%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM637^1 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 08:40:06 AM UTC 2026 % Result : Theorem 21.19s 21.42s % Output : Proof 21.19s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM637^1 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n017.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 11:37:46 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 21.19/21.42 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 21.19/21.42 % SZS status Theorem % 21.19/21.42 % SZS output start Proof % 21.19/21.42 ( % 21.19/21.42 (declare-sort tptp.nat 0) % 21.19/21.42 (declare-sort tptp.set 0) % 21.19/21.42 (declare-const tptp.suc (-> tptp.nat tptp.nat)) % 21.19/21.42 (declare-const tptp.setof (-> (-> tptp.nat Bool) tptp.set)) % 21.19/21.42 (declare-const tptp.x tptp.nat) % 21.19/21.42 (declare-const tptp.esti (-> tptp.nat tptp.set Bool)) % 21.19/21.42 (declare-const tptp.n_1 tptp.nat) % 21.19/21.42 (define @t1 () (= tptp.x tptp.n_1)) % 21.19/21.42 (define @t2 () (not @t1)) % 21.19/21.42 (define @t3 () (@var "Xs" tptp.nat)) % 21.19/21.42 (define @t4 () (@var "Xp" (-> tptp.nat Bool))) % 21.19/21.42 (define @t5 () (_ @t4 @t3)) % 21.19/21.42 (define @t6 () (_ tptp.setof @t4)) % 21.19/21.42 (define @t7 () (_ tptp.esti @t3)) % 21.19/21.42 (define @t8 () (_ @t7 @t6)) % 21.19/21.42 (define @t9 () (@list @t4 @t3)) % 21.19/21.42 (define @t10 () (forall @t9 (=> @t8 @t5))) % 21.19/21.42 (define @t11 () (@var "Xs" tptp.set)) % 21.19/21.42 (define @t12 () (@var "Xx" tptp.nat)) % 21.19/21.42 (define @t13 () (_ (_ tptp.esti @t12) @t11)) % 21.19/21.42 (define @t14 () (@list @t12)) % 21.19/21.42 (define @t15 () (forall @t14 @t13)) % 21.19/21.42 (define @t16 () (_ tptp.suc @t12)) % 21.19/21.42 (define @t17 () (_ (_ tptp.esti @t16) @t11)) % 21.19/21.42 (define @t18 () (forall @t14 (=> @t13 @t17))) % 21.19/21.42 (define @t19 () (=> @t18 @t15)) % 21.19/21.42 (define @t20 () (_ (_ tptp.esti tptp.n_1) @t11)) % 21.19/21.42 (define @t21 () (=> @t20 @t19)) % 21.19/21.42 (define @t22 () (@list @t11)) % 21.19/21.42 (define @t23 () (forall @t22 @t21)) % 21.19/21.42 (define @t24 () (forall @t9 (=> @t5 @t8))) % 21.19/21.42 (define @t25 () (@var "Xa" Bool)) % 21.19/21.42 (define @t26 () (@var "Xx_0" tptp.nat)) % 21.19/21.42 (define @t27 () (_ tptp.suc @t26)) % 21.19/21.42 (define @t28 () (= tptp.x @t27)) % 21.19/21.42 (define @t29 () (not @t28)) % 21.19/21.42 (define @t30 () (forall (@list @t26) @t29)) % 21.19/21.42 (define @t31 () (tptp.setof @t4)) % 21.19/21.42 (define @t32 () (tptp.esti @t3 @t31)) % 21.19/21.42 (define @t33 () (_ @t4 @t3)) % 21.19/21.42 (define @t34 () (not @t5)) % 21.19/21.42 (define @t35 () (or @t34 @t8)) % 21.19/21.42 (define @t36 () (@var "BOUND_VARIABLE_7497" tptp.nat)) % 21.19/21.42 (define @t37 () (tptp.esti @t36 @t11)) % 21.19/21.42 (define @t38 () (tptp.suc @t12)) % 21.19/21.42 (define @t39 () (tptp.esti @t38 @t11)) % 21.19/21.42 (define @t40 () (tptp.esti @t12 @t11)) % 21.19/21.42 (define @t41 () (forall @t14 (or (not @t40) @t39))) % 21.19/21.42 (define @t42 () (not @t41)) % 21.19/21.42 (define @t43 () (tptp.esti tptp.n_1 @t11)) % 21.19/21.42 (define @t44 () (not @t43)) % 21.19/21.42 (define @t45 () (or @t44 @t42 @t37)) % 21.19/21.42 (define @t46 () (@list @t36)) % 21.19/21.42 (define @t47 () (forall @t46 @t45)) % 21.19/21.42 (define @t48 () (forall @t46 @t37)) % 21.19/21.42 (define @t49 () (or @t44 @t42 @t48)) % 21.19/21.42 (define @t50 () (forall @t14 @t40)) % 21.19/21.42 (define @t51 () (not @t20)) % 21.19/21.42 (define @t52 () (or @t51 @t42 @t50)) % 21.19/21.42 (define @t53 () (=> @t41 @t50)) % 21.19/21.42 (define @t54 () (not @t13)) % 21.19/21.42 (define @t55 () (or @t54 @t17)) % 21.19/21.42 (define @t56 () (@var "BOUND_VARIABLE_14728" tptp.nat)) % 21.19/21.42 (define @t57 () (lambda (@list @t56) (not (= tptp.x @t56)))) % 21.19/21.42 (define @t58 () (@purify @t57)) % 21.19/21.42 (define @t59 () (tptp.setof @t58)) % 21.19/21.42 (define @t60 () (not @t8)) % 21.19/21.42 (define @t61 () (or @t60 @t5)) % 21.19/21.42 (define @t62 () (tptp.esti tptp.x @t59)) % 21.19/21.42 (define @t63 () (not @t62)) % 21.19/21.42 (define @t64 () (not (= tptp.x tptp.x))) % 21.19/21.42 (define @t65 () (_ @t57 tptp.x)) % 21.19/21.42 (define @t66 () (_ @t58 tptp.x)) % 21.19/21.42 (define @t67 () (or @t63 @t66)) % 21.19/21.42 (define @t68 () (forall @t9 (or (not @t32) @t33))) % 21.19/21.42 (define @t69 () (@list false)) % 21.19/21.42 (define @t70 () (forall @t14 (or (not (tptp.esti @t12 @t59)) (tptp.esti @t38 @t59)))) % 21.19/21.42 (define @t71 () (@quantifiers_skolemize @t70 0)) % 21.19/21.42 (define @t72 () (tptp.suc @t71)) % 21.19/21.42 (define @t73 () (tptp.esti @t72 @t59)) % 21.19/21.42 (define @t74 () (= tptp.x @t72)) % 21.19/21.42 (define @t75 () (not @t74)) % 21.19/21.42 (define @t76 () (_ @t57 @t72)) % 21.19/21.42 (define @t77 () (_ @t58 @t72)) % 21.19/21.42 (define @t78 () (not @t77)) % 21.19/21.42 (define @t79 () (or @t78 @t73)) % 21.19/21.42 (define @t80 () (forall @t9 (or (not @t33) @t32))) % 21.19/21.42 (define @t81 () (or @t74 @t73)) % 21.19/21.42 (define @t82 () (tptp.suc @t26)) % 21.19/21.42 (define @t83 () (@list true false)) % 21.19/21.42 (define @t84 () (or (not (tptp.esti @t71 @t59)) @t73)) % 21.19/21.42 (define @t85 () (not @t84)) % 21.19/21.42 (define @t86 () (not @t70)) % 21.19/21.42 (define @t87 () (tptp.esti tptp.n_1 @t59)) % 21.19/21.42 (define @t88 () (not @t87)) % 21.19/21.42 (define @t89 () (or @t88 @t86 @t62)) % 21.19/21.42 (define @t90 () (or @t1 @t87)) % 21.19/21.42 (define @t91 () (not @t90)) % 21.19/21.42 (define @t92 () (_ @t57 tptp.n_1)) % 21.19/21.42 (define @t93 () (_ @t58 tptp.n_1)) % 21.19/21.42 (define @t94 () (not @t93)) % 21.19/21.42 (define @t95 () (or @t94 @t87)) % 21.19/21.42 (assume @p1 @t2) % 21.19/21.42 (assume @p2 @t10) % 21.19/21.42 (assume @p3 @t23) % 21.19/21.42 (assume @p4 @t24) % 21.19/21.42 (assume @p5 (forall (@list @t25) (=> (not (not @t25)) @t25))) % 21.19/21.42 (assume @p6 (not (not @t30))) % 21.19/21.42 (assume @p7 true) % 21.19/21.42 (step @p8 :rule refl :args ((tptp.esti @t3 @t6))) % 21.19/21.42 (step @p9 :rule refl :args (@t31)) % 21.19/21.42 (step @p10 :rule refl :args (@t3)) % 21.19/21.42 (step @p11 :rule cong :premises (@p10 @p9) :args (@t32)) % 21.19/21.42 (step @p12 :rule trans :premises (@p11 @p8)) % 21.19/21.42 (step @p13 :rule refl :args (@t7)) % 21.19/21.42 (step @p14 :rule ho_cong :premises (@p13 @p9)) % 21.19/21.42 (step @p15 :rule cong :premises (@p14 @p12) :args ((= (_ @t7 @t31) @t32))) % 21.19/21.42 (step @p16 :rule symm :premises (@p15)) % 21.19/21.42 (step @p17 :rule refl :args (@t8)) % 21.19/21.42 (step @p18 :rule eq_resolve :premises (@p17 @p16)) % 21.19/21.42 (step @p19 :rule refl :args (@t6)) % 21.19/21.42 (step @p20 :rule cong :premises (@p19 @p9) :args ((= @t6 @t31))) % 21.19/21.42 (step @p21 :rule symm :premises (@p20)) % 21.19/21.42 (step @p22 :rule eq_resolve :premises (@p19 @p21)) % 21.19/21.42 (step @p23 :rule ho_cong :premises (@p13 @p22)) % 21.19/21.42 (step @p24 :rule trans :premises (@p23 @p18)) % 21.19/21.42 (step @p25 :rule refl :args (@t33)) % 21.19/21.42 (step @p26 :rule refl :args (@t5)) % 21.19/21.42 (step @p27 :rule cong :premises (@p26 @p25) :args ((= @t5 @t33))) % 21.19/21.42 (step @p28 :rule symm :premises (@p27)) % 21.19/21.42 (step @p29 :rule eq_resolve :premises (@p26 @p28)) % 21.19/21.42 (step @p30 :rule cong :premises (@p29) :args (@t34)) % 21.19/21.42 (step @p31 :rule nary_cong :premises (@p30 @p24) :args (@t35)) % 21.19/21.42 (step @p32 :rule cong :premises (@p31) :args ((forall @t9 @t35))) % 21.19/21.42 (step @p33 :rule bool-impl-elim :args (@t5 @t8)) % 21.19/21.42 (step @p34 :rule cong :premises (@p33) :args (@t24)) % 21.19/21.42 (step @p35 :rule trans :premises (@p34 @p32)) % 21.19/21.42 (step @p36 :rule eq_resolve :premises (@p4 @p35)) % 21.19/21.42 (step @p37 :rule quant-merge-prenex :args ((= (forall @t22 @t47) (forall (@list @t11 @t36) @t45)))) % 21.19/21.42 (step @p38 :rule alpha_equiv :args (@t48 (@list @t36) (@list @t12))) % 21.19/21.42 (step @p39 :rule refl :args (@t42)) % 21.19/21.42 (step @p40 :rule refl :args (@t44)) % 21.19/21.42 (step @p41 :rule nary_cong :premises (@p40 @p39 @p38) :args (@t49)) % 21.19/21.42 (step @p42 :rule quant-miniscope-or :args ((= @t47 @t49))) % 21.19/21.42 (step @p43 :rule trans :premises (@p42 @p41)) % 21.19/21.42 (step @p44 :rule symm :premises (@p43)) % 21.19/21.42 (step @p45 :rule cong :premises (@p44) :args ((forall @t22 (or @t44 @t42 @t50)))) % 21.19/21.42 (step @p46 :rule trans :premises (@p45 @p37)) % 21.19/21.42 (step @p47 :rule refl :args (@t50)) % 21.19/21.42 (step @p48 :rule refl :args (@t43)) % 21.19/21.42 (step @p49 :rule refl :args (@t20)) % 21.19/21.42 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t20 @t43))) % 21.19/21.42 (step @p51 :rule symm :premises (@p50)) % 21.19/21.42 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 