%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO331^5 : 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 : n006.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 09:12:26 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO331^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n006.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 : Wed Jun 3 00:03:34 EDT 2026 % 0.18/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort tptp.a 0) % 0.37/0.61 (declare-const tptp.cK (-> (-> tptp.a Bool) tptp.a Bool)) % 0.37/0.61 (define @t1 () (@var "Xx" tptp.a)) % 0.37/0.61 (define @t2 () (@var "Xx0" tptp.a)) % 0.37/0.61 (define @t3 () (@var "S" (-> tptp.a Bool))) % 0.37/0.61 (define @t4 () (_ @t3 @t2)) % 0.37/0.61 (define @t5 () (@var "Xx1" tptp.a)) % 0.37/0.61 (define @t6 () (_ tptp.cK @t3)) % 0.37/0.61 (define @t7 () (_ @t6 @t5)) % 0.37/0.61 (define @t8 () (_ @t3 @t5)) % 0.37/0.61 (define @t9 () (@list @t5)) % 0.37/0.61 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.37/0.61 (define @t11 () (and @t10 @t4)) % 0.37/0.61 (define @t12 () (@list @t3)) % 0.37/0.61 (define @t13 () (exists @t12 @t11)) % 0.37/0.61 (define @t14 () (@list @t2)) % 0.37/0.61 (define @t15 () (lambda @t14 @t13)) % 0.37/0.61 (define @t16 () (_ (_ tptp.cK @t15) @t1)) % 0.37/0.61 (define @t17 () (_ @t3 @t1)) % 0.37/0.61 (define @t18 () (_ @t6 @t2)) % 0.37/0.61 (define @t19 () (forall @t14 (=> @t4 @t18))) % 0.37/0.61 (define @t20 () (and @t19 @t17)) % 0.37/0.61 (define @t21 () (exists @t12 @t20)) % 0.37/0.61 (define @t22 () (=> @t21 @t16)) % 0.37/0.61 (define @t23 () (@list @t1)) % 0.37/0.61 (define @t24 () (forall @t23 @t22)) % 0.37/0.61 (define @t25 () (@var "X" (-> tptp.a Bool))) % 0.37/0.61 (define @t26 () (_ (_ tptp.cK @t25) @t1)) % 0.37/0.61 (define @t27 () (=> @t26 @t16)) % 0.37/0.61 (define @t28 () (forall @t23 @t27)) % 0.37/0.61 (define @t29 () (_ @t25 @t1)) % 0.37/0.61 (define @t30 () (=> @t29 @t21)) % 0.37/0.61 (define @t31 () (forall @t23 @t30)) % 0.37/0.61 (define @t32 () (=> @t31 @t28)) % 0.37/0.61 (define @t33 () (@list @t25)) % 0.37/0.61 (define @t34 () (forall @t33 @t32)) % 0.37/0.61 (define @t35 () (=> @t34 @t24)) % 0.37/0.61 (define @t36 () (not @t35)) % 0.37/0.61 (define @t37 () (@var "BOUND_VARIABLE_7535" (-> tptp.a Bool))) % 0.37/0.61 (define @t38 () (not (_ @t37 @t1))) % 0.37/0.61 (define @t39 () (not (forall @t14 (or (not (_ @t37 @t2)) (tptp.cK @t37 @t2))))) % 0.37/0.61 (define @t40 () (_ @t3 @t2)) % 0.37/0.61 (define @t41 () (not @t40)) % 0.37/0.61 (define @t42 () (tptp.cK @t3 @t5)) % 0.37/0.61 (define @t43 () (_ @t3 @t5)) % 0.37/0.61 (define @t44 () (not @t43)) % 0.37/0.61 (define @t45 () (or @t44 @t42)) % 0.37/0.61 (define @t46 () (forall @t9 @t45)) % 0.37/0.61 (define @t47 () (not @t46)) % 0.37/0.61 (define @t48 () (or @t47 @t41)) % 0.37/0.61 (define @t49 () (forall @t12 @t48)) % 0.37/0.61 (define @t50 () (not @t49)) % 0.37/0.61 (define @t51 () (lambda @t14 @t50)) % 0.37/0.61 (define @t52 () (tptp.cK @t51 @t1)) % 0.37/0.61 (define @t53 () (or @t52 @t39 @t38)) % 0.37/0.61 (define @t54 () (or @t39 @t38)) % 0.37/0.61 (define @t55 () (or @t54 @t52)) % 0.37/0.61 (define @t56 () (@list @t1 @t37)) % 0.37/0.61 (define @t57 () (forall @t56 @t55)) % 0.37/0.61 (define @t58 () (@list @t37)) % 0.37/0.61 (define @t59 () (forall @t58 @t55)) % 0.37/0.61 (define @t60 () (forall @t58 @t54)) % 0.37/0.61 (define @t61 () (or @t60 @t52)) % 0.37/0.61 (define @t62 () (_ @t3 @t1)) % 0.37/0.61 (define @t63 () (tptp.cK @t3 @t2)) % 0.37/0.61 (define @t64 () (forall @t14 (or @t41 @t63))) % 0.37/0.61 (define @t65 () (not @t64)) % 0.37/0.61 (define @t66 () (forall @t12 (or @t65 (not @t62)))) % 0.37/0.61 (define @t67 () (not @t4)) % 0.37/0.61 (define @t68 () (not @t8)) % 0.37/0.61 (define @t69 () (or @t68 @t7)) % 0.37/0.61 (define @t70 () (forall @t9 @t69)) % 0.37/0.61 (define @t71 () (lambda @t14 (not (forall @t12 (or (not @t70) @t67))))) % 0.37/0.61 (define @t72 () (_ (_ tptp.cK @t51) @t1)) % 0.37/0.61 (define @t73 () (or @t66 @t72)) % 0.37/0.61 (define @t74 () (not @t66)) % 0.37/0.61 (define @t75 () (or @t47 @t67)) % 0.37/0.61 (define @t76 () (and @t46 @t4)) % 0.37/0.61 (define @t77 () (forall @t12 (not @t76))) % 0.37/0.61 (define @t78 () (not @t77)) % 0.37/0.61 (define @t79 () (not @t17)) % 0.37/0.61 (define @t80 () (or @t65 @t79)) % 0.37/0.61 (define @t81 () (and @t64 @t17)) % 0.37/0.61 (define @t82 () (forall @t12 (not @t81))) % 0.37/0.61 (define @t83 () (not @t82)) % 0.37/0.61 (define @t84 () (or @t67 @t18)) % 0.37/0.61 (define @t85 () (@var "BOUND_VARIABLE_7518" tptp.a)) % 0.37/0.61 (define @t86 () (tptp.cK @t51 @t85)) % 0.37/0.61 (define @t87 () (not (tptp.cK @t25 @t85))) % 0.37/0.61 (define @t88 () (_ @t25 @t1)) % 0.37/0.61 (define @t89 () (forall @t23 (or (not @t88) @t74))) % 0.37/0.61 (define @t90 () (not @t89)) % 0.37/0.61 (define @t91 () (or @t90 @t87 @t86)) % 0.37/0.61 (define @t92 () (or @t87 @t86)) % 0.37/0.61 (define @t93 () (or @t90 @t92)) % 0.37/0.61 (define @t94 () (@list @t25 @t85)) % 0.37/0.61 (define @t95 () (forall @t94 @t93)) % 0.37/0.61 (define @t96 () (@list @t85)) % 0.37/0.61 (define @t97 () (forall @t96 @t93)) % 0.37/0.61 (define @t98 () (forall @t96 @t92)) % 0.37/0.61 (define @t99 () (or @t90 @t98)) % 0.37/0.61 (define @t100 () (tptp.cK @t25 @t1)) % 0.37/0.61 (define @t101 () (forall @t23 (or (not @t100) @t52))) % 0.37/0.61 (define @t102 () (not @t26)) % 0.37/0.61 (define @t103 () (or @t102 @t72)) % 0.37/0.61 (define @t104 () (not @t29)) % 0.37/0.61 (define @t105 () (or @t104 @t74)) % 0.37/0.61 (define @t106 () (forall @t56 @t53)) % 0.37/0.61 (define @t107 () (@quantifiers_skolemize @t106 0)) % 0.37/0.61 (define @t108 () (@purify @t51)) % 0.37/0.61 (define @t109 () (tptp.cK @t51 @t107)) % 0.37/0.61 (define @t110 () (@quantifiers_skolemize @t106 1)) % 0.37/0.61 (define @t111 () (tptp.cK @t110 @t107)) % 0.37/0.61 (define @t112 () (not @t111)) % 0.37/0.61 (define @t113 () (forall @t23 (or (not (_ @t110 @t1)) @t74))) % 0.37/0.61 (define @t114 () (not @t113)) % 0.37/0.61 (define @t115 () (or @t114 @t112 @t109)) % 0.37/0.61 (define @t116 () (forall @t94 @t91)) % 0.37/0.61 (define @t117 () (tptp.cK @t108 @t107)) % 0.37/0.61 (define @t118 () (or @t114 @t112 @t117)) % 0.37/0.61 (define @t119 () (_ @t110 @t107)) % 0.37/0.61 (define @t120 () (not @t119)) % 0.37/0.61 (define @t121 () (forall @t14 (or (not (_ @t110 @t2)) (tptp.cK @t110 @t2)))) % 0.37/0.61 (define @t122 () (not @t121)) % 0.37/0.61 (define @t123 () (or @t117 @t122 @t120)) % 0.37/0.61 (define @t124 () (not @t123)) % 0.37/0.61 (define @t125 () (not @t106)) % 0.37/0.61 (define @t126 () (or @t109 @t122 @t120)) % 0.37/0.61 (define @t127 () (not @t126)) % 0.37/0.61 (define @t128 () (@list true)) % 0.37/0.61 (define @t129 () (@list @t123)) % 0.37/0.61 (define @t130 () (or @t120 @t111)) % 0.37/0.61 (define @t131 () (@list false false)) % 0.37/0.61 (define @t132 () (@quantifiers_skolemize @t113 0)) % 0.37/0.61 (define @t133 () (forall @t12 (or @t65 (not (_ @t3 @t132))))) % 0.37/0.61 (define @t134 () (not @t133)) % 0.37/0.61 (define @t135 () (_ @t110 @t132)) % 0.37/0.61 (define @t136 () (not @t135)) % 0.37/0.61 (define @t137 () (or @t136 @t134)) % 0.37/0.61 (define @t138 () (@list @t137)) % 0.37/0.61 (define @t139 () (or @t122 @t136)) % 0.37/0.61 (define @t140 () (not @t139)) % 0.37/0.61 (assume @p1 @t36) % 0.37/0.61 (assume @p2 true) % 0.37/0.61 (step @p3 :rule aci_norm :args ((= @t55 @t53))) % 0.37/0.61 (step @p4 :rule cong :premises (@p3) :args (@t57)) % 0.37/0.61 (step @p5 :rule quant-merge-prenex :args ((= (forall @t23 @t59) @t57))) % 0.37/0.61 (step @p6 :rule refl :args (@t52)) % 0.37/0.61 (step @p7 :rule alpha_equiv :args (@t60 (@list @t37) (@list @t3))) % 0.37/0.61 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t61)) % 0.37/0.61 (step @p9 :rule quant-miniscope-or :args ((= @t59 @t61))) % 0.37/0.61 (step @p10 :rule trans :premises (@p9 @p8)) % 0.37/0.61 (step @p11 :rule symm :premises (@p10)) % 0.37/0.61 (step @p12 :rule cong :premises (@p11) :args ((forall @t23 (or @t66 @t52)))) % 0.37/0.61 (step @p13 :rule trans :premises (@p12 @p5)) % 0.37/0.61 (step @p14 :rule trans :premises (@p13 @p4)) % 0.37/0.61 (step @p15 :rule refl :args ((tptp.cK @t71 @t1))) % 0.37/0.61 (step @p16 :rule refl :args (@t1)) % 0.37/0.61 (step @p17 :rule refl :args (@t40)) % 0.37/0.61 (step @p18 :rule cong :premises (@p17) :args (@t41)) % 0.37/0.61 (step @p19 :rule refl :args (@t42)) % 0.37/0.61 (step @p20 :rule refl :args (@t43)) % 0.37/0.61 (step @p21 :rule cong :premises (@p20) :args (@t44)) % 0.37/0.61 (step @p22 :rule nary_cong :premises (@p21 @p19) :args (@t45)) % 0.37/0.61 (step @p23 :rule cong :premises (@p22) :args (@t46)) % 0.37/0.61 (step @p24 :rule cong :premises (@p23) :args (@t47)) % 0.37/0.61 (step @p25 :rule nary_cong :premises (@p24 @p18) :args (@t48)) % 0.37/0.61 (step @p26 :rule cong :premises (@p25) :args (@t49)) % 0.37/0.61 (step @p27 :rule cong :premises (@p26) :args (@t50)) % 0.37/0.61 (step @p28 :rule cong :premises (@p27) :args (@t51)) % 0.37/0.61 (step @p29 :rule cong :premises (@p28 @p16) :args (@t52)) % 0.37/0.61 (step @p30 :rule trans :premises (@p29 @p15)) % 0.37/0.61 (step @p31 :rule refl :args (tptp.cK)) % 