100.88 (step @p184 :rule instantiate :premises (@p78) :args ((@list @t67 @t127))) % 99.65/100.88 (step @p185 :rule cnf_or_pos :args (@t138)) % 99.65/100.88 (step @p186 :rule reordering :premises (@p185) :args ((or @t137 @t135 @t133 (not @t138)))) % 99.65/100.88 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p183 @p182) :args (@t133 @t86 (@list @t136 @t134 @t138))) % 99.65/100.88 (step @p188 :rule true_intro :premises (@p187)) % 99.65/100.88 (step @p189 :rule instantiate :premises (@p134) :args (@t130)) % 99.65/100.88 (step @p190 :rule cong :premises (@p189) :args (@t139)) % 99.65/100.88 (step @p191 :rule trans :premises (@p190 @p188)) % 99.65/100.88 (step @p192 :rule true_elim :premises (@p191)) % 99.65/100.88 (step @p193 :rule cnf_or_pos :args (@t142)) % 99.65/100.88 (step @p194 :rule reordering :premises (@p193) :args ((or @t141 @t140 (not @t142)))) % 99.65/100.88 (step @p195 :rule chain_m_resolution :premises (@p194 @p192 @p181) :args (@t140 @t91 (@list @t139 @t142))) % 99.65/100.88 (step @p196 :rule instantiate :premises (@p106) :args (@t144)) % 99.65/100.88 (step @p197 :rule instantiate :premises (@p119) :args ((@list @t146 @t145))) % 99.65/100.88 (step @p198 :rule instantiate :premises (@p161) :args ((@list @t73 @t69 @t67))) % 99.65/100.88 (step @p199 :rule true_intro :premises (@p198)) % 99.65/100.88 (step @p200 :rule symm :premises (@p156)) % 99.65/100.88 (step @p201 :rule cong :premises (@p200) :args (@t147)) % 99.65/100.88 (step @p202 :rule cong :premises (@p156 @p201) :args (@t148)) % 99.65/100.88 (step @p203 :rule symm :premises (@p201)) % 99.65/100.88 (step @p204 :rule refl :args (@t70)) % 99.65/100.88 (step @p205 :rule cong :premises (@p204 @p203) :args (@t143)) % 99.65/100.88 (step @p206 :rule trans :premises (@p205 @p202 @p141)) % 99.65/100.88 (step @p207 :rule refl :args (@t67)) % 99.65/100.88 (step @p208 :rule instantiate :premises (@p106) :args (@t150)) % 99.65/100.88 (step @p209 :rule instantiate :premises (@p119) :args ((@list @t152 @t151))) % 99.65/100.88 (step @p210 :rule instantiate :premises (@p78) :args ((@list @t73 @t69))) % 99.65/100.88 (step @p211 :rule instantiate :premises (@p78) :args ((@list @t69 @t73))) % 99.65/100.88 (step @p212 :rule cnf_or_pos :args (@t158)) % 99.65/100.88 (step @p213 :rule reordering :premises (@p212) :args ((or @t157 @t155 @t153 (not @t158)))) % 99.65/100.88 (step @p214 :rule chain_m_resolution :premises (@p213 @p211 @p210 @p209) :args (@t153 @t86 (@list @t156 @t154 @t158))) % 99.65/100.88 (step @p215 :rule true_intro :premises (@p214)) % 99.65/100.88 (step @p216 :rule instantiate :premises (@p134) :args (@t150)) % 99.65/100.88 (step @p217 :rule cong :premises (@p216) :args (@t159)) % 99.65/100.88 (step @p218 :rule trans :premises (@p217 @p215)) % 99.65/100.88 (step @p219 :rule true_elim :premises (@p218)) % 99.65/100.88 (step @p220 :rule cnf_or_pos :args (@t162)) % 99.65/100.88 (step @p221 :rule reordering :premises (@p220) :args ((or @t161 @t160 (not @t162)))) % 99.65/100.88 (step @p222 :rule chain_m_resolution :premises (@p221 @p219 @p208) :args (@t160 @t91 (@list @t159 @t162))) % 99.65/100.88 (step @p223 :rule cong :premises (@p222 @p207) :args (@t128)) % 99.65/100.88 (step @p224 :rule trans :premises (@p195 @p223)) % 99.65/100.88 (step @p225 :rule cong :premises (@p224 @p206) :args (@t145)) % 99.65/100.88 (step @p226 :rule cong :premises (@p225) :args (@t163)) % 99.65/100.88 (step @p227 :rule trans :premises (@p226 @p199)) % 99.65/100.88 (step @p228 :rule true_elim :premises (@p227)) % 99.65/100.88 (step @p229 :rule instantiate :premises (@p161) :args ((@list @t67 @t69 @t73))) % 99.65/100.88 (step @p230 :rule cnf_or_pos :args (@t168)) % 99.65/100.88 (step @p231 :rule reordering :premises (@p230) :args ((or @t167 @t165 @t164 (not @t168)))) % 99.65/100.88 (step @p232 :rule chain_m_resolution :premises (@p231 @p229 @p228 @p197) :args (@t164 @t86 (@list @t166 @t163 @t168))) % 99.65/100.88 (step @p233 :rule true_intro :premises (@p232)) % 99.65/100.88 (step @p234 :rule instantiate :premises (@p134) :args (@t144)) % 99.65/100.88 (step @p235 :rule cong :premises (@p234) :args (@t169)) % 99.65/100.88 (step @p236 :rule trans :premises (@p235 @p233)) % 99.65/100.88 (step @p237 :rule true_elim :premises (@p236)) % 99.65/100.88 (step @p238 :rule cnf_or_pos :args (@t172)) % 99.65/100.88 (step @p239 :rule reordering :premises (@p238) :args ((or @t171 @t170 (not @t172)))) % 99.65/100.88 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p196) :args (@t170 @t91 (@list @t169 @t172))) % 99.65/100.88 (step @p241 :rule cong :premises (@p204 @p201) :args (@t148)) % 99.65/100.88 (step @p242 :rule cong :premises (@p200 @p203) :args (@t75)) % 99.65/100.88 (step @p243 :rule trans :premises (@p242 @p241)) % 99.65/100.88 (step @p244 :rule trans :premises (@p243 @p240 @p195)) % 99.65/100.88 (step @p245 :rule cong :premises (@p244 @p180) :args ((tptp.strict_implies @t75 @t126))) % 99.65/100.88 (step @p246 :rule eq-symm :args (@t173 @t126)) % 99.65/100.88 (step @p247 :rule refl :args (@t175)) % 99.65/100.88 (step @p248 :rule nary_cong :premises (@p247 @p246) :args (@t176)) % 99.65/100.88 (step @p249 :rule refl :args (@t177)) % 99.65/100.88 (step @p250 :rule cong :premises (@p249 @p248) :args ((=> @t177 @t176))) % 99.65/100.88 (assume-push @p369 @t177) % 99.65/100.88 (step @p252 :rule instantiate :premises (@p106) :args (@t178)) % 99.65/100.88 (step-pop @p370 :rule scope :premises (@p252)) % 99.65/100.88 (step @p253 :rule process_scope :premises (@p370) :args (@t176)) % 99.65/100.88 (step @p255 :rule eq_resolve :premises (@p253 @p250)) % 99.65/100.88 (step @p256 :rule implies_elim :premises (@p255)) % 99.65/100.88 (step @p257 :rule chain_m_resolution :premises (@p256 @p106) :args (@t180 (@list false) (@list @t177))) % 99.65/100.88 (step @p258 :rule instantiate :premises (@p119) :args ((@list @t182 @t181))) % 99.65/100.88 (step @p259 :rule instantiate :premises (@p78) :args ((@list @t111 @t69))) % 99.65/100.88 (step @p260 :rule instantiate :premises (@p78) :args ((@list @t69 @t111))) % 99.65/100.88 (step @p261 :rule cnf_or_pos :args (@t188)) % 99.65/100.88 (step @p262 :rule reordering :premises (@p261) :args ((or @t185 @t187 @t183 (not @t188)))) % 99.65/100.88 (step @p263 :rule chain_m_resolution :premises (@p262 @p260 @p259 @p258) :args (@t183 @t86 (@list @t184 @t186 @t188))) % 99.65/100.88 (step @p264 :rule true_intro :premises (@p263)) % 99.65/100.88 (step @p265 :rule instantiate :premises (@p134) :args (@t178)) % 99.65/100.88 (step @p266 :rule cong :premises (@p265) :args (@t174)) % 99.65/100.88 (step @p267 :rule trans :premises (@p266 @p264)) % 99.65/100.88 (step @p268 :rule true_elim :premises (@p267)) % 99.65/100.88 (step @p269 :rule cnf_or_pos :args (@t180)) % 99.65/100.88 (step @p270 :rule reordering :premises (@p269) :args ((or @t175 @t179 (not @t180)))) % 99.65/100.88 (step @p271 :rule chain_m_resolution :premises (@p270 @p268 @p257) :args (@t179 @t91 (@list @t174 @t180))) % 99.65/100.88 (step @p272 :rule symm :premises (@p271)) % 99.65/100.88 (step @p273 :rule symm :premises (@p178)) % 99.65/100.88 (step @p274 :rule cong :premises (@p273 @p179) :args (@t107)) % 99.65/100.88 (step @p275 :rule trans :premises (@p274 @p272)) % 99.65/100.88 (step @p276 :rule symm :premises (@p243)) % 99.65/100.88 (step @p277 :rule trans :premises (@p158 @p142 @p242 @p241)) % 99.65/100.88 (step @p278 :rule trans :premises (@p277 @p276)) % 99.65/100.88 (step @p279 :rule cong :premises (@p278 @p275) :args (@t109)) % 99.65/100.88 (step @p280 :rule trans :premises (@p279 @p245)) % 99.65/100.88 (step @p281 :rule cong :premises (@p280) :args (@t189)) % 99.65/100.88 (step @p282 :rule trans :premises (@p281 @p163)) % 99.65/100.88 (step @p283 :rule true_elim :premises (@p282)) % 99.65/100.88 (step @p284 :rule instantiate :premises (@p161) :args ((@list @t73 @t67 @t69))) % 99.65/100.88 (step @p285 :rule cnf_or_pos :args (@t194)) % 99.65/100.88 (step @p286 :rule reordering :premises (@p285) :args ((or @t193 @t191 @t190 (not @t194)))) % 99.65/100.88 (step @p287 :rule chain_m_resolution :premises (@p286 @p284 @p283 @p160) :args (@t190 @t86 (@list @t192 @t189 @t194))) % 99.65/100.88 (step @p288 :rule true_intro :premises (@p287)) % 99.65/100.88 (step @p289 :rule instantiate :premises (@p134) :args (@t108)) % 99.65/100.88 (step @p290 :rule cong :premises (@p289) :args (@t195)) % 99.65/100.88 (step @p291 :rule trans :premises (@p290 @p288)) % 99.65/100.88 (step @p292 :rule true_elim :premises (@p291)) % 99.65/100.88 (step @p293 :rule cnf_or_pos :args (@t198)) % 99.65/100.88 (step @p294 :rule reordering :premises (@p293) :args ((or @t196 @t197 (not @t198)))) % 99.65/100.88 (step @p295 :rule chain_m_resolution :premises (@p294 @p292 @p159) :args (@t196 @t91 (@list @t195 @t198))) % 99.65/100.88 (step @p296 :rule cong :premises (@p178 @p179) :args (@t173)) % 99.65/100.88 (step @p297 :rule trans :premises (@p296 @p295 @p158 @p142)) % 99.65/100.88 (step @p298 :rule cong :premises (@p297) :args ((tptp.not @t173))) % 99.65/100.88 (step @p299 :rule instantiate :premises (@p98) :args ((@list @t111 @t68))) % 99.65/100.88 (step @p300 :rule refl :args (@t68)) % 99.65/100.88 (step @p301 :rule cong :premises (@p273 @p300) :args (@t199)) % 99.65/100.88 (step @p302 :rule trans :premises (@p301 @p299 @p298 @p100)) % 99.65/100.88 (step @p303 :rule cong :premises (@p302) :args ((tptp.necessarily @t199))) % 99.65/100.88 (step @p304 :rule instantiate :premises (@p88) :args (@t200)) % 99.65/100.88 (step @p305 :rule trans :premises (@p304 @p303 @p90)) % 99.65/100.88 (step @p306 :rule cong :premises (@p305) :args (@t201)) % 99.65/100.88 (step @p307 :rule aci_norm :args ((= (or (or @t64 @t202) @t2) (or @t64 @t202 @t2)))) % 99.65/100.88 (step @p308 :rule refl :args (@t2)) % 99.65/100.88 (step @p309 :rule bool-and-de-morgan :args (@t6 @t39 true)) % 78.44/100.91 (step @p310 :rule nary_cong :premises (@p309 @p308) :args ((or (not @t40) @t2))) % 78.44/100.91 (step @p311 :rule trans :premises (@p310 @p307)) % 78.44/100.91 (step @p312 :rule bool-impl-elim :args (@t40 @t2)) % 78.44/100.91 (step @p313 :rule trans :premises (@p312 @p311)) % 78.44/100.91 (step @p314 :rule cong :premises (@p313) :args (@t41)) % 78.44/100.91 (step @p315 :rule refl :args (tptp.modus_ponens_strict_implies)) % 78.44/100.91 (step @p316 :rule cong :premises (@p315 @p314) :args (@t42)) % 78.44/100.91 (step @p317 :rule eq_resolve :premises (@p33 @p316)) % 78.44/100.91 (step @p318 :rule eq_resolve :premises (@p65 @p317)) % 78.44/100.91 (step @p319 :rule instantiate :premises (@p318) :args (@t200)) % 78.44/100.91 (step @p320 :rule instantiate :premises (@p318) :args (@t112)) % 78.44/100.91 (step @p321 :rule instantiate :premises (@p119) :args (@t115)) % 78.44/100.91 (step @p322 :rule aci_norm :args ((= (or (or @t64 @t63) @t2) @t65))) % 78.44/100.91 (step @p323 :rule bool-and-de-morgan :args (@t6 @t5 true)) % 78.44/100.91 (step @p324 :rule nary_cong :premises (@p323 @p308) :args ((or (not @t7) @t2))) % 78.44/100.91 (step @p325 :rule trans :premises (@p324 @p322)) % 78.44/100.91 (step @p326 :rule bool-impl-elim :args (@t7 @t2)) % 78.44/100.91 (step @p327 :rule trans :premises (@p326 @p325)) % 78.44/100.91 (step @p328 :rule cong :premises (@p327) :args (@t9)) % 78.44/100.91 (step @p329 :rule refl :args (tptp.modus_ponens)) % 78.44/100.91 (step @p330 :rule cong :premises (@p329 @p328) :args (@t10)) % 78.44/100.91 (step @p331 :rule eq_resolve :premises (@p1 @p330)) % 78.44/100.91 (step @p332 :rule cong :premises (@p331) :args (@t62)) % 78.44/100.91 (step @p333 :rule eq_resolve :premises (@p75 @p332)) % 78.44/100.91 (step @p334 :rule skolemize :premises (@p333)) % 78.44/100.91 (step @p335 :rule