%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET600^5 : 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 : n003.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 08:48:10 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET600^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n003.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:04:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort tptp.a 0) % 0.37/0.58 (define @t1 () (@var "Xx" tptp.a)) % 0.37/0.58 (define @t2 () (lambda (@list @t1) false)) % 0.37/0.58 (define @t3 () (@var "Y" (-> tptp.a Bool))) % 0.37/0.58 (define @t4 () (= @t3 @t2)) % 0.37/0.58 (define @t5 () (@var "X" (-> tptp.a Bool))) % 0.37/0.58 (define @t6 () (= @t5 @t2)) % 0.37/0.58 (define @t7 () (and @t6 @t4)) % 0.37/0.58 (define @t8 () (@var "Xz" tptp.a)) % 0.37/0.58 (define @t9 () (_ @t3 @t8)) % 0.37/0.58 (define @t10 () (_ @t5 @t8)) % 0.37/0.58 (define @t11 () (or @t10 @t9)) % 0.37/0.58 (define @t12 () (@list @t8)) % 0.37/0.58 (define @t13 () (lambda @t12 @t11)) % 0.37/0.58 (define @t14 () (= @t13 @t2)) % 0.37/0.58 (define @t15 () (= @t14 @t7)) % 0.37/0.58 (define @t16 () (@list @t5 @t3)) % 0.37/0.58 (define @t17 () (forall @t16 @t15)) % 0.37/0.58 (define @t18 () (not @t17)) % 0.37/0.58 (define @t19 () (_ @t3 @t8)) % 0.37/0.58 (define @t20 () (_ @t5 @t8)) % 0.37/0.58 (define @t21 () (lambda @t12 (or @t20 @t19))) % 0.37/0.58 (define @t22 () (@var "BOUND_VARIABLE_7492" tptp.a)) % 0.37/0.58 (define @t23 () (@list @t22)) % 0.37/0.58 (define @t24 () (lambda @t23 false)) % 0.37/0.58 (define @t25 () (and (= @t5 @t24) (= @t3 @t24))) % 0.37/0.58 (define @t26 () (= @t21 @t24)) % 0.37/0.58 (define @t27 () (= @t13 @t24)) % 0.37/0.58 (define @t28 () (= @t27 @t25)) % 0.37/0.58 (define @t29 () (@list @t22)) % 0.37/0.58 (define @t30 () (forall @t16 (= @t25 (= @t24 @t21)))) % 0.37/0.58 (define @t31 () (@quantifiers_skolemize @t30 1)) % 0.37/0.58 (define @t32 () (@quantifiers_skolemize @t30 0)) % 0.37/0.58 (define @t33 () (or (_ @t32 @t8) (_ @t31 @t8))) % 0.37/0.58 (define @t34 () (lambda @t12 @t33)) % 0.37/0.58 (define @t35 () (@purify @t34)) % 0.37/0.58 (define @t36 () (@purify @t24)) % 0.37/0.58 (define @t37 () (= @t36 @t35)) % 0.37/0.58 (define @t38 () (= @t31 @t36)) % 0.37/0.58 (define @t39 () (= @t32 @t36)) % 0.37/0.58 (define @t40 () (and @t39 @t38)) % 0.37/0.58 (define @t41 () (= @t40 @t37)) % 0.37/0.58 (define @t42 () (not @t41)) % 0.37/0.58 (define @t43 () (not @t30)) % 0.37/0.58 (define @t44 () (= @t24 @t31)) % 0.37/0.58 (define @t45 () (= @t24 @t32)) % 0.37/0.58 (define @t46 () (and @t45 @t44)) % 0.37/0.58 (define @t47 () (= @t24 @t34)) % 0.37/0.58 (define @t48 () (= @t47 @t46)) % 0.37/0.58 (define @t49 () (not @t48)) % 0.37/0.58 (define @t50 () (and (= @t32 @t24) (= @t31 @t24))) % 0.37/0.58 (define @t51 () (= @t50 @t47)) % 0.37/0.58 (define @t52 () (not @t51)) % 0.37/0.58 (define @t53 () (@list true)) % 0.37/0.58 (define @t54 () (not @t40)) % 0.37/0.58 (define @t55 () (@const 0 