%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG093+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:45:39 AM UTC 2026 % Result : Theorem 0.53s 0.74s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG093+2 : TPTP v9.2.1. Released v4.0.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n004.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 14:06:52 EDT 2026 % 0.15/0.34 % CPUTime : % 0.33/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.53/0.74 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.53/0.74 % SZS status Theorem % 0.53/0.74 % SZS output start Proof % 0.53/0.74 ( % 0.53/0.74 (declare-sort $$unsorted 0) % 0.53/0.74 (declare-const tptp.xJ $$unsorted) % 0.53/0.74 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.53/0.74 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.74 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.53/0.74 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.74 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.53/0.74 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.74 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.53/0.74 (declare-const tptp.xI $$unsorted) % 0.53/0.74 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.53/0.74 (declare-const tptp.sz10 $$unsorted) % 0.53/0.74 (declare-const tptp.sz00 $$unsorted) % 0.53/0.74 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.53/0.74 (define @t1 () (@var "W0" $$unsorted)) % 0.53/0.74 (define @t2 () (tptp.aElement0 @t1)) % 0.53/0.74 (define @t3 () (@list @t1)) % 0.53/0.74 (define @t4 () (tptp.aElement0 tptp.sz00)) % 0.53/0.74 (define @t5 () (tptp.smndt0 @t1)) % 0.53/0.74 (define @t6 () (@var "W1" $$unsorted)) % 0.53/0.74 (define @t7 () (tptp.sdtpldt0 @t1 @t6)) % 0.53/0.74 (define @t8 () (tptp.aElement0 @t6)) % 0.53/0.74 (define @t9 () (and @t2 @t8)) % 0.53/0.74 (define @t10 () (@list @t1 @t6)) % 0.53/0.74 (define @t11 () (tptp.sdtasdt0 @t1 @t6)) % 0.53/0.74 (define @t12 () (@var "W2" $$unsorted)) % 0.53/0.74 (define @t13 () (tptp.sdtpldt0 @t6 @t12)) % 0.53/0.74 (define @t14 () (tptp.aElement0 @t12)) % 0.53/0.74 (define @t15 () (and @t2 @t8 @t14)) % 0.53/0.74 (define @t16 () (@list @t1 @t6 @t12)) % 0.53/0.74 (define @t17 () (tptp.sdtasdt0 @t6 @t1)) % 0.53/0.74 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.53/0.74 (define @t19 () (tptp.aSet0 @t1)) % 0.53/0.74 (define @t20 () (tptp.aElementOf0 @t6 @t1)) % 0.53/0.74 (define @t21 () (@list @t6)) % 0.53/0.74 (define @t22 () (tptp.aElementOf0 @t12 @t1)) % 0.53/0.74 (define @t23 () (tptp.aElementOf0 @t12 @t6)) % 0.53/0.74 (define @t24 () (@list @t12)) % 0.53/0.74 (define @t25 () (and @t19 (tptp.aSet0 @t6))) % 0.53/0.74 (define @t26 () (@var "W3" $$unsorted)) % 0.53/0.74 (define @t27 () (@var "W5" $$unsorted)) % 0.53/0.74 (define @t28 () (@var "W4" $$unsorted)) % 0.53/0.74 (define @t29 () (tptp.aElementOf0 @t26 @t12)) % 0.53/0.74 (define @t30 () (@list @t26)) % 0.53/0.74 (define @t31 () (tptp.aSet0 @t12)) % 0.53/0.74 (define @t32 () (tptp.sdtpldt1 @t1 @t6)) % 0.53/0.74 (define @t33 () (tptp.aIdeal0 @t1)) % 0.53/0.74 (define @t34 () (tptp.aElementOf0 @t17 tptp.xJ)) % 0.53/0.74 (define @t35 () (forall @t21 (=> @t8 @t34))) % 0.53/0.74 (define @t36 () (tptp.aElementOf0 @t7 tptp.xJ)) % 0.53/0.74 (define @t37 () (tptp.aElementOf0 @t6 tptp.xJ)) % 0.53/0.74 (define @t38 () (forall @t21 (=> @t37 @t36))) % 0.53/0.74 (define @t39 () (and @t38 @t35)) % 0.53/0.74 (define @t40 () (tptp.aElementOf0 @t1 tptp.xJ)) % 0.53/0.74 (define @t41 () (=> @t40 @t39)) % 0.53/0.74 (define @t42 () (forall @t3 @t41)) % 0.53/0.74 (define @t43 () (tptp.aElementOf0 @t17 tptp.xI)) % 0.53/0.74 (define @t44 () (forall @t21 (=> @t8 @t43))) % 0.53/0.74 (define @t45 () (tptp.aElementOf0 @t7 tptp.xI)) % 0.53/0.74 (define @t46 () (tptp.aElementOf0 @t6 tptp.xI)) % 0.53/0.74 (define @t47 () (forall @t21 (=> @t46 @t45))) % 0.53/0.74 (define @t48 () (and @t47 @t44)) % 0.53/0.74 (define @t49 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.53/0.74 (define @t50 () (=> @t49 @t48)) % 0.53/0.74 (define @t51 () (forall @t3 @t50)) % 0.53/0.74 (define @t52 () (tptp.sdtasasdt0 tptp.xI tptp.xJ)) % 0.53/0.74 (define @t53 () (tptp.aIdeal0 @t52)) % 0.53/0.74 (define @t54 () (tptp.aElementOf0 @t17 @t52)) % 0.53/0.74 (define @t55 () (forall @t21 (=> @t8 @t54))) % 0.53/0.74 (define @t56 () (tptp.aElementOf0 @t7 @t52)) % 0.53/0.74 (define @t57 () (tptp.aElementOf0 @t6 @t52)) % 0.53/0.74 (define @t58 () (forall @t21 (=> @t57 @t56))) % 0.53/0.74 (define @t59 () (and @t58 @t55)) % 0.53/0.74 (define @t60 () (tptp.aElementOf0 @t1 @t52)) % 0.53/0.74 (define @t61 () (=> @t60 @t59)) % 0.53/0.74 (define @t62 () (forall @t3 @t61)) % 0.53/0.74 (define @t63 () (or @t62 @t53)) % 0.53/0.74 (define @t64 () (and (tptp.aSet0 @t52) (forall @t3 (= @t60 (and @t49 @t40))))) % 0.53/0.74 (define @t65 () (=> @t64 @t63)) % 0.53/0.74 (define @t66 () (not @t65)) % 0.53/0.74 (define @t67 () (@var "BOUND_VARIABLE_7957" $$unsorted)) % 0.53/0.74 (define @t68 () (or (not (tptp.aElement0 @t67)) (tptp.aElementOf0 (tptp.sdtasdt0 @t67 @t1) @t52))) % 0.53/0.74 (define @t69 () (@var "BOUND_VARIABLE_7950" $$unsorted)) % 0.53/0.74 (define @t70 () (or (not (tptp.aElementOf0 @t69 @t52)) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 @t69) @t52))) % 0.53/0.74 (define @t71 () (and @t70 @t68)) % 0.53/0.74 (define @t72 () (not @t60)) % 0.53/0.74 (define @t73 () (or @t72 @t71)) % 0.53/0.74 (define @t74 () (forall (@list @t1 @t69 @t67) @t73)) % 0.53/0.74 (define @t75 () (@list @t69 @t67)) % 0.53/0.74 (define @t76 () (forall @t75 @t73)) % 0.53/0.74 (define @t77 () (forall (@list @t67) @t68)) % 0.53/0.74 (define @t78 () (@list @t6)) % 0.53/0.74 (define @t79 () (forall @t75 @t68)) % 0.53/0.74 (define @t80 () (forall (@list @t69) @t70)) % 0.53/0.74 (define @t81 () (forall @t75 @t70)) % 0.53/0.74 (define @t82 () (and @t81 @t79)) % 0.53/0.74 (define @t83 () (forall @t75 @t71)) % 0.53/0.74 (define @t84 () (or @t72 @t83)) % 0.53/0.74 (define @t85 () (not @t8)) % 0.53/0.74 (define @t86 () (and (forall @t21 (or (not @t57) @t56)) (forall @t21 (or @t85 @t54)))) % 0.53/0.74 (define @t87 () (@quantifiers_skolemize @t74 1)) % 0.53/0.74 (define @t88 () (@quantifiers_skolemize @t74 0)) % 0.53/0.74 (define @t89 () (tptp.sdtpldt0 @t88 @t87)) % 0.53/0.74 (define @t90 () (@quantifiers_skolemize @t74 2)) % 0.53/0.74 (define @t91 () (tptp.aElement0 @t90)) % 0.53/0.74 (define @t92 () (tptp.sdtasdt0 @t90 @t88)) % 0.53/0.74 (define @t93 () (tptp.aElementOf0 @t92 @t52)) % 0.53/0.74 (define @t94 () (not @t91)) % 0.53/0.74 (define @t95 () (or @t94 @t93)) % 0.53/0.74 (define @t96 () (@var "BOUND_VARIABLE_7897" $$unsorted)) % 0.53/0.74 (define @t97 () (or (not (tptp.aElement0 @t96)) (tptp.aElementOf0 (tptp.sdtasdt0 @t96 @t1) tptp.xI))) % 0.53/0.74 (define @t98 () (@var "BOUND_VARIABLE_7890" $$unsorted)) % 0.53/0.74 (define @t99 () (or (not (tptp.aElementOf0 @t98 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 @t98) tptp.xI))) % 0.53/0.74 (define @t100 () (and @t99 @t97)) % 0.53/0.74 (define @t101 () (not @t49)) % 0.53/0.74 (define @t102 () (or @t101 @t100)) % 0.53/0.74 (define @t103 () (@list @t98 @t96)) % 0.53/0.74 (define @t104 () (forall @t103 @t102)) % 0.53/0.74 (define @t105 () (forall (@list @t96) @t97)) % 0.53/0.74 (define @t106 () (forall @t103 @t97)) % 0.53/0.74 (define @t107 () (forall (@list @t98) @t99)) % 0.53/0.74 (define @t108 () (forall @t103 @t99)) % 0.53/0.74 (define @t109 () (and @t108 @t106)) % 0.53/0.74 (define @t110 () (forall @t103 @t100)) % 0.53/0.74 (define @t111 () (or @t101 @t110)) % 0.53/0.74 (define @t112 () (and (forall @t21 (or (not @t46) @t45)) (forall @t21 (or @t85 @t43)))) % 0.53/0.74 (define @t113 () (@list @t88 @t87 @t90)) % 0.53/0.74 (define @t114 () (tptp.aElementOf0 @t88 @t52)) % 0.53/0.74 (define @t115 () (tptp.aElementOf0 @t89 @t52)) % 0.53/0.74 (define @t116 () (tptp.aElementOf0 @t87 @t52)) % 0.53/0.74 (define @t117 () (not @t116)) % 0.53/0.74 (define @t118 () (or @t117 @t115)) % 0.53/0.74 (define @t119 () (and @t118 @t95)) % 0.53/0.74 (define @t120 () (not @t114)) % 0.53/0.74 (define @t121 () (or @t120 @t119)) % 0.53/0.74 (define @t122 () (@list true)) % 0.53/0.74 (define @t123 () (@list @t121)) % 0.53/0.74 (define @t124 () (tptp.aElementOf0 @t88 tptp.xJ)) % 0.53/0.74 (define @t125 () (tptp.aElementOf0 @t88 tptp.xI)) % 0.53/0.74 (define @t126 () (and @t125 @t124)) % 0.53/0.74 (define @t127 () (= @t114 @t126)) % 0.53/0.74 (define @t128 () (@list false false)) % 0.53/0.74 (define @t129 () (not @t126)) % 0.53/0.74 (define @t130 () (@list false)) % 0.53/0.74 (define @t131 () (@list @t126)) % 0.53/0.74 (define @t132 () (tptp.aElementOf0 @t92 tptp.xI)) % 0.53/0.74 (define @t133 () (or @t94 @t132)) % 0.53/0.74 (define @t134 () (tptp.aElementOf0 @t89 tptp.xI)) % 0.53/0.74 (define @t135 () (tptp.aElementOf0 @t87 tptp.xI)) % 0.53/0.74 (define @t136 () (not @t135)) % 0.53/0.74 (define @t137 () (or @t136 @t134)) % 0.53/0.74 (define @t138 () (and @t137 @t133)) % 0.53/0.74 (define @t139 () (not @t125)) % 0.53/0.74 (define @t140 () (or @t139 @t138)) % 0.53/0.74 (define @t141 () (@var "BOUND_VARIABLE_7927" $$unsorted)) % 0.53/0.74 (define @t142 () (or (not (tptp.aElement0 @t141)) (tptp.aElementOf0 (tptp.sdtasdt0 @t141 @t1) tptp.xJ))) % 0.53/0.74 (define @t143 () (@var "BOUND_VARIABLE_7920" $$unsorted)) % 0.53/0.74 (define @t144 () (or (not (tptp.aElementOf0 @t143 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 @t143) tptp.xJ))) % 0.53/0.74 (define @t145 () (and @t144 @t142)) % 0.53/0.74 (define @t146 () (not @t40)) % 0.53/0.74 (define @t147 () (or @t146 @t145)) % 0.53/0.74 (define @t148 () (@list @t143 @t141)) % 0.53/0.74 (define @t149 () (forall @t148 @t147)) % 0.53/0.74 (define @t150 () (forall (@list @t141) @t142)) % 0.53/0.74 (define @t151 () (forall @t148 @t142)) % 0.53/0.74 (define @t152 () (forall (@list @t143) @t144)) % 0.53/0.74 (define @t153 () (forall @t148 @t144)) % 0.53/0.74 (define @t154 () (and @t153 @t151)) % 0.53/0.74 (define @t155 () (forall @t148 @t145)) % 0.53/0.74 (define @t156 () (or @t146 @t155)) % 0.53/0.74 (define @t157 () (and (forall @t21 (or (not @t37) @t36)) (forall @t21 (or @t85 @t34)))) % 0.53/0.74 (define @t158 () (tptp.aElementOf0 @t92 tptp.xJ)) % 0.53/0.74 (define @t159 () (or @t94 @t158)) % 0.53/0.74 (define @t160 () (tptp.aElementOf0 @t89 tptp.xJ)) % 0.53/0.74 (define @t161 () (tptp.aElementOf0 @t87 tptp.xJ)) % 0.53/0.74 (define @t162 () (not @t161)) % 0.53/0.74 (define @t163 () (or @t162 @t160)) % 0.53/0.74 (define @t164 () (and @t163 @t159)) % 0.53/0.74 (define @t165 () (not @t124)) % 0.53/0.74 (define @t166 () (or @t165 @t164)) % 0.53/0.74 (define @t167 () (and @t132 @t158)) % 0.53/0.74 (define @t168 () (= @t93 @t167)) % 0.53/0.74 (define @t169 () (@list true false)) % 0.53/0.74 (define @t170 () (@list @t118)) % 0.53/0.74 (define @t171 () (and @t134 @t160)) % 0.53/0.74 (define @t172 () (= @t115 @t171)) % 0.53/0.74 (define @t173 () (not @t171)) % 0.53/0.74 (define @t174 () (@list @t88 @t87 tptp.sz00)) % 0.53/0.74 (define @t175 () (tptp.sdtasdt0 