%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG091+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 : n006.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 08:45:38 AM UTC 2026 % Result : Theorem 15.97s 16.39s % Output : Proof 15.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG091+1 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n006.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:06:49 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 15.97/16.39 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 15.97/16.39 --- Run --no-e-matching --full-saturate-quant at 6... % 15.97/16.39 % SZS status Theorem % 15.97/16.39 % SZS output start Proof % 15.97/16.39 ( % 15.97/16.39 (declare-sort $$unsorted 0) % 15.97/16.39 (declare-const tptp.xm $$unsorted) % 15.97/16.39 (declare-const tptp.xk $$unsorted) % 15.97/16.39 (declare-const tptp.xx $$unsorted) % 15.97/16.39 (declare-const tptp.xy $$unsorted) % 15.97/16.39 (declare-const tptp.xn $$unsorted) % 15.97/16.39 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 15.97/16.39 (declare-const tptp.sz00 $$unsorted) % 15.97/16.39 (declare-const tptp.xI $$unsorted) % 15.97/16.39 (declare-const tptp.sz10 $$unsorted) % 15.97/16.39 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 15.97/16.39 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.97/16.39 (declare-const tptp.xl $$unsorted) % 15.97/16.39 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 15.97/16.39 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.97/16.39 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 15.97/16.39 (declare-const tptp.xz $$unsorted) % 15.97/16.39 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 15.97/16.39 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 15.97/16.39 (declare-const tptp.xJ $$unsorted) % 15.97/16.39 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 15.97/16.39 (define @t1 () (@var "W0" $$unsorted)) % 15.97/16.39 (define @t2 () (tptp.aElement0 @t1)) % 15.97/16.39 (define @t3 () (@list @t1)) % 15.97/16.39 (define @t4 () (tptp.smndt0 @t1)) % 15.97/16.39 (define @t5 () (@var "W1" $$unsorted)) % 15.97/16.39 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 15.97/16.39 (define @t7 () (tptp.aElement0 @t5)) % 15.97/16.39 (define @t8 () (and @t2 @t7)) % 15.97/16.39 (define @t9 () (@list @t1 @t5)) % 15.97/16.39 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 15.97/16.39 (define @t11 () (@var "W2" $$unsorted)) % 15.97/16.39 (define @t12 () (tptp.sdtpldt0 @t5 @t11)) % 15.97/16.39 (define @t13 () (tptp.aElement0 @t11)) % 15.97/16.39 (define @t14 () (and @t2 @t7 @t13)) % 15.97/16.39 (define @t15 () (@list @t1 @t5 @t11)) % 15.97/16.39 (define @t16 () (tptp.sdtasdt0 @t5 @t1)) % 15.97/16.39 (define @t17 () (tptp.smndt0 tptp.sz10)) % 15.97/16.39 (define @t18 () (tptp.aSet0 @t1)) % 15.97/16.39 (define @t19 () (tptp.aElementOf0 @t5 @t1)) % 15.97/16.39 (define @t20 () (@list @t5)) % 15.97/16.39 (define @t21 () (tptp.aElementOf0 @t11 @t1)) % 15.97/16.39 (define @t22 () (tptp.aElementOf0 @t11 @t5)) % 15.97/16.39 (define @t23 () (@list @t11)) % 15.97/16.39 (define @t24 () (tptp.aSet0 @t5)) % 15.97/16.39 (define @t25 () (and @t18 @t24)) % 15.97/16.39 (define @t26 () (@var "W3" $$unsorted)) % 15.97/16.39 (define @t27 () (@var "W5" $$unsorted)) % 15.97/16.39 (define @t28 () (@var "W4" $$unsorted)) % 15.97/16.39 (define @t29 () (tptp.sdtpldt0 @t28 @t27)) % 15.97/16.39 (define @t30 () (tptp.aElementOf0 @t27 @t5)) % 15.97/16.39 (define @t31 () (tptp.aElementOf0 @t28 @t1)) % 15.97/16.39 (define @t32 () (and @t31 @t30 (= @t29 @t26))) % 15.97/16.39 (define @t33 () (@list @t28 @t27)) % 15.97/16.39 (define @t34 () (exists @t33 @t32)) % 15.97/16.39 (define @t35 () (tptp.aElementOf0 @t26 @t11)) % 15.97/16.39 (define @t36 () (= @t35 @t34)) % 15.97/16.39 (define @t37 () (@list @t26)) % 15.97/16.39 (define @t38 () (forall @t37 @t36)) % 15.97/16.39 (define @t39 () (tptp.aSet0 @t11)) % 15.97/16.39 (define @t40 () (and @t39 @t38)) % 15.97/16.39 (define @t41 () (tptp.sdtpldt1 @t1 @t5)) % 15.97/16.39 (define @t42 () (= @t11 @t41)) % 15.97/16.39 (define @t43 () (= @t42 @t40)) % 15.97/16.39 (define @t44 () (forall @t23 @t43)) % 15.97/16.39 (define @t45 () (=> @t25 @t44)) % 15.97/16.39 (define @t46 () (forall @t9 @t45)) % 15.97/16.39 (define @t47 () (tptp.aElementOf0 (tptp.sdtasdt0 @t11 @t5) @t1)) % 15.97/16.39 (define @t48 () (forall @t23 (=> @t13 @t47))) % 15.97/16.39 (define @t49 () (tptp.aElementOf0 @t12 @t1)) % 15.97/16.39 (define @t50 () (forall @t23 (=> @t21 @t49))) % 15.97/16.39 (define @t51 () (and @t50 @t48)) % 15.97/16.39 (define @t52 () (=> @t19 @t51)) % 15.97/16.39 (define @t53 () (forall @t20 @t52)) % 15.97/16.39 (define @t54 () (and @t18 @t53)) % 15.97/16.39 (define @t55 () (tptp.aIdeal0 @t1)) % 15.97/16.39 (define @t56 () (= @t55 @t54)) % 15.97/16.39 (define @t57 () (forall @t3 @t56)) % 15.97/16.39 (define @t58 () (tptp.aIdeal0 tptp.xJ)) % 15.97/16.39 (define @t59 () (tptp.aIdeal0 tptp.xI)) % 15.97/16.39 (define @t60 () (tptp.sdtpldt1 tptp.xI tptp.xJ)) % 15.97/16.39 (define @t61 () (tptp.sdtpldt0 tptp.xk tptp.xl)) % 15.97/16.39 (define @t62 () (tptp.sdtpldt0 tptp.xm tptp.xn)) % 15.97/16.39 (define @t63 () (tptp.sdtpldt0 tptp.xl tptp.xn)) % 15.97/16.39 (define @t64 () (tptp.aElementOf0 @t63 tptp.xJ)) % 15.97/16.39 (define @t65 () (tptp.sdtpldt0 tptp.xk tptp.xm)) % 15.97/16.39 (define @t66 () (tptp.aElementOf0 @t65 tptp.xI)) % 15.97/16.39 (define @t67 () (tptp.sdtasdt0 tptp.xz tptp.xl)) % 15.97/16.39 (define @t68 () (tptp.aElementOf0 @t67 tptp.xJ)) % 15.97/16.39 (define @t69 () (tptp.sdtasdt0 tptp.xz tptp.xk)) % 15.97/16.39 (define @t70 () (tptp.aElementOf0 @t69 tptp.xI)) % 15.97/16.39 (define @t71 () (tptp.sdtpldt0 @t65 @t63)) % 15.97/16.39 (define @t72 () (tptp.sdtpldt0 tptp.xx tptp.xy)) % 15.97/16.39 (define @t73 () (= @t72 @t71)) % 15.97/16.39 (define @t74 () (tptp.sdtpldt0 @t69 @t67)) % 15.97/16.39 (define @t75 () (tptp.sdtasdt0 tptp.xz tptp.xx)) % 15.97/16.39 (define @t76 () (= @t75 @t74)) % 15.97/16.39 (define @t77 () (tptp.aElementOf0 @t75 @t60)) % 15.97/16.39 (define @t78 () (tptp.aElementOf0 @t72 @t60)) % 15.97/16.39 (define @t79 () (and @t78 @t77)) % 15.97/16.39 (define @t80 () (not @t79)) % 15.97/16.39 (define @t81 () (@var "BOUND_VARIABLE_7790" $$unsorted)) % 15.97/16.39 (define @t82 () (tptp.aElementOf0 @t26 @t81)) % 15.97/16.39 (define @t83 () (= @t26 @t29)) % 15.97/16.39 (define @t84 () (not @t83)) % 15.97/16.39 (define @t85 () (not @t30)) % 15.97/16.39 (define @t86 () (not @t31)) % 15.97/16.39 (define @t87 () (or @t86 @t85 @t84)) % 15.97/16.39 (define @t88 () (not (forall @t33 @t87))) % 15.97/16.39 (define @t89 () (forall @t37 (= @t82 @t88))) % 15.97/16.39 (define @t90 () (tptp.aSet0 @t81)) % 15.97/16.39 (define @t91 () (and @t90 @t89)) % 15.97/16.39 (define @t92 () (= (= @t81 @t41) @t91)) % 15.97/16.39 (define @t93 () (not @t24)) % 15.97/16.39 (define @t94 () (not @t18)) % 15.97/16.39 (define @t95 () (or @t94 @t93 @t92)) % 15.97/16.39 (define @t96 () (@list @t1 @t5 @t81)) % 15.97/16.39 (define @t97 () (forall @t96 @t95)) % 15.97/16.39 (define @t98 () (@list @t81)) % 15.97/16.39 (define @t99 () (forall @t98 @t95)) % 15.97/16.39 (define @t100 () (forall @t98 @t92)) % 15.97/16.39 (define @t101 () (@list @t11)) % 15.97/16.39 (define @t102 () (or @t94 @t93 @t100)) % 15.97/16.39 (define @t103 () (forall @t23 (= @t42 (and @t39 (forall @t37 (= @t35 @t88)))))) % 15.97/16.39 (define @t104 () (or @t94 @t93 @t103)) % 15.97/16.39 (define @t105 () (and @t31 @t30 @t83)) % 15.97/16.39 (define @t106 () (forall @t33 (not @t105))) % 15.97/16.39 (define @t107 () (not @t106)) % 15.97/16.39 (define @t108 () (not (tptp.aElementOf0 @t27 tptp.xJ))) % 15.97/16.39 (define @t109 () (not (tptp.aElementOf0 @t28 tptp.xI))) % 15.97/16.39 (define @t110 () (forall @t37 (= (not (forall @t33 (or @t109 @t108 @t84))) (tptp.aElementOf0 @t26 @t60)))) % 15.97/16.39 (define @t111 () (and (tptp.aSet0 @t60) @t110)) % 15.97/16.39 (define @t112 () (= (= @t60 @t60) @t111)) % 15.97/16.39 (define @t113 () (tptp.aSet0 tptp.xJ)) % 15.97/16.39 (define @t114 () (not @t113)) % 15.97/16.39 (define @t115 () (tptp.aSet0 tptp.xI)) % 15.97/16.39 (define @t116 () (not @t115)) % 15.97/16.39 (define @t117 () (or @t116 @t114 @t112)) % 15.97/16.39 (define @t118 () (forall @t96 (or @t94 @t93 (= (= @t41 @t81) (and @t90 (forall @t37 (= @t88 @t82))))))) % 15.97/16.39 (define @t119 () (or @t116 @t114 @t111)) % 15.97/16.39 (define @t120 () (@list false)) % 15.97/16.39 (define @t121 () (@var "BOUND_VARIABLE_7848" $$unsorted)) % 15.97/16.39 (define @t122 () (tptp.sdtasdt0 @t121 @t5)) % 15.97/16.39 (define @t123 () (not (tptp.aElement0 @t121))) % 15.97/16.39 (define @t124 () (or @t123 (tptp.aElementOf0 @t122 @t1))) % 15.97/16.39 (define @t125 () (@var "BOUND_VARIABLE_7841" $$unsorted)) % 15.97/16.39 (define @t126 () (tptp.sdtpldt0 @t5 @t125)) % 15.97/16.39 (define @t127 () (or (not (tptp.aElementOf0 @t125 @t1)) (tptp.aElementOf0 @t126 @t1))) % 15.97/16.39 (define @t128 () (and @t127 @t124)) % 15.97/16.39 (define @t129 () (not @t19)) % 15.97/16.39 (define @t130 () (or @t129 @t128)) % 15.97/16.39 (define @t131 () (@list @t5 @t125 @t121)) % 15.97/16.39 (define @t132 () (@list @t125 @t121)) % 15.97/16.39 (define @t133 () (forall @t132 @t130)) % 15.97/16.39 (define @t134 () (forall (@list @t121) @t124)) % 15.97/16.39 (define @t135 () (forall @t132 @t124)) % 15.97/16.39 (define @t136 () (forall (@list @t125) @t127)) % 15.97/16.39 (define @t137 () (forall @t132 @t127)) % 15.97/16.39 (define @t138 () (and @t137 @t135)) % 15.97/16.39 (define @t139 () (forall @t132 @t128)) % 15.97/16.39 (define @t140 () (or @t129 @t139)) % 15.97/16.39 (define @t141 () (and (forall @t23 (or (not @t21) @t49)) (forall @t23 (or (not @t13) @t47)))) % 15.97/16.39 (define @t142 () (and @t113 (forall @t131 (or (not (tptp.aElementOf0 @t5 tptp.xJ)) (and (or (not (tptp.aElementOf0 @t125 tptp.xJ)) (tptp.aElementOf0 @t126 tptp.xJ)) (or @t123 (tptp.aElementOf0 @t122 tptp.xJ))))))) % 15.97/16.39 (define @t143 () (= @t58 @t142)) % 15.97/16.39 (define @t144 () (@list false false)) % 15.97/16.39 (define @t145 () (and @t115 (forall @t131 (or (not (tptp.aElementOf0 @t5 tptp.xI)) (and (or (not (tptp.aElementOf0 @t125 tptp.xI)) (tptp.aElementOf0 @t126 tptp.xI)) (or @t123 (tptp.aElementOf0 @t122 tptp.xI))))))) % 15.97/16.39 (define @t146 () (= @t59 @t145)) % 15.97/16.39 (define @t147 () (@list false false false)) % 15.97/16.39 (define @t148 () (tptp.sdtasdt0 tptp.xz @t61)) % 15.97/16.39 (define @t149 () (not (= @t148 @t29))) % 15.97/16.39 (define @t150 () (or @t109 @t108 @t149)) % 15.97/16.39 (define @t151 () (forall @t33 @t150)) % 15.97/16.39 (define @t152 () (not @t151)) % 15.97/16.39 (define @t153 () (tptp.aElementOf0 @t148 @t60)) % 15.97/16.39 (define @t154 () (= @t152 @t153)) % 15.97/16.39 (define @t155 () (forall @t33 (or @t109 @t108 (not (= @t29 @t148))))) % 15.97/16.39 (define @t156 () (not @t155)) % 15.97/16.39 (define @t157 () (= @t153 @t156)) % 15.97/16.39 (define @t158 () (@list @t110)) % 15.97/16.39 (define @t159 () (tptp.sdtpldt0 @t61 @t62)) % 15.97/16.39 (define @t160 () (not (= @t159 @t29))) % 15.97/16.39 (define @t161 () (or @t109 @t108 @t160)) % 15.97/16.39 (define @t162 () (forall @t33 @t161)) % 15.97/16.39 (define @t163 () (not @t162)) % 15.97/16.39 (define @t164 () (tptp.aElementOf0 @t159 @t60)) % 15.97/16.39 (define @t165 () (= @t163 @t164)) % 15.97/16.39 (define @t166 () (forall @t33 (or @t109 @t108 (not (= @t29 @t159))))) % 15.97/16.39 (define @t167 () (not @t166)) % 15.97/16.39 (define @t168 () (= @t164 @t167)) % 15.97/16.39 (define @t169 () (= @t71 @t159)) % 15.97/16.39 (define @t170 () (not @t169)) % 15.97/16.39 (define @t171 () (not @t64)) % 15.97/16.39 (define @t172 () (not @t66)) % 15.97/16.39 (define @t173 () (or @t172 @t171 @t170)) % 15.97/16.39 (define @t174 () (not @t173)) % 15.97/16.39 (define @t175 () (not @t168)) % 15.97/16.39 (define @t176 () (@list true false)) % 15.97/16.39 (define @t177 () (not @t157)) % 15.97/16.39 (define @t178 () (= @t74 @t148)) % 15.97/16.39 (define @t179 () (not @t178)) % 15.97/16.39 (define @t180 () (not @t68)) % 15.97/16.39 (define @t181 () (not @t70)) % 15.97/16.39 (define @t182 () (or @t181 @t180 @t179)) % 15.97/16.39 (define @t183 () (not @t182)) % 15.97/16.39 (assume @p1 (forall @t3 (=> @t2 true))) % 15.97/16.39 (assume @p2 (tptp.aElement0 tptp.sz00)) % 15.97/16.39 (assume @p3 (tptp.aElement0 tptp.sz10)) % 15.97/16.39 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t4)))) % 15.97/16.39 (assume @p5 (forall @t9 (=> @t8 (tptp.aElement0 @t6)))) % 15.97/16.39 (assume @p6 (forall @t9 (=> @t8 (tptp.aElement0 @t10)))) % 15.97/16.39 (assume @p7 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 15.97/16.39 (assume @p8 (forall @t15 (=> @t14 (= (tptp.sdtpldt0 @t6 @t11) (tptp.sdtpldt0 @t1 @t12))))) % 15.97/16.39 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 15.97/16.39 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 15.97/16.39 (assume @p11 (forall @t9 (=> @t8 (= @t10 @t16)))) % 15.97/16.39 (assume @p12 (forall @t15 (=> @t14 (= (tptp.sdtasdt0 @t10 @t11) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t5 @t11)))))) % 15.97/16.39 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 15.97/16.39 (assume @p14 (forall @t15 (=> @t14 (and (= (tptp.sdtasdt0 @t1 @t12) (tptp.sdtpldt0 @t10 (tptp.sdtasdt0 @t1 @t11))) (= (tptp.sdtasdt0 @t12 @t1) (tptp.sdtpldt0 @t16 (tptp.sdtasdt0 @t11 @t1))))))) % 15.97/16.39 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t17 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t17)))))) % 15.97/16.39 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 15.97/16.39 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or (= @t1 tptp.sz00) (= @t5 tptp.sz00)))))) % 15.97/16.39 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 15.97/16.39 (assume @p19 (forall @t3 (=> @t18 true))) % 15.97/16.39 (assume @p20 (forall @t3 (=> @t18 (forall @t20 (=> @t19 @t7))))) % 15.97/16.39 (assume @p21 (forall @t9 (=> @t25 (=> (and (forall @t23 (=> @t21 @t22)) (forall @t23 (=> @t22 @t21))) (= @t1 @t5))))) % 15.97/16.39 (assume @p22 @t46) % 15.97/16.39 (assume @p23 (forall @t9 (=> @t25 (forall @t23 (= (= @t11 (tptp.sdtasasdt0 @t1 @t5)) (and @t39 (forall @t37 (= @t35 (and (tptp.aElementOf0 @t26 @t1) (tptp.aElementOf0 @t26 @t5)))))))))) % 15.97/16.39 (assume @p24 @t57) % 15.97/16.39 (assume @p25 (and @t59 @t58)) % 15.97/16.39 (assume @p26 (and (tptp.aElementOf0 tptp.xx @t60) (tptp.aElementOf0 tptp.xy @t60) (tptp.aElement0 tptp.xz))) % 15.97/16.39 (assume @p27 (and (tptp.aElementOf0 tptp.xk tptp.xI) (tptp.aElementOf0 tptp.xl tptp.xJ) (= tptp.xx @t61))) % 15.97/16.39 (assume @p28 (and (tptp.aElementOf0 tptp.xm tptp.xI) (tptp.aElementOf0 tptp.xn tptp.xJ) (= tptp.xy @t62))) % 15.97/16.39 (assume @p29 (and @t66 @t64)) % 15.97/16.39 (assume @p30 (and @t70 @t68)) % 15.97/16.39 (assume @p31 @t73) % 15.97/16.39 (assume @p32 @t76) % 15.97/16.39 (assume @p33 @t80) % 15.97/16.39 (assume @p34 true) % 15.97/16.39 (step @p35 :rule eq-symm :args (@t82 @t88)) % 15.97/16.39 (step @p36 :rule cong :premises (@p35) :args (@t89)) % 15.97/16.39 (step @p37 :rule refl :args (@t90)) % 15.97/16.39 (step @p38 :rule nary_cong :premises (@p37 @p36) :args (@t91)) % 15.97/16.39 (step @p39 :rule eq-symm :args (@t81 @t41)) % 15.97/16.39 (step @p40 :rule cong :premises (@p39 @p38) :args (@t92)) % 15.97/16.39 (step @p41 :rule refl :args (@t93)) % 15.97/16.39 (step @p42 :rule refl :args (@t94)) % 15.97/16.39 (step @p43 :rule nary_cong :premises (@p42 @p41 @p40) :args (@t95)) % 15.97/16.39 (step @p44 :rule cong :premises (@p43) :args (@t97)) % 15.97/16.39 (step @p45 :rule quant-merge-prenex :args ((= (forall @t9 @t99) @t97))) % 15.97/16.39 (step @p46 :rule alpha_equiv :args (@t100 (@list @t81) @t101)) % 15.97/16.39 (step @p47 :rule refl :args (@t93)) % 15.97/16.39 (step @p48 :rule refl :args (@t94)) % 15.97/16.39 (step @p49 :rule nary_cong :premises (@p48 @p47 @p46) :args (@t102)) % 