%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG099+1 : TPTP v9.2.1. Released v4.0.0. % 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 : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:45:40 AM UTC 2026 % Result : Theorem 0.44s 0.65s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG099+1 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n016.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 14:07:39 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.44/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.44/0.65 % SZS status Theorem % 0.44/0.65 % SZS output start Proof % 0.44/0.65 ( % 0.44/0.65 (declare-sort $$unsorted 0) % 0.44/0.65 (declare-const tptp.xw $$unsorted) % 0.44/0.65 (declare-const tptp.xa $$unsorted) % 0.44/0.65 (declare-const tptp.xb $$unsorted) % 0.44/0.65 (declare-const tptp.xx $$unsorted) % 0.44/0.65 (declare-const tptp.xy $$unsorted) % 0.44/0.65 (declare-const tptp.xI $$unsorted) % 0.44/0.65 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sz00 $$unsorted) % 0.44/0.65 (declare-const tptp.sz10 $$unsorted) % 0.44/0.65 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.xJ $$unsorted) % 0.44/0.65 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.44/0.65 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.44/0.65 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.44/0.65 (define @t1 () (@var "W0" $$unsorted)) % 0.44/0.65 (define @t2 () (tptp.aElement0 @t1)) % 0.44/0.65 (define @t3 () (@list @t1)) % 0.44/0.65 (define @t4 () (tptp.smndt0 @t1)) % 0.44/0.65 (define @t5 () (@var "W1" $$unsorted)) % 0.44/0.65 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.44/0.65 (define @t7 () (tptp.aElement0 @t6)) % 0.44/0.65 (define @t8 () (tptp.aElement0 @t5)) % 0.44/0.65 (define @t9 () (and @t2 @t8)) % 0.44/0.65 (define @t10 () (@list @t1 @t5)) % 0.44/0.65 (define @t11 () (forall @t10 (=> @t9 @t7))) % 0.44/0.65 (define @t12 () (tptp.sdtasdt0 @t1 @t5)) % 0.44/0.65 (define @t13 () (tptp.aElement0 @t12)) % 0.44/0.65 (define @t14 () (forall @t10 (=> @t9 @t13))) % 0.44/0.65 (define @t15 () (@var "W2" $$unsorted)) % 0.44/0.65 (define @t16 () (tptp.sdtpldt0 @t5 @t15)) % 0.44/0.65 (define @t17 () (tptp.aElement0 @t15)) % 0.44/0.65 (define @t18 () (and @t2 @t8 @t17)) % 0.44/0.65 (define @t19 () (@list @t1 @t5 @t15)) % 0.44/0.65 (define @t20 () (tptp.sdtasdt0 @t5 @t1)) % 0.44/0.65 (define @t21 () (tptp.smndt0 tptp.sz10)) % 0.44/0.65 (define @t22 () (tptp.aSet0 @t1)) % 0.44/0.65 (define @t23 () (tptp.aElementOf0 @t5 @t1)) % 0.44/0.65 (define @t24 () (@list @t5)) % 0.44/0.65 (define @t25 () (forall @t24 (=> @t23 @t8))) % 0.44/0.65 (define @t26 () (=> @t22 @t25)) % 0.44/0.65 (define @t27 () (forall @t3 @t26)) % 0.44/0.65 (define @t28 () (tptp.aElementOf0 @t15 @t1)) % 0.44/0.65 (define @t29 () (tptp.aElementOf0 @t15 @t5)) % 0.44/0.65 (define @t30 () (@list @t15)) % 0.44/0.65 (define @t31 () (and @t22 (tptp.aSet0 @t5))) % 0.44/0.65 (define @t32 () (@var "W3" $$unsorted)) % 0.44/0.65 (define @t33 () (@var "W5" $$unsorted)) % 0.44/0.65 (define @t34 () (@var "W4" $$unsorted)) % 0.44/0.65 (define @t35 () (tptp.aElementOf0 @t32 @t15)) % 0.44/0.65 (define @t36 () (@list @t32)) % 0.44/0.65 (define @t37 () (tptp.aSet0 @t15)) % 0.44/0.65 (define @t38 () (tptp.sdtpldt1 @t1 @t5)) % 0.44/0.65 (define @t39 () (tptp.sdtasasdt0 @t1 @t5)) % 0.44/0.65 (define @t40 () (tptp.aElementOf0 (tptp.sdtasdt0 @t15 @t5) @t1)) % 0.44/0.65 (define @t41 () (forall @t30 (=> @t17 @t40))) % 