%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO559^1 : TPTP v9.2.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n021.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 09:13:07 AM UTC 2026 % Result : Theorem 0.61s 0.80s % Output : Proof 0.61s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO559^1 : TPTP v9.2.1. Released v5.2.0. % 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n021.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Wed Jun 3 00:22:05 EDT 2026 % 0.18/0.35 % CPUTime : % 0.32/0.49 %----Proving TH0 % 0.61/0.80 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.61/0.80 % SZS status Theorem % 0.61/0.80 % SZS output start Proof % 0.61/0.80 ( % 0.61/0.80 (declare-const tptp.epsoo (-> (-> (-> Bool Bool) Bool) Bool Bool)) % 0.61/0.80 (declare-const tptp.epso (-> (-> Bool Bool) Bool)) % 0.61/0.80 (define @t1 () (@var "P" (-> Bool Bool))) % 0.61/0.80 (define @t2 () (_ tptp.epso @t1)) % 0.61/0.80 (define @t3 () (_ @t1 @t2)) % 0.61/0.80 (define @t4 () (@var "X" Bool)) % 0.61/0.80 (define @t5 () (_ @t1 @t4)) % 0.61/0.80 (define @t6 () (@list @t4)) % 0.61/0.80 (define @t7 () (exists @t6 @t5)) % 0.61/0.80 (define @t8 () (=> @t7 @t3)) % 0.61/0.80 (define @t9 () (@list @t1)) % 0.61/0.80 (define @t10 () (forall @t9 @t8)) % 0.61/0.80 (define @t11 () (@var "P" (-> (-> Bool Bool) Bool))) % 0.61/0.80 (define @t12 () (_ tptp.epsoo @t11)) % 0.61/0.80 (define @t13 () (_ @t11 @t12)) % 0.61/0.80 (define @t14 () (@var "X" (-> Bool Bool))) % 0.61/0.80 (define @t15 () (_ @t11 @t14)) % 0.61/0.80 (define @t16 () (@list @t14)) % 0.61/0.80 (define @t17 () (exists @t16 @t15)) % 0.61/0.80 (define @t18 () (=> @t17 @t13)) % 0.61/0.80 (define @t19 () (@list @t11)) % 0.61/0.80 (define @t20 () (forall @t19 @t18)) % 0.61/0.80 (define @t21 () (_ tptp.epsoo tptp.epso)) % 0.61/0.80 (define @t22 () (=> (_ @t21 false) (_ @t21 true))) % 0.61/0.80 (define @t23 () (not @t22)) % 0.61/0.80 (define @t24 () (_ @t11 @t12)) % 0.61/0.80 (define @t25 () (@var "BOUND_VARIABLE_7474" (-> Bool Bool))) % 0.61/0.80 (define @t26 () (not (_ @t11 @t25))) % 0.61/0.80 (define @t27 () (or @t26 @t24)) % 0.61/0.80 (define @t28 () (forall (@list @t11 @t25) @t27)) % 0.61/0.80 (define @t29 () (@list @t25)) % 0.61/0.80 (define @t30 () (forall @t29 @t27)) % 0.61/0.80 (define @t31 () (forall @t29 @t26)) % 0.61/0.80 (define @t32 () (or @t31 @t24)) % 0.61/0.80 (define @t33 () (_ @t11 @t14)) % 0.61/0.80 (define @t34 () (forall @t16 (not @t33))) % 0.61/0.80 (define @t35 () (or @t34 @t13)) % 0.61/0.80 (define @t36 () (not @t34)) % 0.61/0.80 (define @t37 () (not @t15)) % 0.61/0.80 (define @t38 () (forall @t16 @t37)) % 0.61/0.80 (define @t39 () (not @t38)) % 0.61/0.80 (define @t40 () (tptp.epso @t1)) % 0.61/0.80 (define @t41 () (_ @t1 @t40)) % 0.61/0.80 (define @t42 () (@var "BOUND_VARIABLE_7452" Bool)) % 0.61/0.80 (define @t43 () (not (_ @t1 @t42))) % 0.61/0.80 (define @t44 () (or @t43 @t41)) % 0.61/0.80 (define @t45 () (forall (@list @t1 @t42) @t44)) % 0.61/0.80 (define @t46 () (@list @t42)) % 