%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV185^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 08:55:34 AM UTC 2026 % Result : Theorem 0.40s 0.59s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV185^5 : TPTP v9.2.1. Released v4.0.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n021.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 18:18:50 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.40/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.59 % SZS status Theorem % 0.40/0.59 % SZS output start Proof % 0.40/0.59 ( % 0.40/0.59 (declare-sort tptp.b 0) % 0.40/0.59 (define @t1 () (@var "Xy" tptp.b)) % 0.40/0.59 (define @t2 () (@var "S0" (-> tptp.b Bool))) % 0.40/0.59 (define @t3 () (_ @t2 @t1)) % 0.40/0.59 (define @t4 () (@var "S" (-> (-> tptp.b Bool) Bool))) % 0.40/0.59 (define @t5 () (_ @t4 @t2)) % 0.40/0.59 (define @t6 () (@list @t2)) % 0.40/0.59 (define @t7 () (forall @t6 (=> @t5 @t3))) % 0.40/0.59 (define @t8 () (@var "X" (-> tptp.b Bool))) % 0.40/0.59 (define @t9 () (@var "P" (-> (-> tptp.b Bool) tptp.b Bool))) % 0.40/0.59 (define @t10 () (_ (_ @t9 @t8) @t1)) % 0.40/0.59 (define @t11 () (@var "Xx" tptp.b)) % 0.40/0.59 (define @t12 () (_ @t2 @t11)) % 0.40/0.59 (define @t13 () (forall @t6 (=> @t5 @t12))) % 0.40/0.59 (define @t14 () (_ @t8 @t11)) % 0.40/0.59 (define @t15 () (=> @t14 @t13)) % 0.40/0.59 (define @t16 () (@list @t11)) % 0.40/0.59 (define @t17 () (forall @t16 @t15)) % 0.40/0.59 (define @t18 () (and @t17 @t10)) % 0.40/0.59 (define @t19 () (=> @t18 @t7)) % 0.40/0.59 (define @t20 () (@list @t8 @t1)) % 0.40/0.59 (define @t21 () (forall @t20 @t19)) % 0.40/0.59 (define @t22 () (@var "Xx" (-> tptp.b Bool))) % 0.40/0.59 (define @t23 () (_ @t22 @t1)) % 0.40/0.59 (define @t24 () (@var "Xx0" tptp.b)) % 0.40/0.59 (define @t25 () (_ @t22 @t24)) % 0.40/0.59 (define @t26 () (_ @t8 @t24)) % 0.40/0.59 (define @t27 () (@list @t24)) % 0.40/0.59 (define @t28 () (forall @t27 (=> @t26 @t25))) % 0.40/0.59 (define @t29 () (and @t28 @t10)) % 0.40/0.59 (define @t30 () (=> @t29 @t23)) % 0.40/0.59 (define @t31 () (forall @t20 @t30)) % 0.40/0.59 (define @t32 () (_ @t4 @t22)) % 0.40/0.59 (define @t33 () (=> @t32 @t31)) % 0.40/0.59 (define @t34 () (@list @t22)) % 0.40/0.59 (define @t35 () (forall @t34 @t33)) % 0.40/0.59 (define @t36 () (=> @t35 @t21)) % 0.40/0.59 (define @t37 () (@list @t9 @t4)) % 0.40/0.59 (define @t38 () (forall @t37 @t36)) % 0.40/0.59 (define @t39 () (not @t38)) % 0.40/0.59 (define @t40 () (@var "BOUND_VARIABLE_7563" tptp.b)) % 0.40/0.59 (define @t41 () (@var "BOUND_VARIABLE_7565" (-> tptp.b Bool))) % 0.40/0.59 (define @t42 () (_ @t41 @t40)) % 0.40/0.59 (define @t43 () (not (_ @t4 @t41))) % 0.40/0.59 (define @t44 () (@var "BOUND_VARIABLE_7561" (-> tptp.b Bool))) % 0.40/0.59 (define @t45 () (not (_ @t9 @t44 @t40))) % 0.40/0.59 (define @t46 () (@var "BOUND_VARIABLE_7519" (-> tptp.b Bool))) % 0.40/0.59 (define @t47 () (_ @t46 @t11)) % 0.40/0.59 (define @t48 () (not (_ @t4 @t46))) % 0.40/0.59 (define @t49 () (@list @t11 @t46)) % 0.40/0.59 (define @t50 () (not (forall @t49 (or (not (_ @t44 @t11)) @t48 @t47)))) % 0.40/0.59 (define @t51 () (@var "BOUND_VARIABLE_7486" tptp.b)) % 0.40/0.59 (define @t52 () (_ @t22 @t51)) % 0.40/0.59 (define @t53 () (@var "BOUND_VARIABLE_7484" (-> tptp.b Bool))) % 0.40/0.59 (define @t54 () (not (_ @t9 @t53 @t51))) % 0.40/0.59 (define @t55 () (_ @t22 @t24)) % 0.40/0.59 (define @t56 () (not (forall @t27 (or (not (_ @t53 @t24)) @t55)))) % 0.40/0.59 (define @t57 () (_ @t4 @t22)) % 0.40/0.59 (define @t58 () (not @t57)) % 0.40/0.59 (define @t59 () (or @t58 @t56 @t54 @t52)) % 0.40/0.59 (define @t60 () (@list @t22 @t53 @t51)) % 0.40/0.59 (define @t61 () (forall @t60 @t59)) % 0.40/0.59 (define @t62 () (not @t61)) % 0.40/0.59 (define @t63 () (or @t62 @t50 @t45 @t43 @t42)) % 0.40/0.59 (define @t64 () (or @t50 @t45 @t43 @t42)) % 0.40/0.59 (define @t65 () (or @t62 @t64)) % 0.40/0.59 (define @t66 () (@list @t9 @t4 @t44 @t40 @t41)) % 0.40/0.59 (define @t67 () (forall @t66 @t65)) % 0.40/0.59 (define @t68 () (@list @t44 @t40 @t41)) % 0.40/0.59 (define @t69 () (forall @t68 @t65)) % 0.40/0.59 (define @t70 () (forall @t68 @t64)) % 0.40/0.59 (define @t71 () (@var "BOUND_VARIABLE_7545" (-> tptp.b Bool))) % 0.40/0.59 (define @t72 () (or @t62 @t70)) % 0.40/0.59 (define @t73 () (_ @t71 @t1)) % 0.40/0.59 (define @t74 () (not (_ @t4 @t71))) % 0.40/0.59 (define @t75 () (_ @t9 @t8 @t1)) % 0.40/0.59 (define @t76 () (not @t75)) % 0.40/0.59 (define @t77 () (_ @t8 @t11)) % 0.40/0.59 (define @t78 () (not @t77)) % 0.40/0.59 (define @t79 () (or @t78 @t48 @t47)) % 0.40/0.59 (define @t80 () (forall @t49 @t79)) % 0.40/0.59 (define @t81 () (not @t80)) % 0.40/0.59 (define @t82 () (or @t81 @t76 @t74 @t73)) % 0.40/0.59 (define @t83 () (@list @t8 @t1 @t71)) % 0.40/0.59 (define @t84 () (forall @t83 @t82)) % 0.40/0.59 (define @t85 () (or @t74 @t73)) % 0.40/0.59 (define @t86 () (or @t81 @t76 @t85)) % 0.40/0.59 (define @t87 () (forall @t83 @t86)) % 0.40/0.59 (define @t88 () (@list @t71)) % 0.40/0.59 (define @t89 () (forall @t88 @t86)) % 0.40/0.59 (define @t90 () (forall @t88 @t85)) % 0.40/0.59 (define @t91 () (@list @t2)) % 0.40/0.59 (define @t92 () (or @t81 @t76 @t90)) % 0.40/0.59 (define @t93 () (_ @t2 @t1)) % 0.40/0.59 (define @t94 () (_ @t4 @t2)) % 0.40/0.59 (define @t95 () (not @t94)) % 0.40/0.59 (define @t96 () (forall @t6 (or @t95 @t93))) % 0.40/0.59 (define @t97 () (not @t10)) % 0.40/0.59 (define @t98 () (or @t81 @t97 @t96)) % 0.40/0.59 (define @t99 () (and @t80 @t10)) % 0.40/0.59 (define @t100 () (not @t5)) % 0.40/0.59 (define @t101 () (or @t100 @t3)) % 0.40/0.59 (define @t102 () (or @t48 @t47)) % 0.40/0.59 (define @t103 () (or @t78 @t102)) % 0.40/0.59 (define @t104 () (forall @t49 @t103)) % 0.40/0.59 (define @t105 () (@list @t46)) % 0.40/0.59 (define @t106 () (forall @t105 @t103)) % 0.40/0.59 (define @t107 () (forall @t105 @t102)) % 0.40/0.59 (define @t108 () (or @t78 @t107)) % 0.40/0.59 (define @t109 () (_ @t2 @t11)) % 0.40/0.59 (define @t110 () (forall @t6 (or @t95 @t109))) % 0.40/0.59 (define @t111 () (not @t14)) % 0.40/0.59 (define @t112 () (or @t111 @t110)) % 