0.44/0.65 (define @t42 () (tptp.aElementOf0 @t16 @t1)) % 0.44/0.65 (define @t43 () (forall @t30 (=> @t28 @t42))) % 0.44/0.65 (define @t44 () (and @t43 @t41)) % 0.44/0.65 (define @t45 () (=> @t23 @t44)) % 0.44/0.65 (define @t46 () (forall @t24 @t45)) % 0.44/0.65 (define @t47 () (and @t22 @t46)) % 0.44/0.65 (define @t48 () (tptp.aIdeal0 @t1)) % 0.44/0.65 (define @t49 () (= @t48 @t47)) % 0.44/0.65 (define @t50 () (forall @t3 @t49)) % 0.44/0.65 (define @t51 () (and @t48 (tptp.aIdeal0 @t5))) % 0.44/0.65 (define @t52 () (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t15) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5)) @t15))) % 0.44/0.65 (define @t53 () (tptp.aIdeal0 @t15)) % 0.44/0.65 (define @t54 () (and @t2 @t8 @t53)) % 0.44/0.65 (define @t55 () (forall @t19 (=> @t54 @t52))) % 0.44/0.65 (define @t56 () (tptp.aIdeal0 tptp.xJ)) % 0.44/0.65 (define @t57 () (tptp.aIdeal0 tptp.xI)) % 0.44/0.65 (define @t58 () (tptp.aElement0 tptp.xy)) % 0.44/0.65 (define @t59 () (tptp.aElement0 tptp.xx)) % 0.44/0.65 (define @t60 () (tptp.aElementOf0 tptp.xb tptp.xJ)) % 0.44/0.65 (define @t61 () (tptp.aElementOf0 tptp.xa tptp.xI)) % 0.44/0.65 (define @t62 () (tptp.sdtasdt0 tptp.xx tptp.xb)) % 0.44/0.65 (define @t63 () (tptp.sdtasdt0 tptp.xy tptp.xa)) % 0.44/0.65 (define @t64 () (tptp.sdtpldt0 @t63 @t62)) % 0.44/0.65 (define @t65 () (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) % 0.44/0.65 (define @t66 () (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) % 0.44/0.65 (define @t67 () (tptp.sdteqdtlpzmzozddtrp0 @t1 tptp.xy tptp.xJ)) % 0.44/0.65 (define @t68 () (tptp.sdteqdtlpzmzozddtrp0 @t1 tptp.xx tptp.xI)) % 0.44/0.65 (define @t69 () (and @t2 @t68 @t67)) % 0.44/0.65 (define @t70 () (exists @t3 @t69)) % 0.44/0.65 (define @t71 () (not @t70)) % 0.44/0.65 (define @t72 () (not @t67)) % 0.44/0.65 (define @t73 () (not @t68)) % 0.44/0.65 (define @t74 () (not @t2)) % 0.44/0.65 (define @t75 () (or @t74 @t73 @t72)) % 0.44/0.65 (define @t76 () (forall @t3 @t75)) % 0.44/0.65 (define @t77 () (forall @t3 (not @t69))) % 0.44/0.65 (define @t78 () (not @t77)) % 0.44/0.65 (define @t79 () (not @t53)) % 0.44/0.65 (define @t80 () (not @t8)) % 0.44/0.65 (define @t81 () (or @t74 @t80 @t79 @t52)) % 0.44/0.65 (define @t82 () (or @t74 @t80 @t79)) % 0.44/0.65 (define @t83 () (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)) % 0.44/0.65 (define @t84 () (not @t56)) % 0.44/0.65 (define @t85 () (not @t58)) % 0.44/0.65 (define @t86 () (tptp.aElement0 tptp.xw)) % 0.44/0.65 (define @t87 () (not @t86)) % 0.44/0.65 (define @t88 () (or @t87 @t85 @t84 (= @t83 @t66))) % 0.44/0.65 (define @t89 () (forall @t19 @t81)) % 0.44/0.65 (define @t90 () (= @t66 @t83)) % 0.44/0.65 (define @t91 () (or @t87 @t85 @t84 @t90)) % 0.44/0.65 (define @t92 () (@list false)) % 0.44/0.65 (define @t93 () (@list @t89)) % 0.44/0.65 (define @t94 () (or @t74 @t80)) % 0.44/0.65 (define @t95 () (not @t9)) % 0.44/0.65 (define @t96 () (@var "BOUND_VARIABLE_7744" $$unsorted)) % 0.44/0.65 (define @t97 () (tptp.aElement0 @t96)) % 0.44/0.65 (define @t98 () (not (tptp.aElementOf0 @t96 @t1))) % 0.44/0.65 (define @t99 () (not @t22)) % 0.44/0.65 (define @t100 () (or @t98 @t97)) % 0.44/0.65 (define @t101 () (or @t99 @t100)) % 0.44/0.65 (define @t102 () (forall (@list @t1 @t96) @t101)) % 0.44/0.65 (define @t103 () (@list @t96)) % 0.44/0.65 (define @t104 () (forall @t103 @t101)) % 0.44/0.65 (define @t105 () (forall @t103 @t100)) % 0.44/0.65 (define @t106 () (or @t99 @t105)) % 0.44/0.65 (define @t107 () (not @t23)) % 0.44/0.65 (define @t108 () (forall @t24 (or @t107 @t8))) % 0.44/0.65 (define @t109 () (@var "BOUND_VARIABLE_7856" $$unsorted)) % 0.44/0.65 (define @t110 () (tptp.sdtasdt0 @t109 @t5)) % 0.44/0.65 (define @t111 () (not (tptp.aElement0 @t109))) % 0.44/0.65 (define @t112 () (or @t111 (tptp.aElementOf0 @t110 @t1))) % 0.44/0.65 (define @t113 () (@var "BOUND_VARIABLE_7849" $$unsorted)) % 0.44/0.65 (define @t114 () (tptp.sdtpldt0 @t5 @t113)) % 0.44/0.65 (define @t115 () (or (not (tptp.aElementOf0 @t113 @t1)) (tptp.aElementOf0 @t114 @t1))) % 0.44/0.65 (define @t116 () (and @t115 @t112)) % 0.44/0.65 (define @t117 () (or @t107 @t116)) % 0.44/0.65 (define @t118 () (@list @t5 @t113 @t109)) % 0.44/0.65 (define @t119 () (@list @t113 @t109)) % 0.44/0.65 (define @t120 () (forall @t119 @t117)) % 0.44/0.65 (define @t121 () (forall (@list @t109) @t112)) % 0.44/0.65 (define @t122 () (@list @t15)) % 0.44/0.65 (define @t123 () (forall @t119 @t112)) % 0.44/0.65 (define @t124 () (forall (@list @t113) @t115)) % 0.44/0.65 (define @t125 () (forall @t119 @t115)) % 0.44/0.65 (define @t126 () (and @t125 @t123)) % 0.44/0.65 (define @t127 () (forall @t119 @t116)) % 0.44/0.65 (define @t128 () (or @t107 @t127)) % 0.44/0.65 (define @t129 () (and (forall @t30 (or (not @t28) @t42)) (forall @t30 (or (not @t17) @t40)))) % 0.44/0.65 (define @t130 () (tptp.aSet0 tptp.xJ)) % 0.44/0.65 (define @t131 () (and @t130 (forall @t118 (or (not (tptp.aElementOf0 @t5 tptp.xJ)) (and (or (not (tptp.aElementOf0 @t113 tptp.xJ)) (tptp.aElementOf0 @t114 tptp.xJ)) (or @t111 (tptp.aElementOf0 @t110 tptp.xJ))))))) % 0.44/0.65 (define @t132 () (= @t56 @t131)) % 0.44/0.65 (define @t133 () (@list false false)) % 0.44/0.65 (define @t134 () (tptp.aElement0 tptp.xb)) % 0.44/0.65 (define @t135 () (not @t60)) % 0.44/0.65 (define @t136 () (not @t130)) % 0.44/0.65 (define @t137 () (or @t136 @t135 @t134)) % 0.44/0.65 (define @t138 () (@list false false false)) % 0.44/0.65 (define @t139 () (tptp.aElement0 @t62)) % 0.44/0.65 (define @t140 () (not @t134)) % 0.44/0.65 (define @t141 () (not @t59)) % 0.44/0.65 (define @t142 () (or @t141 @t140 @t139)) % 0.44/0.65 (define @t143 () (tptp.aSet0 tptp.xI)) % 0.44/0.65 (define @t144 () (and @t143 (forall @t118 (or (not (tptp.aElementOf0 @t5 tptp.xI)) (and (or (not (tptp.aElementOf0 @t113 tptp.xI)) (tptp.aElementOf0 @t114 tptp.xI)) (or @t111 (tptp.aElementOf0 @t110 tptp.xI))))))) % 0.44/0.65 (define @t145 () (= @t57 @t144)) % 0.44/0.65 (define @t146 () (not @t57)) % 0.44/0.65 (define @t147 () (tptp.aElement0 tptp.xa)) % 0.44/0.65 (define @t148 () (not @t61)) % 0.44/0.65 (define @t149 () (not @t143)) % 0.44/0.65 (define @t150 () (or @t149 @t148 @t147)) % 0.44/0.65 (define @t151 () (tptp.aElement0 @t63)) % 0.44/0.65 (define @t152 () (not @t147)) % 0.44/0.65 (define @t153 () (or @t85 @t152 @t151)) % 0.44/0.65 (define @t154 () (tptp.aElement0 @t64)) % 0.44/0.65 (define @t155 () (not @t139)) % 0.44/0.65 (define @t156 () (not @t151)) % 0.44/0.65 (define @t157 () (or @t156 @t155 @t154)) % 0.44/0.65 (define @t158 () (@list false false false false)) % 0.44/0.65 (define @t159 () (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI)) % 0.44/0.65 (define @t160 () (or @t87 @t141 @t146 (= @t159 @t65))) % 0.44/0.65 (define @t161 () (= @t65 @t159)) % 0.44/0.65 (define @t162 () (or @t87 @t141 @t146 @t161)) % 0.44/0.65 (define @t163 () (not @t83)) % 0.44/0.65 (define @t164 () (not @t159)) % 0.44/0.65 (define @t165 () (or @t87 @t164 @t163)) % 0.44/0.65 (define @t166 () (not @t165)) % 0.44/0.65 (assume @p1 (forall @t3 (=> @t2 true))) % 0.44/0.65 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.44/0.65 (assume @p3 (tptp.aElement0 tptp.sz10)) % 0.44/0.65 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 0.44/0.65 (assume @p5 @t11) % 0.44/0.65 (assume @p6 @t14) % 0.44/0.65 (assume @p7 (forall @t10 (=> @t9 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.44/0.65 (assume @p8 (forall @t19 (=> @t18 (= (tptp.sdtpldt0 @t6 @t15) (tptp.sdtpldt0 @t1 @t16))))) % 0.44/0.65 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.44/0.65 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.44/0.65 (assume @p11 (forall @t10 (=> @t9 (= @t12 @t20)))) % 0.44/0.65 (assume @p12 (forall @t19 (=> @t18 (= (tptp.sdtasdt0 @t12 @t15) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t15)))))) % 0.44/0.65 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.44/0.65 (assume @p14 (forall @t19 (=> @t18 (and (= (tptp.sdtasdt0 @t1 @t16) (tptp.sdtpldt0 @t12 (tptp.sdtasdt0 @t1 @t15))) (= (tptp.sdtasdt0 @t16 @t1) (tptp.sdtpldt0 @t20 (tptp.sdtasdt0 @t15 @t1))))))) % 0.44/0.65 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t21 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t21)))))) % 0.44/0.65 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.44/0.65 (assume @p17 (forall @t10 (=> @t9 (=> (= @t12 tptp.sz00) (or (= @t1 tptp.sz00) (= @t5 tptp.sz00)))))) % 0.44/0.65 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.44/0.65 (assume @p19 (forall @t3 (=> @t22 true))) % 0.44/0.65 (assume @p20 @t27) % 0.44/0.65 (assume @p21 (forall @t10 (=> @t31 (=> (and (forall @t30 (=> @t28 @t29)) (forall @t30 (=> @t29 @t28))) (= @t1 @t5))))) % 0.44/0.65 (assume @p22 (forall @t10 (=> @t31 (forall @t30 (= (= @t15 @t38) (and @t37 (forall @t36 (= @t35 (exists (@list @t34 @t33) (and (tptp.aElementOf0 @t34 @t1) (tptp.aElementOf0 @t33 @t5) (= (tptp.sdtpldt0 @t34 @t33) @t32))))))))))) % 0.44/0.65 (assume @p23 (forall @t10 (=> @t31 (forall @t30 (= (= @t15 @t39) (and @t37 (forall @t36 (= @t35 (and (tptp.aElementOf0 @t32 @t1) (tptp.aElementOf0 @t32 @t5)))))))))) % 0.44/0.65 (assume @p24 @t50) % 0.44/0.65 (assume @p25 (forall @t10 (=> @t51 (tptp.aIdeal0 @t38)))) % 0.44/0.65 (assume @p26 (forall @t10 (=> @t51 (tptp.aIdeal0 @t39)))) % 0.44/0.65 (assume @p27 @t55) % 0.44/0.65 (assume @p28 (and @t57 @t56)) % 0.44/0.65 (assume @p29 (forall @t3 (=> @t2 (tptp.aElementOf0 @t1 (tptp.sdtpldt1 tptp.xI tptp.xJ))))) % 0.44/0.65 (assume @p30 (and @t59 @t58)) % 0.44/0.65 (assume @p31 (and @t61 @t60 (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10))) % 0.44/0.65 (assume @p32 (= tptp.xw @t64)) % 0.44/0.65 (assume @p33 @t65) % 0.44/0.65 (assume @p34 @t66) % 0.44/0.65 (assume @p35 @t71) % 0.44/0.65 (assume @p36 true) % 0.44/0.65 (step @p37 :rule bool-double-not-elim :args (@t76)) % 0.44/0.65 (step @p38 :rule aci_norm :args ((= (or @t74 (or @t73 @t72)) @t75))) % 0.44/0.65 (step @p39 :rule bool-and-de-morgan :args (@t68 @t67 true)) % 0.44/0.65 (step @p40 :rule refl :args (@t74)) % 0.44/0.65 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or @t74 (not (and @t68 @t67))))) % 0.44/0.65 (step @p42 :rule bool-and-de-morgan :args (@t2 @t68 (and @t67))) % 0.44/0.65 (step @p43 :rule trans :premises (@p42 @p41)) % 0.44/0.65 (step @p44 :rule trans :premises (@p43 @p38)) % 0.44/0.65 (step @p45 :rule cong :premises (@p44) :args (@t77)) % 0.44/0.66 (step @p46 :rule cong :premises (@p45) :args (@t78)) % 0.44/0.66 (step @p47 :rule exists-elim :args ((= @t70 @t78))) % 0.44/0.66 (step @p48 :rule trans :premises (@p47 @p46)) % 0.44/0.66 (step @p49 :rule cong :premises (@p48) :args (@t71)) % 0.44/0.66 (step @p50 :rule trans :premises (@p49 @p37)) % 0.44/0.66 (step @p51 :rule eq_resolve :premises (@p35 @p50)) % 0.44/0.66 (step @p52 :rule aci_norm :args ((= (or @t82 @t52) @t81))) % 0.44/0.66 (step @p53 :rule refl :args (@t52)) % 0.44/0.66 (step @p54 :rule aci_norm :args ((= (or @t74 (or @t80 @t79)) @t82))) % 0.44/0.66 (step @p55 :rule bool-and-de-morgan :args (@t8 @t53 true)) % 0.44/0.66 (step @p56 :rule nary_cong :premises (@p40 @p55) :args ((or @t74 (not (and @t8 @t53))))) % 0.44/0.66 (step @p57 :rule bool-and-de-morgan :args (@t2 @t8 (and @t53))) % 0.44/0.66 (step @p58 :rule trans :premises (@p57 @p56)) % 0.44/0.66 (step @p59 :rule trans :premises (@p58 @p54)) % 0.44/0.66 (step @p60 :rule nary_cong :premises (@p59 @p53) :args ((or (not @t54) @t52))) % 0.44/0.66 (step @p61 :rule trans :premises (@p60 @p52)) % 0.44/0.66 (step @p62 :rule bool-impl-elim :args (@t54 @t52)) % 0.44/0.66 (step @p63 :rule trans :premises (@p62 @p61)) % 0.44/0.66 (step @p64 :rule cong :premises (@p63) :args (@t55)) % 0.44/0.66 (step @p65 :rule eq_resolve :premises (@p27 @p64)) % 0.44/0.66 (step @p66 :rule eq-symm :args (@t83 @t66)) % 0.44/0.66 (step @p67 :rule refl :args (@t84)) % 0.44/0.66 (step @p68 :rule refl :args (@t85)) % 0.44/0.66 (step @p69 :rule refl :args (@t87)) % 0.44/0.66 (step @p70 :rule nary_cong :premises (@p69 @p68 @p67 @p66) :args (@t88)) % 0.44/0.66 (step @p71 :rule refl :args (@t89)) % 0.44/0.66 (step @p72 :rule cong :premises (@p71 @p70) :args ((=> @t89 @t88))) % 0.44/0.66 (assume-push @p230 @t89) % 0.44/0.66 (step @p74 :rule instantiate :premises (@p65) :args ((@list tptp.xw tptp.xy tptp.xJ))) % 0.44/0.66 (step-pop @p231 :rule scope :premises (@p74)) % 0.44/0.66 (step @p75 :rule process_scope :premises (@p231) :args (@t88)) % 0.44/0.66 (step @p77 :rule eq_resolve :premises (@p75 @p72)) % 0.44/0.66 (step @p78 :rule implies_elim :premises (@p77)) % 0.44/0.66 (step @p79 :rule chain_m_resolution :premises (@p78 @p65) :args (@t91 @t92 @t93)) % 0.44/0.66 (step @p80 :rule aci_norm :args ((= (or @t94 @t7) (or @t74 @t80 @t7)))) % 0.44/0.66 (step @p81 :rule refl :args (@t7)) % 0.44/0.66 (step @p82 :rule bool-and-de-morgan :args (@t2 @t8 true)) % 0.44/0.66 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or @t95 @t7))) % 0.44/0.66 (step @p84 :rule trans :premises (@p83 @p80)) % 0.44/0.66 (step @p85 :rule bool-impl-elim :args (@t9 @t7)) % 0.44/0.66 (step @p86 :rule trans :premises (@p85 @p84)) % 0.44/0.66 (step @p87 :rule cong :premises (@p86) :args (@t11)) % 0.44/0.66 (step @p88 :rule eq_resolve :premises (@p5 @p87)) % 0.44/0.66 (step @p89 :rule instantiate :premises (@p88) :args ((@list @t63 @t62))) % 0.44/0.66 (step @p90 :rule aci_norm :args ((= (or @t94 @t13) (or @t74 @t80 @t13)))) % 0.44/0.66 (step @p91 :rule refl :args (@t13)) % 0.44/0.66 (step @p92 :rule nary_cong :premises (@p82 @p91) :args ((or @t95 @t13))) % 0.44/0.66 (step @p93 :rule trans :premises (@p92 @p90)) % 0.44/0.66 (step @p94 :rule bool-impl-elim :args (@t9 @t13)) % 0.44/0.66 (step @p95 :rule trans :premises (@p94 @p93)) % 0.44/0.66 (step @p96 :rule cong :premises (@p95) :args (@t14)) % 0.44/0.66 (step @p97 :rule eq_resolve :premises (@p6 @p96)) % 0.44/0.66 (step @p98 :rule instantiate :premises (@p97) :args ((@list tptp.xx tptp.xb))) % 0.44/0.66 (step @p99 :rule aci_norm :args ((= @t101 (or @t99 @t98 @t97)))) % 0.44/0.66 (step @p100 :rule cong :premises (@p99) :args (@t102)) % 0.44/0.66 (step @p101 :rule quant-merge-prenex :args ((= (forall @t3 @t104) @t102))) % 0.44/0.66 (step @p102 :rule alpha_equiv :args (@t105 (@list @t96) (@list @t5))) % 0.44/0.66 (step @p103 :rule refl :args (@t99)) % 0.44/0.66 (step @p104 :rule nary_cong :premises (@p103 @p102) :args (@t106)) % 0.44/0.66 (step @p105 :rule quant-miniscope-or :args ((= @t104 @t106))) % 0.44/0.66 (step @p106 :rule trans :premises (@p105 @p104)) % 0.44/0.66 (step @p107 :rule symm :premises (@p106)) % 0.44/0.66 (step @p108 :rule cong :premises (@p107) :args ((forall @t3 (or @t99 @t108)))) % 0.44/0.66 (step @p109 :rule trans :premises (@p108 @p101)) % 0.44/0.66 (step @p110 :rule trans :premises (@p109 @p100)) % 0.44/0.66 (step @p111 :rule bool-impl-elim :args (@t22 @t108)) % 0.44/0.66 (step @p112 :rule cong :premises (@p111) :args ((forall @t3 (=> @t22 @t108)))) % 0.44/0.66 (step @p113 :rule trans :premises (@p112 @p110)) % 0.44/0.66 (step @p114 :rule bool-impl-elim :args (@t23 @t8)) % 0.44/0.66 (step @p115 :rule cong :premises (@p114) :args (@t25)) % 0.44/0.66 (step @p116 :rule refl :args (@t22)) % 0.44/0.66 (step @p117 :rule cong :premises (@p116 @p115) :args (@t26)) % 0.44/0.66 (step @p118 :rule cong :premises (@p117) :args (@t27)) % 0.44/0.66 (step @p119 :rule trans :premises (@p118 @p113)) % 0.44/0.66 (step @p120 :rule eq_resolve :premises (@p20 @p119)) % 0.44/0.66 (step @p121 :rule instantiate :premises (@p120) :args ((@list tptp.xJ tptp.xb))) % 0.44/0.66 (step @p122 :rule quant-merge-prenex :args ((= (forall @t24 @t120) (forall @t118 @t117)))) % 0.44/0.66 (step @p123 :rule alpha_equiv :args (@t121 (@list @t109) @t122)) % 0.44/0.66 (step @p124 :rule quant-unused-vars :args ((= @t123 @t121))) % 0.44/0.66 (step @p125 :rule trans :premises (@p124 @p123)) % 0.44/0.66 (step @p126 :rule alpha_equiv :args (@t124 (@list @t113) @t122)) % 0.44/0.66 (step @p127 :rule quant-unused-vars :args ((= @t125 @t124))) % 0.44/0.66 (step @p128 :rule trans :premises (@p127 @p126)) % 0.44/0.66 (step @p129 :rule nary_cong :premises (@p128 @p125) :args (@t126)) % 0.44/0.66 (step @p130 :rule quant-miniscope-and :args ((= @t127 @t126))) % 0.44/0.66 (step @p131 :rule trans :premises (@p130 @p129)) % 0.44/0.66 (step @p132 :rule refl :args (@t107)) % 0.44/0.66 (step @p133 :rule nary_cong :premises (@p132 @p131) :args (@t128)) % 0.44/0.66 (step @p134 :rule quant-miniscope-or :args ((= @t120 @t128))) % 0.44/0.66 (step @p135 :rule trans :premises (@p134 @p133)) % 0.44/0.66 (step @p136 :rule symm :premises (@p135)) % 0.44/0.66 (step @p137 :rule cong :premises (@p136) :args ((forall @t24 (or @t107 @t129)))) % 0.44/0.66 (step @p138 :rule trans :premises (@p137 @p122)) % 0.44/0.66 (step @p139 :rule bool-impl-elim :args (@t23 @t129)) % 0.44/0.66 (step @p140 :rule cong :premises (@p139) :args ((forall @t24 (=> @t23 @t129)))) % 0.44/0.66 (step @p141 :rule trans :premises (@p140 @p138)) % 0.44/0.66 (step @p142 :rule bool-impl-elim :args (@t17 @t40)) % 0.44/0.66 (step @p143 :rule cong :premises (@p142) :args (@t41)) % 0.44/0.66 (step @p144 :rule bool-impl-elim :args (@t28 @t42)) % 0.44/0.66 (step @p145 :rule cong :premises (@p144) :args (@t43)) % 0.44/0.66 (step @p146 :rule nary_cong :premises (@p145 @p143) :args (@t44)) % 0.44/0.66 (step @p147 :rule refl :args (@t23)) % 0.44/0.66 (step @p148 :rule cong :premises (@p147 @p146) :args (@t45)) % 0.44/0.66 (step @p149 :rule cong :premises (@p148) :args (@t46)) % 0.44/0.66 (step @p150 :rule trans :premises (@p149 @p141)) % 0.44/0.66 (step @p151 :rule nary_cong :premises (@p116 @p150) :args (@t47)) % 0.44/0.66 (step @p152 :rule refl :args (@t48)) % 0.44/0.66 (step @p153 :rule cong :premises (@p152 @p151) :args (@t49)) % 0.44/0.66 (step @p154 :rule cong :premises (@p153) :args (@t50)) % 0.44/0.66 (step @p155 :rule eq_resolve :premises (@p24 @p154)) % 0.44/0.66 (step @p156 :rule instantiate :premises (@p155) :args ((@list tptp.xJ))) % 0.44/0.66 (step @p157 :rule and_elim :premises (@p28) :args (1)) % 0.44/0.66 (step @p158 :rule cnf_equiv_pos1 :args (@t132)) % 0.44/0.66 (step @p159 :rule reordering :premises (@p158) :args ((or @t84 @t131 (not @t132)))) % 0.44/0.66 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p156) :args (@t131 @t133 (@list @t56 @t132))) % 0.44/0.66 (step @p161 :rule cnf_and_pos :args (@t131 0)) % 0.44/0.66 (step @p162 :rule reordering :premises (@p161) :args ((or @t130 (not @t131)))) % 0.44/0.66 (step @p163 :rule chain_m_resolution :premises (@p162 @p160) :args (@t130 @t92 (@list @t131))) % 0.44/0.66 (step @p164 :rule and_elim :premises (@p31) :args (1)) % 0.44/0.66 (step @p165 :rule cnf_or_pos :args (@t137)) % 0.44/0.66 (step @p166 :rule reordering :premises (@p165) :args ((or @t135 @t134 @t136 (not @t137)))) % 0.44/0.66 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p163 @p121) :args (@t134 @t138 (@list @t60 @t130 @t137))) % 0.44/0.66 (step @p168 :rule and_elim :premises (@p30) :args (0)) % 0.44/0.66 (step @p169 :rule cnf_or_pos :args (@t142)) % 0.44/0.66 (step @p170 :rule reordering :premises (@p169) :args ((or @t141 @t139 @t140 (not @t142)))) % 0.44/0.66 (step @p171 :rule chain_m_resolution :premises (@p170 @p168 @p167 @p98) :args (@t139 @t138 (@list @t59 @t134 @t142))) % 0.44/0.66 (step @p172 :rule instantiate :premises (@p97) :args ((@list tptp.xy tptp.xa))) % 0.44/0.66 (step @p173 :rule instantiate :premises (@p120) :args ((@list tptp.xI tptp.xa))) % 0.44/0.66 (step @p174 :rule instantiate :premises (@p155) :args ((@list tptp.xI))) % 0.44/0.66 (step @p175 :rule and_elim :premises (@p28) :args (0)) % 0.44/0.66 (step @p176 :rule cnf_equiv_pos1 :args (@t145)) % 0.44/0.66 (step @p177 :rule reordering :premises (@p176) :args ((or @t146 @t144 (not @t145)))) % 0.44/0.66 (step @p178 :rule chain_m_resolution :premises (@p177 @p175 @p174) :args (@t144 @t133 (@list @t57 @t145))) % 0.44/0.66 (step @p179 :rule cnf_and_pos :args (@t144 0)) % 0.44/0.66 (step @p180 :rule reordering :premises (@p179) :args ((or @t143 (not @t144)))) % 0.44/0.66 (step @p181 :rule chain_m_resolution :premises (@p180 @p178) :args (@t143 @t92 (@list @t144))) % 0.44/0.66 (step @p182 :rule and_elim :premises (@p31) :args (0)) % 0.44/0.66 (step @p183 :rule cnf_or_pos :args (@t150)) % 0.44/0.66 (step @p184 :rule reordering :premises (@p183) :args ((or @t148 @t147 @t149 (not @t150)))) % 0.44/0.66 (step @p185 :rule chain_m_resolution :premises (@p184 @p182 @p181 @p173) :args (@t147 @t138 (@list @t61 @t143 @t150))) % 0.44/0.66 (step @p186 :rule and_elim :premises (@p30) :args (1)) % 0.44/0.66 (step @p187 :rule cnf_or_pos :args (@t153)) % 0.44/0.66 (step @p188 :rule reordering :premises (@p187) :args ((or @t85 @t151 @t152 (not @t153)))) % 0.44/0.66 (step @p189 :rule chain_m_resolution :premises (@p188 @p186 @p185 @p172) :args (@t151 @t138 (@list @t58 @t147 @t153))) % 0.44/0.66 (step @p190 :rule cnf_or_pos :args (@t157)) % 0.44/0.66 (step @p191 :rule reordering :premises (@p190) :args ((or @t156 @t155 @t154 (not @t157)))) % 0.44/0.66 (step @p192 :rule chain_m_resolution :premises (@p191 @p189 @p171 @p89) :args (@t154 @t138 (@list @t151 @t139 @t157))) % 0.44/0.66 (step @p193 :rule true_intro :premises (@p192)) % 0.44/0.66 (step @p194 :rule cong :premises (@p32) :args (@t86)) % 0.44/0.66 (step @p195 :rule trans :premises (@p194 @p193)) % 0.44/0.66 (step @p196 :rule true_elim :premises (@p195)) % 0.44/0.66 (step @p197 :rule cnf_or_pos :args (@t91)) % 0.44/0.66 (step @p198 :rule reordering :premises (@p197) :args ((or @t84 @t85 @t87 @t90 (not @t91)))) % 0.44/0.66 (step @p199 :rule chain_m_resolution :premises (@p198 @p157 @p186 @p196 @p79) :args (@t90 @t158 (@list @t56 @t58 @t86 @t91))) % 0.44/0.66 (step @p200 :rule cnf_equiv_pos1 :args (@t90)) % 0.44/0.66 (step @p201 :rule reordering :premises (@p200) :args ((or (not @t66) @t83 (not @t90)))) % 0.44/0.66 (step @p202 :rule chain_m_resolution :premises (@p201 @p34 @p199) :args (@t83 @t133 (@list @t66 @t90))) % 0.44/0.66 (step @p203 :rule eq-symm :args (@t159 @t65)) % 0.44/0.66 (step @p204 :rule refl :args (@t146)) % 0.44/0.66 (step @p205 :rule refl :args (@t141)) % 0.44/0.66 (step @p206 :rule nary_cong :premises (@p69 @p205 @p204 @p203) :args (@t160)) % 0.44/0.66 (step @p207 :rule cong :premises (@p71 @p206) :args ((=> @t89 @t160))) % 0.44/0.66 (assume-push @p232 @t89) % 0.44/0.66 (step @p209 :rule instantiate :premises (@p65) :args ((@list tptp.xw tptp.xx tptp.xI))) % 0.44/0.66 (step-pop @p233 :rule scope :premises (@p209)) % 0.44/0.66 (step @p210 :rule process_scope :premises (@p233) :args (@t160)) % 0.44/0.66 (step @p212 :rule eq_resolve :premises (@p210 @p207)) % 0.44/0.66 (step @p213 :rule implies_elim :premises (@p212)) % 0.44/0.66 (step @p214 :rule chain_m_resolution :premises (@p213 @p65) :args (@t162 @t92 @t93)) % 0.44/0.66 (step @p215 :rule cnf_or_pos :args (@t162)) % 0.44/0.66 (step @p216 :rule reordering :premises (@p215) :args ((or @t146 @t141 @t87 @t161 (not @t162)))) % 0.44/0.66 (step @p217 :rule chain_m_resolution :premises (@p216 @p175 @p168 @p196 @p214) :args (@t161 @t158 (@list @t57 @t59 @t86 @t162))) % 0.44/0.66 (step @p218 :rule cnf_equiv_pos1 :args (@t161)) % 0.44/0.66 (step @p219 :rule reordering :premises (@p218) :args ((or (not @t65) @t159 (not @t161)))) % 0.44/0.66 (step @p220 :rule chain_m_resolution :premises (@p219 @p33 @p217) :args (@t159 @t133 (@list @t65 @t161))) % 0.44/0.66 (step @p221 :rule cnf_or_pos :args (@t165)) % 0.44/0.66 (step @p222 :rule reordering :premises (@p221) :args ((or @t87 @t164 @t163 @t166))) % 0.44/0.66 (step @p223 :rule chain_m_resolution :premises (@p222 @p196 @p220 @p202) :args (@t166 @t138 (@list @t86 @t159 @t83))) % 0.44/0.66 (assume-push @p234 @t76) % 0.44/0.66 (step @p225 :rule instantiate :premises (@p51) :args ((@list tptp.xw))) % 0.44/0.66 (step-pop @p235 :rule scope :premises (@p225)) % 0.44/0.66 (step @p226 :rule process_scope :premises (@p235) :args (@t165)) % 0.44/0.66 (step @p228 :rule implies_elim :premises (@p226)) % 0.44/0.66 (step @p229 false :rule chain_m_resolution :premises (@p228 @p223 @p51) :args (false (@list true false) (@list @t165 @t76))) % 0.44/0.66 ) % 0.44/0.66 % SZS output end Proof % 0.44/0.66 % cvc5 exiting %------------------------------------------------------------------------------