0.37/0.61 (step @p32 :rule ho_cong :premises (@p31 @p28)) % 0.37/0.61 (step @p33 :rule ho_cong :premises (@p32 @p16)) % 0.37/0.61 (step @p34 :rule cong :premises (@p33 @p30) :args ((= @t72 @t52))) % 0.37/0.61 (step @p35 :rule symm :premises (@p34)) % 0.37/0.61 (step @p36 :rule refl :args ((_ (_ tptp.cK @t71) @t1))) % 0.37/0.61 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.37/0.61 (step @p38 :rule refl :args (@t66)) % 0.37/0.61 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t73)) % 0.37/0.61 (step @p40 :rule cong :premises (@p39) :args ((forall @t23 @t73))) % 0.37/0.61 (step @p41 :rule trans :premises (@p40 @p14)) % 0.37/0.61 (step @p42 :rule refl :args (@t72)) % 0.37/0.61 (step @p43 :rule bool-double-not-elim :args (@t66)) % 0.37/0.61 (step @p44 :rule nary_cong :premises (@p43 @p42) :args ((or (not @t74) @t72))) % 0.37/0.61 (step @p45 :rule bool-impl-elim :args (@t74 @t72)) % 0.37/0.61 (step @p46 :rule trans :premises (@p45 @p44)) % 0.37/0.61 (step @p47 :rule cong :premises (@p46) :args ((forall @t23 (=> @t74 @t72)))) % 0.37/0.61 (step @p48 :rule trans :premises (@p47 @p41)) % 0.37/0.61 (step @p49 :rule refl :args (@t1)) % 0.37/0.61 (step @p50 :rule refl :args (@t4)) % 0.37/0.61 (step @p51 :rule cong :premises (@p50 @p17) :args ((= @t4 @t40))) % 0.37/0.61 (step @p52 :rule symm :premises (@p51)) % 0.37/0.61 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.37/0.61 (step @p54 :rule cong :premises (@p53) :args (@t67)) % 0.37/0.61 (step @p55 :rule refl :args (@t47)) % 0.37/0.61 (step @p56 :rule nary_cong :premises (@p55 @p54) :args (@t75)) % 0.37/0.61 (step @p57 :rule cong :premises (@p56) :args ((forall @t12 @t75))) % 0.37/0.61 (step @p58 :rule bool-and-de-morgan :args (@t46 @t4 true)) % 0.37/0.61 (step @p59 :rule cong :premises (@p58) :args (@t77)) % 0.37/0.61 (step @p60 :rule trans :premises (@p59 @p57)) % 0.37/0.61 (step @p61 :rule cong :premises (@p60) :args (@t78)) % 0.37/0.61 (step @p62 :rule exists-elim :args ((= (exists @t12 @t76) @t78))) % 0.37/0.61 (step @p63 :rule trans :premises (@p62 @p61)) % 0.37/0.61 (step @p64 :rule refl :args (@t4)) % 0.37/0.61 (step @p65 :rule refl :args (@t7)) % 0.37/0.61 (step @p66 :rule cong :premises (@p65 @p19) :args ((= @t7 @t42))) % 0.37/0.61 (step @p67 :rule symm :premises (@p66)) % 0.37/0.61 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.37/0.61 (step @p69 :rule refl :args (@t8)) % 0.37/0.61 (step @p70 :rule cong :premises (@p69 @p20) :args ((= @t8 @t43))) % 0.37/0.61 (step @p71 :rule symm :premises (@p70)) % 0.37/0.61 (step @p72 :rule eq_resolve :premises (@p69 @p71)) % 0.37/0.61 (step @p73 :rule cong :premises (@p72) :args (@t68)) % 0.37/0.61 (step @p74 :rule nary_cong :premises (@p73 @p68) :args (@t69)) % 0.37/0.61 (step @p75 :rule cong :premises (@p74) :args (@t70)) % 0.37/0.61 (step @p76 :rule bool-impl-elim :args (@t8 @t7)) % 0.37/0.61 (step @p77 :rule cong :premises (@p76) :args (@t10)) % 0.37/0.61 (step @p78 :rule trans :premises (@p77 @p75)) % 0.37/0.61 (step @p79 :rule nary_cong :premises (@p78 @p64) :args (@t11)) % 