%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN062+2 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n013.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 08:42:52 AM UTC 2026 % Result : Theorem 0.43s 0.63s % Output : Proof 0.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.13 % Problem : NUN062+2 : TPTP v9.2.1. Released v7.3.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n013.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 12:38:15 EDT 2026 % 0.19/0.35 % CPUTime : % 0.26/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.43/0.63 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.43/0.63 % SZS status Theorem % 0.43/0.63 % SZS output start Proof % 0.43/0.63 ( % 0.43/0.63 (declare-sort $$unsorted 0) % 0.43/0.63 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.43/0.63 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.43/0.63 (define @t1 () (@var "Y24" $$unsorted)) % 0.43/0.63 (define @t2 () (@var "X19" $$unsorted)) % 0.43/0.63 (define @t3 () (= @t2 @t1)) % 0.43/0.63 (define @t4 () (tptp.r1 @t2)) % 0.43/0.63 (define @t5 () (@list @t1)) % 0.43/0.63 (define @t6 () (@var "Y21" $$unsorted)) % 0.43/0.63 (define @t7 () (@var "X12" $$unsorted)) % 0.43/0.63 (define @t8 () (= @t7 @t6)) % 0.43/0.63 (define @t9 () (@var "X11" $$unsorted)) % 0.43/0.63 (define @t10 () (tptp.r2 @t9 @t7)) % 0.43/0.63 (define @t11 () (@var "Y22" $$unsorted)) % 0.43/0.63 (define @t12 () (@var "X15" $$unsorted)) % 0.43/0.63 (define @t13 () (= @t12 @t11)) % 0.43/0.63 (define @t14 () (@var "X14" $$unsorted)) % 0.43/0.63 (define @t15 () (@var "X13" $$unsorted)) % 0.43/0.63 (define @t16 () (tptp.r3 @t15 @t14 @t12)) % 0.43/0.63 (define @t17 () (@var "Y23" $$unsorted)) % 0.43/0.63 (define @t18 () (@var "X18" $$unsorted)) % 0.43/0.63 (define @t19 () (= @t18 @t17)) % 0.43/0.63 (define @t20 () (@var "X17" $$unsorted)) % 0.43/0.63 (define @t21 () (@var "X16" $$unsorted)) % 0.43/0.63 (define @t22 () (tptp.r4 @t21 @t20 @t18)) % 0.43/0.63 (define @t23 () (@var "Y7" $$unsorted)) % 0.43/0.63 (define @t24 () (@var "X8" $$unsorted)) % 0.43/0.63 (define @t25 () (@var "X1" $$unsorted)) % 0.43/0.63 (define @t26 () (tptp.r3 @t25 @t24 @t23)) % 0.43/0.63 (define @t27 () (@var "Y4" $$unsorted)) % 0.43/0.63 (define @t28 () (tptp.r2 @t23 @t27)) % 0.43/0.63 (define @t29 () (and @t28 @t26)) % 0.43/0.63 (define @t30 () (@list @t23)) % 0.43/0.63 (define @t31 () (exists @t30 @t29)) % 0.43/0.63 (define @t32 () (@var "Y5" $$unsorted)) % 0.43/0.63 (define @t33 () (= @t32 @t27)) % 0.43/0.63 (define @t34 () (@var "Y15" $$unsorted)) % 0.43/0.63 (define @t35 () (tptp.r3 @t25 @t34 @t32)) % 0.43/0.63 (define @t36 () (tptp.r2 @t24 @t34)) % 0.43/0.63 (define @t37 () (and @t36 @t35)) % 0.43/0.63 (define @t38 () (@list @t34)) % 0.43/0.63 (define @t39 () (exists @t38 @t37)) % 0.43/0.63 (define @t40 () (and @t39 @t33)) % 0.43/0.63 (define @t41 () (@list @t32)) % 0.43/0.63 (define @t42 () (exists @t41 @t40)) % 0.43/0.63 (define @t43 () (and @t42 @t31)) % 0.43/0.63 (define @t44 () (@list @t27)) % 0.43/0.63 (define @t45 () (exists @t44 @t43)) % 0.43/0.63 (define @t46 () (forall (@list @t25 @t24) @t45)) % 0.43/0.63 (define @t47 () (@var "Y6" $$unsorted)) % 0.43/0.63 (define @t48 () (@var "X9" $$unsorted)) % 0.43/0.63 (define @t49 () (@var "X2" $$unsorted)) % 0.43/0.63 (define @t50 () (@var "Y2" $$unsorted)) % 0.43/0.63 (define @t51 () (@var "Y3" $$unsorted)) % 0.43/0.63 (define @t52 () (= @t51 @t50)) % 0.43/0.63 (define @t53 () (@var "Y14" $$unsorted)) % 0.43/0.63 (define @t54 () (@list @t51)) % 0.43/0.63 (define @t55 () (@var "X10" $$unsorted)) % 0.43/0.63 (define @t56 () (@var "X3" $$unsorted)) % 0.43/0.63 (define @t57 () (@var "Y12" $$unsorted)) % 0.43/0.63 (define @t58 () (@var "Y13" $$unsorted)) % 0.43/0.63 (define @t59 () (@var "X4" $$unsorted)) % 0.43/0.63 (define @t60 () (@var "Y9" $$unsorted)) % 0.43/0.63 (define @t61 () (@var "Y16" $$unsorted)) % 0.43/0.63 (define @t62 () (@var "Y18" $$unsorted)) % 0.43/0.63 (define @t63 () (@var "Y8" $$unsorted)) % 0.43/0.63 (define @t64 () (@var "Y17" $$unsorted)) % 0.43/0.63 (define @t65 () (@var "X5" $$unsorted)) % 0.43/0.63 (define @t66 () (@var "Y11" $$unsorted)) % 0.43/0.63 (define @t67 () (@var "X6" $$unsorted)) % 0.43/0.63 (define @t68 () (@var "Y1" $$unsorted)) % 0.43/0.63 (define @t69 () (@var "Y19" $$unsorted)) % 0.43/0.63 (define @t70 () (@var "Y10" $$unsorted)) % 0.43/0.63 (define @t71 () (@var "X7" $$unsorted)) % 0.43/0.63 (define @t72 () (not (tptp.r2 @t71 @t70))) % 0.43/0.63 (define @t73 () (@var "Y20" $$unsorted)) % 0.43/0.63 (define @t74 () (not (= @t73 @t70))) % 0.43/0.63 (define @t75 () (not (tptp.r1 @t73))) % 0.43/0.63 (define @t76 () (or @t75 @t74)) % 0.43/0.63 (define @t77 () (@list @t73)) % 0.43/0.63 (define @t78 () (forall @t77 @t76)) % 0.43/0.63 (define @t79 () (or @t78 @t72)) % 0.43/0.63 (define @t80 () (forall (@list @t71 @t70) @t79)) % 0.43/0.63 (define @t81 () (tptp.r3 @t25 @t68 @t51)) % 0.43/0.63 (define @t82 () (and @t81 @t52)) % 0.43/0.63 (define @t83 () (exists @t54 @t82)) % 0.43/0.63 (define @t84 () (not (= @t68 @t27))) % 0.43/0.63 (define @t85 () (not (tptp.r1 @t27))) % 0.43/0.63 (define @t86 () (or @t85 @t84)) % 0.43/0.63 (define @t87 () (forall @t44 @t86)) % 0.43/0.63 (define @t88 () (and @t87 @t83)) % 0.43/0.63 (define @t89 () (@list @t50 @t68)) % 0.43/0.63 (define @t90 () (exists @t89 @t88)) % 0.43/0.63 (define @t91 () (@list @t25)) % 0.43/0.63 (define @t92 () (forall @t91 @t90)) % 0.43/0.63 (define @t93 () (not @t92)) % 0.43/0.63 (define @t94 () (@var "BOUND_VARIABLE_7880" $$unsorted)) % 0.43/0.63 (define @t95 () (not (tptp.r3 @t25 @t24 @t94))) % 0.43/0.63 (define @t96 () (not (tptp.r2 @t94 @t27))) % 0.43/0.63 (define @t97 () (@var "BOUND_VARIABLE_7873" $$unsorted)) % 0.43/0.63 (define @t98 () (not (tptp.r3 @t25 @t97 @t27))) % 0.43/0.63 (define @t99 () (not (tptp.r2 @t24 @t97))) % 0.43/0.63 (define @t100 () (or @t96 @t95)) % 0.43/0.63 (define @t101 () (or @t99 @t98)) % 0.43/0.63 (define @t102 () (or @t101 @t100)) % 0.43/0.63 (define @t103 () (@list @t27 @t97 @t94)) % 0.43/0.63 (define @t104 () (forall @t103 @t102)) % 0.43/0.63 (define @t105 () (forall (@list @t97 @t94) @t102)) % 0.43/0.63 (define @t106 () (forall (@list @t94) @t100)) % 0.43/0.63 (define @t107 () (forall (@list @t97) @t101)) % 0.43/0.63 (define @t108 () (@var "BOUND_VARIABLE_7835" $$unsorted)) % 0.43/0.63 (define @t109 () (@list @t108)) % 0.43/0.63 (define @t110 () (or @t107 @t106)) % 0.43/0.63 (define @t111 () (forall @t30 (or (not @t28) (not @t26)))) % 0.43/0.63 (define @t112 () (not (tptp.r3 @t25 @t108 @t27))) % 0.43/0.63 (define @t113 () (not (tptp.r2 @t24 @t108))) % 0.43/0.63 (define @t114 () (or @t113 @t112)) % 0.43/0.63 (define @t115 () (@list @t108)) % 0.43/0.63 (define @t116 () (forall @t115 @t114)) % 0.43/0.63 (define @t117 () (not @t111)) % 0.43/0.63 (define @t118 () (not @t116)) % 0.43/0.63 (define @t119 () (and @t118 @t117)) % 0.43/0.63 (define @t120 () (forall @t44 (not @t119))) % 0.43/0.63 (define @t121 () (not @t120)) % 0.43/0.63 (define @t122 () (forall @t30 (not @t29))) % 0.43/0.63 (define @t123 () (not @t122)) % 0.43/0.63 (define @t124 () (not (= @t27 @t27))) % 0.43/0.63 (define @t125 () (or @t124 @t113 @t112)) % 0.43/0.63 (define @t126 () (not (tptp.r3 @t25 @t108 @t32))) % 0.43/0.63 (define @t127 () (= @t27 @t32)) % 0.43/0.63 (define @t128 () (not @t127)) % 0.43/0.63 (define @t129 () (or @t128 @t128 @t113 @t126)) % 0.43/0.63 (define @t130 () (or @t128 @t113 @t126)) % 0.43/0.63 (define @t131 () (forall @t41 @t130)) % 0.43/0.63 (define @t132 () (forall @t115 @t131)) % 0.43/0.63 (define @t133 () (forall (@list @t108 @t32) @t130)) % 0.43/0.63 (define @t134 () (@list @t32 @t108)) % 0.43/0.63 (define @t135 () (or @t113 @t126)) % 0.43/0.63 (define @t136 () (or @t135 @t128)) % 0.43/0.63 (define @t137 () (forall @t134 @t136)) % 0.43/0.63 (define @t138 () (forall @t115 @t136)) % 0.43/0.63 (define @t139 () (forall @t115 @t135)) % 0.43/0.63 (define @t140 () (or @t139 @t128)) % 0.43/0.63 (define @t141 () (forall @t38 (or (not @t36) (not @t35)))) % 0.43/0.63 (define @t142 () (not @t141)) % 0.43/0.63 (define @t143 () (and @t142 @t127)) % 0.43/0.63 (define @t144 () (forall @t41 (not @t143))) % 0.43/0.63 (define @t145 () (not @t144)) % 0.43/0.63 (define @t146 () (forall @t38 (not @t37))) % 0.43/0.63 (define @t147 () (not @t146)) % 0.43/0.63 (define @t148 () (@var "BOUND_VARIABLE_7637" $$unsorted)) % 0.43/0.63 (define @t149 () (tptp.r1 @t148)) % 0.43/0.63 (define @t150 () (@quantifiers_skolemize (forall @t5 (or (not (forall (@list @t148) (or (not @t149) (and @t149 (= @t1 @t148))))) (not (tptp.r1 @t1)))) 0)) % 0.43/0.63 (define @t151 () (tptp.r3 @t25 @t68 @t50)) % 0.43/0.63 (define @t152 () (not @t151)) % 0.43/0.63 (define @t153 () (tptp.r1 @t68)) % 0.43/0.63 (define @t154 () (forall @t91 (not (forall @t89 (or @t153 @t152))))) % 0.43/0.63 (define @t155 () (@quantifiers_skolemize @t154 0)) % 0.43/0.63 (define @t156 () (forall @t103 (or (not (tptp.r2 @t150 @t97)) (not (tptp.r3 @t155 @t97 @t27)) @t96 (not (tptp.r3 @t155 @t150 @t94))))) % 0.43/0.63 (define @t157 () (@quantifiers_skolemize @t156 0)) % 0.43/0.63 (define @t158 () (@quantifiers_skolemize @t156 1)) % 0.43/0.63 (define @t159 () (tptp.r3 @t155 @t158 @t157)) % 0.43/0.63 (define @t160 () (@quantifiers_skolemize @t156 2)) % 0.43/0.63 (define @t161 () (not @t159)) % 0.43/0.63 (define @t162 () (tptp.r2 @t150 @t158)) % 0.43/0.63 (define @t163 () (not @t162)) % 0.43/0.63 (define @t164 () (or @t163 @t161 (not (tptp.r2 @t160 @t157)) (not (tptp.r3 @t155 @t150 @t160)))) % 0.43/0.63 (define @t165 () (@list true)) % 0.43/0.63 (define @t166 () (@list @t164)) % 0.43/0.63 (define @t167 () (not @t153)) % 0.43/0.63 (define @t168 () (and @t167 @t151)) % 0.43/0.63 (define @t169 () (forall @t89 (not @t168))) % 0.43/0.63 (define @t170 () (not @t169)) % 0.43/0.63 (define @t171 () (not (= @t50 @t50))) % 0.43/0.63 (define @t172 () (or @t152 @t171)) % 0.43/0.63 (define @t173 () (= @t50 @t51)) % 0.43/0.63 (define @t174 () (not @t173)) % 0.43/0.63 (define @t175 () (not @t81)) % 0.43/0.63 (define @t176 () (or @t174 @t175 @t174)) % 0.43/0.63 (define @t177 () (or @t175 @t174)) % 0.43/0.63 (define @t178 () (and @t81 @t173)) % 0.43/0.63 (define @t179 () (forall @t54 (not @t178))) % 0.43/0.63 (define @t180 () (not @t179)) % 0.43/0.63 (define @t181 () (not (= @t68 @t68))) % 0.43/0.63 (define @t182 () (or @t167 @t181)) % 0.43/0.63 (define @t183 () (not (= @t27 @t68))) % 0.43/0.63 (define @t184 () (or @t183 @t85 @t183)) % 0.43/0.63 (define @t185 () (or @t85 @t183)) % 0.43/0.63 (define @t186 () (forall @t89 (or @t153 (not (tptp.r3 @t155 @t68 @t50))))) % 0.43/0.63 (define @t187 () (not @t154)) % 0.43/0.63 (define @t188 () (not (not @t186))) % 0.43/0.63 (define @t189 () (not (tptp.r1 @t70))) % 0.43/0.63 (define @t190 () (not (= @t70 @t70))) % 0.43/0.63 (define @t191 () (or @t189 @t190)) % 0.43/0.63 (define @t192 () (not (= @t70 @t73))) % 0.43/0.63 (define @t193 () (or @t192 @t75 @t192)) % 0.43/0.63 (define @t194 () (or @t75 @t192)) % 0.43/0.63 (define @t195 () (tptp.r1 @t158)) % 0.43/0.63 (define @t196 () (not @t195)) % 0.43/0.63 (define @t197 () (or @t196 @t163)) % 0.43/0.63 (define @t198 () (or @t195 @t161)) % 0.43/0.63 (assume @p1 (exists @t5 (forall (@list @t2) (or (and (not @t4) (not @t3)) (and @t4 @t3))))) % 0.43/0.63 (assume @p2 (forall (@list @t9) (exists (@list @t6) (forall (@list @t7) (or (and (not @t10) (not @t8)) (and @t10 @t8)))))) % 0.43/0.63 (assume @p3 (forall (@list @t15 @t14) (exists (@list @t11) (forall (@list @t12) (or (and (not @t16) (not @t13)) (and @t16 @t13)))))) % 0.43/0.63 (assume @p4 (forall (@list @t21 @t20) (exists (@list @t17) (forall (@list @t18) (or (and (not @t22) (not @t19)) (and @t22 @t19)))))) % 0.43/0.63 (assume @p5 @t46) % 0.43/0.63 (assume @p6 (forall (@list @t49 @t48) (exists (@list @t50) (and (exists @t54 (and (exists (@list @t53) (and (tptp.r2 @t48 @t53) (tptp.r4 @t49 @t53 @t51))) @t52)) (exists (@list @t47) (and (tptp.r3 @t47 @t49 @t50) (tptp.r4 @t49 @t48 @t47))))))) % 0.43/0.63 (assume @p7 (forall (@list @t56 @t55) (or (forall (@list @t57) (or (forall (@list @t58) (or (not (tptp.r2 @t56 @t58)) (not (= @t58 @t57)))) (not (tptp.r2 @t55 @t57)))) (= @t56 @t55)))) % 0.43/0.63 (assume @p8 (forall (@list @t59) (exists (@list @t60) (and (exists (@list @t61) (and (tptp.r1 @t61) (tptp.r3 @t59 @t61 @t60))) (= @t60 @t59))))) % 0.43/0.63 (assume @p9 (forall (@list @t65) (exists (@list @t63) (and (exists (@list @t64) (and (tptp.r1 @t64) (tptp.r4 @t65 @t64 @t63))) (exists (@list @t62) (and (tptp.r1 @t62) (= @t63 @t62))))))) % 0.43/0.63 (assume @p10 (forall (@list @t67) (or (exists (@list @t69) (and (tptp.r1 @t69) (= @t67 @t69))) (exists (@list @t68 @t66) (and (tptp.r2 @t68 @t66) (= @t67 @t66)))))) % 0.43/0.63 (assume @p11 @t80) % 0.43/0.63 (assume @p12 @t93) % 0.43/0.63 (assume @p13 true) % 0.43/0.63 (step @p14 :rule aci_norm :args ((= @t102 (or @t99 @t98 @t96 @t95)))) % 0.43/0.63 (step @p15 :rule cong :premises (@p14) :args (@t104)) % 0.43/0.63 (step @p16 :rule quant-merge-prenex :args ((= (forall @t44 @t105) @t104))) % 0.43/0.63 (step @p17 :rule alpha_equiv :args (@t106 (@list @t94) (@list @t23))) % 0.43/0.63 (step @p18 :rule alpha_equiv :args (@t107 (@list @t97) @t109)) % 0.43/0.63 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t110)) % 0.43/0.63 (step @p20 :rule quant-miniscope-or :args ((= @t105 @t110))) % 0.43/0.63 (step @p21 :rule trans :premises (@p20 @p19)) % 0.43/0.63 (step @p22 :rule symm :premises (@p21)) % 0.43/0.63 (step @p23 :rule cong :premises (@p22) :args ((forall @t44 (or @t116 @t111)))) % 0.43/0.63 (step @p24 :rule trans :premises (@p23 @p16)) % 0.43/0.63 (step @p25 :rule trans :premises (@p24 @p15)) % 0.43/0.63 (step @p26 :rule bool-double-not-elim :args (@t111)) % 0.43/0.63 (step @p27 :rule bool-double-not-elim :args (@t116)) % 0.43/0.63 (step @p28 :rule nary_cong :premises (@p27 @p26) :args ((or (not @t118) (not @t117)))) % 0.43/0.63 (step @p29 :rule bool-and-de-morgan :args (@t118 @t117 true)) % 0.43/0.63 (step @p30 :rule trans :premises (@p29 @p28)) % 0.43/0.63 (step @p31 :rule cong :premises (@p30) :args (@t120)) % 0.43/0.63 (step @p32 :rule trans :premises (@p31 @p25)) % 0.43/0.63 (step @p33 :rule cong :premises (@p32) :args (@t121)) % 0.43/0.63 (step @p34 :rule exists-elim :args ((= (exists @t44 @t119) @t121))) % 0.43/0.63 (step @p35 :rule trans :premises (@p34 @p33)) % 0.43/0.63 (step @p36 :rule bool-and-de-morgan :args (@t28 @t26 true)) % 0.43/0.63 (step @p37 :rule cong :premises (@p36) :args (@t122)) % 0.43/0.63 (step @p38 :rule cong :premises (@p37) :args (@t123)) % 0.43/0.63 (step @p39 :rule exists-elim :args ((= @t31 @t123))) % 0.43/0.63 (step @p40 :rule trans :premises (@p39 @p38)) % 0.43/0.63 (step @p41 :rule aci_norm :args ((= (or false @t113 @t112) @t114))) % 0.43/0.63 (step @p42 :rule refl :args (@t112)) % 0.43/0.63 (step @p43 :rule refl :args (@t113)) % 0.43/0.63 (step @p44 :rule evaluate :args ((not true))) % 0.43/0.63 (step @p45 :rule eq-refl :args (@t27)) % 0.43/0.63 (step @p46 :rule cong :premises (@p45) :args (@t124)) % 0.43/0.63 (step @p47 :rule trans :premises (@p46 @p44)) % 0.43/0.63 (step @p48 :rule nary_cong :premises (@p47 @p43 @p42) :args (@t125)) % 0.43/0.63 (step @p49 :rule trans :premises (@p48 @p41)) % 0.43/0.63 (step @p50 :rule cong :premises (@p49) :args ((forall @t115 @t125))) % 0.43/0.63 (step @p51 :rule quant-var-elim-eq :args ((= (forall @t41 (or (not @t33) @t128 @t113 @t126)) @t125))) % 0.43/0.63 (step @p52 :rule refl :args (@t126)) % 0.43/0.63 (step @p53 :rule refl :args (@t113)) % 0.43/0.63 (step @p54 :rule refl :args (@t128)) % 0.43/0.63 (step @p55 :rule eq-symm :args (@t27 @t32)) % 0.43/0.63 (step @p56 :rule cong :premises (@p55) :args (@t128)) % 0.43/0.63 (step @p57 :rule nary_cong :premises (@p56 @p54 @p53 @p52) :args (@t129)) % 0.43/0.63 (step @p58 :rule aci_norm :args ((= @t130 @t129))) % 0.43/0.63 (step @p59 :rule trans :premises (@p58 @p57)) % 0.43/0.63 (step @p60 :rule cong :premises (@p59) :args (@t131)) % 0.43/0.63 (step @p61 :rule trans :premises (@p60 @p51)) % 0.43/0.63 (step @p62 :rule cong :premises (@p61) :args (@t132)) % 0.43/0.63 (step @p63 :rule quant-merge-prenex :args ((= @t132 @t133))) % 0.43/0.63 (step @p64 :rule symm :premises (@p63)) % 0.43/0.63 (step @p65 :rule quant_var_reordering :args ((= (forall @t134 @t130) @t133))) % 0.43/0.63 (step @p66 :rule trans :premises (@p65 @p64 @p62)) % 0.43/0.63 (step @p67 :rule trans :premises (@p66 @p50)) % 0.43/0.63 (step @p68 :rule aci_norm :args ((= @t136 @t130))) % 0.43/0.63 (step @p69 :rule cong :premises (@p68) :args (@t137)) % 0.43/0.63 (step @p70 :rule trans :premises (@p69 @p67)) % 0.43/0.63 (step @p71 :rule quant-merge-prenex :args ((= (forall @t41 @t138) @t137))) % 0.43/0.63 (step @p72 :rule alpha_equiv :args (@t139 @t109 (@list @t34))) % 0.43/0.63 (step @p73 :rule nary_cong :premises (@p72 @p54) :args (@t140)) % 0.43/0.63 (step @p74 :rule quant-miniscope-or :args ((= @t138 @t140))) % 0.43/0.63 (step @p75 :rule trans :premises (@p74 @p73)) % 0.43/0.63 (step @p76 :rule symm :premises (@p75)) % 0.43/0.63 (step @p77 :rule cong :premises (@p76) :args ((forall @t41 (or @t141 @t128)))) % 0.43/0.63 (step @p78 :rule trans :premises (@p77 @p71)) % 0.43/0.63 (step @p79 :rule trans :premises (@p78 @p70)) % 0.43/0.63 (step @p80 :rule bool-double-not-elim :args (@t141)) % 0.43/0.63 (step @p81 :rule nary_cong :premises (@p80 @p54) :args ((or (not @t142) @t128))) % 0.43/0.63 (step @p82 :rule bool-and-de-morgan :args (@t142 @t127 true)) % 0.43/0.63 (step @p83 :rule trans :premises (@p82 @p81)) % 0.43/0.63 (step @p84 :rule cong :premises (@p83) :args (@t144)) % 0.43/0.63 (step @p85 :rule trans :premises (@p84 @p79)) % 0.43/0.63 (step @p86 :rule cong :premises (@p85) :args (@t145)) % 0.43/0.63 (step @p87 :rule exists-elim :args ((= 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0.43/0.63 (step @p103 :rule instantiate :premises (@p102) :args ((@list @t155 @t150))) % 0.43/0.63 (step @p104 :rule skolemize :premises (@p103)) % 0.43/0.63 (step @p105 :rule bool-double-not-elim :args (@t159)) % 0.43/0.63 (step @p106 :rule refl :args (@t164)) % 0.43/0.63 (step @p107 :rule nary_cong :premises (@p106 @p105) :args ((or @t164 (not @t161)))) % 0.43/0.63 (step @p108 :rule cnf_or_neg :args (@t164 1)) % 0.43/0.63 (step @p109 :rule eq_resolve :premises (@p108 @p107)) % 0.43/0.63 (step @p110 :rule reordering :premises (@p109) :args ((or @t159 @t164))) % 0.43/0.63 (step @p111 :rule chain_m_resolution :premises (@p110 @p104) :args (@t159 @t165 @t166)) % 0.43/0.63 (step @p112 :rule refl :args (@t152)) % 0.43/0.63 (step @p113 :rule bool-double-not-elim :args (@t153)) % 0.43/0.63 (step @p114 :rule nary_cong :premises (@p113 @p112) :args ((or (not @t167) @t152))) % 0.43/0.63 (step @p115 :rule bool-and-de-morgan :args (@t167 @t151 true)) % 0.43/0.63 (step @p116 :rule trans :premises 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:args (@t175)) % 0.43/0.63 (step @p132 :rule eq-symm :args (@t50 @t51)) % 0.43/0.63 (step @p133 :rule cong :premises (@p132) :args (@t174)) % 0.43/0.63 (step @p134 :rule nary_cong :premises (@p133 @p131 @p130) :args (@t176)) % 0.43/0.63 (step @p135 :rule aci_norm :args ((= @t177 @t176))) % 0.43/0.63 (step @p136 :rule trans :premises (@p135 @p134)) % 0.43/0.63 (step @p137 :rule cong :premises (@p136) :args ((forall @t54 @t177))) % 0.43/0.63 (step @p138 :rule trans :premises (@p137 @p129)) % 0.43/0.63 (step @p139 :rule trans :premises (@p138 @p128)) % 0.43/0.63 (step @p140 :rule bool-and-de-morgan :args (@t81 @t173 true)) % 0.43/0.63 (step @p141 :rule cong :premises (@p140) :args (@t179)) % 0.43/0.63 (step @p142 :rule trans :premises (@p141 @p139)) % 0.43/0.63 (step @p143 :rule cong :premises (@p142) :args (@t180)) % 0.43/0.63 (step @p144 :rule trans :premises (@p143 @p121)) % 0.43/0.63 (step @p145 :rule exists-elim :args ((= (exists @t54 @t178) @t180))) % 0.43/0.63 (step @p146 :rule trans :premises (@p145 @p144)) % 0.43/0.63 (step @p147 :rule eq-symm :args (@t51 @t50)) % 0.43/0.63 (step @p148 :rule refl :args (@t81)) % 0.43/0.63 (step @p149 :rule nary_cong :premises (@p148 @p147) :args (@t82)) % 0.43/0.63 (step @p150 :rule cong :premises (@p149) :args (@t83)) % 0.43/0.63 (step @p151 :rule trans :premises (@p150 @p146)) % 0.43/0.63 (step @p152 :rule aci_norm :args ((= (or @t167 false) @t167))) % 0.43/0.63 (step @p153 :rule eq-refl :args (@t68)) % 0.43/0.63 (step @p154 :rule cong :premises (@p153) :args (@t181)) % 0.43/0.63 (step @p155 :rule trans :premises (@p154 @p44)) % 0.43/0.63 (step @p156 :rule refl :args (@t167)) % 0.43/0.63 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t182)) % 0.43/0.63 (step @p158 :rule trans :premises (@p157 @p152)) % 0.43/0.63 (step @p159 :rule quant-var-elim-eq :args ((= (forall @t44 @t184) @t182))) % 0.43/0.63 (step @p160 :rule aci_norm :args ((= @t185 @t184))) % 0.43/0.63 (step @p161 :rule cong :premises (@p160) :args 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refl :args (@t72)) % 0.43/0.63 (step @p192 :rule aci_norm :args ((= (or @t189 false) @t189))) % 