15.97/16.39 (step @p50 :rule quant-miniscope-or :args ((= @t99 @t102))) % 15.97/16.39 (step @p51 :rule trans :premises (@p50 @p49)) % 15.97/16.39 (step @p52 :rule symm :premises (@p51)) % 15.97/16.39 (step @p53 :rule cong :premises (@p52) :args ((forall @t9 @t104))) % 15.97/16.39 (step @p54 :rule trans :premises (@p53 @p45)) % 15.97/16.39 (step @p55 :rule trans :premises (@p54 @p44)) % 15.97/16.39 (step @p56 :rule aci_norm :args ((= (or (or @t94 @t93) @t103) @t104))) % 15.97/16.39 (step @p57 :rule refl :args (@t103)) % 15.97/16.39 (step @p58 :rule bool-and-de-morgan :args (@t18 @t24 true)) % 15.97/16.39 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((or (not @t25) @t103))) % 15.97/16.39 (step @p60 :rule trans :premises (@p59 @p56)) % 15.97/16.39 (step @p61 :rule bool-impl-elim :args (@t25 @t103)) % 15.97/16.39 (step @p62 :rule trans :premises (@p61 @p60)) % 15.97/16.39 (step @p63 :rule cong :premises (@p62) :args ((forall @t9 (=> @t25 @t103)))) % 15.97/16.39 (step @p64 :rule trans :premises (@p63 @p55)) % 15.97/16.39 (step @p65 :rule aci_norm :args ((= (or @t86 (or @t85 @t84)) @t87))) % 15.97/16.39 (step @p66 :rule bool-and-de-morgan :args (@t30 @t83 true)) % 15.97/16.39 (step @p67 :rule refl :args (@t86)) % 15.97/16.39 (step @p68 :rule nary_cong :premises (@p67 @p66) :args ((or @t86 (not (and @t30 @t83))))) % 15.97/16.39 (step @p69 :rule bool-and-de-morgan :args (@t31 @t30 (and @t83))) % 15.97/16.39 (step @p70 :rule trans :premises (@p69 @p68)) % 15.97/16.39 (step @p71 :rule trans :premises (@p70 @p65)) % 15.97/16.39 (step @p72 :rule cong :premises (@p71) :args (@t106)) % 15.97/16.39 (step @p73 :rule cong :premises (@p72) :args (@t107)) % 15.97/16.39 (step @p74 :rule exists-elim :args ((= (exists @t33 @t105) @t107))) % 15.97/16.39 (step @p75 :rule trans :premises (@p74 @p73)) % 15.97/16.39 (step @p76 :rule eq-symm :args (@t29 @t26)) % 15.97/16.39 (step @p77 :rule refl :args (@t30)) % 15.97/16.39 (step @p78 :rule refl :args (@t31)) % 15.97/16.39 (step @p79 :rule nary_cong :premises (@p78 @p77 @p76) :args (@t32)) % 15.97/16.39 (step @p80 :rule cong :premises (@p79) :args (@t34)) % 15.97/16.39 (step @p81 :rule trans :premises (@p80 @p75)) % 15.97/16.39 (step @p82 :rule refl :args (@t35)) % 15.97/16.39 (step @p83 :rule cong :premises (@p82 @p81) :args (@t36)) % 15.97/16.39 (step @p84 :rule cong :premises (@p83) :args (@t38)) % 15.97/16.39 (step @p85 :rule refl :args (@t39)) % 15.97/16.39 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t40)) % 15.97/16.39 (step @p87 :rule refl :args (@t42)) % 15.97/16.39 (step @p88 :rule cong :premises (@p87 @p86) :args (@t43)) % 15.97/16.39 (step @p89 :rule cong :premises (@p88) :args (@t44)) % 15.97/16.39 (step @p90 :rule refl :args (@t25)) % 15.97/16.39 (step @p91 :rule cong :premises (@p90 @p89) :args (@t45)) % 15.97/16.39 (step @p92 :rule cong :premises (@p91) :args (@t46)) % 15.97/16.39 (step @p93 :rule trans :premises (@p92 @p64)) % 15.97/16.39 (step @p94 :rule eq_resolve :premises (@p22 @p93)) % 15.97/16.39 (step @p95 :rule bool-eq-true :args (@t111)) % 15.97/16.39 (step @p96 :rule eq-symm :args (true @t111)) % 15.97/16.39 (step @p97 :rule trans :premises (@p96 @p95)) % 15.97/16.39 (step @p98 :rule refl :args (@t111)) % 15.97/16.39 (step @p99 :rule eq-refl :args (@t60)) % 15.97/16.39 (step @p100 :rule cong :premises (@p99 @p98) :args (@t112)) % 15.97/16.39 (step @p101 :rule trans :premises (@p100 @p97)) % 15.97/16.39 (step @p102 :rule refl :args (@t114)) % 15.97/16.39 (step @p103 :rule refl :args (@t116)) % 15.97/16.39 (step @p104 :rule nary_cong :premises (@p103 @p102 @p101) :args (@t117)) % 15.97/16.39 (step @p105 :rule refl :args (@t118)) % 15.97/16.39 (step @p106 :rule cong :premises (@p105 @p104) :args ((=> @t118 @t117))) % 15.97/16.39 (assume-push @p267 @t118) % 15.97/16.39 (step @p108 :rule instantiate :premises (@p94) :args ((@list tptp.xI tptp.xJ @t60))) % 15.97/16.39 (step-pop @p268 :rule scope :premises (@p108)) % 15.97/16.39 (step @p109 :rule process_scope :premises (@p268) :args (@t117)) % 15.97/16.39 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 15.97/16.39 (step @p112 :rule implies_elim :premises (@p111)) % 15.97/16.39 (step @p113 :rule chain_m_resolution :premises (@p112 @p94) :args (@t119 @t120 (@list @t118))) % 15.97/16.39 (step @p114 :rule quant-merge-prenex :args ((= (forall @t20 @t133) (forall @t131 @t130)))) % 15.97/16.39 (step @p115 :rule alpha_equiv :args (@t134 (@list @t121) @t101)) % 15.97/16.39 (step @p116 :rule quant-unused-vars :args ((= @t135 @t134))) % 15.97/16.39 (step @p117 :rule trans :premises (@p116 @p115)) % 15.97/16.39 (step @p118 :rule alpha_equiv :args (@t136 (@list @t125) @t101)) % 15.97/16.39 (step @p119 :rule quant-unused-vars :args ((= @t137 @t136))) % 15.97/16.39 (step @p120 :rule trans :premises (@p119 @p118)) % 15.97/16.39 (step @p121 :rule nary_cong :premises (@p120 @p117) :args (@t138)) % 15.97/16.39 (step @p122 :rule quant-miniscope-and :args ((= @t139 @t138))) % 15.97/16.39 (step @p123 :rule trans :premises (@p122 @p121)) % 15.97/16.39 (step @p124 :rule refl :args (@t129)) % 15.97/16.39 (step @p125 :rule nary_cong :premises (@p124 @p123) :args (@t140)) % 15.97/16.39 (step @p126 :rule quant-miniscope-or :args ((= @t133 @t140))) % 15.97/16.39 (step @p127 :rule trans :premises (@p126 @p125)) % 15.97/16.39 (step @p128 :rule symm :premises (@p127)) % 15.97/16.39 (step @p129 :rule cong :premises (@p128) :args ((forall @t20 (or @t129 @t141)))) % 15.97/16.39 (step @p130 :rule trans :premises (@p129 @p114)) % 15.97/16.39 (step @p131 :rule bool-impl-elim :args (@t19 @t141)) % 15.97/16.39 (step @p132 :rule cong :premises (@p131) :args ((forall @t20 (=> @t19 @t141)))) % 15.97/16.39 (step @p133 :rule trans :premises (@p132 @p130)) % 15.97/16.39 (step @p134 :rule bool-impl-elim :args (@t13 @t47)) % 15.97/16.39 (step @p135 :rule cong :premises (@p134) :args (@t48)) % 15.97/16.39 (step @p136 :rule bool-impl-elim :args (@t21 @t49)) % 15.97/16.39 (step @p137 :rule cong :premises (@p136) :args (@t50)) % 15.97/16.39 (step @p138 :rule nary_cong :premises (@p137 @p135) :args (@t51)) % 15.97/16.39 (step @p139 :rule refl :args (@t19)) % 15.97/16.39 (step @p140 :rule cong :premises (@p139 @p138) :args (@t52)) % 15.97/16.39 (step @p141 :rule cong :premises (@p140) :args (@t53)) % 15.97/16.39 (step @p142 :rule trans :premises (@p141 @p133)) % 15.97/16.39 (step @p143 :rule refl :args (@t18)) % 15.97/16.39 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t54)) % 15.97/16.39 (step @p145 :rule refl :args (@t55)) % 15.97/16.39 (step @p146 :rule cong :premises (@p145 @p144) :args (@t56)) % 15.97/16.39 (step @p147 :rule cong :premises (@p146) :args (@t57)) % 15.97/16.39 (step @p148 :rule eq_resolve :premises (@p24 @p147)) % 15.97/16.39 (step @p149 :rule instantiate :premises (@p148) :args ((@list tptp.xJ))) % 15.97/16.39 (step @p150 :rule and_elim :premises (@p25) :args (1)) % 15.97/16.39 (step @p151 :rule cnf_equiv_pos1 :args (@t143)) % 15.97/16.39 (step @p152 :rule reordering :premises (@p151) :args ((or (not @t58) @t142 (not @t143)))) % 15.97/16.39 (step @p153 :rule chain_m_resolution :premises (@p152 @p150 @p149) :args (@t142 @t144 (@list @t58 @t143))) % 15.97/16.39 (step @p154 :rule cnf_and_pos :args (@t142 0)) % 15.97/16.39 (step @p155 :rule reordering :premises (@p154) :args ((or @t113 (not @t142)))) % 15.97/16.39 (step @p156 :rule chain_m_resolution :premises (@p155 @p153) :args (@t113 @t120 (@list @t142))) % 15.97/16.39 (step @p157 :rule instantiate :premises (@p148) :args ((@list tptp.xI))) % 15.97/16.39 (step @p158 :rule and_elim :premises (@p25) :args (0)) % 15.97/16.39 (step @p159 :rule cnf_equiv_pos1 :args (@t146)) % 15.97/16.39 (step @p160 :rule reordering :premises (@p159) :args ((or (not @t59) @t145 (not @t146)))) % 15.97/16.39 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p157) :args (@t145 @t144 (@list @t59 @t146))) % 15.97/16.39 (step @p162 :rule cnf_and_pos :args (@t145 0)) % 15.97/16.39 (step @p163 :rule reordering :premises (@p162) :args ((or @t115 (not @t145)))) % 15.97/16.39 (step @p164 :rule chain_m_resolution :premises (@p163 @p161) :args (@t115 @t120 (@list @t145))) % 15.97/16.39 (step @p165 :rule cnf_or_pos :args (@t119)) % 15.97/16.39 (step @p166 :rule reordering :premises (@p165) :args ((or @t116 @t114 @t111 (not @t119)))) % 15.97/16.39 (step @p167 :rule chain_m_resolution :premises (@p166 @p164 @p156 @p113) :args (@t111 @t147 (@list @t115 @t113 @t119))) % 15.97/16.39 (step @p168 :rule cnf_and_pos :args (@t111 1)) % 15.97/16.39 (step @p169 :rule reordering :premises (@p168) :args ((or @t110 (not @t111)))) % 15.97/16.39 (step @p170 :rule chain_m_resolution :premises (@p169 @p167) :args (@t110 @t120 (@list @t111))) % 15.97/16.39 (step @p171 :rule eq-symm :args (@t148 @t29)) % 15.97/16.39 (step @p172 :rule cong :premises (@p171) :args (@t149)) % 15.97/16.39 (step @p173 :rule refl :args (@t108)) % 15.97/16.39 (step @p174 :rule refl :args (@t109)) % 15.97/16.39 (step @p175 :rule nary_cong :premises (@p174 @p173 @p172) :args (@t150)) % 15.97/16.39 (step @p176 :rule cong :premises (@p175) :args (@t151)) % 15.97/16.39 (step @p177 :rule cong :premises (@p176) :args (@t152)) % 15.97/16.39 (step @p178 :rule refl :args (@t153)) % 15.97/16.39 (step @p179 :rule cong :premises (@p178 @p177) :args ((= @t153 @t152))) % 15.97/16.39 (step @p180 :rule eq-symm :args (@t152 @t153)) % 15.97/16.39 (step @p181 :rule trans :premises (@p180 @p179)) % 15.97/16.39 (step @p182 :rule refl :args (@t110)) % 15.97/16.39 (step @p183 :rule cong :premises (@p182 @p181) :args ((=> @t110 @t154))) % 15.97/16.39 (assume-push @p269 @t110) % 15.97/16.39 (step @p185 :rule instantiate :premises (@p170) :args ((@list @t148))) % 15.97/16.39 (step-pop @p270 :rule scope :premises (@p185)) % 15.97/16.39 (step @p186 :rule process_scope :premises (@p270) :args (@t154)) % 15.97/16.39 (step @p188 :rule eq_resolve :premises (@p186 @p183)) % 15.97/16.39 (step @p189 :rule implies_elim :premises (@p188)) % 15.97/16.39 (step @p190 :rule chain_m_resolution :premises (@p189 @p170) :args (@t157 @t120 @t158)) % 15.97/16.39 (step @p191 :rule eq-symm :args (@t159 @t29)) % 15.97/16.39 (step @p192 :rule cong :premises (@p191) :args (@t160)) % 15.97/16.39 (step @p193 :rule nary_cong :premises (@p174 @p173 @p192) :args (@t161)) % 15.97/16.39 (step @p194 :rule cong :premises (@p193) :args (@t162)) % 15.97/16.39 (step @p195 :rule cong :premises (@p194) :args (@t163)) % 15.97/16.39 (step @p196 :rule refl :args (@t164)) % 15.97/16.39 (step @p197 :rule cong :premises (@p196 @p195) :args ((= @t164 @t163))) % 15.97/16.39 (step @p198 :rule eq-symm :args (@t163 @t164)) % 15.97/16.39 (step @p199 :rule trans :premises (@p198 @p197)) % 15.97/16.39 (step @p200 :rule cong :premises (@p182 @p199) :args ((=> @t110 @t165))) % 15.97/16.39 (assume-push @p271 @t110) % 15.97/16.39 (step @p202 :rule instantiate :premises (@p170) :args ((@list @t159))) % 15.97/16.39 (step-pop @p272 :rule scope :premises (@p202)) % 15.97/16.39 (step @p203 :rule process_scope :premises (@p272) :args (@t165)) % 15.97/16.39 (step @p205 :rule eq_resolve :premises (@p203 @p200)) % 15.97/16.39 (step @p206 :rule implies_elim :premises (@p205)) % 15.97/16.39 (step @p207 :rule chain_m_resolution :premises (@p206 @p170) :args (@t168 @t120 @t158)) % 15.97/16.39 (step @p208 :rule eq-symm :args (@t159 @t71)) % 15.97/16.39 (step @p209 :rule refl :args (@t71)) % 15.97/16.39 (step @p210 :rule and_elim :premises (@p28) :args (2)) % 15.97/16.39 (step @p211 :rule and_elim :premises (@p27) :args (2)) % 15.97/16.39 (step @p212 :rule cong :premises (@p211 @p210) :args (@t72)) % 15.97/16.39 (step @p213 :rule cong :premises (@p212 @p209) :args (@t73)) % 15.97/16.39 (step @p214 :rule trans :premises (@p213 @p208)) % 15.97/16.39 (step @p215 :rule eq_resolve :premises (@p31 @p214)) % 15.97/16.39 (step @p216 :rule and_elim :premises (@p29) :args (1)) % 15.97/16.39 (step @p217 :rule and_elim :premises (@p29) :args (0)) % 15.97/16.39 (step @p218 :rule cnf_or_pos :args (@t173)) % 15.97/16.39 (step @p219 :rule reordering :premises (@p218) :args ((or @t172 @t171 @t170 @t174))) % 15.97/16.39 (step @p220 :rule chain_m_resolution :premises (@p219 @p217 @p216 @p215) :args (@t174 @t147 (@list @t66 @t64 @t169))) % 15.97/16.39 (assume-push @p273 @t166) % 15.97/16.39 (step @p222 :rule instantiate :premises (@p273) :args ((@list @t65 @t63))) % 15.97/16.39 (step-pop @p274 :rule scope :premises (@p222)) % 15.97/16.39 (step @p223 :rule process_scope :premises (@p274) :args (@t173)) % 15.97/16.39 (step @p225 :rule implies_elim :premises (@p223)) % 15.97/16.39 (step @p226 :rule chain_m_resolution :premises (@p225 @p220) :args (@t167 (@list true) (@list @t173))) % 15.97/16.39 (step @p227 :rule bool-double-not-elim :args (@t166)) % 15.97/16.39 (step @p228 :rule refl :args (@t175)) % 15.97/16.39 (step @p229 :rule nary_cong :premises (@p228 @p196 @p227) :args ((or @t175 @t164 (not @t167)))) % 15.97/16.39 (step @p230 :rule cnf_equiv_pos2 :args (@t168)) % 15.97/16.39 (step @p231 :rule eq_resolve :premises (@p230 @p229)) % 15.97/16.39 (step @p232 :rule reordering :premises (@p231) :args ((or @t164 @t166 @t175))) % 15.97/16.39 (step @p233 :rule chain_m_resolution :premises (@p232 @p226 @p207) :args (@t164 @t176 (@list @t166 @t168))) % 15.97/16.39 (step @p234 :rule refl :args (@t60)) % 15.97/16.39 (step @p235 :rule refl :args (tptp.xz)) % 15.97/16.39 (step @p236 :rule cong :premises (@p235 @p211) :args (@t75)) % 15.97/16.39 (step @p237 :rule cong :premises (@p236 @p234) :args (@t77)) % 15.97/16.39 (step @p238 :rule cong :premises (@p212 @p234) :args (@t78)) % 15.97/16.39 (step @p239 :rule nary_cong :premises (@p238 @p237) :args (@t79)) % 15.97/16.39 (step @p240 :rule cong :premises (@p239) :args (@t80)) % 15.97/16.39 (step @p241 :rule eq_resolve :premises (@p33 @p240)) % 15.97/16.39 (step @p242 :rule not_and :premises (@p241)) % 15.97/16.39 (step @p243 :rule chain_m_resolution :premises (@p242 @p233) :args ((not @t153) @t120 (@list @t164))) % 15.97/16.39 (step @p244 :rule bool-double-not-elim :args (@t155)) % 15.97/16.39 (step @p245 :rule refl :args (@t177)) % 15.97/16.39 (step @p246 :rule nary_cong :premises (@p245 @p178 @p244) :args ((or @t177 @t153 (not @t156)))) % 15.97/16.39 (step @p247 :rule cnf_equiv_pos2 :args (@t157)) % 15.97/16.39 (step @p248 :rule eq_resolve :premises (@p247 @p246)) % 15.97/16.39 (step @p249 :rule reordering :premises (@p248) :args ((or @t153 @t155 @t177))) % 15.97/16.39 (step @p250 :rule chain_m_resolution :premises (@p249 @p243 @p190) :args (@t155 @t176 (@list @t153 @t157))) % 15.97/16.39 (step @p251 :rule eq-symm :args (@t148 @t74)) % 15.97/16.39 (step @p252 :rule refl :args (@t74)) % 15.97/16.39 (step @p253 :rule cong :premises (@p236 @p252) :args (@t76)) % 15.97/16.39 (step @p254 :rule trans :premises (@p253 @p251)) % 15.97/16.39 (step @p255 :rule eq_resolve :premises (@p32 @p254)) % 15.97/16.39 (step @p256 :rule and_elim :premises (@p30) :args (1)) % 15.97/16.39 (step @p257 :rule and_elim :premises (@p30) :args (0)) % 15.97/16.39 (step @p258 :rule cnf_or_pos :args (@t182)) % 15.97/16.39 (step @p259 :rule reordering :premises (@p258) :args ((or @t181 @t180 @t179 @t183))) % 15.97/16.39 (step @p260 :rule chain_m_resolution :premises (@p259 @p257 @p256 @p255) :args (@t183 @t147 (@list @t70 @t68 @t178))) % 15.97/16.39 (assume-push @p275 @t155) % 15.97/16.39 (step @p262 :rule instantiate :premises (@p275) :args ((@list @t69 @t67))) % 15.97/16.39 (step-pop @p276 :rule scope :premises (@p262)) % 15.97/16.39 (step @p263 :rule process_scope :premises (@p276) :args (@t182)) % 15.97/16.39 (step @p265 :rule implies_elim :premises (@p263)) % 15.97/16.39 (step @p266 false :rule chain_m_resolution :premises (@p265 @p260 @p250) :args (false @t176 (@list @t182 @t155))) % 15.97/16.39 ) % 15.97/16.39 % SZS output end Proof % 15.97/16.39 % cvc5 exiting %------------------------------------------------------------------------------