0.37/0.61 (step @p80 :rule cong :premises (@p79) :args (@t13)) % 0.37/0.61 (step @p81 :rule trans :premises (@p80 @p63)) % 0.37/0.61 (step @p82 :rule cong :premises (@p81) :args (@t15)) % 0.37/0.61 (step @p83 :rule refl :args (tptp.cK)) % 0.37/0.61 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.37/0.61 (step @p85 :rule ho_cong :premises (@p84 @p49)) % 0.37/0.61 (step @p86 :rule refl :args (@t62)) % 0.37/0.61 (step @p87 :rule refl :args (@t17)) % 0.37/0.61 (step @p88 :rule cong :premises (@p87 @p86) :args ((= @t17 @t62))) % 0.37/0.61 (step @p89 :rule symm :premises (@p88)) % 0.37/0.61 (step @p90 :rule eq_resolve :premises (@p87 @p89)) % 0.37/0.61 (step @p91 :rule cong :premises (@p90) :args (@t79)) % 0.37/0.61 (step @p92 :rule refl :args (@t65)) % 0.37/0.61 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t80)) % 0.37/0.61 (step @p94 :rule cong :premises (@p93) :args ((forall @t12 @t80))) % 0.37/0.61 (step @p95 :rule bool-and-de-morgan :args (@t64 @t17 true)) % 0.37/0.61 (step @p96 :rule cong :premises (@p95) :args (@t82)) % 0.37/0.61 (step @p97 :rule trans :premises (@p96 @p94)) % 0.37/0.61 (step @p98 :rule cong :premises (@p97) :args (@t83)) % 0.37/0.61 (step @p99 :rule exists-elim :args ((= (exists @t12 @t81) @t83))) % 0.37/0.61 (step @p100 :rule trans :premises (@p99 @p98)) % 0.37/0.61 (step @p101 :rule refl :args (@t17)) % 0.37/0.61 (step @p102 :rule refl :args (@t63)) % 0.37/0.61 (step @p103 :rule refl :args (@t18)) % 0.37/0.61 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t18 @t63))) % 0.37/0.61 (step @p105 :rule symm :premises (@p104)) % 0.37/0.61 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.37/0.61 (step @p107 :rule nary_cong :premises (@p54 @p106) :args (@t84)) % 0.37/0.61 (step @p108 :rule cong :premises (@p107) :args ((forall @t14 @t84))) % 0.37/0.61 (step @p109 :rule bool-impl-elim :args (@t4 @t18)) % 0.37/0.61 (step @p110 :rule cong :premises (@p109) :args (@t19)) % 0.37/0.61 (step @p111 :rule trans :premises (@p110 @p108)) % 0.37/0.61 (step @p112 :rule nary_cong :premises (@p111 @p101) :args (@t20)) % 0.37/0.61 (step @p113 :rule cong :premises (@p112) :args (@t21)) % 0.37/0.61 (step @p114 :rule trans :premises (@p113 @p100)) % 0.37/0.61 (step @p115 :rule cong :premises (@p114 @p85) :args (@t22)) % 0.37/0.61 (step @p116 :rule cong :premises (@p115) :args (@t24)) % 0.37/0.61 (step @p117 :rule trans :premises (@p116 @p48)) % 0.37/0.61 (step @p118 :rule aci_norm :args ((= @t93 @t91))) % 0.37/0.61 (step @p119 :rule cong :premises (@p118) :args (@t95)) % 0.37/0.61 (step @p120 :rule quant-merge-prenex :args ((= (forall @t33 @t97) @t95))) % 0.37/0.61 (step @p121 :rule alpha_equiv :args (@t98 (@list @t85) (@list @t1))) % 0.37/0.61 (step @p122 :rule refl :args (@t90)) % 0.37/0.61 (step @p123 :rule nary_cong :premises (@p122 @p121) :args (@t99)) % 0.37/0.61 (step @p124 :rule quant-miniscope-or :args ((= @t97 @t99))) % 0.37/0.61 (step @p125 :rule trans :premises (@p124 @p123)) % 0.37/0.61 (step @p126 :rule symm :premises (@p125)) % 0.37/0.61 (step @p127 :rule