%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU861^5 : 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 : n009.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 08:53:26 AM UTC 2026 % Result : Theorem 9.53s 9.76s % Output : Proof 9.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU861^5 : 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 % 0.16/0.34 % Computer : n009.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:55:44 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 9.53/9.76 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 9.53/9.76 % SZS status Theorem % 9.53/9.76 % SZS output start Proof % 9.53/9.76 ( % 9.53/9.76 (declare-sort tptp.a 0) % 9.53/9.76 (declare-const tptp.cC (-> tptp.a Bool)) % 9.53/9.76 (declare-const tptp.cB (-> tptp.a Bool)) % 9.53/9.76 (define @t1 () (@var "P" (-> (-> tptp.a Bool) Bool))) % 9.53/9.76 (define @t2 () (_ @t1 tptp.cB)) % 9.53/9.76 (define @t3 () (@var "Z" (-> tptp.a Bool))) % 9.53/9.76 (define @t4 () (_ @t1 @t3)) % 9.53/9.76 (define @t5 () (@var "Xx" tptp.a)) % 9.53/9.76 (define @t6 () (@var "Xx_28" tptp.a)) % 9.53/9.76 (define @t7 () (@var "Y" (-> tptp.a Bool))) % 9.53/9.76 (define @t8 () (_ @t7 @t6)) % 9.53/9.76 (define @t9 () (or @t8 (= @t6 @t5))) % 9.53/9.76 (define @t10 () (_ @t3 @t6)) % 9.53/9.76 (define @t11 () (=> @t10 @t9)) % 9.53/9.76 (define @t12 () (@list @t6)) % 9.53/9.76 (define @t13 () (forall @t12 @t11)) % 9.53/9.76 (define @t14 () (_ @t1 @t7)) % 9.53/9.76 (define @t15 () (and @t14 @t13)) % 9.53/9.76 (define @t16 () (=> @t15 @t4)) % 9.53/9.76 (define @t17 () (@list @t7 @t5 @t3)) % 9.53/9.76 (define @t18 () (forall @t17 @t16)) % 9.53/9.76 (define @t19 () (@var "E" (-> tptp.a Bool))) % 9.53/9.76 (define @t20 () (_ @t1 @t19)) % 9.53/9.76 (define @t21 () (@var "Xt" tptp.a)) % 9.53/9.76 (define @t22 () (_ @t19 @t21)) % 9.53/9.76 (define @t23 () (@list @t21)) % 9.53/9.76 (define @t24 () (exists @t23 @t22)) % 9.53/9.76 (define @t25 () (not @t24)) % 9.53/9.76 (define @t26 () (=> @t25 @t20)) % 9.53/9.76 (define @t27 () (@list @t19)) % 9.53/9.76 (define @t28 () (forall @t27 @t26)) % 9.53/9.76 (define @t29 () (and @t28 @t18)) % 9.53/9.76 (define @t30 () (=> @t29 @t2)) % 9.53/9.76 (define @t31 () (@list @t1)) % 9.53/9.76 (define @t32 () (forall @t31 @t30)) % 9.53/9.76 (define @t33 () (_ tptp.cC @t5)) % 9.53/9.76 (define @t34 () (_ tptp.cB @t5)) % 9.53/9.76 (define @t35 () (@list @t5)) % 9.53/9.76 (define @t36 () (forall @t35 (=> @t34 @t33))) % 9.53/9.76 (define @t37 () (_ @t1 tptp.cC)) % 9.53/9.76 (define @t38 () (@var "Xx_27" tptp.a)) % 9.53/9.76 (define @t39 () (_ @t7 @t38)) % 9.53/9.76 (define @t40 () (or @t39 (= @t38 @t5))) % 9.53/9.76 (define @t41 () (_ @t3 @t38)) % 9.53/9.76 (define @t42 () (=> @t41 @t40)) % 9.53/9.76 (define @t43 () (@list @t38)) % 9.53/9.76 (define @t44 () (forall @t43 @t42)) % 9.53/9.76 (define @t45 () (and @t14 @t44)) % 9.53/9.76 (define @t46 () (=> @t45 @t4)) % 9.53/9.76 (define @t47 () (forall @t17 @t46)) % 9.53/9.76 (define @t48 () (and @t28 @t47)) % 9.53/9.76 (define @t49 () (=> @t48 @t37)) % 9.53/9.76 (define @t50 () (forall @t31 @t49)) % 9.53/9.76 (define @t51 () (and @t50 @t36)) % 9.53/9.76 (define @t52 () (=> @t51 @t32)) % 9.53/9.76 (define @t53 () (not @t52)) % 9.53/9.76 (define @t54 () (_ @t1 tptp.cB)) % 9.53/9.76 (define @t55 () (_ @t1 @t3)) % 9.53/9.76 (define @t56 () (= @t5 @t6)) % 9.53/9.76 (define @t57 () (_ @t7 @t6)) % 9.53/9.76 (define @t58 () (_ @t3 @t6)) % 9.53/9.76 (define @t59 () (forall @t12 (or (not @t58) @t57 @t56))) % 9.53/9.76 (define @t60 () (not @t59)) % 9.53/9.76 (define @t61 () (_ @t1 @t7)) % 9.53/9.76 (define @t62 () (not @t61)) % 9.53/9.76 (define @t63 () (forall @t17 (or @t62 @t60 @t55))) % 9.53/9.76 (define @t64 () (not @t63)) % 9.53/9.76 (define @t65 () (_ @t1 @t19)) % 9.53/9.76 (define @t66 () (_ @t19 @t21)) % 9.53/9.76 (define @t67 () (forall @t23 (not @t66))) % 9.53/9.76 (define @t68 () (not @t67)) % 9.53/9.76 (define @t69 () (forall @t27 (or @t68 @t65))) % 9.53/9.76 (define @t70 () (not @t69)) % 9.53/9.76 (define @t71 () (or @t70 @t64 @t2)) % 9.53/9.76 (define @t72 () (and @t69 @t63)) % 9.53/9.76 (define @t73 () (not @t14)) % 9.53/9.76 (define @t74 () (or @t73 @t60 @t4)) % 9.53/9.76 (define @t75 () (and @t14 @t59)) % 9.53/9.76 (define @t76 () (not @t10)) % 9.53/9.76 (define @t77 () (or @t76 @t8 @t56)) % 9.53/9.76 (define @t78 () (or @t8 @t56)) % 9.53/9.76 (define @t79 () (or @t68 @t20)) % 9.53/9.76 (define @t80 () (not @t22)) % 9.53/9.76 (define @t81 () (forall @t23 @t80)) % 9.53/9.76 (define @t82 () (not @t81)) % 9.53/9.76 (define @t83 () (tptp.cC @t5)) % 9.53/9.76 (define @t84 () (tptp.cB @t5)) % 9.53/9.76 (define @t85 () (not @t34)) % 9.53/9.76 (define @t86 () (or @t85 @t33)) % 9.53/9.76 (define @t87 () (_ @t1 tptp.cC)) % 9.53/9.76 (define @t88 () (= @t5 @t38)) % 9.53/9.76 (define @t89 () (_ @t7 @t38)) % 9.53/9.76 (define @t90 () (_ @t3 @t38)) % 9.53/9.76 (define @t91 () (forall @t43 (or (not @t90) @t89 @t88))) % 9.53/9.76 (define @t92 () (not @t91)) % 9.53/9.76 (define @t93 () (forall @t17 (or @t62 @t92 @t55))) % 9.53/9.76 (define @t94 () (not @t93)) % 9.53/9.76 (define @t95 () (or @t70 @t94 @t37)) % 9.53/9.76 (define @t96 () (and @t69 @t93)) % 9.53/9.76 (define @t97 () (or @t73 @t92 @t4)) % 9.53/9.76 (define @t98 () (and @t14 @t91)) % 9.53/9.76 (define @t99 () (not @t41)) % 9.53/9.76 (define @t100 () (or @t99 @t39 @t88)) % 9.53/9.76 (define @t101 () (or @t39 @t88)) % 9.53/9.76 (define @t102 () (@quantifiers_skolemize (forall @t31 (or @t70 @t64 @t54)) 0)) % 9.53/9.76 (define @t103 () (_ @t102 @t3)) % 9.53/9.76 (define @t104 () (not (_ @t102 @t7))) % 9.53/9.76 (define @t105 () (forall @t17 (or @t104 @t60 @t103))) % 9.53/9.76 (define @t106 () (_ @t102 tptp.cB)) % 9.53/9.76 (define @t107 () (not @t105)) % 9.53/9.76 (define @t108 () (forall @t27 (or @t68 (_ @t102 @t19)))) % 9.53/9.76 (define @t109 () (not @t108)) % 9.53/9.76 (define @t110 () (or @t109 @t107 @t106)) % 9.53/9.76 (define @t111 () (@list true)) % 9.53/9.76 (define @t112 () (@list @t110)) % 9.53/9.76 (define @t113 () (@var "BOUND_VARIABLE_1875435" tptp.a)) % 9.53/9.76 (define @t114 () (lambda (@list @t113) (tptp.cB @t113))) % 9.53/9.76 (define @t115 () (_ @t102 @t114)) % 9.53/9.76 (define @t116 () (@const 0 tptp.a)) % 9.53/9.76 (define @t117 () (tptp.cC @t6)) % 9.53/9.76 (define @t118 () (@var "BOUND_VARIABLE_1875131" tptp.a)) % 9.53/9.76 (define @t119 () (lambda (@list @t118) (tptp.cC @t118))) % 9.53/9.76 (define @t120 () (_ @t119 @t6)) % 9.53/9.76 (define @t121 () (tptp.cB @t6)) % 9.53/9.76 (define @t122 () (_ @t114 @t6)) % 9.53/9.76 (define @t123 () (not @t122)) % 9.53/9.76 (define @t124 () (or @t123 @t120 (= @t116 @t6))) % 9.53/9.76 (define @t125 () (forall @t12 @t124)) % 9.53/9.76 (define @t126 () (not @t125)) % 9.53/9.76 (define @t127 () (_ @t102 @t119)) % 9.53/9.76 (define @t128 () (not @t127)) % 9.53/9.76 (define @t129 () (or @t128 @t126 @t115)) % 9.53/9.76 (define @t130 () (forall @t12 (or (not @t121) @t117 (= @t6 @t116)))) % 9.53/9.76 (define @t131 () (not @t130)) % 9.53/9.76 (define @t132 () (_ @t102 tptp.cC)) % 9.53/9.76 (define @t133 () (not @t132)) % 9.53/9.76 (define @t134 () (or @t133 @t131 @t106)) % 9.53/9.76 (define @t135 () (@list false)) % 9.53/9.76 (define @t136 () (@list @t105)) % 9.53/9.76 (define @t137 () (@var "BOUND_VARIABLE_2098781" (-> tptp.a Bool))) % 9.53/9.76 (define @t138 () (@var "BOUND_VARIABLE_2098782" tptp.a)) % 9.53/9.76 (define @t139 () (@var "BOUND_VARIABLE_2098784" tptp.a)) % 9.53/9.76 (define @t140 () (@var "BOUND_VARIABLE_2098783" (-> tptp.a Bool))) % 9.53/9.76 (define @t141 () (@list @t137 @t138 @t140 @t139)) % 9.53/9.76 (define @t142 () (forall @t17 (or @t104 @t92 @t103))) % 9.53/9.76 (define @t143 () (not @t142)) % 9.53/9.76 (define @t144 () (or @t109 @t143 @t132)) % 9.53/9.76 (define @t145 () (@quantifiers_skolemize @t130 0)) % 9.53/9.76 (define @t146 () (tptp.cC @t145)) % 9.53/9.76 (define @t147 () (tptp.cB @t145)) % 9.53/9.76 (define @t148 () (not @t147)) % 9.53/9.76 (define @t149 () (or @t148 @t146 (= @t116 @t145))) % 9.53/9.76 (define @t150 () (not @t149)) % 9.53/9.76 (define @t151 () (or @t148 @t146 (= @t145 @t116))) % 9.53/9.76 (define @t152 () (not @t151)) % 9.53/9.76 (define @t153 () (@list @t149)) % 9.53/9.76 (define @t154 () (or @t148 @t146)) % 9.53/9.76 (define @t155 () (not @t154)) % 9.53/9.76 (define @t156 () (forall @t35 (or (not @t84) @t83))) % 9.53/9.76 (assume @p1 @t53) % 9.53/9.76 (assume @p2 true) % 9.53/9.76 (step @p3 :rule refl :args (@t54)) % 9.53/9.76 (step @p4 :rule refl :args (@t2)) % 9.53/9.76 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t2 @t54))) % 9.53/9.76 (step @p6 :rule symm :premises (@p5)) % 9.53/9.76 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 9.53/9.76 (step @p8 :rule refl :args (@t64)) % 9.53/9.76 (step @p9 :rule refl :args (@t70)) % 9.53/9.76 (step @p10 :rule nary_cong :premises (@p9 @p8 @p7) :args (@t71)) % 9.53/9.76 (step @p11 :rule cong :premises (@p10) :args ((forall @t31 @t71))) % 9.53/9.76 (step @p12 :rule aci_norm :args ((= (or (or @t70 @t64) @t2) @t71))) % 9.53/9.76 (step @p13 :rule bool-and-de-morgan :args (@t69 @t63 true)) % 9.53/9.76 (step @p14 :rule nary_cong :premises (@p13 @p4) :args ((or (not @t72) @t2))) % 9.53/9.76 (step @p15 :rule trans :premises (@p14 @p12)) % 9.53/9.76 (step @p16 :rule bool-impl-elim :args (@t72 @t2)) % 9.53/9.76 (step @p17 :rule trans :premises (@p16 @p15)) % 9.53/9.76 (step @p18 :rule cong :premises (@p17) :args ((forall @t31 (=> @t72 @t2)))) % 9.53/9.76 (step @p19 :rule trans :premises (@p18 @p11)) % 9.53/9.76 (step @p20 :rule refl :args (@t2)) % 9.53/9.76 (step @p21 :rule refl :args (@t55)) % 9.53/9.76 (step @p22 :rule refl :args (@t4)) % 9.53/9.76 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t4 @t55))) % 9.53/9.76 (step @p24 :rule symm :premises (@p23)) % 9.53/9.76 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 9.53/9.76 (step @p26 :rule refl :args (@t60)) % 9.53/9.76 (step @p27 :rule refl :args (@t61)) % 9.53/9.76 (step @p28 :rule refl :args (@t14)) % 9.53/9.76 (step @p29 :rule cong :premises (@p28 @p27) :args ((= @t14 @t61))) % 9.53/9.76 (step @p30 :rule symm :premises (@p29)) % 9.53/9.76 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 9.53/9.76 (step @p32 :rule cong :premises (@p31) :args (@t73)) % 9.53/9.76 (step @p33 :rule nary_cong :premises (@p32 @p26 @p25) :args (@t74)) % 9.53/9.76 (step @p34 :rule cong :premises (@p33) :args ((forall @t17 @t74))) % 9.53/9.76 (step @p35 :rule aci_norm :args ((= (or (or @t73 @t60) @t4) @t74))) % 9.53/9.76 (step @p36 :rule bool-and-de-morgan :args (@t14 @t59 true)) % 9.53/9.76 (step @p37 :rule nary_cong :premises (@p36 @p22) :args ((or (not @t75) @t4))) % 9.53/9.76 (step @p38 :rule trans :premises (@p37 @p35)) % 9.53/9.76 (step @p39 :rule bool-impl-elim :args (@t75 @t4)) % 9.53/9.76 (step @p40 :rule trans :premises (@p39 @p38)) % 9.53/9.76 (step @p41 :rule cong :premises (@p40) :args ((forall @t17 (=> @t75 @t4)))) % 9.53/9.76 (step @p42 :rule trans :premises (@p41 @p34)) % 9.53/9.76 (step @p43 :rule refl :args (@t4)) % 9.53/9.76 (step @p44 :rule refl :args (@t56)) % 9.53/9.76 (step @p45 :rule refl :args (@t57)) % 9.53/9.76 (step @p46 :rule refl :args (@t8)) % 9.53/9.76 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t8 @t57))) % 9.53/9.76 (step @p48 :rule symm :premises (@p47)) % 9.53/9.76 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 9.53/9.76 (step @p50 :rule refl :args (@t58)) % 9.53/9.76 (step @p51 :rule refl :args (@t10)) % 9.53/9.76 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t10 @t58))) % 9.53/9.76 (step @p53 :rule symm :premises (@p52)) % 9.53/9.76 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 9.53/9.76 (step @p55 :rule cong :premises (@p54) :args (@t76)) % 9.53/9.76 (step @p56 :rule nary_cong :premises (@p55 @p49 @p44) :args (@t77)) % 9.53/9.76 (step @p57 :rule cong :premises (@p56) :args ((forall @t12 @t77))) % 9.53/9.76 (step @p58 :rule aci_norm :args ((= (or @t76 @t78) @t77))) % 9.53/9.76 (step @p59 :rule bool-impl-elim :args (@t10 @t78)) % 9.53/9.76 (step @p60 :rule trans :premises (@p59 @p58)) % 9.53/9.76 (step @p61 :rule cong :premises (@p60) :args ((forall @t12 (=> @t10 @t78)))) % 9.53/9.76 (step @p62 :rule trans :premises (@p61 @p57)) % 9.53/9.76 (step @p63 :rule eq-symm :args (@t6 @t5)) % 9.53/9.76 (step @p64 :rule refl :args (@t8)) % 9.53/9.76 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t9)) % 9.53/9.76 (step @p66 :rule refl :args (@t10)) % 9.53/9.76 (step @p67 :rule cong :premises (@p66 @p65) :args (@t11)) % 9.53/9.76 (step @p68 :rule cong :premises (@p67) :args (@t13)) % 9.53/9.76 (step @p69 :rule trans :premises (@p68 @p62)) % 9.53/9.76 (step @p70 :rule refl :args (@t14)) % 9.53/9.76 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t15)) % 9.53/9.76 (step @p72 :rule cong :premises (@p71 @p43) :args (@t16)) % 9.53/9.76 (step @p73 :rule cong :premises (@p72) :args (@t18)) % 9.53/9.76 (step @p74 :rule trans :premises (@p73 @p42)) % 9.53/9.76 (step @p75 :rule refl :args (@t65)) % 9.53/9.76 (step @p76 :rule refl :args (@t20)) % 9.53/9.76 (step @p77 :rule cong :premises (@p76 @p75) :args ((= @t20 @t65))) % 9.53/9.76 (step @p78 :rule symm :premises (@p77)) % 9.53/9.76 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 9.53/9.76 (step @p80 :rule refl :args (@t68)) % 9.53/9.76 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t79)) % 9.53/9.76 (step @p82 :rule cong :premises (@p81) :args ((forall @t27 @t79))) % 9.53/9.76 (step @p83 :rule bool-impl-elim :args (@t67 @t20)) % 9.53/9.76 (step @p84 :rule cong :premises (@p83) :args ((forall @t27 (=> @t67 @t20)))) % 9.53/9.76 (step @p85 :rule trans :premises (@p84 @p82)) % 9.53/9.76 (step @p86 :rule refl :args (@t20)) % 9.53/9.76 (step @p87 :rule bool-double-not-elim :args (@t67)) % 9.53/9.76 (step @p88 :rule refl :args (@t66)) % 9.53/9.76 (step @p89 :rule refl :args (@t22)) % 9.53/9.76 (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t22 @t66))) % 9.53/9.76 (step @p91 :rule symm :premises (@p90)) % 9.53/9.76 (step @p92 :rule eq_resolve :premises (@p89 @p91)) % 9.53/9.76 (step @p93 :rule cong :premises (@p92) :args (@t80)) % 9.53/9.76 (step @p94 :rule cong :premises (@p93) :args (@t81)) % 9.53/9.76 (step @p95 :rule cong :premises (@p94) :args (@t82)) % 9.53/9.76 (step @p96 :rule exists-elim :args ((= @t24 @t82))) % 9.53/9.76 (step @p97 :rule trans :premises (@p96 @p95)) % 9.53/9.76 (step @p98 :rule cong :premises (@p97) :args (@t25)) % 9.53/9.76 (step @p99 :rule trans :premises (@p98 @p87)) % 9.53/9.76 (step @p100 :rule cong :premises (@p99 @p86) :args (@t26)) % 9.53/9.76 (step @p101 :rule cong :premises (@p100) :args (@t28)) % 9.53/9.76 (step @p102 :rule trans :premises (@p101 @p85)) % 9.53/9.76 (step @p103 :rule nary_cong :premises (@p102 @p74) :args (@t29)) % 9.53/9.76 (step @p104 :rule cong :premises (@p103 @p20) :args (@t30)) % 9.53/9.76 (step @p105 :rule cong :premises (@p104) :args (@t32)) % 9.53/9.76 (step @p106 :rule trans :premises (@p105 @p19)) % 9.53/9.76 (step @p107 :rule refl :args (@t83)) % 9.53/9.76 (step @p108 :rule refl :args (@t33)) % 9.53/9.76 (step @p109 :rule cong :premises (@p108 @p107) :args ((= @t33 @t83))) % 9.53/9.76 (step @p110 :rule symm :premises (@p109)) % 9.53/9.76 (step @p111 :rule eq_resolve :premises (@p108 @p110)) % 9.53/9.76 (step @p112 :rule refl :args (@t84)) % 9.53/9.76 (step @p113 :rule refl :args (@t34)) % 9.53/9.76 (step @p114 :rule cong :premises (@p113 @p112) :args ((= @t34 @t84))) % 9.53/9.76 (step @p115 :rule symm :premises (@p114)) % 9.53/9.76 (step @p116 :rule eq_resolve :premises (@p113 @p115)) % 9.53/9.76 (step @p117 :rule cong :premises (@p116) :args (@t85)) % 9.53/9.76 (step @p118 :rule nary_cong :premises (@p117 @p111) :args (@t86)) % 9.53/9.76 (step @p119 :rule cong :premises (@p118) :args ((forall @t35 @t86))) % 9.53/9.76 (step @p120 :rule bool-impl-elim :args (@t34 @t33)) % 9.53/9.76 (step @p121 :rule cong :premises (@p120) :args (@t36)) % 9.53/9.76 (step @p122 :rule trans :premises (@p121 @p119)) % 9.53/9.76 (step @p123 :rule refl :args (@t87)) % 9.53/9.76 (step @p124 :rule refl :args (@t37)) % 9.53/9.76 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t37 @t87))) % 9.53/9.76 (step @p126 :rule symm :premises (@p125)) % 9.53/9.76 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 9.53/9.76 (step @p128 :rule refl :args (@t94)) % 9.53/9.76 (step @p129 :rule nary_cong :premises (@p9 @p128 @p127) :args (@t95)) % 9.53/9.76 (step @p130 :rule cong :premises (@p129) :args ((forall @t31 @t95))) % 9.53/9.76 (step @p131 :rule aci_norm :args ((= (or (or @t70 @t94) @t37) @t95))) % 9.53/9.76 (step @p132 :rule bool-and-de-morgan :args (@t69 @t93 true)) % 9.53/9.76 (step @p133 :rule nary_cong :premises (@p132 @p124) :args ((or (not @t96) @t37))) % 9.53/9.76 (step @p134 :rule trans :premises (@p133 @p131)) % 9.53/9.76 (step @p135 :rule bool-impl-elim :args (@t96 @t37)) % 9.53/9.76 (step @p136 :rule trans :premises (@p135 @p134)) % 9.53/9.76 (step @p137 :rule cong :premises (@p136) :args ((forall @t31 (=> @t96 @t37)))) % 9.53/9.76 (step @p138 :rule trans :premises (@p137 @p130)) % 9.53/9.76 (step @p139 :rule refl :args (@t37)) % 9.53/9.76 (step @p140 :rule refl :args (@t92)) % 