0.43/0.63 (step @p193 :rule eq-refl :args (@t70)) % 0.43/0.63 (step @p194 :rule cong :premises (@p193) :args (@t190)) % 0.43/0.63 (step @p195 :rule trans :premises (@p194 @p44)) % 0.43/0.63 (step @p196 :rule refl :args (@t189)) % 0.43/0.63 (step @p197 :rule nary_cong :premises (@p196 @p195) :args (@t191)) % 0.43/0.63 (step @p198 :rule trans :premises (@p197 @p192)) % 0.43/0.63 (step @p199 :rule quant-var-elim-eq :args ((= (forall @t77 (or @t74 @t75 @t192)) @t191))) % 0.43/0.63 (step @p200 :rule refl :args (@t192)) % 0.43/0.63 (step @p201 :rule refl :args (@t75)) % 0.43/0.63 (step @p202 :rule eq-symm :args (@t70 @t73)) % 0.43/0.63 (step @p203 :rule cong :premises (@p202) :args (@t192)) % 0.43/0.63 (step @p204 :rule nary_cong :premises (@p203 @p201 @p200) :args (@t193)) % 0.43/0.63 (step @p205 :rule aci_norm :args ((= @t194 @t193))) % 0.43/0.63 (step @p206 :rule trans :premises (@p205 @p204)) % 0.43/0.63 (step @p207 :rule cong :premises (@p206) :args ((forall @t77 @t194))) % 0.43/0.64 (step @p208 :rule trans :premises (@p207 @p199)) % 0.43/0.64 (step @p209 :rule trans :premises (@p208 @p198)) % 0.43/0.64 (step @p210 :rule eq-symm :args (@t73 @t70)) % 0.43/0.64 (step @p211 :rule cong :premises (@p210) :args (@t74)) % 0.43/0.64 (step @p212 :rule refl :args (@t75)) % 0.43/0.64 (step @p213 :rule nary_cong :premises (@p212 @p211) :args (@t76)) % 0.43/0.64 (step @p214 :rule cong :premises (@p213) :args (@t78)) % 0.43/0.64 (step @p215 :rule trans :premises (@p214 @p209)) % 0.43/0.64 (step @p216 :rule nary_cong :premises (@p215 @p191) :args (@t79)) % 0.43/0.64 (step @p217 :rule cong :premises (@p216) :args (@t80)) % 0.43/0.64 (step @p218 :rule eq_resolve :premises (@p11 @p217)) % 0.43/0.64 (step @p219 :rule instantiate :premises (@p218) :args ((@list @t150 @t158))) % 0.43/0.64 (step @p220 :rule bool-double-not-elim :args (@t162)) % 0.43/0.64 (step @p221 :rule nary_cong :premises (@p106 @p220) :args ((or @t164 (not @t163)))) % 0.43/0.64 (step @p222 :rule cnf_or_neg :args (@t164 0)) % 0.43/0.64 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.43/0.64 (step @p224 :rule reordering :premises (@p223) :args ((or @t162 @t164))) % 0.43/0.64 (step @p225 :rule chain_m_resolution :premises (@p224 @p104) :args (@t162 @t165 @t166)) % 0.43/0.64 (step @p226 :rule cnf_or_pos :args (@t197)) % 0.43/0.64 (step @p227 :rule reordering :premises (@p226) :args ((or @t163 @t196 (not @t197)))) % 0.43/0.64 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p219) :args (@t196 (@list false false) (@list @t162 @t197))) % 0.43/0.64 (step @p229 :rule cnf_or_pos :args (@t198)) % 0.43/0.64 (step @p230 :rule reordering :premises (@p229) :args ((or @t161 @t195 (not @t198)))) % 0.43/0.64 (step @p231 false :rule chain_m_resolution :premises (@p230 @p228 @p190 @p111) :args (false (@list true false false) (@list @t195 @t198 @t159))) % 0.43/0.64 ) % 0.43/0.64 % SZS output end Proof % 0.43/0.64 % cvc5 exiting %------------------------------------------------------------------------------