%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV311^5 : 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 : n029.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 08:55:45 AM UTC 2026 % Result : Theorem 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV311^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n029.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 18:28:47 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.48 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort tptp.a 0) % 0.38/0.58 (declare-const tptp.cF (-> (-> tptp.a Bool) tptp.a Bool)) % 0.38/0.58 (define @t1 () (@var "Xx" tptp.a)) % 0.38/0.58 (define @t2 () (@var "S" (-> tptp.a Bool))) % 0.38/0.58 (define @t3 () (_ @t2 @t1)) % 0.38/0.58 (define @t4 () (@var "Xx0" tptp.a)) % 0.38/0.58 (define @t5 () (_ @t2 @t4)) % 0.38/0.58 (define @t6 () (_ tptp.cF @t2)) % 0.38/0.58 (define @t7 () (_ @t6 @t4)) % 0.38/0.58 (define @t8 () (@list @t4)) % 0.38/0.58 (define @t9 () (forall @t8 (=> @t7 @t5))) % 0.38/0.58 (define @t10 () (=> @t9 @t3)) % 0.38/0.58 (define @t11 () (@list @t2)) % 0.38/0.58 (define @t12 () (forall @t11 @t10)) % 0.38/0.58 (define @t13 () (@var "Xx1" tptp.a)) % 0.38/0.58 (define @t14 () (_ @t2 @t13)) % 0.38/0.58 (define @t15 () (_ @t6 @t13)) % 0.38/0.58 (define @t16 () (@list @t13)) % 0.38/0.58 (define @t17 () (forall @t16 (=> @t15 @t14))) % 0.38/0.58 (define @t18 () (=> @t17 @t5)) % 0.38/0.58 (define @t19 () (forall @t11 @t18)) % 0.38/0.58 (define @t20 () (lambda @t8 @t19)) % 0.38/0.58 (define @t21 () (=> (_ (_ tptp.cF @t20) @t1) @t12)) % 0.38/0.58 (define @t22 () (@list @t1)) % 0.38/0.58 (define @t23 () (forall @t22 @t21)) % 0.38/0.58 (define @t24 () (@var "Y" (-> tptp.a Bool))) % 0.38/0.58 (define @t25 () (_ (_ tptp.cF @t24) @t1)) % 0.38/0.58 (define @t26 () (@var "X" (-> tptp.a Bool))) % 0.38/0.58 (define @t27 () (_ (_ tptp.cF @t26) @t1)) % 0.38/0.58 (define @t28 () (forall @t22 (=> @t27 @t25))) % 0.38/0.58 (define @t29 () (_ @t24 @t1)) % 0.38/0.58 (define @t30 () (_ @t26 @t1)) % 0.38/0.58 (define @t31 () (forall @t22 (=> @t30 @t29))) % 0.38/0.58 (define @t32 () (=> @t31 @t28)) % 0.38/0.58 (define @t33 () (@list @t26 @t24)) % 0.38/0.58 (define @t34 () (forall @t33 @t32)) % 0.38/0.58 (define @t35 () (=> @t34 @t23)) % 0.38/0.58 (define @t36 () (not @t35)) % 0.38/0.58 (define @t37 () (@var "BOUND_VARIABLE_7529" (-> tptp.a Bool))) % 0.38/0.58 (define @t38 () (_ @t37 @t1)) % 0.38/0.58 (define @t39 () (not (forall @t8 (or (not (tptp.cF @t37 @t4)) (_ @t37 @t4))))) % 0.38/0.58 (define @t40 () (_ @t2 @t4)) % 0.38/0.58 (define @t41 () (_ @t2 @t13)) % 0.38/0.58 (define @t42 () (tptp.cF @t2 @t13)) % 0.38/0.58 (define @t43 () (not @t42)) % 0.38/0.58 (define @t44 () (or @t43 @t41)) % 0.38/0.58 (define @t45 () (forall @t16 @t44)) % 0.38/0.58 (define @t46 () (not @t45)) % 0.38/0.58 (define @t47 () (or @t46 @t40)) % 0.38/0.58 (define @t48 () (forall @t11 @t47)) % 0.38/0.58 (define @t49 () (lambda @t8 @t48)) % 0.38/0.58 (define @t50 () (tptp.cF @t49 @t1)) % 0.38/0.58 (define @t51 () (not @t50)) % 0.38/0.58 (define @t52 () (or @t51 @t39 @t38)) % 