%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO376^5 : 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 : n024.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 09:12:31 AM UTC 2026 % Result : Theorem 0.16s 0.37s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO376^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 19:06:15 EDT 2026 % 0.08/0.25 % CPUTime : % 0.08/0.32 %----Proving TH0 % 0.16/0.37 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.16/0.37 % SZS status Theorem % 0.16/0.37 % SZS output start Proof % 0.16/0.37 ( % 0.16/0.37 (declare-const tptp.cP (-> (-> Bool Bool) Bool)) % 0.16/0.37 (declare-const tptp.cF (-> Bool Bool)) % 0.16/0.37 (declare-const tptp.cG (-> Bool Bool)) % 0.16/0.37 (define @t1 () (@var "Xx" Bool)) % 0.16/0.37 (define @t2 () (_ tptp.cG @t1)) % 0.16/0.37 (define @t3 () (_ tptp.cF @t1)) % 0.16/0.37 (define @t4 () (not @t3)) % 0.16/0.37 (define @t5 () (or @t4 @t2)) % 0.16/0.37 (define @t6 () (@list @t1)) % 0.16/0.37 (define @t7 () (lambda @t6 @t5)) % 0.16/0.37 (define @t8 () (or @t3 @t2)) % 0.16/0.37 (define @t9 () (lambda @t6 @t8)) % 0.16/0.37 (define @t10 () (or (_ tptp.cP @t9) (_ tptp.cP @t7))) % 0.16/0.37 (define @t11 () (_ tptp.cP tptp.cG)) % 0.16/0.37 (define @t12 () (_ tptp.cP tptp.cF)) % 0.16/0.37 (define @t13 () (and @t12 @t11)) % 0.16/0.37 (define @t14 () (=> @t13 @t10)) % 0.16/0.37 (define @t15 () (not @t14)) % 0.16/0.37 (define @t16 () (@purify @t7)) % 0.16/0.37 (define @t17 () (tptp.cP @t16)) % 0.16/0.37 (define @t18 () (_ tptp.cP @t16)) % 0.16/0.37 (define @t19 () (@purify @t9)) % 0.16/0.37 (define @t20 () (tptp.cP @t19)) % 0.16/0.37 (define @t21 () (_ tptp.cP @t19)) % 0.16/0.37 (define @t22 () (tptp.cP tptp.cG)) % 0.16/0.37 (define @t23 () (tptp.cP tptp.cF)) % 0.16/0.37 (define @t24 () (= tptp.cG @t16)) % 0.16/0.37 (define @t25 () (not @t24)) % 0.16/0.37 (define @t26 () (not @t22)) % 0.16/0.37 (define @t27 () (not @t17)) % 0.16/0.37 (define @t28 () (= false true)) % 0.16/0.37 (define @t29 () (and @t22 @t24 @t27)) % 0.16/0.37 (define @t30 () (@list true false)) % 0.16/0.37 (define @t31 () (@const 0 Bool)) % 0.16/0.37 (define @t32 () (@purify @t31)) % 0.16/0.37 (define @t33 () (tptp.cG @t32)) % 0.16/0.37 (define @t34 () (_ @t16 @t32)) % 0.16/0.37 (define @t35 () (_ @t16 @t31)) % 0.16/0.37 (define @t36 () (tptp.cG @t31)) % 0.16/0.37 (define @t37 () (= @t36 @t35)) % 0.16/0.37 (define @t38 () (not @t37)) % 0.16/0.37 (define @t39 () (or @t24 @t38)) % 0.16/0.37 (define @t40 () (= @t34 @t33)) % 0.16/0.37 (define @t41 () (@list true)) % 0.16/0.37 (define @t42 () (tptp.cG @t1)) % 0.16/0.37 (define @t43 () (tptp.cF @t1)) % 0.16/0.37 (define @t44 () (or (not @t43) @t42)) % 0.16/0.37 (define @t45 () (_ @t16 @t1)) % 0.16/0.37 (define @t46 () (= @t5 @t45)) % 0.16/0.37 (define @t47 () (_ @t7 @t1)) % 0.16/0.37 (define @t48 () (= @t45 @t47)) % 0.16/0.37 (define @t49 () (forall @t6 @t48)) % 0.16/0.37 (define @t50 () (@list @t32)) % 0.16/0.37 (define @t51 () (tptp.cF @t32)) % 0.16/0.37 (define @t52 () (not @t51)) % 0.16/0.37 (define @t53 () (or @t52 @t33)) % 0.16/0.37 (define @t54 () (= @t34 @t53)) % 0.16/0.37 (define @t55 () (not @t54)) % 0.16/0.37 (define @t56 () (not @t53)) % 0.16/0.37 (define @t57 () (not @t33)) % 0.16/0.37 (define @t58 () (@list true false false true)) % 0.16/0.37 (define @t59 () (= tptp.cF @t19)) % 0.16/0.37 (define @t60 () (not @t59)) % 0.16/0.37 (define @t61 () (not @t23)) % 0.16/0.37 (define @t62 () (not @t20)) % 0.16/0.37 (define @t63 () (not @t62)) % 0.16/0.37 (define @t64 () (and @t23 @t59 @t62)) % 0.16/0.37 (define @t65 () (@const 1 Bool)) % 0.16/0.37 (define @t66 () (@purify @t65)) % 0.16/0.37 (define @t67 () (tptp.cF @t66)) % 0.16/0.37 (define @t68 () (_ @t19 @t66)) % 0.16/0.37 (define @t69 () (_ @t19 @t65)) % 0.16/0.37 (define @t70 () (tptp.cF @t65)) % 0.16/0.37 (define @t71 () (= @t70 @t69)) % 0.16/0.37 (define @t72 () (not @t71)) % 0.16/0.37 (define @t73 () (or @t59 @t72)) % 0.16/0.37 (define @t74 () (= @t68 @t67)) % 0.16/0.37 (define @t75 () (or @t43 @t42)) % 0.16/0.37 (define @t76 () (_ @t19 @t1)) % 0.16/0.37 (define @t77 () (= @t8 @t76)) % 0.16/0.37 (define @t78 () (_ @t9 @t1)) % 0.16/0.37 (define @t79 () (= @t76 @t78)) % 0.16/0.37 (define @t80 () (forall @t6 @t79)) % 0.16/0.37 (define @t81 () (tptp.cG @t66)) % 0.16/0.37 (define @t82 () (or @t67 @t81)) % 0.16/0.37 (define @t83 () (= @t68 @t82)) % 0.16/0.37 (define @t84 () (not @t83)) % 0.16/0.37 (define @t85 () (not @t82)) % 0.16/0.37 (define @t86 () (@list @t82 @t83 @t67 @t74)) % 0.16/0.37 (define @t87 () (not @t68)) % 0.16/0.37 (define @t88 () (not @t81)) % 0.16/0.37 (define @t89 () (not @t32)) % 0.16/0.37 (define @t90 () (not @t66)) % 0.16/0.37 (define @t91 () (not @t57)) % 0.16/0.37 (define @t92 () (= true false)) % 0.16/0.37 (define @t93 () (and @t57 @t32 @t66 @t81)) % 0.16/0.37 (define @t94 () (= tptp.cG @t19)) % 0.16/0.37 (define @t95 () (not @t94)) % 0.16/0.37 (define @t96 () (and @t22 @t94 @t62)) % 0.16/0.37 (define @t97 () (@const 2 Bool)) % 0.16/0.37 (define @t98 () (@purify @t97)) % 0.16/0.37 (define @t99 () (tptp.cG @t98)) % 0.16/0.37 (define @t100 () (_ @t19 @t98)) % 0.16/0.37 (define @t101 () (_ @t19 @t97)) % 0.16/0.37 (define @t102 () (tptp.cG @t97)) % 0.16/0.37 (define @t103 () (= @t102 @t101)) % 0.16/0.37 (define @t104 () (not @t103)) % 0.16/0.37 (define @t105 () (or @t94 @t104)) % 0.16/0.37 (define @t106 () (= @t100 @t99)) % 0.16/0.37 (define @t107 () (not @t99)) % 0.16/0.37 (define @t108 () (not @t98)) % 0.16/0.37 (define @t109 () (and @t57 @t32 @t98 @t99)) % 0.16/0.37 (define @t110 () (not @t108)) % 0.16/0.37 (define @t111 () (not @t100)) % 0.16/0.37 (define @t112 () (not @t111)) % 0.16/0.37 (define @t113 () (not @t90)) % 0.16/0.37 (define @t114 () (and @t68 @t90 @t108 @t111)) % 0.16/0.37 (define @t115 () (not @t107)) % 0.16/0.37 (define @t116 () (and @t81 @t90 @t108 @t107)) % 0.16/0.37 (define @t117 () (or @t51 @t33)) % 0.16/0.37 (define @t118 () (not @t117)) % 0.16/0.37 (define @t119 () (@list true true)) % 0.16/0.37 (define @t120 () (_ @t19 @t32)) % 0.16/0.37 (define @t121 () (= @t120 @t117)) % 0.16/0.37 (define @t122 () (not @t120)) % 0.16/0.37 (define @t123 () (not @t122)) % 0.16/0.37 (define @t124 () (and @t122 @t32 @t98 @t100)) % 0.16/0.37 (define @t125 () (not @t89)) % 0.16/0.37 (define @t126 () (and @t81 @t90 @t89 @t57)) % 0.16/0.37 (define @t127 () (and @t81 @t66 @t98 @t107)) % 0.16/0.37 (define @t128 () (and @t122 @t89 @t108 @t100)) % 0.16/0.37 (define @t129 () (and @t68 @t66 @t98 @t111)) % 0.16/0.37 (define @t130 () (and @t57 @t89 @t108 @t99)) % 0.16/0.37 (assume @p1 @t15) % 0.16/0.37 (assume @p2 true) % 0.16/0.37 (step @p3 :rule refl :args (@t17)) % 0.16/0.37 (step @p4 :rule refl :args (@t18)) % 0.16/0.37 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t18 @t17))) % 0.16/0.37 (step @p6 :rule symm :premises (@p5)) % 0.16/0.37 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.16/0.37 (step @p8 :rule eq-refl :args (@t7)) % 0.16/0.37 (step @p9 :rule skolem_intro :args (@t16)) % 0.16/0.37 (step @p10 :rule refl :args (@t7)) % 0.16/0.37 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t7 @t16))) % 0.16/0.37 (step @p12 :rule trans :premises (@p11 @p8)) % 0.16/0.37 (step @p13 :rule true_elim :premises (@p12)) % 0.16/0.37 (step @p14 :rule refl :args (tptp.cP)) % 0.16/0.37 (step @p15 :rule ho_cong :premises (@p14 @p13)) % 0.16/0.37 (step @p16 :rule trans :premises (@p15 @p7)) % 0.16/0.37 (step @p17 :rule refl :args (@t20)) % 0.16/0.37 (step @p18 :rule refl :args (@t21)) % 0.16/0.37 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t21 @t20))) % 0.16/0.37 (step @p20 :rule symm :premises (@p19)) % 0.16/0.37 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.16/0.37 (step @p22 :rule eq-refl :args (@t9)) % 0.16/0.37 (step @p23 :rule skolem_intro :args (@t19)) % 0.16/0.37 (step @p24 :rule refl :args (@t9)) % 0.16/0.37 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t9 @t19))) % 0.16/0.37 (step @p26 :rule trans :premises (@p25 @p22)) % 0.16/0.37 (step @p27 :rule true_elim :premises (@p26)) % 0.16/0.37 (step @p28 :rule ho_cong :premises (@p14 @p27)) % 0.16/0.37 (step @p29 :rule trans :premises (@p28 @p21)) % 0.16/0.37 (step @p30 :rule nary_cong :premises (@p29 @p16) :args (@t10)) % 0.16/0.37 (step @p31 :rule refl :args (@t22)) % 0.16/0.37 (step @p32 :rule refl :args (@t11)) % 0.16/0.37 (step @p33 :rule cong :premises (@p32 @p31) :args ((= @t11 @t22))) % 0.16/0.37 (step @p34 :rule symm :premises (@p33)) % 0.16/0.37 (step @p35 :rule eq_resolve :premises (@p32 @p34)) % 0.16/0.37 (step @p36 :rule refl :args (@t23)) % 0.16/0.37 (step @p37 :rule refl :args (@t12)) % 0.16/0.37 (step @p38 :rule cong :premises (@p37 @p36) :args ((= @t12 @t23))) % 0.16/0.37 (step @p39 :rule symm :premises (@p38)) % 0.16/0.37 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 0.16/0.37 (step @p41 :rule nary_cong :premises (@p40 @p35) :args (@t13)) % 0.16/0.37 (step @p42 :rule cong :premises (@p41 @p30) :args (@t14)) % 0.16/0.37 (step @p43 :rule cong :premises (@p42) :args (@t15)) % 0.16/0.37 (step @p44 :rule eq_resolve :premises (@p1 @p43)) % 0.16/0.37 (step @p45 :rule not_implies_elim1 :premises (@p44)) % 0.16/0.37 (step @p46 :rule and_elim :premises (@p45) :args (1)) % 0.16/0.37 (step @p47 :rule not_implies_elim2 :premises (@p44)) % 0.16/0.37 (step @p48 :rule not_or_elim :premises (@p47) :args (1)) % 0.16/0.37 (step @p49 :rule refl :args (@t25)) % 0.16/0.37 (step @p50 :rule bool-double-not-elim :args (@t17)) % 0.16/0.37 (step @p51 :rule refl :args (@t26)) % 0.16/0.37 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49) :args ((or @t26 (not @t27) @t25))) % 0.16/0.37 (assume-push @p668 @t22) % 0.16/0.37 (assume-push @p669 @t24) % 0.16/0.37 (assume-push @p670 @t27) % 0.16/0.37 (step @p56 :rule evaluate :args (@t28)) % 0.16/0.37 (step @p57 :rule true_intro :premises (@p46)) % 0.16/0.37 (step @p58 :rule symm :premises (@p669)) % 0.16/0.37 (step @p59 :rule cong :premises (@p58) :args (@t17)) % 0.16/0.37 (step @p60 :rule false_intro :premises (@p48)) % 0.16/0.37 (step @p61 :rule symm :premises (@p60)) % 0.16/0.37 (step @p62 :rule trans :premises (@p61 @p59 @p57)) % 0.16/0.37 (step @p63 false :rule eq_resolve :premises (@p62 @p56)) % 0.16/0.37 (step-pop @p671 :rule scope :premises (@p63)) % 0.16/0.37 (step-pop @p672 :rule scope :premises (@p671)) % 0.16/0.37 (step-pop @p673 :rule scope :premises (@p672)) % 0.16/0.37 (step @p64 :rule process_scope :premises (@p673) :args (false)) % 0.16/0.37 (assume-push @p674 @t22) % 0.16/0.37 (assume-push @p675 @t27) % 0.16/0.37 (assume-push @p676 @t24) % 0.16/0.37 (step @p71 :rule and_intro :premises (@p46 @p676 @p48)) % 0.16/0.37 (step-pop @p677 :rule scope :premises (@p71)) % 0.16/0.37 (step-pop @p678 :rule scope :premises (@p677)) % 0.16/0.37 (step-pop @p679 :rule scope :premises (@p678)) % 0.16/0.37 (step @p72 :rule process_scope :premises (@p679) :args (@t29)) % 0.16/0.37 (step @p76 :rule implies_elim :premises (@p72)) % 0.16/0.37 (step @p77 :rule resolution :premises (@p76 @p64) :args (true @t29)) % 0.16/0.37 (step @p78 :rule not_and :premises (@p77)) % 0.16/0.37 (step @p79 :rule eq_resolve :premises (@p78 @p52)) % 0.16/0.37 (step @p80 :rule reordering :premises (@p79) :args ((or @t17 @t26 @t25))) % 0.16/0.37 (step @p81 :rule chain_m_resolution :premises (@p80 @p48 @p46) :args (@t25 @t30 (@list @t17 @t22))) % 0.16/0.37 (step @p82 :rule eq-symm :args (@t33 @t34)) % 0.16/0.37 (step @p83 :rule eq-refl :args (@t31)) % 0.16/0.37 (step @p84 :rule skolem_intro :args (@t32)) % 0.16/0.37 (step @p85 :rule refl :args (@t31)) % 0.16/0.37 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t31 @t32))) % 0.16/0.37 (step @p87 :rule trans :premises (@p86 @p83)) % 0.16/0.37 (step @p88 :rule true_elim :premises (@p87)) % 0.16/0.37 (step @p89 :rule cong :premises (@p88) :args (@t35)) % 0.16/0.37 (step @p90 :rule cong :premises (@p88) :args (@t36)) % 0.16/0.37 (step @p91 :rule cong :premises (@p90 @p89) :args (@t37)) % 0.16/0.37 (step @p92 :rule trans :premises (@p91 @p82)) % 0.16/0.37 (step @p93 :rule cong :premises (@p92) :args (@t38)) % 0.16/0.37 (step @p94 :rule refl :args (@t24)) % 0.16/0.37 (step @p95 :rule nary_cong :premises (@p94 @p93) :args (@t39)) % 0.16/0.37 ; WARNING: add trust step for TRUST % 0.16/0.37 ; trust TRUST THEORY_LEMMA % 0.16/0.37 (step @p96 :rule trust :premises () :args (@t39)) % 0.16/0.37 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 0.16/0.37 (step @p98 :rule