9.53/9.76 (step @p141 :rule nary_cong :premises (@p32 @p140 @p25) :args (@t97)) % 9.53/9.76 (step @p142 :rule cong :premises (@p141) :args ((forall @t17 @t97))) % 9.53/9.76 (step @p143 :rule aci_norm :args ((= (or (or @t73 @t92) @t4) @t97))) % 9.53/9.76 (step @p144 :rule bool-and-de-morgan :args (@t14 @t91 true)) % 9.53/9.76 (step @p145 :rule nary_cong :premises (@p144 @p22) :args ((or (not @t98) @t4))) % 9.53/9.76 (step @p146 :rule trans :premises (@p145 @p143)) % 9.53/9.76 (step @p147 :rule bool-impl-elim :args (@t98 @t4)) % 9.53/9.76 (step @p148 :rule trans :premises (@p147 @p146)) % 9.53/9.76 (step @p149 :rule cong :premises (@p148) :args ((forall @t17 (=> @t98 @t4)))) % 9.53/9.76 (step @p150 :rule trans :premises (@p149 @p142)) % 9.53/9.76 (step @p151 :rule refl :args (@t88)) % 9.53/9.76 (step @p152 :rule refl :args (@t89)) % 9.53/9.76 (step @p153 :rule refl :args (@t39)) % 9.53/9.76 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t39 @t89))) % 9.53/9.76 (step @p155 :rule symm :premises (@p154)) % 9.53/9.76 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 9.53/9.76 (step @p157 :rule refl :args (@t90)) % 9.53/9.76 (step @p158 :rule refl :args (@t41)) % 9.53/9.76 (step @p159 :rule cong :premises (@p158 @p157) :args ((= @t41 @t90))) % 9.53/9.76 (step @p160 :rule symm :premises (@p159)) % 9.53/9.76 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 9.53/9.76 (step @p162 :rule cong :premises (@p161) :args (@t99)) % 9.53/9.76 (step @p163 :rule nary_cong :premises (@p162 @p156 @p151) :args (@t100)) % 9.53/9.76 (step @p164 :rule cong :premises (@p163) :args ((forall @t43 @t100))) % 9.53/9.76 (step @p165 :rule aci_norm :args ((= (or @t99 @t101) @t100))) % 9.53/9.76 (step @p166 :rule bool-impl-elim :args (@t41 @t101)) % 9.53/9.76 (step @p167 :rule trans :premises (@p166 @p165)) % 9.53/9.76 (step @p168 :rule cong :premises (@p167) :args ((forall @t43 (=> @t41 @t101)))) % 9.53/9.76 (step @p169 :rule trans :premises (@p168 @p164)) % 9.53/9.76 (step @p170 :rule eq-symm :args (@t38 @t5)) % 9.53/9.76 (step @p171 :rule refl :args (@t39)) % 9.53/9.76 (step @p172 :rule nary_cong :premises (@p171 @p170) :args (@t40)) % 9.53/9.76 (step @p173 :rule refl :args (@t41)) % 9.53/9.76 (step @p174 :rule cong :premises (@p173 @p172) :args (@t42)) % 9.53/9.76 (step @p175 :rule cong :premises (@p174) :args (@t44)) % 9.53/9.76 (step @p176 :rule trans :premises (@p175 @p169)) % 9.53/9.76 (step @p177 :rule nary_cong :premises (@p70 @p176) :args (@t45)) % 9.53/9.76 (step @p178 :rule cong :premises (@p177 @p43) :args (@t46)) % 9.53/9.76 (step @p179 :rule cong :premises (@p178) :args (@t47)) % 9.53/9.76 (step @p180 :rule trans :premises (@p179 @p150)) % 9.53/9.76 (step @p181 :rule nary_cong :premises (@p102 @p180) :args (@t48)) % 9.53/9.76 (step @p182 :rule cong :premises (@p181 @p139) :args (@t49)) % 9.53/9.76 (step @p183 :rule cong :premises (@p182) :args (@t50)) % 9.53/9.76 (step @p184 :rule trans :premises (@p183 @p138)) % 9.53/9.76 (step @p185 :rule nary_cong :premises (@p184 @p122) :args (@t51)) % 9.53/9.76 (step @p186 :rule cong :premises (@p185 @p106) :args (@t52)) % 9.53/9.76 (step @p187 :rule cong :premises (@p186) :args (@t53)) % 9.53/9.76 (step @p188 :rule eq_resolve :premises (@p1 @p187)) % 9.53/9.76 (step @p189 :rule not_implies_elim1 :premises (@p188)) % 9.53/9.76 (step @p190 :rule and_elim :premises (@p189) :args (1)) % 9.53/9.76 (step @p191 :rule not_implies_elim2 :premises (@p188)) % 9.53/9.76 (step @p192 :rule skolemize :premises (@p191)) % 9.53/9.76 (step @p193 :rule bool-double-not-elim :args (@t105)) % 9.53/9.76 (step @p194 :rule refl :args (@t110)) % 9.53/9.76 (step @p195 :rule nary_cong :premises (@p194 @p193) :args ((or @t110 (not @t107)))) % 9.53/9.76 (step @p196 :rule cnf_or_neg :args (@t110 1)) % 9.53/9.76 (step @p197 :rule eq_resolve :premises (@p196 @p195)) % 9.53/9.76 (step @p198 :rule reordering :premises (@p197) :args ((or @t105 @t110))) % 9.53/9.76 (step @p199 :rule chain_m_resolution :premises (@p198 @p192) :args (@t105 @t111 @t112)) % 9.53/9.76 (step @p200 :rule lambda-elim :args ((= @t114 tptp.cB))) % 9.53/9.76 (step @p201 :rule cong :premises (@p200) :args (@t115)) % 9.53/9.76 (step @p202 :rule eq-symm :args (@t116 @t6)) % 9.53/9.76 (step @p203 :rule beta-reduce :args ((= @t120 @t117))) % 9.53/9.76 (step @p204 :rule beta-reduce :args ((= @t122 @t121))) % 9.53/9.76 (step @p205 :rule cong :premises (@p204) :args (@t123)) % 9.53/9.76 (step @p206 :rule nary_cong :premises (@p205 @p203 @p202) :args (@t124)) % 9.53/9.76 (step @p207 :rule cong :premises (@p206) :args (@t125)) % 9.53/9.76 (step @p208 :rule cong :premises (@p207) :args (@t126)) % 9.53/9.76 (step @p209 :rule lambda-elim :args ((= @t119 tptp.cC))) % 9.53/9.76 (step @p210 :rule cong :premises (@p209) :args (@t127)) % 9.53/9.76 (step @p211 :rule cong :premises (@p210) :args (@t128)) % 9.53/9.76 (step @p212 :rule nary_cong :premises (@p211 @p208 @p201) :args (@t129)) % 9.53/9.76 (step @p213 :rule refl :args (@t105)) % 9.53/9.76 (step @p214 :rule cong :premises (@p213 @p212) :args ((=> @t105 @t129))) % 9.53/9.76 (assume-push @p279 @t105) % 9.53/9.76 (step @p216 :rule instantiate :premises (@p199) :args ((@list @t119 @t116 @t114))) % 9.53/9.76 (step-pop @p280 :rule scope :premises (@p216)) % 9.53/9.76 (step @p217 :rule process_scope :premises (@p280) :args (@t129)) % 9.53/9.76 (step @p219 :rule eq_resolve :premises (@p217 @p214)) % 9.53/9.76 (step @p220 :rule implies_elim :premises (@p219)) % 9.53/9.76 (step @p221 :rule chain_m_resolution :premises (@p220 @p199) :args (@t134 @t135 @t136)) % 9.53/9.76 (step @p222 :rule and_elim :premises (@p189) :args (0)) % 9.53/9.76 (step @p223 :rule instantiate :premises (@p222) :args ((@list @t102))) % 9.53/9.76 (step @p224 :rule alpha_equiv :args ((forall (@list @t140 @t139 @t137) (or (not (_ @t102 @t140)) (not (forall (@list @t138) (or (not (_ @t137 @t138)) (_ @t140 @t138) (= @t139 @t138)))) (_ @t102 @t137))) @t141 (@list @t3 @t38 @t7 @t5))) % 9.53/9.76 (step @p225 :rule alpha_equiv :args (@t105 (@list @t3 @t6 @t7 @t5) @t141)) % 9.53/9.76 (step @p226 :rule trans :premises (@p225 @p224)) % 9.53/9.76 (step @p227 :rule equiv_elim1 :premises (@p226)) % 9.53/9.76 (step @p228 :rule chain_m_resolution :premises (@p227 @p199) :args (@t142 @t135 @t136)) % 9.53/9.76 (step @p229 :rule bool-double-not-elim :args (@t108)) % 9.53/9.76 (step @p230 :rule nary_cong :premises (@p194 @p229) :args ((or @t110 (not @t109)))) % 9.53/9.76 (step @p231 :rule cnf_or_neg :args (@t110 0)) % 9.53/9.76 (step @p232 :rule eq_resolve :premises (@p231 @p230)) % 9.53/9.76 (step @p233 :rule reordering :premises (@p232) :args ((or @t108 @t110))) % 9.53/9.76 (step @p234 :rule chain_m_resolution :premises (@p233 @p192) :args (@t108 @t111 @t112)) % 9.53/9.76 (step @p235 :rule cnf_or_pos :args (@t144)) % 9.53/9.76 (step @p236 :rule reordering :premises (@p235) :args ((or @t109 @t132 @t143 (not @t144)))) % 9.53/9.76 (step @p237 :rule chain_m_resolution :premises (@p236 @p234 @p228 @p223) :args (@t132 (@list false false false) (@list @t108 @t142 @t144))) % 9.53/9.76 (step @p238 :rule cnf_or_neg :args (@t110 2)) % 9.53/9.76 (step @p239 :rule chain_m_resolution :premises (@p238 @p192) :args ((not @t106) @t111 @t112)) % 9.53/9.76 (step @p240 :rule cnf_or_pos :args (@t134)) % 9.53/9.76 (step @p241 :rule reordering :premises (@p240) :args ((or @t106 @t133 @t131 (not @t134)))) % 9.53/9.76 (step @p242 :rule chain_m_resolution :premises (@p241 @p239 @p237 @p221) :args (@t131 (@list true false false) (@list @t106 @t132 @t134))) % 9.53/9.76 (step @p243 :rule refl :args (@t150)) % 9.53/9.76 (step @p244 :rule bool-double-not-elim :args (@t130)) % 9.53/9.76 (step @p245 :rule nary_cong :premises (@p244 @p243) :args ((or (not @t131) @t150))) % 9.53/9.76 (step @p246 :rule eq-symm :args (@t145 @t116)) % 9.53/9.76 (step @p247 :rule refl :args (@t146)) % 9.53/9.76 (step @p248 :rule refl :args (@t148)) % 9.53/9.76 (step @p249 :rule nary_cong :premises (@p248 @p247 @p246) :args (@t151)) % 9.53/9.76 (step @p250 :rule cong :premises (@p249) :args (@t152)) % 9.53/9.76 (step @p251 :rule refl :args (@t131)) % 9.53/9.76 (step @p252 :rule cong :premises (@p251 @p250) :args ((=> @t131 @t152))) % 9.53/9.76 (assume-push @p281 @t131) % 9.53/9.76 (step @p254 :rule skolemize :premises (@p242)) % 9.53/9.76 (step-pop @p282 :rule scope :premises (@p254)) % 9.53/9.76 (step @p255 :rule process_scope :premises (@p282) :args (@t152)) % 9.53/9.76 (step @p257 :rule eq_resolve :premises (@p255 @p252)) % 9.53/9.76 (step @p258 :rule implies_elim :premises (@p257)) % 9.53/9.76 (step @p259 :rule eq_resolve :premises (@p258 @p245)) % 9.53/9.76 (step @p260 :rule chain_m_resolution :premises (@p259 @p242) :args (@t150 @t111 (@list @t130))) % 9.53/9.76 (step @p261 :rule cnf_or_neg :args (@t149 1)) % 9.53/9.76 (step @p262 :rule chain_m_resolution :premises (@p261 @p260) :args ((not @t146) @t111 @t153)) % 9.53/9.76 (step @p263 :rule bool-double-not-elim :args (@t147)) % 9.53/9.76 (step @p264 :rule refl :args (@t149)) % 9.53/9.76 (step @p265 :rule nary_cong :premises (@p264 @p263) :args ((or @t149 (not @t148)))) % 9.53/9.76 (step @p266 :rule cnf_or_neg :args (@t149 0)) % 9.53/9.76 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 9.53/9.76 (step @p268 :rule reordering :premises (@p267) :args ((or @t147 @t149))) % 9.53/9.76 (step @p269 :rule chain_m_resolution :premises (@p268 @p260) :args (@t147 @t111 @t153)) % 9.53/9.76 (step @p270 :rule cnf_or_pos :args (@t154)) % 9.53/9.76 (step @p271 :rule reordering :premises (@p270) :args ((or @t148 @t146 @t155))) % 9.53/9.76 (step @p272 :rule chain_m_resolution :premises (@p271 @p269 @p262) :args (@t155 (@list false true) (@list @t147 @t146))) % 9.53/9.76 (assume-push @p283 @t156) % 9.53/9.76 (step @p274 :rule instantiate :premises (@p190) :args ((@list @t145))) % 9.53/9.76 (step-pop @p284 :rule scope :premises (@p274)) % 9.53/9.76 (step @p275 :rule process_scope :premises (@p284) :args (@t154)) % 9.53/9.76 (step @p277 :rule implies_elim :premises (@p275)) % 9.53/9.76 (step @p278 false :rule chain_m_resolution :premises (@p277 @p272 @p190) :args (false (@list true false) (@list @t154 @t156))) % 9.53/9.76 ) % 9.53/9.76 % SZS output end Proof % 9.53/9.76 % cvc5 exiting %------------------------------------------------------------------------------