%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU864^5 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n014.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:53:27 AM UTC 2026 % Result : Theorem 0.38s 0.56s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU864^5 : TPTP v9.2.1. Released v4.0.0. % 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 : n014.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:56:13 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.48 %----Proving TH0 % 0.38/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.56 % SZS status Theorem % 0.38/0.56 % SZS output start Proof % 0.38/0.56 ( % 0.38/0.56 (declare-sort tptp.a 0) % 0.38/0.56 (declare-const tptp.t tptp.a) % 0.38/0.56 (define @t1 () (@var "Xy" tptp.a)) % 0.38/0.56 (define @t2 () (@list @t1)) % 0.38/0.56 (define @t3 () (lambda @t2 (= tptp.t @t1))) % 0.38/0.56 (define @t4 () (@var "X" (-> (-> tptp.a Bool) Bool))) % 0.38/0.56 (define @t5 () (_ @t4 @t3)) % 0.38/0.56 (define @t6 () (@var "Xz" tptp.a)) % 0.38/0.56 (define @t7 () (@var "Xt_0" tptp.a)) % 0.38/0.56 (define @t8 () (= @t7 @t6)) % 0.38/0.56 (define @t9 () (@var "Xx" (-> tptp.a Bool))) % 0.38/0.56 (define @t10 () (_ @t9 @t6)) % 0.38/0.56 (define @t11 () (or @t10 @t8)) % 0.38/0.56 (define @t12 () (@list @t6)) % 0.38/0.56 (define @t13 () (lambda @t12 @t11)) % 0.38/0.56 (define @t14 () (_ @t4 @t13)) % 0.38/0.56 (define @t15 () (= tptp.t @t7)) % 0.38/0.56 (define @t16 () (@list @t7)) % 0.38/0.56 (define @t17 () (forall @t16 (=> @t15 @t14))) % 0.38/0.56 (define @t18 () (_ @t4 @t9)) % 0.38/0.56 (define @t19 () (=> @t18 @t17)) % 0.38/0.56 (define @t20 () (@list @t9)) % 0.38/0.56 (define @t21 () (forall @t20 @t19)) % 0.38/0.56 (define @t22 () (lambda @t2 false)) % 0.38/0.56 (define @t23 () (and (_ @t4 @t22) @t21)) % 0.38/0.56 (define @t24 () (=> @t23 @t5)) % 0.38/0.56 (define @t25 () (@list @t4)) % 0.38/0.56 (define @t26 () (forall @t25 @t24)) % 0.38/0.56 (define @t27 () (not @t26)) % 0.38/0.56 (define @t28 () (= tptp.t @t6)) % 0.38/0.56 (define @t29 () (@var "BOUND_VARIABLE_7532" tptp.a)) % 0.38/0.56 (define @t30 () (lambda (@list @t29) false)) % 0.38/0.56 (define @t31 () (@purify @t30)) % 0.38/0.56 (define @t32 () (or (_ @t31 @t6) @t28)) % 0.38/0.56 (define @t33 () (lambda @t12 @t32)) % 0.38/0.56 (define @t34 () (@purify @t33)) % 0.38/0.56 (define @t35 () (_ @t34 @t6)) % 0.38/0.56 (define @t36 () (_ @t33 @t6)) % 0.38/0.56 (define @t37 () (= @t35 @t36)) % 0.38/0.56 (define @t38 () (forall @t12 @t37)) % 0.38/0.56 (define @t39 () (_ @t4 @t3)) % 0.38/0.56 (define @t40 () (_ @t9 @t6)) % 0.38/0.56 (define @t41 () (lambda @t12 (or @t40 @t28))) % 0.38/0.56 (define @t42 () (_ @t4 @t41)) % 0.38/0.56 (define @t43 () (_ @t4 @t9)) % 0.38/0.56 (define @t44 () (forall @t20 (or (not @t43) @t42))) % 0.38/0.56 (define @t45 () (not @t44)) % 0.38/0.56 (define @t46 () (_ @t4 @t30)) % 0.38/0.56 (define @t47 () (_ @t4 @t30)) % 0.38/0.56 (define @t48 () (not @t47)) % 0.38/0.56 (define @t49 () (or @t48 @t45 @t5)) % 0.38/0.56 (define @t50 () (and @t47 @t44)) % 0.38/0.56 (define @t51 () (not @t18)) % 0.38/0.56 (define @t52 () (or @t51 @t42)) % 0.38/0.56 (define @t53 () (not (= tptp.t tptp.t))) % 0.38/0.56 (define @t54 () (or @t53 @t42)) % 0.38/0.56 (define @t55 () (or @t40 @t8)) % 0.38/0.56 (define @t56 () (lambda @t12 @t55)) % 0.38/0.56 (define @t57 () (_ @t4 @t56)) % 0.38/0.56 (define @t58 () (not @t15)) % 0.38/0.56 (define @t59 () (or @t58 @t58 @t57)) % 0.38/0.56 (define @t60 () (or @t58 @t57)) % 0.38/0.56 (define @t61 () (or @t58 @t14)) % 0.38/0.56 (define @t62 () (@purify @t3)) % 0.38/0.56 (define @t63 () (forall @t25 (or (not @t46) @t45 @t39))) % 0.38/0.56 (define @t64 () (@quantifiers_skolemize @t63 0)) % 0.38/0.56 (define @t65 () (_ @t64 @t62)) % 0.38/0.56 (define @t66 () (forall @t20 (or (not (_ @t64 @t9)) (_ @t64 @t41)))) % 0.38/0.56 (define @t67 () (not @t66)) % 0.38/0.56 (define @t68 () (_ @t64 @t31)) % 0.38/0.56 (define @t69 () (not @t68)) % 0.38/0.56 (define @t70 () (or @t69 @t67 @t65)) % 0.38/0.56 (define @t71 () (not @t70)) % 0.38/0.56 (define @t72 () (not @t63)) % 0.38/0.56 (define @t73 () (_ @t64 @t3)) % 0.38/0.56 (define @t74 () (_ @t64 @t30)) % 0.38/0.56 (define @t75 () (not @t74)) % 0.38/0.56 (define @t76 () (or @t75 @t67 @t73)) % 0.38/0.56 (define @t77 () (not @t76)) % 0.38/0.56 (define @t78 () (@list true)) % 0.38/0.56 (define @t79 () (@list @t70)) % 0.38/0.56 (define @t80 () (_ @t64 @t33)) % 0.38/0.56 (define @t81 () (or @t69 @t80)) % 0.38/0.56 (define @t82 () (_ @t64 @t34)) % 0.38/0.56 (define @t83 () (or @t69 @t82)) % 0.38/0.56 (define @t84 () (not @t65)) % 0.38/0.56 (define @t85 () (= @t62 @t34)) % 0.38/0.56 (define @t86 () (not @t85)) % 0.38/0.56 (define @t87 () (not @t82)) % 0.38/0.56 (define @t88 () (and @t84 @t85 @t82)) % 0.38/0.56 (define @t89 () (@list true false)) % 0.38/0.56 (define @t90 () (@const 0 tptp.a)) % 0.38/0.56 (define @t91 () (= tptp.t @t90)) % 0.38/0.56 (define @t92 () (_ @t34 @t90)) % 0.38/0.56 (define @t93 () (= (_ @t3 @t90) @t91)) % 0.38/0.56 (define @t94 () (_ @t62 @t90)) % 0.38/0.56 (define @t95 () (= @t94 @t92)) % 0.38/0.56 (define @t96 () (not @t95)) % 0.38/0.56 (define @t97 () (or @t85 @t96)) % 0.38/0.56 (define @t98 () (= @t92 @t91)) % 0.38/0.56 (define @t99 () (_ @t30 @t90)) % 0.38/0.56 (define @t100 () (_ @t31 @t90)) % 0.38/0.56 (define @t101 () (or @t100 @t91)) % 0.38/0.56 (define @t102 () (= @t92 @t101)) % 0.38/0.56 (define @t103 () (forall @t12 (= @t32 @t35))) % 0.38/0.56 (define @t104 () (= @t101 @t92)) % 0.38/0.56 (assume @p1 @t27) % 0.38/0.56 (assume @p2 true) % 0.38/0.56 (step @p3 :rule eq-symm :args (@t35 @t32)) % 0.38/0.56 (step @p4 :rule beta-reduce :args ((= @t36 @t32))) % 0.38/0.56 (step @p5 :rule refl :args (@t35)) % 0.38/0.56 (step @p6 :rule cong :premises (@p5 @p4) :args (@t37)) % 0.38/0.56 (step @p7 :rule trans :premises (@p6 @p3)) % 0.38/0.56 (step @p8 :rule cong :premises (@p7) :args (@t38)) % 0.38/0.56 (step @p9 :rule quant-unused-vars :args ((= (forall @t12 true) true))) % 0.38/0.56 (step @p10 :rule eq-refl :args (@t36)) % 0.38/0.56 (step @p11 :rule cong :premises (@p10) :args ((forall @t12 (= @t36 @t36)))) % 0.38/0.56 (step @p12 :rule trans :premises (@p11 @p9)) % 0.38/0.56 (step @p13 :rule refl :args (@t36)) % 0.38/0.56 (step @p14 :rule refl :args (@t6)) % 0.38/0.56 (step @p15 :rule skolem_intro :args (@t34)) % 0.38/0.56 (step @p16 :rule ho_cong :premises (@p15 @p14)) % 0.38/0.56 (step @p17 :rule cong :premises (@p16 @p13) :args (@t37)) % 0.38/0.56 (step @p18 :rule cong :premises (@p17) :args (@t38)) % 0.38/0.56 (step @p19 :rule trans :premises (@p18 @p12)) % 0.38/0.56 (step @p20 :rule true_elim :premises (@p19)) % 0.38/0.56 (step @p21 :rule eq_resolve :premises (@p20 @p8)) % 0.38/0.56 (step @p22 :rule refl :args (@t39)) % 0.38/0.56 (step @p23 :rule refl :args (@t5)) % 0.38/0.56 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t5 @t39))) % 0.38/0.56 (step @p25 :rule symm :premises (@p24)) % 0.38/0.56 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.38/0.56 (step @p27 :rule refl :args (@t45)) % 0.38/0.56 (step @p28 :rule refl :args ((_ @t4 @t30))) % 0.38/0.56 (step @p29 :rule refl :args (@t30)) % 0.38/0.56 (step @p30 :rule cong :premises (@p29) :args (@t46)) % 0.38/0.56 (step @p31 :rule trans :premises (@p30 @p28)) % 0.38/0.56 (step @p32 :rule refl :args (@t4)) % 0.38/0.56 (step @p33 :rule ho_cong :premises (@p32 @p29)) % 0.38/0.56 (step @p34 :rule cong :premises (@p33 @p31) :args ((= @t47 @t46))) % 0.38/0.56 (step @p35 :rule symm :premises (@p34)) % 0.38/0.56 (step @p36 :rule refl :args ((_ @t4 @t30))) % 0.38/0.56 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.38/0.56 (step @p38 :rule cong :premises (@p37) :args (@t48)) % 0.38/0.56 (step @p39 :rule nary_cong :premises (@p38 @p27 @p26) :args (@t49)) % 0.38/0.56 (step @p40 :rule cong :premises (@p39) :args ((forall @t25 @t49))) % 0.38/0.56 (step @p41 :rule aci_norm :args ((= (or (or @t48 @t45) @t5) @t49))) % 0.38/0.56 (step @p42 :rule bool-and-de-morgan :args (@t47 @t44 true)) % 0.38/0.56 (step @p43 :rule nary_cong :premises (@p42 @p23) :args ((or (not @t50) @t5))) % 0.38/0.56 (step @p44 :rule trans :premises (@p43 @p41)) % 0.38/0.56 (step @p45 :rule bool-impl-elim :args (@t50 @t5)) % 0.38/0.56 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.56 (step @p47 :rule cong :premises (@p46) :args ((forall @t25 (=> @t50 @t5)))) % 0.38/0.56 (step @p48 :rule trans :premises (@p47 @p40)) % 0.38/0.56 (step @p49 :rule refl :args (@t5)) % 0.38/0.56 (step @p50 :rule refl :args (@t42)) % 0.38/0.56 (step @p51 :rule refl :args (@t43)) % 0.38/0.56 (step @p52 :rule refl :args (@t18)) % 0.38/0.56 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t18 @t43))) % 0.38/0.56 (step @p54 :rule symm :premises (@p53)) % 0.38/0.56 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.38/0.56 (step @p56 :rule cong :premises (@p55) :args (@t51)) % 0.38/0.56 (step @p57 :rule nary_cong :premises (@p56 @p50) :args (@t52)) % 0.38/0.56 (step @p58 :rule cong :premises (@p57) :args ((forall @t20 @t52))) % 0.38/0.56 (step @p59 :rule bool-impl-elim :args (@t18 @t42)) % 0.38/0.56 (step @p60 :rule cong :premises (@p59) :args ((forall @t20 (=> @t18 @t42)))) % 0.38/0.56 (step @p61 :rule trans :premises (@p60 @p58)) % 0.38/0.56 (step @p62 :rule aci_norm :args ((= (or false @t42) @t42))) % 0.38/0.56 (step @p63 :rule refl :args (@t42)) % 0.38/0.56 (step @p64 :rule evaluate :args ((not true))) % 0.38/0.56 (step @p65 :rule eq-refl :args (tptp.t)) % 0.38/0.56 (step @p66 :rule cong :premises (@p65) :args (@t53)) % 0.38/0.56 (step @p67 :rule trans :premises (@p66 @p64)) % 0.38/0.56 (step @p68 :rule nary_cong :premises (@p67 @p63) :args (@t54)) % 0.38/0.56 (step @p69 :rule trans :premises (@p68 @p62)) % 0.38/0.56 (step @p70 :rule quant-var-elim-eq :args ((= (forall @t16 (or (not (= @t7 tptp.t)) @t58 @t57)) @t54))) % 0.38/0.56 (step @p71 :rule refl :args (@t57)) % 0.38/0.56 (step @p72 :rule refl :args (@t58)) % 0.38/0.56 (step @p73 :rule eq-symm :args (tptp.t @t7)) % 0.38/0.56 (step @p74 :rule cong :premises (@p73) :args (@t58)) % 0.38/0.56 (step @p75 :rule nary_cong :premises (@p74 @p72 @p71) :args (@t59)) % 0.38/0.56 (step @p76 :rule aci_norm :args ((= @t60 @t59))) % 0.38/0.56 (step @p77 :rule trans :premises (@p76 @p75)) % 0.38/0.56 (step @p78 :rule cong :premises (@p77) :args ((forall @t16 @t60))) % 0.38/0.56 (step @p79 :rule trans :premises (@p78 @p70)) % 0.38/0.56 (step @p80 :rule trans :premises (@p79 @p69)) % 0.38/0.56 (step @p81 :rule refl :args ((_ @t4 @t13))) % 0.38/0.56 (step @p82 :rule refl :args (@t8)) % 0.38/0.56 (step @p83 :rule refl :args (@t40)) % 0.38/0.56 (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t55)) % 0.38/0.56 (step @p85 :rule cong :premises (@p84) :args (@t56)) % 0.38/0.56 (step @p86 :rule cong :premises (@p85) :args (@t57)) % 0.38/0.56 (step @p87 :rule trans :premises (@p86 @p81)) % 0.38/0.56 (step @p88 :rule ho_cong :premises (@p32 @p85)) % 0.38/0.56 (step @p89 :rule cong :premises (@p88 @p87) :args ((= (_ @t4 @t56) @t57))) % 0.38/0.56 (step @p90 :rule symm :premises (@p89)) % 0.38/0.56 (step @p91 :rule refl :args (@t14)) % 0.38/0.56 (step @p92 :rule eq_resolve :premises (@p91 @p90)) % 0.38/0.56 (step @p93 :rule refl :args (@t10)) % 0.38/0.56 (step @p94 :rule cong :premises (@p93 @p83) :args ((= @t10 @t40))) % 0.38/0.56 (step @p95 :rule symm :premises (@p94)) % 0.38/0.56 (step @p96 :rule eq_resolve :premises (@p93 @p95)) % 0.38/0.56 (step @p97 :rule nary_cong :premises (@p96 @p82) :args (@t11)) % 0.38/0.56 (step @p98 :rule cong :premises (@p97) :args (@t13)) % 0.38/0.56 (step @p99 :rule ho_cong :premises (@p32 @p98)) % 0.38/0.56 (step @p100 :rule trans :premises (@p99 @p92)) % 0.38/0.56 (step @p101 :rule nary_cong :premises (@p72 @p100) :args (@t61)) % 0.38/0.56 (step @p102 :rule cong :premises (@p101) :args ((forall @t16 @t61))) % 0.38/0.56 (step @p103 :rule trans :premises (@p102 @p80)) % 0.38/0.56 (step @p104 :rule bool-impl-elim :args (@t15 @t14)) % 0.38/0.56 (step @p105 :rule cong :premises (@p104) :args (@t17)) % 0.38/0.56 (step @p106 :rule trans :premises (@p105 @p103)) % 0.38/0.56 (step @p107 :rule refl :args (@t18)) % 0.38/0.56 (step @p108 :rule cong :premises (@p107 @p106) :args (@t19)) % 0.38/0.56 (step @p109 :rule cong :premises (@p108) :args (@t21)) % 0.38/0.56 (step @p110 :rule trans :premises (@p109 @p61)) % 0.38/0.56 (step @p111 :rule symm :premises (@p29)) % 0.38/0.56 (step @p112 :rule alpha_equiv :args (@t22 (@list @t1) (@list @t29))) % 0.38/0.56 (step @p113 :rule trans :premises (@p112 @p111)) % 0.38/0.56 (step @p114 :rule refl :args (@t4)) % 0.38/0.56 (step @p115 :rule ho_cong :premises (@p114 @p113)) % 0.38/0.56 (step @p116 :rule nary_cong :premises (@p115 @p110) :args (@t23)) % 0.38/0.56 (step @p117 :rule cong :premises (@p116 @p49) :args (@t24)) % 0.38/0.56 (step @p118 :rule cong :premises (@p117) :args (@t26)) % 0.38/0.56 (step @p119 :rule trans :premises (@p118 @p48)) % 0.38/0.56 (step @p120 :rule cong :premises (@p119) :args (@t27)) % 0.38/0.56 (step @p121 :rule eq_resolve :premises (@p1 @p120)) % 0.38/0.56 (step @p122 :rule refl :args (@t71)) % 0.38/0.56 (step @p123 :rule bool-double-not-elim :args (@t63)) % 0.38/0.56 (step @p124 :rule nary_cong :premises (@p123 @p122) :args ((or (not @t72) @t71))) % 0.38/0.56 (step @p125 :rule eq-refl :args (@t3)) % 0.38/0.56 (step @p126 :rule skolem_intro :args (@t62)) % 0.38/0.56 (step @p127 :rule refl :args (@t3)) % 0.38/0.56 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t3 @t62))) % 0.38/0.56 (step @p129 :rule trans :premises (@p128 @p125)) % 0.38/0.56 (step @p130 :rule true_elim :premises (@p129)) % 0.38/0.56 (step @p131 :rule cong :premises (@p130) :args (@t73)) % 0.38/0.56 (step @p132 :rule refl :args (@t67)) % 0.38/0.56 (step @p133 :rule eq-refl :args (@t30)) % 0.38/0.56 (step @p134 :rule refl :args (@t30)) % 0.38/0.56 (step @p135 :rule cong :premises (@p134 @p111) :args ((= @t30 @t30))) % 0.38/0.56 (step @p136 :rule trans :premises (@p135 @p133)) % 0.38/0.56 (step @p137 :rule skolem_intro :args (@t31)) % 0.38/0.56 (step @p138 :rule cong :premises (@p134 @p137) :args ((= @t30 @t31))) % 0.38/0.56 (step @p139 :rule trans :premises (@p138 @p136)) % 0.38/0.56 (step @p140 :rule true_elim :premises (@p139)) % 0.38/0.56 (step @p141 :rule cong :premises (@p140) :args (@t74)) % 0.38/0.56 (step @p142 :rule cong :premises (@p141) :args (@t75)) % 0.38/0.56 (step @p143 :rule nary_cong :premises (@p142 @p132 @p131) :args (@t76)) % 0.38/0.56 (step @p144 :rule cong :premises (@p143) :args (@t77)) % 0.38/0.56 (step @p145 :rule refl :args (@t72)) % 0.38/0.56 (step @p146 :rule cong :premises (@p145 @p144) :args ((=> @t72 @t77))) % 0.38/0.56 (assume-push @p271 @t72) % 0.38/0.56 (step @p148 :rule skolemize :premises (@p121)) % 0.38/0.56 (step-pop @p272 :rule scope :premises (@p148)) % 0.38/0.56 (step @p149 :rule process_scope :premises (@p272) :args (@t77)) % 0.38/0.56 (step @p151 :rule eq_resolve :premises (@p149 @p146)) % 0.38/0.56 (step @p152 :rule implies_elim :premises (@p151)) % 0.38/0.56 (step @p153 :rule eq_resolve :premises (@p152 @p124)) % 0.38/0.56 (step @p154 :rule chain_m_resolution :premises (@p153 @p121) :args (@t71 @t78 (@list @t63))) % 0.38/0.56 (step @p155 :rule bool-double-not-elim :args (@t66)) % 0.38/0.56 (step @p156 :rule refl :args (@t70)) % 0.38/0.56 (step @p157 :rule nary_cong :premises (@p156 @p155) :args ((or @t70 (not @t67)))) % 0.38/0.56 (step @p158 :rule cnf_or_neg :args (@t70 1)) % 0.38/0.56 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.38/0.56 (step @p160 :rule reordering :premises (@p159) :args ((or @t66 @t70))) % 0.38/0.56 (step @p161 :rule chain_m_resolution :premises (@p160 @p154) :args (@t66 @t78 @t79)) % 0.38/0.56 (step @p162 :rule eq-refl :args ((lambda @t12 (or (_ @t30 @t6) @t28)))) % 0.38/0.56 (step @p163 :rule refl :args (@t28)) % 0.38/0.56 (step @p164 :rule ho_cong :premises (@p137 @p14)) % 0.38/0.56 (step @p165 :rule nary_cong :premises (@p164 @p163) :args (@t32)) % 0.38/0.56 (step @p166 :rule cong :premises (@p165) :args (@t33)) % 0.38/0.56 (step @p167 :rule trans :premises (@p15 @p166)) % 0.38/0.56 (step @p168 :rule cong :premises (@p166 @p167) :args ((= @t33 @t34))) % 0.38/0.56 (step @p169 :rule trans :premises (@p168 @p162)) % 0.38/0.56 (step @p170 :rule true_elim :premises (@p169)) % 0.38/0.56 (step @p171 :rule cong :premises (@p170) :args (@t80)) % 0.38/0.56 (step @p172 :rule refl :args (@t69)) % 0.38/0.56 (step @p173 :rule nary_cong :premises (@p172 @p171) :args (@t81)) % 0.38/0.56 (step @p174 :rule refl :args (@t66)) % 0.38/0.56 (step @p175 :rule cong :premises (@p174 @p173) :args ((=> @t66 @t81))) % 0.38/0.56 (assume-push @p273 @t66) % 0.38/0.56 (step @p177 :rule instantiate :premises (@p161) :args ((@list @t31))) % 0.38/0.56 (step-pop @p274 :rule scope :premises (@p177)) % 0.38/0.56 (step @p178 :rule process_scope :premises (@p274) :args (@t81)) % 0.38/0.56 (step @p180 :rule eq_resolve :premises (@p178 @p175)) % 0.38/0.56 (step @p181 :rule implies_elim :premises (@p180)) % 0.38/0.56 (step @p182 :rule chain_m_resolution :premises (@p181 @p161) :args (@t83 (@list false) (@list @t66))) % 0.38/0.56 (step @p183 :rule bool-double-not-elim :args (@t68)) % 0.38/0.56 (step @p184 :rule nary_cong :premises (@p156 @p183) :args ((or @t70 (not @t69)))) % 0.38/0.56 (step @p185 :rule cnf_or_neg :args (@t70 0)) % 