cong :premises (@p126) :args ((forall @t33 (or @t90 @t101)))) % 0.37/0.61 (step @p128 :rule trans :premises (@p127 @p120)) % 0.37/0.61 (step @p129 :rule trans :premises (@p128 @p119)) % 0.37/0.61 (step @p130 :rule bool-impl-elim :args (@t89 @t101)) % 0.37/0.61 (step @p131 :rule cong :premises (@p130) :args ((forall @t33 (=> @t89 @t101)))) % 0.37/0.61 (step @p132 :rule trans :premises (@p131 @p129)) % 0.37/0.61 (step @p133 :rule refl :args (@t100)) % 0.37/0.61 (step @p134 :rule refl :args (@t26)) % 0.37/0.61 (step @p135 :rule cong :premises (@p134 @p133) :args ((= @t26 @t100))) % 0.37/0.61 (step @p136 :rule symm :premises (@p135)) % 0.37/0.61 (step @p137 :rule eq_resolve :premises (@p134 @p136)) % 0.37/0.61 (step @p138 :rule cong :premises (@p137) :args (@t102)) % 0.37/0.61 (step @p139 :rule nary_cong :premises (@p138 @p37) :args (@t103)) % 0.37/0.61 (step @p140 :rule cong :premises (@p139) :args ((forall @t23 @t103))) % 0.37/0.61 (step @p141 :rule bool-impl-elim :args (@t26 @t72)) % 0.37/0.61 (step @p142 :rule cong :premises (@p141) :args ((forall @t23 (=> @t26 @t72)))) % 0.37/0.61 (step @p143 :rule trans :premises (@p142 @p140)) % 0.37/0.61 (step @p144 :rule refl :args (@t26)) % 0.37/0.61 (step @p145 :rule cong :premises (@p144 @p85) :args (@t27)) % 0.37/0.61 (step @p146 :rule cong :premises (@p145) :args (@t28)) % 0.37/0.61 (step @p147 :rule trans :premises (@p146 @p143)) % 0.37/0.61 (step @p148 :rule refl :args (@t74)) % 0.37/0.61 (step @p149 :rule refl :args (@t88)) % 0.37/0.61 (step @p150 :rule refl :args (@t29)) % 0.37/0.61 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t29 @t88))) % 0.37/0.61 (step @p152 :rule symm :premises (@p151)) % 0.37/0.61 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.37/0.61 (step @p154 :rule cong :premises (@p153) :args (@t104)) % 0.37/0.61 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t105)) % 0.37/0.61 (step @p156 :rule cong :premises (@p155) :args ((forall @t23 @t105))) % 0.37/0.61 (step @p157 :rule bool-impl-elim :args (@t29 @t74)) % 0.37/0.61 (step @p158 :rule cong :premises (@p157) :args ((forall @t23 (=> @t29 @t74)))) % 0.37/0.61 (step @p159 :rule trans :premises (@p158 @p156)) % 0.37/0.61 (step @p160 :rule refl :args (@t29)) % 0.37/0.61 (step @p161 :rule cong :premises (@p160 @p114) :args (@t30)) % 0.37/0.61 (step @p162 :rule cong :premises (@p161) :args (@t31)) % 0.37/0.61 (step @p163 :rule trans :premises (@p162 @p159)) % 0.37/0.61 (step @p164 :rule cong :premises (@p163 @p147) :args (@t32)) % 0.37/0.61 (step @p165 :rule cong :premises (@p164) :args (@t34)) % 0.37/0.61 (step @p166 :rule trans :premises (@p165 @p132)) % 0.37/0.61 (step @p167 :rule cong :premises (@p166 @p117) :args (@t35)) % 0.37/0.61 (step @p168 :rule cong :premises (@p167) :args (@t36)) % 0.37/0.61 (step @p169 :rule eq_resolve :premises (@p1 @p168)) % 0.37/0.61 (step @p170 :rule not_implies_elim1 :premises (@p169)) % 0.37/0.61 (step @p171 :rule refl :args (@t107)) % 0.37/0.61 (step @p172 :rule eq-refl :args (@t51)) % 0.37/0.61 (step @p173 :rule skolem_intro :args (@t108)) % 0.37/0.61 (step @p174 :rule refl :args (@t51)) % 0.37/0.61 (step @p175 :rule cong :premises (@p174 @p173) :args ((= @t51 @t108))) % 0.37/0.61 (step @p176 :rule trans :premises (@p175 @p172)) % 0.37/0.61 (step @p177 :rule true_elim :premises (@p176)) % 0.37/0.61 (step @p178 :rule cong :premises (@p177 @p171) :args (@t109)) % 0.37/0.61 (step @p179 :rule refl :args (@t112)) % 0.37/0.61 (step @p180 :rule refl :args (@t114)) % 0.37/0.61 (step @p181 :rule nary_cong :premises (@p180 @p179 @p178) :args (@t115)) % 0.37/0.61 (step @p182 :rule refl :args (@t116)) % 0.37/0.61 (step @p183 :rule cong :premises (@p182 @p181) :args ((=> @t116 @t115))) % 0.37/0.61 (assume-push @p254 @t116) % 0.37/0.61 (step @p185 :rule instantiate :premises (@p170) :args ((@list @t110 @t107))) % 0.37/0.61 (step-pop @p255 :rule scope :premises (@p185)) % 0.37/0.61 (step @p186 :rule process_scope :premises (@p255) :args (@t115)) % 0.37/0.61 (step @p188 :rule eq_resolve :premises (@p186 @p183)) % 0.37/0.61 (step @p189 :rule implies_elim :premises (@p188)) % 0.37/0.61 (step @p190 :rule chain_m_resolution :premises (@p189 @p170) :args (@t118 (@list false) (@list @t116))) % 0.37/0.61 (step @p191 :rule not_implies_elim2 :premises (@p169)) % 0.37/0.61 (step @p192 :rule refl :args (@t124)) % 0.37/0.61 (step @p193 :rule bool-double-not-elim :args (@t106)) % 0.37/0.61 (step @p194 :rule nary_cong :premises (@p193 @p192) :args ((or (not @t125) @t124))) % 0.37/0.61 (step @p195 :rule refl :args (@t120)) % 0.37/0.61 (step @p196 :rule refl :args (@t122)) % 0.37/0.61 (step @p197 :rule nary_cong :premises (@p178 @p196 @p195) :args (@t126)) % 0.37/0.61 (step @p198 :rule cong :premises (@p197) :args (@t127)) % 0.37/0.61 (step @p199 :rule refl :args (@t125)) % 0.37/0.61 (step @p200 :rule cong :premises (@p199 @p198) :args ((=> @t125 @t127))) % 0.37/0.61 (assume-push @p256 @t125) % 0.37/0.61 (step @p202 :rule skolemize :premises (@p191)) % 0.37/0.61 (step-pop @p257 :rule scope :premises (@p202)) % 0.37/0.61 (step @p203 :rule process_scope :premises (@p257) :args (@t127)) % 0.37/0.61 (step @p205 :rule eq_resolve :premises (@p203 @p200)) % 0.37/0.61 (step @p206 :rule implies_elim :premises (@p205)) % 0.37/0.61 (step @p207 :rule eq_resolve :premises (@p206 @p194)) % 0.37/0.61 (step @p208 :rule chain_m_resolution :premises (@p207 @p191) :args (@t124 @t128 (@list @t106))) % 0.37/0.61 (step @p209 :rule bool-double-not-elim :args (@t121)) % 0.37/0.61 (step @p210 :rule refl :args (@t123)) % 0.37/0.61 (step @p211 :rule nary_cong :premises (@p210 @p209) :args ((or @t123 (not @t122)))) % 0.37/0.61 (step @p212 :rule cnf_or_neg :args (@t123 1)) % 0.37/0.61 (step @p213 :rule eq_resolve :premises (@p212 @p211)) % 0.37/0.61 (step @p214 :rule reordering :premises (@p213) :args ((or @t121 @t123))) % 0.37/0.61 (step @p215 :rule chain_m_resolution :premises (@p214 @p208) :args (@t121 @t128 @t129)) % 0.37/0.61 (step @p216 :rule instantiate :premises (@p215) :args ((@list @t107))) % 0.37/0.61 (step @p217 :rule bool-double-not-elim :args (@t119)) % 0.37/0.61 (step @p218 :rule nary_cong :premises (@p210 @p217) :args ((or @t123 (not @t120)))) % 0.37/0.61 (step @p219 :rule cnf_or_neg :args (@t123 2)) % 0.37/0.61 (step @p220 :rule eq_resolve :premises (@p219 @p218)) % 0.37/0.61 (step @p221 :rule reordering :premises (@p220) :args ((or @t119 @t123))) % 0.37/0.61 (step @p222 :rule chain_m_resolution :premises (@p221 @p208) :args (@t119 @t128 @t129)) % 0.37/0.61 (step @p223 :rule cnf_or_pos :args (@t130)) % 0.37/0.61 (step @p224 :rule reordering :premises (@p223) :args ((or @t120 @t111 (not @t130)))) % 0.37/0.61 (step @p225 :rule chain_m_resolution :premises (@p224 @p222 @p216) :args (@t111 @t131 (@list @t119 @t130))) % 0.37/0.61 (step @p226 :rule cnf_or_neg :args (@t123 0)) % 0.37/0.61 (step @p227 :rule chain_m_resolution :premises (@p226 @p208) :args ((not @t117) @t128 @t129)) % 0.37/0.61 (step @p228 :rule cnf_or_pos :args (@t118)) % 0.37/0.61 (step @p229 :rule reordering :premises (@p228) :args ((or @t117 @t112 @t114 (not @t118)))) % 0.37/0.61 (step @p230 :rule chain_m_resolution :premises (@p229 @p227 @p225 @p190) :args (@t114 (@list true false false) (@list @t117 @t111 @t118))) % 0.37/0.61 (step @p231 :rule skolemize :premises (@p230)) % 0.37/0.61 (step @p232 :rule bool-double-not-elim :args (@t133)) % 0.37/0.61 (step @p233 :rule refl :args (@t137)) % 0.37/0.61 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t137 (not @t134)))) % 0.37/0.61 (step @p235 :rule cnf_or_neg :args (@t137 1)) % 0.37/0.61 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.37/0.61 (step @p237 :rule reordering :premises (@p236) :args ((or @t133 @t137))) % 0.37/0.61 (step @p238 :rule chain_m_resolution :premises (@p237 @p231) :args (@t133 @t128 @t138)) % 0.37/0.61 (step @p239 :rule bool-double-not-elim :args (@t135)) % 0.37/0.61 (step @p240 :rule nary_cong :premises (@p233 @p239) :args ((or @t137 (not @t136)))) % 0.37/0.61 (step @p241 :rule cnf_or_neg :args (@t137 0)) % 0.37/0.61 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.37/0.61 (step @p243 :rule reordering :premises (@p242) :args ((or @t135 @t137))) % 0.37/0.61 (step @p244 :rule chain_m_resolution :premises (@p243 @p231) :args (@t135 @t128 @t138)) % 0.37/0.61 (step @p245 :rule cnf_or_pos :args (@t139)) % 0.37/0.61 (step @p246 :rule reordering :premises (@p245) :args ((or @t122 @t136 @t140))) % 0.37/0.61 (step @p247 :rule chain_m_resolution :premises (@p246 @p215 @p244) :args (@t140 @t131 (@list @t121 @t135))) % 0.37/0.61 (assume-push @p258 @t133) % 0.37/0.61 (step @p249 :rule instantiate :premises (@p238) :args ((@list @t110))) % 0.37/0.61 (step-pop @p259 :rule scope :premises (@p249)) % 0.37/0.61 (step @p250 :rule process_scope :premises (@p259) :args (@t139)) % 0.37/0.61 (step @p252 :rule implies_elim :premises (@p250)) % 0.37/0.61 (step @p253 false :rule chain_m_resolution :premises (@p252 @p247 @p238) :args (false (@list true false) (@list @t139 @t133))) % 0.37/0.61 ) % 0.37/0.61 % SZS output end Proof % 0.37/0.61 % cvc5 exiting %------------------------------------------------------------------------------