%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN069+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 : n017.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 08:42:53 AM UTC 2026 % Result : Theorem 0.36s 0.58s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN069+2 : TPTP v9.2.1. Released v7.3.0. % 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 : n017.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 12:37:16 EDT 2026 % 0.15/0.34 % CPUTime : % 0.29/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.58 % SZS status Theorem % 0.36/0.58 % SZS output start Proof % 0.36/0.58 ( % 0.36/0.58 (declare-sort $$unsorted 0) % 0.36/0.58 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.36/0.58 (define @t1 () (@var "Y24" $$unsorted)) % 0.36/0.58 (define @t2 () (@var "X19" $$unsorted)) % 0.36/0.58 (define @t3 () (= @t2 @t1)) % 0.36/0.58 (define @t4 () (tptp.r1 @t2)) % 0.36/0.58 (define @t5 () (and @t4 @t3)) % 0.36/0.58 (define @t6 () (not @t3)) % 0.36/0.58 (define @t7 () (not @t4)) % 0.36/0.58 (define @t8 () (and @t7 @t6)) % 0.36/0.58 (define @t9 () (or @t8 @t5)) % 0.36/0.58 (define @t10 () (@list @t2)) % 0.36/0.58 (define @t11 () (forall @t10 @t9)) % 0.36/0.58 (define @t12 () (@list @t1)) % 0.36/0.58 (define @t13 () (exists @t12 @t11)) % 0.36/0.58 (define @t14 () (@var "Y21" $$unsorted)) % 0.36/0.58 (define @t15 () (@var "X12" $$unsorted)) % 0.36/0.58 (define @t16 () (= @t15 @t14)) % 0.36/0.58 (define @t17 () (@var "X11" $$unsorted)) % 0.36/0.58 (define @t18 () (tptp.r2 @t17 @t15)) % 0.36/0.58 (define @t19 () (and @t18 @t16)) % 0.36/0.58 (define @t20 () (not @t16)) % 0.36/0.58 (define @t21 () (not @t18)) % 0.36/0.58 (define @t22 () (and @t21 @t20)) % 0.36/0.58 (define @t23 () (or @t22 @t19)) % 0.36/0.58 (define @t24 () (@list @t15)) % 0.36/0.58 (define @t25 () (forall @t24 @t23)) % 0.36/0.58 (define @t26 () (@list @t14)) % 0.36/0.58 (define @t27 () (exists @t26 @t25)) % 0.36/0.58 (define @t28 () (forall (@list @t17) @t27)) % 0.36/0.58 (define @t29 () (@var "Y22" $$unsorted)) % 0.36/0.58 (define @t30 () (@var "X15" $$unsorted)) % 0.36/0.58 (define @t31 () (= @t30 @t29)) % 0.36/0.58 (define @t32 () (@var "X14" $$unsorted)) % 0.36/0.58 (define @t33 () (@var "X13" $$unsorted)) % 0.36/0.58 (define @t34 () (tptp.r3 @t33 @t32 @t30)) % 0.36/0.58 (define @t35 () (@var "Y23" $$unsorted)) % 0.36/0.58 (define @t36 () (@var "X18" $$unsorted)) % 0.36/0.58 (define @t37 () (= @t36 @t35)) % 0.36/0.58 (define @t38 () (@var "X17" $$unsorted)) % 0.36/0.58 (define @t39 () (@var "X16" $$unsorted)) % 0.36/0.58 (define @t40 () (tptp.r4 @t39 @t38 @t36)) % 0.36/0.58 (define @t41 () (@var "Y7" $$unsorted)) % 0.36/0.58 (define @t42 () (@var "X8" $$unsorted)) % 0.36/0.58 (define @t43 () (@var "X1" $$unsorted)) % 0.36/0.58 (define @t44 () (@var "Y4" $$unsorted)) % 0.36/0.58 (define @t45 () (@var "Y5" $$unsorted)) % 0.36/0.58 (define @t46 () (@var "Y15" $$unsorted)) % 0.36/0.58 (define @t47 () (@var "Y6" $$unsorted)) % 0.36/0.58 (define @t48 () (@var "X9" $$unsorted)) % 0.36/0.58 (define @t49 () (@var "X2" $$unsorted)) % 0.36/0.58 (define @t50 () (@var "Y2" $$unsorted)) % 0.36/0.58 (define @t51 () (@var "Y3" $$unsorted)) % 0.36/0.58 (define @t52 () (@var "Y14" $$unsorted)) % 0.36/0.58 (define @t53 () (@list @t50)) % 0.36/0.58 (define @t54 () (@var "X10" $$unsorted)) % 0.36/0.58 (define @t55 () (@var "X3" $$unsorted)) % 0.36/0.58 (define @t56 () (@var "Y12" $$unsorted)) % 0.36/0.58 (define @t57 () (@var "Y13" $$unsorted)) % 0.36/0.58 (define @t58 () (@var "X4" $$unsorted)) % 0.36/0.58 (define @t59 () (@var "Y9" $$unsorted)) % 0.36/0.58 (define @t60 () (@var "Y16" $$unsorted)) % 0.36/0.58 (define @t61 () (@var "Y18" $$unsorted)) % 0.36/0.58 (define @t62 () (@var "Y8" $$unsorted)) % 0.36/0.58 (define @t63 () (@var "Y17" $$unsorted)) % 0.36/0.58 (define @t64 () (@var "X5" $$unsorted)) % 0.36/0.58 (define @t65 () (@var "Y11" $$unsorted)) % 0.36/0.58 (define @t66 () (@var "X6" $$unsorted)) % 0.36/0.58 (define @t67 () (@var "Y1" $$unsorted)) % 0.36/0.58 (define @t68 () (@var "Y19" $$unsorted)) % 0.36/0.58 (define @t69 () (@var "Y10" $$unsorted)) % 0.36/0.58 (define @t70 () (@var "X7" $$unsorted)) % 0.36/0.58 (define @t71 () (@var "Y20" $$unsorted)) % 0.36/0.58 (define @t72 () (tptp.r2 @t50 @t67)) % 0.36/0.58 (define @t73 () (tptp.r1 @t50)) % 0.36/0.58 (define @t74 () (and @t73 @t72)) % 0.36/0.58 (define @t75 () (exists @t53 @t74)) % 0.36/0.58 (define @t76 () (and (= @t67 @t67) @t75)) % 0.36/0.58 (define @t77 () (@list @t67)) % 0.36/0.58 (define @t78 () (exists @t77 @t76)) % 0.36/0.58 (define @t79 () (not @t78)) % 0.36/0.58 (define @t80 () (or (not @t73) (not @t72))) % 0.36/0.58 (define @t81 () (forall (@list @t67 @t50) @t80)) % 0.36/0.58 (define @t82 () (forall @t53 @t80)) % 0.36/0.58 (define @t83 () (not @t82)) % 0.36/0.58 (define @t84 () (forall @t77 (not @t83))) % 0.36/0.58 (define @t85 () (not @t84)) % 0.36/0.58 (define @t86 () (forall @t53 (not @t74))) % 0.36/0.58 (define @t87 () (not @t86)) % 0.36/0.58 (define @t88 () (@var "BOUND_VARIABLE_7678" $$unsorted)) % 0.36/0.58 (define @t89 () (= @t14 @t88)) % 0.36/0.58 (define @t90 () (tptp.r2 @t17 @t88)) % 0.36/0.58 (define @t91 () (@list @t88)) % 0.36/0.58 (define @t92 () (forall @t91 (or (not @t90) (and @t90 @t89)))) % 0.36/0.58 (define @t93 () (tptp.r2 @t17 @t14)) % 0.36/0.58 (define @t94 () (and @t92 @t93)) % 0.36/0.58 (define @t95 () (forall @t26 (not @t94))) % 0.36/0.58 (define @t96 () (not @t95)) % 0.36/0.58 (define @t97 () (= @t14 @t14)) % 0.36/0.58 (define @t98 () (and @t93 @t97)) % 0.36/0.58 (define @t99 () (not @t97)) % 0.36/0.58 (define @t100 () (or @t99 @t98)) % 0.36/0.58 (define @t101 () (@var "BOUND_VARIABLE_7687" $$unsorted)) % 0.36/0.58 (define @t102 () (= @t14 @t101)) % 0.36/0.58 (define @t103 () (and (tptp.r2 @t17 @t101) @t102)) % 0.36/0.58 (define @t104 () (not @t102)) % 0.36/0.58 (define @t105 () (@list @t101)) % 0.36/0.58 (define @t106 () (or @t104 @t104 @t103)) % 0.36/0.58 (define @t107 () (or @t104 @t103)) % 0.36/0.58 (define @t108 () (forall @t105 @t107)) % 0.36/0.58 (define @t109 () (= @t14 @t15)) % 0.36/0.58 (define @t110 () (and @t18 @t109)) % 0.36/0.58 (define @t111 () (not @t109)) % 0.36/0.58 (define @t112 () (or @t111 @t110)) % 0.36/0.58 (define @t113 () (forall @t24 @t112)) % 0.36/0.58 (define @t114 () (@list @t15)) % 0.36/0.58 (define @t115 () (or @t21 @t110)) % 0.36/0.58 (define @t116 () (forall @t24 @t115)) % 0.36/0.58 (define @t117 () (and @t116 @t113)) % 0.36/0.58 (define @t118 () (tptp.r1 @t1)) % 0.36/0.58 (define @t119 () (@var "BOUND_VARIABLE_7631" $$unsorted)) % 0.36/0.58 (define @t120 () (tptp.r1 @t119)) % 0.36/0.58 (define @t121 () (not @t120)) % 0.36/0.58 (define @t122 () (@list @t119)) % 0.36/0.58 (define @t123 () (forall @t122 (or @t121 (and @t120 (= @t1 @t119))))) % 0.36/0.58 (define @t124 () (forall @t12 (or (not @t123) (not @t118)))) % 0.36/0.58 (define @t125 () (@quantifiers_skolemize @t124 0)) % 0.36/0.58 (define @t126 () (tptp.r2 @t125 @t88)) % 0.36/0.58 (define @t127 () (not @t126)) % 0.36/0.58 (define @t128 () (forall @t26 (or (not (forall @t91 (or @t127 (and @t126 @t89)))) (not (tptp.r2 @t125 @t14))))) % 0.36/0.58 (define @t129 () (@quantifiers_skolemize @t128 0)) % 0.36/0.58 (define @t130 () (tptp.r2 @t125 @t129)) % 0.36/0.58 (define @t131 () (not @t130)) % 0.36/0.58 (define @t132 () (or (not (forall @t91 (or @t127 (and @t126 (= @t88 @t129))))) @t131)) % 0.36/0.58 (define @t133 () (not @t132)) % 0.36/0.58 (define @t134 () (not @t128)) % 0.36/0.58 (define @t135 () (and @t126 (= @t129 @t88))) % 0.36/0.58 (define @t136 () (or @t127 @t135)) % 0.36/0.58 (define @t137 () (forall @t91 @t136)) % 0.36/0.58 (define @t138 () (not @t137)) % 0.36/0.58 (define @t139 () (or @t138 @t131)) % 0.36/0.58 (define @t140 () (not @t139)) % 0.36/0.58 (define @t141 () (@list true)) % 0.36/0.58 (define @t142 () (and @t123 @t118)) % 0.36/0.58 (define @t143 () (forall @t12 (not @t142))) % 0.36/0.58 (define @t144 () (not @t143)) % 0.36/0.58 (define @t145 () (= @t1 @t1)) % 0.36/0.58 (define @t146 () (and @t118 @t145)) % 0.36/0.58 (define @t147 () (not @t145)) % 0.36/0.58 (define @t148 () (or @t147 @t146)) % 0.36/0.58 (define @t149 () (@var "BOUND_VARIABLE_7640" $$unsorted)) % 0.36/0.58 (define @t150 () (= @t1 @t149)) % 0.36/0.58 (define @t151 () (and (tptp.r1 @t149) @t150)) % 0.36/0.58 (define @t152 () (not @t150)) % 0.36/0.58 (define @t153 () (@list @t149)) % 0.36/0.58 (define @t154 () (or @t152 @t152 @t151)) % 0.36/0.58 (define @t155 () (or @t152 @t151)) % 0.36/0.58 (define @t156 () (forall @t153 @t155)) % 0.36/0.58 (define @t157 () (= @t1 @t2)) % 0.36/0.58 (define @t158 () (and @t4 @t157)) % 0.36/0.58 (define @t159 () (not @t157)) % 0.36/0.58 (define @t160 () (or @t159 @t158)) % 0.36/0.58 (define @t161 () (forall @t10 @t160)) % 0.36/0.58 (define @t162 () (@list @t2)) % 0.36/0.58 (define @t163 () (or @t7 @t158)) % 0.36/0.58 (define @t164 () (forall @t10 @t163)) % 0.36/0.58 (define @t165 () (and @t164 @t161)) % 0.36/0.58 (define @t166 () (tptp.r1 @t125)) % 0.36/0.58 (define @t167 () (not @t166)) % 0.36/0.58 (define @t168 () (or (not (forall @t122 (or @t121 (and @t120 (= @t119 @t125))))) @t167)) % 0.36/0.58 (define @t169 () (not @t168)) % 0.36/0.58 (define @t170 () (not @t124)) % 0.36/0.58 (define @t171 () (and @t120 (= @t125 @t119))) % 0.36/0.58 (define @t172 () (or @t121 @t171)) % 0.36/0.58 (define @t173 () (forall @t122 @t172)) % 0.36/0.58 (define @t174 () (not @t173)) % 0.36/0.58 (define @t175 () (or @t174 @t167)) % 0.36/0.58 (define @t176 () (not @t175)) % 0.36/0.58 (define @t177 () (or @t167 @t131)) % 0.36/0.58 (define @t178 () (not @t177)) % 0.36/0.58 (assume @p1 @t13) % 0.36/0.58 (assume @p2 @t28) % 0.36/0.58 (assume @p3 (forall (@list @t33 @t32) (exists (@list @t29) (forall (@list @t30) (or (and (not @t34) (not @t31)) (and @t34 @t31)))))) % 0.36/0.58 (assume @p4 (forall (@list @t39 @t38) (exists (@list @t35) (forall (@list @t36) (or (and (not @t40) (not @t37)) (and @t40 @t37)))))) % 0.36/0.58 (assume @p5 (forall (@list @t43 @t42) (exists (@list @t44) (and (exists (@list @t45) (and (exists (@list @t46) (and (tptp.r2 @t42 @t46) (tptp.r3 @t43 @t46 @t45))) (= @t45 @t44))) (exists (@list @t41) (and (tptp.r2 @t41 @t44) (tptp.r3 @t43 @t42 @t41))))))) % 0.36/0.58 (assume @p6 (forall (@list @t49 @t48) (exists @t53 (and (exists (@list @t51) (and (exists (@list @t52) (and (tptp.r2 @t48 @t52) (tptp.r4 @t49 @t52 @t51))) (= @t51 @t50))) (exists (@list @t47) (and (tptp.r3 @t47 @t49 @t50) (tptp.r4 @t49 @t48 @t47))))))) % 0.36/0.58 (assume @p7 (forall (@list @t55 @t54) (or (forall (@list @t56) (or (forall (@list @t57) (or (not (tptp.r2 @t55 @t57)) (not (= @t57 @t56)))) (not (tptp.r2 @t54 @t56)))) (= @t55 @t54)))) % 0.36/0.58 (assume @p8 (forall (@list @t58) (exists (@list @t59) (and (exists (@list @t60) (and (tptp.r1 @t60) (tptp.r3 @t58 @t60 @t59))) (= @t59 @t58))))) % 0.36/0.58 (assume @p9 (forall (@list @t64) (exists (@list @t62) (and (exists (@list @t63) (and (tptp.r1 @t63) (tptp.r4 @t64 @t63 @t62))) (exists (@list @t61) (and (tptp.r1 @t61) (= @t62 @t61))))))) % 0.36/0.58 (assume @p10 (forall (@list @t66) (or (exists (@list @t68) (and (tptp.r1 @t68) (= @t66 @t68))) (exists (@list @t67 @t65) (and (tptp.r2 @t67 @t65) (= @t66 @t65)))))) % 0.36/0.58 (assume @p11 (forall (@list @t70 @t69) (or (forall (@list @t71) (or (not (tptp.r1 @t71)) (not (= @t71 @t69)))) (not (tptp.r2 @t70 @t69))))) % 0.36/0.58 (assume @p12 @t79) % 0.36/0.58 (assume @p13 true) % 0.36/0.58 (step @p14 :rule bool-double-not-elim :args (@t81)) % 0.36/0.58 (step @p15 :rule quant-merge-prenex :args ((= (forall @t77 @t82) @t81))) % 0.36/0.58 (step @p16 :rule bool-double-not-elim :args (@t82)) % 0.36/0.58 (step @p17 :rule cong :premises (@p16) :args (@t84)) % 0.36/0.58 (step @p18 :rule trans :premises (@p17 @p15)) % 0.36/0.58 (step @p19 :rule cong :premises (@p18) :args (@t85)) % 0.36/0.58 (step @p20 :rule exists-elim :args ((= (exists @t77 @t83) @t85))) % 0.36/0.58 (step @p21 :rule trans :premises (@p20 @p19)) % 0.36/0.58 (step @p22 :rule aci_norm :args ((= (and true @t83) @t83))) % 0.36/0.58 (step @p23 :rule bool-and-de-morgan :args (@t73 @t72 true)) % 0.36/0.58 (step @p24 :rule cong :premises (@p23) :args (@t86)) % 0.36/0.58 (step @p25 :rule cong :premises (@p24) :args (@t87)) % 0.36/0.58 (step @p26 :rule exists-elim :args ((= @t75 @t87))) % 0.36/0.58 (step @p27 :rule trans :premises (@p26 @p25)) % 0.36/0.58 (step @p28 :rule eq-refl :args (@t67)) % 0.36/0.58 (step @p29 :rule nary_cong :premises (@p28 @p27) :args (@t76)) % 0.36/0.58 (step @p30 :rule trans :premises (@p29 @p22)) % 0.36/0.58 (step @p31 :rule cong :premises (@p30) :args (@t78)) % 0.36/0.58 (step @p32 :rule trans :premises (@p31 @p21)) % 0.36/0.58 (step @p33 :rule cong :premises (@p32) :args (@t79)) % 0.36/0.58 (step @p34 :rule trans :premises (@p33 @p14)) % 0.36/0.58 (step @p35 :rule eq_resolve :premises (@p12 @p34)) % 0.36/0.58 (step @p36 :rule bool-and-de-morgan :args (@t92 @t93 true)) % 0.36/0.58 (step @p37 :rule cong :premises (@p36) :args (@t95)) % 0.36/0.58 (step @p38 :rule cong :premises (@p37) :args (@t96)) % 0.36/0.58 (step @p39 :rule exists-elim :args ((= (exists @t26 @t94) @t96))) % 0.36/0.58 (step @p40 :rule trans :premises (@p39 @p38)) % 0.36/0.58 (step @p41 :rule aci_norm :args ((= (or false @t93) @t93))) % 0.36/0.58 (step @p42 :rule aci_norm :args ((= (and @t93 true) @t93))) % 0.36/0.58 (step @p43 :rule eq-refl :args (@t14)) % 0.36/0.58 (step @p44 :rule refl :args (@t93)) % 0.36/0.58 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t98)) % 0.36/0.58 (step @p46 :rule trans :premises (@p45 @p42)) % 0.36/0.58 (step @p47 :rule evaluate :args ((not true))) % 0.36/0.58 (step @p48 :rule cong :premises (@p43) :args (@t99)) % 0.36/0.58 (step @p49 :rule trans :premises (@p48 @p47)) % 0.36/0.58 (step @p50 :rule nary_cong :premises (@p49 @p46) :args (@t100)) % 0.36/0.58 (step @p51 :rule trans :premises (@p50 @p41)) % 0.36/0.58 (step @p52 :rule quant-var-elim-eq :args ((= (forall @t105 (or (not (= @t101 @t14)) @t104 @t103)) @t100))) % 0.36/0.58 (step @p53 :rule refl :args (@t103)) % 0.36/0.58 (step @p54 :rule refl :args (@t104)) % 0.36/0.58 (step @p55 :rule eq-symm :args (@t14 @t101)) % 0.36/0.58 (step @p56 :rule cong :premises (@p55) :args (@t104)) % 0.36/0.58 (step @p57 :rule nary_cong :premises (@p56 @p54 @p53) :args (@t106)) % 0.36/0.58 (step @p58 :rule aci_norm :args ((= @t107 @t106))) % 0.36/0.58 (step @p59 :rule trans :premises (@p58 @p57)) % 0.36/0.58 (step @p60 :rule cong :premises (@p59) :args (@t108)) % 0.36/0.58 (step @p61 :rule trans :premises (@p60 @p52)) % 0.36/0.58 (step @p62 :rule trans :premises (@p61 @p51)) % 0.36/0.58 (step @p63 :rule refl :args (@t92)) % 0.36/0.58 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((and @t92 @t108))) % 0.36/0.58 (step @p65 :rule alpha_equiv :args (@t113 @t114 (@list @t101))) % 0.36/0.58 (step @p66 :rule alpha_equiv :args (@t116 @t114 (@list @t88))) % 0.36/0.58 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t117)) % 0.36/0.58 (step @p68 :rule quant-miniscope-and :args ((= (forall @t24 (and @t115 @t112)) @t117))) % 0.36/0.58 (step @p69 :rule trans :premises (@p68 @p67)) % 0.36/0.58 (step @p70 :rule trans :premises (@p69 @p64)) % 0.36/0.58 (step @p71 :rule bool-or-and-distrib :args (@t21 @t111 true @t110 false)) % 0.36/0.58 (step @p72 :rule cong :premises (@p71) :args ((forall @t24 (or (and @t21 @t111) @t110)))) % 0.36/0.58 (step @p73 :rule