0.38/0.56 (step @p186 :rule eq_resolve :premises (@p185 @p184)) % 0.38/0.56 (step @p187 :rule reordering :premises (@p186) :args ((or @t68 @t70))) % 0.38/0.56 (step @p188 :rule chain_m_resolution :premises (@p187 @p154) :args (@t68 @t78 @t79)) % 0.38/0.56 (step @p189 :rule cnf_or_pos :args (@t83)) % 0.38/0.56 (step @p190 :rule reordering :premises (@p189) :args ((or @t69 @t82 (not @t83)))) % 0.38/0.56 (step @p191 :rule chain_m_resolution :premises (@p190 @p188 @p182) :args (@t82 (@list false false) (@list @t68 @t83))) % 0.38/0.56 (step @p192 :rule cnf_or_neg :args (@t70 2)) % 0.38/0.56 (step @p193 :rule chain_m_resolution :premises (@p192 @p154) :args (@t84 @t78 @t79)) % 0.38/0.56 (step @p194 :rule refl :args (@t86)) % 0.38/0.56 (step @p195 :rule refl :args (@t87)) % 0.38/0.56 (step @p196 :rule bool-double-not-elim :args (@t65)) % 0.38/0.56 (step @p197 :rule nary_cong :premises (@p196 @p195 @p194) :args ((or (not @t84) @t87 @t86))) % 0.38/0.56 (assume-push @p275 @t84) % 0.38/0.56 (assume-push @p276 @t85) % 0.38/0.56 (assume-push @p277 @t82) % 0.38/0.56 (step @p201 :rule evaluate :args ((= true false))) % 0.38/0.56 (step @p202 :rule false_intro :premises (@p193)) % 0.38/0.56 (step @p203 :rule symm :premises (@p276)) % 0.38/0.56 (step @p204 :rule cong :premises (@p203) :args (@t82)) % 0.38/0.56 (step @p205 :rule true_intro :premises (@p191)) % 0.38/0.56 (step @p206 :rule symm :premises (@p205)) % 0.38/0.56 (step @p207 :rule trans :premises (@p206 @p204 @p202)) % 0.38/0.56 (step @p208 false :rule eq_resolve :premises (@p207 @p201)) % 0.38/0.56 (step-pop @p278 :rule scope :premises (@p208)) % 0.38/0.56 (step-pop @p279 :rule scope :premises (@p278)) % 0.38/0.56 (step-pop @p280 :rule scope :premises (@p279)) % 0.38/0.56 (step @p209 :rule process_scope :premises (@p280) :args (false)) % 0.38/0.56 (assume-push @p281 @t84) % 0.38/0.56 (assume-push @p282 @t82) % 0.38/0.56 (assume-push @p283 @t85) % 0.38/0.56 (step @p216 :rule and_intro :premises (@p193 @p283 @p191)) % 0.38/0.56 (step-pop @p284 :rule scope :premises (@p216)) % 0.38/0.56 (step-pop @p285 :rule scope :premises (@p284)) % 0.38/0.56 (step-pop @p286 :rule scope :premises (@p285)) % 0.38/0.56 (step @p217 :rule process_scope :premises (@p286) :args (@t88)) % 0.38/0.56 (step @p221 :rule implies_elim :premises (@p217)) % 0.38/0.56 (step @p222 :rule resolution :premises (@p221 @p209) :args (true @t88)) % 0.38/0.56 (step @p223 :rule not_and :premises (@p222)) % 0.38/0.56 (step @p224 :rule eq_resolve :premises (@p223 @p197)) % 0.38/0.56 (step @p225 :rule chain_m_resolution :premises (@p224 @p193 @p191) :args (@t86 @t89 (@list @t65 @t82))) % 0.38/0.56 (step @p226 :rule eq-symm :args (@t91 @t92)) % 0.38/0.56 (step @p227 :rule refl :args (@t92)) % 0.38/0.56 (step @p228 :rule eq-refl :args (@t91)) % 0.38/0.56 (step @p229 :rule refl :args (@t91)) % 0.38/0.56 (step @p230 :rule beta-reduce :args (@t93)) % 0.38/0.56 (step @p231 :rule cong :premises (@p230 @p229) :args (@t93)) % 0.38/0.56 (step @p232 :rule trans :premises (@p231 @p228)) % 0.38/0.56 (step @p233 :rule refl :args (@t90)) % 0.38/0.56 (step @p234 :rule ho_cong :premises (@p126 @p233)) % 0.38/0.56 (step @p235 :rule cong :premises (@p234 @p229) :args ((= @t94 @t91))) % 0.38/0.56 (step @p236 :rule trans :premises (@p235 @p232)) % 0.38/0.56 (step @p237 :rule true_elim :premises (@p236)) % 0.38/0.56 (step @p238 :rule cong :premises (@p237 @p227) :args (@t95)) % 0.38/0.56 (step @p239 :rule trans :premises (@p238 @p226)) % 0.38/0.56 (step @p240 :rule cong :premises (@p239) :args (@t96)) % 0.38/0.56 (step @p241 :rule refl :args (@t85)) % 0.38/0.56 (step @p242 :rule nary_cong :premises (@p241 @p240) :args (@t97)) % 0.38/0.56 ; WARNING: add trust step for TRUST % 0.38/0.57 ; trust TRUST THEORY_LEMMA % 0.38/0.57 (step @p243 :rule trust :premises () :args (@t97)) % 0.38/0.57 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 0.38/0.57 (step @p245 :rule chain_m_resolution :premises (@p244 @p225) :args ((not @t98) @t78 (@list @t85))) % 0.38/0.57 (step @p246 :rule aci_norm :args ((= (or false @t91) @t91))) % 0.38/0.57 (step @p247 :rule evaluate :args ((not false))) % 0.38/0.57 (step @p248 :rule beta-reduce :args ((= @t99 false))) % 0.38/0.57 (step @p249 :rule cong :premises (@p248) :args ((not @t99))) % 0.38/0.57 (step @p250 :rule trans :premises (@p249 @p247)) % 0.38/0.57 (step @p251 :rule ho_cong :premises (@p137 @p233)) % 0.38/0.57 (step @p252 :rule cong :premises (@p251) :args ((not @t100))) % 0.38/0.57 (step @p253 :rule bool-eq-false :args (@t100)) % 0.38/0.57 (step @p254 :rule trans :premises (@p253 @p252 @p250)) % 0.38/0.57 (step @p255 :rule true_elim :premises (@p254)) % 0.38/0.57 (step @p256 :rule nary_cong :premises (@p255 @p229) :args (@t101)) % 0.38/0.57 (step @p257 :rule trans :premises (@p256 @p246)) % 0.38/0.57 (step @p258 :rule cong :premises (@p227 @p257) :args (@t102)) % 0.38/0.57 (step @p259 :rule refl :args (@t103)) % 0.38/0.57 (step @p260 :rule cong :premises (@p259 @p258) :args ((=> @t103 @t102))) % 0.38/0.57 (step @p261 :rule eq-symm :args (@t101 @t92)) % 0.38/0.57 (step @p262 :rule cong :premises (@p259 @p261) :args ((=> @t103 @t104))) % 0.38/0.57 (assume-push @p287 @t103) % 0.38/0.57 (step @p264 :rule instantiate :premises (@p21) :args ((@list @t90))) % 0.38/0.57 (step-pop @p288 :rule scope :premises (@p264)) % 0.38/0.57 (step @p265 :rule process_scope :premises (@p288) :args (@t104)) % 0.38/0.57 (step @p267 :rule eq_resolve :premises (@p265 @p262)) % 0.38/0.57 (step @p268 :rule eq_resolve :premises (@p267 @p260)) % 0.38/0.57 (step @p269 :rule implies_elim :premises (@p268)) % 0.38/0.57 (step @p270 false :rule chain_m_resolution :premises (@p269 @p245 @p21) :args (false @t89 (@list @t98 @t103))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------