tptp.sz00 @t88)) % 0.53/0.74 (define @t176 () (not @t4)) % 0.53/0.74 (define @t177 () (and @t137 (or @t176 (tptp.aElementOf0 @t175 tptp.xI)))) % 0.53/0.74 (define @t178 () (or @t139 @t177)) % 0.53/0.74 (define @t179 () (and @t135 @t161)) % 0.53/0.74 (define @t180 () (= @t116 @t179)) % 0.53/0.74 (define @t181 () (not @t179)) % 0.53/0.74 (define @t182 () (@list @t179)) % 0.53/0.74 (define @t183 () (and @t163 (or @t176 (tptp.aElementOf0 @t175 tptp.xJ)))) % 0.53/0.74 (define @t184 () (or @t165 @t183)) % 0.53/0.74 (assume @p1 (forall @t3 (=> @t2 true))) % 0.53/0.74 (assume @p2 @t4) % 0.53/0.74 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.53/0.74 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t5)))) % 0.53/0.74 (assume @p5 (forall @t10 (=> @t9 (tptp.aElement0 @t7)))) % 0.53/0.74 (assume @p6 (forall @t10 (=> @t9 (tptp.aElement0 @t11)))) % 0.53/0.74 (assume @p7 (forall @t10 (=> @t9 (= @t7 (tptp.sdtpldt0 @t6 @t1))))) % 0.53/0.74 (assume @p8 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t7 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 0.53/0.74 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.53/0.74 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 0.53/0.74 (assume @p11 (forall @t10 (=> @t9 (= @t11 @t17)))) % 0.53/0.74 (assume @p12 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t11 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t6 @t12)))))) % 0.53/0.74 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.53/0.74 (assume @p14 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t11 (tptp.sdtasdt0 @t1 @t12))) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 (tptp.sdtasdt0 @t12 @t1))))))) % 0.53/0.74 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t5) (= @t5 (tptp.sdtasdt0 @t1 @t18)))))) % 0.53/0.74 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.53/0.74 (assume @p17 (forall @t10 (=> @t9 (=> (= @t11 tptp.sz00) (or (= @t1 tptp.sz00) (= @t6 tptp.sz00)))))) % 0.53/0.74 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.53/0.74 (assume @p19 (forall @t3 (=> @t19 true))) % 0.53/0.74 (assume @p20 (forall @t3 (=> @t19 (forall @t21 (=> @t20 @t8))))) % 0.53/0.74 (assume @p21 (forall @t10 (=> @t25 (=> (and (forall @t24 (=> @t22 @t23)) (forall @t24 (=> @t23 @t22))) (= @t1 @t6))))) % 0.53/0.74 (assume @p22 (forall @t10 (=> @t25 (forall @t24 (= (= @t12 @t32) (and @t31 (forall @t30 (= @t29 (exists (@list @t28 @t27) (and (tptp.aElementOf0 @t28 @t1) (tptp.aElementOf0 @t27 @t6) (= (tptp.sdtpldt0 @t28 @t27) @t26))))))))))) % 0.53/0.74 (assume @p23 (forall @t10 (=> @t25 (forall @t24 (= (= @t12 (tptp.sdtasasdt0 @t1 @t6)) (and @t31 (forall @t30 (= @t29 (and (tptp.aElementOf0 @t26 @t1) (tptp.aElementOf0 @t26 @t6)))))))))) % 0.53/0.74 (assume @p24 (forall @t3 (= @t33 (and @t19 (forall @t21 (=> @t20 (and (forall @t24 (=> @t22 (tptp.aElementOf0 @t13 @t1))) (forall @t24 (=> @t14 (tptp.aElementOf0 (tptp.sdtasdt0 @t12 @t6) @t1)))))))))) % 0.53/0.74 (assume @p25 (forall @t10 (=> (and @t33 (tptp.aIdeal0 @t6)) (tptp.aIdeal0 @t32)))) % 0.53/0.74 (assume @p26 (and (tptp.aSet0 tptp.xI) @t51 (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) @t42 (tptp.aIdeal0 tptp.xJ))) % 0.53/0.74 (assume @p27 @t66) % 0.53/0.74 (assume @p28 true) % 0.53/0.74 (step @p29 :rule refl :args (@t53)) % 0.53/0.74 (step @p30 :rule quant-merge-prenex :args ((= (forall @t3 @t76) @t74))) % 0.53/0.74 (step @p31 :rule alpha_equiv :args (@t77 (@list @t67) @t78)) % 0.53/0.74 (step @p32 :rule quant-unused-vars :args ((= @t79 @t77))) % 0.53/0.74 (step @p33 :rule trans :premises (@p32 @p31)) % 0.53/0.74 (step @p34 :rule alpha_equiv :args (@t80 (@list @t69) @t78)) % 0.53/0.74 (step @p35 :rule