trans :premises (@p72 @p70)) % 0.36/0.58 (step @p74 :rule eq-symm :args (@t15 @t14)) % 0.36/0.58 (step @p75 :rule refl :args (@t18)) % 0.36/0.58 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t19)) % 0.36/0.58 (step @p77 :rule cong :premises (@p74) :args (@t20)) % 0.36/0.58 (step @p78 :rule refl :args (@t21)) % 0.36/0.58 (step @p79 :rule nary_cong :premises (@p78 @p77) :args (@t22)) % 0.36/0.58 (step @p80 :rule nary_cong :premises (@p79 @p76) :args (@t23)) % 0.36/0.58 (step @p81 :rule cong :premises (@p80) :args (@t25)) % 0.36/0.58 (step @p82 :rule trans :premises (@p81 @p73)) % 0.36/0.58 (step @p83 :rule cong :premises (@p82) :args (@t27)) % 0.36/0.58 (step @p84 :rule trans :premises (@p83 @p40)) % 0.36/0.58 (step @p85 :rule cong :premises (@p84) :args (@t28)) % 0.36/0.58 (step @p86 :rule eq_resolve :premises (@p2 @p85)) % 0.36/0.58 (step @p87 :rule instantiate :premises (@p86) :args ((@list @t125))) % 0.36/0.58 (step @p88 :rule refl :args (@t133)) % 0.36/0.58 (step @p89 :rule bool-double-not-elim :args (@t128)) % 0.36/0.58 (step @p90 :rule nary_cong :premises (@p89 @p88) :args ((or (not @t134) @t133))) % 0.36/0.58 (step @p91 :rule refl :args (@t131)) % 0.36/0.58 (step @p92 :rule eq-symm :args (@t129 @t88)) % 0.36/0.58 (step @p93 :rule refl :args (@t126)) % 0.36/0.58 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t135)) % 0.36/0.58 (step @p95 :rule refl :args (@t127)) % 0.36/0.58 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t136)) % 0.36/0.58 (step @p97 :rule cong :premises (@p96) :args (@t137)) % 0.36/0.58 (step @p98 :rule cong :premises (@p97) :args (@t138)) % 0.36/0.58 (step @p99 :rule nary_cong :premises (@p98 @p91) :args (@t139)) % 0.36/0.58 (step @p100 :rule cong :premises (@p99) :args (@t140)) % 0.36/0.58 (step @p101 :rule refl :args (@t134)) % 0.36/0.58 (step @p102 :rule cong :premises (@p101 @p100) :args ((=> @t134 @t140))) % 0.36/0.58 (assume-push @p206 @t134) % 0.36/0.58 (step @p104 :rule skolemize :premises (@p87)) % 0.36/0.58 (step-pop @p207 :rule scope :premises (@p104)) % 0.36/0.58 (step @p105 :rule process_scope :premises (@p207) :args (@t140)) % 0.36/0.58 (step @p107 :rule eq_resolve :premises (@p105 @p102)) % 0.36/0.58 (step @p108 :rule implies_elim :premises (@p107)) % 0.36/0.58 (step @p109 :rule eq_resolve :premises (@p108 @p90)) % 0.36/0.58 (step @p110 :rule chain_m_resolution :premises (@p109 @p87) :args (@t133 @t141 (@list @t128))) % 0.36/0.58 (step @p111 :rule bool-double-not-elim :args (@t130)) % 0.36/0.58 (step @p112 :rule refl :args (@t132)) % 0.36/0.58 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or @t132 (not @t131)))) % 0.36/0.58 (step @p114 :rule cnf_or_neg :args (@t132 1)) % 0.36/0.58 (step @p115 :rule eq_resolve :premises (@p114 @p113)) % 0.36/0.58 (step @p116 :rule reordering :premises (@p115) :args ((or @t130 @t132))) % 0.36/0.58 (step @p117 :rule chain_m_resolution :premises (@p116 @p110) :args (@t130 @t141 (@list @t132))) % 0.36/0.58 (step @p118 :rule bool-and-de-morgan :args (@t123 @t118 true)) % 0.36/0.58 (step @p119 :rule cong :premises (@p118) :args (@t143)) % 0.36/0.58 (step @p120 :rule cong :premises (@p119) :args (@t144)) % 0.36/0.58 (step @p121 :rule exists-elim :args ((= (exists @t12 @t142) @t144))) % 0.36/0.58 (step @p122 :rule trans :premises (@p121 @p120)) % 0.36/0.58 (step @p123 :rule aci_norm :args ((= (or false @t118) @t118))) % 0.36/0.58 (step @p124 :rule aci_norm :args ((= (and @t118 true) @t118))) % 0.36/0.58 (step @p125 :rule eq-refl :args (@t1)) % 0.36/0.58 (step @p126 :rule refl :args (@t118)) % 0.36/0.58 (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t146)) % 0.36/0.58 (step @p128 :rule trans :premises (@p127 @p124)) % 0.36/0.58 (step @p129 :rule cong :premises (@p125) :args (@t147)) % 0.36/0.58 (step @p130 :rule trans :premises (@p129 @p47)) % 0.36/0.58 (step @p131 :rule nary_cong :premises (@p130 @p128) :args (@t148)) % 0.36/0.58 (step @p132 :rule trans :premises (@p131 @p123)) % 0.36/0.58 (step @p133 :rule quant-var-elim-eq :args ((= (forall @t153 (or (not (= @t149 @t1)) @t152 @t151)) @t148))) % 0.36/0.58 (step @p134 :rule refl :args (@t151)) % 0.36/0.58 (step @p135 :rule refl :args (@t152)) % 0.36/0.58 (step @p136 :rule eq-symm :args (@t1 @t149)) % 0.36/0.58 (step @p137 :rule cong :premises (@p136) :args (@t152)) % 0.36/0.58 (step @p138 :rule nary_cong :premises (@p137 @p135 @p134) :args (@t154)) % 0.36/0.58 (step @p139 :rule aci_norm :args ((= @t155 @t154))) % 0.36/0.58 (step @p140 :rule trans :premises (@p139 @p138)) % 0.36/0.58 (step @p141 :rule cong :premises (@p140) :args (@t156)) % 0.36/0.58 (step @p142 :rule trans :premises (@p141 @p133)) % 0.36/0.58 (step @p143 :rule trans :premises (@p142 @p132)) % 0.36/0.58 (step @p144 :rule refl :args (@t123)) % 0.36/0.58 (step @p145 :rule nary_cong :premises (@p144 @p143) :args ((and @t123 @t156))) % 0.36/0.58 (step @p146 :rule alpha_equiv :args (@t161 @t162 (@list @t149))) % 0.36/0.58 (step @p147 :rule alpha_equiv :args (@t164 @t162 (@list @t119))) % 0.36/0.58 (step @p148 :rule nary_cong :premises (@p147 @p146) :args (@t165)) % 0.36/0.58 (step @p149 :rule quant-miniscope-and :args ((= (forall @t10 (and @t163 @t160)) @t165))) % 0.36/0.58 (step @p150 :rule trans :premises (@p149 @p148)) % 0.36/0.59 (step @p151 :rule trans :premises (@p150 @p145)) % 0.36/0.59 (step @p152 :rule bool-or-and-distrib :args (@t7 @t159 true @t158 false)) % 0.36/0.59 (step @p153 :rule cong :premises (@p152) :args ((forall @t10 (or (and @t7 @t159) @t158)))) % 0.36/0.59 (step @p154 :rule trans :premises (@p153 @p151)) % 0.36/0.59 (step @p155 :rule eq-symm :args (@t2 @t1)) % 0.36/0.59 (step @p156 :rule refl :args (@t4)) % 0.36/0.59 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t5)) % 0.36/0.59 (step @p158 :rule cong :premises (@p155) :args (@t6)) % 0.36/0.59 (step @p159 :rule refl :args (@t7)) % 0.36/0.59 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t8)) % 0.36/0.59 (step @p161 :rule nary_cong :premises (@p160 @p157) :args (@t9)) % 0.36/0.59 (step @p162 :rule cong :premises (@p161) :args (@t11)) % 0.36/0.59 (step @p163 :rule trans :premises (@p162 @p154)) % 0.36/0.59 (step @p164 :rule cong :premises (@p163) :args (@t13)) % 0.36/0.59 (step @p165 :rule trans :premises (@p164 @p122)) % 0.36/0.59 (step @p166 :rule eq_resolve :premises (@p1 @p165)) % 0.36/0.59 (step @p167 :rule refl :args (@t169)) % 0.36/0.59 (step @p168 :rule bool-double-not-elim :args (@t124)) % 0.36/0.59 (step @p169 :rule nary_cong :premises (@p168 @p167) :args ((or (not @t170) @t169))) % 0.36/0.59 (step @p170 :rule refl :args (@t167)) % 0.36/0.59 (step @p171 :rule eq-symm :args (@t125 @t119)) % 0.36/0.59 (step @p172 :rule refl :args (@t120)) % 0.36/0.59 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t171)) % 0.36/0.59 (step @p174 :rule refl :args (@t121)) % 0.36/0.59 (step @p175 :rule nary_cong :premises (@p174 @p173) :args (@t172)) % 0.36/0.59 (step @p176 :rule cong :premises (@p175) :args (@t173)) % 0.36/0.59 (step @p177 :rule cong :premises (@p176) :args (@t174)) % 0.36/0.59 (step @p178 :rule nary_cong :premises (@p177 @p170) :args (@t175)) % 0.36/0.59 (step @p179 :rule cong :premises (@p178) :args (@t176)) % 0.36/0.59 (step @p180 :rule refl :args (@t170)) % 0.36/0.59 (step @p181 :rule cong :premises (@p180 @p179) :args ((=> @t170 @t176))) % 0.36/0.59 (assume-push @p208 @t170) % 0.36/0.59 (step @p183 :rule skolemize :premises (@p166)) % 0.36/0.59 (step-pop @p209 :rule scope :premises (@p183)) % 0.36/0.59 (step @p184 :rule process_scope :premises (@p209) :args (@t176)) % 0.36/0.59 (step @p186 :rule eq_resolve :premises (@p184 @p181)) % 0.36/0.59 (step @p187 :rule implies_elim :premises (@p186)) % 0.36/0.59 (step @p188 :rule eq_resolve :premises (@p187 @p169)) % 0.36/0.59 (step @p189 :rule chain_m_resolution :premises (@p188 @p166) :args (@t169 @t141 (@list @t124))) % 0.36/0.59 (step @p190 :rule bool-double-not-elim :args (@t166)) % 0.36/0.59 (step @p191 :rule refl :args (@t168)) % 0.36/0.59 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or @t168 (not @t167)))) % 0.36/0.59 (step @p193 :rule cnf_or_neg :args (@t168 1)) % 0.36/0.59 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.36/0.59 (step @p195 :rule reordering :premises (@p194) :args ((or @t166 @t168))) % 0.36/0.59 (step @p196 :rule chain_m_resolution :premises (@p195 @p189) :args (@t166 @t141 (@list @t168))) % 0.36/0.59 (step @p197 :rule cnf_or_pos :args (@t177)) % 0.36/0.59 (step @p198 :rule reordering :premises (@p197) :args ((or @t167 @t131 @t178))) % 0.36/0.59 (step @p199 :rule chain_m_resolution :premises (@p198 @p196 @p117) :args (@t178 (@list false false) (@list @t166 @t130))) % 0.36/0.59 (assume-push @p210 @t81) % 0.36/0.59 (step @p201 :rule instantiate :premises (@p35) :args ((@list @t129 @t125))) % 0.36/0.59 (step-pop @p211 :rule scope :premises (@p201)) % 0.36/0.59 (step @p202 :rule process_scope :premises (@p211) :args (@t177)) % 0.36/0.59 (step @p204 :rule implies_elim :premises (@p202)) % 0.36/0.59 (step @p205 false :rule chain_m_resolution :premises (@p204 @p199 @p35) :args (false (@list true false) (@list @t177 @t81))) % 0.36/0.59 ) % 0.36/0.59 % SZS output end Proof % 0.36/0.59 % cvc5 exiting %------------------------------------------------------------------------------