%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO026^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 09:11:48 AM UTC 2026 % Result : Theorem 0.36s 0.58s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO026^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/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 23:51:29 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.36/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.58 % SZS status Theorem % 0.36/0.58 % SZS output start Proof % 0.36/0.58 ( % 0.36/0.58 (declare-const tptp.p (-> (-> Bool Bool) Bool)) % 0.36/0.58 (define @t1 () (@var "Y" (-> Bool Bool))) % 0.36/0.58 (define @t2 () (_ tptp.p @t1)) % 0.36/0.58 (define @t3 () (@list @t1)) % 0.36/0.58 (define @t4 () (forall @t3 @t2)) % 0.36/0.58 (define @t5 () (@var "X" Bool)) % 0.36/0.58 (define @t6 () (@list @t5)) % 0.36/0.58 (define @t7 () (lambda @t6 true)) % 0.36/0.58 (define @t8 () (lambda @t6 false)) % 0.36/0.58 (define @t9 () (lambda @t6 (not @t5))) % 0.36/0.58 (define @t10 () (lambda @t6 @t5)) % 0.36/0.58 (define @t11 () (and (_ tptp.p @t10) (_ tptp.p @t9) (_ tptp.p @t8) (_ tptp.p @t7))) % 0.36/0.58 (define @t12 () (=> @t11 @t4)) % 0.36/0.58 (define @t13 () (not @t12)) % 0.36/0.58 (define @t14 () (tptp.p @t1)) % 0.36/0.58 (define @t15 () (forall @t3 @t14)) % 0.36/0.58 (define @t16 () (@var "BOUND_VARIABLE_7454" Bool)) % 0.36/0.58 (define @t17 () (lambda (@list @t16) true)) % 0.36/0.58 (define @t18 () (@purify @t17)) % 0.36/0.58 (define @t19 () (tptp.p @t18)) % 0.36/0.58 (define @t20 () (_ tptp.p @t18)) % 0.36/0.58 (define @t21 () (@var "BOUND_VARIABLE_7467" Bool)) % 0.36/0.58 (define @t22 () (lambda (@list @t21) false)) % 0.36/0.58 (define @t23 () (@purify @t22)) % 0.36/0.58 (define @t24 () (tptp.p @t23)) % 0.36/0.58 (define @t25 () (_ tptp.p @t23)) % 0.36/0.58 (define @t26 () (@var "BOUND_VARIABLE_7480" Bool)) % 0.36/0.58 (define @t27 () (= @t26 true)) % 0.36/0.58 (define @t28 () (@list @t26)) % 0.36/0.58 (define @t29 () (lambda @t28 (ite @t27 false true))) % 0.36/0.58 (define @t30 () (@purify @t29)) % 0.36/0.58 (define @t31 () (tptp.p @t30)) % 0.36/0.58 (define @t32 () (_ tptp.p @t30)) % 0.36/0.58 (define @t33 () (not @t27)) % 0.36/0.58 (define @t34 () (not true)) % 0.36/0.58 (define @t35 () (@var "BOUND_VARIABLE_7495" Bool)) % 0.36/0.58 (define @t36 () (= @t35 false)) % 0.36/0.58 (define @t37 () (ite @t36 false true)) % 0.36/0.58 (define @t38 () (@list @t35)) % 0.36/0.58 (define @t39 () (lambda @t38 @t37)) % 0.36/0.58 (define @t40 () (@purify @t39)) % 0.36/0.58 (define @t41 () (tptp.p @t40)) % 0.36/0.58 (define @t42 () (_ tptp.p @t40)) % 0.36/0.58 (define @t43 () (= false @t35)) % 0.36/0.58 (define @t44 () (not @t36)) % 0.36/0.58 (define @t45 () (and (_ tptp.p @t39) (_ tptp.p @t29) (_ tptp.p @t22) (_ tptp.p @t17))) % 0.36/0.58 (define @t46 () (=> @t45 @t15)) % 0.36/0.58 (define @t47 () (@list @t5)) % 0.36/0.58 (define @t48 () (@quantifiers_skolemize @t15 0)) % 0.36/0.58 (define @t49 () (= @t18 @t48)) % 0.36/0.58 (define @t50 () (not @t49)) % 0.36/0.58 (define @t51 () (tptp.p @t48)) % 0.36/0.58 (define @t52 () (not @t19)) % 0.36/0.58 (define @t53 () (not @t51)) % 0.36/0.58 (define @t54 () (not @t53)) % 0.36/0.58 (define @t55 () (= false true)) % 0.36/0.58 (define @t56 () (and @t19 @t49 @t53)) % 0.36/0.58 (define @t57 () (@list false true)) % 0.36/0.58 (define @t58 () (@const 0 Bool)) % 0.36/0.58 (define @t59 () (@purify @t58)) % 0.36/0.58 (define @t60 () (_ @t48 @t59)) % 0.36/0.58 (define @t61 () (_ @t48 @t58)) % 0.36/0.58 (define @t62 () (_ @t18 @t58)) % 0.36/0.58 (define @t63 () (= @t62 @t61)) % 0.36/0.58 (define @t64 () (not @t63)) % 0.36/0.58 (define @t65 () (or @t49 @t64)) % 0.36/0.58 (define @t66 () (not @t60)) % 0.36/0.58 (define @t67 () (@list true)) % 0.36/0.58 (define @t68 () (= @t23 @t48)) % 0.36/0.58 (define @t69 () (not @t68)) % 0.36/0.58 (define @t70 () (not @t24)) % 0.36/0.58 (define @t71 () (and @t24 @t68 @t53)) % 0.36/0.58 (define @t72 () (@const 1 Bool)) % 0.36/0.58 (define @t73 () (@purify @t72)) % 0.36/0.58 (define @t74 () (_ @t48 @t73)) % 0.36/0.58 (define @t75 () (_ @t48 @t72)) % 0.36/0.58 (define @t76 () (_ @t22 @t72)) % 0.36/0.58 (define @t77 () (_ @t23 @t73)) % 0.36/0.58 (define @t78 () (_ @t23 @t72)) % 0.36/0.58 (define @t79 () (= @t78 @t75)) % 0.36/0.58 (define @t80 () (not @t79)) % 0.36/0.58 (define @t81 () (or @t68 @t80)) % 0.36/0.58 (define @t82 () (not @t59)) % 0.36/0.58 (define @t83 () (not @t74)) % 0.36/0.58 (define @t84 () (not @t73)) % 0.36/0.58 (define @t85 () (not @t66)) % 0.36/0.58 (define @t86 () (and @t74 @t73 @t59 @t66)) % 0.36/0.58 (define @t87 () (= @t30 @t48)) % 0.36/0.58 (define @t88 () (not @t87)) % 0.36/0.58 (define @t89 () (not @t31)) % 0.36/0.58 (define @t90 () (and @t31 @t87 @t53)) % 0.36/0.58 (define @t91 () (@const 2 Bool)) % 0.36/0.58 (define @t92 () (@purify @t91)) % 0.36/0.58 (define @t93 () (not @t92)) % 0.36/0.58 (define @t94 () (_ @t48 @t92)) % 0.36/0.58 (define @t95 () (_ @t48 @t91)) % 0.36/0.58 (define @t96 () (not @t91)) % 0.36/0.58 (define @t97 () (= @t91 true)) % 0.36/0.58 (define @t98 () (not @t97)) % 0.36/0.58 (define @t99 () (_ @t29 @t91)) % 0.36/0.58 (define @t100 () (_ @t30 @t91)) % 0.36/0.58 (define @t101 () (= @t100 @t95)) % 0.36/0.58 (define @t102 () (not @t101)) % 0.36/0.58 (define @t103 () (or @t87 @t102)) % 0.36/0.58 (define @t104 () (= @t94 @t93)) % 0.36/0.58 (define @t105 () (not @t94)) % 0.36/0.58 (define @t106 () (not @t93)) % 0.36/0.58 (define @t107 () (and @t66 @t59 @t92 @t94)) % 0.36/0.58 (define @t108 () (@list false)) % 0.36/0.58 (define @t109 () (not @t84)) % 0.36/0.58 (define @t110 () (and @t74 @t84 @t93 @t105)) % 0.36/0.58 (define @t111 () (not @t82)) % 0.36/0.58 (define @t112 () (and @t74 @t84 @t82 @t66)) % 0.36/0.58 (define @t113 () (@list false true true)) % 0.36/0.58 (define @t114 () (@const 3 Bool)) % 0.36/0.58 (define @t115 () (@purify @t114)) % 0.36/0.58 (define @t116 () (_ @t48 @t115)) % 0.36/0.58 (define @t117 () (= @t115 @t116)) % 0.36/0.58 (define @t118 () (not @t116)) % 0.36/0.58 (define @t119 () (not @t115)) % 0.36/0.58 (define @t120 () (and @t115 @t73 @t74)) % 0.36/0.58 (define @t121 () (and @t119 @t66 @t82)) % 0.36/0.58 (define @t122 () (_ @t48 @t114)) % 0.36/0.58 (define @t123 () (= @t114 false)) % 0.36/0.58 (define @t124 () (not @t123)) % 0.36/0.58 (define @t125 () (_ @t39 @t114)) % 0.36/0.58 (define @t126 () (_ @t40 @t115)) % 0.36/0.58 (define @t127 () (_ @t40 @t114)) % 0.36/0.58 (define @t128 () (= @t127 @t122)) % 0.36/0.58 (define @t129 () (not @t128)) % 0.36/0.58 (define @t130 () (= @t40 @t48)) % 0.36/0.58 (define @t131 () (or @t130 @t129)) % 0.36/0.58 (define @t132 () (not @t130)) % 0.36/0.58 (define @t133 () (not @t41)) % 0.36/0.58 (define @t134 () (and @t41 @t130 @t53)) % 0.36/0.58 (assume @p1 @t13) % 0.36/0.58 (assume @p2 true) % 0.36/0.58 (step @p3 :rule refl :args (@t15)) % 0.36/0.58 (step @p4 :rule refl :args (@t19)) % 0.36/0.58 (step @p5 :rule refl :args (@t20)) % 0.36/0.58 (step @p6 :rule cong :premises (@p5 @p4) :args ((= @t20 @t19))) % 0.36/0.58 (step @p7 :rule symm :premises (@p6)) % 0.36/0.58 (step @p8 :rule eq_resolve :premises (@p5 @p7)) % 0.36/0.58 (step @p9 :rule eq-refl :args (@t17)) % 0.36/0.58 (step @p10 :rule refl :args (@t17)) % 0.36/0.58 (step @p11 :rule symm :premises (@p10)) % 0.36/0.58 (step @p12 :rule refl :args (@t17)) % 0.36/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t17 @t17))) % 0.36/0.58 (step @p14 :rule trans :premises (@p13 @p9)) % 0.36/0.58 (step @p15 :rule skolem_intro :args (@t18)) % 0.36/0.58 (step @p16 :rule cong :premises (@p12 @p15) :args ((= @t17 @t18))) % 0.36/0.58 (step @p17 :rule trans :premises (@p16 @p14)) % 0.36/0.58 (step @p18 :rule true_elim :premises (@p17)) % 0.36/0.58 (step @p19 :rule refl :args (tptp.p)) % 0.36/0.58 (step @p20 :rule ho_cong :premises (@p19 @p18)) % 0.36/0.58 (step @p21 :rule trans :premises (@p20 @p8)) % 0.36/0.58 (step @p22 :rule refl :args (@t24)) % 0.36/0.58 (step @p23 :rule refl :args (@t25)) % 0.36/0.58 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t25 @t24))) % 0.36/0.58 (step @p25 :rule symm :premises (@p24)) % 0.36/0.58 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.36/0.58 (step @p27 :rule eq-refl :args (@t22)) % 0.36/0.58 (step @p28 :rule refl :args (@t22)) % 0.36/0.58 (step @p29 :rule symm :premises (@p28)) % 0.36/0.58 (step @p30 :rule refl :args (@t22)) % 0.36/0.58 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t22 @t22))) % 0.36/0.58 (step @p32 :rule trans :premises (@p31 @p27)) % 0.36/0.58 (step @p33 :rule skolem_intro :args (@t23)) % 0.36/0.58 (step @p34 :rule cong :premises (@p30 @p33) :args ((= @t22 @t23))) % 0.36/0.58 (step @p35 :rule trans :premises (@p34 @p32)) % 0.36/0.58 (step @p36 :rule true_elim :premises (@p35)) % 0.36/0.58 (step @p37 :rule ho_cong :premises (@p19 @p36)) % 0.36/0.58 (step @p38 :rule trans :premises (@p37 @p26)) % 0.36/0.58 (step @p39 :rule refl :args (@t31)) % 0.36/0.58 (step @p40 :rule refl :args (@t32)) % 0.36/0.58 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t32 @t31))) % 0.36/0.58 (step @p42 :rule symm :premises (@p41)) % 0.36/0.58 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 0.36/0.58 (step @p44 :rule eq-refl :args (@t29)) % 0.36/0.58 (step @p45 :rule refl :args (@t29)) % 0.36/0.58 (step @p46 :rule symm :premises (@p45)) % 0.36/0.58 (step @p47 :rule bool-eq-true :args (@t26)) % 0.36/0.58 (step @p48 :rule cong :premises (@p47) :args (@t33)) % 0.36/0.58 (step @p49 :rule bool-eq-false :args (@t27)) % 0.36/0.58 (step @p50 :rule trans :premises (@p49 @p48)) % 0.36/0.58 (step @p51 :rule evaluate :args (@t34)) % 0.36/0.58 (step @p52 :rule ite-neg-branch :premises (@p51) :args (@t27 false true)) % 0.36/0.58 (step @p53 :rule trans :premises (@p52 @p50)) % 0.36/0.58 (step @p54 :rule symm :premises (@p53)) % 0.36/0.58 (step @p55 :rule cong :premises (@p54) :args ((lambda @t28 (not @t26)))) % 0.36/0.58 (step @p56 :rule trans :premises (@p55 @p46)) % 0.36/0.58 (step @p57 :rule bool-eq-true :args (@t26)) % 0.36/0.58 (step @p58 :rule cong :premises (@p57) :args (@t33)) % 0.36/0.58 (step @p59 :rule aci_norm :args ((= (and @t33 true) @t33))) % 0.36/0.58 (step @p60 :rule ite-then-false :args (@t27 true)) % 0.36/0.58 (step @p61 :rule trans :premises (@p60 @p59)) % 0.36/0.58 (step @p62 :rule trans :premises (@p61 @p58)) % 0.36/0.58 (step @p63 :rule cong :premises (@p62) :args (@t29)) % 0.36/0.58 (step @p64 :rule trans :premises (@p63 @p56)) % 0.36/0.58 (step @p65 :rule refl :args (@t29)) % 0.36/0.58 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t29 @t29))) % 0.36/0.58 (step @p67 :rule trans :premises (@p66 @p44)) % 0.36/0.58 (step @p68 :rule skolem_intro :args (@t30)) % 0.36/0.58 (step @p69 :rule cong :premises (@p65 @p68) :args ((= @t29 @t30))) % 0.36/0.58 (step @p70 :rule trans :premises (@p69 @p67)) % 0.36/0.58 (step @p71 :rule true_elim :premises (@p70)) % 0.36/0.58 (step @p72 :rule ho_cong :premises (@p19 @p71)) % 0.36/0.58 (step @p73 :rule trans :premises (@p72 @p43)) % 0.36/0.58 (step @p74 :rule refl :args (@t41)) % 0.36/0.58 (step @p75 :rule refl :args (@t42)) % 0.36/0.58 (step @p76 :rule cong :premises (@p75 @p74) :args ((= @t42 @t41))) % 0.36/0.58 (step @p77 :rule symm :premises (@p76)) % 0.36/0.58 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.36/0.58 (step @p79 :rule eq-refl :args (@t39)) % 0.36/0.58 (step @p80 :rule refl :args (@t39)) % 0.36/0.58 (step @p81 :rule symm :premises (@p80)) % 0.36/0.58 (step @p82 :rule eq-symm :args (false @t35)) % 0.36/0.58 (step @p83 :rule true_intro :premises (@p82)) % 0.36/0.58 (step @p84 :rule eq-symm :args (@t36 @t43)) % 0.36/0.58 (step @p85 :rule trans :premises (@p84 @p83)) % 0.36/0.58 (step @p86 :rule refl :args (@t35)) % 0.36/0.58 (step @p87 :rule cong :premises (@p51 @p86) :args ((= @t34 @t35))) % 0.36/0.58 (step @p88 :rule bool-not-eq-elim1 :args (true @t35)) % 0.36/0.58 (step @p89 :rule trans :premises (@p88 @p87)) % 0.36/0.58 (step @p90 :rule ite-neg-branch :premises (@p89) :args (@t36 @t43 (= true @t35))) % 0.36/0.58 (step @p91 :rule trans :premises (@p90 @p85)) % 0.36/0.58 (step @p92 :rule eq-ite-lift :args (@t36 false true @t35)) % 0.36/0.58 (step @p93 :rule trans :premises (@p92 @p91)) % 0.36/0.58 (step @p94 :rule eq-symm :args (@t35 @t37)) % 0.36/0.58 (step @p95 :rule trans :premises (@p94 @p93)) % 0.36/0.58 (step @p96 :rule true_elim :premises (@p95)) % 0.36/0.58 (step @p97 :rule cong :premises (@p96) :args ((lambda @t38 @t35))) % 0.36/0.58 (step @p98 :rule trans :premises (@p97 @p81)) % 0.36/0.58 (step @p99 :rule bool-double-not-elim :args (@t35)) % 0.36/0.58 (step @p100 :rule bool-eq-false :args (@t35)) % 0.36/0.58 (step @p101 :rule cong :premises (@p100) :args (@t44)) % 0.36/0.58 (step @p102 :rule trans :premises (@p101 @p99)) % 0.36/0.58 (step @p103 :rule aci_norm :args ((= (and @t44 true) @t44))) % 0.36/0.58 (step @p104 :rule ite-then-false :args (@t36 true)) % 0.36/0.58 (step @p105 :rule trans :premises (@p104 @p103)) % 0.36/0.58 (step @p106 :rule trans :premises (@p105 @p102)) % 0.36/0.58 (step @p107 :rule cong :premises (@p106) :args (@t39)) % 0.36/0.58 (step @p108 :rule trans :premises (@p107 @p98)) % 0.36/0.58 (step @p109 :rule refl :args (@t39)) % 0.36/0.58 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t39 @t39))) % 0.36/0.58 (step @p111 :rule trans :premises (@p110 @p79)) % 0.36/0.58 (step @p112 :rule skolem_intro :args (@t40)) % 0.36/0.58 (step @p113 :rule cong :premises (@p109 @p112) :args ((= @t39 @t40))) % 0.36/0.58 (step @p114 :rule trans :premises (@p113 @p111)) % 0.36/0.58 (step @p115 :rule true_elim :premises (@p114)) % 0.36/0.58 (step @p116 :rule ho_cong :premises (@p19 @p115)) % 0.36/0.58 (step @p117 :rule trans :premises (@p116 @p78)) % 0.36/0.58 (step @p118 :rule nary_cong :premises (@p117 @p73 @p38 @p21) :args (@t45)) % 0.36/0.58 (step @p119 :rule cong :premises (@p118 @p3) :args (@t46)) % 0.36/0.58 (step @p120 :rule cong :premises (@p119) :args ((not @t46))) % 0.36/0.58 (step @p121 :rule refl :args (@t14)) % 0.36/0.58 (step @p122 :rule refl :args (@t2)) % 0.36/0.58 (step @p123 :rule cong :premises (@p122 @p121) :args ((= @t2 @t14))) % 0.36/0.58 (step @p124 :rule symm :premises (@p123)) % 0.36/0.58 (step @p125 :rule eq_resolve :premises (@p122 @p124)) % 0.36/0.58 (step @p126 :rule cong :premises (@p125) :args (@t4)) % 0.36/0.58 (step @p127 :rule symm :premises (@p10)) % 0.36/0.58 (step @p128 :rule alpha_equiv :args (@t7 @t47 (@list @t16))) % 0.36/0.58 (step @p129 :rule trans :premises (@p128 @p127)) % 0.36/0.58 (step @p130 :rule ho_cong :premises (@p19 @p129)) % 0.36/0.58 (step @p131 :rule symm :premises (@p28)) % 0.36/0.58 (step @p132 :rule alpha_equiv :args (@t8 @t47 (@list @t21))) % 0.36/0.58 (step @p133 :rule trans :premises (@p132 @p131)) % 0.36/0.58 (step @p134 :rule ho_cong :premises (@p19 @p133)) % 0.36/0.58 (step @p135 :rule alpha_equiv :args (@t9 @t47 (@list @t26))) % 0.36/0.58 (step @p136 :rule trans :premises (@p135 @p55)) % 0.36/0.58 (step @p137 :rule trans :premises (@p136 @p46)) % 0.36/0.58 (step @p138 :rule ho_cong :premises (@p19 @p137)) % 0.36/0.58 (step @p139 :rule alpha_equiv :args (@t10 @t47 (@list @t35))) % 0.36/0.58 (step @p140 :rule trans :premises (@p139 @p97)) % 0.36/0.58 (step @p141 :rule trans :premises (@p140 @p81)) % 0.36/0.58 (step @p142 :rule ho_cong :premises (@p19 @p141)) % 0.36/0.58 (step @p143 :rule nary_cong :premises (@p142 @p138 @p134 @p130) :args (@t11)) % 0.36/0.58 (step @p144 :rule cong :premises (@p143 @p126) :args (@t12)) % 0.36/0.58 (step @p145 :rule cong :premises (@p144) :args (@t13)) % 0.36/0.58 (step @p146 :rule trans :premises (@p145 @p120)) % 0.36/0.58 (step @p147 :rule eq_resolve :premises (@p1 @p146)) % 0.36/0.58 (step @p148 :rule not_implies_elim1 :premises (@p147)) % 0.36/0.58 (step @p149 :rule and_elim :premises (@p148) :args (0)) % 0.36/0.58 (step @p150 :rule not_implies_elim2 :premises (@p147)) % 0.36/0.58 (step @p151 :rule skolemize :premises (@p150)) % 0.36/0.58 (step @p152 :rule and_elim :premises (@p148) :args (3)) % 0.36/0.58 (step @p153 :rule refl :args (@t50)) % 0.36/0.58 (step @p154 :rule bool-double-not-elim :args (@t51)) % 0.36/0.58 (step @p155 :rule refl :args (@t52)) % 0.36/0.58 (step @p156 :rule nary_cong :premises (@p155 @p154 @p153) :args ((or @t52 @t54 @t50))) % 0.36/0.58 (assume-push @p626 @t19) % 0.36/0.58 (assume-push @p627 @t49) % 0.36/0.58 (assume-push @p628 @t53) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p161 :rule true_intro :premises (@p152)) % 0.36/0.58 (step @p162 :rule symm :premises (@p627)) % 0.36/0.58 (step @p163 :rule cong :premises (@p162) :args (@t51)) % 0.36/0.58 (step @p164 :rule false_intro :premises (@p151)) % 0.36/0.58 (step @p165 :rule symm :premises (@p164)) % 0.36/0.58 (step @p166 :rule trans :premises (@p165 @p163 @p161)) % 0.36/0.58 (step @p167 false :rule eq_resolve :premises (@p166 @p160)) % 0.36/0.58 (step-pop @p629 :rule scope :premises (@p167)) % 0.36/0.58 (step-pop @p630 :rule scope :premises (@p629)) % 0.36/0.58 (step-pop @p631 :rule scope :premises (@p630)) % 0.36/0.58 (step @p168 :rule process_scope :premises (@p631) :args (false)) % 0.36/0.58 (assume-push @p632 @t19) % 0.36/0.58 (assume-push @p633 @t53) % 0.36/0.58 (assume-push @p634 @t49) % 0.36/0.58 (step @p175 :rule and_intro :premises (@p152 @p634 @p151)) % 0.36/0.58 (step-pop @p635 :rule scope :premises (@p175)) % 0.36/0.58 (step-pop @p636 :rule scope :premises (@p635)) % 0.36/0.58 (step-pop @p637 :rule scope :premises (@p636)) % 0.36/0.58 (step @p176 :rule process_scope :premises (@p637) :args (@t56)) % 0.36/0.58 (step @p180 :rule implies_elim :premises (@p176)) % 0.36/0.58 (step @p181 :rule resolution :premises (@p180 @p168) :args (true @t56)) % 0.36/0.58 (step @p182 :rule not_and :premises (@p181)) % 0.36/0.58 (step @p183 :rule eq_resolve :premises (@p182 @p156)) % 0.36/0.58 (step @p184 :rule chain_m_resolution :premises (@p183 @p152 @p151) :args (@t50 @t57 (@list @t19 @t51))) % 0.36/0.58 (step @p185 :rule bool-eq-true :args (@t60)) % 0.36/0.58 (step @p186 :rule eq-symm :args (true @t60)) % 0.36/0.58 (step @p187 :rule trans :premises (@p186 @p185)) % 0.36/0.58 (step @p188 :rule eq-refl :args (@t58)) % 0.36/0.58 (step @p189 :rule skolem_intro :args (@t59)) % 0.36/0.58 (step @p190 :rule refl :args (@t58)) % 0.36/0.58 (step @p191 :rule cong :premises (@p190 @p189) :args ((= @t58 @t59))) % 0.36/0.58 (step @p192 :rule trans :premises (@p191 @p188)) % 0.36/0.58 (step @p193 :rule true_elim :premises (@p192)) % 0.36/0.58 (step @p194 :rule cong :premises (@p193) :args (@t61)) % 0.36/0.58 (step @p195 :rule beta-reduce :args ((= (_ @t17 @t58) true))) % 0.36/0.58 (step @p196 :rule ho_cong :premises (@p15 @p189)) % 0.36/0.58 (step @p197 :rule bool-eq-true :args ((_ @t18 @t59))) % 0.36/0.58 (step @p198 :rule trans :premises (@p197 @p196 @p195)) % 0.36/0.58 (step @p199 :rule true_elim :premises (@p198)) % 0.36/0.58 (step @p200 :rule cong :premises (@p193) :args (@t62)) % 0.36/0.58 (step @p201 :rule trans :premises (@p200 @p199)) % 0.36/0.58 (step @p202 :rule cong :premises (@p201 @p194) :args (@t63)) % 0.36/0.58 (step @p203 :rule trans :premises (@p202 @p187)) % 0.36/0.58 (step @p204 :rule cong :premises (@p203) :args (@t64)) % 0.36/0.58 (step @p205 :rule refl :args (@t49)) % 0.36/0.58 (step @p206 :rule nary_cong :premises (@p205 @p204) :args (@t65)) % 0.36/0.58 ; WARNING: add trust step for TRUST % 0.36/0.58 ; trust TRUST THEORY_LEMMA % 0.36/0.58 (step @p207 :rule trust :premises () :args (@t65)) % 0.36/0.58 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 0.36/0.58 (step @p209 :rule chain_m_resolution :premises (@p208 @p184) :args (@t66 @t67 (@list @t49))) % 0.36/0.58 (step @p210 :rule and_elim :premises (@p148) :args (2)) % 0.36/0.58 (step @p211 :rule refl :args (@t69)) % 0.36/0.58 (step @p212 :rule refl :args (@t70)) % 0.36/0.58 (step @p213 :rule nary_cong :premises (@p212 @p154 @p211) :args ((or @t70 @t54 @t69))) % 0.36/0.58 (assume-push @p638 @t24) % 0.36/0.58 (assume-push @p639 @t68) % 0.36/0.58 (assume-push @p640 @t53) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p217 :rule true_intro :premises (@p210)) % 0.36/0.58 (step @p218 :rule symm :premises (@p639)) % 0.36/0.58 (step @p219 :rule cong :premises (@p218) :args (@t51)) % 0.36/0.58 (step @p164 :rule false_intro :premises (@p151)) % 0.36/0.58 (step @p165 :rule symm :premises (@p164)) % 0.36/0.58 (step @p220 :rule trans :premises (@p165 @p219 @p217)) % 0.36/0.58 (step @p221 false :rule eq_resolve :premises (@p220 @p160)) % 0.36/0.58 (step-pop @p641 :rule scope :premises (@p221)) % 0.36/0.58 (step-pop @p642 :rule scope :premises (@p641)) % 0.36/0.58 (step-pop @p643 :rule scope :premises (@p642)) % 0.36/0.58 (step @p222 :rule process_scope :premises (@p643) :args (false)) % 0.36/0.58 (assume-push @p644 @t24) % 0.36/0.58 (assume-push @p645 @t53) % 0.36/0.58 (assume-push @p646 @t68) % 0.36/0.58 (step @p229 :rule and_intro :premises (@p210 @p646 @p151)) % 0.36/0.58 (step-pop @p647 :rule scope :premises (@p229)) % 0.36/0.58 (step-pop @p648 :rule scope :premises (@p647)) % 0.36/0.58 (step-pop @p649 :rule scope :premises (@p648)) % 0.36/0.58 (step @p230 :rule process_scope :premises (@p649) :args (@t71)) % 0.36/0.58 (step @p234 :rule implies_elim :premises (@p230)) % 0.36/0.58 (step @p235 :rule resolution :premises (@p234 @p222) :args (true @t71)) % 0.36/0.58 (step @p236 :rule not_and :premises (@p235)) % 0.36/0.58 (step @p237 :rule eq_resolve :premises (@p236 @p213)) % 0.36/0.58 (step @p238 :rule chain_m_resolution :premises (@p237 @p210 @p151) :args (@t69 @t57 (@list @t24 @t51))) % 0.36/0.58 (step @p239 :rule bool-double-not-elim :args (@t74)) % 0.36/0.58 (step @p240 :rule bool-eq-false :args (@t74)) % 0.36/0.58 (step @p241 :rule eq-symm :args (false @t74)) % 0.36/0.58 (step @p242 :rule trans :premises (@p241 @p240)) % 0.36/0.58 (step @p243 :rule eq-refl :args (@t72)) % 0.36/0.58 (step @p244 :rule skolem_intro :args (@t73)) % 0.36/0.58 (step @p245 :rule refl :args (@t72)) % 0.36/0.58 (step @p246 :rule cong :premises (@p245 @p244) :args ((= @t72 @t73))) % 0.36/0.58 (step @p247 :rule trans :premises (@p246 @p243)) % 0.36/0.58 (step @p248 :rule true_elim :premises (@p247)) % 0.36/0.58 (step @p249 :rule cong :premises (@p248) :args (@t75)) % 0.36/0.58 (step @p250 :rule evaluate :args ((not false))) % 0.36/0.58 (step @p251 :rule beta-reduce :args ((= @t76 false))) % 0.36/0.58 (step @p252 :rule cong :premises (@p251) :args ((not @t76))) % 0.36/0.58 (step @p253 :rule trans :premises (@p252 @p250)) % 0.36/0.58 (step @p254 :rule ho_cong :premises (@p33 @p244)) % 0.36/0.58 (step @p255 :rule cong :premises (@p254) :args ((not @t77))) % 0.36/0.58 (step @p256 :rule bool-eq-false :args (@t77)) % 0.36/0.58 (step @p257 :rule trans :premises (@p256 @p255 @p253)) % 0.36/0.58 (step @p258 :rule true_elim :premises (@p257)) % 0.36/0.58 (step @p259 :rule cong :premises (@p248) :args (@t78)) % 0.36/0.58 (step @p260 :rule trans :premises (@p259 @p258)) % 0.36/0.58 (step @p261 :rule cong :premises (@p260 @p249) :args (@t79)) % 0.36/0.58 (step @p262 :rule trans :premises (@p261 @p242)) % 0.36/0.58 (step @p263 :rule cong :premises (@p262) :args (@t80)) % 0.36/0.58 (step @p264 :rule trans :premises (@p263 @p239)) % 0.36/0.58 (step @p265 :rule refl :args (@t68)) % 0.36/0.58 (step @p266 :rule nary_cong :premises (@p265 @p264) :args (@t81)) % 0.36/0.58 ; trust TRUST THEORY_LEMMA % 0.36/0.58 (step @p267 :rule trust :premises () :args (@t81)) % 0.36/0.58 (step @p268 :rule eq_resolve :premises (@p267 @p266)) % 0.36/0.58 (step @p269 :rule chain_m_resolution :premises (@p268 @p238) :args (@t74 @t67 (@list @t68))) % 0.36/0.58 (step @p270 :rule bool-double-not-elim :args (@t60)) % 0.36/0.58 (step @p271 :rule refl :args (@t82)) % 0.36/0.58 (step @p272 :rule refl :args (@t83)) % 0.36/0.58 (step @p273 :rule refl :args (@t84)) % 0.36/0.58 (step @p274 :rule nary_cong :premises (@p273 @p272 @p271 @p270) :args ((or @t84 @t83 @t82 @t85))) % 0.36/0.58 (assume-push @p650 @t74) % 0.36/0.58 (assume-push @p651 @t73) % 0.36/0.58 (assume-push @p652 @t59) % 0.36/0.58 (assume-push @p653 @t66) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p279 :rule true_intro :premises (@p650)) % 0.36/0.58 (step @p280 :rule true_intro :premises (@p651)) % 0.36/0.58 (step @p281 :rule symm :premises (@p280)) % 0.36/0.58 (step @p282 :rule true_intro :premises (@p652)) % 0.36/0.58 (step @p283 :rule trans :premises (@p282 @p281)) % 0.36/0.58 (step @p284 :rule cong :premises (@p283) :args (@t60)) % 0.36/0.58 (step @p285 :rule false_intro :premises (@p653)) % 0.36/0.58 (step @p286 :rule symm :premises (@p285)) % 0.36/0.58 (step @p287 :rule trans :premises (@p286 @p284 @p279)) % 0.36/0.58 (step @p288 false :rule eq_resolve :premises (@p287 @p160)) % 0.36/0.58 (step-pop @p654 :rule scope :premises (@p288)) % 0.36/0.58 (step-pop @p655 :rule scope :premises (@p654)) % 0.36/0.58 (step-pop @p656 :rule scope :premises (@p655)) % 0.36/0.58 (step-pop @p657 :rule scope :premises (@p656)) % 0.36/0.58 (step @p289 :rule process_scope :premises (@p657) :args (false)) % 0.36/0.58 (assume-push @p658 @t73) % 0.36/0.58 (assume-push @p659 @t74) % 0.36/0.58 (assume-push @p660 @t59) % 0.36/0.58 (assume-push @p661 @t66) % 0.36/0.58 (step @p298 :rule and_intro :premises (@p659 @p658 @p660 @p661)) % 0.36/0.58 (step-pop @p662 :rule scope :premises (@p298)) % 0.36/0.58 (step-pop @p663 :rule scope :premises (@p662)) % 0.36/0.58 (step-pop @p664 :rule scope :premises (@p663)) % 0.36/0.58 (step-pop @p665 :rule scope :premises (@p664)) % 0.36/0.58 (step @p299 :rule process_scope :premises (@p665) :args (@t86)) % 0.36/0.58 (step @p304 :rule implies_elim :premises (@p299)) % 0.36/0.58 (step @p305 :rule resolution :premises (@p304 @p289) :args (true @t86)) % 0.36/0.58 (step @p306 :rule not_and :premises (@p305)) % 0.36/0.58 (step @p307 :rule eq_resolve :premises (@p306 @p274)) % 0.36/0.58 (step @p308 :rule reordering :premises (@p307) :args ((or @t83 @t84 @t60 @t82))) % 0.36/0.58 (step @p309 :rule and_elim :premises (@p148) :args (1)) % 0.36/0.58 (step @p310 :rule refl :args (@t88)) % 0.36/0.58 (step @p311 :rule refl :args (@t89)) % 0.36/0.58 (step @p312 :rule nary_cong :premises (@p311 @p154 @p310) :args ((or @t89 @t54 @t88))) % 0.36/0.58 (assume-push @p666 @t31) % 0.36/0.58 (assume-push @p667 @t87) % 0.36/0.58 (assume-push @p668 @t53) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p316 :rule true_intro :premises (@p309)) % 0.36/0.58 (step @p317 :rule symm :premises (@p667)) % 0.36/0.58 (step @p318 :rule cong :premises (@p317) :args (@t51)) % 0.36/0.58 (step @p164 :rule false_intro :premises (@p151)) % 0.36/0.58 (step @p165 :rule symm :premises (@p164)) % 0.36/0.58 (step @p319 :rule trans :premises (@p165 @p318 @p316)) % 0.36/0.58 (step @p320 false :rule eq_resolve :premises (@p319 @p160)) % 0.36/0.58 (step-pop @p669 :rule scope :premises (@p320)) % 0.36/0.58 (step-pop @p670 :rule scope :premises (@p669)) % 0.36/0.58 (step-pop @p671 :rule scope :premises (@p670)) % 0.36/0.58 (step @p321 :rule process_scope :premises (@p671) :args (false)) % 0.36/0.58 (assume-push @p672 @t31) % 0.36/0.58 (assume-push @p673 @t53) % 0.36/0.58 (assume-push @p674 @t87) % 0.36/0.58 (step @p328 :rule and_intro :premises (@p309 @p674 @p151)) % 0.36/0.58 (step-pop @p675 :rule scope :premises (@p328)) % 0.36/0.58 (step-pop @p676 :rule scope :premises (@p675)) % 0.36/0.58 (step-pop @p677 :rule scope :premises (@p676)) % 0.36/0.58 (step @p329 :rule process_scope :premises (@p677) :args (@t90)) % 0.36/0.58 (step @p333 :rule implies_elim :premises (@p329)) % 0.36/0.58 (step @p334 :rule resolution :premises (@p333 @p321) :args (true @t90)) % 0.36/0.58 (step @p335 :rule not_and :premises (@p334)) % 0.36/0.58 (step @p336 :rule eq_resolve :premises (@p335 @p312)) % 0.36/0.58 (step @p337 :rule chain_m_resolution :premises (@p336 @p309 @p151) :args (@t88 @t57 (@list @t31 @t51))) % 0.36/0.58 (step @p338 :rule eq-symm :args (@t93 @t94)) % 0.36/0.58 (step @p339 :rule eq-refl :args (@t91)) % 0.36/0.58 (step @p340 :rule skolem_intro :args (@t92)) % 0.36/0.58 (step @p341 :rule refl :args (@t91)) % 0.36/0.58 (step @p342 :rule cong :premises (@p341 @p340) :args ((= @t91 @t92))) % 0.36/0.58 (step @p343 :rule trans :premises (@p342 @p339)) % 0.36/0.58 (step @p344 :rule true_elim :premises (@p343)) % 0.36/0.58 (step @p345 :rule cong :premises (@p344) :args (@t95)) % 0.36/0.58 (step @p346 :rule eq-refl :args (@t96)) % 0.36/0.58 (step @p347 :rule bool-eq-true :args (@t91)) % 0.36/0.58 (step @p348 :rule cong :premises (@p347) :args (@t98)) % 0.36/0.58 (step @p349 :rule aci_norm :args ((= (and @t98 true) @t98))) % 0.36/0.58 (step @p350 :rule ite-then-false :args (@t97 true)) % 0.36/0.58 (step @p351 :rule trans :premises (@p350 @p349)) % 0.36/0.58 (step @p352 :rule trans :premises (@p351 @p348)) % 0.36/0.58 (step @p353 :rule beta-reduce :args ((= @t99 (ite @t97 false true)))) % 0.36/0.58 (step @p354 :rule trans :premises (@p353 @p352)) % 0.36/0.58 (step @p355 :rule refl :args (@t96)) % 0.36/0.58 (step @p356 :rule cong :premises (@p355 @p354) :args ((= @t96 @t99))) % 0.36/0.58 (step @p357 :rule trans :premises (@p356 @p346)) % 0.36/0.58 (step @p358 :rule eq-symm :args (@t99 @t96)) % 0.36/0.58 (step @p359 :rule trans :premises (@p358 @p357)) % 0.36/0.58 (step @p360 :rule cong :premises (@p340) :args (@t93)) % 0.36/0.58 (step @p361 :rule ho_cong :premises (@p68 @p340)) % 0.36/0.58 (step @p362 :rule cong :premises (@p361 @p360) :args ((= (_ @t30 @t92) @t93))) % 0.36/0.58 (step @p363 :rule trans :premises (@p362 @p359)) % 0.36/0.58 (step @p364 :rule true_elim :premises (@p363)) % 0.36/0.58 (step @p365 :rule cong :premises (@p344) :args (@t100)) % 0.36/0.58 (step @p366 :rule trans :premises (@p365 @p364)) % 0.36/0.58 (step @p367 :rule cong :premises (@p366 @p345) :args (@t101)) % 0.36/0.58 (step @p368 :rule trans :premises (@p367 @p338)) % 0.36/0.58 (step @p369 :rule cong :premises (@p368) :args (@t102)) % 0.36/0.58 (step @p370 :rule refl :args (@t87)) % 0.36/0.58 (step @p371 :rule nary_cong :premises (@p370 @p369) :args (@t103)) % 0.36/0.58 ; trust TRUST THEORY_LEMMA % 0.36/0.58 (step @p372 :rule trust :premises () :args (@t103)) % 0.36/0.58 (step @p373 :rule eq_resolve :premises (@p372 @p371)) % 0.36/0.58 (step @p374 :rule chain_m_resolution :premises (@p373 @p337) :args ((not @t104) @t67 (@list @t87))) % 0.36/0.58 (step @p375 :rule bool-double-not-elim :args (@t92)) % 0.36/0.58 (step @p376 :rule refl :args (@t105)) % 0.36/0.58 (step @p377 :rule refl :args (@t104)) % 0.36/0.58 (step @p378 :rule nary_cong :premises (@p377 @p376 @p375) :args ((or @t104 @t105 @t106))) % 0.36/0.58 (step @p379 :rule cnf_equiv_neg2 :args (@t104)) % 0.36/0.58 (step @p380 :rule eq_resolve :premises (@p379 @p378)) % 0.36/0.58 (step @p381 :rule reordering :premises (@p380) :args ((or @t92 @t104 @t105))) % 0.36/0.58 (step @p382 :rule refl :args (@t93)) % 0.36/0.58 (step @p383 :rule nary_cong :premises (@p382 @p376 @p271 @p270) :args ((or @t93 @t105 @t82 @t85))) % 0.36/0.58 (assume-push @p678 @t66) % 0.36/0.58 (assume-push @p679 @t59) % 0.36/0.58 (assume-push @p680 @t92) % 0.36/0.58 (assume-push @p681 @t94) % 0.36/0.58 (step @p388 :rule evaluate :args ((= true false))) % 0.36/0.58 (step @p389 :rule false_intro :premises (@p678)) % 0.36/0.58 (step @p390 :rule true_intro :premises (@p679)) % 0.36/0.58 (step @p391 :rule symm :premises (@p390)) % 0.36/0.58 (step @p392 :rule true_intro :premises (@p680)) % 0.36/0.58 (step @p393 :rule trans :premises (@p392 @p391)) % 0.36/0.58 (step @p394 :rule cong :premises (@p393) :args (@t94)) % 0.36/0.58 (step @p395 :rule true_intro :premises (@p681)) % 0.36/0.58 (step @p396 :rule symm :premises (@p395)) % 0.36/0.58 (step @p397 :rule trans :premises (@p396 @p394 @p389)) % 0.36/0.58 (step @p398 false :rule eq_resolve :premises (@p397 @p388)) % 0.36/0.58 (step-pop @p682 :rule scope :premises (@p398)) % 0.36/0.58 (step-pop @p683 :rule scope :premises (@p682)) % 0.36/0.58 (step-pop @p684 :rule scope :premises (@p683)) % 0.36/0.58 (step-pop @p685 :rule scope :premises (@p684)) % 0.36/0.58 (step @p399 :rule process_scope :premises (@p685) :args (false)) % 0.36/0.58 (assume-push @p686 @t92) % 0.36/0.58 (assume-push @p687 @t94) % 0.36/0.58 (assume-push @p688 @t59) % 0.36/0.58 (assume-push @p689 @t66) % 0.36/0.58 (step @p408 :rule and_intro :premises (@p689 @p688 @p686 @p687)) % 0.36/0.58 (step-pop @p690 :rule scope :premises (@p408)) % 0.36/0.58 (step-pop @p691 :rule scope :premises (@p690)) % 0.36/0.58 (step-pop @p692 :rule scope :premises (@p691)) % 0.36/0.58 (step-pop @p693 :rule scope :premises (@p692)) % 0.36/0.58 (step @p409 :rule process_scope :premises (@p693) :args (@t107)) % 0.36/0.58 (step @p414 :rule implies_elim :premises (@p409)) % 0.36/0.58 (step @p415 :rule resolution :premises (@p414 @p399) :args (true @t107)) % 0.36/0.58 (step @p416 :rule not_and :premises (@p415)) % 0.36/0.58 (step @p417 :rule eq_resolve :premises (@p416 @p383)) % 0.36/0.58 (step @p418 :rule reordering :premises (@p417) :args ((or @t93 @t105 @t60 @t82))) % 0.36/0.58 (step @p419 :rule chain_m_resolution :premises (@p418 @p381) :args ((or @t104 @t105 @t60 @t82) @t108 (@list @t92))) % 0.36/0.58 (step @p420 :rule cnf_equiv_neg1 :args (@t104)) % 0.36/0.58 (step @p421 :rule reordering :premises (@p420) :args ((or @t94 @t93 @t104))) % 0.36/0.58 (step @p422 :rule bool-double-not-elim :args (@t73)) % 0.36/0.58 (step @p423 :rule bool-double-not-elim :args (@t94)) % 0.36/0.58 (step @p424 :rule nary_cong :premises (@p375 @p423 @p272 @p422) :args ((or @t106 (not @t105) @t83 @t109))) % 0.36/0.58 (assume-push @p694 @t74) % 0.36/0.58 (assume-push @p695 @t84) % 0.36/0.58 (assume-push @p696 @t93) % 0.36/0.58 (assume-push @p697 @t105) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p429 :rule true_intro :premises (@p694)) % 0.36/0.58 (step @p430 :rule false_intro :premises (@p695)) % 0.36/0.58 (step @p431 :rule symm :premises (@p430)) % 0.36/0.58 (step @p432 :rule false_intro :premises (@p696)) % 0.36/0.58 (step @p433 :rule trans :premises (@p432 @p431)) % 0.36/0.58 (step @p434 :rule cong :premises (@p433) :args (@t94)) % 0.36/0.58 (step @p435 :rule false_intro :premises (@p697)) % 0.36/0.58 (step @p436 :rule symm :premises (@p435)) % 0.36/0.58 (step @p437 :rule trans :premises (@p436 @p434 @p429)) % 0.36/0.58 (step @p438 false :rule eq_resolve :premises (@p437 @p160)) % 0.36/0.58 (step-pop @p698 :rule scope :premises (@p438)) % 0.36/0.58 (step-pop @p699 :rule scope :premises (@p698)) % 0.36/0.58 (step-pop @p700 :rule scope :premises (@p699)) % 0.36/0.58 (step-pop @p701 :rule scope :premises (@p700)) % 0.36/0.58 (step @p439 :rule process_scope :premises (@p701) :args (false)) % 0.36/0.58 (assume-push @p702 @t93) % 0.36/0.58 (assume-push @p703 @t105) % 0.36/0.58 (assume-push @p704 @t74) % 0.36/0.58 (assume-push @p705 @t84) % 0.36/0.58 (step @p448 :rule and_intro :premises (@p704 @p705 @p702 @p703)) % 0.36/0.58 (step-pop @p706 :rule scope :premises (@p448)) % 0.36/0.58 (step-pop @p707 :rule scope :premises (@p706)) % 0.36/0.58 (step-pop @p708 :rule scope :premises (@p707)) % 0.36/0.58 (step-pop @p709 :rule scope :premises (@p708)) % 0.36/0.58 (step @p449 :rule process_scope :premises (@p709) :args (@t110)) % 0.36/0.58 (step @p454 :rule implies_elim :premises (@p449)) % 0.36/0.58 (step @p455 :rule resolution :premises (@p454 @p439) :args (true @t110)) % 0.36/0.58 (step @p456 :rule not_and :premises (@p455)) % 0.36/0.58 (step @p457 :rule eq_resolve :premises (@p456 @p424)) % 0.36/0.58 (step @p458 :rule reordering :premises (@p457) :args ((or @t92 @t94 @t73 @t83))) % 0.36/0.58 (step @p459 :rule chain_m_resolution :premises (@p458 @p421 @p419) :args ((or @t104 @t73 @t83 @t60 @t82) (@list true true) (@list @t92 @t94))) % 0.36/0.58 (step @p460 :rule chain_m_resolution :premises (@p459 @p374 @p209 @p269 @p308 @p209 @p269) :args (@t82 (@list true true false true true false) (@list @t104 @t60 @t74 @t73 @t60 @t74))) % 0.36/0.58 (step @p461 :rule bool-double-not-elim :args (@t59)) % 0.36/0.58 (step @p462 :rule nary_cong :premises (@p272 @p422 @p270 @p461) :args ((or @t83 @t109 @t85 @t111))) % 0.36/0.58 (assume-push @p710 @t74) % 0.36/0.58 (assume-push @p711 @t84) % 0.36/0.58 (assume-push @p712 @t82) % 0.36/0.58 (assume-push @p713 @t66) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p467 :rule true_intro :premises (@p710)) % 0.36/0.58 (step @p468 :rule false_intro :premises (@p711)) % 0.36/0.58 (step @p469 :rule symm :premises (@p468)) % 0.36/0.58 (step @p470 :rule false_intro :premises (@p712)) % 0.36/0.58 (step @p471 :rule trans :premises (@p470 @p469)) % 0.36/0.58 (step @p472 :rule cong :premises (@p471) :args (@t60)) % 0.36/0.58 (step @p473 :rule false_intro :premises (@p713)) % 0.36/0.58 (step @p474 :rule symm :premises (@p473)) % 0.36/0.58 (step @p475 :rule trans :premises (@p474 @p472 @p467)) % 0.36/0.58 (step @p476 false :rule eq_resolve :premises (@p475 @p160)) % 0.36/0.58 (step-pop @p714 :rule scope :premises (@p476)) % 0.36/0.58 (step-pop @p715 :rule scope :premises (@p714)) % 0.36/0.58 (step-pop @p716 :rule scope :premises (@p715)) % 0.36/0.58 (step-pop @p717 :rule scope :premises (@p716)) % 0.36/0.58 (step @p477 :rule process_scope :premises (@p717) :args (false)) % 0.36/0.58 (assume-push @p718 @t74) % 0.36/0.58 (assume-push @p719 @t84) % 0.36/0.58 (assume-push @p720 @t66) % 0.36/0.58 (assume-push @p721 @t82) % 0.36/0.58 (step @p486 :rule and_intro :premises (@p718 @p719 @p721 @p720)) % 0.36/0.58 (step-pop @p722 :rule scope :premises (@p486)) % 0.36/0.58 (step-pop @p723 :rule scope :premises (@p722)) % 0.36/0.58 (step-pop @p724 :rule scope :premises (@p723)) % 0.36/0.58 (step-pop @p725 :rule scope :premises (@p724)) % 0.36/0.58 (step @p487 :rule process_scope :premises (@p725) :args (@t112)) % 0.36/0.58 (step @p492 :rule implies_elim :premises (@p487)) % 0.36/0.58 (step @p493 :rule resolution :premises (@p492 @p477) :args (true @t112)) % 0.36/0.58 (step @p494 :rule not_and :premises (@p493)) % 0.36/0.58 (step @p495 :rule eq_resolve :premises (@p494 @p462)) % 0.36/0.58 (step @p496 :rule reordering :premises (@p495) :args ((or @t73 @t83 @t59 @t60))) % 0.36/0.58 (step @p497 :rule chain_m_resolution :premises (@p496 @p269 @p460 @p209) :args (@t73 @t113 (@list @t74 @t59 @t60))) % 0.36/0.58 (step @p498 :rule cnf_equiv_neg2 :args (@t117)) % 0.36/0.58 (step @p499 :rule reordering :premises (@p498) :args ((or @t119 @t117 @t118))) % 0.36/0.58 (assume-push @p726 @t115) % 0.36/0.58 (assume-push @p727 @t73) % 0.36/0.58 (assume-push @p728 @t74) % 0.36/0.58 (assume-push @p729 @t74) % 0.36/0.58 (assume-push @p730 @t73) % 0.36/0.58 (assume-push @p731 @t115) % 0.36/0.58 (step @p506 :rule true_intro :premises (@p728)) % 0.36/0.58 (step @p507 :rule true_intro :premises (@p727)) % 0.36/0.58 (step @p508 :rule symm :premises (@p507)) % 0.36/0.58 (step @p509 :rule true_intro :premises (@p726)) % 0.36/0.58 (step @p510 :rule trans :premises (@p509 @p508)) % 0.36/0.58 (step @p511 :rule cong :premises (@p510) :args (@t116)) % 0.36/0.58 (step @p512 :rule trans :premises (@p511 @p506)) % 0.36/0.58 (step @p513 :rule true_elim :premises (@p512)) % 0.36/0.58 (step-pop @p732 :rule scope :premises (@p513)) % 0.36/0.58 (step-pop @p733 :rule scope :premises (@p732)) % 0.36/0.58 (step-pop @p734 :rule scope :premises (@p733)) % 0.36/0.58 (step @p514 :rule process_scope :premises (@p734) :args (@t116)) % 0.36/0.58 (step @p518 :rule and_intro :premises (@p728 @p727 @p726)) % 0.36/0.58 (step @p519 :rule modus_ponens :premises (@p518 @p514)) % 0.36/0.58 (step-pop @p735 :rule scope :premises (@p519)) % 0.36/0.58 (step-pop @p736 :rule scope :premises (@p735)) % 0.36/0.58 (step-pop @p737 :rule scope :premises (@p736)) % 0.36/0.58 (step @p520 :rule process_scope :premises (@p737) :args (@t116)) % 0.36/0.58 (step @p524 :rule implies_elim :premises (@p520)) % 0.36/0.58 (step @p525 :rule cnf_and_neg :args (@t120)) % 0.36/0.58 (step @p526 :rule resolution :premises (@p525 @p524) :args (true @t120)) % 0.36/0.58 (step @p527 :rule reordering :premises (@p526) :args ((or @t116 @t119 @t83 @t84))) % 0.36/0.58 (step @p528 :rule chain_m_resolution :premises (@p527 @p499) :args ((or @t119 @t117 @t83 @t84) @t67 (@list @t116))) % 0.36/0.58 (step @p529 :rule cnf_equiv_neg1 :args (@t117)) % 0.36/0.58 (step @p530 :rule reordering :premises (@p529) :args ((or @t115 @t116 @t117))) % 0.36/0.58 (step @p531 :rule refl :args (@t118)) % 0.36/0.58 (step @p532 :rule bool-double-not-elim :args (@t115)) % 0.36/0.58 (step @p533 :rule nary_cong :premises (@p532 @p270 @p461 @p531) :args ((or (not @t119) @t85 @t111 @t118))) % 0.36/0.58 (assume-push @p738 @t119) % 0.36/0.58 (assume-push @p739 @t66) % 0.36/0.58 (assume-push @p740 @t82) % 0.36/0.58 (assume-push @p741 @t66) % 0.36/0.58 (assume-push @p742 @t82) % 0.36/0.58 (assume-push @p743 @t119) % 0.36/0.58 (step @p540 :rule false_intro :premises (@p739)) % 0.36/0.58 (step @p541 :rule false_intro :premises (@p740)) % 0.36/0.58 (step @p542 :rule symm :premises (@p541)) % 0.36/0.58 (step @p543 :rule