tptp.a)) % 0.37/0.58 (define @t56 () (_ @t31 @t55)) % 0.37/0.58 (define @t57 () (_ @t24 @t55)) % 0.37/0.58 (define @t58 () (_ @t36 @t55)) % 0.37/0.58 (define @t59 () (= @t56 @t58)) % 0.37/0.58 (define @t60 () (not @t59)) % 0.37/0.58 (define @t61 () (or @t38 @t60)) % 0.37/0.58 (define @t62 () (_ @t31 @t22)) % 0.37/0.58 (define @t63 () (not @t62)) % 0.37/0.58 (define @t64 () (forall @t23 @t63)) % 0.37/0.58 (define @t65 () (@var "BOUND_VARIABLE_7656" tptp.a)) % 0.37/0.58 (define @t66 () (_ @t32 @t22)) % 0.37/0.58 (define @t67 () (not @t66)) % 0.37/0.58 (define @t68 () (forall @t23 @t67)) % 0.37/0.58 (define @t69 () (@var "BOUND_VARIABLE_7650" tptp.a)) % 0.37/0.58 (define @t70 () (and @t68 @t64)) % 0.37/0.58 (define @t71 () (or @t66 @t62)) % 0.37/0.58 (define @t72 () (forall @t23 (= false @t71))) % 0.37/0.58 (define @t73 () (=> @t37 @t72)) % 0.37/0.58 (define @t74 () (forall (@list @t65) (not (_ @t31 @t65)))) % 0.37/0.58 (define @t75 () (and (forall (@list @t69) (not (_ @t32 @t69))) @t74)) % 0.37/0.58 (define @t76 () (not @t56)) % 0.37/0.58 (define @t77 () (@const 1 tptp.a)) % 0.37/0.58 (define @t78 () (_ @t32 @t77)) % 0.37/0.58 (define @t79 () (=> @t39 (= @t78 false))) % 0.37/0.58 (define @t80 () (_ @t31 @t77)) % 0.37/0.58 (define @t81 () (=> @t38 (= @t80 false))) % 0.37/0.58 (define @t82 () (or @t78 @t80)) % 0.37/0.58 (define @t83 () (= (_ @t34 @t77) @t82)) % 0.37/0.58 (define @t84 () (_ @t35 @t77)) % 0.37/0.58 (define @t85 () (_ @t24 @t77)) % 0.37/0.58 (define @t86 () (_ @t36 @t77)) % 0.37/0.58 (define @t87 () (= @t86 @t84)) % 0.37/0.58 (define @t88 () (not @t87)) % 0.37/0.58 (define @t89 () (or @t37 @t88)) % 0.37/0.58 (define @t90 () (not @t39)) % 0.37/0.58 (define @t91 () (@list false)) % 0.37/0.58 (define @t92 () (@list true true)) % 0.37/0.58 (define @t93 () (= @t32 @t35)) % 0.37/0.58 (define @t94 () (not @t93)) % 0.37/0.58 (define @t95 () (not @t37)) % 0.37/0.58 (define @t96 () (and @t37 @t90)) % 0.37/0.58 (define @t97 () (@list true false)) % 0.37/0.58 (define @t98 () (@const 2 tptp.a)) % 0.37/0.58 (define @t99 () (_ @t35 @t98)) % 0.37/0.58 (define @t100 () (_ @t32 @t98)) % 0.37/0.58 (define @t101 () (= @t100 @t99)) % 0.37/0.58 (define @t102 () (not @t101)) % 0.37/0.58 (define @t103 () (=> (= @t35 @t36) (= @t99 false))) % 0.37/0.58 (define @t104 () (_ @t35 @t8)) % 0.37/0.58 (define @t105 () (_ @t34 @t8)) % 0.37/0.58 (define @t106 () (= @t104 @t105)) % 0.37/0.58 (define @t107 () (forall @t12 @t106)) % 0.37/0.58 (define @t108 () (or @t100 (_ @t31 @t98))) % 0.37/0.58 (define @t109 () (forall @t12 (= @t33 @t104))) % 0.37/0.58 (define @t110 () (= @t108 @t99)) % 0.37/0.58 (define @t111 () (= @t99 @t108)) % 0.37/0.58 (define @t112 () (not @t108)) % 0.37/0.58 (assume @p1 @t18) % 0.37/0.58 (assume @p2 true) % 0.37/0.58 (step @p3 :rule eq-symm :args (@t21 @t24)) % 0.37/0.58 (step @p4 :rule refl :args (@t25)) % 0.37/0.58 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t25 @t26))) % 0.37/0.58 (step @p6 :rule eq-symm :args (@t26 @t25)) % 0.37/0.58 (step @p7 :rule trans :premises (@p6 @p5)) % 0.37/0.58 (step @p8 :rule cong :premises (@p7) :args ((forall @t16 (= @t26 @t25)))) % 0.37/0.58 (step @p9 :rule refl :args (@t25)) % 0.37/0.58 (step @p10 :rule refl :args (@t24)) % 0.37/0.58 (step @p11 :rule refl :args (@t19)) % 0.37/0.58 (step @p12 :rule refl :args (@t9)) % 0.37/0.58 (step @p13 :rule cong :premises (@p12 @p11) :args ((= @t9 @t19))) % 0.37/0.58 (step @p14 :rule symm :premises (@p13)) % 0.37/0.58 (step @p15 :rule eq_resolve :premises (@p12 @p14)) % 0.37/0.58 (step @p16 :rule refl :args (@t20)) % 0.37/0.58 (step @p17 :rule refl :args (@t10)) % 0.37/0.58 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t10 @t20))) % 0.37/0.58 (step @p19 :rule symm :premises (@p18)) % 0.37/0.58 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.37/0.58 (step @p21 :rule nary_cong :premises (@p20 @p15) :args (@t11)) % 0.37/0.58 (step @p22 :rule cong :premises (@p21) :args (@t13)) % 0.37/0.58 (step @p23 :rule cong :premises (@p22 @p10) :args (@t27)) % 0.37/0.58 (step @p24 :rule cong :premises (@p23 @p9) :args (@t28)) % 0.37/0.58 (step @p25 :rule cong :premises (@p24) :args ((forall @t16 @t28))) % 0.37/0.58 (step @p26 :rule trans :premises (@p25 @p8)) % 0.37/0.58 (step @p27 :rule refl :args (@t24)) % 0.37/0.58 (step @p28 :rule symm :premises (@p27)) % 0.37/0.58 (step @p29 :rule alpha_equiv :args (@t2 (@list @t1) @t29)) % 0.37/0.58 (step @p30 :rule trans :premises (@p29 @p28)) % 0.37/0.58 (step @p31 :rule refl :args (@t3)) % 0.37/0.58 (step @p32 :rule cong :premises (@p31 @p30) :args (@t4)) % 0.37/0.58 (step @p33 :rule refl :args (@t5)) % 0.37/0.58 (step @p34 :rule cong :premises (@p33 @p30) :args (@t6)) % 0.37/0.58 (step @p35 :rule nary_cong :premises (@p34 @p32) :args (@t7)) % 0.37/0.58 (step @p36 :rule refl :args (@t13)) % 0.37/0.58 (step @p37 :rule cong :premises (@p36 @p30) :args (@t14)) % 0.37/0.58 (step @p38 :rule cong :premises (@p37 @p35) :args (@t15)) % 0.37/0.58 (step @p39 :rule cong :premises (@p38) :args (@t17)) % 0.37/0.58 (step @p40 :rule trans :premises (@p39 @p26)) % 0.37/0.58 (step @p41 :rule cong :premises (@p40) :args (@t18)) % 0.37/0.58 (step @p42 :rule eq_resolve :premises (@p1 @p41)) % 0.37/0.58 (step @p43 :rule refl :args (@t42)) % 0.37/0.58 (step @p44 :rule bool-double-not-elim :args (@t30)) % 0.37/0.58 (step @p45 :rule nary_cong :premises (@p44 @p43) :args ((or (not @t43) @t42))) % 0.37/0.58 (step @p46 :rule eq-symm :args (@t37 @t40)) % 0.37/0.58 (step @p47 :rule eq-symm :args (@t36 @t31)) % 0.37/0.58 (step @p48 :rule refl :args (@t31)) % 0.37/0.58 (step @p49 :rule eq-refl :args (@t24)) % 0.37/0.58 (step @p50 :rule refl :args (@t24)) % 0.37/0.58 (step @p51 :rule cong :premises (@p50 @p28) :args ((= @t24 @t24))) % 0.37/0.58 (step @p52 :rule trans :premises (@p51 @p49)) % 0.37/0.58 (step @p53 :rule skolem_intro :args (@t36)) % 0.37/0.58 (step @p54 :rule cong :premises (@p50 @p53) :args ((= @t24 @t36))) % 0.37/0.58 (step @p55 :rule trans :premises (@p54 @p52)) % 0.37/0.58 (step @p56 :rule true_elim :premises (@p55)) % 0.37/0.58 (step @p57 :rule cong :premises (@p56 @p48) :args (@t44)) % 0.37/0.58 (step @p58 :rule trans :premises (@p57 @p47)) % 0.37/0.58 (step @p59 :rule eq-symm :args (@t36 @t32)) % 0.37/0.58 (step @p60 :rule refl :args (@t32)) % 0.37/0.58 (step @p61 :rule cong :premises (@p56 @p60) :args (@t45)) % 0.37/0.58 (step @p62 :rule trans :premises (@p61 @p59)) % 0.37/0.58 (step @p63 :rule nary_cong :premises (@p62 @p58) :args (@t46)) % 0.37/0.58 (step @p64 :rule eq-refl :args (@t34)) % 0.37/0.58 (step @p65 :rule skolem_intro :args (@t35)) % 0.37/0.58 (step @p66 :rule refl :args (@t34)) % 0.37/0.58 (step @p67 :rule cong :premises (@p66 @p65) :args ((= @t34 @t35))) % 0.37/0.58 (step @p68 :rule trans :premises (@p67 @p64)) % 0.37/0.58 (step @p69 :rule true_elim :premises (@p68)) % 0.37/0.58 (step @p70 :rule cong :premises (@p56 @p69) :args (@t47)) % 0.37/0.58 (step @p71 :rule cong :premises (@p70 @p63) :args (@t48)) % 0.37/0.58 (step @p72 :rule trans :premises (@p71 @p46)) % 0.37/0.58 (step @p73 :rule cong :premises (@p72) :args (@t49)) % 0.37/0.58 (step @p74 :rule refl :args (@t43)) % 0.37/0.58 (step @p75 :rule cong :premises (@p74 @p73) :args ((=> @t43 @t49))) % 0.37/0.58 (step @p76 :rule eq-symm :args (@t46 @t47)) % 0.37/0.58 (step @p77 :rule refl :args (@t47)) % 0.37/0.58 (step @p78 :rule eq-symm :args (@t31 @t24)) % 0.37/0.58 (step @p79 :rule eq-symm :args (@t32 @t24)) % 0.37/0.58 (step @p80 :rule nary_cong :premises (@p79 @p78) :args (@t50)) % 0.37/0.58 (step @p81 :rule cong :premises (@p80 @p77) :args (@t51)) % 0.37/0.58 (step @p82 :rule trans :premises (@p81 @p76)) % 0.37/0.58 (step @p83 :rule cong :premises (@p82) :args (@t52)) % 0.37/0.58 (step @p84 :rule cong :premises (@p74 @p83) :args ((=> @t43 @t52))) % 0.37/0.58 (step @p85 :rule trans :premises (@p84 @p75)) % 0.37/0.58 (assume-push @p269 @t43) % 0.37/0.58 (step @p87 :rule skolemize :premises (@p42)) % 0.37/0.58 (step-pop @p270 :rule scope :premises (@p87)) % 0.37/0.58 (step @p88 :rule process_scope :premises (@p270) :args (@t52)) % 0.37/0.58 (step @p90 :rule eq_resolve :premises (@p88 @p85)) % 0.37/0.58 (step @p91 :rule implies_elim :premises (@p90)) % 0.37/0.58 (step @p92 :rule eq_resolve :premises (@p91 @p45)) % 0.37/0.58 (step @p93 :rule chain_m_resolution :premises (@p92 @p42) :args (@t42 @t53 (@list @t30))) % 0.37/0.58 (step @p94 :rule cnf_and_pos :args (@t40 1)) % 0.37/0.58 (step @p95 :rule reordering :premises (@p94) :args ((or @t38 @t54))) % 0.37/0.58 (step @p96 :rule bool-double-not-elim :args (@t56)) % 0.37/0.58 (step @p97 :rule bool-eq-false :args (@t56)) % 0.37/0.58 (step @p98 :rule evaluate :args ((not false))) % 0.37/0.58 (step @p99 :rule beta-reduce :args ((= @t57 false))) % 0.37/0.58 (step @p100 :rule cong :premises (@p99) :args ((not @t57))) % 0.37/0.58 (step @p101 :rule trans :premises (@p100 @p98)) % 0.37/0.58 (step @p102 :rule refl :args (@t55)) % 0.37/0.58 (step @p103 :rule ho_cong :premises (@p53 @p102)) % 0.37/0.58 (step @p104 :rule cong :premises (@p103) :args ((not @t58))) % 0.37/0.58 (step @p105 :rule bool-eq-false :args (@t58)) % 0.37/0.58 (step @p106 :rule trans :premises (@p105 @p104 @p101)) % 0.37/0.58 (step @p107 :rule true_elim :premises (@p106)) % 0.37/0.58 (step @p108 :rule refl :args (@t56)) % 0.37/0.58 (step @p109 :rule cong :premises (@p108 @p107) :args (@t59)) % 0.37/0.58 (step @p110 :rule trans :premises (@p109 @p97)) % 0.37/0.58 (step @p111 :rule cong :premises (@p110) :args (@t60)) % 0.37/0.58 (step @p112 :rule trans :premises (@p111 @p96)) % 0.37/0.58 (step @p113 :rule refl :args (@t38)) % 0.37/0.58 (step @p114 :rule nary_cong :premises (@p113 @p112) :args (@t61)) % 0.37/0.58 ; WARNING: add trust step for TRUST % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p115 :rule trust :premises () :args (@t61)) % 0.37/0.58 (step @p116 :rule eq_resolve :premises (@p115 @p114)) % 0.37/0.58 (step @p117 :rule cnf_equiv_neg1 :args (@t41)) % 0.37/0.58 (step @p118 :rule reordering :premises (@p117) :args ((or @t40 @t37 @t41))) % 0.37/0.58 (step @p119 :rule alpha_equiv :args (@t64 @t29 (@list @t65))) % 0.37/0.58 (step @p120 :rule alpha_equiv :args (@t68 @t29 (@list @t69))) % 0.37/0.58 (step @p121 :rule nary_cong :premises (@p120 @p119) :args (@t70)) % 0.37/0.58 (step @p122 :rule quant-miniscope-and :args ((= (forall @t23 (and @t67 @t63)) @t70))) % 0.37/0.58 (step @p123 :rule trans :premises (@p122 @p121)) % 0.37/0.58 (step @p124 :rule bool-or-de-morgan :args (@t66 @t62 false)) % 0.37/0.58 (step @p125 :rule cong :premises (@p124) :args ((forall @t23 (not @t71)))) % 0.37/0.58 (step @p126 :rule trans :premises (@p125 @p123)) % 0.37/0.58 (step @p127 :rule bool-eq-false :args (@t71)) % 0.37/0.58 (step @p128 :rule eq-symm :args (false @t71)) % 0.37/0.58 (step @p129 :rule trans :premises (@p128 @p127)) % 0.37/0.58 (step @p130 :rule cong :premises (@p129) :args (@t72)) % 0.37/0.58 (step @p131 :rule trans :premises (@p130 @p126)) % 0.37/0.58 (step @p132 :rule refl :args (@t37)) % 0.37/0.58 (step @p133 :rule cong :premises (@p132 @p131) :args (@t73)) % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p134 :rule trust :premises () :args (@t73)) % 0.37/0.58 (step @p135 :rule eq_resolve :premises (@p134 @p133)) % 0.37/0.58 (step @p136 :rule implies_elim :premises (@p135)) % 0.37/0.58 (step @p137 :rule cnf_and_pos :args (@t75 1)) % 0.37/0.58 (step @p138 :rule reordering :premises (@p137) :args ((or @t74 (not @t75)))) % 0.37/0.58 (assume-push @p271 @t74) % 0.37/0.58 (step @p140 :rule instantiate :premises (@p271) :args ((@list @t55))) % 0.37/0.58 (step-pop @p272 :rule scope :premises (@p140)) % 0.37/0.58 (step @p141 :rule process_scope :premises (@p272) :args (@t76)) % 0.37/0.58 (step @p143 :rule implies_elim :premises (@p141)) % 0.37/0.58 (step @p144 :rule reordering :premises (@p143) :args ((or @t76 (not @t74)))) % 0.37/0.58 (step @p145 :rule chain_m_resolution :premises (@p144 @p138 @p136 @p118 @p93 @p116 @p95) :args (@t38 (@list false false false true false true) (@list @t74 @t75 @t37 @t41 @t56 @t40))) % 0.37/0.58 (step @p146 :rule bool-eq-false :args (@t78)) % 0.37/0.58 (step @p147 :rule refl :args (@t39)) % 0.37/0.58 (step @p148 :rule cong :premises (@p147 @p146) :args (@t79)) % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p149 :rule trust :premises () :args (@t79)) % 0.37/0.58 (step @p150 :rule eq_resolve :premises (@p149 @p148)) % 0.37/0.58 (step @p151 :rule implies_elim :premises (@p150)) % 0.37/0.58 (step @p152 :rule cnf_and_neg :args (@t40)) % 0.37/0.58 (step @p153 :rule bool-eq-false :args (@t80)) % 0.37/0.58 (step @p154 :rule cong :premises (@p113 @p153) :args (@t81)) % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p155 :rule trust :premises () :args (@t81)) % 0.37/0.58 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.37/0.58 (step @p157 :rule implies_elim :premises (@p156)) % 0.37/0.58 (step @p158 :rule cnf_equiv_neg2 :args (@t41)) % 0.37/0.58 (step @p159 :rule aci_norm :args ((= (or @t37 @t82) (or @t37 @t78 @t80)))) % 0.37/0.58 (step @p160 :rule bool-double-not-elim :args (@t82)) % 0.37/0.58 (step @p161 :rule bool-eq-false :args (@t82)) % 0.37/0.58 (step @p162 :rule eq-symm :args (false @t82)) % 0.37/0.58 (step @p163 :rule trans :premises (@p162 @p161)) % 0.37/0.58 (step @p164 :rule eq-refl :args (@t82)) % 0.37/0.58 (step @p165 :rule refl :args (@t82)) % 0.37/0.58 (step @p166 :rule beta-reduce :args (@t83)) % 0.37/0.58 (step @p167 :rule cong :premises (@p166 @p165) :args (@t83)) % 0.37/0.58 (step @p168 :rule trans :premises (@p167 @p164)) % 0.37/0.58 (step @p169 :rule refl :args (@t77)) % 0.37/0.58 (step @p170 :rule ho_cong :premises (@p65 @p169)) % 0.37/0.58 (step @p171 :rule cong :premises (@p170 @p165) :args ((= @t84 @t82))) % 0.37/0.58 (step @p172 :rule trans :premises (@p171 @p168)) % 0.37/0.58 (step @p173 :rule true_elim :premises (@p172)) % 0.37/0.58 (step @p174 :rule beta-reduce :args ((= @t85 false))) % 0.37/0.58 (step @p175 :rule cong :premises (@p174) :args ((not @t85))) % 0.37/0.58 (step @p176 :rule trans :premises (@p175 @p98)) % 0.37/0.58 (step @p177 :rule ho_cong :premises (@p53 @p169)) % 0.37/0.58 (step @p178 :rule cong :premises (@p177) :args ((not @t86))) % 0.37/0.58 (step @p179 :rule bool-eq-false :args (@t86)) % 0.37/0.58 (step @p180 :rule trans :premises (@p179 @p178 @p176)) % 0.37/0.58 (step @p181 :rule true_elim :premises (@p180)) % 0.37/0.58 (step @p182 :rule cong :premises (@p181 @p173) :args (@t87)) % 0.37/0.58 (step @p183 :rule trans :premises (@p182 @p163)) % 0.37/0.58 (step @p184 :rule cong :premises (@p183) :args (@t88)) % 0.37/0.58 (step @p185 :rule trans :premises (@p184 @p160)) % 0.37/0.58 (step @p186 :rule nary_cong :premises (@p132 @p185) :args (@t89)) % 0.37/0.58 (step @p187 :rule trans :premises (@p186 @p159)) % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p188 :rule trust :premises () :args (@t89)) % 0.37/0.58 (step @p189 :rule