chain_m_resolution :premises (@p97 @p81) :args ((not @t40) @t41 (@list @t24))) % 0.16/0.37 (step @p99 :rule cnf_equiv_neg1 :args (@t40)) % 0.16/0.37 (step @p100 :rule reordering :premises (@p99) :args ((or @t34 @t33 @t40))) % 0.16/0.37 (step @p101 :rule eq-symm :args (@t44 @t45)) % 0.16/0.37 (step @p102 :rule cong :premises (@p101) :args ((forall @t6 (= @t44 @t45)))) % 0.16/0.37 (step @p103 :rule refl :args (@t45)) % 0.16/0.37 (step @p104 :rule refl :args (@t42)) % 0.16/0.37 (step @p105 :rule refl :args (@t2)) % 0.16/0.37 (step @p106 :rule cong :premises (@p105 @p104) :args ((= @t2 @t42))) % 0.16/0.37 (step @p107 :rule symm :premises (@p106)) % 0.16/0.37 (step @p108 :rule eq_resolve :premises (@p105 @p107)) % 0.16/0.37 (step @p109 :rule refl :args (@t43)) % 0.16/0.37 (step @p110 :rule refl :args (@t3)) % 0.16/0.37 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t3 @t43))) % 0.16/0.37 (step @p112 :rule symm :premises (@p111)) % 0.16/0.37 (step @p113 :rule eq_resolve :premises (@p110 @p112)) % 0.16/0.37 (step @p114 :rule cong :premises (@p113) :args (@t4)) % 0.16/0.37 (step @p115 :rule nary_cong :premises (@p114 @p108) :args (@t5)) % 0.16/0.37 (step @p116 :rule cong :premises (@p115 @p103) :args (@t46)) % 0.16/0.37 (step @p117 :rule cong :premises (@p116) :args ((forall @t6 @t46))) % 0.16/0.37 (step @p118 :rule trans :premises (@p117 @p102)) % 0.16/0.37 (step @p119 :rule eq-symm :args (@t45 @t5)) % 0.16/0.37 (step @p120 :rule beta-reduce :args ((= @t47 @t5))) % 0.16/0.37 (step @p121 :rule refl :args (@t45)) % 0.16/0.37 (step @p122 :rule cong :premises (@p121 @p120) :args (@t48)) % 0.16/0.37 (step @p123 :rule trans :premises (@p122 @p119)) % 0.16/0.37 (step @p124 :rule cong :premises (@p123) :args (@t49)) % 0.16/0.37 (step @p125 :rule trans :premises (@p124 @p118)) % 0.16/0.37 (step @p126 :rule quant-unused-vars :args ((= (forall @t6 true) true))) % 0.16/0.37 (step @p127 :rule eq-refl :args (@t47)) % 0.16/0.37 (step @p128 :rule cong :premises (@p127) :args ((forall @t6 (= @t47 @t47)))) % 0.16/0.37 (step @p129 :rule trans :premises (@p128 @p126)) % 0.16/0.37 (step @p130 :rule refl :args (@t47)) % 0.16/0.37 (step @p131 :rule refl :args (@t1)) % 0.16/0.37 (step @p132 :rule ho_cong :premises (@p9 @p131)) % 0.16/0.37 (step @p133 :rule cong :premises (@p132 @p130) :args (@t48)) % 0.16/0.37 (step @p134 :rule cong :premises (@p133) :args (@t49)) % 0.16/0.37 (step @p135 :rule trans :premises (@p134 @p129)) % 0.16/0.37 (step @p136 :rule true_elim :premises (@p135)) % 0.16/0.37 (step @p137 :rule eq_resolve :premises (@p136 @p125)) % 0.16/0.37 (step @p138 :rule instantiate :premises (@p137) :args (@t50)) % 0.16/0.37 (step @p139 :rule cnf_equiv_pos2 :args (@t54)) % 0.16/0.37 (step @p140 :rule reordering :premises (@p139) :args ((or @t34 @t56 @t55))) % 0.16/0.37 (step @p141 :rule cnf_or_neg :args (@t53 1)) % 0.16/0.37 (step @p142 :rule reordering :premises (@p141) :args ((or @t57 @t53))) % 0.16/0.37 (step @p143 :rule chain_m_resolution :premises (@p142 @p140 @p138 @p100 @p98) :args (@t34 @t58 (@list @t53 @t54 @t33 @t40))) % 0.16/0.37 (step @p144 :rule cnf_equiv_neg2 :args (@t40)) % 0.16/0.37 (step @p145 :rule chain_m_resolution :premises (@p144 @p98 @p143) :args (@t57 @t30 (@list @t40 @t34))) % 0.16/0.37 (step @p146 :rule and_elim :premises (@p45) :args (0)) % 0.16/0.37 (step @p147 :rule not_or_elim :premises (@p47) :args (0)) % 0.16/0.37 (step @p148 :rule refl :args (@t60)) % 0.16/0.37 (step @p149 :rule bool-double-not-elim :args (@t20)) % 0.16/0.37 (step @p150 :rule refl :args (@t61)) % 0.16/0.37 (step @p151 :rule nary_cong :premises (@p150 @p149 @p148) :args ((or @t61 @t63 @t60))) % 0.16/0.37 (assume-push @p680 @t23) % 0.16/0.37 (assume-push @p681 @t59) % 0.16/0.37 (assume-push @p682 @t62) % 0.16/0.37 (step @p56 :rule evaluate :args (@t28)) % 0.16/0.37 (step @p155 :rule true_intro :premises (@p146)) % 0.16/0.37 (step @p156 :rule symm :premises (@p681)) % 0.16/0.37 (step @p157 :rule cong :premises (@p156) :args (@t20)) % 0.16/0.37 (step @p158 :rule false_intro :premises (@p147)) % 0.16/0.37 (step @p159 :rule symm :premises (@p158)) % 0.16/0.37 (step @p160 :rule trans :premises (@p159 @p157 @p155)) % 0.16/0.37 (step @p161 false :rule eq_resolve :premises (@p160 @p56)) % 0.16/0.37 (step-pop @p683 :rule scope :premises (@p161)) % 0.16/0.37 (step-pop @p684 :rule scope :premises (@p683)) % 0.16/0.37 (step-pop @p685 :rule scope :premises (@p684)) % 0.16/0.37 (step @p162 :rule process_scope :premises (@p685) :args (false)) % 0.16/0.37 (assume-push @p686 @t23) % 0.16/0.37 (assume-push @p687 @t62) % 0.16/0.37 (assume-push @p688 @t59) % 0.16/0.37 (step @p169 :rule and_intro :premises (@p146 @p688 @p147)) % 0.16/0.37 (step-pop @p689 :rule scope :premises (@p169)) % 0.16/0.37 (step-pop @p690 :rule scope :premises (@p689)) % 0.16/0.37 (step-pop @p691 :rule scope :premises (@p690)) % 0.16/0.37 (step @p170 :rule process_scope :premises (@p691) :args (@t64)) % 0.16/0.37 (step @p174 :rule implies_elim :premises (@p170)) % 0.16/0.37 (step @p175 :rule resolution :premises (@p174 @p162) :args (true @t64)) % 0.16/0.37 (step @p176 :rule not_and :premises (@p175)) % 0.16/0.37 (step @p177 :rule eq_resolve :premises (@p176 @p151)) % 0.16/0.37 (step @p178 :rule reordering :premises (@p177) :args ((or @t20 @t61 @t60))) % 0.16/0.37 (step @p179 :rule chain_m_resolution :premises (@p178 @p147 @p146) :args (@t60 @t30 (@list @t20 @t23))) % 0.16/0.37 (step @p180 :rule eq-symm :args (@t67 @t68)) % 0.16/0.37 (step @p181 :rule eq-refl :args (@t65)) % 0.16/0.37 (step @p182 :rule skolem_intro :args (@t66)) % 0.16/0.37 (step @p183 :rule refl :args (@t65)) % 0.16/0.37 (step @p184 :rule cong :premises (@p183 @p182) :args ((= @t65 @t66))) % 0.16/0.37 (step @p185 :rule trans :premises (@p184 @p181)) % 0.16/0.37 (step @p186 :rule true_elim :premises (@p185)) % 0.16/0.37 (step @p187 :rule cong :premises (@p186) :args (@t69)) % 0.16/0.37 (step @p188 :rule cong :premises (@p186) :args (@t70)) % 0.16/0.37 (step @p189 :rule cong :premises (@p188 @p187) :args (@t71)) % 0.16/0.37 (step @p190 :rule trans :premises (@p189 @p180)) % 0.16/0.37 (step @p191 :rule cong :premises (@p190) :args (@t72)) % 0.16/0.37 (step @p192 :rule refl :args (@t59)) % 0.16/0.37 (step @p193 :rule nary_cong :premises (@p192 @p191) :args (@t73)) % 0.16/0.37 ; trust TRUST THEORY_LEMMA % 0.16/0.37 (step @p194 :rule trust :premises () :args (@t73)) % 0.16/0.37 (step @p195 :rule eq_resolve :premises (@p194 @p193)) % 0.16/0.37 (step @p196 :rule chain_m_resolution :premises (@p195 @p179) :args ((not @t74) @t41 (@list @t59))) % 0.16/0.37 (step @p197 :rule cnf_equiv_neg1 :args (@t74)) % 0.16/0.37 (step @p198 :rule reordering :premises (@p197) :args ((or @t68 @t67 @t74))) % 0.16/0.37 (step @p199 :rule eq-symm :args (@t75 @t76)) % 0.16/0.37 (step @p200 :rule cong :premises (@p199) :args ((forall @t6 (= @t75 @t76)))) % 0.16/0.37 (step @p201 :rule refl :args (@t76)) % 0.16/0.37 (step @p202 :rule nary_cong :premises (@p113 @p108) :args (@t8)) % 0.16/0.37 (step @p203 :rule cong :premises (@p202 @p201) :args (@t77)) % 0.16/0.37 (step @p204 :rule cong :premises (@p203) :args ((forall @t6 @t77))) % 0.16/0.37 (step @p205 :rule trans :premises (@p204 @p200)) % 0.16/0.37 (step @p206 :rule eq-symm :args (@t76 @t8)) % 0.16/0.37 (step @p207 :rule beta-reduce :args ((= @t78 @t8))) % 0.16/0.37 (step @p208 :rule refl :args (@t76)) % 0.16/0.37 (step @p209 :rule cong :premises (@p208 @p207) :args (@t79)) % 0.16/0.37 (step @p210 :rule trans :premises (@p209 @p206)) % 0.16/0.37 (step @p211 :rule cong :premises (@p210) :args (@t80)) % 0.16/0.37 (step @p212 :rule trans :premises (@p211 @p205)) % 0.16/0.37 (step @p213 :rule eq-refl :args (@t78)) % 0.16/0.37 (step @p214 :rule cong :premises (@p213) :args ((forall @t6 (= @t78 @t78)))) % 0.16/0.37 (step @p215 :rule trans :premises (@p214 @p126)) % 0.16/0.37 (step @p216 :rule refl :args (@t78)) % 0.16/0.37 (step @p217 :rule ho_cong :premises (@p23 @p131)) % 0.16/0.37 (step @p218 :rule cong :premises (@p217 @p216) :args (@t79)) % 0.16/0.37 (step @p219 :rule cong :premises (@p218) :args (@t80)) % 0.16/0.37 (step @p220 :rule trans :premises (@p219 @p215)) % 0.16/0.37 (step @p221 :rule true_elim :premises (@p220)) % 0.16/0.37 (step @p222 :rule eq_resolve :premises (@p221 @p212)) % 0.16/0.37 (step @p223 :rule instantiate :premises (@p222) :args ((@list @t66))) % 0.16/0.37 (step @p224 :rule cnf_equiv_pos2 :args (@t83)) % 0.16/0.37 (step @p225 :rule reordering :premises (@p224) :args ((or @t68 @t85 @t84))) % 0.16/0.37 (step @p226 :rule cnf_or_neg :args (@t82 0)) % 0.16/0.37 (step @p227 :rule reordering :premises (@p226) :args ((or (not @t67) @t82))) % 0.16/0.37 (step @p228 :rule chain_m_resolution :premises (@p227 @p225 @p223 @p198 @p196) :args (@t68 @t58 @t86)) % 0.16/0.37 (step @p229 :rule cnf_equiv_neg2 :args (@t74)) % 0.16/0.37 (step @p230 :rule cnf_equiv_pos1 :args (@t83)) % 0.16/0.37 (step @p231 :rule reordering :premises (@p230) :args ((or @t87 @t82 @t84))) % 0.16/0.37 (step @p232 :rule cnf_or_pos :args (@t82)) % 0.16/0.37 (step @p233 :rule reordering :premises (@p232) :args ((or @t67 @t81 @t85))) % 0.16/0.37 (step @p234 :rule chain_m_resolution :premises (@p233 @p231 @p223 @p229 @p196) :args ((or @t87 @t81) (@list false false true true) @t86)) % 0.16/0.37 (step @p235 :rule chain_m_resolution :premises (@p234 @p228) :args (@t81 (@list false) (@list @t68))) % 0.16/0.37 (step @p236 :rule refl :args (@t88)) % 0.16/0.37 (step @p237 :rule bool-double-not-elim :args (@t33)) % 0.16/0.37 (step @p238 :rule refl :args (@t89)) % 0.16/0.37 (step @p239 :rule refl :args (@t90)) % 0.16/0.37 (step @p240 :rule nary_cong :premises (@p239 @p238 @p237 @p236) :args ((or @t90 @t89 @t91 @t88))) % 0.16/0.37 (assume-push @p692 @t57) % 0.16/0.37 (assume-push @p693 @t32) % 0.16/0.37 (assume-push @p694 @t66) % 0.16/0.37 (assume-push @p695 @t81) % 0.16/0.37 (step @p245 :rule evaluate :args (@t92)) % 0.16/0.37 (step @p246 :rule false_intro :premises (@p692)) % 0.16/0.37 (step @p247 :rule true_intro :premises (@p693)) % 0.16/0.37 (step @p248 :rule symm :premises (@p247)) % 0.16/0.37 (step @p249 :rule true_intro :premises (@p694)) % 0.16/0.37 (step @p250 :rule trans :premises (@p249 @p248)) % 0.16/0.37 (step @p251 :rule cong :premises (@p250) :args (@t81)) % 0.16/0.37 (step @p252 :rule true_intro :premises (@p695)) % 0.16/0.37 (step @p253 :rule symm :premises (@p252)) % 0.16/0.37 (step @p254 :rule trans :premises (@p253 @p251 @p246)) % 0.16/0.37 (step @p255 false :rule eq_resolve :premises (@p254 @p245)) % 0.16/0.37 (step-pop @p696 :rule scope :premises (@p255)) % 0.16/0.37 (step-pop @p697 :rule scope :premises (@p696)) % 0.16/0.37 (step-pop @p698 :rule scope :premises (@p697)) % 0.16/0.37 (step-pop @p699 :rule scope :premises (@p698)) % 0.16/0.37 (step @p256 :rule process_scope :premises (@p699) :args (false)) % 0.16/0.37 (assume-push @p700 @t66) % 0.16/0.37 (assume-push @p701 @t32) % 0.16/0.37 (assume-push @p702 @t57) % 0.16/0.37 (assume-push @p703 @t81) % 0.16/0.37 (step @p265 :rule and_intro :premises (@p702 @p701 @p700 @p703)) % 0.16/0.37 (step-pop @p704 :rule scope :premises (@p265)) % 0.16/0.37 (step-pop @p705 :rule scope :premises (@p704)) % 0.16/0.37 (step-pop @p706 :rule scope :premises (@p705)) % 0.16/0.37 (step-pop @p707 :rule scope :premises (@p706)) % 0.16/0.37 (step @p266 :rule process_scope :premises (@p707) :args (@t93)) % 0.16/0.37 (step @p271 :rule implies_elim :premises (@p266)) % 0.16/0.37 (step @p272 :rule resolution :premises (@p271 @p256) :args (true @t93)) % 0.16/0.37 (step @p273 :rule not_and :premises (@p272)) % 0.16/0.37 (step @p274 :rule eq_resolve :premises (@p273 @p240)) % 0.16/0.37 (step @p275 :rule reordering :premises (@p274) :args ((or @t90 @t33 @t89 @t88))) % 0.16/0.37 (step @p276 :rule refl :args (@t95)) % 0.16/0.37 (step @p277 :rule nary_cong :premises (@p51 @p149 @p276) :args ((or @t26 @t63 @t95))) % 0.16/0.37 (assume-push @p708 @t22) % 0.16/0.37 (assume-push @p709 @t94) % 0.16/0.37 (assume-push @p710 @t62) % 0.16/0.37 (step @p56 :rule evaluate :args (@t28)) % 0.16/0.37 (step @p57 :rule true_intro :premises (@p46)) % 0.16/0.37 (step @p281 :rule symm :premises (@p709)) % 0.16/0.37 (step @p282 :rule cong :premises (@p281) :args (@t20)) % 0.16/0.37 (step @p158 :rule false_intro :premises (@p147)) % 0.16/0.37 (step @p159 :rule symm :premises (@p158)) % 0.16/0.37 (step @p283 :rule trans :premises (@p159 @p282 @p57)) % 0.16/0.37 (step @p284 false :rule eq_resolve :premises (@p283 @p56)) % 0.16/0.37 (step-pop @p711 :rule scope :premises (@p284)) % 0.16/0.37 (step-pop @p712 :rule scope :premises (@p711)) % 0.16/0.37 (step-pop @p713 :rule scope :premises (@p712)) % 0.16/0.37 (step @p285 :rule process_scope :premises (@p713) :args (false)) % 0.16/0.37 (assume-push @p714 @t22) % 0.16/0.37 (assume-push @p715 @t62) % 0.16/0.37 (assume-push @p716 @t94) % 0.16/0.37 (step @p292 :rule and_intro :premises (@p46 @p716 @p147)) % 0.16/0.37 (step-pop @p717 :rule scope :premises (@p292)) % 0.16/0.37 (step-pop @p718 :rule scope :premises (@p717)) % 0.16/0.37 (step-pop @p719 :rule scope :premises (@p718)) % 0.16/0.37 (step @p293 :rule process_scope :premises (@p719) :args (@t96)) % 0.16/0.37 (step @p297 :rule implies_elim :premises (@p293)) % 0.16/0.37 (step @p298 :rule resolution :premises (@p297 @p285) :args (true @t96)) % 0.16/0.37 (step @p299 :rule not_and :premises (@p298)) % 0.16/0.37 (step @p300 :rule eq_resolve :premises (@p299 @p277)) % 0.16/0.37 (step @p301 :rule reordering :premises (@p300) :args ((or @t20 @t26 @t95))) % 0.16/0.37 (step @p302 :rule chain_m_resolution :premises (@p301 @p147 @p46) :args (@t95 @t30 (@list @t20 @t22))) % 0.16/0.37 (step @p303 :rule eq-symm :args (@t99 @t100)) % 0.16/0.37 (step @p304 :rule eq-refl :args (@t97)) % 0.16/0.37 (step @p305 :rule skolem_intro :args (@t98)) % 0.16/0.37 (step @p306 :rule refl :args (@t97)) % 0.16/0.37 (step @p307 :rule cong :premises (@p306 @p305) :args ((= @t97 @t98))) % 0.16/0.37 (step @p308 :rule trans :premises (@p307 @p304)) % 0.16/0.37 (step @p309 :rule true_elim :premises (@p308)) % 0.16/0.37 (step @p310 :rule cong :premises (@p309) :args (@t101)) % 0.16/0.37 (step @p311 :rule cong :premises (@p309) :args (@t102)) % 0.16/0.37 (step @p312 :rule cong :premises (@p311 @p310) :args (@t103)) % 0.16/0.37 (step @p313 :rule trans :premises (@p312 @p303)) % 0.16/0.37 (step @p314 :rule cong :premises (@p313) :args (@t104)) % 0.16/0.37 (step @p315 :rule refl :args (@t94)) % 0.16/0.37 (step @p316 :rule nary_cong :premises (@p315 @p314) :args (@t105)) % 0.16/0.37 ; trust TRUST THEORY_LEMMA % 0.16/0.37 (step @p317 :rule trust :premises () :args (@t105)) % 0.16/0.37 (step @p318 :rule eq_resolve :premises (@p317 @p316)) % 0.16/0.37 (step @p319 :rule chain_m_resolution :premises (@p318 @p302) :args ((not @t106) @t41 (@list @t94))) % 0.16/0.37 (step @p320 :rule cnf_equiv_neg1 :args (@t106)) % 0.16/0.37 (step @p321 :rule reordering :premises (@p320) :args ((or @t100 @t99 @t106))) % 0.16/0.37 (step @p322 :rule refl :args (@t107)) % 0.16/0.37 (step @p323 :rule refl :args (@t108)) % 0.16/0.37 (step @p324 :rule nary_cong :premises (@p323 @p322 @p238 @p237) :args ((or @t108 @t107 @t89 @t91))) % 0.16/0.37 (assume-push @p720 @t57) % 0.16/0.37 (assume-push @p721 @t32) % 0.16/0.37 (assume-push @p722 @t98) % 0.16/0.37 (assume-push @p723 @t99) % 0.16/0.37 (step @p245 :rule evaluate :args (@t92)) % 0.16/0.37 (step @p329 :rule false_intro :premises (@p720)) % 0.16/0.37 (step @p330 :rule true_intro :premises (@p721)) % 0.16/0.37 (step @p331 :rule symm :premises (@p330)) % 0.16/0.37 (step @p332 :rule true_intro :premises (@p722)) % 0.16/0.37 (step @p333 :rule trans :premises (@p332 @p331)) % 0.16/0.37 (step @p334 :rule cong :premises (@p333) :args (@t99)) % 0.16/0.37 (step @p335 :rule true_intro :premises (@p723)) % 0.16/0.37 (step @p336 :rule symm :premises (@p335)) % 0.16/0.37 (step @p337 :rule trans :premises (@p336 @p334 @p329)) % 0.16/0.37 (step @p338 false :rule eq_resolve :premises (@p337 @p245)) % 0.16/0.37 (step-pop @p724 :rule scope :premises (@p338)) % 0.16/0.37 (step-pop @p725 :rule scope :premises (@p724)) % 0.16/0.37 (step-pop @p726 :rule scope :premises (@p725)) % 0.16/0.37 (step-pop @p727 :rule scope :premises (@p726)) % 0.16/0.37 (step @p339 :rule process_scope :premises (@p727) :args (false)) % 0.16/0.37 (assume-push @p728 @t98) % 0.16/0.37 (assume-push @p729 @t99) % 0.16/0.37 (assume-push @p730 @t32) % 0.16/0.37 (assume-push @p731 @t57) % 0.16/0.37 (step @p348 :rule and_intro :premises (@p731 @p730 @p728 @p729)) % 0.16/0.37 (step-pop @p732 :rule scope :premises (@p348)) % 0.16/0.37 (step-pop @p733 :rule scope :premises (@p732)) % 0.16/0.37 (step-pop @p734 :rule scope :premises (@p733)) % 0.16/0.37 (step-pop @p735 :rule scope :premises (@p734)) % 0.16/0.37 (step @p349 :rule process_scope :premises (@p735) :args (@t109)) % 0.16/0.37 (step @p354 :rule implies_elim :premises (@p349)) % 0.16/0.37 (step @p355 :rule resolution :premises (@p354 @p339) :args (true @t109)) % 0.16/0.37 (step @p356 :rule not_and :premises (@p355)) % 0.16/0.37 (step @p357 :rule eq_resolve :premises (@p356 @p324)) % 0.16/0.37 (step @p358 :rule reordering :premises (@p357) :args ((or @t107 @t108 @t33 @t89))) % 0.16/0.37 (step @p359 :rule bool-double-not-elim :args (@t98)) % 0.16/0.37 (step @p360 :rule 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(step @p620 :rule and_intro :premises (@p841 @p840 @p842 @p843)) % 0.16/0.38 (step-pop @p844 :rule scope :premises (@p620)) % 0.16/0.38 (step-pop @p845 :rule scope :premises (@p844)) % 0.16/0.38 (step-pop @p846 :rule scope :premises (@p845)) % 0.16/0.38 (step-pop @p847 :rule scope :premises (@p846)) % 0.16/0.38 (step @p621 :rule process_scope :premises (@p847) :args (@t129)) % 0.16/0.38 (step @p626 :rule implies_elim :premises (@p621)) % 0.16/0.38 (step @p627 :rule resolution :premises (@p626 @p611) :args (true @t129)) % 0.16/0.38 (step @p628 :rule not_and :premises (@p627)) % 0.16/0.38 (step @p629 :rule eq_resolve :premises (@p628 @p596)) % 0.16/0.38 (step @p630 :rule reordering :premises (@p629) :args ((or @t87 @t90 @t100 @t108))) % 0.16/0.38 (step @p631 :rule chain_m_resolution :premises (@p630 @p228 @p523 @p594) :args (@t108 (@list false false true) (@list @t68 @t66 @t100))) % 0.16/0.38 (step @p632 :rule nary_cong :premises (@p322 @p359 @p237 @p487) :args ((or @t107 @t110 @t91 @t125))) % 0.16/0.38 (assume-push @p848 @t57) % 0.16/0.38 (assume-push @p849 @t89) % 0.16/0.38 (assume-push @p850 @t108) % 0.16/0.38 (assume-push @p851 @t99) % 0.16/0.38 (step @p245 :rule evaluate :args (@t92)) % 0.16/0.38 (step @p637 :rule false_intro :premises (@p848)) % 0.16/0.38 (step @p638 :rule false_intro :premises (@p849)) % 0.16/0.38 (step @p639 :rule symm :premises (@p638)) % 0.16/0.38 (step @p640 :rule false_intro :premises (@p850)) % 0.16/0.38 (step @p641 :rule trans :premises (@p640 @p639)) % 0.16/0.38 (step @p642 :rule cong :premises (@p641) :args (@t99)) % 0.16/0.38 (step @p643 :rule true_intro :premises (@p851)) % 0.16/0.38 (step @p644 :rule symm :premises (@p643)) % 0.16/0.38 (step @p645 :rule trans :premises (@p644 @p642 @p637)) % 0.16/0.38 (step @p646 false :rule eq_resolve :premises (@p645 @p245)) % 0.16/0.38 (step-pop @p852 :rule scope :premises (@p646)) % 0.16/0.38 (step-pop @p853 :rule scope :premises (@p852)) % 0.16/0.38 (step-pop @p854 :rule scope :premises (@p853)) % 0.16/0.38 (step-pop @p855 :rule scope :premises (@p854)) % 0.16/0.38 (step @p647 :rule process_scope :premises (@p855) :args (false)) % 0.16/0.38 (assume-push @p856 @t99) % 0.16/0.38 (assume-push @p857 @t108) % 0.16/0.38 (assume-push @p858 @t57) % 0.16/0.38 (assume-push @p859 @t89) % 0.16/0.38 (step @p656 :rule and_intro :premises (@p858 @p859 @p857 @p856)) % 0.16/0.38 (step-pop @p860 :rule scope :premises (@p656)) % 0.16/0.38 (step-pop @p861 :rule scope :premises (@p860)) % 0.16/0.38 (step-pop @p862 :rule scope :premises (@p861)) % 0.16/0.38 (step-pop @p863 :rule scope :premises (@p862)) % 0.16/0.38 (step @p657 :rule process_scope :premises (@p863) :args (@t130)) % 0.16/0.38 (step @p662 :rule implies_elim :premises (@p657)) % 0.16/0.38 (step @p663 :rule resolution :premises (@p662 @p647) :args (true @t130)) % 0.16/0.38 (step @p664 :rule not_and :premises (@p663)) % 0.16/0.38 (step @p665 :rule eq_resolve :premises (@p664 @p632)) % 0.16/0.38 (step @p666 :rule reordering :premises (@p665) :args ((or @t98 @t107 @t32 @t33))) % 0.16/0.38 (step @p667 false :rule chain_m_resolution :premises (@p666 @p631 @p595 @p486 @p145) :args (false (@list true false true true) (@list @t98 @t99 @t32 @t33))) % 0.16/0.38 ) % 0.16/0.38 % SZS output end Proof % 0.16/0.38 % cvc5 exiting %------------------------------------------------------------------------------