quant-unused-vars :args ((= @t81 @t80))) % 0.53/0.74 (step @p36 :rule trans :premises (@p35 @p34)) % 0.53/0.74 (step @p37 :rule nary_cong :premises (@p36 @p33) :args (@t82)) % 0.53/0.74 (step @p38 :rule quant-miniscope-and :args ((= @t83 @t82))) % 0.53/0.74 (step @p39 :rule trans :premises (@p38 @p37)) % 0.53/0.74 (step @p40 :rule refl :args (@t72)) % 0.53/0.74 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t84)) % 0.53/0.74 (step @p42 :rule quant-miniscope-or :args ((= @t76 @t84))) % 0.53/0.74 (step @p43 :rule trans :premises (@p42 @p41)) % 0.53/0.74 (step @p44 :rule symm :premises (@p43)) % 0.53/0.74 (step @p45 :rule cong :premises (@p44) :args ((forall @t3 (or @t72 @t86)))) % 0.53/0.74 (step @p46 :rule trans :premises (@p45 @p30)) % 0.53/0.74 (step @p47 :rule bool-impl-elim :args (@t60 @t86)) % 0.53/0.74 (step @p48 :rule cong :premises (@p47) :args ((forall @t3 (=> @t60 @t86)))) % 0.53/0.74 (step @p49 :rule trans :premises (@p48 @p46)) % 0.53/0.74 (step @p50 :rule bool-impl-elim :args (@t8 @t54)) % 0.53/0.74 (step @p51 :rule cong :premises (@p50) :args (@t55)) % 0.53/0.74 (step @p52 :rule bool-impl-elim :args (@t57 @t56)) % 0.53/0.74 (step @p53 :rule cong :premises (@p52) :args (@t58)) % 0.53/0.74 (step @p54 :rule nary_cong :premises (@p53 @p51) :args (@t59)) % 0.53/0.74 (step @p55 :rule refl :args (@t60)) % 0.53/0.74 (step @p56 :rule cong :premises (@p55 @p54) :args (@t61)) % 0.53/0.74 (step @p57 :rule cong :premises (@p56) :args (@t62)) % 0.53/0.74 (step @p58 :rule trans :premises (@p57 @p49)) % 0.53/0.74 (step @p59 :rule nary_cong :premises (@p58 @p29) :args (@t63)) % 0.53/0.74 (step @p60 :rule refl :args (@t64)) % 0.53/0.74 (step @p61 :rule cong :premises (@p60 @p59) :args (@t65)) % 0.53/0.74 (step @p62 :rule cong :premises (@p61) :args (@t66)) % 0.53/0.74 (step @p63 :rule eq_resolve :premises (@p27 @p62)) % 0.53/0.74 (step @p64 :rule not_implies_elim1 :premises (@p63)) % 0.53/0.74 (step @p65 :rule and_elim :premises (@p64) :args (1)) % 0.53/0.74 (step @p66 :rule instantiate :premises (@p65) :args ((@list @t89))) % 0.53/0.74 (step @p67 :rule bool-double-not-elim :args (@t91)) % 0.53/0.74 (step @p68 :rule refl :args (@t95)) % 0.53/0.74 (step @p69 :rule nary_cong :premises (@p68 @p67) :args ((or @t95 (not @t94)))) % 0.53/0.74 (step @p70 :rule cnf_or_neg :args (@t95 0)) % 0.53/0.74 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.53/0.74 (step @p72 :rule reordering :premises (@p71) :args ((or @t91 @t95))) % 0.53/0.74 (step @p73 :rule cnf_or_neg :args (@t95 1)) % 0.53/0.74 (step @p74 :rule quant-merge-prenex :args ((= (forall @t3 @t104) (forall (@list @t1 @t98 @t96) @t102)))) % 0.53/0.74 (step @p75 :rule alpha_equiv :args (@t105 (@list @t96) @t78)) % 0.53/0.74 (step @p76 :rule quant-unused-vars :args ((= @t106 @t105))) % 0.53/0.74 (step @p77 :rule trans :premises (@p76 @p75)) % 0.53/0.74 (step @p78 :rule alpha_equiv :args (@t107 (@list @t98) @t78)) % 0.53/0.74 (step @p79 :rule quant-unused-vars :args ((= @t108 @t107))) % 0.53/0.74 (step @p80 :rule trans :premises (@p79 @p78)) % 0.53/0.74 (step @p81 :rule nary_cong :premises (@p80 @p77) :args (@t109)) % 0.53/0.74 (step @p82 :rule quant-miniscope-and :args ((= @t110 @t109))) % 0.53/0.74 (step @p83 :rule trans :premises (@p82 @p81)) % 0.53/0.74 (step @p84 :rule refl :args (@t101)) % 0.53/0.74 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t111)) % 0.53/0.74 (step @p86 :rule quant-miniscope-or :args ((= @t104 @t111))) % 0.53/0.74 (step @p87 :rule trans :premises (@p86 @p85)) % 0.53/0.74 (step @p88 :rule symm :premises (@p87)) % 0.53/0.74 (step @p89 :rule cong :premises (@p88) :args ((forall @t3 (or @t101 @t112)))) % 0.53/0.74 (step @p90 :rule trans :premises (@p89 @p74)) % 0.53/0.74 (step @p91 :rule bool-impl-elim :args (@t49 @t112)) % 0.53/0.74 (step @p92 :rule cong :premises (@p91) :args ((forall @t3 (=> @t49 @t112)))) % 0.53/0.74 (step @p93 :rule trans :premises (@p92 @p90)) % 0.53/0.74 (step @p94 :rule bool-impl-elim :args (@t8 @t43)) % 0.53/0.74 (step @p95 :rule cong :premises (@p94) :args (@t44)) % 0.53/0.74 (step @p96 :rule bool-impl-elim :args (@t46 @t45)) % 0.53/0.74 (step @p97 :rule cong :premises (@p96) :args (@t47)) % 0.53/0.74 (step @p98 :rule nary_cong :premises (@p97 @p95) :args (@t48)) % 0.53/0.74 (step @p99 :rule refl :args (@t49)) % 0.53/0.74 (step @p100 :rule cong :premises (@p99 @p98) :args (@t50)) % 0.53/0.74 (step @p101 :rule cong :premises (@p100) :args (@t51)) % 0.53/0.74 (step @p102 :rule trans :premises (@p101 @p93)) % 0.53/0.74 (step @p103 :rule and_elim :premises (@p26) :args (1)) % 0.53/0.74 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.53/0.74 (step @p105 :rule instantiate :premises (@p104) :args (@t113)) % 0.53/0.74 (step @p106 :rule instantiate :premises (@p65) :args ((@list @t88))) % 0.53/0.74 (step @p107 :rule not_implies_elim2 :premises (@p63)) % 0.53/0.74 (step @p108 :rule not_or_elim :premises (@p107) :args (0)) % 0.53/0.74 (step @p109 :rule skolemize :premises (@p108)) % 0.53/0.74 (step @p110 :rule bool-double-not-elim :args (@t114)) % 0.53/0.74 (step @p111 :rule refl :args (@t121)) % 0.53/0.74 (step @p112 :rule nary_cong :premises (@p111 @p110) :args ((or @t121 (not @t120)))) % 0.53/0.74 (step @p113 :rule cnf_or_neg :args (@t121 0)) % 0.53/0.74 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.53/0.74 (step @p115 :rule reordering :premises (@p114) :args ((or @t114 @t121))) % 0.53/0.74 (step @p116 :rule chain_m_resolution :premises (@p115 @p109) :args (@t114 @t122 @t123)) % 0.53/0.74 (step @p117 :rule cnf_equiv_pos1 :args (@t127)) % 0.53/0.74 (step @p118 :rule reordering :premises (@p117) :args ((or @t120 @t126 (not @t127)))) % 0.53/0.74 (step @p119 :rule chain_m_resolution :premises (@p118 @p116 @p106) :args (@t126 @t128 (@list @t114 @t127))) % 0.53/0.74 (step @p120 :rule cnf_and_pos :args (@t126 0)) % 0.53/0.74 (step @p121 :rule reordering :premises (@p120) :args ((or @t125 @t129))) % 0.53/0.74 (step @p122 :rule chain_m_resolution :premises (@p121 @p119) :args (@t125 @t130 @t131)) % 0.53/0.74 (step @p123 :rule cnf_or_pos :args (@t140)) % 0.53/0.74 (step @p124 :rule reordering :premises (@p123) :args ((or @t139 @t138 (not @t140)))) % 0.53/0.74 (step @p125 :rule chain_m_resolution :premises (@p124 @p122 @p105) :args (@t138 @t128 (@list @t125 @t140))) % 0.53/0.74 (step @p126 :rule cnf_and_pos :args (@t138 1)) % 0.53/0.74 (step @p127 :rule reordering :premises (@p126) :args ((or @t133 (not @t138)))) % 0.53/0.74 (step @p128 :rule chain_m_resolution :premises (@p127 @p125) :args (@t133 @t130 (@list @t138))) % 0.53/0.74 (step @p129 :rule cnf_or_pos :args (@t133)) % 0.53/0.74 (step @p130 :rule reordering :premises (@p129) :args ((or @t94 @t132 (not @t133)))) % 0.53/0.74 (step @p131 :rule quant-merge-prenex :args ((= (forall @t3 @t149) (forall (@list @t1 @t143 @t141) @t147)))) % 0.53/0.74 (step @p132 :rule alpha_equiv :args (@t150 (@list @t141) @t78)) % 0.53/0.74 (step @p133 :rule quant-unused-vars :args ((= @t151 @t150))) % 0.53/0.74 (step @p134 :rule trans :premises (@p133 @p132)) % 0.53/0.74 (step @p135 :rule alpha_equiv :args (@t152 (@list @t143) @t78)) % 0.53/0.74 (step @p136 :rule quant-unused-vars :args ((= @t153 @t152))) % 0.53/0.74 (step @p137 :rule trans :premises (@p136 @p135)) % 0.53/0.74 (step @p138 :rule nary_cong :premises (@p137 @p134) :args (@t154)) % 0.53/0.74 (step @p139 :rule quant-miniscope-and :args ((= @t155 @t154))) % 0.53/0.74 (step @p140 :rule trans :premises (@p139 @p138)) % 0.53/0.74 (step @p141 :rule refl :args (@t146)) % 0.53/0.74 (step @p142 :rule nary_cong :premises (@p141 @p140) :args (@t156)) % 0.53/0.74 (step @p143 :rule quant-miniscope-or :args ((= @t149 @t156))) % 0.53/0.74 (step @p144 :rule trans :premises (@p143 @p142)) % 0.53/0.74 (step @p145 :rule symm :premises (@p144)) % 0.53/0.74 (step @p146 :rule cong :premises (@p145) :args ((forall @t3 (or @t146 @t157)))) % 0.53/0.74 (step @p147 :rule trans :premises (@p146 @p131)) % 0.53/0.74 (step @p148 :rule bool-impl-elim :args (@t40 @t157)) % 0.53/0.74 (step @p149 :rule cong :premises (@p148) :args ((forall @t3 (=> @t40 @t157)))) % 0.53/0.74 (step @p150 :rule trans :premises (@p149 @p147)) % 0.53/0.74 (step @p151 :rule bool-impl-elim :args (@t8 @t34)) % 0.53/0.74 (step @p152 :rule cong :premises (@p151) :args (@t35)) % 0.53/0.74 (step @p153 :rule bool-impl-elim :args (@t37 @t36)) % 0.53/0.74 (step @p154 :rule cong :premises (@p153) :args (@t38)) % 0.53/0.74 (step @p155 :rule nary_cong :premises (@p154 @p152) :args (@t39)) % 0.53/0.74 (step @p156 :rule refl :args (@t40)) % 0.53/0.74 (step @p157 :rule cong :premises (@p156 @p155) :args (@t41)) % 0.53/0.74 (step @p158 :rule cong :premises (@p157) :args (@t42)) % 0.53/0.74 (step @p159 :rule trans :premises (@p158 @p150)) % 0.53/0.74 (step @p160 :rule and_elim :premises (@p26) :args (4)) % 0.53/0.74 (step @p161 :rule eq_resolve :premises (@p160 @p159)) % 0.53/0.74 (step @p162 :rule instantiate :premises (@p161) :args (@t113)) % 0.53/0.74 (step @p163 :rule cnf_and_pos :args (@t126 1)) % 0.53/0.74 (step @p164 :rule reordering :premises (@p163) :args ((or @t124 @t129))) % 0.53/0.74 (step @p165 :rule chain_m_resolution :premises (@p164 @p119) :args (@t124 @t130 @t131)) % 0.53/0.74 (step @p166 :rule cnf_or_pos :args (@t166)) % 0.53/0.74 (step @p167 :rule reordering :premises (@p166) :args ((or @t165 @t164 (not @t166)))) % 0.53/0.74 (step @p168 :rule chain_m_resolution :premises (@p167 @p165 @p162) :args (@t164 @t128 (@list @t124 @t166))) % 0.53/0.74 (step @p169 :rule cnf_and_pos :args (@t164 1)) % 0.53/0.74 (step @p170 :rule reordering :premises (@p169) :args ((or @t159 (not @t164)))) % 0.53/0.74 (step @p171 :rule chain_m_resolution :premises (@p170 @p168) :args (@t159 @t130 (@list @t164))) % 0.53/0.74 (step @p172 :rule cnf_or_pos :args (@t159)) % 0.53/0.74 (step @p173 :rule reordering :premises (@p172) :args ((or @t94 @t158 (not @t159)))) % 0.53/0.74 (step @p174 :rule instantiate :premises (@p65) :args ((@list @t92))) % 0.53/0.74 (step @p175 :rule cnf_equiv_pos2 :args (@t168)) % 0.53/0.74 (step @p176 :rule reordering :premises (@p175) :args ((or @t93 (not @t167) (not @t168)))) % 0.53/0.74 (step @p177 :rule cnf_and_neg :args (@t167)) % 0.53/0.74 (step @p178 :rule chain_m_resolution :premises (@p177 @p176 @p174 @p173 @p171 @p130 @p128 @p73 @p72) :args (@t95 (@list true false false false false false true false) (@list @t167 @t168 @t158 @t159 @t132 @t133 @t93 @t91))) % 0.53/0.74 (step @p179 :rule cnf_or_neg :args (@t121 1)) % 0.53/0.74 (step @p180 :rule chain_m_resolution :premises (@p179 @p109) :args ((not @t119) @t122 @t123)) % 0.53/0.74 (step @p181 :rule cnf_and_neg :args (@t119)) % 0.53/0.74 (step @p182 :rule chain_m_resolution :premises (@p181 @p180 @p178) :args ((not @t118) @t169 (@list @t119 @t95))) % 0.53/0.74 (step @p183 :rule cnf_or_neg :args (@t118 1)) % 0.53/0.74 (step @p184 :rule chain_m_resolution :premises (@p183 @p182) :args ((not @t115) @t122 @t170)) % 0.53/0.74 (step @p185 :rule cnf_equiv_pos2 :args (@t172)) % 0.53/0.74 (step @p186 :rule