%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV417^5 : 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 : n026.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 08:55:55 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV417^5 : 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 % 0.17/0.34 % Computer : n026.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 18:32:25 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort tptp.a 0) % 0.37/0.57 (declare-const tptp.cP (-> (-> tptp.a Bool) Bool)) % 0.37/0.57 (define @t1 () (@var "Xx" tptp.a)) % 0.37/0.57 (define @t2 () (@list @t1)) % 0.37/0.57 (define @t3 () (lambda @t2 false)) % 0.37/0.57 (define @t4 () (@var "X" (-> tptp.a Bool))) % 0.37/0.57 (define @t5 () (= @t4 @t3)) % 0.37/0.57 (define @t6 () (and @t5 (_ tptp.cP @t3))) % 0.37/0.57 (define @t7 () (@var "Z" (-> tptp.a Bool))) % 0.37/0.57 (define @t8 () (_ @t7 @t1)) % 0.37/0.57 (define @t9 () (@var "Y" (-> tptp.a Bool))) % 0.37/0.57 (define @t10 () (_ @t9 @t1)) % 0.37/0.57 (define @t11 () (and @t10 @t8)) % 0.37/0.57 (define @t12 () (lambda @t2 @t11)) % 0.37/0.57 (define @t13 () (_ tptp.cP @t12)) % 0.37/0.57 (define @t14 () (= @t12 @t3)) % 0.37/0.57 (define @t15 () (_ @t4 @t1)) % 0.37/0.57 (define @t16 () (forall @t2 (=> @t15 @t8))) % 0.37/0.57 (define @t17 () (forall @t2 (=> @t15 @t10))) % 0.37/0.57 (define @t18 () (and @t17 @t16 @t14 @t13)) % 0.37/0.57 (define @t19 () (=> @t18 @t6)) % 0.37/0.57 (define @t20 () (@list @t4 @t9 @t7)) % 0.37/0.57 (define @t21 () (forall @t20 @t19)) % 0.37/0.57 (define @t22 () (not @t21)) % 0.37/0.57 (define @t23 () (@var "BOUND_VARIABLE_7546" tptp.a)) % 0.37/0.57 (define @t24 () (lambda (@list @t23) false)) % 0.37/0.57 (define @t25 () (tptp.cP @t24)) % 0.37/0.57 (define @t26 () (= @t4 @t24)) % 0.37/0.57 (define @t27 () (and @t26 @t25)) % 0.37/0.57 (define @t28 () (_ @t7 @t1)) % 0.37/0.57 (define @t29 () (_ @t9 @t1)) % 0.37/0.57 (define @t30 () (and @t29 @t28)) % 0.37/0.57 (define @t31 () (lambda @t2 @t30)) % 0.37/0.57 (define @t32 () (tptp.cP @t31)) % 0.37/0.57 (define @t33 () (not @t32)) % 0.37/0.57 (define @t34 () (not (= @t31 @t24))) % 0.37/0.57 (define @t35 () (_ @t4 @t1)) % 0.37/0.57 (define @t36 () (not @t35)) % 0.37/0.57 (define @t37 () (forall @t2 (or @t36 @t28))) % 0.37/0.57 (define @t38 () (not @t37)) % 0.37/0.57 (define @t39 () (forall @t2 (or @t36 @t29))) % 0.37/0.57 (define @t40 () (not @t39)) % 0.37/0.57 (define @t41 () (or @t40 @t38 @t34 @t33 @t27)) % 0.37/0.57 (define @t42 () (_ tptp.cP @t24)) % 0.37/0.57 (define @t43 () (and @t26 @t42)) % 0.37/0.57 (define @t44 () (not @t13)) % 0.37/0.57 (define @t45 () (= @t12 @t24)) % 0.37/0.57 (define @t46 () (not @t45)) % 0.37/0.57 (define @t47 () (or @t40 @t38 @t46 @t44 @t43)) % 0.37/0.57 (define @t48 () (or @t40 @t38 @t46 @t44)) % 0.37/0.57 (define @t49 () (and @t39 @t37 @t45 @t13)) % 0.37/0.57 (define @t50 () (not @t15)) % 0.37/0.57 (define @t51 () (or @t50 @t8)) % 0.37/0.57 (define @t52 () (or @t50 @t10)) % 0.37/0.57 (define @t53 () (@purify @t24)) % 0.37/0.57 (define @t54 () (tptp.cP @t53)) % 0.37/0.57 (define @t55 () (forall @t20 (or @t40 @t38 (not (= @t24 @t31)) @t33 @t27))) % 0.37/0.57 (define @t56 () (@quantifiers_skolemize @t55 0)) % 0.37/0.57 (define @t57 () (= @t56 @t53)) % 0.37/0.57 (define @t58 () (and @t57 @t54)) % 0.37/0.57 (define @t59 () (@quantifiers_skolemize @t55 2)) % 0.37/0.57 (define @t60 () (_ @t59 @t1)) % 0.37/0.57 (define @t61 () (@quantifiers_skolemize @t55 1)) % 0.37/0.57 (define @t62 () (_ @t61 @t1)) % 0.37/0.57 (define @t63 () (and @t62 @t60)) % 0.37/0.57 (define @t64 () (lambda @t2 @t63)) % 0.37/0.57 (define @t65 () (@purify @t64)) % 0.37/0.57 (define @t66 () (tptp.cP @t65)) % 0.37/0.57 (define @t67 () (not @t66)) % 0.37/0.57 (define @t68 () (= @t53 @t65)) % 0.37/0.57 (define @t69 () (not @t68)) % 0.37/0.57 (define @t70 () (not (_ @t56 @t1))) % 0.37/0.57 (define @t71 () (forall @t2 (or @t70 @t60))) % 0.37/0.57 (define @t72 () (not @t71)) % 0.37/0.57 (define @t73 () (forall @t2 (or @t70 @t62))) % 0.37/0.57 (define @t74 () (not @t73)) % 0.37/0.57 (define @t75 () (or @t74 @t72 @t69 @t67 @t58)) % 0.37/0.57 (define @t76 () (not @t75)) % 0.37/0.57 (define @t77 () (not @t55)) % 0.37/0.57 (define @t78 () (= @t24 @t56)) % 0.37/0.57 (define @t79 () (and @t78 @t25)) % 0.37/0.57 (define @t80 () (tptp.cP @t64)) % 0.37/0.57 (define @t81 () (not @t80)) % 0.37/0.57 (define @t82 () (= @t24 @t64)) % 0.37/0.57 (define @t83 () (not @t82)) % 0.37/0.57 (define @t84 () (or @t74 @t72 @t83 @t81 @t79)) % 0.37/0.57 (define @t85 () (not @t84)) % 0.37/0.57 (define @t86 () (and (= @t56 @t24) @t25)) % 0.37/0.57 (define @t87 () (or @t74 @t72 @t83 @t81 @t86)) % 0.37/0.57 (define @t88 () (not @t87)) % 0.37/0.57 (define @t89 () (@list true)) % 0.37/0.57 (define @t90 () (@list @t75)) % 0.37/0.57 (define @t91 () (_ @t65 @t1)) % 0.37/0.57 (define @t92 () (_ @t64 @t1)) % 0.37/0.57 (define @t93 () (= @t91 @t92)) % 0.37/0.57 (define @t94 () (forall @t2 @t93)) % 0.37/0.57 (define @t95 () (@const 0 tptp.a)) % 0.37/0.57 (define @t96 () (@list @t95)) % 0.37/0.57 (define @t97 () (_ @t56 @t95)) % 0.37/0.57 (define @t98 () (_ @t24 @t95)) % 0.37/0.57 (define @t99 () (_ @t53 @t95)) % 0.37/0.57 (define @t100 () (= @t97 @t99)) % 0.37/0.57 (define @t101 () (not @t100)) % 0.37/0.57 (define @t102 () (or @t57 @t101)) % 0.37/0.57 (define @t103 () (_ @t59 @t95)) % 0.37/0.57 (define @t104 () (not @t97)) % 0.37/0.57 (define @t105 () (or @t104 @t103)) % 0.37/0.57 (define @t106 () (@list false false)) % 0.37/0.57 (define @t107 () (_ @t61 @t95)) % 0.37/0.57 (define @t108 () (or @t104 @t107)) % 0.37/0.57 (define @t109 () (and @t107 @t103)) % 0.37/0.57 (define @t110 () (_ @t65 @t95)) % 0.37/0.57 (define @t111 () (= @t109 @t110)) % 0.37/0.57 (define @t112 () (_ @t64 @t95)) % 0.37/0.57 (define @t113 () (_ @t64 @t95)) % 0.37/0.57 (define @t114 () (_ @t65 @t95)) % 0.37/0.57 (define @t115 () (not @t114)) % 0.37/0.57 (define @t116 () (=> (= @t65 @t53) (= @t114 false))) % 0.37/0.57 (assume @p1 @t22) % 0.37/0.57 (assume @p2 true) % 0.37/0.57 (step @p3 :rule refl :args (@t27)) % 0.37/0.57 (step @p4 :rule refl :args (@t33)) % 0.37/0.57 (step @p5 :rule eq-symm :args (@t31 @t24)) % 0.37/0.57 (step @p6 :rule cong :premises (@p5) :args (@t34)) % 0.37/0.57 (step @p7 :rule refl :args (@t38)) % 0.37/0.57 (step @p8 :rule refl :args (@t40)) % 0.37/0.57 (step @p9 :rule nary_cong :premises (@p8 @p7 @p6 @p4 @p3) :args (@t41)) % 0.37/0.57 (step @p10 :rule cong :premises (@p9) :args ((forall @t20 @t41))) % 0.37/0.57 (step @p11 :rule refl :args (@t25)) % 0.37/0.57 (step @p12 :rule refl :args (@t24)) % 0.37/0.57 (step @p13 :rule cong :premises (@p12) :args (@t25)) % 0.37/0.57 (step @p14 :rule trans :premises (@p13 @p11)) % 0.37/0.57 (step @p15 :rule refl :args (tptp.cP)) % 0.37/0.57 (step @p16 :rule ho_cong :premises (@p15 @p12)) % 0.37/0.57 (step @p17 :rule cong :premises (@p16 @p14) :args ((= @t42 @t25))) % 0.37/0.57 (step @p18 :rule symm :premises (@p17)) % 0.37/0.57 (step @p19 :rule refl :args ((_ tptp.cP @t24))) % 0.37/0.57 (step @p20 :rule eq_resolve :premises (@p19 @p18)) % 0.37/0.57 (step @p21 :rule refl :args (@t26)) % 0.37/0.57 (step @p22 :rule nary_cong :premises (@p21 @p20) :args (@t43)) % 0.37/0.57 (step @p23 :rule refl :args ((tptp.cP @t12))) % 0.37/0.57 (step @p24 :rule refl :args (@t28)) % 0.37/0.57 (step @p25 :rule refl :args (@t29)) % 0.37/0.57 (step @p26 :rule nary_cong :premises (@p25 @p24) :args (@t30)) % 0.37/0.57 (step @p27 :rule cong :premises (@p26) :args (@t31)) % 0.37/0.57 (step @p28 :rule cong :premises (@p27) :args (@t32)) % 0.37/0.57 (step @p29 :rule trans :premises (@p28 @p23)) % 0.37/0.57 (step @p30 :rule ho_cong :premises (@p15 @p27)) % 0.37/0.57 (step @p31 :rule cong :premises (@p30 @p29) :args ((= (_ tptp.cP @t31) @t32))) % 0.37/0.57 (step @p32 :rule symm :premises (@p31)) % 0.37/0.57 (step @p33 :rule refl :args (@t13)) % 0.37/0.57 (step @p34 :rule eq_resolve :premises (@p33 @p32)) % 0.37/0.57 (step @p35 :rule refl :args (@t8)) % 0.37/0.57 (step @p36 :rule cong :premises (@p35 @p24) :args ((= @t8 @t28))) % 0.37/0.57 (step @p37 :rule symm :premises (@p36)) % 0.37/0.57 (step @p38 :rule eq_resolve :premises (@p35 @p37)) % 0.37/0.57 (step @p39 :rule refl :args (@t10)) % 0.37/0.57 (step @p40 :rule cong :premises (@p39 @p25) :args ((= @t10 @t29))) % 0.37/0.57 (step @p41 :rule symm :premises (@p40)) % 0.37/0.57 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.37/0.57 (step @p43 :rule nary_cong :premises (@p42 @p38) :args (@t11)) % 0.37/0.57 (step @p44 :rule cong :premises (@p43) :args (@t12)) % 0.37/0.57 (step @p45 :rule ho_cong :premises (@p15 @p44)) % 0.37/0.57 (step @p46 :rule trans :premises (@p45 @p34)) % 0.37/0.57 (step @p47 :rule cong :premises (@p46) :args (@t44)) % 0.37/0.57 (step @p48 :rule refl :args (@t24)) % 0.37/0.57 (step @p49 :rule cong :premises (@p44 @p48) :args (@t45)) % 0.37/0.57 (step @p50 :rule cong :premises (@p49) :args (@t46)) % 0.37/0.57 (step @p51 :rule refl :args (@t38)) % 0.37/0.57 (step @p52 :rule refl :args (@t40)) % 0.37/0.57 (step @p53 :rule nary_cong :premises (@p52 @p51 @p50 @p47 @p22) :args (@t47)) % 0.37/0.57 (step @p54 :rule cong :premises (@p53) :args ((forall @t20 @t47))) % 0.37/0.57 (step @p55 :rule trans :premises (@p54 @p10)) % 0.37/0.57 (step @p56 :rule aci_norm :args ((= (or @t48 @t43) @t47))) % 0.37/0.57 (step @p57 :rule refl :args (@t43)) % 0.37/0.57 (step @p58 :rule aci_norm :args ((= (or @t40 (or @t38 (or @t46 @t44))) @t48))) % 0.37/0.57 (step @p59 :rule bool-and-de-morgan :args (@t45 @t13 true)) % 0.37/0.57 (step @p60 :rule nary_cong :premises (@p51 @p59) :args ((or @t38 (not (and @t45 @t13))))) % 0.37/0.57 (step @p61 :rule bool-and-de-morgan :args (@t37 @t45 (and @t13))) % 0.37/0.57 (step @p62 :rule trans :premises (@p61 @p60)) % 0.37/0.57 (step @p63 :rule nary_cong :premises (@p52 @p62) :args ((or @t40 (not (and @t37 @t45 @t13))))) % 0.37/0.57 (step @p64 :rule bool-and-de-morgan :args (@t39 @t37 (and @t45 @t13))) % 0.37/0.57 (step @p65 :rule trans :premises (@p64 @p63)) % 0.37/0.57 (step @p66 :rule trans :premises (@p65 @p58)) % 0.37/0.57 (step @p67 :rule nary_cong :premises (@p66 @p57) :args ((or (not @t49) @t43))) % 0.37/0.57 (step @p68 :rule trans :premises (@p67 @p56)) % 0.37/0.57 (step @p69 :rule bool-impl-elim :args (@t49 @t43)) % 0.37/0.57 (step @p70 :rule trans :premises (@p69 @p68)) % 0.37/0.57 (step @p71 :rule cong :premises (@p70) :args ((forall @t20 (=> @t49 @t43)))) % 0.37/0.57 (step @p72 :rule trans :premises (@p71 @p55)) % 0.37/0.57 (step @p73 :rule symm :premises (@p12)) % 0.37/0.57 (step @p74 :rule alpha_equiv :args (@t3 (@list @t1) (@list @t23))) % 0.37/0.57 (step @p75 :rule trans :premises (@p74 @p73)) % 0.37/0.57 (step @p76 :rule refl :args (tptp.cP)) % 0.37/0.57 (step @p77 :rule ho_cong :premises (@p76 @p75)) % 0.37/0.57 (step @p78 :rule refl :args (@t4)) % 0.37/0.57 (step @p79 :rule cong :premises (@p78 @p75) :args (@t5)) % 0.37/0.57 (step @p80 :rule nary_cong :premises (@p79 @p77) :args (@t6)) % 0.37/0.57 (step @p81 :rule refl :args (@t13)) % 0.37/0.57 (step @p82 :rule refl :args (@t12)) % 0.37/0.57 (step @p83 :rule cong :premises (@p82 @p75) :args (@t14)) % 0.37/0.57 (step @p84 :rule refl :args (@t35)) % 0.37/0.57 (step @p85 :rule refl :args (@t15)) % 0.37/0.57 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t15 @t35))) % 0.37/0.57 (step @p87 :rule symm :premises (@p86)) % 0.37/0.57 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.37/0.57 (step @p89 :rule cong :premises (@p88) :args (@t50)) % 0.37/0.57 (step @p90 :rule nary_cong :premises (@p89 @p38) :args (@t51)) % 0.37/0.57 (step @p91 :rule cong :premises (@p90) :args ((forall @t2 @t51))) % 0.37/0.57 (step @p92 :rule bool-impl-elim :args (@t15 @t8)) % 0.37/0.57 (step @p93 :rule cong :premises (@p92) :args (@t16)) % 0.37/0.57 (step @p94 :rule trans :premises (@p93 @p91)) % 0.37/0.57 (step @p95 :rule nary_cong :premises (@p89 @p42) :args (@t52)) % 0.37/0.57 (step @p96 :rule cong :premises (@p95) :args ((forall @t2 @t52))) % 0.37/0.57 (step @p97 :rule bool-impl-elim :args (@t15 @t10)) % 0.37/0.57 (step @p98 :rule cong :premises (@p97) :args (@t17)) % 0.37/0.57 (step @p99 :rule trans :premises (@p98 @p96)) % 0.37/0.57 (step @p100 :rule nary_cong :premises (@p99 @p94 @p83 @p81) :args (@t18)) % 0.37/0.57 (step @p101 :rule cong :premises (@p100 @p80) :args (@t19)) % 0.37/0.57 (step @p102 :rule cong :premises (@p101) :args (@t21)) % 0.37/0.57 (step @p103 :rule trans :premises (@p102 @p72)) % 0.37/0.57 (step @p104 :rule cong :premises (@p103) :args (@t22)) % 0.37/0.57 (step @p105 :rule eq_resolve :premises (@p1 @p104)) % 0.37/0.57 (step @p106 :rule refl :args (@t76)) % 0.37/0.57 (step @p107 :rule bool-double-not-elim :args (@t55)) % 0.37/0.57 (step @p108 :rule nary_cong :premises (@p107 @p106) :args ((or (not @t77) @t76))) % 0.37/0.57 (step @p109 :rule eq-refl :args (@t24)) % 0.37/0.57 (step @p110 :rule refl :args (@t24)) % 0.37/0.57 (step @p111 :rule cong :premises (@p110 @p73) :args ((= @t24 @t24))) % 0.37/0.57 (step @p112 :rule trans :premises (@p111 @p109)) % 0.37/0.57 (step @p113 :rule skolem_intro :args (@t53)) % 0.37/0.57 (step @p114 :rule cong :premises (@p110 @p113) :args ((= @t24 @t53))) % 0.37/0.57 (step @p115 :rule trans :premises (@p114 @p112)) % 0.37/0.57 (step @p116 :rule true_elim :premises (@p115)) % 0.37/0.57 (step @p117 :rule cong :premises (@p116) :args (@t25)) % 0.37/0.57 (step @p118 :rule eq-symm :args (@t53 @t56)) % 0.37/0.57 (step @p119 :rule refl :args (@t56)) % 0.37/0.57 (step @p120 :rule cong :premises (@p116 @p119) :args (@t78)) % 0.37/0.57 (step @p121 :rule trans :premises (@p120 @p118)) % 0.37/0.57 (step @p122 :rule nary_cong :premises (@p121 @p117) :args (@t79)) % 0.37/0.57 (step @p123 :rule eq-refl :args (@t64)) % 0.37/0.57 (step @p124 :rule skolem_intro :args (@t65)) % 0.37/0.57 (step @p125 :rule refl :args (@t64)) % 0.37/0.57 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t64 @t65))) % 0.37/0.57 (step @p127 :rule trans :premises (@p126 @p123)) % 0.37/0.57 (step @p128 :rule true_elim :premises (@p127)) % 0.37/0.57 (step @p129 :rule cong :premises (@p128) :args (@t80)) % 0.37/0.57 (step @p130 :rule cong :premises (@p129) :args (@t81)) % 0.37/0.57 (step @p131 :rule cong :premises (@p116 @p128) :args (@t82)) % 0.37/0.57 (step @p132 :rule cong :premises (@p131) :args (@t83)) % 0.37/0.57 (step @p133 :rule refl :args (@t72)) % 0.37/0.57 (step @p134 :rule refl :args (@t74)) % 0.37/0.57 (step @p135 :rule nary_cong :premises (@p134 @p133 @p132 @p130 @p122) :args (@t84)) % 0.37/0.57 (step @p136 :rule cong :premises (@p135) :args (@t85)) % 0.37/0.57 (step @p137 :rule refl :args (@t77)) % 0.37/0.57 (step @p138 :rule cong :premises (@p137 @p136) :args ((=> @t77 @t85))) % 0.37/0.57 (step @p139 :rule refl :args (@t25)) % 0.37/0.57 (step @p140 :rule eq-symm :args (@t56 @t24)) % 0.37/0.57 (step @p141 :rule nary_cong :premises (@p140 @p139) :args (@t86)) % 0.37/0.57 (step @p142 :rule refl :args (@t81)) % 0.37/0.57 (step @p143 :rule refl :args (@t83)) % 0.37/0.57 (step @p144 :rule nary_cong :premises (@p134 @p133 @p143 @p142 @p141) :args (@t87)) % 0.37/0.57 (step @p145 :rule cong :premises (@p144) :args (@t88)) % 0.37/0.57 (step @p146 :rule cong :premises (@p137 @p145) :args ((=> @t77 @t88))) % 0.37/0.57 (step @p147 :rule trans :premises (@p146 @p138)) % 0.37/0.57 (assume-push @p268 @t77) % 0.37/0.57 (step @p149 :rule skolemize :premises (@p105)) % 0.37/0.57 (step-pop @p269 :rule scope :premises (@p149)) % 0.37/0.57 (step @p150 :rule process_scope :premises (@p269) :args (@t88)) % 0.37/0.57 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 0.37/0.57 (step @p153 :rule implies_elim :premises (@p152)) % 0.37/0.57 (step @p154 :rule eq_resolve :premises (@p153 @p108)) % 0.37/0.57 (step @p155 :rule chain_m_resolution :premises (@p154 @p105) :args (@t76 @t89 (@list @t55))) % 0.37/0.57 (step @p156 :rule bool-double-not-elim :args (@t68)) % 0.37/0.57 (step @p157 :rule refl :args (@t75)) % 0.37/0.57 (step @p158 :rule nary_cong :premises (@p157 @p156) :args ((or @t75 (not @t69)))) % 0.37/0.57 (step @p159 :rule cnf_or_neg :args (@t75 2)) % 0.37/0.57 (step @p160 :rule eq_resolve :premises (@p159 @p158)) % 0.37/0.57 (step @p161 :rule reordering :premises (@p160) :args ((or @t68 @t75))) % 0.37/0.57 (step @p162 :rule chain_m_resolution :premises (@p161 @p155) :args (@t68 @t89 @t90)) % 0.37/0.57 (step @p163 :rule eq-symm :args (@t91 @t63)) % 0.37/0.57 (step @p164 :rule beta-reduce :args ((= @t92 @t63))) % 0.37/0.57 (step @p165 :rule refl :args (@t91)) % 0.37/0.57 (step @p166 :rule cong :premises (@p165 @p164) :args (@t93)) % 0.37/0.57 (step @p167 :rule trans :premises (@p166 @p163)) % 0.37/0.57 (step @p168 :rule cong :premises (@p167) :args (@t94)) % 0.37/0.57 (step @p169 :rule quant-unused-vars :args ((= (forall @t2 true) true))) % 0.37/0.57 (step @p170 :rule eq-refl :args (@t92)) % 0.37/0.57 (step @p171 :rule cong :premises (@p170) :args ((forall @t2 (= @t92 @t92)))) % 0.37/0.57 (step @p172 :rule trans :premises (@p171 @p169)) % 0.37/0.57 (step @p173 :rule refl :args (@t92)) % 0.37/0.57 (step @p174 :rule refl :args (@t1)) % 0.37/0.57 (step @p175 :rule ho_cong :premises (@p124 @p174)) % 0.37/0.57 (step @p176 :rule cong :premises (@p175 @p173) :args (@t93)) % 0.37/0.57 (step @p177 :rule cong :premises (@p176) :args (@t94)) % 0.37/0.57 (step @p178 :rule trans :premises (@p177 @p172)) % 0.37/0.57 (step @p179 :rule true_elim :premises (@p178)) % 0.37/0.57 (step @p180 :rule eq_resolve :premises (@p179 @p168)) % 0.37/0.57 (step @p181 :rule instantiate :premises (@p180) :args (@t96)) % 0.37/0.57 (step @p182 :rule bool-double-not-elim :args (@t71)) % 0.37/0.57 (step @p183 :rule nary_cong :premises (@p157 @p182) :args ((or @t75 (not @t72)))) % 0.37/0.57 (step @p184 :rule cnf_or_neg :args (@t75 1)) % 0.37/0.57 (step @p185 :rule eq_resolve :premises (@p184 @p183)) % 0.37/0.57 (step @p186 :rule reordering :premises (@p185) :args ((or @t71 @t75))) % 0.37/0.57 (step @p187 :rule chain_m_resolution :premises (@p186 @p155) :args (@t71 @t89 @t90)) % 0.37/0.57 (step @p188 :rule instantiate :premises (@p187) :args (@t96)) % 0.37/0.57 (step @p189 :rule bool-double-not-elim :args (@t66)) % 0.37/0.57 (step @p190 :rule nary_cong :premises (@p157 @p189) :args ((or @t75 (not @t67)))) % 0.37/0.57 (step @p191 :rule cnf_or_neg :args (@t75 3)) % 0.37/0.57 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.37/0.57 (step @p193 :rule reordering :premises (@p192) :args ((or @t66 @t75))) % 0.37/0.57 (step @p194 :rule chain_m_resolution :premises (@p193 @p155) :args (@t66 @t89 @t90)) % 0.37/0.57 (step @p195 :rule true_intro :premises (@p194)) % 0.37/0.57 (step @p196 :rule cong :premises (@p162) :args (@t54)) % 0.37/0.57 (step @p197 :rule trans :premises (@p196 @p195)) % 0.37/0.57 (step @p198 :rule true_elim :premises (@p197)) % 0.37/0.57 (step @p199 :rule cnf_or_neg :args (@t75 4)) % 0.37/0.57 (step @p200 :rule chain_m_resolution :premises (@p199 @p155) :args ((not @t58) @t89 @t90)) % 0.37/0.57 (step @p201 :rule cnf_and_neg :args (@t58)) % 0.37/0.57 (step @p202 :rule chain_m_resolution :premises (@p201 @p200 @p198) :args ((not @t57) (@list true false) (@list @t58 @t54))) % 0.37/0.57 (step @p203 :rule bool-double-not-elim :args (@t97)) % 0.37/0.57 (step @p204 :rule bool-eq-false :args (@t97)) % 0.37/0.57 (step @p205 :rule evaluate :args ((not false))) % 0.37/0.57 (step @p206 :rule beta-reduce :args ((= @t98 false))) % 0.37/0.57 (step @p207 :rule cong :premises (@p206) :args ((not @t98))) % 0.37/0.57 (step @p208 :rule trans :premises (@p207 @p205)) % 0.37/0.57 (step @p209 :rule refl :args (@t95)) % 0.37/0.57 (step @p210 :rule ho_cong :premises (@p113 @p209)) % 0.37/0.57 (step @p211 :rule cong :premises (@p210) :args ((not @t99))) % 0.37/0.57 (step @p212 :rule bool-eq-false :args (@t99)) % 0.37/0.57 (step @p213 :rule trans :premises (@p212 @p211 @p208)) % 0.37/0.57 (step @p214 :rule true_elim :premises (@p213)) % 0.37/0.57 (step @p215 :rule refl :args (@t97)) % 0.37/0.57 (step @p216 :rule cong :premises (@p215 @p214) :args (@t100)) % 0.37/0.57 (step @p217 :rule trans :premises (@p216 @p204)) % 0.37/0.57 (step @p218 :rule cong :premises (@p217) :args (@t101)) % 0.37/0.57 (step @p219 :rule trans :premises (@p218 @p203)) % 0.37/0.57 (step @p220 :rule refl :args (@t57)) % 0.37/0.57 (step @p221 :rule nary_cong :premises (@p220 @p219) :args (@t102)) % 0.37/0.57 ; WARNING: add trust step for TRUST % 0.37/0.57 ; trust TRUST THEORY_LEMMA % 0.37/0.57 (step @p222 :rule trust :premises () :args (@t102)) % 0.37/0.57 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.37/0.57 (step @p224 :rule chain_m_resolution :premises (@p223 @p202) :args (@t97 @t89 (@list @t57))) % 0.37/0.57 (step @p225 :rule cnf_or_pos :args (@t105)) % 0.37/0.57 (step @p226 :rule reordering :premises (@p225) :args ((or @t104 @t103 (not @t105)))) % 0.37/0.57 (step @p227 :rule chain_m_resolution :premises (@p226 @p224 @p188) :args (@t103 @t106 (@list @t97 @t105))) % 0.37/0.57 (step @p228 :rule bool-double-not-elim :args (@t73)) % 0.37/0.57 (step @p229 :rule nary_cong :premises (@p157 @p228) :args ((or @t75 (not @t74)))) % 0.37/0.57 (step @p230 :rule cnf_or_neg :args (@t75 0)) % 0.37/0.57 (step @p231 :rule eq_resolve :premises (@p230 @p229)) % 0.37/0.57 (step @p232 :rule reordering :premises (@p231) :args ((or @t73 @t75))) % 0.37/0.57 (step @p233 :rule chain_m_resolution :premises (@p232 @p155) :args (@t73 @t89 @t90)) % 0.37/0.57 (step @p234 :rule instantiate :premises (@p233) :args (@t96)) % 0.37/0.57 (step @p235 :rule cnf_or_pos :args (@t108)) % 0.37/0.57 (step @p236 :rule reordering :premises (@p235) :args ((or @t104 @t107 (not @t108)))) % 0.37/0.57 (step @p237 :rule chain_m_resolution :premises (@p236 @p224 @p234) :args (@t107 @t106 (@list @t97 @t108))) % 0.37/0.57 (step @p238 :rule cnf_and_neg :args (@t109)) % 0.37/0.57 (step @p239 :rule reordering :premises (@p238) :args ((or (not @t107) (not @t103) @t109))) % 0.37/0.57 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p227) :args (@t109 @t106 (@list @t107 @t103))) % 0.37/0.57 (step @p241 :rule cnf_equiv_pos1 :args (@t111)) % 0.37/0.57 (step @p242 :rule reordering :premises (@p241) :args ((or @t110 (not @t109) (not @t111)))) % 0.37/0.57 (step @p243 :rule chain_m_resolution :premises (@p242 @p240 @p181) :args (@t110 @t106 (@list @t109 @t111))) % 0.37/0.57 (step @p244 :rule eq-refl :args (@t109)) % 0.37/0.57 (step @p245 :rule beta-reduce :args ((= @t112 @t109))) % 0.37/0.57 (step @p246 :rule beta-reduce :args ((= @t113 @t109))) % 0.37/0.57 (step @p247 :rule cong :premises (@p246 @p245) :args ((= @t113 @t112))) % 0.37/0.57 (step @p248 :rule trans :premises (@p247 @p244)) % 0.37/0.57 (step @p249 :rule eq-symm :args (@t112 @t113)) % 0.37/0.57 (step @p250 :rule trans :premises (@p249 @p248)) % 0.37/0.57 (step @p251 :rule ho_cong :premises (@p124 @p209)) % 0.37/0.57 (step @p252 :rule ho_cong :premises (@p124 @p209)) % 0.37/0.57 (step @p253 :rule cong :premises (@p252 @p251) :args ((= @t110 @t114))) % 0.37/0.57 (step @p254 :rule eq-symm :args (@t114 @t110)) % 0.37/0.57 (step @p255 :rule trans :premises (@p254 @p253 @p250)) % 0.37/0.57 (step @p256 :rule true_elim :premises (@p255)) % 0.37/0.57 (step @p257 :rule cong :premises (@p256) :args (@t115)) % 0.37/0.57 (step @p258 :rule refl :args (@t68)) % 0.37/0.57 (step @p259 :rule cong :premises (@p258 @p257) :args ((=> @t68 @t115))) % 0.37/0.57 (step @p260 :rule bool-eq-false :args (@t114)) % 0.37/0.57 (step @p261 :rule eq-symm :args (@t65 @t53)) % 0.37/0.57 (step @p262 :rule cong :premises (@p261 @p260) :args (@t116)) % 0.37/0.57 (step @p263 :rule trans :premises (@p262 @p259)) % 0.37/0.57 ; trust TRUST THEORY_LEMMA % 0.37/0.57 (step @p264 :rule trust :premises () :args (@t116)) % 0.37/0.57 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 0.37/0.57 (step @p266 :rule implies_elim :premises (@p265)) % 0.37/0.57 (step @p267 false :rule chain_m_resolution :premises (@p266 @p243 @p162) :args (false @t106 (@list @t110 @t68))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------