eq_resolve :premises (@p188 @p187)) % 0.37/0.58 (step @p190 :rule chain_m_resolution :premises (@p189 @p158 @p93 @p157 @p152 @p151) :args ((or @t90 (not @t38)) (@list true true true false true) (@list @t37 @t41 @t80 @t40 @t78))) % 0.37/0.58 (step @p191 :rule chain_m_resolution :premises (@p190 @p145) :args (@t90 @t91 (@list @t38))) % 0.37/0.58 (step @p192 :rule cnf_and_pos :args (@t40 0)) % 0.37/0.58 (step @p193 :rule reordering :premises (@p192) :args ((or @t39 @t54))) % 0.37/0.58 (step @p194 :rule chain_m_resolution :premises (@p193 @p191) :args (@t54 @t53 (@list @t39))) % 0.37/0.58 (step @p195 :rule chain_m_resolution :premises (@p118 @p194 @p93) :args (@t37 @t92 (@list @t40 @t41))) % 0.37/0.58 (step @p196 :rule refl :args (@t94)) % 0.37/0.58 (step @p197 :rule bool-double-not-elim :args (@t39)) % 0.37/0.58 (step @p198 :rule refl :args (@t95)) % 0.37/0.58 (step @p199 :rule nary_cong :premises (@p198 @p197 @p196) :args ((or @t95 (not @t90) @t94))) % 0.37/0.58 (assume-push @p273 @t37) % 0.37/0.58 (assume-push @p274 @t90) % 0.37/0.58 (assume-push @p275 @t90) % 0.37/0.58 (assume-push @p276 @t37) % 0.37/0.58 (step @p204 :rule false_intro :premises (@p274)) % 0.37/0.58 (step @p205 :rule symm :premises (@p273)) % 0.37/0.58 (step @p206 :rule cong :premises (@p60 @p205) :args (@t93)) % 0.37/0.58 (step @p207 :rule trans :premises (@p206 @p204)) % 0.37/0.58 (step @p208 :rule false_elim :premises (@p207)) % 0.37/0.58 (step-pop @p277 :rule scope :premises (@p208)) % 0.37/0.58 (step-pop @p278 :rule scope :premises (@p277)) % 0.37/0.58 (step @p209 :rule process_scope :premises (@p278) :args (@t94)) % 0.37/0.58 (step @p212 :rule and_intro :premises (@p274 @p273)) % 0.37/0.58 (step @p213 :rule modus_ponens :premises (@p212 @p209)) % 0.37/0.58 (step-pop @p279 :rule scope :premises (@p213)) % 0.37/0.58 (step-pop @p280 :rule scope :premises (@p279)) % 0.37/0.58 (step @p214 :rule process_scope :premises (@p280) :args (@t94)) % 0.37/0.58 (step @p217 :rule implies_elim :premises (@p214)) % 0.37/0.58 (step @p218 :rule cnf_and_neg :args (@t96)) % 0.37/0.58 (step @p219 :rule resolution :premises (@p218 @p217) :args (true @t96)) % 0.37/0.58 (step @p220 :rule eq_resolve :premises (@p219 @p199)) % 0.37/0.58 (step @p221 :rule reordering :premises (@p220) :args ((or @t39 @t95 @t94))) % 0.37/0.58 (step @p222 :rule chain_m_resolution :premises (@p221 @p191 @p195) :args (@t94 @t97 (@list @t39 @t37))) % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p223 :rule trust :premises () :args ((or @t93 @t102))) % 0.37/0.58 (step @p224 :rule chain_m_resolution :premises (@p223 @p222) :args (@t102 @t53 (@list @t93))) % 0.37/0.58 (step @p225 :rule bool-eq-false :args (@t99)) % 0.37/0.58 (step @p226 :rule eq-symm :args (@t35 @t36)) % 0.37/0.58 (step @p227 :rule cong :premises (@p226 @p225) :args (@t103)) % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p228 :rule trust :premises () :args (@t103)) % 0.37/0.58 (step @p229 :rule eq_resolve :premises (@p228 @p227)) % 