reordering :premises (@p185) :args ((or @t115 @t173 (not @t172)))) % 0.53/0.74 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p66) :args (@t173 @t169 (@list @t115 @t172))) % 0.53/0.74 (step @p188 :rule instantiate :premises (@p104) :args (@t174)) % 0.53/0.74 (step @p189 :rule cnf_or_pos :args (@t178)) % 0.53/0.74 (step @p190 :rule reordering :premises (@p189) :args ((or @t139 @t177 (not @t178)))) % 0.53/0.74 (step @p191 :rule chain_m_resolution :premises (@p190 @p122 @p188) :args (@t177 @t128 (@list @t125 @t178))) % 0.53/0.74 (step @p192 :rule cnf_and_pos :args (@t177 0)) % 0.53/0.74 (step @p193 :rule reordering :premises (@p192) :args ((or @t137 (not @t177)))) % 0.53/0.74 (step @p194 :rule chain_m_resolution :premises (@p193 @p191) :args (@t137 @t130 (@list @t177))) % 0.53/0.74 (step @p195 :rule instantiate :premises (@p65) :args ((@list @t87))) % 0.53/0.74 (step @p196 :rule bool-double-not-elim :args (@t116)) % 0.53/0.74 (step @p197 :rule refl :args (@t118)) % 0.53/0.74 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or @t118 (not @t117)))) % 0.53/0.74 (step @p199 :rule cnf_or_neg :args (@t118 0)) % 0.53/0.74 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.53/0.74 (step @p201 :rule reordering :premises (@p200) :args ((or @t116 @t118))) % 0.53/0.74 (step @p202 :rule chain_m_resolution :premises (@p201 @p182) :args (@t116 @t122 @t170)) % 0.53/0.74 (step @p203 :rule cnf_equiv_pos1 :args (@t180)) % 0.53/0.74 (step @p204 :rule reordering :premises (@p203) :args ((or @t117 @t179 (not @t180)))) % 0.53/0.74 (step @p205 :rule chain_m_resolution :premises (@p204 @p202 @p195) :args (@t179 @t128 (@list @t116 @t180))) % 0.53/0.74 (step @p206 :rule cnf_and_pos :args (@t179 0)) % 0.53/0.74 (step @p207 :rule reordering :premises (@p206) :args ((or @t135 @t181))) % 0.53/0.74 (step @p208 :rule chain_m_resolution :premises (@p207 @p205) :args (@t135 @t130 @t182)) % 0.53/0.74 (step @p209 :rule cnf_or_pos :args (@t137)) % 0.53/0.74 (step @p210 :rule reordering :premises (@p209) :args ((or @t136 @t134 (not @t137)))) % 0.53/0.74 (step @p211 :rule chain_m_resolution :premises (@p210 @p208 @p194) :args (@t134 @t128 (@list @t135 @t137))) % 0.53/0.74 (step @p212 :rule instantiate :premises (@p161) :args (@t174)) % 0.53/0.74 (step @p213 :rule cnf_or_pos :args (@t184)) % 0.53/0.74 (step @p214 :rule reordering :premises (@p213) :args ((or @t165 @t183 (not @t184)))) % 0.53/0.74 (step @p215 :rule chain_m_resolution :premises (@p214 @p165 @p212) :args (@t183 @t128 (@list @t124 @t184))) % 0.53/0.74 (step @p216 :rule cnf_and_pos :args (@t183 0)) % 0.53/0.74 (step @p217 :rule reordering :premises (@p216) :args ((or @t163 (not @t183)))) % 0.53/0.74 (step @p218 :rule chain_m_resolution :premises (@p217 @p215) :args (@t163 @t130 (@list @t183))) % 0.53/0.74 (step @p219 :rule cnf_and_pos :args (@t179 1)) % 0.53/0.74 (step @p220 :rule reordering :premises (@p219) :args ((or @t161 @t181))) % 0.53/0.74 (step @p221 :rule chain_m_resolution :premises (@p220 @p205) :args (@t161 @t130 @t182)) % 0.53/0.74 (step @p222 :rule cnf_or_pos :args (@t163)) % 0.53/0.74 (step @p223 :rule reordering :premises (@p222) :args ((or @t162 @t160 (not @t163)))) % 0.53/0.74 (step @p224 :rule chain_m_resolution :premises (@p223 @p221 @p218) :args (@t160 @t128 (@list @t161 @t163))) % 0.53/0.74 (step @p225 :rule cnf_and_neg :args (@t171)) % 0.53/0.74 (step @p226 false :rule chain_m_resolution :premises (@p225 @p224 @p211 @p187) :args (false (@list false false true) (@list @t160 @t134 @t171))) % 0.53/0.74 ) % 0.53/0.74 % SZS output end Proof % 0.53/0.74 % cvc5 exiting %------------------------------------------------------------------------------