bool-double-not-elim :args (@t203)) % 78.44/100.91 (step @p336 :rule refl :args (@t208)) % 78.44/100.91 (step @p337 :rule nary_cong :premises (@p336 @p335) :args ((or @t208 (not @t205)))) % 78.44/100.91 (step @p338 :rule cnf_or_neg :args (@t208 1)) % 78.44/100.91 (step @p339 :rule eq_resolve :premises (@p338 @p337)) % 78.44/100.91 (step @p340 :rule reordering :premises (@p339) :args ((or @t203 @t208))) % 78.44/100.91 (step @p341 :rule chain_m_resolution :premises (@p340 @p334) :args (@t203 @t209 @t210)) % 78.44/100.91 (step @p342 :rule true_intro :premises (@p341)) % 78.44/100.91 (step @p343 :rule instantiate :premises (@p98) :args ((@list @t67 @t68))) % 78.44/100.91 (step @p344 :rule symm :premises (@p343)) % 78.44/100.91 (step @p345 :rule cong :premises (@p344) :args (@t211)) % 78.44/100.91 (step @p346 :rule trans :premises (@p345 @p342)) % 78.44/100.91 (step @p347 :rule true_elim :premises (@p346)) % 78.44/100.91 (step @p348 :rule bool-double-not-elim :args (@t206)) % 78.44/100.91 (step @p349 :rule nary_cong :premises (@p336 @p348) :args ((or @t208 (not @t207)))) % 78.44/100.91 (step @p350 :rule cnf_or_neg :args (@t208 0)) % 78.44/100.91 (step @p351 :rule eq_resolve :premises (@p350 @p349)) % 78.44/100.91 (step @p352 :rule reordering :premises (@p351) :args ((or @t206 @t208))) % 78.44/100.91 (step @p353 :rule chain_m_resolution :premises (@p352 @p334) :args (@t206 @t209 @t210)) % 78.44/100.91 (step @p354 :rule cnf_or_pos :args (@t214)) % 78.44/100.91 (step @p355 :rule reordering :premises (@p354) :args ((or @t207 @t213 @t212 (not @t214)))) % 78.44/100.91 (step @p356 :rule chain_m_resolution :premises (@p355 @p353 @p347 @p321) :args (@t212 @t86 (@list @t206 @t211 @t214))) % 78.44/100.91 (step @p357 :rule cnf_or_pos :args (@t217)) % 78.44/100.91 (step @p358 :rule reordering :premises (@p357) :args ((or @t216 @t120 @t215 (not @t217)))) % 78.44/100.91 (step @p359 :rule chain_m_resolution :premises (@p358 @p356 @p167 @p320) :args (@t215 @t86 (@list @t212 @t119 @t217))) % 78.44/100.91 (step @p360 :rule cnf_or_neg :args (@t208 2)) % 78.44/100.91 (step @p361 :rule chain_m_resolution :premises (@p360 @p334) :args ((not @t204) @t209 @t210)) % 78.44/100.91 (step @p362 :rule cnf_or_pos :args (@t220)) % 78.44/100.91 (step @p363 :rule reordering :premises (@p362) :args ((or @t204 @t219 @t218 (not @t220)))) % 78.44/100.91 (step @p364 :rule chain_m_resolution :premises (@p363 @p361 @p359 @p319) :args (@t218 (@list true false false) (@list @t204 @t215 @t220))) % 78.44/100.91 (step @p365 :rule false_intro :premises (@p364)) % 78.44/100.91 (step @p366 :rule symm :premises (@p365)) % 78.44/100.91 (step @p367 :rule trans :premises (@p366 @p306 @p80)) % 78.44/100.91 (step @p368 false :rule eq_resolve :premises (@p367 @p77)) % 78.44/100.91 ) % 78.44/100.91 % SZS output end Proof % 78.44/100.91 % cvc5 exiting %------------------------------------------------------------------------------