false_intro :premises (@p738)) % 0.36/0.58 (step @p544 :rule trans :premises (@p543 @p542)) % 0.36/0.58 (step @p545 :rule cong :premises (@p544) :args (@t116)) % 0.36/0.58 (step @p546 :rule trans :premises (@p545 @p540)) % 0.36/0.58 (step @p547 :rule false_elim :premises (@p546)) % 0.36/0.58 (step-pop @p744 :rule scope :premises (@p547)) % 0.36/0.58 (step-pop @p745 :rule scope :premises (@p744)) % 0.36/0.58 (step-pop @p746 :rule scope :premises (@p745)) % 0.36/0.58 (step @p548 :rule process_scope :premises (@p746) :args (@t118)) % 0.36/0.58 (step @p552 :rule and_intro :premises (@p739 @p740 @p738)) % 0.36/0.58 (step @p553 :rule modus_ponens :premises (@p552 @p548)) % 0.36/0.58 (step-pop @p747 :rule scope :premises (@p553)) % 0.36/0.58 (step-pop @p748 :rule scope :premises (@p747)) % 0.36/0.58 (step-pop @p749 :rule scope :premises (@p748)) % 0.36/0.58 (step @p554 :rule process_scope :premises (@p749) :args (@t118)) % 0.36/0.58 (step @p558 :rule implies_elim :premises (@p554)) % 0.36/0.58 (step @p559 :rule cnf_and_neg :args (@t121)) % 0.36/0.58 (step @p560 :rule resolution :premises (@p559 @p558) :args (true @t121)) % 0.36/0.58 (step @p561 :rule eq_resolve :premises (@p560 @p533)) % 0.36/0.58 (step @p562 :rule reordering :premises (@p561) :args ((or @t115 @t118 @t59 @t60))) % 0.36/0.58 (step @p563 :rule chain_m_resolution :premises (@p562 @p530 @p528 @p308) :args ((or @t117 @t83 @t84 @t60) @t113 (@list @t116 @t115 @t59))) % 0.36/0.58 (step @p564 :rule chain_m_resolution :premises (@p563 @p269 @p497 @p209) :args (@t117 (@list false false true) (@list @t74 @t73 @t60))) % 0.36/0.58 (step @p565 :rule eq-refl :args (@t114)) % 0.36/0.58 (step @p566 :rule skolem_intro :args (@t115)) % 0.36/0.58 (step @p567 :rule refl :args (@t114)) % 0.36/0.58 (step @p568 :rule cong :premises (@p567 @p566) :args ((= @t114 @t115))) % 0.36/0.58 (step @p569 :rule trans :premises (@p568 @p565)) % 0.36/0.58 (step @p570 :rule true_elim :premises (@p569)) % 0.36/0.58 (step @p571 :rule cong :premises (@p570) :args (@t122)) % 0.36/0.58 (step @p572 :rule bool-double-not-elim :args (@t114)) % 0.36/0.58 (step @p573 :rule bool-eq-false :args (@t114)) % 0.36/0.58 (step @p574 :rule cong :premises (@p573) :args (@t124)) % 0.36/0.58 (step @p575 :rule trans :premises (@p574 @p572)) % 0.36/0.58 (step @p576 :rule aci_norm :args ((= (and @t124 true) @t124))) % 0.36/0.58 (step @p577 :rule ite-then-false :args (@t123 true)) % 0.36/0.58 (step @p578 :rule trans :premises (@p577 @p576)) % 0.36/0.58 (step @p579 :rule trans :premises (@p578 @p575)) % 0.36/0.58 (step @p580 :rule beta-reduce :args ((= @t125 (ite @t123 false true)))) % 0.36/0.58 (step @p581 :rule trans :premises (@p580 @p579)) % 0.36/0.58 (step @p582 :rule cong :premises (@p567 @p581) :args ((= @t114 @t125))) % 0.36/0.58 (step @p583 :rule trans :premises (@p582 @p565)) % 0.36/0.58 (step @p584 :rule ho_cong :premises (@p112 @p566)) % 0.36/0.58 (step @p585 :rule cong :premises (@p566 @p584) :args ((= @t115 @t126))) % 0.36/0.58 (step @p586 :rule eq-symm :args (@t126 @t115)) % 0.36/0.58 (step @p587 :rule trans :premises (@p586 @p585 @p583)) % 0.36/0.58 (step @p588 :rule true_elim :premises (@p587)) % 0.36/0.58 (step @p589 :rule cong :premises (@p570) :args (@t127)) % 0.36/0.58 (step @p590 :rule trans :premises (@p589 @p588)) % 0.36/0.58 (step @p591 :rule cong :premises (@p590 @p571) :args (@t128)) % 0.36/0.58 (step @p592 :rule cong :premises (@p591) :args (@t129)) % 0.36/0.58 (step @p593 :rule refl :args (@t130)) % 0.36/0.58 (step @p594 :rule nary_cong :premises (@p593 @p592) :args (@t131)) % 0.36/0.58 ; trust TRUST THEORY_LEMMA % 0.36/0.58 (step @p595 :rule trust :premises () :args (@t131)) % 0.36/0.58 (step @p596 :rule eq_resolve :premises (@p595 @p594)) % 0.36/0.58 (step @p597 :rule chain_m_resolution :premises (@p596 @p564) :args (@t130 @t108 (@list @t117))) % 0.36/0.58 (step @p598 :rule refl :args (@t132)) % 0.36/0.58 (step @p599 :rule refl :args (@t133)) % 0.36/0.58 (step @p600 :rule nary_cong :premises (@p599 @p154 @p598) :args ((or @t133 @t54 @t132))) % 0.36/0.58 (assume-push @p750 @t41) % 0.36/0.58 (assume-push @p751 @t130) % 0.36/0.58 (assume-push @p752 @t53) % 0.36/0.58 (step @p160 :rule evaluate :args (@t55)) % 0.36/0.58 (step @p604 :rule true_intro :premises (@p149)) % 0.36/0.58 (step @p605 :rule symm :premises (@p751)) % 0.36/0.58 (step @p606 :rule cong :premises (@p605) :args (@t51)) % 0.36/0.58 (step @p164 :rule false_intro :premises (@p151)) % 0.36/0.58 (step @p165 :rule symm :premises (@p164)) % 0.36/0.58 (step @p607 :rule trans :premises (@p165 @p606 @p604)) % 0.36/0.58 (step @p608 false :rule eq_resolve :premises (@p607 @p160)) % 0.36/0.58 (step-pop @p753 :rule scope :premises (@p608)) % 0.36/0.58 (step-pop @p754 :rule scope :premises (@p753)) % 0.36/0.58 (step-pop @p755 :rule scope :premises (@p754)) % 0.36/0.58 (step @p609 :rule process_scope :premises (@p755) :args (false)) % 0.36/0.58 (assume-push @p756 @t41) % 0.36/0.58 (assume-push @p757 @t53) % 0.36/0.58 (assume-push @p758 @t130) % 0.36/0.58 (step @p616 :rule and_intro :premises (@p149 @p758 @p151)) % 0.36/0.58 (step-pop @p759 :rule scope :premises (@p616)) % 0.36/0.58 (step-pop @p760 :rule scope :premises (@p759)) % 0.36/0.58 (step-pop @p761 :rule scope :premises (@p760)) % 0.36/0.58 (step @p617 :rule process_scope :premises (@p761) :args (@t134)) % 0.36/0.58 (step @p621 :rule implies_elim :premises (@p617)) % 0.36/0.58 (step @p622 :rule resolution :premises (@p621 @p609) :args (true @t134)) % 0.36/0.58 (step @p623 :rule not_and :premises (@p622)) % 0.36/0.58 (step @p624 :rule eq_resolve :premises (@p623 @p600)) % 0.36/0.58 (step @p625 false :rule chain_m_resolution :premises (@p624 @p597 @p151 @p149) :args (false (@list false true false) (@list @t130 @t51 @t41))) % 0.36/0.58 ) % 0.36/0.58 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------