0.40/0.59 (define @t113 () (or @t100 @t12)) % 0.40/0.59 (define @t114 () (or @t56 @t54 @t52)) % 0.40/0.59 (define @t115 () (or @t58 @t114)) % 0.40/0.59 (define @t116 () (forall @t60 @t115)) % 0.40/0.59 (define @t117 () (@list @t53 @t51)) % 0.40/0.59 (define @t118 () (forall @t117 @t115)) % 0.40/0.59 (define @t119 () (forall @t117 @t114)) % 0.40/0.59 (define @t120 () (or @t58 @t119)) % 0.40/0.59 (define @t121 () (_ @t22 @t1)) % 0.40/0.59 (define @t122 () (_ @t8 @t24)) % 0.40/0.59 (define @t123 () (forall @t27 (or (not @t122) @t55))) % 0.40/0.59 (define @t124 () (not @t123)) % 0.40/0.59 (define @t125 () (forall @t20 (or @t124 @t76 @t121))) % 0.40/0.59 (define @t126 () (not @t32)) % 0.40/0.59 (define @t127 () (or @t126 @t125)) % 0.40/0.59 (define @t128 () (or @t124 @t97 @t23)) % 0.40/0.59 (define @t129 () (and @t123 @t10)) % 0.40/0.59 (define @t130 () (not @t26)) % 0.40/0.59 (define @t131 () (or @t130 @t25)) % 0.40/0.59 (define @t132 () (forall @t66 @t63)) % 0.40/0.59 (define @t133 () (@quantifiers_skolemize @t132 1)) % 0.40/0.59 (define @t134 () (@quantifiers_skolemize @t132 2)) % 0.40/0.59 (define @t135 () (forall @t49 (or (not (_ @t134 @t11)) (not (_ @t133 @t46)) @t47))) % 0.40/0.59 (define @t136 () (@quantifiers_skolemize @t132 3)) % 0.40/0.59 (define @t137 () (@quantifiers_skolemize @t132 4)) % 0.40/0.59 (define @t138 () (_ @t137 @t136)) % 0.40/0.59 (define @t139 () (_ @t133 @t137)) % 0.40/0.59 (define @t140 () (not @t139)) % 0.40/0.59 (define @t141 () (@quantifiers_skolemize @t132 0)) % 0.40/0.59 (define @t142 () (_ @t141 @t134 @t136)) % 0.40/0.59 (define @t143 () (not @t142)) % 0.40/0.59 (define @t144 () (not @t135)) % 0.40/0.59 (define @t145 () (forall @t60 (or (not (_ @t133 @t22)) @t56 (not (_ @t141 @t53 @t51)) @t52))) % 0.40/0.59 (define @t146 () (not @t145)) % 0.40/0.59 (define @t147 () (or @t146 @t144 @t143 @t140 @t138)) % 0.40/0.59 (define @t148 () (@list true)) % 0.40/0.59 (define @t149 () (@list @t147)) % 0.40/0.59 (define @t150 () (forall @t27 (or (not (_ @t134 @t24)) (_ @t137 @t24)))) % 0.40/0.59 (define @t151 () (not @t150)) % 0.40/0.59 (define @t152 () (or @t140 @t151 @t143 @t138)) % 0.40/0.59 (define @t153 () (@quantifiers_skolemize @t150 0)) % 0.40/0.59 (define @t154 () (_ @t137 @t153)) % 0.40/0.59 (define @t155 () (_ @t134 @t153)) % 0.40/0.59 (define @t156 () (not @t155)) % 0.40/0.59 (define @t157 () (or @t156 @t154)) % 0.40/0.59 (define @t158 () (@list @t157)) % 0.40/0.59 (define @t159 () (or @t156 @t140 @t154)) % 0.40/0.59 (define @t160 () (not @t159)) % 0.40/0.59 (assume @p1 @t39) % 0.40/0.59 (assume @p2 true) % 0.40/0.59 (step @p3 :rule aci_norm :args ((= @t65 @t63))) % 0.40/0.59 (step @p4 :rule cong :premises (@p3) :args (@t67)) % 0.40/0.59 (step @p5 :rule quant-merge-prenex :args ((= (forall @t37 @t69) @t67))) % 0.40/0.59 (step @p6 :rule alpha_equiv :args (@t70 (@list @t44 @t40 @t41) (@list @t8 @t1 @t71))) % 0.40/0.59 (step @p7 :rule refl :args (@t62)) % 0.40/0.59 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t72)) % 0.40/0.59 (step @p9 :rule quant-miniscope-or :args ((= @t69 @t72))) % 0.40/0.59 (step @p10 :rule trans :premises (@p9 @p8)) % 0.40/0.59 (step @p11 :rule symm :premises (@p10)) % 0.40/0.59 (step @p12 :rule cong :premises (@p11) :args ((forall @t37 (or @t62 @t84)))) % 0.40/0.59 (step @p13 :rule trans :premises (@p12 @p5)) % 0.40/0.59 (step @p14 :rule trans :premises (@p13 @p4)) % 0.40/0.59 (step @p15 :rule bool-impl-elim :args (@t61 @t84)) % 0.40/0.59 (step @p16 :rule cong :premises (@p15) :args ((forall @t37 (=> @t61 @t84)))) % 0.40/0.59 (step @p17 :rule trans :premises (@p16 @p14)) % 0.40/0.59 (step @p18 :rule aci_norm :args ((= @t86 @t82))) % 0.40/0.59 (step @p19 :rule cong :premises (@p18) :args (@t87)) % 0.40/0.59 (step @p20 :rule quant-merge-prenex :args ((= (forall @t20 @t89) @t87))) % 0.40/0.59 (step @p21 :rule alpha_equiv :args (@t90 (@list @t71) @t91)) % 0.40/0.59 (step @p22 :rule refl :args (@t76)) % 0.40/0.59 (step @p23 :rule refl :args (@t81)) % 0.40/0.59 (step @p24 :rule nary_cong :premises (@p23 @p22 @p21) :args (@t92)) % 0.40/0.59 (step @p25 :rule quant-miniscope-or :args ((= @t89 @t92))) % 0.40/0.59 (step @p26 :rule trans :premises (@p25 @p24)) % 0.40/0.59 (step @p27 :rule symm :premises (@p26)) % 0.40/0.59 (step @p28 :rule cong :premises (@p27) :args ((forall @t20 (or @t81 @t76 @t96)))) % 0.40/0.59 (step @p29 :rule trans :premises (@p28 @p20)) % 0.40/0.59 (step @p30 :rule trans :premises (@p29 @p19)) % 0.40/0.59 (step @p31 :rule refl :args (@t96)) % 0.40/0.59 (step @p32 :rule refl :args (@t75)) % 0.40/0.59 (step @p33 :rule refl :args (@t10)) % 0.40/0.59 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t10 @t75))) % 0.40/0.59 (step @p35 :rule symm :premises (@p34)) % 0.40/0.59 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.40/0.59 (step @p37 :rule cong :premises (@p36) :args (@t97)) % 0.40/0.59 (step @p38 :rule nary_cong :premises (@p23 @p37 @p31) :args (@t98)) % 0.40/0.59 (step @p39 :rule cong :premises (@p38) :args ((forall @t20 @t98))) % 0.40/0.59 (step @p40 :rule trans :premises (@p39 @p30)) % 0.40/0.59 (step @p41 :rule aci_norm :args ((= (or (or @t81 @t97) @t96) @t98))) % 0.40/0.59 (step @p42 :rule bool-and-de-morgan :args (@t80 @t10 true)) % 0.40/0.59 (step @p43 :rule nary_cong :premises (@p42 @p31) :args ((or (not @t99) @t96))) % 0.40/0.59 (step @p44 :rule trans :premises (@p43 @p41)) % 0.40/0.59 (step @p45 :rule bool-impl-elim :args (@t99 @t96)) % 0.40/0.59 (step @p46 :rule trans :premises (@p45 @p44)) % 0.40/0.59 (step @p47 :rule cong :premises (@p46) :args ((forall @t20 (=> @t99 @t96)))) % 0.40/0.59 (step @p48 :rule trans :premises (@p47 @p40)) % 0.40/0.59 (step @p49 :rule refl :args (@t93)) % 0.40/0.59 (step @p50 :rule refl :args (@t3)) % 0.40/0.59 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t3 @t93))) % 0.40/0.59 (step @p52 :rule symm :premises (@p51)) % 0.40/0.59 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.40/0.59 (step @p54 :rule refl :args (@t94)) % 0.40/0.59 (step @p55 :rule refl :args (@t5)) % 0.40/0.59 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t5 @t94))) % 0.40/0.59 (step @p57 :rule symm :premises (@p56)) % 0.40/0.59 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.40/0.59 (step @p59 :rule cong :premises (@p58) :args (@t100)) % 0.40/0.59 (step @p60 :rule nary_cong :premises (@p59 @p53) :args (@t101)) % 0.40/0.59 (step @p61 :rule cong :premises (@p60) :args ((forall @t6 @t101))) % 0.40/0.59 (step @p62 :rule bool-impl-elim :args (@t5 @t3)) % 0.40/0.59 (step @p63 :rule cong :premises (@p62) :args (@t7)) % 0.40/0.59 (step @p64 :rule trans :premises (@p63 @p61)) % 0.40/0.59 (step @p65 :rule refl :args (@t10)) % 0.40/0.59 (step @p66 :rule aci_norm :args ((= @t103 @t79))) % 0.40/0.59 (step @p67 :rule cong :premises (@p66) :args (@t104)) % 0.40/0.59 (step @p68 :rule quant-merge-prenex :args ((= (forall @t16 @t106) @t104))) % 0.40/0.59 (step @p69 :rule alpha_equiv :args (@t107 (@list @t46) @t91)) % 0.40/0.59 (step @p70 :rule refl :args (@t78)) % 0.40/0.59 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t108)) % 0.40/0.59 (step @p72 :rule quant-miniscope-or :args ((= @t106 @t108))) % 0.40/0.59 (step @p73 :rule trans :premises (@p72 @p71)) % 0.40/0.59 (step @p74 :rule symm :premises (@p73)) % 0.40/0.59 (step @p75 :rule cong :premises (@p74) :args ((forall @t16 (or @t78 @t110)))) % 0.40/0.59 (step @p76 :rule trans :premises (@p75 @p68)) % 0.40/0.59 (step @p77 :rule trans :premises (@p76 @p67)) % 0.40/0.59 (step @p78 :rule refl :args (@t110)) % 0.40/0.59 (step @p79 :rule refl :args (@t77)) % 0.40/0.59 (step @p80 :rule refl :args (@t14)) % 0.40/0.59 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t14 @t77))) % 0.40/0.59 (step @p82 :rule symm :premises (@p81)) % 0.40/0.59 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.40/0.59 (step @p84 :rule cong :premises (@p83) :args (@t111)) % 0.40/0.59 (step @p85 :rule nary_cong :premises (@p84 @p78) :args (@t112)) % 0.40/0.59 (step @p86 :rule cong :premises (@p85) :args ((forall @t16 @t112))) % 0.40/0.59 (step @p87 :rule trans :premises (@p86 @p77)) % 0.40/0.59 (step @p88 :rule bool-impl-elim :args (@t14 @t110)) % 0.40/0.59 (step @p89 :rule cong :premises (@p88) :args ((forall @t16 (=> @t14 @t110)))) % 0.40/0.59 (step @p90 :rule trans :premises (@p89 @p87)) % 0.40/0.59 (step @p91 :rule refl :args (@t109)) % 0.40/0.59 (step @p92 :rule refl :args (@t12)) % 0.40/0.59 (step @p93 :rule cong :premises (@p92 @p91) :args ((= @t12 @t109))) % 0.40/0.59 (step @p94 :rule symm :premises (@p93)) % 0.40/0.59 (step @p95 :rule eq_resolve :premises (@p92 @p94)) % 0.40/0.59 (step @p96 :rule nary_cong :premises (@p59 @p95) :args (@t113)) % 0.40/0.59 (step @p97 :rule cong :premises (@p96) :args ((forall @t6 @t113))) % 0.40/0.59 (step @p98 :rule bool-impl-elim :args (@t5 @t12)) % 0.40/0.59 (step @p99 :rule cong :premises (@p98) :args (@t13)) % 0.40/0.59 (step @p100 :rule trans :premises (@p99 @p97)) % 0.40/0.59 (step @p101 :rule refl :args (@t14)) % 0.40/0.59 (step @p102 :rule cong :premises (@p101 @p100) :args (@t15)) % 0.40/0.59 (step @p103 :rule cong :premises (@p102) :args (@t17)) % 0.40/0.59 (step @p104 :rule trans :premises (@p103 @p90)) % 0.40/0.59 (step @p105 :rule nary_cong :premises (@p104 @p65) :args (@t18)) % 0.40/0.59 (step @p106 :rule cong :premises (@p105 @p64) :args (@t19)) % 0.40/0.59 (step @p107 :rule cong :premises (@p106) :args (@t21)) % 0.40/0.59 (step @p108 :rule trans :premises (@p107 @p48)) % 0.40/0.59 (step @p109 :rule aci_norm :args ((= @t115 @t59))) % 0.40/0.59 (step @p110 :rule cong :premises (@p109) :args (@t116)) % 0.40/0.59 (step @p111 :rule quant-merge-prenex :args ((= (forall @t34 @t118) @t116))) % 0.40/0.59 (step @p112 :rule alpha_equiv :args (@t119 (@list @t53 @t51) (@list @t8 @t1))) % 0.40/0.59 (step @p113 :rule refl :args (@t58)) % 0.40/0.59 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t120)) % 0.40/0.59 (step @p115 :rule quant-miniscope-or :args ((= @t118 @t120))) % 0.40/0.59 (step @p116 :rule trans :premises (@p115 @p114)) % 0.40/0.59 (step @p117 :rule symm :premises (@p116)) % 0.40/0.59 (step @p118 :rule cong :premises (@p117) :args ((forall @t34 (or @t58 @t125)))) % 0.40/0.59 (step @p119 :rule trans :premises (@p118 @p111)) % 0.40/0.59 (step @p120 :rule trans :premises (@p119 @p110)) % 0.40/0.59 (step @p121 :rule refl :args (@t125)) % 0.40/0.59 (step @p122 :rule refl :args (@t57)) % 0.40/0.59 (step @p123 :rule refl :args (@t32)) % 0.40/0.59 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t32 @t57))) % 0.40/0.59 (step @p125 :rule symm :premises (@p124)) % 0.40/0.59 (step @p126 :rule eq_resolve :premises (@p123 @p125)) % 0.40/0.59 (step @p127 :rule cong :premises (@p126) :args (@t126)) % 0.40/0.59 (step @p128 :rule nary_cong :premises (@p127 @p121) :args (@t127)) % 0.40/0.59 (step @p129 :rule cong :premises (@p128) :args ((forall @t34 @t127))) % 0.40/0.59 (step @p130 :rule trans :premises (@p129 @p120)) % 0.40/0.59 (step @p131 :rule bool-impl-elim :args (@t32 @t125)) % 0.40/0.59 (step @p132 :rule cong :premises (@p131) :args ((forall @t34 (=> @t32 @t125)))) % 0.40/0.59 (step @p133 :rule trans :premises (@p132 @p130)) % 0.40/0.59 (step @p134 :rule refl :args (@t121)) % 0.40/0.59 (step @p135 :rule refl :args (@t23)) % 0.40/0.59 (step @p136 :rule cong :premises (@p135 @p134) :args ((= @t23 @t121))) % 0.40/0.59 (step @p137 :rule symm :premises (@p136)) % 0.40/0.59 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 0.40/0.59 (step @p139 :rule refl :args (@t124)) % 0.40/0.59 (step @p140 :rule nary_cong :premises (@p139 @p37 @p138) :args (@t128)) % 0.40/0.59 (step @p141 :rule cong :premises (@p140) :args ((forall @t20 @t128))) % 0.40/0.59 (step @p142 :rule aci_norm :args ((= (or (or @t124 @t97) @t23) @t128))) % 0.40/0.59 (step @p143 :rule bool-and-de-morgan :args (@t123 @t10 true)) % 0.40/0.59 (step @p144 :rule nary_cong :premises (@p143 @p135) :args ((or (not @t129) @t23))) % 0.40/0.59 (step @p145 :rule trans :premises (@p144 @p142)) % 0.40/0.59 (step @p146 :rule bool-impl-elim :args (@t129 @t23)) % 0.40/0.59 (step @p147 :rule trans :premises (@p146 @p145)) % 0.40/0.59 (step @p148 :rule cong :premises (@p147) :args ((forall @t20 (=> @t129 @t23)))) % 0.40/0.59 (step @p149 :rule trans :premises (@p148 @p141)) % 0.40/0.59 (step @p150 :rule refl :args (@t23)) % 0.40/0.59 (step @p151 :rule refl :args (@t55)) % 0.40/0.59 (step @p152 :rule refl :args (@t25)) % 0.40/0.59 (step @p153 :rule cong :premises (@p152 @p151) :args ((= @t25 @t55))) % 0.40/0.59 (step @p154 :rule symm :premises (@p153)) % 0.40/0.59 (step @p155 :rule eq_resolve :premises (@p152 @p154)) % 0.40/0.59 (step @p156 :rule refl :args (@t122)) % 0.40/0.59 (step @p157 :rule refl :args (@t26)) % 0.40/0.59 (step @p158 :rule cong :premises (@p157 @p156) :args ((= @t26 @t122))) % 0.40/0.59 (step @p159 :rule symm :premises (@p158)) % 0.40/0.59 (step @p160 :rule eq_resolve :premises (@p157 @p159)) % 0.40/0.59 (step @p161 :rule cong :premises (@p160) :args (@t130)) % 0.40/0.59 (step @p162 :rule nary_cong :premises (@p161 @p155) :args (@t131)) % 0.40/0.59 (step @p163 :rule cong :premises (@p162) :args ((forall @t27 @t131))) % 0.40/0.59 (step @p164 :rule bool-impl-elim :args (@t26 @t25)) % 0.40/0.59 (step @p165 :rule cong :premises (@p164) :args (@t28)) % 0.40/0.59 (step @p166 :rule trans :premises (@p165 @p163)) % 0.40/0.59 (step @p167 :rule nary_cong :premises (@p166 @p65) :args (@t29)) % 0.40/0.59 (step @p168 :rule cong :premises (@p167 @p150) :args (@t30)) % 0.40/0.59 (step @p169 :rule cong :premises (@p168) :args (@t31)) % 0.40/0.59 (step @p170 :rule trans :premises (@p169 @p149)) % 0.40/0.59 (step @p171 :rule refl :args (@t32)) % 0.40/0.59 (step @p172 :rule cong :premises (@p171 @p170) :args (@t33)) % 0.40/0.59 (step @p173 :rule cong :premises (@p172) :args (@t35)) % 0.40/0.59 (step @p174 :rule trans :premises (@p173 @p133)) % 0.40/0.59 (step @p175 :rule cong :premises (@p174 @p108) :args (@t36)) % 0.40/0.59 (step @p176 :rule cong :premises (@p175) :args (@t38)) % 0.40/0.59 (step @p177 :rule trans :premises (@p176 @p17)) % 0.40/0.59 (step @p178 :rule cong :premises (@p177) :args (@t39)) % 0.40/0.59 (step @p179 :rule eq_resolve :premises (@p1 @p178)) % 0.40/0.59 (step @p180 :rule skolemize :premises (@p179)) % 0.40/0.59 (step @p181 :rule bool-double-not-elim :args (@t135)) % 0.40/0.59 (step @p182 :rule refl :args (@t147)) % 0.40/0.59 (step @p183 :rule nary_cong :premises (@p182 @p181) :args ((or @t147 (not @t144)))) % 0.40/0.59 (step @p184 :rule cnf_or_neg :args (@t147 1)) % 0.40/0.59 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.40/0.59 (step @p186 :rule reordering :premises (@p185) :args ((or @t135 @t147))) % 0.40/0.59 (step @p187 :rule chain_m_resolution :premises (@p186 @p180) :args (@t135 @t148 @t149)) % 0.40/0.59 (step @p188 :rule bool-double-not-elim :args (@t145)) % 0.40/0.59 (step @p189 :rule nary_cong :premises (@p182 @p188) :args ((or @t147 (not @t146)))) % 0.40/0.59 (step @p190 :rule cnf_or_neg :args (@t147 0)) % 0.40/0.59 (step @p191 :rule eq_resolve :premises (@p190 @p189)) % 0.40/0.59 (step @p192 :rule reordering :premises (@p191) :args ((or @t145 @t147))) % 0.40/0.59 (step @p193 :rule chain_m_resolution :premises (@p192 @p180) :args (@t145 @t148 @t149)) % 0.40/0.59 (step @p194 :rule instantiate :premises (@p193) :args ((@list @t137 @t134 @t136))) % 0.40/0.59 (step @p195 :rule cnf_or_neg :args (@t147 4)) % 0.40/0.59 (step @p196 :rule chain_m_resolution :premises (@p195 @p180) :args ((not @t138) @t148 @t149)) % 0.40/0.59 (step @p197 :rule bool-double-not-elim :args (@t139)) % 0.40/0.59 (step @p198 :rule nary_cong :premises (@p182 @p197) :args ((or @t147 (not @t140)))) % 0.40/0.59 (step @p199 :rule cnf_or_neg :args (@t147 3)) % 0.40/0.59 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.40/0.59 (step @p201 :rule reordering :premises (@p200) :args ((or @t139 @t147))) % 0.40/0.59 (step @p202 :rule chain_m_resolution :premises (@p201 @p180) :args (@t139 @t148 @t149)) % 0.40/0.59 (step @p203 :rule bool-double-not-elim :args (@t142)) % 0.40/0.59 (step @p204 :rule nary_cong :premises (@p182 @p203) :args ((or @t147 (not @t143)))) % 0.40/0.59 (step @p205 :rule cnf_or_neg :args (@t147 2)) % 0.40/0.59 (step @p206 :rule eq_resolve :premises (@p205 @p204)) % 0.40/0.59 (step @p207 :rule reordering :premises (@p206) :args ((or @t142 @t147))) % 0.40/0.59 (step @p208 :rule chain_m_resolution :premises (@p207 @p180) :args (@t142 @t148 @t149)) % 0.40/0.59 (step @p209 :rule cnf_or_pos :args (@t152)) % 0.40/0.59 (step @p210 :rule reordering :premises (@p209) :args ((or @t143 @t140 @t138 @t151 (not @t152)))) % 0.40/0.59 (step @p211 :rule chain_m_resolution :premises (@p210 @p208 @p202 @p196 @p194) :args (@t151 (@list false false true false) (@list @t142 @t139 @t138 @t152))) % 0.40/0.59 (step @p212 :rule skolemize :premises (@p211)) % 0.40/0.59 (step @p213 :rule cnf_or_neg :args (@t157 1)) % 0.40/0.59 (step @p214 :rule chain_m_resolution :premises (@p213 @p212) :args ((not @t154) @t148 @t158)) % 0.40/0.59 (step @p215 :rule bool-double-not-elim :args (@t155)) % 0.40/0.59 (step @p216 :rule refl :args (@t157)) % 0.40/0.59 (step @p217 :rule nary_cong :premises (@p216 @p215) :args ((or @t157 (not @t156)))) % 0.40/0.59 (step @p218 :rule cnf_or_neg :args (@t157 0)) % 0.40/0.59 (step @p219 :rule eq_resolve :premises (@p218 @p217)) % 0.40/0.59 (step @p220 :rule reordering :premises (@p219) :args ((or @t155 @t157))) % 0.40/0.59 (step @p221 :rule chain_m_resolution :premises (@p220 @p212) :args (@t155 @t148 @t158)) % 0.40/0.59 (step @p222 :rule cnf_or_pos :args (@t159)) % 0.40/0.59 (step @p223 :rule reordering :premises (@p222) :args ((or @t140 @t156 @t154 @t160))) % 0.40/0.59 (step @p224 :rule chain_m_resolution :premises (@p223 @p202 @p221 @p214) :args (@t160 (@list false false true) (@list @t139 @t155 @t154))) % 0.40/0.59 (assume-push @p231 @t135) % 0.40/0.59 (step @p226 :rule instantiate :premises (@p187) :args ((@list @t153 @t137))) % 0.40/0.59 (step-pop @p232 :rule scope :premises (@p226)) % 0.40/0.59 (step @p227 :rule process_scope :premises (@p232) :args (@t159)) % 0.40/0.59 (step @p229 :rule implies_elim :premises (@p227)) % 0.40/0.59 (step @p230 false :rule chain_m_resolution :premises (@p229 @p224 @p187) :args (false (@list true false) (@list @t159 @t135))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------