0.37/0.58 (step @p230 :rule implies_elim :premises (@p229)) % 0.37/0.58 (step @p231 :rule chain_m_resolution :premises (@p230 @p195) :args ((not @t99) @t91 (@list @t37))) % 0.37/0.58 (step @p232 :rule cnf_equiv_neg1 :args (@t101)) % 0.37/0.58 (step @p233 :rule reordering :premises (@p232) :args ((or @t100 @t99 @t101))) % 0.37/0.58 (step @p234 :rule chain_m_resolution :premises (@p233 @p231 @p224) :args (@t100 @t92 (@list @t99 @t101))) % 0.37/0.58 (step @p235 :rule eq-symm :args (@t104 @t33)) % 0.37/0.58 (step @p236 :rule beta-reduce :args ((= @t105 @t33))) % 0.37/0.58 (step @p237 :rule refl :args (@t104)) % 0.37/0.58 (step @p238 :rule cong :premises (@p237 @p236) :args (@t106)) % 0.37/0.58 (step @p239 :rule trans :premises (@p238 @p235)) % 0.37/0.58 (step @p240 :rule cong :premises (@p239) :args (@t107)) % 0.37/0.58 (step @p241 :rule quant-unused-vars :args ((= (forall @t12 true) true))) % 0.37/0.58 (step @p242 :rule eq-refl :args (@t105)) % 0.37/0.58 (step @p243 :rule cong :premises (@p242) :args ((forall @t12 (= @t105 @t105)))) % 0.37/0.58 (step @p244 :rule trans :premises (@p243 @p241)) % 0.37/0.58 (step @p245 :rule refl :args (@t105)) % 0.37/0.58 (step @p246 :rule refl :args (@t8)) % 0.37/0.58 (step @p247 :rule ho_cong :premises (@p65 @p246)) % 0.37/0.58 (step @p248 :rule cong :premises (@p247 @p245) :args (@t106)) % 0.37/0.58 (step @p249 :rule cong :premises (@p248) :args (@t107)) % 0.37/0.58 (step @p250 :rule trans :premises (@p249 @p244)) % 0.37/0.58 (step @p251 :rule true_elim :premises (@p250)) % 0.37/0.58 (step @p252 :rule eq_resolve :premises (@p251 @p240)) % 0.37/0.58 (step @p253 :rule eq-symm :args (@t108 @t99)) % 0.37/0.58 (step @p254 :rule refl :args (@t109)) % 0.37/0.58 (step @p255 :rule cong :premises (@p254 @p253) :args ((=> @t109 @t110))) % 0.37/0.58 (assume-push @p281 @t109) % 0.37/0.58 (step @p257 :rule instantiate :premises (@p252) :args ((@list @t98))) % 0.37/0.58 (step-pop @p282 :rule scope :premises (@p257)) % 0.37/0.58 (step @p258 :rule process_scope :premises (@p282) :args (@t110)) % 0.37/0.58 (step @p260 :rule eq_resolve :premises (@p258 @p255)) % 0.37/0.58 (step @p261 :rule implies_elim :premises (@p260)) % 0.37/0.58 (step @p262 :rule chain_m_resolution :premises (@p261 @p252) :args (@t111 @t91 (@list @t109))) % 0.37/0.58 (step @p263 :rule cnf_equiv_pos2 :args (@t111)) % 0.37/0.58 (step @p264 :rule reordering :premises (@p263) :args ((or @t99 @t112 (not @t111)))) % 0.37/0.58 (step @p265 :rule chain_m_resolution :premises (@p264 @p231 @p262) :args (@t112 @t97 (@list @t99 @t111))) % 0.37/0.58 (step @p266 :rule cnf_or_neg :args (@t108 0)) % 0.37/0.58 (step @p267 :rule reordering :premises (@p266) :args ((or (not @t100) @t108))) % 0.37/0.58 (step @p268 false :rule chain_m_resolution :premises (@p267 @p265 @p234) :args (false @t97 (@list @t108 @t100))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.59 % cvc5 exiting %------------------------------------------------------------------------------