%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV245^6 : TPTP v9.2.1. Released v5.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 08:55:40 AM UTC 2026 % Result : Theorem 0.35s 0.59s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV245^6 : TPTP v9.2.1. Released v5.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n013.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 18:22:00 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.35/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.35/0.59 % SZS status Theorem % 0.35/0.59 % SZS output start Proof % 0.35/0.59 ( % 0.35/0.59 (declare-sort tptp.a 0) % 0.35/0.59 (declare-const tptp.cK (-> (-> tptp.a Bool) tptp.a Bool)) % 0.35/0.59 (define @t1 () (@var "Xx" tptp.a)) % 0.35/0.59 (define @t2 () (@var "Xx0" tptp.a)) % 0.35/0.59 (define @t3 () (@var "S" (-> tptp.a Bool))) % 0.35/0.59 (define @t4 () (_ @t3 @t2)) % 0.35/0.59 (define @t5 () (@var "Xx1" tptp.a)) % 0.35/0.59 (define @t6 () (_ tptp.cK @t3)) % 0.35/0.59 (define @t7 () (_ @t6 @t5)) % 0.35/0.59 (define @t8 () (_ @t3 @t5)) % 0.35/0.59 (define @t9 () (@list @t5)) % 0.35/0.59 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.35/0.59 (define @t11 () (and @t10 @t4)) % 0.35/0.59 (define @t12 () (@list @t3)) % 0.35/0.59 (define @t13 () (exists @t12 @t11)) % 0.35/0.59 (define @t14 () (@list @t2)) % 0.35/0.59 (define @t15 () (lambda @t14 @t13)) % 0.35/0.59 (define @t16 () (_ @t3 @t1)) % 0.35/0.59 (define @t17 () (_ @t6 @t2)) % 0.35/0.59 (define @t18 () (forall @t14 (=> @t4 @t17))) % 0.35/0.59 (define @t19 () (and @t18 @t16)) % 0.35/0.59 (define @t20 () (exists @t12 @t19)) % 0.35/0.59 (define @t21 () (=> @t20 (_ (_ tptp.cK @t15) @t1))) % 0.35/0.59 (define @t22 () (@list @t1)) % 0.35/0.59 (define @t23 () (forall @t22 @t21)) % 0.35/0.59 (define @t24 () (@var "Y" (-> tptp.a Bool))) % 0.35/0.59 (define @t25 () (_ (_ tptp.cK @t24) @t1)) % 0.35/0.59 (define @t26 () (@var "X" (-> tptp.a Bool))) % 0.35/0.59 (define @t27 () (_ (_ tptp.cK @t26) @t1)) % 0.35/0.59 (define @t28 () (forall @t22 (=> @t27 @t25))) % 0.35/0.59 (define @t29 () (_ @t24 @t1)) % 0.35/0.59 (define @t30 () (_ @t26 @t1)) % 0.35/0.59 (define @t31 () (forall @t22 (=> @t30 @t29))) % 0.35/0.59 (define @t32 () (=> @t31 @t28)) % 0.35/0.59 (define @t33 () (@list @t26 @t24)) % 0.35/0.59 (define @t34 () (forall @t33 @t32)) % 0.35/0.59 (define @t35 () (=> @t34 @t23)) % 0.35/0.59 (define @t36 () (not @t35)) % 0.35/0.59 (define @t37 () (_ @t3 @t2)) % 0.35/0.59 (define @t38 () (not @t37)) % 0.35/0.59 (define @t39 () (tptp.cK @t3 @t5)) % 0.35/0.59 (define @t40 () (_ @t3 @t5)) % 0.35/0.59 (define @t41 () (not @t40)) % 0.35/0.59 (define @t42 () (or @t41 @t39)) % 0.35/0.59 (define @t43 () (forall @t9 @t42)) % 0.35/0.59 (define @t44 () (not @t43)) % 0.35/0.59 (define @t45 () (or @t44 @t38)) % 0.35/0.59 (define @t46 () (forall @t12 @t45)) % 0.35/0.59 (define @t47 () (not @t46)) % 0.35/0.59 (define @t48 () (lambda @t14 @t47)) % 0.35/0.59 (define @t49 () (@purify @t48)) % 0.35/0.59 (define @t50 () (_ @t49 @t2)) % 0.35/0.59 (define @t51 () (_ @t48 @t2)) % 0.35/0.59 (define @t52 () (= @t50 @t51)) % 0.35/0.59 (define @t53 () (forall @t14 @t52)) % 0.35/0.59 (define @t54 () (@var "BOUND_VARIABLE_7537" (-> tptp.a Bool))) % 0.35/0.59 (define @t55 () (not (_ @t54 @t1))) % 0.35/0.59 (define @t56 () (not (forall @t14 (or (not (_ @t54 @t2)) (tptp.cK @t54 @t2))))) % 0.35/0.59 (define @t57 () (tptp.cK @t48 @t1)) % 0.35/0.59 (define @t58 () (or @t57 @t56 @t55)) % 0.35/0.59 (define @t59 () (@list @t1 @t54)) % 0.35/0.59 (define @t60 () (forall @t59 @t58)) % 0.35/0.59 (define @t61 () (@quantifiers_skolemize @t60 1)) % 0.35/0.59 (define @t62 () (forall @t22 (or (not (_ @t61 @t1)) (_ @t49 @t1)))) % 0.35/0.59 (define @t63 () (@quantifiers_skolemize @t62 0)) % 0.35/0.59 (define @t64 () (forall @t12 (or @t44 (not (_ @t3 @t63))))) % 0.35/0.59 (define @t65 () (not @t64)) % 0.35/0.59 (define @t66 () (_ @t49 @t63)) % 0.35/0.59 (define @t67 () (forall @t14 (= @t47 @t50))) % 0.35/0.59 (define @t68 () (= @t65 @t66)) % 0.35/0.59 (define @t69 () (= @t66 @t65)) % 0.35/0.59 (define @t70 () (@list false)) % 0.35/0.59 (define @t71 () (or @t56 @t55)) % 0.35/0.59 (define @t72 () (or @t71 @t57)) % 0.35/0.59 (define @t73 () (forall @t59 @t72)) % 0.35/0.59 (define @t74 () (@list @t54)) % 0.35/0.59 (define @t75 () (forall @t74 @t72)) % 0.35/0.59 (define @t76 () (forall @t74 @t71)) % 0.35/0.59 (define @t77 () (or @t76 @t57)) % 0.35/0.59 (define @t78 () (_ @t3 @t1)) % 0.35/0.59 (define @t79 () (tptp.cK @t3 @t2)) % 0.35/0.59 (define @t80 () (forall @t14 (or @t38 @t79))) % 0.35/0.59 (define @t81 () (not @t80)) % 0.35/0.59 (define @t82 () (forall @t12 (or @t81 (not @t78)))) % 0.35/0.59 (define @t83 () (not @t4)) % 0.35/0.59 (define @t84 () (not @t8)) % 0.35/0.59 (define @t85 () (or @t84 @t7)) % 0.35/0.59 (define @t86 () (forall @t9 @t85)) % 0.35/0.59 (define @t87 () (lambda @t14 (not (forall @t12 (or (not @t86) @t83))))) % 0.35/0.59 (define @t88 () (_ (_ tptp.cK @t48) @t1)) % 0.35/0.59 (define @t89 () (or @t82 @t88)) % 0.35/0.59 (define @t90 () (not @t82)) % 0.35/0.59 (define @t91 () (or @t44 @t83)) % 0.35/0.59 (define @t92 () (and @t43 @t4)) % 0.35/0.59 (define @t93 () (forall @t12 (not @t92))) % 0.35/0.59 (define @t94 () (not @t93)) % 0.35/0.59 (define @t95 () (not @t16)) % 0.35/0.59 (define @t96 () (or @t81 @t95)) % 0.35/0.59 (define @t97 () (and @t80 @t16)) % 0.35/0.59 (define @t98 () (forall @t12 (not @t97))) % 0.35/0.59 (define @t99 () (not @t98)) % 0.35/0.59 (define @t100 () (or @t83 @t17)) % 0.35/0.59 (define @t101 () (@var "BOUND_VARIABLE_7475" tptp.a)) % 0.35/0.59 (define @t102 () (tptp.cK @t24 @t101)) % 0.35/0.59 (define @t103 () (not (tptp.cK @t26 @t101))) % 0.35/0.59 (define @t104 () (_ @t24 @t1)) % 0.35/0.59 (define @t105 () (_ @t26 @t1)) % 0.35/0.59 (define @t106 () (forall @t22 (or (not @t105) @t104))) % 0.35/0.59 (define @t107 () (not @t106)) % 0.35/0.59 (define @t108 () (or @t103 @t102)) % 0.35/0.59 (define @t109 () (or @t107 @t108)) % 0.35/0.59 (define @t110 () (forall (@list @t26 @t24 @t101) @t109)) % 0.35/0.59 (define @t111 () (@list @t101)) % 0.35/0.59 (define @t112 () (forall @t111 @t109)) % 0.35/0.59 (define @t113 () (forall @t111 @t108)) % 0.35/0.59 (define @t114 () (or @t107 @t113)) % 0.35/0.59 (define @t115 () (tptp.cK @t24 @t1)) % 0.35/0.59 (define @t116 () (tptp.cK @t26 @t1)) % 0.35/0.59 (define @t117 () (forall @t22 (or (not @t116) @t115))) % 0.35/0.59 (define @t118 () (not @t27)) % 0.35/0.59 (define @t119 () (or @t118 @t25)) % 0.35/0.59 (define @t120 () (not @t30)) % 0.35/0.59 (define @t121 () (or @t120 @t29)) % 0.35/0.59 (define @t122 () (@quantifiers_skolemize @t60 0)) % 0.35/0.59 (define @t123 () (_ @t61 @t122)) % 0.35/0.59 (define @t124 () (not @t123)) % 0.35/0.59 (define @t125 () (forall @t14 (or (not (_ @t61 @t2)) (tptp.cK @t61 @t2)))) % 0.35/0.59 (define @t126 () (not @t125)) % 0.35/0.59 (define @t127 () (tptp.cK @t49 @t122)) % 0.35/0.59 (define @t128 () (or @t127 @t126 @t124)) % 0.35/0.59 (define @t129 () (not @t128)) % 0.35/0.59 (define @t130 () (not @t60)) % 0.35/0.59 (define @t131 () (tptp.cK @t48 @t122)) % 0.35/0.59 (define @t132 () (or @t131 @t126 @t124)) % 0.35/0.59 (define @t133 () (not @t132)) % 0.35/0.59 (define @t134 () (@list true)) % 0.35/0.59 (define @t135 () (@list @t128)) % 0.35/0.59 (define @t136 () (tptp.cK @t61 @t122)) % 0.35/0.59 (define @t137 () (or @t124 @t136)) % 0.35/0.59 (define @t138 () (@list false false)) % 0.35/0.59 (define @t139 () (not @t136)) % 0.35/0.59 (define @t140 () (not @t62)) % 0.35/0.59 (define @t141 () (or @t140 @t139 @t127)) % 0.35/0.59 (define @t142 () (_ @t61 @t63)) % 0.35/0.59 (define @t143 () (not @t142)) % 0.35/0.59 (define @t144 () (or @t143 @t66)) % 0.35/0.59 (define @t145 () (@list @t144)) % 0.35/0.59 (define @t146 () (not @t69)) % 0.35/0.59 (define @t147 () (@list true false)) % 0.35/0.59 (define @t148 () (forall @t9 (or (not (_ @t61 @t5)) (tptp.cK @t61 @t5)))) % 0.35/0.59 (define @t149 () (not @t148)) % 0.35/0.59 (define @t150 () (or @t149 @t143)) % 0.35/0.59 (define @t151 () (not @t150)) % 0.35/0.59 (assume @p1 @t36) % 0.35/0.59 (assume @p2 true) % 0.35/0.59 (step @p3 :rule eq-symm :args (@t50 @t47)) % 0.35/0.59 (step @p4 :rule beta-reduce :args ((= @t51 @t47))) % 0.35/0.59 (step @p5 :rule refl :args (@t50)) % 0.35/0.59 (step @p6 :rule cong :premises (@p5 @p4) :args (@t52)) % 0.35/0.59 (step @p7 :rule trans :premises (@p6 @p3)) % 0.35/0.59 (step @p8 :rule cong :premises (@p7) :args (@t53)) % 0.35/0.59 (step @p9 :rule quant-unused-vars :args ((= (forall @t14 true) true))) % 0.35/0.59 (step @p10 :rule eq-refl :args (@t51)) % 0.35/0.59 (step @p11 :rule cong :premises (@p10) :args ((forall @t14 (= @t51 @t51)))) % 0.35/0.59 (step @p12 :rule trans :premises (@p11 @p9)) % 0.35/0.59 (step @p13 :rule refl :args (@t51)) % 0.35/0.59 (step @p14 :rule refl :args (@t2)) % 0.35/0.59 (step @p15 :rule skolem_intro :args (@t49)) % 0.35/0.59 (step @p16 :rule ho_cong :premises (@p15 @p14)) % 0.35/0.59 (step @p17 :rule cong :premises (@p16 @p13) :args (@t52)) % 0.35/0.59 (step @p18 :rule cong :premises (@p17) :args (@t53)) % 0.35/0.59 (step @p19 :rule trans :premises (@p18 @p12)) % 0.35/0.59 (step @p20 :rule true_elim :premises (@p19)) % 0.35/0.59 (step @p21 :rule eq_resolve :premises (@p20 @p8)) % 0.35/0.59 (step @p22 :rule eq-symm :args (@t65 @t66)) % 0.35/0.59 (step @p23 :rule refl :args (@t67)) % 0.35/0.59 (step @p24 :rule cong :premises (@p23 @p22) :args ((=> @t67 @t68))) % 0.35/0.59 (assume-push @p279 @t67) % 0.35/0.59 (step @p26 :rule instantiate :premises (@p21) :args ((@list @t63))) % 0.35/0.59 (step-pop @p280 :rule scope :premises (@p26)) % 0.35/0.59 (step @p27 :rule process_scope :premises (@p280) :args (@t68)) % 0.35/0.59 (step @p29 :rule eq_resolve :premises (@p27 @p24)) % 0.35/0.59 (step @p30 :rule implies_elim :premises (@p29)) % 0.35/0.59 (step @p31 :rule chain_m_resolution :premises (@p30 @p21) :args (@t69 @t70 (@list @t67))) % 0.35/0.59 (step @p32 :rule aci_norm :args ((= @t72 @t58))) % 0.35/0.59 (step @p33 :rule cong :premises (@p32) :args (@t73)) % 0.35/0.59 (step @p34 :rule quant-merge-prenex :args ((= (forall @t22 @t75) @t73))) % 0.35/0.59 (step @p35 :rule refl :args (@t57)) % 0.35/0.59 (step @p36 :rule alpha_equiv :args (@t76 (@list @t54) (@list @t3))) % 0.35/0.59 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t77)) % 0.35/0.59 (step @p38 :rule quant-miniscope-or :args ((= @t75 @t77))) % 0.35/0.59 (step @p39 :rule trans :premises (@p38 @p37)) % 0.35/0.59 (step @p40 :rule symm :premises (@p39)) % 0.35/0.59 (step @p41 :rule cong :premises (@p40) :args ((forall @t22 (or @t82 @t57)))) % 0.35/0.59 (step @p42 :rule trans :premises (@p41 @p34)) % 0.35/0.59 (step @p43 :rule trans :premises (@p42 @p33)) % 0.35/0.59 (step @p44 :rule refl :args ((tptp.cK @t87 @t1))) % 0.35/0.59 (step @p45 :rule refl :args (@t1)) % 0.35/0.59 (step @p46 :rule refl :args (@t37)) % 0.35/0.59 (step @p47 :rule cong :premises (@p46) :args (@t38)) % 0.35/0.59 (step @p48 :rule refl :args (@t39)) % 0.35/0.59 (step @p49 :rule refl :args (@t40)) % 0.35/0.59 (step @p50 :rule cong :premises (@p49) :args (@t41)) % 0.35/0.59 (step @p51 :rule nary_cong :premises (@p50 @p48) :args (@t42)) % 0.35/0.59 (step @p52 :rule cong :premises (@p51) :args (@t43)) % 0.35/0.59 (step @p53 :rule cong :premises (@p52) :args (@t44)) % 0.35/0.59 (step @p54 :rule nary_cong :premises (@p53 @p47) :args (@t45)) % 0.35/0.59 (step @p55 :rule cong :premises (@p54) :args (@t46)) % 0.35/0.59 (step @p56 :rule cong :premises (@p55) :args (@t47)) % 0.35/0.59 (step @p57 :rule cong :premises (@p56) :args (@t48)) % 0.35/0.59 (step @p58 :rule cong :premises (@p57 @p45) :args (@t57)) % 0.35/0.59 (step @p59 :rule trans :premises (@p58 @p44)) % 0.35/0.59 (step @p60 :rule refl :args (tptp.cK)) % 0.35/0.59 (step @p61 :rule ho_cong :premises (@p60 @p57)) % 0.35/0.59 (step @p62 :rule ho_cong :premises (@p61 @p45)) % 0.35/0.59 (step @p63 :rule cong :premises (@p62 @p59) :args ((= @t88 @t57))) % 0.35/0.59 (step @p64 :rule symm :premises (@p63)) % 0.35/0.59 (step @p65 :rule refl :args ((_ (_ tptp.cK @t87) @t1))) % 0.35/0.59 (step @p66 :rule eq_resolve :premises (@p65 @p64)) % 0.35/0.59 (step @p67 :rule refl :args (@t82)) % 0.35/0.59 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t89)) % 0.35/0.59 (step @p69 :rule cong :premises (@p68) :args ((forall @t22 @t89))) % 0.35/0.59 (step @p70 :rule trans :premises (@p69 @p43)) % 0.35/0.59 (step @p71 :rule refl :args (@t88)) % 0.35/0.59 (step @p72 :rule bool-double-not-elim :args (@t82)) % 0.35/0.59 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or (not @t90) @t88))) % 0.35/0.59 (step @p74 :rule bool-impl-elim :args (@t90 @t88)) % 0.35/0.59 (step @p75 :rule trans :premises (@p74 @p73)) % 0.35/0.59 (step @p76 :rule cong :premises (@p75) :args ((forall @t22 (=> @t90 @t88)))) % 0.35/0.59 (step @p77 :rule trans :premises (@p76 @p70)) % 0.35/0.59 (step @p78 :rule refl :args (@t1)) % 0.35/0.59 (step @p79 :rule refl :args (@t4)) % 0.35/0.59 (step @p80 :rule cong :premises (@p79 @p46) :args ((= @t4 @t37))) % 0.35/0.59 (step @p81 :rule symm :premises (@p80)) % 0.35/0.59 (step @p82 :rule eq_resolve :premises (@p79 @p81)) % 0.35/0.59 (step @p83 :rule cong :premises (@p82) :args (@t83)) % 0.35/0.59 (step @p84 :rule refl :args (@t44)) % 0.35/0.59 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t91)) % 0.35/0.59 (step @p86 :rule cong :premises (@p85) :args ((forall @t12 @t91))) % 0.35/0.59 (step @p87 :rule bool-and-de-morgan :args (@t43 @t4 true)) % 0.35/0.59 (step @p88 :rule cong :premises (@p87) :args (@t93)) % 0.35/0.59 (step @p89 :rule trans :premises (@p88 @p86)) % 0.35/0.59 (step @p90 :rule cong :premises (@p89) :args (@t94)) % 0.35/0.59 (step @p91 :rule exists-elim :args ((= (exists @t12 @t92) @t94))) % 0.35/0.59 (step @p92 :rule trans :premises (@p91 @p90)) % 0.35/0.59 (step @p93 :rule refl :args (@t4)) % 0.35/0.59 (step @p94 :rule refl :args (@t7)) % 0.35/0.59 (step @p95 :rule cong :premises (@p94 @p48) :args ((= @t7 @t39))) % 0.35/0.59 (step @p96 :rule symm :premises (@p95)) % 0.35/0.59 (step @p97 :rule eq_resolve :premises (@p94 @p96)) % 0.35/0.59 (step @p98 :rule refl :args (@t8)) % 0.35/0.59 (step @p99 :rule cong :premises (@p98 @p49) :args ((= @t8 @t40))) % 0.35/0.59 (step @p100 :rule symm :premises (@p99)) % 0.35/0.59 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.35/0.59 (step @p102 :rule cong :premises (@p101) :args (@t84)) % 0.35/0.59 (step @p103 :rule nary_cong :premises (@p102 @p97) :args (@t85)) % 0.35/0.59 (step @p104 :rule cong :premises (@p103) :args (@t86)) % 0.35/0.59 (step @p105 :rule bool-impl-elim :args (@t8 @t7)) % 0.35/0.59 (step @p106 :rule cong :premises (@p105) :args (@t10)) % 0.35/0.59 (step @p107 :rule trans :premises (@p106 @p104)) % 0.35/0.59 (step @p108 :rule nary_cong :premises (@p107 @p93) :args (@t11)) % 0.35/0.59 (step @p109 :rule cong :premises (@p108) :args (@t13)) % 0.35/0.59 (step @p110 :rule trans :premises (@p109 @p92)) % 0.35/0.59 (step @p111 :rule cong :premises (@p110) :args (@t15)) % 0.35/0.59 (step @p112 :rule refl :args (tptp.cK)) % 0.35/0.59 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.35/0.59 (step @p114 :rule ho_cong :premises (@p113 @p78)) % 0.35/0.59 (step @p115 :rule refl :args (@t78)) % 0.35/0.59 (step @p116 :rule refl :args (@t16)) % 0.35/0.59 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t16 @t78))) % 0.35/0.59 (step @p118 :rule symm :premises (@p117)) % 0.35/0.59 (step @p119 :rule eq_resolve :premises (@p116 @p118)) % 0.35/0.59 (step @p120 :rule cong :premises (@p119) :args (@t95)) % 0.35/0.59 (step @p121 :rule refl :args (@t81)) % 0.35/0.59 (step @p122 :rule nary_cong :premises (@p121 @p120) :args (@t96)) % 0.35/0.59 (step @p123 :rule cong :premises (@p122) :args ((forall @t12 @t96))) % 0.35/0.59 (step @p124 :rule bool-and-de-morgan :args (@t80 @t16 true)) % 0.35/0.59 (step @p125 :rule cong :premises (@p124) :args (@t98)) % 0.35/0.59 (step @p126 :rule trans :premises (@p125 @p123)) % 0.35/0.59 (step @p127 :rule cong :premises (@p126) :args (@t99)) % 0.35/0.59 (step @p128 :rule exists-elim :args ((= (exists @t12 @t97) @t99))) % 0.35/0.59 (step @p129 :rule trans :premises (@p128 @p127)) % 0.35/0.59 (step @p130 :rule refl :args (@t16)) % 0.35/0.59 (step @p131 :rule refl :args (@t79)) % 0.35/0.59 (step @p132 :rule refl :args (@t17)) % 0.35/0.59 (step @p133 :rule cong :premises (@p132 @p131) :args ((= @t17 @t79))) % 0.35/0.59 (step @p134 :rule symm :premises (@p133)) % 0.35/0.59 (step @p135 :rule eq_resolve :premises (@p132 @p134)) % 0.35/0.59 (step @p136 :rule nary_cong :premises (@p83 @p135) :args (@t100)) % 0.35/0.59 (step @p137 :rule cong :premises (@p136) :args ((forall @t14 @t100))) % 0.35/0.59 (step @p138 :rule bool-impl-elim :args (@t4 @t17)) % 0.35/0.59 (step @p139 :rule cong :premises (@p138) :args (@t18)) % 0.35/0.59 (step @p140 :rule trans :premises (@p139 @p137)) % 0.35/0.59 (step @p141 :rule nary_cong :premises (@p140 @p130) :args (@t19)) % 0.35/0.59 (step @p142 :rule cong :premises (@p141) :args (@t20)) % 0.35/0.59 (step @p143 :rule trans :premises (@p142 @p129)) % 0.35/0.59 (step @p144 :rule cong :premises (@p143 @p114) :args (@t21)) % 0.35/0.59 (step @p145 :rule cong :premises (@p144) :args (@t23)) % 0.35/0.59 (step @p146 :rule trans :premises (@p145 @p77)) % 0.35/0.59 (step @p147 :rule aci_norm :args ((= @t109 (or @t107 @t103 @t102)))) % 0.35/0.59 (step @p148 :rule cong :premises (@p147) :args (@t110)) % 0.35/0.59 (step @p149 :rule quant-merge-prenex :args ((= (forall @t33 @t112) @t110))) % 0.35/0.59 (step @p150 :rule alpha_equiv :args (@t113 (@list @t101) (@list @t1))) % 0.35/0.59 (step @p151 :rule refl :args (@t107)) % 0.35/0.59 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t114)) % 0.35/0.59 (step @p153 :rule quant-miniscope-or :args ((= @t112 @t114))) % 0.35/0.59 (step @p154 :rule trans :premises (@p153 @p152)) % 0.35/0.59 (step @p155 :rule symm :premises (@p154)) % 0.35/0.59 (step @p156 :rule cong :premises (@p155) :args ((forall @t33 (or @t107 @t117)))) % 0.35/0.59 (step @p157 :rule trans :premises (@p156 @p149)) % 0.35/0.59 (step @p158 :rule trans :premises (@p157 @p148)) % 0.35/0.59 (step @p159 :rule bool-impl-elim :args (@t106 @t117)) % 0.35/0.59 (step @p160 :rule cong :premises (@p159) :args ((forall @t33 (=> @t106 @t117)))) % 0.35/0.59 (step @p161 :rule trans :premises (@p160 @p158)) % 0.35/0.59 (step @p162 :rule refl :args (@t115)) % 0.35/0.59 (step @p163 :rule refl :args (@t25)) % 0.35/0.59 (step @p164 :rule cong :premises (@p163 @p162) :args ((= @t25 @t115))) % 0.35/0.59 (step @p165 :rule symm :premises (@p164)) % 0.35/0.59 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 0.35/0.59 (step @p167 :rule refl :args (@t116)) % 0.35/0.59 (step @p168 :rule refl :args (@t27)) % 0.35/0.59 (step @p169 :rule cong :premises (@p168 @p167) :args ((= @t27 @t116))) % 0.35/0.59 (step @p170 :rule symm :premises (@p169)) % 0.35/0.59 (step @p171 :rule eq_resolve :premises (@p168 @p170)) % 0.35/0.59 (step @p172 :rule cong :premises (@p171) :args (@t118)) % 0.35/0.59 (step @p173 :rule nary_cong :premises (@p172 @p166) :args (@t119)) % 0.35/0.59 (step @p174 :rule cong :premises (@p173) :args ((forall @t22 @t119))) % 0.35/0.59 (step @p175 :rule bool-impl-elim :args (@t27 @t25)) % 0.35/0.59 (step @p176 :rule cong :premises (@p175) :args (@t28)) % 0.35/0.59 (step @p177 :rule trans :premises (@p176 @p174)) % 0.35/0.59 (step @p178 :rule refl :args (@t104)) % 0.35/0.59 (step @p179 :rule refl :args (@t29)) % 0.35/0.59 (step @p180 :rule cong :premises (@p179 @p178) :args ((= @t29 @t104))) % 0.35/0.59 (step @p181 :rule symm :premises (@p180)) % 0.35/0.59 (step @p182 :rule eq_resolve :premises (@p179 @p181)) % 0.35/0.59 (step @p183 :rule refl :args (@t105)) % 0.35/0.59 (step @p184 :rule refl :args (@t30)) % 0.35/0.59 (step @p185 :rule cong :premises (@p184 @p183) :args ((= @t30 @t105))) % 0.35/0.59 (step @p186 :rule symm :premises (@p185)) % 0.35/0.59 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 0.35/0.59 (step @p188 :rule cong :premises (@p187) :args (@t120)) % 0.35/0.59 (step @p189 :rule nary_cong :premises (@p188 @p182) :args (@t121)) % 0.35/0.59 (step @p190 :rule cong :premises (@p189) :args ((forall @t22 @t121))) % 0.35/0.59 (step @p191 :rule bool-impl-elim :args (@t30 @t29)) % 0.35/0.59 (step @p192 :rule cong :premises (@p191) :args (@t31)) % 0.35/0.59 (step @p193 :rule trans :premises (@p192 @p190)) % 0.35/0.59 (step @p194 :rule cong :premises (@p193 @p177) :args (@t32)) % 0.35/0.59 (step @p195 :rule cong :premises (@p194) :args (@t34)) % 0.35/0.59 (step @p196 :rule trans :premises (@p195 @p161)) % 0.35/0.59 (step @p197 :rule cong :premises (@p196 @p146) :args (@t35)) % 0.35/0.59 (step @p198 :rule cong :premises (@p197) :args (@t36)) % 0.35/0.59 (step @p199 :rule eq_resolve :premises (@p1 @p198)) % 0.35/0.59 (step @p200 :rule not_implies_elim1 :premises (@p199)) % 0.35/0.59 (step @p201 :rule instantiate :premises (@p200) :args ((@list @t61 @t49 @t122))) % 0.35/0.59 (step @p202 :rule not_implies_elim2 :premises (@p199)) % 0.35/0.59 (step @p203 :rule refl :args (@t129)) % 0.35/0.59 (step @p204 :rule bool-double-not-elim :args (@t60)) % 0.35/0.59 (step @p205 :rule nary_cong :premises (@p204 @p203) :args ((or (not @t130) @t129))) % 0.35/0.59 (step @p206 :rule refl :args (@t124)) % 0.35/0.59 (step @p207 :rule refl :args (@t126)) % 0.35/0.59 (step @p208 :rule refl :args (@t122)) % 0.35/0.59 (step @p209 :rule eq-refl :args (@t48)) % 0.35/0.59 (step @p210 :rule refl :args (@t48)) % 0.35/0.59 (step @p211 :rule cong :premises (@p210 @p15) :args ((= @t48 @t49))) % 0.35/0.59 (step @p212 :rule trans :premises (@p211 @p209)) % 0.35/0.59 (step @p213 :rule true_elim :premises (@p212)) % 0.35/0.59 (step @p214 :rule cong :premises (@p213 @p208) :args (@t131)) % 0.35/0.59 (step @p215 :rule nary_cong :premises (@p214 @p207 @p206) :args (@t132)) % 0.35/0.59 (step @p216 :rule cong :premises (@p215) :args (@t133)) % 0.35/0.59 (step @p217 :rule refl :args (@t130)) % 0.35/0.59 (step @p218 :rule cong :premises (@p217 @p216) :args ((=> @t130 @t133))) % 0.35/0.59 (assume-push @p281 @t130) % 0.35/0.59 (step @p220 :rule skolemize :premises (@p202)) % 0.35/0.59 (step-pop @p282 :rule scope :premises (@p220)) % 0.35/0.59 (step @p221 :rule process_scope :premises (@p282) :args (@t133)) % 0.35/0.59 (step @p223 :rule eq_resolve :premises (@p221 @p218)) % 0.35/0.59 (step @p224 :rule implies_elim :premises (@p223)) % 0.35/0.59 (step @p225 :rule eq_resolve :premises (@p224 @p205)) % 0.35/0.59 (step @p226 :rule chain_m_resolution :premises (@p225 @p202) :args (@t129 @t134 (@list @t60))) % 0.35/0.59 (step @p227 :rule bool-double-not-elim :args (@t125)) % 0.35/0.59 (step @p228 :rule refl :args (@t128)) % 0.35/0.59 (step @p229 :rule nary_cong :premises (@p228 @p227) :args ((or @t128 (not @t126)))) % 0.35/0.59 (step @p230 :rule cnf_or_neg :args (@t128 1)) % 0.35/0.59 (step @p231 :rule eq_resolve :premises (@p230 @p229)) % 0.35/0.59 (step @p232 :rule reordering :premises (@p231) :args ((or @t125 @t128))) % 0.35/0.59 (step @p233 :rule chain_m_resolution :premises (@p232 @p226) :args (@t125 @t134 @t135)) % 0.35/0.59 (step @p234 :rule instantiate :premises (@p233) :args ((@list @t122))) % 0.35/0.59 (step @p235 :rule bool-double-not-elim :args (@t123)) % 0.35/0.59 (step @p236 :rule nary_cong :premises (@p228 @p235) :args ((or @t128 (not @t124)))) % 0.35/0.59 (step @p237 :rule cnf_or_neg :args (@t128 2)) % 0.35/0.59 (step @p238 :rule eq_resolve :premises (@p237 @p236)) % 0.35/0.59 (step @p239 :rule reordering :premises (@p238) :args ((or @t123 @t128))) % 0.35/0.59 (step @p240 :rule chain_m_resolution :premises (@p239 @p226) :args (@t123 @t134 @t135)) % 0.35/0.59 (step @p241 :rule cnf_or_pos :args (@t137)) % 0.35/0.59 (step @p242 :rule reordering :premises (@p241) :args ((or @t124 @t136 (not @t137)))) % 0.35/0.59 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p234) :args (@t136 @t138 (@list @t123 @t137))) % 0.35/0.59 (step @p244 :rule cnf_or_neg :args (@t128 0)) % 0.35/0.59 (step @p245 :rule chain_m_resolution :premises (@p244 @p226) :args ((not @t127) @t134 @t135)) % 0.35/0.59 (step @p246 :rule cnf_or_pos :args (@t141)) % 0.35/0.59 (step @p247 :rule reordering :premises (@p246) :args ((or @t127 @t139 @t140 (not @t141)))) % 0.35/0.59 (step @p248 :rule chain_m_resolution :premises (@p247 @p245 @p243 @p201) :args (@t140 (@list true false false) (@list @t127 @t136 @t141))) % 0.35/0.59 (step @p249 :rule skolemize :premises (@p248)) % 0.35/0.59 (step @p250 :rule cnf_or_neg :args (@t144 1)) % 0.35/0.59 (step @p251 :rule chain_m_resolution :premises (@p250 @p249) :args ((not @t66) @t134 @t145)) % 0.35/0.59 (step @p252 :rule bool-double-not-elim :args (@t64)) % 0.35/0.59 (step @p253 :rule refl :args (@t66)) % 0.35/0.59 (step @p254 :rule refl :args (@t146)) % 0.35/0.59 (step @p255 :rule nary_cong :premises (@p254 @p253 @p252) :args ((or @t146 @t66 (not @t65)))) % 0.35/0.59 (step @p256 :rule cnf_equiv_pos2 :args (@t69)) % 0.35/0.59 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 0.35/0.59 (step @p258 :rule reordering :premises (@p257) :args ((or @t66 @t64 @t146))) % 0.35/0.59 (step @p259 :rule chain_m_resolution :premises (@p258 @p251 @p31) :args (@t64 @t147 (@list @t66 @t69))) % 0.35/0.59 (step @p260 :rule alpha_equiv :args (@t125 (@list @t2) (@list @t5))) % 0.35/0.59 (step @p261 :rule equiv_elim1 :premises (@p260)) % 0.35/0.59 (step @p262 :rule chain_m_resolution :premises (@p261 @p233) :args (@t148 @t70 (@list @t125))) % 0.35/0.59 (step @p263 :rule bool-double-not-elim :args (@t142)) % 0.35/0.59 (step @p264 :rule refl :args (@t144)) % 0.35/0.59 (step @p265 :rule nary_cong :premises (@p264 @p263) :args ((or @t144 (not @t143)))) % 0.35/0.59 (step @p266 :rule cnf_or_neg :args (@t144 0)) % 0.35/0.59 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 0.35/0.59 (step @p268 :rule reordering :premises (@p267) :args ((or @t142 @t144))) % 0.35/0.59 (step @p269 :rule chain_m_resolution :premises (@p268 @p249) :args (@t142 @t134 @t145)) % 0.35/0.59 (step @p270 :rule cnf_or_pos :args (@t150)) % 0.35/0.59 (step @p271 :rule reordering :premises (@p270) :args ((or @t143 @t149 @t151))) % 0.35/0.59 (step @p272 :rule chain_m_resolution :premises (@p271 @p269 @p262) :args (@t151 @t138 (@list @t142 @t148))) % 0.35/0.59 (assume-push @p283 @t64) % 0.35/0.59 (step @p274 :rule instantiate :premises (@p259) :args ((@list @t61))) % 0.35/0.59 (step-pop @p284 :rule scope :premises (@p274)) % 0.35/0.59 (step @p275 :rule process_scope :premises (@p284) :args (@t150)) % 0.35/0.59 (step @p277 :rule implies_elim :premises (@p275)) % 0.35/0.59 (step @p278 false :rule chain_m_resolution :premises (@p277 @p272 @p259) :args (false @t147 (@list @t150 @t64))) % 0.35/0.59 ) % 0.35/0.59 % SZS output end Proof % 0.35/0.59 % cvc5 exiting %------------------------------------------------------------------------------