21.19/21.42 (step @p53 :rule cong :premises (@p52) :args (@t51)) % 21.19/21.42 (step @p54 :rule nary_cong :premises (@p53 @p39 @p47) :args (@t52)) % 21.19/21.42 (step @p55 :rule cong :premises (@p54) :args ((forall @t22 @t52))) % 21.19/21.42 (step @p56 :rule trans :premises (@p55 @p46)) % 21.19/21.42 (step @p57 :rule aci_norm :args ((= (or @t51 (or @t42 @t50)) @t52))) % 21.19/21.42 (step @p58 :rule bool-impl-elim :args (@t41 @t50)) % 21.19/21.42 (step @p59 :rule refl :args (@t51)) % 21.19/21.42 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or @t51 @t53))) % 21.19/21.42 (step @p61 :rule trans :premises (@p60 @p57)) % 21.19/21.42 (step @p62 :rule bool-impl-elim :args (@t20 @t53)) % 21.19/21.42 (step @p63 :rule trans :premises (@p62 @p61)) % 21.19/21.42 (step @p64 :rule cong :premises (@p63) :args ((forall @t22 (=> @t20 @t53)))) % 21.19/21.42 (step @p65 :rule trans :premises (@p64 @p56)) % 21.19/21.42 (step @p66 :rule refl :args (@t40)) % 21.19/21.42 (step @p67 :rule refl :args (@t13)) % 21.19/21.42 (step @p68 :rule cong :premises (@p67 @p66) :args ((= @t13 @t40))) % 21.19/21.42 (step @p69 :rule symm :premises (@p68)) % 21.19/21.42 (step @p70 :rule eq_resolve :premises (@p67 @p69)) % 21.19/21.42 (step @p71 :rule cong :premises (@p70) :args (@t15)) % 21.19/21.42 (step @p72 :rule refl :args ((tptp.esti @t16 @t11))) % 21.19/21.42 (step @p73 :rule refl :args (@t11)) % 21.19/21.42 (step @p74 :rule refl :args (@t38)) % 21.19/21.42 (step @p75 :rule cong :premises (@p74 @p73) :args (@t39)) % 21.19/21.42 (step @p76 :rule trans :premises (@p75 @p72)) % 21.19/21.42 (step @p77 :rule refl :args (tptp.esti)) % 21.19/21.42 (step @p78 :rule ho_cong :premises (@p77 @p74)) % 21.19/21.42 (step @p79 :rule ho_cong :premises (@p78 @p73)) % 21.19/21.42 (step @p80 :rule cong :premises (@p79 @p76) :args ((= (_ (_ tptp.esti @t38) @t11) @t39))) % 21.19/21.42 (step @p81 :rule symm :premises (@p80)) % 21.19/21.42 (step @p82 :rule refl :args (@t17)) % 21.19/21.42 (step @p83 :rule eq_resolve :premises (@p82 @p81)) % 21.19/21.42 (step @p84 :rule refl :args (@t16)) % 21.19/21.42 (step @p85 :rule cong :premises (@p84 @p74) :args ((= @t16 @t38))) % 21.19/21.42 (step @p86 :rule symm :premises (@p85)) % 21.19/21.42 (step @p87 :rule eq_resolve :premises (@p84 @p86)) % 21.19/21.42 (step @p88 :rule ho_cong :premises (@p77 @p87)) % 21.19/21.42 (step @p89 :rule ho_cong :premises (@p88 @p73)) % 21.19/21.42 (step @p90 :rule trans :premises (@p89 @p83)) % 21.19/21.42 (step @p91 :rule cong :premises (@p70) :args (@t54)) % 21.19/21.42 (step @p92 :rule nary_cong :premises (@p91 @p90) :args (@t55)) % 21.19/21.42 (step @p93 :rule cong :premises (@p92) :args ((forall @t14 @t55))) % 21.19/21.42 (step @p94 :rule bool-impl-elim :args (@t13 @t17)) % 21.19/21.42 (step @p95 :rule cong :premises (@p94) :args (@t18)) % 21.19/21.42 (step @p96 :rule trans :premises (@p95 @p93)) % 21.19/21.42 (step @p97 :rule cong :premises (@p96 @p71) :args (@t19)) % 21.19/21.42 (step @p98 :rule refl :args (@t20)) % 21.19/21.42 (step @p99 :rule cong :premises (@p98 @p97) :args (@t21)) % 21.19/21.42 (step @p100 :rule cong :premises (@p99) :args (@t23)) % 21.19/21.42 (step @p101 :rule trans :premises (@p100 @p65)) % 21.19/21.42 (step @p102 :rule eq_resolve :premises (@p3 @p101)) % 21.19/21.42 (step @p103 :rule instantiate :premises (@p102) :args ((@list @t59 tptp.x))) % 21.19/21.42 (step @p104 :rule cong :premises (@p24) :args (@t60)) % 21.19/21.42 (step @p105 :rule nary_cong :premises (@p104 @p29) :args (@t61)) % 21.19/21.42 (step @p106 :rule cong :premises (@p105) :args ((forall @t9 @t61))) % 21.19/21.42 (step @p107 :rule bool-impl-elim :args (@t8 @t5)) % 21.19/21.42 (step @p108 :rule cong :premises (@p107) :args (@t10)) % 21.19/21.42 (step @p109 :rule trans :premises (@p108 @p106)) % 21.19/21.42 (step @p110 :rule eq_resolve :premises (@p2 @p109)) % 21.19/21.42 (step @p111 :rule aci_norm :args ((= (or @t63 false) @t63))) % 21.19/21.42 (step @p112 :rule evaluate :args ((not false))) % 21.19/21.42 (step @p113 :rule evaluate :args ((not true))) % 21.19/21.42 (step @p114 :rule eq-refl :args (tptp.x)) % 21.19/21.42 (step @p115 :rule cong :premises (@p114) :args (@t64)) % 21.19/21.42 (step @p116 :rule trans :premises (@p115 @p113)) % 21.19/21.42 (step @p117 :rule beta-reduce :args ((= @t65 @t64))) % 21.19/21.42 (step @p118 :rule trans :premises (@p117 @p116)) % 21.19/21.42 (step @p119 :rule cong :premises (@p118) :args ((not @t65))) % 21.19/21.42 (step @p120 :rule trans :premises (@p119 @p112)) % 21.19/21.42 (step @p121 :rule refl :args (tptp.x)) % 21.19/21.42 (step @p122 :rule skolem_intro :args (@t58)) % 21.19/21.42 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 21.19/21.42 (step @p124 :rule cong :premises (@p123) :args ((not @t66))) % 21.19/21.42 (step @p125 :rule bool-eq-false :args (@t66)) % 21.19/21.42 (step @p126 :rule trans :premises (@p125 @p124 @p120)) % 21.19/21.42 (step @p127 :rule true_elim :premises (@p126)) % 21.19/21.42 (step @p128 :rule refl :args (@t63)) % 21.19/21.42 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t67)) % 21.19/21.42 (step @p130 :rule trans :premises (@p129 @p111)) % 21.19/21.42 (step @p131 :rule refl :args (@t68)) % 21.19/21.42 (step @p132 :rule cong :premises (@p131 @p130) :args ((=> @t68 @t67))) % 21.19/21.42 (assume-push @p224 @t68) % 21.19/21.42 (step @p134 :rule instantiate :premises (@p110) :args ((@list @t58 tptp.x))) % 21.19/21.42 (step-pop @p225 :rule scope :premises (@p134)) % 21.19/21.42 (step @p135 :rule process_scope :premises (@p225) :args (@t67)) % 21.19/21.42 (step @p137 :rule eq_resolve :premises (@p135 @p132)) % 21.19/21.42 (step @p138 :rule implies_elim :premises (@p137)) % 21.19/21.42 (step @p139 :rule chain_m_resolution :premises (@p138 @p110) :args (@t63 @t69 (@list @t68))) % 21.19/21.42 (step @p140 :rule refl :args (@t73)) % 21.19/21.42 (step @p141 :rule bool-double-not-elim :args (@t74)) % 21.19/21.42 (step @p142 :rule eq-refl :args (@t75)) % 21.19/21.42 (step @p143 :rule beta-reduce :args ((= @t76 @t75))) % 21.19/21.42 (step @p144 :rule refl :args (@t75)) % 21.19/21.42 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t75 @t76))) % 21.19/21.42 (step @p146 :rule trans :premises (@p145 @p142)) % 21.19/21.42 (step @p147 :rule eq-symm :args (@t76 @t75)) % 21.19/21.42 (step @p148 :rule trans :premises (@p147 @p146)) % 21.19/21.42 (step @p149 :rule refl :args (@t72)) % 21.19/21.42 (step @p150 :rule ho_cong :premises (@p122 @p149)) % 21.19/21.42 (step @p151 :rule cong :premises (@p150 @p144) :args ((= @t77 @t75))) % 21.19/21.42 (step @p152 :rule trans :premises (@p151 @p148)) % 21.19/21.42 (step @p153 :rule true_elim :premises (@p152)) % 21.19/21.42 (step @p154 :rule cong :premises (@p153) :args (@t78)) % 21.19/21.42 (step @p155 :rule trans :premises (@p154 @p141)) % 21.19/21.42 (step @p156 :rule nary_cong :premises (@p155 @p140) :args (@t79)) % 21.19/21.42 (step @p157 :rule refl :args (@t80)) % 21.19/21.42 (step @p158 :rule cong :premises (@p157 @p156) :args ((=> @t80 @t79))) % 21.19/21.42 (assume-push @p226 @t80) % 21.19/21.42 (step @p160 :rule instantiate :premises (@p36) :args ((@list @t58 @t72))) % 21.19/21.42 (step-pop @p227 :rule scope :premises (@p160)) % 21.19/21.42 (step @p161 :rule process_scope :premises (@p227) :args (@t79)) % 21.19/21.42 (step @p163 :rule eq_resolve :premises (@p161 @p158)) % 21.19/21.42 (step @p164 :rule implies_elim :premises (@p163)) % 21.19/21.42 (step @p165 :rule chain_m_resolution :premises (@p164 @p36) :args (@t81 @t69 (@list @t80))) % 21.19/21.42 (step @p166 :rule refl :args (@t82)) % 21.19/21.42 (step @p167 :rule refl :args (@t27)) % 21.19/21.42 (step @p168 :rule cong :premises (@p167 @p166) :args ((= @t27 @t82))) % 21.19/21.42 (step @p169 :rule symm :premises (@p168)) % 21.19/21.42 (step @p170 :rule eq_resolve :premises (@p167 @p169)) % 21.19/21.42 (step @p171 :rule refl :args (tptp.x)) % 21.19/21.42 (step @p172 :rule cong :premises (@p171 @p170) :args (@t28)) % 21.19/21.42 (step @p173 :rule cong :premises (@p172) :args (@t29)) % 21.19/21.42 (step @p174 :rule cong :premises (@p173) :args (@t30)) % 21.19/21.42 (step @p175 :rule bool-double-not-elim :args (@t30)) % 21.19/21.42 (step @p176 :rule trans :premises (@p175 @p174)) % 21.19/21.42 (step @p177 :rule eq_resolve :premises (@p6 @p176)) % 21.19/21.42 (step @p178 :rule instantiate :premises (@p177) :args ((@list @t71))) % 21.19/21.42 (step @p179 :rule cnf_or_pos :args (@t81)) % 21.19/21.42 (step @p180 :rule reordering :premises (@p179) :args ((or @t73 @t74 (not @t81)))) % 21.19/21.42 (step @p181 :rule chain_m_resolution :premises (@p180 @p178 @p165) :args (@t73 @t83 (@list @t74 @t81))) % 21.19/21.42 (step @p182 :rule cnf_or_neg :args (@t84 1)) % 21.19/21.42 (step @p183 :rule chain_m_resolution :premises (@p182 @p181) :args (@t84 @t69 (@list @t73))) % 21.19/21.42 (step @p184 :rule refl :args (@t85)) % 21.19/21.42 (step @p185 :rule bool-double-not-elim :args (@t70)) % 21.19/21.42 (step @p186 :rule nary_cong :premises (@p185 @p184) :args ((or (not @t86) @t85))) % 21.19/21.42 (assume-push @p228 @t86) % 21.19/21.42 (step @p188 :rule skolemize :premises (@p228)) % 21.19/21.42 (step-pop @p229 :rule scope :premises (@p188)) % 21.19/21.42 (step @p189 :rule process_scope :premises (@p229) :args (@t85)) % 21.19/21.42 (step @p191 :rule implies_elim :premises (@p189)) % 21.19/21.42 (step @p192 :rule eq_resolve :premises (@p191 @p186)) % 21.19/21.42 (step @p193 :rule chain_m_resolution :premises (@p192 @p183) :args (@t70 @t69 (@list @t84))) % 21.19/21.42 (step @p194 :rule cnf_or_pos :args (@t89)) % 21.19/21.42 (step @p195 :rule reordering :premises (@p194) :args ((or @t88 @t86 @t62 (not @t89)))) % 21.19/21.42 (step @p196 :rule chain_m_resolution :premises (@p195 @p193 @p139 @p103) :args (@t88 (@list false true false) (@list @t70 @t62 @t89))) % 21.19/21.42 (step @p197 :rule cnf_or_pos :args (@t90)) % 21.19/21.42 (step @p198 :rule reordering :premises (@p197) :args ((or @t1 @t87 @t91))) % 21.19/21.42 (step @p199 :rule chain_m_resolution :premises (@p198 @p1 @p196) :args (@t91 (@list true true) (@list @t1 @t87))) % 21.19/21.42 (step @p200 :rule refl :args (@t87)) % 21.19/21.42 (step @p201 :rule bool-double-not-elim :args (@t1)) % 21.19/21.42 (step @p202 :rule eq-refl :args (@t2)) % 21.19/21.42 (step @p203 :rule beta-reduce :args ((= @t92 @t2))) % 21.19/21.42 (step @p204 :rule refl :args (@t2)) % 21.19/21.42 (step @p205 :rule cong :premises (@p204 @p203) :args ((= @t2 @t92))) % 21.19/21.42 (step @p206 :rule trans :premises (@p205 @p202)) % 21.19/21.42 (step @p207 :rule refl :args (tptp.n_1)) % 21.19/21.42 (step @p208 :rule ho_cong :premises (@p122 @p207)) % 21.19/21.42 (step @p209 :rule cong :premises (@p204 @p208) :args ((= @t2 @t93))) % 21.19/21.42 (step @p210 :rule eq-symm :args (@t93 @t2)) % 21.19/21.42 (step @p211 :rule trans :premises (@p210 @p209 @p206)) % 21.19/21.42 (step @p212 :rule true_elim :premises (@p211)) % 21.19/21.42 (step @p213 :rule cong :premises (@p212) :args (@t94)) % 21.19/21.42 (step @p214 :rule trans :premises (@p213 @p201)) % 21.19/21.42 (step @p215 :rule nary_cong :premises (@p214 @p200) :args (@t95)) % 21.19/21.42 (step @p216 :rule cong :premises (@p157 @p215) :args ((=> @t80 @t95))) % 21.19/21.42 (assume-push @p230 @t80) % 21.19/21.42 (step @p218 :rule instantiate :premises (@p36) :args ((@list @t58 tptp.n_1))) % 21.19/21.42 (step-pop @p231 :rule scope :premises (@p218)) % 21.19/21.42 (step @p219 :rule process_scope :premises (@p231) :args (@t95)) % 21.19/21.42 (step @p221 :rule eq_resolve :premises (@p219 @p216)) % 21.19/21.42 (step @p222 :rule implies_elim :premises (@p221)) % 21.19/21.42 (step @p223 false :rule chain_m_resolution :premises (@p222 @p199 @p36) :args (false @t83 (@list @t90 @t80))) % 21.19/21.42 ) % 21.19/21.42 % SZS output end Proof % 21.19/21.42 % cvc5 exiting %------------------------------------------------------------------------------