0.61/0.80 (define @t47 () (forall @t46 @t44)) % 0.61/0.80 (define @t48 () (forall @t46 @t43)) % 0.61/0.80 (define @t49 () (or @t48 @t41)) % 0.61/0.80 (define @t50 () (_ @t1 @t4)) % 0.61/0.80 (define @t51 () (forall @t6 (not @t50))) % 0.61/0.80 (define @t52 () (or @t51 @t3)) % 0.61/0.80 (define @t53 () (not @t51)) % 0.61/0.80 (define @t54 () (not @t5)) % 0.61/0.80 (define @t55 () (forall @t6 @t54)) % 0.61/0.80 (define @t56 () (not @t55)) % 0.61/0.80 (define @t57 () (@var "BOUND_VARIABLE_15696" Bool)) % 0.61/0.80 (define @t58 () (= @t57 false)) % 0.61/0.80 (define @t59 () (ite @t58 false true)) % 0.61/0.80 (define @t60 () (@list @t57)) % 0.61/0.80 (define @t61 () (lambda @t60 @t59)) % 0.61/0.80 (define @t62 () (= false @t57)) % 0.61/0.80 (define @t63 () (not true)) % 0.61/0.80 (define @t64 () (not @t58)) % 0.61/0.80 (define @t65 () (@purify @t61)) % 0.61/0.80 (define @t66 () (tptp.epso @t61)) % 0.61/0.80 (define @t67 () (@purify true)) % 0.61/0.80 (define @t68 () (not @t67)) % 0.61/0.80 (define @t69 () (or @t68 @t66)) % 0.61/0.80 (define @t70 () (@var "BOUND_VARIABLE_15705" Bool)) % 0.61/0.80 (define @t71 () (lambda (@list @t70) @t70)) % 0.61/0.80 (define @t72 () (tptp.epso @t71)) % 0.61/0.80 (define @t73 () (_ @t71 @t72)) % 0.61/0.80 (define @t74 () (_ @t71 @t67)) % 0.61/0.80 (define @t75 () (not @t74)) % 0.61/0.80 (define @t76 () (or @t75 @t73)) % 0.61/0.80 (define @t77 () (tptp.epso @t65)) % 0.61/0.80 (define @t78 () (or @t68 @t77)) % 0.61/0.80 (define @t79 () (@list false)) % 0.61/0.80 (define @t80 () (@list @t45)) % 0.61/0.80 (define @t81 () (@list false false)) % 0.61/0.80 (define @t82 () (tptp.epso @t21)) % 0.61/0.80 (define @t83 () (@purify @t82)) % 0.61/0.80 (define @t84 () (tptp.epsoo tptp.epso @t83)) % 0.61/0.80 (define @t85 () (_ @t21 @t83)) % 0.61/0.80 (define @t86 () (@purify false)) % 0.61/0.80 (define @t87 () (tptp.epsoo tptp.epso @t86)) % 0.61/0.80 (define @t88 () (_ @t21 @t86)) % 0.61/0.80 (define @t89 () (not @t88)) % 0.61/0.80 (define @t90 () (_ @t21 @t82)) % 0.61/0.80 (define @t91 () (or @t89 @t90)) % 0.61/0.80 (define @t92 () (_ tptp.epso @t21)) % 0.61/0.80 (define @t93 () (_ @t21 @t82)) % 0.61/0.80 (define @t94 () (_ @t21 @t86)) % 0.61/0.80 (define @t95 () (not @t94)) % 0.61/0.80 (define @t96 () (or @t95 @t93)) % 0.61/0.80 (define @t97 () (not @t87)) % 0.61/0.80 (define @t98 () (or @t97 @t84)) % 0.61/0.80 (define @t99 () (tptp.epsoo tptp.epso @t67)) % 0.61/0.80 (define @t100 () (_ @t21 @t67)) % 0.61/0.80 (define @t101 () (not @t84)) % 0.61/0.80 (define @t102 () (not @t83)) % 0.61/0.80 (define @t103 () (not @t99)) % 0.61/0.80 (define @t104 () (and @t103 @t67 @t83 @t84)) % 0.61/0.80 (define @t105 () (not @t82)) % 0.61/0.80 (define @t106 () (not @t77)) % 0.61/0.80 (define @t107 () (or @t106 @t82)) % 0.61/0.80 (define @t108 () (not @t107)) % 0.61/0.80 (define @t109 () (@list true false)) % 0.61/0.80 (assume @p1 @t10) % 0.61/0.80 (assume @p2 @t20) % 0.61/0.80 (assume @p3 @t23) % 0.61/0.80 (assume @p4 true) % 0.61/0.80 (step @p5 :rule quant-merge-prenex :args ((= (forall @t19 @t30) @t28))) % 0.61/0.80 (step @p6 :rule refl :args (@t24)) % 0.61/0.80 (step @p7 :rule alpha_equiv :args (@t31 (@list @t25) (@list @t14))) % 0.61/0.80 (step @p8 :rule nary_cong :premises (@p7 @p6) :args (@t32)) % 0.61/0.80 (step @p9 :rule quant-miniscope-or :args ((= @t30 @t32))) % 0.61/0.80 (step @p10 :rule trans :premises (@p9 @p8)) % 0.61/0.80 (step @p11 :rule symm :premises (@p10)) % 0.61/0.80 (step @p12 :rule cong :premises (@p11) :args ((forall @t19 (or @t34 @t24)))) % 0.61/0.80 (step @p13 :rule trans :premises (@p12 @p5)) % 0.61/0.80 (step @p14 :rule refl :args (@t24)) % 0.61/0.80 (step @p15 :rule refl :args (@t13)) % 0.61/0.80 (step @p16 :rule cong :premises (@p15 @p14) :args ((= @t13 @t24))) % 0.61/0.80 (step @p17 :rule symm :premises (@p16)) % 0.61/0.80 (step @p18 :rule eq_resolve :premises (@p15 @p17)) % 0.61/0.80 (step @p19 :rule refl :args (@t34)) % 0.61/0.80 (step @p20 :rule nary_cong :premises (@p19 @p18) :args (@t35)) % 0.61/0.80 (step @p21 :rule cong :premises (@p20) :args ((forall @t19 @t35))) % 0.61/0.80 (step @p22 :rule trans :premises (@p21 @p13)) % 0.61/0.80 (step @p23 :rule bool-double-not-elim :args (@t34)) % 0.61/0.80 (step @p24 :rule nary_cong :premises (@p23 @p15) :args ((or (not @t36) @t13))) % 0.61/0.80 (step @p25 :rule bool-impl-elim :args (@t36 @t13)) % 0.61/0.80 (step @p26 :rule trans :premises (@p25 @p24)) % 0.61/0.80 (step @p27 :rule cong :premises (@p26) :args ((forall @t19 (=> @t36 @t13)))) % 0.61/0.80 (step @p28 :rule trans :premises (@p27 @p22)) % 0.61/0.80 (step @p29 :rule refl :args (@t13)) % 0.61/0.80 (step @p30 :rule refl :args (@t33)) % 0.61/0.80 (step @p31 :rule refl :args (@t15)) % 0.61/0.80 (step @p32 :rule cong :premises (@p31 @p30) :args ((= @t15 @t33))) % 0.61/0.80 (step @p33 :rule symm :premises (@p32)) % 0.61/0.80 (step @p34 :rule eq_resolve :premises (@p31 @p33)) % 0.61/0.80 (step @p35 :rule cong :premises (@p34) :args (@t37)) % 0.61/0.80 (step @p36 :rule cong :premises (@p35) :args (@t38)) % 0.61/0.80 (step @p37 :rule cong :premises (@p36) :args (@t39)) % 0.61/0.80 (step @p38 :rule exists-elim :args ((= @t17 @t39))) % 0.61/0.80 (step @p39 :rule trans :premises (@p38 @p37)) % 0.61/0.80 (step @p40 :rule cong :premises (@p39 @p29) :args (@t18)) % 0.61/0.80 (step @p41 :rule cong :premises (@p40) :args (@t20)) % 0.61/0.80 (step @p42 :rule trans :premises (@p41 @p28)) % 0.61/0.80 (step @p43 :rule eq_resolve :premises (@p2 @p42)) % 0.61/0.80 (step @p44 :rule quant-merge-prenex :args ((= (forall @t9 @t47) @t45))) % 0.61/0.80 (step @p45 :rule refl :args (@t41)) % 0.61/0.80 (step @p46 :rule alpha_equiv :args (@t48 (@list @t42) (@list @t4))) % 0.61/0.80 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t49)) % 0.61/0.80 (step @p48 :rule quant-miniscope-or :args ((= @t47 @t49))) % 0.61/0.80 (step @p49 :rule trans :premises (@p48 @p47)) % 0.61/0.80 (step @p50 :rule symm :premises (@p49)) % 0.61/0.80 (step @p51 :rule cong :premises (@p50) :args ((forall @t9 (or @t51 @t41)))) % 0.61/0.80 (step @p52 :rule trans :premises (@p51 @p44)) % 0.61/0.80 (step @p53 :rule refl :args ((_ @t1 @t2))) % 0.61/0.80 (step @p54 :rule refl :args (@t40)) % 0.61/0.80 (step @p55 :rule cong :premises (@p54) :args (@t41)) % 0.61/0.80 (step @p56 :rule trans :premises (@p55 @p53)) % 0.61/0.80 (step @p57 :rule refl :args (@t1)) % 0.61/0.80 (step @p58 :rule ho_cong :premises (@p57 @p54)) % 0.61/0.80 (step @p59 :rule cong :premises (@p58 @p56) :args ((= (_ @t1 @t40) @t41))) % 0.61/0.80 (step @p60 :rule symm :premises (@p59)) % 0.61/0.80 (step @p61 :rule refl :args (@t3)) % 0.61/0.80 (step @p62 :rule eq_resolve :premises (@p61 @p60)) % 0.61/0.80 (step @p63 :rule refl :args (@t2)) % 0.61/0.80 (step @p64 :rule cong :premises (@p63 @p54) :args ((= @t2 @t40))) % 0.61/0.80 (step @p65 :rule symm :premises (@p64)) % 0.61/0.80 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.61/0.80 (step @p67 :rule ho_cong :premises (@p57 @p66)) % 0.61/0.80 (step @p68 :rule trans :premises (@p67 @p62)) % 0.61/0.80 (step @p69 :rule refl :args (@t51)) % 0.61/0.80 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t52)) % 0.61/0.80 (step @p71 :rule cong :premises (@p70) :args ((forall @t9 @t52))) % 0.61/0.80 (step @p72 :rule trans :premises (@p71 @p52)) % 0.61/0.80 (step @p73 :rule bool-double-not-elim :args (@t51)) % 0.61/0.80 (step @p74 :rule nary_cong :premises (@p73 @p61) :args ((or (not @t53) @t3))) % 0.61/0.80 (step @p75 :rule bool-impl-elim :args (@t53 @t3)) % 0.61/0.80 (step @p76 :rule trans :premises (@p75 @p74)) % 0.61/0.80 (step @p77 :rule cong :premises (@p76) :args ((forall @t9 (=> @t53 @t3)))) % 0.61/0.80 (step @p78 :rule trans :premises (@p77 @p72)) % 0.61/0.80 (step @p79 :rule refl :args (@t3)) % 0.61/0.80 (step @p80 :rule refl :args (@t50)) % 0.61/0.80 (step @p81 :rule refl :args (@t5)) % 0.61/0.80 (step @p82 :rule cong :premises (@p81 @p80) :args ((= @t5 @t50))) % 0.61/0.80 (step @p83 :rule symm :premises (@p82)) % 0.61/0.80 (step @p84 :rule eq_resolve :premises (@p81 @p83)) % 0.61/0.80 (step @p85 :rule cong :premises (@p84) :args (@t54)) % 0.61/0.80 (step @p86 :rule cong :premises (@p85) :args (@t55)) % 0.61/0.80 (step @p87 :rule cong :premises (@p86) :args (@t56)) % 0.61/0.80 (step @p88 :rule exists-elim :args ((= @t7 @t56))) % 0.61/0.80 (step @p89 :rule trans :premises (@p88 @p87)) % 0.61/0.80 (step @p90 :rule cong :premises (@p89 @p79) :args (@t8)) % 0.61/0.80 (step @p91 :rule cong :premises (@p90) :args (@t10)) % 0.61/0.80 (step @p92 :rule trans :premises (@p91 @p78)) % 0.61/0.80 (step @p93 :rule eq_resolve :premises (@p1 @p92)) % 0.61/0.80 (step @p94 :rule eq-refl :args (@t61)) % 0.61/0.80 (step @p95 :rule refl :args (@t61)) % 0.61/0.80 (step @p96 :rule symm :premises (@p95)) % 0.61/0.80 (step @p97 :rule eq-symm :args (false @t57)) % 0.61/0.80 (step @p98 :rule true_intro :premises (@p97)) % 0.61/0.80 (step @p99 :rule eq-symm :args (@t58 @t62)) % 0.61/0.80 (step @p100 :rule trans :premises (@p99 @p98)) % 0.61/0.80 (step @p101 :rule refl :args (@t57)) % 0.61/0.80 (step @p102 :rule evaluate :args (@t63)) % 0.61/0.80 (step @p103 :rule cong :premises (@p102 @p101) :args ((= @t63 @t57))) % 0.61/0.80 (step @p104 :rule bool-not-eq-elim1 :args (true @t57)) % 0.61/0.80 (step @p105 :rule trans :premises (@p104 @p103)) % 0.61/0.80 (step @p106 :rule ite-neg-branch :premises (@p105) :args (@t58 @t62 (= true @t57))) % 0.61/0.80 (step @p107 :rule trans :premises (@p106 @p100)) % 0.61/0.80 (step @p108 :rule eq-ite-lift :args (@t58 false true @t57)) % 0.61/0.80 (step @p109 :rule trans :premises (@p108 @p107)) % 0.61/0.80 (step @p110 :rule eq-symm :args (@t57 @t59)) % 0.61/0.80 (step @p111 :rule trans :premises (@p110 @p109)) % 0.61/0.80 (step @p112 :rule true_elim :premises (@p111)) % 0.61/0.80 (step @p113 :rule cong :premises (@p112) :args ((lambda @t60 @t57))) % 0.61/0.80 (step @p114 :rule trans :premises (@p113 @p96)) % 0.61/0.80 (step @p115 :rule bool-double-not-elim :args (@t57)) % 0.61/0.80 (step @p116 :rule bool-eq-false :args (@t57)) % 0.61/0.80 (step @p117 :rule cong :premises (@p116) :args (@t64)) % 0.61/0.80 (step @p118 :rule trans :premises (@p117 @p115)) % 0.61/0.80 (step @p119 :rule aci_norm :args ((= (and @t64 true) @t64))) % 0.61/0.80 (step @p120 :rule ite-then-false :args (@t58 true)) % 0.61/0.80 (step @p121 :rule trans :premises (@p120 @p119)) % 0.61/0.80 (step @p122 :rule trans :premises (@p121 @p118)) % 0.61/0.80 (step @p123 :rule cong :premises (@p122) :args (@t61)) % 0.61/0.80 (step @p124 :rule trans :premises (@p123 @p114)) % 0.61/0.80 (step @p125 :rule refl :args (@t61)) % 0.61/0.80 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t61 @t61))) % 0.61/0.80 (step @p127 :rule trans :premises (@p126 @p94)) % 0.61/0.80 (step @p128 :rule skolem_intro :args (@t65)) % 0.61/0.80 (step @p129 :rule cong :premises (@p125 @p128) :args ((= @t61 @t65))) % 0.61/0.80 (step @p130 :rule trans :premises (@p129 @p127)) % 0.61/0.80 (step @p131 :rule true_elim :premises (@p130)) % 0.61/0.80 (step @p132 :rule cong :premises (@p131) :args (@t66)) % 0.61/0.80 (step @p133 :rule refl :args (@t68)) % 0.61/0.80 (step @p134 :rule nary_cong :premises (@p133 @p132) :args (@t69)) % 0.61/0.80 (step @p135 :rule refl :args (@t45)) % 0.61/0.80 (step @p136 :rule cong :premises (@p135 @p134) :args ((=> @t45 @t69))) % 0.61/0.80 (step @p137 :rule beta-reduce :args ((= (_ @t71 @t66) @t66))) % 0.61/0.80 (step @p138 :rule alpha_equiv :args (@t71 (@list @t70) (@list @t57))) % 0.61/0.80 (step @p139 :rule trans :premises (@p138 @p113)) % 0.61/0.80 (step @p140 :rule trans :premises (@p139 @p96)) % 0.61/0.80 (step @p141 :rule cong :premises (@p140) :args (@t72)) % 0.61/0.80 (step @p142 :rule cong :premises (@p141) :args (@t73)) % 0.61/0.80 (step @p143 :rule trans :premises (@p142 @p137)) % 0.61/0.80 (step @p144 :rule beta-reduce :args ((= @t74 @t67))) % 0.61/0.80 (step @p145 :rule cong :premises (@p144) :args (@t75)) % 0.61/0.80 (step @p146 :rule nary_cong :premises (@p145 @p143) :args (@t76)) % 0.61/0.80 (step @p147 :rule cong :premises (@p135 @p146) :args ((=> @t45 @t76))) % 0.61/0.80 (assume-push @p283 @t45) % 0.61/0.80 (step @p149 :rule instantiate :premises (@p93) :args ((@list @t71 @t67))) % 0.61/0.80 (step-pop @p284 :rule scope :premises (@p149)) % 0.61/0.80 (step @p150 :rule process_scope :premises (@p284) :args (@t76)) % 0.61/0.80 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 0.61/0.80 (step @p153 :rule eq_resolve :premises (@p152 @p136)) % 0.61/0.80 (step @p154 :rule implies_elim :premises (@p153)) % 0.61/0.80 (step @p155 :rule chain_m_resolution :premises (@p154 @p93) :args (@t78 @t79 @t80)) % 0.61/0.80 (step @p156 :rule bool-eq-true :args (@t67)) % 0.61/0.80 (step @p157 :rule skolem_intro :args (@t67)) % 0.61/0.80 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 0.61/0.80 (step @p159 :rule cnf_or_pos :args (@t78)) % 0.61/0.80 (step @p160 :rule reordering :premises (@p159) :args ((or @t68 @t77 (not @t78)))) % 0.61/0.80 (step @p161 :rule chain_m_resolution :premises (@p160 @p158 @p155) :args (@t77 @t81 (@list @t67 @t78))) % 0.61/0.80 (step @p162 :rule refl :args (@t84)) % 0.61/0.80 (step @p163 :rule refl :args (@t85)) % 0.61/0.80 (step @p164 :rule cong :premises (@p163 @p162) :args ((= @t85 @t84))) % 0.61/0.80 (step @p165 :rule symm :premises (@p164)) % 0.61/0.80 (step @p166 :rule eq_resolve :premises (@p163 @p165)) % 0.61/0.80 (step @p167 :rule eq-refl :args (@t82)) % 0.61/0.80 (step @p168 :rule skolem_intro :args (@t83)) % 0.61/0.80 (step @p169 :rule refl :args (@t82)) % 0.61/0.80 (step @p170 :rule cong :premises (@p169 @p168) :args ((= @t82 @t83))) % 0.61/0.80 (step @p171 :rule trans :premises (@p170 @p167)) % 0.61/0.80 (step @p172 :rule true_elim :premises (@p171)) % 0.61/0.80 (step @p173 :rule refl :args (@t21)) % 0.61/0.80 (step @p174 :rule ho_cong :premises (@p173 @p172)) % 0.61/0.80 (step @p175 :rule trans :premises (@p174 @p166)) % 0.61/0.80 (step @p176 :rule refl :args (@t87)) % 0.61/0.80 (step @p177 :rule refl :args (@t88)) % 0.61/0.80 (step @p178 :rule cong :premises (@p177 @p176) :args ((= @t88 @t87))) % 0.61/0.80 (step @p179 :rule symm :premises (@p178)) % 0.61/0.80 (step @p180 :rule eq_resolve :premises (@p177 @p179)) % 0.61/0.80 (step @p181 :rule cong :premises (@p180) :args (@t89)) % 0.61/0.80 (step @p182 :rule nary_cong :premises (@p181 @p175) :args (@t91)) % 0.61/0.80 (step @p183 :rule cong :premises (@p135 @p182) :args ((=> @t45 @t91))) % 0.61/0.80 (step @p184 :rule refl :args (@t82)) % 0.61/0.80 (step @p185 :rule refl :args (@t21)) % 0.61/0.80 (step @p186 :rule ho_cong :premises (@p185 @p184)) % 0.61/0.80 (step @p187 :rule refl :args ((_ @t21 @t92))) % 0.61/0.80 (step @p188 :rule cong :premises (@p184) :args (@t93)) % 0.61/0.80 (step @p189 :rule trans :premises (@p188 @p187)) % 0.61/0.80 (step @p190 :rule cong :premises (@p189 @p186) :args ((= @t93 @t90))) % 0.61/0.80 (step @p191 :rule symm :premises (@p190)) % 0.61/0.80 (step @p192 :rule refl :args ((_ @t21 @t92))) % 0.61/0.80 (step @p193 :rule eq_resolve :premises (@p192 @p191)) % 0.61/0.80 (step @p194 :rule refl :args (@t94)) % 