0.38/0.58 (define @t53 () (or @t39 @t38)) % 0.38/0.58 (define @t54 () (or @t51 @t53)) % 0.38/0.58 (define @t55 () (@list @t1 @t37)) % 0.38/0.58 (define @t56 () (forall @t55 @t54)) % 0.38/0.58 (define @t57 () (@list @t37)) % 0.38/0.58 (define @t58 () (forall @t57 @t54)) % 0.38/0.58 (define @t59 () (forall @t57 @t53)) % 0.38/0.58 (define @t60 () (or @t51 @t59)) % 0.38/0.58 (define @t61 () (_ @t2 @t1)) % 0.38/0.58 (define @t62 () (tptp.cF @t2 @t4)) % 0.38/0.58 (define @t63 () (forall @t8 (or (not @t62) @t40))) % 0.38/0.58 (define @t64 () (not @t63)) % 0.38/0.58 (define @t65 () (forall @t11 (or @t64 @t61))) % 0.38/0.58 (define @t66 () (not @t15)) % 0.38/0.58 (define @t67 () (or @t66 @t14)) % 0.38/0.58 (define @t68 () (forall @t16 @t67)) % 0.38/0.58 (define @t69 () (lambda @t8 (forall @t11 (or (not @t68) @t5)))) % 0.38/0.58 (define @t70 () (_ (_ tptp.cF @t49) @t1)) % 0.38/0.58 (define @t71 () (not @t70)) % 0.38/0.58 (define @t72 () (or @t71 @t65)) % 0.38/0.58 (define @t73 () (or @t64 @t3)) % 0.38/0.58 (define @t74 () (not @t7)) % 0.38/0.58 (define @t75 () (or @t74 @t5)) % 0.38/0.58 (define @t76 () (or @t46 @t5)) % 0.38/0.58 (define @t77 () (@var "BOUND_VARIABLE_7475" tptp.a)) % 0.38/0.58 (define @t78 () (tptp.cF @t24 @t77)) % 0.38/0.58 (define @t79 () (not (tptp.cF @t26 @t77))) % 0.38/0.58 (define @t80 () (_ @t24 @t1)) % 0.38/0.58 (define @t81 () (_ @t26 @t1)) % 0.38/0.58 (define @t82 () (forall @t22 (or (not @t81) @t80))) % 0.38/0.58 (define @t83 () (not @t82)) % 0.38/0.58 (define @t84 () (or @t79 @t78)) % 0.38/0.58 (define @t85 () (or @t83 @t84)) % 0.38/0.58 (define @t86 () (forall (@list @t26 @t24 @t77) @t85)) % 0.38/0.58 (define @t87 () (@list @t77)) % 0.38/0.58 (define @t88 () (forall @t87 @t85)) % 0.38/0.58 (define @t89 () (forall @t87 @t84)) % 0.38/0.58 (define @t90 () (or @t83 @t89)) % 0.38/0.58 (define @t91 () (tptp.cF @t24 @t1)) % 0.38/0.58 (define @t92 () (tptp.cF @t26 @t1)) % 0.38/0.58 (define @t93 () (forall @t22 (or (not @t92) @t91))) % 0.38/0.58 (define @t94 () (not @t27)) % 0.38/0.58 (define @t95 () (or @t94 @t25)) % 0.38/0.58 (define @t96 () (not @t30)) % 0.38/0.58 (define @t97 () (or @t96 @t29)) % 0.38/0.58 (define @t98 () (forall @t55 @t52)) % 0.38/0.58 (define @t99 () (@quantifiers_skolemize @t98 0)) % 0.38/0.58 (define @t100 () (@quantifiers_skolemize @t98 1)) % 0.38/0.58 (define @t101 () (@purify @t49)) % 0.38/0.58 (define @t102 () (_ @t100 @t99)) % 0.38/0.58 (define @t103 () (forall @t8 (or (not (tptp.cF @t100 @t4)) (_ @t100 @t4)))) % 0.38/0.58 (define @t104 () (not @t103)) % 0.38/0.58 (define @t105 () (tptp.cF @t101 @t99)) % 0.38/0.58 (define @t106 () (not @t105)) % 0.38/0.58 (define @t107 () (or @t106 @t104 @t102)) % 0.38/0.58 (define @t108 () (not @t107)) % 0.38/0.58 (define @t109 () (not @t98)) % 0.38/0.58 (define @t110 () (tptp.cF @t49 @t99)) % 0.38/0.58 (define @t111 () (not @t110)) % 0.38/0.58 (define @t112 () (or @t111 @t104 @t102)) % 0.38/0.58 (define @t113 () (not @t112)) % 0.38/0.58 (define @t114 () (@list true)) % 0.38/0.58 (define @t115 () (@list @t107)) % 0.38/0.58 (define @t116 () (tptp.cF @t100 @t99)) % 0.38/0.58 (define @t117 () (not @t116)) % 0.38/0.58 (define @t118 () (or @t117 @t102)) % 0.38/0.58 (define @t119 () (forall @t22 (or (not (_ @t101 @t1)) (_ @t100 @t1)))) % 0.38/0.58 (define @t120 () (not @t119)) % 0.38/0.58 (define @t121 () (or @t120 @t106 @t116)) % 0.38/0.58 (define @t122 () (@quantifiers_skolemize @t119 0)) % 0.38/0.58 (define @t123 () (_ @t100 @t122)) % 0.38/0.58 (define @t124 () (_ @t101 @t122)) % 0.38/0.58 (define @t125 () (not @t124)) % 0.38/0.58 (define @t126 () (or @t125 @t123)) % 0.38/0.58 (define @t127 () (@list @t126)) % 0.38/0.58 (define @t128 () (forall @t16 (or (not (tptp.cF @t100 @t13)) (_ @t100 @t13)))) % 0.38/0.58 (define @t129 () (@list false)) % 0.38/0.58 (define @t130 () (_ @t101 @t4)) % 0.38/0.58 (define @t131 () (_ @t49 @t4)) % 0.38/0.58 (define @t132 () (= @t130 @t131)) % 0.38/0.58 (define @t133 () (forall @t8 @t132)) % 0.38/0.58 (define @t134 () (forall @t11 (or @t46 (_ @t2 @t122)))) % 0.38/0.58 (define @t135 () (forall @t8 (= @t48 @t130))) % 0.38/0.58 (define @t136 () (= @t134 @t124)) % 0.38/0.58 (define @t137 () (= @t124 @t134)) % 0.38/0.58 (define @t138 () (not @t128)) % 0.38/0.58 (define @t139 () (or @t138 @t123)) % 0.38/0.58 (assume @p1 @t36) % 0.38/0.58 (assume @p2 true) % 0.38/0.58 (step @p3 :rule aci_norm :args ((= @t54 @t52))) % 0.38/0.58 (step @p4 :rule cong :premises (@p3) :args (@t56)) % 0.38/0.58 (step @p5 :rule quant-merge-prenex :args ((= (forall @t22 @t58) @t56))) % 0.38/0.58 (step @p6 :rule alpha_equiv :args (@t59 (@list @t37) (@list @t2))) % 0.38/0.58 (step @p7 :rule refl :args (@t51)) % 0.38/0.58 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t60)) % 0.38/0.58 (step @p9 :rule quant-miniscope-or :args ((= @t58 @t60))) % 0.38/0.58 (step @p10 :rule trans :premises (@p9 @p8)) % 0.38/0.58 (step @p11 :rule symm :premises (@p10)) % 0.38/0.58 (step @p12 :rule cong :premises (@p11) :args ((forall @t22 (or @t51 @t65)))) % 0.38/0.58 (step @p13 :rule trans :premises (@p12 @p5)) % 0.38/0.58 (step @p14 :rule trans :premises (@p13 @p4)) % 0.38/0.58 (step @p15 :rule refl :args (@t65)) % 0.38/0.58 (step @p16 :rule refl :args ((tptp.cF @t69 @t1))) % 0.38/0.58 (step @p17 :rule refl :args (@t1)) % 0.38/0.58 (step @p18 :rule refl :args (@t40)) % 0.38/0.58 (step @p19 :rule refl :args (@t41)) % 0.38/0.58 (step @p20 :rule refl :args (@t42)) % 0.38/0.58 (step @p21 :rule cong :premises (@p20) :args (@t43)) % 0.38/0.58 (step @p22 :rule nary_cong :premises (@p21 @p19) :args (@t44)) % 0.38/0.58 (step @p23 :rule cong :premises (@p22) :args (@t45)) % 0.38/0.58 (step @p24 :rule cong :premises (@p23) :args (@t46)) % 0.38/0.58 (step @p25 :rule nary_cong :premises (@p24 @p18) :args (@t47)) % 0.38/0.58 (step @p26 :rule cong :premises (@p25) :args (@t48)) % 0.38/0.58 (step @p27 :rule cong :premises (@p26) :args (@t49)) % 0.38/0.58 (step @p28 :rule cong :premises (@p27 @p17) :args (@t50)) % 0.38/0.58 (step @p29 :rule trans :premises (@p28 @p16)) % 0.38/0.58 (step @p30 :rule refl :args (tptp.cF)) % 0.38/0.58 (step @p31 :rule ho_cong :premises (@p30 @p27)) % 0.38/0.58 (step @p32 :rule ho_cong :premises (@p31 @p17)) % 0.38/0.58 (step @p33 :rule cong :premises (@p32 @p29) :args ((= @t70 @t50))) % 0.38/0.58 (step @p34 :rule symm :premises (@p33)) % 0.38/0.58 (step @p35 :rule refl :args ((_ (_ tptp.cF @t69) @t1))) % 0.38/0.58 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 0.38/0.58 (step @p37 :rule cong :premises (@p36) :args (@t71)) % 0.38/0.58 (step @p38 :rule nary_cong :premises (@p37 @p15) :args (@t72)) % 0.38/0.58 (step @p39 :rule cong :premises (@p38) :args ((forall @t22 @t72))) % 0.38/0.58 (step @p40 :rule trans :premises (@p39 @p14)) % 0.38/0.58 (step @p41 :rule bool-impl-elim :args (@t70 @t65)) % 0.38/0.58 (step @p42 :rule cong :premises (@p41) :args ((forall @t22 (=> @t70 @t65)))) % 0.38/0.58 (step @p43 :rule trans :premises (@p42 @p40)) % 0.38/0.58 (step @p44 :rule refl :args (@t61)) % 0.38/0.58 (step @p45 :rule refl :args (@t3)) % 0.38/0.58 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t3 @t61))) % 0.38/0.58 (step @p47 :rule symm :premises (@p46)) % 0.38/0.58 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.38/0.58 (step @p49 :rule refl :args (@t64)) % 0.38/0.58 (step @p50 :rule nary_cong :premises (@p49 @p48) :args (@t73)) % 0.38/0.58 (step @p51 :rule cong :premises (@p50) :args ((forall @t11 @t73))) % 0.38/0.58 (step @p52 :rule bool-impl-elim :args (@t63 @t3)) % 0.38/0.58 (step @p53 :rule cong :premises (@p52) :args ((forall @t11 (=> @t63 @t3)))) % 0.38/0.58 (step @p54 :rule trans :premises (@p53 @p51)) % 0.38/0.58 (step @p55 :rule refl :args (@t3)) % 0.38/0.58 (step @p56 :rule refl :args (@t5)) % 0.38/0.58 (step @p57 :rule cong :premises (@p56 @p18) :args ((= @t5 @t40))) % 0.38/0.58 (step @p58 :rule symm :premises (@p57)) % 0.38/0.58 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 0.38/0.58 (step @p60 :rule refl :args (@t62)) % 0.38/0.58 (step @p61 :rule refl :args (@t7)) % 0.38/0.58 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t7 @t62))) % 0.38/0.58 (step @p63 :rule symm :premises (@p62)) % 0.38/0.58 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.38/0.58 (step @p65 :rule cong :premises (@p64) :args (@t74)) % 0.38/0.58 (step @p66 :rule nary_cong :premises (@p65 @p59) :args (@t75)) % 0.38/0.58 (step @p67 :rule cong :premises (@p66) :args ((forall @t8 @t75))) % 0.38/0.58 (step @p68 :rule bool-impl-elim :args (@t7 @t5)) % 0.38/0.58 (step @p69 :rule cong :premises (@p68) :args (@t9)) % 0.38/0.58 (step @p70 :rule trans :premises (@p69 @p67)) % 0.38/0.58 (step @p71 :rule cong :premises (@p70 @p55) :args (@t10)) % 0.38/0.58 (step @p72 :rule cong :premises (@p71) :args (@t12)) % 0.38/0.58 (step @p73 :rule trans :premises (@p72 @p54)) % 0.38/0.58 (step @p74 :rule refl :args (@t1)) % 0.38/0.58 (step @p75 :rule refl :args (@t46)) % 0.38/0.58 (step @p76 :rule nary_cong :premises (@p75 @p59) :args (@t76)) % 0.38/0.58 (step @p77 :rule cong :premises (@p76) :args ((forall @t11 @t76))) % 0.38/0.58 (step @p78 :rule bool-impl-elim :args (@t45 @t5)) % 0.38/0.58 (step @p79 :rule cong :premises (@p78) :args ((forall @t11 (=> @t45 @t5)))) % 0.38/0.58 (step @p80 :rule trans :premises (@p79 @p77)) % 