0.61/0.80 (step @p195 :rule cong :premises (@p194) :args (@t95)) % 0.61/0.80 (step @p196 :rule nary_cong :premises (@p195 @p193) :args (@t96)) % 0.61/0.80 (step @p197 :rule cong :premises (@p135 @p196) :args ((=> @t45 @t96))) % 0.61/0.80 (assume-push @p285 @t45) % 0.61/0.80 (step @p199 :rule instantiate :premises (@p93) :args ((@list @t21 @t86))) % 0.61/0.80 (step-pop @p286 :rule scope :premises (@p199)) % 0.61/0.80 (step @p200 :rule process_scope :premises (@p286) :args (@t96)) % 0.61/0.80 (step @p202 :rule eq_resolve :premises (@p200 @p197)) % 0.61/0.80 (step @p203 :rule eq_resolve :premises (@p202 @p183)) % 0.61/0.80 (step @p204 :rule implies_elim :premises (@p203)) % 0.61/0.80 (step @p205 :rule chain_m_resolution :premises (@p204 @p93) :args (@t98 @t79 @t80)) % 0.61/0.80 (step @p206 :rule refl :args (@t99)) % 0.61/0.80 (step @p207 :rule refl :args (@t100)) % 0.61/0.80 (step @p208 :rule cong :premises (@p207 @p206) :args ((= @t100 @t99))) % 0.61/0.80 (step @p209 :rule symm :premises (@p208)) % 0.61/0.80 (step @p210 :rule eq_resolve :premises (@p207 @p209)) % 0.61/0.80 (step @p211 :rule symm :premises (@p157)) % 0.61/0.80 (step @p212 :rule ho_cong :premises (@p173 @p211)) % 0.61/0.80 (step @p213 :rule trans :premises (@p212 @p210)) % 0.61/0.80 (step @p214 :rule evaluate :args ((not false))) % 0.61/0.80 (step @p215 :rule skolem_intro :args (@t86)) % 0.61/0.80 (step @p216 :rule cong :premises (@p215) :args ((not @t86))) % 0.61/0.80 (step @p217 :rule bool-eq-false :args (@t86)) % 0.61/0.80 (step @p218 :rule eq-symm :args (false @t86)) % 0.61/0.80 (step @p219 :rule trans :premises (@p218 @p217)) % 0.61/0.80 (step @p220 :rule trans :premises (@p219 @p216 @p214)) % 0.61/0.80 (step @p221 :rule true_elim :premises (@p220)) % 0.61/0.80 (step @p222 :rule ho_cong :premises (@p173 @p221)) % 0.61/0.80 (step @p223 :rule trans :premises (@p222 @p180)) % 0.61/0.80 (step @p224 :rule cong :premises (@p223 @p213) :args (@t22)) % 0.61/0.80 (step @p225 :rule cong :premises (@p224) :args (@t23)) % 0.61/0.80 (step @p226 :rule eq_resolve :premises (@p3 @p225)) % 0.61/0.80 (step @p227 :rule not_implies_elim1 :premises (@p226)) % 0.61/0.80 (step @p228 :rule cnf_or_pos :args (@t98)) % 0.61/0.80 (step @p229 :rule reordering :premises (@p228) :args ((or @t97 @t84 (not @t98)))) % 0.61/0.80 (step @p230 :rule chain_m_resolution :premises (@p229 @p227 @p205) :args (@t84 @t81 (@list @t87 @t98))) % 0.61/0.80 (step @p231 :rule not_implies_elim2 :premises (@p226)) % 0.61/0.80 (step @p232 :rule refl :args (@t101)) % 0.61/0.80 (step @p233 :rule refl :args (@t102)) % 0.61/0.80 (step @p234 :rule bool-double-not-elim :args (@t99)) % 0.61/0.80 (step @p235 :rule nary_cong :premises (@p133 @p234 @p233 @p232) :args ((or @t68 (not @t103) @t102 @t101))) % 0.61/0.80 (assume-push @p287 @t103) % 0.61/0.80 (assume-push @p288 @t67) % 0.61/0.80 (assume-push @p289 @t83) % 0.61/0.80 (assume-push @p290 @t84) % 0.61/0.80 (step @p240 :rule evaluate :args ((= true false))) % 0.61/0.80 (step @p241 :rule false_intro :premises (@p231)) % 0.61/0.81 (step @p242 :rule true_intro :premises (@p289)) % 0.61/0.81 (step @p243 :rule trans :premises (@p242 @p211)) % 0.61/0.81 (step @p244 :rule refl :args (tptp.epso)) % 0.61/0.81 (step @p245 :rule cong :premises (@p244 @p243) :args (@t84)) % 0.61/0.81 (step @p246 :rule true_intro :premises (@p230)) % 0.61/0.81 (step @p247 :rule symm :premises (@p246)) % 0.61/0.81 (step @p248 :rule trans :premises (@p247 @p245 @p241)) % 0.61/0.81 (step @p249 false :rule eq_resolve :premises (@p248 @p240)) % 0.61/0.81 (step-pop @p291 :rule scope :premises (@p249)) % 0.61/0.81 (step-pop @p292 :rule scope :premises (@p291)) % 0.61/0.81 (step-pop @p293 :rule scope :premises (@p292)) % 0.61/0.81 (step-pop @p294 :rule scope :premises (@p293)) % 0.61/0.81 (step @p250 :rule process_scope :premises (@p294) :args (false)) % 0.61/0.81 (assume-push @p295 @t67) % 0.61/0.81 (assume-push @p296 @t103) % 0.61/0.81 (assume-push @p297 @t83) % 0.61/0.81 (assume-push @p298 @t84) % 0.61/0.81 (step @p259 :rule and_intro :premises (@p231 @p158 @p297 @p230)) % 0.61/0.81 (step-pop @p299 :rule scope :premises (@p259)) % 0.61/0.81 (step-pop @p300 :rule scope :premises (@p299)) % 0.61/0.81 (step-pop @p301 :rule scope :premises (@p300)) % 0.61/0.81 (step-pop @p302 :rule scope :premises (@p301)) % 0.61/0.81 (step @p260 :rule process_scope :premises (@p302) :args (@t104)) % 0.61/0.81 (step @p265 :rule implies_elim :premises (@p260)) % 0.61/0.81 (step @p266 :rule resolution :premises (@p265 @p250) :args (true @t104)) % 0.61/0.81 (step @p267 :rule not_and :premises (@p266)) % 0.61/0.81 (step @p268 :rule eq_resolve :premises (@p267 @p235)) % 0.61/0.81 (step @p269 :rule reordering :premises (@p268) :args ((or @t99 @t68 @t101 @t102))) % 0.61/0.81 (step @p270 :rule chain_m_resolution :premises (@p269 @p231 @p158 @p230) :args (@t102 (@list true false false) (@list @t99 @t67 @t84))) % 0.61/0.81 (step @p271 :rule equiv_elim1 :premises (@p172)) % 0.61/0.81 (step @p272 :rule reordering :premises (@p271) :args ((or @t83 @t105))) % 0.61/0.81 (step @p273 :rule chain_m_resolution :premises (@p272 @p270) :args (@t105 (@list true) (@list @t83))) % 0.61/0.81 (step @p274 :rule cnf_or_pos :args (@t107)) % 0.61/0.81 (step @p275 :rule reordering :premises (@p274) :args ((or @t82 @t106 @t108))) % 0.61/0.81 (step @p276 :rule chain_m_resolution :premises (@p275 @p273 @p161) :args (@t108 @t109 (@list @t82 @t77))) % 0.61/0.81 (assume-push @p303 @t28) % 0.61/0.81 (step @p278 :rule instantiate :premises (@p43) :args ((@list tptp.epso @t65))) % 0.61/0.81 (step-pop @p304 :rule scope :premises (@p278)) % 0.61/0.81 (step @p279 :rule process_scope :premises (@p304) :args (@t107)) % 0.61/0.81 (step @p281 :rule implies_elim :premises (@p279)) % 0.61/0.81 (step @p282 false :rule chain_m_resolution :premises (@p281 @p276 @p43) :args (false @t109 (@list @t107 @t28))) % 0.61/0.81 ) % 0.61/0.81 % SZS output end Proof % 0.61/0.81 % cvc5 exiting %------------------------------------------------------------------------------