0.38/0.58 (step @p81 :rule refl :args (@t5)) % 0.38/0.58 (step @p82 :rule refl :args (@t14)) % 0.38/0.58 (step @p83 :rule cong :premises (@p82 @p19) :args ((= @t14 @t41))) % 0.38/0.58 (step @p84 :rule symm :premises (@p83)) % 0.38/0.58 (step @p85 :rule eq_resolve :premises (@p82 @p84)) % 0.38/0.58 (step @p86 :rule refl :args (@t15)) % 0.38/0.58 (step @p87 :rule cong :premises (@p86 @p20) :args ((= @t15 @t42))) % 0.38/0.58 (step @p88 :rule symm :premises (@p87)) % 0.38/0.58 (step @p89 :rule eq_resolve :premises (@p86 @p88)) % 0.38/0.58 (step @p90 :rule cong :premises (@p89) :args (@t66)) % 0.38/0.58 (step @p91 :rule nary_cong :premises (@p90 @p85) :args (@t67)) % 0.38/0.58 (step @p92 :rule cong :premises (@p91) :args (@t68)) % 0.38/0.58 (step @p93 :rule bool-impl-elim :args (@t15 @t14)) % 0.38/0.58 (step @p94 :rule cong :premises (@p93) :args (@t17)) % 0.38/0.58 (step @p95 :rule trans :premises (@p94 @p92)) % 0.38/0.58 (step @p96 :rule cong :premises (@p95 @p81) :args (@t18)) % 0.38/0.58 (step @p97 :rule cong :premises (@p96) :args (@t19)) % 0.38/0.58 (step @p98 :rule trans :premises (@p97 @p80)) % 0.38/0.58 (step @p99 :rule cong :premises (@p98) :args (@t20)) % 0.38/0.58 (step @p100 :rule refl :args (tptp.cF)) % 0.38/0.58 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.38/0.58 (step @p102 :rule ho_cong :premises (@p101 @p74)) % 0.38/0.58 (step @p103 :rule cong :premises (@p102 @p73) :args (@t21)) % 0.38/0.58 (step @p104 :rule cong :premises (@p103) :args (@t23)) % 0.38/0.58 (step @p105 :rule trans :premises (@p104 @p43)) % 0.38/0.58 (step @p106 :rule aci_norm :args ((= @t85 (or @t83 @t79 @t78)))) % 0.38/0.58 (step @p107 :rule cong :premises (@p106) :args (@t86)) % 0.38/0.58 (step @p108 :rule quant-merge-prenex :args ((= (forall @t33 @t88) @t86))) % 0.38/0.58 (step @p109 :rule alpha_equiv :args (@t89 (@list @t77) (@list @t1))) % 0.38/0.58 (step @p110 :rule refl :args (@t83)) % 0.38/0.58 (step @p111 :rule nary_cong :premises (@p110 @p109) :args (@t90)) % 0.38/0.58 (step @p112 :rule quant-miniscope-or :args ((= @t88 @t90))) % 0.38/0.58 (step @p113 :rule trans :premises (@p112 @p111)) % 0.38/0.58 (step @p114 :rule symm :premises (@p113)) % 0.38/0.58 (step @p115 :rule cong :premises (@p114) :args ((forall @t33 (or @t83 @t93)))) % 0.38/0.58 (step @p116 :rule trans :premises (@p115 @p108)) % 0.38/0.58 (step @p117 :rule trans :premises (@p116 @p107)) % 0.38/0.58 (step @p118 :rule bool-impl-elim :args (@t82 @t93)) % 0.38/0.58 (step @p119 :rule cong :premises (@p118) :args ((forall @t33 (=> @t82 @t93)))) % 0.38/0.58 (step @p120 :rule trans :premises (@p119 @p117)) % 0.38/0.58 (step @p121 :rule refl :args (@t91)) % 0.38/0.58 (step @p122 :rule refl :args (@t25)) % 0.38/0.58 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t25 @t91))) % 0.38/0.58 (step @p124 :rule symm :premises (@p123)) % 0.38/0.58 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.38/0.58 (step @p126 :rule refl :args (@t92)) % 0.38/0.58 (step @p127 :rule refl :args (@t27)) % 0.38/0.58 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t27 @t92))) % 0.38/0.58 (step @p129 :rule symm :premises (@p128)) % 0.38/0.58 (step @p130 :rule eq_resolve :premises (@p127 @p129)) % 0.38/0.58 (step @p131 :rule cong :premises (@p130) :args (@t94)) % 0.38/0.58 (step @p132 :rule nary_cong :premises (@p131 @p125) :args (@t95)) % 0.38/0.58 (step @p133 :rule cong :premises (@p132) :args ((forall @t22 @t95))) % 0.38/0.58 (step @p134 :rule bool-impl-elim :args (@t27 @t25)) % 0.38/0.58 (step @p135 :rule cong :premises (@p134) :args (@t28)) % 0.38/0.58 (step @p136 :rule trans :premises (@p135 @p133)) % 0.38/0.58 (step @p137 :rule refl :args (@t80)) % 0.38/0.58 (step @p138 :rule refl :args (@t29)) % 0.38/0.58 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t29 @t80))) % 0.38/0.58 (step @p140 :rule symm :premises (@p139)) % 0.38/0.58 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.38/0.58 (step @p142 :rule refl :args (@t81)) % 0.38/0.58 (step @p143 :rule refl :args (@t30)) % 0.38/0.58 (step @p144 :rule cong :premises (@p143 @p142) :args ((= @t30 @t81))) % 0.38/0.58 (step @p145 :rule symm :premises (@p144)) % 0.38/0.58 (step @p146 :rule eq_resolve :premises (@p143 @p145)) % 0.38/0.58 (step @p147 :rule cong :premises (@p146) :args (@t96)) % 0.38/0.58 (step @p148 :rule nary_cong :premises (@p147 @p141) :args (@t97)) % 0.38/0.58 (step @p149 :rule cong :premises (@p148) :args ((forall @t22 @t97))) % 0.38/0.58 (step @p150 :rule bool-impl-elim :args (@t30 @t29)) % 0.38/0.58 (step @p151 :rule cong :premises (@p150) :args (@t31)) % 0.38/0.58 (step @p152 :rule trans :premises (@p151 @p149)) % 0.38/0.58 (step @p153 :rule cong :premises (@p152 @p136) :args (@t32)) % 0.38/0.58 (step @p154 :rule cong :premises (@p153) :args (@t34)) % 0.38/0.58 (step @p155 :rule trans :premises (@p154 @p120)) % 0.38/0.58 (step @p156 :rule cong :premises (@p155 @p105) :args (@t35)) % 0.38/0.58 (step @p157 :rule cong :premises (@p156) :args (@t36)) % 0.38/0.58 (step @p158 :rule eq_resolve :premises (@p1 @p157)) % 0.38/0.58 (step @p159 :rule not_implies_elim1 :premises (@p158)) % 0.38/0.58 (step @p160 :rule instantiate :premises (@p159) :args ((@list @t101 @t100 @t99))) % 0.38/0.58 (step @p161 :rule not_implies_elim2 :premises (@p158)) % 0.38/0.58 (step @p162 :rule refl :args (@t108)) % 0.38/0.58 (step @p163 :rule bool-double-not-elim :args (@t98)) % 0.38/0.58 (step @p164 :rule nary_cong :premises (@p163 @p162) :args ((or (not @t109) @t108))) % 0.38/0.58 (step @p165 :rule refl :args (@t102)) % 0.38/0.58 (step @p166 :rule refl :args (@t104)) % 0.38/0.58 (step @p167 :rule refl :args (@t99)) % 0.38/0.58 (step @p168 :rule eq-refl :args (@t49)) % 0.38/0.58 (step @p169 :rule skolem_intro :args (@t101)) % 0.38/0.58 (step @p170 :rule refl :args (@t49)) % 0.38/0.58 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t49 @t101))) % 0.38/0.58 (step @p172 :rule trans :premises (@p171 @p168)) % 0.38/0.58 (step @p173 :rule true_elim :premises (@p172)) % 0.38/0.58 (step @p174 :rule cong :premises (@p173 @p167) :args (@t110)) % 0.38/0.58 (step @p175 :rule cong :premises (@p174) :args (@t111)) % 0.38/0.58 (step @p176 :rule nary_cong :premises (@p175 @p166 @p165) :args (@t112)) % 0.38/0.58 (step @p177 :rule cong :premises (@p176) :args (@t113)) % 0.38/0.58 (step @p178 :rule refl :args (@t109)) % 0.38/0.58 (step @p179 :rule cong :premises (@p178 @p177) :args ((=> @t109 @t113))) % 0.38/0.58 (assume-push @p258 @t109) % 0.38/0.58 (step @p181 :rule skolemize :premises (@p161)) % 0.38/0.58 (step-pop @p259 :rule scope :premises (@p181)) % 0.38/0.58 (step @p182 :rule process_scope :premises (@p259) :args (@t113)) % 0.38/0.58 (step @p184 :rule eq_resolve :premises (@p182 @p179)) % 0.38/0.58 (step @p185 :rule implies_elim :premises (@p184)) % 0.38/0.58 (step @p186 :rule eq_resolve :premises (@p185 @p164)) % 0.38/0.58 (step @p187 :rule chain_m_resolution :premises (@p186 @p161) :args (@t108 @t114 (@list @t98))) % 0.38/0.58 (step @p188 :rule bool-double-not-elim :args (@t103)) % 0.38/0.58 (step @p189 :rule refl :args (@t107)) % 0.38/0.58 (step @p190 :rule nary_cong :premises (@p189 @p188) :args ((or @t107 (not @t104)))) % 0.38/0.58 (step @p191 :rule cnf_or_neg :args (@t107 1)) % 0.38/0.58 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.38/0.58 (step @p193 :rule reordering :premises (@p192) :args ((or @t103 @t107))) % 0.38/0.58 (step @p194 :rule chain_m_resolution :premises (@p193 @p187) :args (@t103 @t114 @t115)) % 0.38/0.58 (step @p195 :rule instantiate :premises (@p194) :args ((@list @t99))) % 0.38/0.58 (step @p196 :rule cnf_or_neg :args (@t107 2)) % 0.38/0.58 (step @p197 :rule chain_m_resolution :premises (@p196 @p187) :args ((not @t102) @t114 @t115)) % 0.38/0.58 (step @p198 :rule cnf_or_pos :args (@t118)) % 0.38/0.58 (step @p199 :rule reordering :premises (@p198) :args ((or @t102 @t117 (not @t118)))) % 0.38/0.58 (step @p200 :rule chain_m_resolution :premises (@p199 @p197 @p195) :args (@t117 (@list true false) (@list @t102 @t118))) % 0.38/0.58 (step @p201 :rule bool-double-not-elim :args (@t105)) % 0.38/0.58 (step @p202 :rule nary_cong :premises (@p189 @p201) :args ((or @t107 (not @t106)))) % 0.38/0.58 (step @p203 :rule cnf_or_neg :args (@t107 0)) % 0.38/0.58 (step @p204 :rule eq_resolve :premises (@p203 @p202)) % 0.38/0.58 (step @p205 :rule reordering :premises (@p204) :args ((or @t105 @t107))) % 0.38/0.58 (step @p206 :rule chain_m_resolution :premises (@p205 @p187) :args (@t105 @t114 @t115)) % 0.38/0.58 (step @p207 :rule cnf_or_pos :args (@t121)) % 0.38/0.58 (step @p208 :rule reordering :premises (@p207) :args ((or @t106 @t116 @t120 (not @t121)))) % 0.38/0.58 (step @p209 :rule chain_m_resolution :premises (@p208 @p206 @p200 @p160) :args (@t120 (@list false true false) (@list @t105 @t116 @t121))) % 0.38/0.58 (step @p210 :rule skolemize :premises (@p209)) % 0.38/0.58 (step @p211 :rule cnf_or_neg :args (@t126 1)) % 0.38/0.58 (step @p212 :rule chain_m_resolution :premises (@p211 @p210) :args ((not @t123) @t114 @t127)) % 0.38/0.58 (step @p213 :rule alpha_equiv :args (@t103 (@list @t4) (@list @t13))) % 0.38/0.58 (step @p214 :rule equiv_elim1 :premises (@p213)) % 0.38/0.58 (step @p215 :rule chain_m_resolution :premises (@p214 @p194) :args (@t128 @t129 (@list @t103))) % 0.38/0.58 (step @p216 :rule eq-symm :args (@t130 @t48)) % 0.38/0.58 (step @p217 :rule beta-reduce :args ((= @t131 @t48))) % 0.38/0.58 (step @p218 :rule refl :args (@t130)) % 0.38/0.58 (step @p219 :rule cong :premises (@p218 @p217) :args (@t132)) % 0.38/0.58 (step @p220 :rule trans :premises (@p219 @p216)) % 0.38/0.58 (step @p221 :rule cong :premises (@p220) :args (@t133)) % 0.38/0.58 (step @p222 :rule quant-unused-vars :args ((= (forall @t8 true) true))) % 0.38/0.58 (step @p223 :rule eq-refl :args (@t131)) % 0.38/0.58 (step @p224 :rule cong :premises (@p223) :args ((forall @t8 (= @t131 @t131)))) % 0.38/0.58 (step @p225 :rule trans :premises (@p224 @p222)) % 0.38/0.58 (step @p226 :rule refl :args (@t131)) % 0.38/0.58 (step @p227 :rule refl :args (@t4)) % 0.38/0.58 (step @p228 :rule ho_cong :premises (@p169 @p227)) % 0.38/0.58 (step @p229 :rule cong :premises (@p228 @p226) :args (@t132)) % 0.38/0.58 (step @p230 :rule cong :premises (@p229) :args (@t133)) % 0.38/0.58 (step @p231 :rule trans :premises (@p230 @p225)) % 0.38/0.58 (step @p232 :rule true_elim :premises (@p231)) % 0.38/0.58 (step @p233 :rule eq_resolve :premises (@p232 @p221)) % 0.38/0.58 (step @p234 :rule eq-symm :args (@t134 @t124)) % 0.38/0.58 (step @p235 :rule refl :args (@t135)) % 0.38/0.58 (step @p236 :rule cong :premises (@p235 @p234) :args ((=> @t135 @t136))) % 0.38/0.58 (assume-push @p260 @t135) % 0.38/0.58 (step @p238 :rule instantiate :premises (@p233) :args ((@list @t122))) % 0.38/0.58 (step-pop @p261 :rule scope :premises (@p238)) % 0.38/0.58 (step @p239 :rule process_scope :premises (@p261) :args (@t136)) % 0.38/0.58 (step @p241 :rule eq_resolve :premises (@p239 @p236)) % 0.38/0.58 (step @p242 :rule implies_elim :premises (@p241)) % 0.38/0.58 (step @p243 :rule chain_m_resolution :premises (@p242 @p233) :args (@t137 @t129 (@list @t135))) % 0.38/0.58 (step @p244 :rule bool-double-not-elim :args (@t124)) % 0.38/0.58 (step @p245 :rule refl :args (@t126)) % 0.38/0.58 (step @p246 :rule nary_cong :premises (@p245 @p244) :args ((or @t126 (not @t125)))) % 0.38/0.58 (step @p247 :rule cnf_or_neg :args (@t126 0)) % 0.38/0.58 (step @p248 :rule eq_resolve :premises (@p247 @p246)) % 0.38/0.58 (step @p249 :rule reordering :premises (@p248) :args ((or @t124 @t126))) % 0.38/0.58 (step @p250 :rule chain_m_resolution :premises (@p249 @p210) :args (@t124 @t114 @t127)) % 0.38/0.58 (step @p251 :rule cnf_equiv_pos1 :args (@t137)) % 0.38/0.58 (step @p252 :rule reordering :premises (@p251) :args ((or @t125 @t134 (not @t137)))) % 0.38/0.58 (step @p253 :rule chain_m_resolution :premises (@p252 @p250 @p243) :args (@t134 (@list false false) (@list @t124 @t137))) % 0.38/0.58 (step @p254 :rule instantiate :premises (@p253) :args ((@list @t100))) % 0.38/0.58 (step @p255 :rule cnf_or_pos :args (@t139)) % 0.38/0.58 (step @p256 :rule reordering :premises (@p255) :args ((or @t123 @t138 (not @t139)))) % 0.38/0.58 (step @p257 false :rule chain_m_resolution :premises (@p256 @p254 @p215 @p212) :args (false (@list false false true) (@list @t139 @t128 @t123))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------