%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM665^1 : 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 : n007.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 08:40:18 AM UTC 2026 % Result : Theorem 0.94s 1.16s % Output : Proof 0.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM665^1 : 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 % 0.16/0.33 % Computer : n007.cluster.edu % 0.16/0.33 % Model : x86_64 x86_64 % 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.33 % Memory : 8042.1875MB % 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.33 % CPULimit : 300 % 0.16/0.33 % WCLimit : 300 % 0.16/0.33 % DateTime : Tue Jun 2 11:47:41 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.94/1.16 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.94/1.16 % SZS status Theorem % 0.94/1.16 % SZS output start Proof % 0.94/1.16 ( % 0.94/1.16 (declare-sort tptp.nat 0) % 0.94/1.16 (declare-const tptp.some (-> (-> tptp.nat Bool) Bool)) % 0.94/1.16 (declare-const tptp.z tptp.nat) % 0.94/1.16 (declare-const tptp.diffprop (-> tptp.nat tptp.nat tptp.nat Bool)) % 0.94/1.16 (declare-const tptp.moreis (-> tptp.nat tptp.nat Bool)) % 0.94/1.16 (declare-const tptp.lessis (-> tptp.nat tptp.nat Bool)) % 0.94/1.16 (declare-const tptp.x tptp.nat) % 0.94/1.16 (declare-const tptp.y tptp.nat) % 0.94/1.16 (define @t1 () (_ (_ tptp.moreis tptp.x) tptp.y)) % 0.94/1.16 (define @t2 () (@var "Xu" tptp.nat)) % 0.94/1.16 (define @t3 () (_ (_ tptp.diffprop tptp.y) tptp.z)) % 0.94/1.16 (define @t4 () (_ @t3 @t2)) % 0.94/1.16 (define @t5 () (@list @t2)) % 0.94/1.16 (define @t6 () (lambda @t5 @t4)) % 0.94/1.16 (define @t7 () (@var "Xv" tptp.nat)) % 0.94/1.16 (define @t8 () (@var "Xx" tptp.nat)) % 0.94/1.16 (define @t9 () (@var "Xz" tptp.nat)) % 0.94/1.16 (define @t10 () (_ (_ (_ tptp.diffprop @t9) @t8) @t7)) % 0.94/1.16 (define @t11 () (@list @t7)) % 0.94/1.16 (define @t12 () (lambda @t11 @t10)) % 0.94/1.16 (define @t13 () (_ tptp.some @t12)) % 0.94/1.16 (define @t14 () (@var "Xy" tptp.nat)) % 0.94/1.16 (define @t15 () (_ tptp.lessis @t14)) % 0.94/1.16 (define @t16 () (_ @t15 @t9)) % 0.94/1.16 (define @t17 () (=> @t16 @t13)) % 0.94/1.16 (define @t18 () (_ (_ (_ tptp.diffprop @t14) @t8) @t7)) % 0.94/1.16 (define @t19 () (lambda @t11 @t18)) % 0.94/1.16 (define @t20 () (_ tptp.some @t19)) % 0.94/1.16 (define @t21 () (@list @t8 @t14 @t9)) % 0.94/1.16 (define @t22 () (forall @t21 (=> @t20 @t17))) % 0.94/1.16 (define @t23 () (_ @t15 @t8)) % 0.94/1.16 (define @t24 () (_ (_ tptp.moreis @t8) @t14)) % 0.94/1.16 (define @t25 () (@list @t8 @t14)) % 0.94/1.16 (define @t26 () (forall @t25 (=> @t24 @t23))) % 0.94/1.16 (define @t27 () (_ (_ tptp.diffprop tptp.x) tptp.z)) % 0.94/1.16 (define @t28 () (_ @t27 @t2)) % 0.94/1.16 (define @t29 () (lambda @t5 @t28)) % 0.94/1.16 (define @t30 () (not (_ tptp.some @t29))) % 0.94/1.16 (define @t31 () (tptp.diffprop tptp.x tptp.z @t2)) % 0.94/1.16 (define @t32 () (@purify @t29)) % 0.94/1.16 (define @t33 () (_ @t32 @t2)) % 0.94/1.16 (define @t34 () (= @t28 @t33)) % 0.94/1.16 (define @t35 () (_ @t29 @t2)) % 0.94/1.16 (define @t36 () (= @t33 @t35)) % 0.94/1.16 (define @t37 () (forall @t5 @t36)) % 0.94/1.16 (define @t38 () (tptp.diffprop @t9 @t8 @t7)) % 0.94/1.16 (define @t39 () (lambda @t11 @t38)) % 0.94/1.16 (define @t40 () (tptp.some @t39)) % 0.94/1.16 (define @t41 () (tptp.lessis @t14 @t9)) % 0.94/1.16 (define @t42 () (not @t16)) % 0.94/1.16 (define @t43 () (tptp.diffprop @t14 @t8 @t7)) % 0.94/1.16 (define @t44 () (lambda @t11 @t43)) % 0.94/1.16 (define @t45 () (tptp.some @t44)) % 0.94/1.16 (define @t46 () (not @t20)) % 0.94/1.16 (define @t47 () (or @t46 @t42 @t13)) % 0.94/1.16 (define @t48 () (lambda @t11 (tptp.diffprop tptp.x tptp.z @t7))) % 0.94/1.16 (define @t49 () (tptp.some @t48)) % 0.94/1.16 (define @t50 () (tptp.lessis tptp.y tptp.x)) % 0.94/1.16 (define @t51 () (not @t50)) % 0.94/1.16 (define @t52 () (lambda @t11 (tptp.diffprop tptp.y tptp.z @t7))) % 0.94/1.16 (define @t53 () (tptp.some @t52)) % 0.94/1.16 (define @t54 () (not @t53)) % 0.94/1.16 (define @t55 () (or @t54 @t51 @t49)) % 0.94/1.16 (define @t56 () (forall @t21 (or (not @t45) (not @t41) @t40))) % 0.94/1.16 (define @t57 () (tptp.some @t27)) % 0.94/1.16 (define @t58 () (tptp.some @t3)) % 0.94/1.16 (define @t59 () (not @t58)) % 0.94/1.16 (define @t60 () (or @t59 @t51 @t57)) % 0.94/1.16 (define @t61 () (@list false)) % 0.94/1.16 (define @t62 () (@purify @t6)) % 0.94/1.16 (define @t63 () (tptp.some @t62)) % 0.94/1.16 (define @t64 () (_ tptp.some @t62)) % 0.94/1.16 (define @t65 () (tptp.diffprop tptp.y tptp.z @t2)) % 0.94/1.16 (define @t66 () (_ @t62 @t2)) % 0.94/1.16 (define @t67 () (= @t4 @t66)) % 0.94/1.16 (define @t68 () (_ @t6 @t2)) % 0.94/1.16 (define @t69 () (= @t66 @t68)) % 0.94/1.16 (define @t70 () (forall @t5 @t69)) % 0.94/1.16 (define @t71 () (@const 0 tptp.nat)) % 0.94/1.16 (define @t72 () (_ @t62 @t71)) % 0.94/1.16 (define @t73 () (tptp.diffprop tptp.y tptp.z @t71)) % 0.94/1.16 (define @t74 () (forall @t5 (= @t66 @t65))) % 0.94/1.16 (define @t75 () (= @t72 @t73)) % 0.94/1.16 (define @t76 () (= @t73 @t72)) % 0.94/1.16 (define @t77 () (not @t76)) % 0.94/1.16 (define @t78 () (= @t3 @t62)) % 0.94/1.16 (define @t79 () (tptp.lessis @t14 @t8)) % 0.94/1.16 (define @t80 () (tptp.moreis @t8 @t14)) % 0.94/1.16 (define @t81 () (not @t24)) % 0.94/1.16 (define @t82 () (or @t81 @t23)) % 0.94/1.16 (define @t83 () (tptp.moreis tptp.x tptp.y)) % 0.94/1.16 (define @t84 () (not @t83)) % 0.94/1.16 (define @t85 () (or @t84 @t50)) % 0.94/1.16 (define @t86 () (tptp.some @t32)) % 0.94/1.16 (define @t87 () (_ tptp.some @t32)) % 0.94/1.16 (define @t88 () (= @t27 @t32)) % 0.94/1.16 (define @t89 () (not @t88)) % 0.94/1.16 (define @t90 () (not @t57)) % 0.94/1.16 (define @t91 () (not @t86)) % 0.94/1.16 (define @t92 () (and @t57 @t88 @t91)) % 0.94/1.16 (define @t93 () (@list true false)) % 0.94/1.16 (define @t94 () (@const 1 tptp.nat)) % 0.94/1.16 (define @t95 () (_ @t32 @t94)) % 0.94/1.16 (define @t96 () (tptp.diffprop tptp.x tptp.z @t94)) % 0.94/1.16 (define @t97 () (= @t96 @t95)) % 0.94/1.16 (define @t98 () (not @t97)) % 0.94/1.16 (define @t99 () (forall @t5 (= @t33 @t31))) % 0.94/1.16 (define @t100 () (= @t95 @t96)) % 0.94/1.16 (assume @p1 @t1) % 0.94/1.16 (assume @p2 (_ tptp.some @t6)) % 0.94/1.16 (assume @p3 @t22) % 0.94/1.16 (assume @p4 @t26) % 0.94/1.16 (assume @p5 @t30) % 0.94/1.16 (assume @p6 true) % 0.94/1.16 (step @p7 :rule eq-symm :args (@t31 @t33)) % 0.94/1.16 (step @p8 :rule cong :premises (@p7) :args ((forall @t5 (= @t31 @t33)))) % 0.94/1.16 (step @p9 :rule refl :args (@t33)) % 0.94/1.16 (step @p10 :rule refl :args (@t31)) % 0.94/1.16 (step @p11 :rule refl :args (@t28)) % 0.94/1.16 (step @p12 :rule cong :premises (@p11 @p10) :args ((= @t28 @t31))) % 0.94/1.16 (step @p13 :rule symm :premises (@p12)) % 0.94/1.16 (step @p14 :rule eq_resolve :premises (@p11 @p13)) % 0.94/1.16 (step @p15 :rule cong :premises (@p14 @p9) :args (@t34)) % 0.94/1.16 (step @p16 :rule cong :premises (@p15) :args ((forall @t5 @t34))) % 0.94/1.16 (step @p17 :rule trans :premises (@p16 @p8)) % 0.94/1.16 (step @p18 :rule eq-symm :args (@t33 @t28)) % 0.94/1.16 (step @p19 :rule beta-reduce :args ((= @t35 @t28))) % 0.94/1.16 (step @p20 :rule refl :args (@t33)) % 0.94/1.16 (step @p21 :rule cong :premises (@p20 @p19) :args (@t36)) % 0.94/1.16 (step @p22 :rule trans :premises (@p21 @p18)) % 0.94/1.16 (step @p23 :rule cong :premises (@p22) :args (@t37)) % 0.94/1.16 (step @p24 :rule trans :premises (@p23 @p17)) % 0.94/1.16 (step @p25 :rule quant-unused-vars :args ((= (forall @t5 true) true))) % 0.94/1.16 (step @p26 :rule eq-refl :args (@t35)) % 0.94/1.16 (step @p27 :rule cong :premises (@p26) :args ((forall @t5 (= @t35 @t35)))) % 0.94/1.16 (step @p28 :rule trans :premises (@p27 @p25)) % 0.94/1.16 (step @p29 :rule refl :args (@t35)) % 0.94/1.16 (step @p30 :rule refl :args (@t2)) % 0.94/1.16 (step @p31 :rule skolem_intro :args (@t32)) % 0.94/1.16 (step @p32 :rule ho_cong :premises (@p31 @p30)) % 0.94/1.16 (step @p33 :rule cong :premises (@p32 @p29) :args (@t36)) % 0.94/1.16 (step @p34 :rule cong :premises (@p33) :args (@t37)) % 0.94/1.16 (step @p35 :rule trans :premises (@p34 @p28)) % 0.94/1.16 (step @p36 :rule true_elim :premises (@p35)) % 0.94/1.16 (step @p37 :rule eq_resolve :premises (@p36 @p24)) % 0.94/1.16 (step @p38 :rule refl :args ((tptp.some @t12))) % 0.94/1.16 (step @p39 :rule refl :args (@t38)) % 0.94/1.16 (step @p40 :rule cong :premises (@p39) :args (@t39)) % 0.94/1.16 (step @p41 :rule cong :premises (@p40) :args (@t40)) % 0.94/1.16 (step @p42 :rule trans :premises (@p41 @p38)) % 0.94/1.16 (step @p43 :rule refl :args (tptp.some)) % 0.94/1.16 (step @p44 :rule ho_cong :premises (@p43 @p40)) % 0.94/1.16 (step @p45 :rule cong :premises (@p44 @p42) :args ((= (_ tptp.some @t39) @t40))) % 0.94/1.16 (step @p46 :rule symm :premises (@p45)) % 0.94/1.16 (step @p47 :rule refl :args (@t13)) % 0.94/1.16 (step @p48 :rule eq_resolve :premises (@p47 @p46)) % 0.94/1.16 (step @p49 :rule refl :args (@t10)) % 0.94/1.16 (step @p50 :rule cong :premises (@p49 @p39) :args ((= @t10 @t38))) % 0.94/1.16 (step @p51 :rule symm :premises (@p50)) % 0.94/1.16 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.94/1.16 (step @p53 :rule cong :premises (@p52) :args (@t12)) % 0.94/1.16 (step @p54 :rule ho_cong :premises (@p43 @p53)) % 0.94/1.16 (step @p55 :rule trans :premises (@p54 @p48)) % 0.94/1.16 (step @p56 :rule refl :args (@t41)) % 0.94/1.16 (step @p57 :rule refl :args (@t16)) % 0.94/1.16 (step @p58 :rule cong :premises (@p57 @p56) :args ((= @t16 @t41))) % 0.94/1.16 (step @p59 :rule symm :premises (@p58)) % 0.94/1.16 (step @p60 :rule eq_resolve :premises (@p57 @p59)) % 0.94/1.16 (step @p61 :rule cong :premises (@p60) :args (@t42)) % 0.94/1.16 (step @p62 :rule refl :args ((tptp.some @t19))) % 0.94/1.16 (step @p63 :rule refl :args (@t43)) % 0.94/1.16 (step @p64 :rule cong :premises (@p63) :args (@t44)) % 0.94/1.16 (step @p65 :rule cong :premises (@p64) :args (@t45)) % 0.94/1.16 (step @p66 :rule trans :premises (@p65 @p62)) % 0.94/1.16 (step @p67 :rule ho_cong :premises (@p43 @p64)) % 0.94/1.16 (step @p68 :rule cong :premises (@p67 @p66) :args ((= (_ tptp.some @t44) @t45))) % 0.94/1.16 (step @p69 :rule symm :premises (@p68)) % 0.94/1.16 (step @p70 :rule refl :args (@t20)) % 0.94/1.16 (step @p71 :rule eq_resolve :premises (@p70 @p69)) % 0.94/1.16 (step @p72 :rule refl :args (@t18)) % 0.94/1.16 (step @p73 :rule cong :premises (@p72 @p63) :args ((= @t18 @t43))) % 0.94/1.16 (step @p74 :rule symm :premises (@p73)) % 0.94/1.16 (step @p75 :rule eq_resolve :premises (@p72 @p74)) % 0.94/1.16 (step @p76 :rule cong :premises (@p75) :args (@t19)) % 0.94/1.16 (step @p77 :rule ho_cong :premises (@p43 @p76)) % 0.94/1.16 (step @p78 :rule trans :premises (@p77 @p71)) % 0.94/1.16 (step @p79 :rule cong :premises (@p78) :args (@t46)) % 0.94/1.16 (step @p80 :rule nary_cong :premises (@p79 @p61 @p55) :args (@t47)) % 0.94/1.16 (step @p81 :rule cong :premises (@p80) :args ((forall @t21 @t47))) % 0.94/1.16 (step @p82 :rule aci_norm :args ((= (or @t46 (or @t42 @t13)) @t47))) % 0.94/1.16 (step @p83 :rule bool-impl-elim :args (@t16 @t13)) % 0.94/1.16 (step @p84 :rule refl :args (@t46)) % 0.94/1.16 (step @p85 :rule nary_cong :premises (@p84 @p83) :args ((or @t46 @t17))) % 0.94/1.16 (step @p86 :rule trans :premises (@p85 @p82)) % 0.94/1.16 (step @p87 :rule bool-impl-elim :args (@t20 @t17)) % 0.94/1.16 (step @p88 :rule trans :premises (@p87 @p86)) % 0.94/1.16 (step @p89 :rule cong :premises (@p88) :args (@t22)) % 0.94/1.16 (step @p90 :rule trans :premises (@p89 @p81)) % 0.94/1.16 (step @p91 :rule eq_resolve :premises (@p3 @p90)) % 0.94/1.16 (step @p92 :rule lambda-elim :args ((= @t48 @t27))) % 0.94/1.16 (step @p93 :rule cong :premises (@p92) :args (@t49)) % 0.94/1.16 (step @p94 :rule refl :args (@t51)) % 0.94/1.16 (step @p95 :rule lambda-elim :args ((= @t52 @t3))) % 0.94/1.16 (step @p96 :rule cong :premises (@p95) :args (@t53)) % 0.94/1.16 (step @p97 :rule cong :premises (@p96) :args (@t54)) % 0.94/1.16 (step @p98 :rule nary_cong :premises (@p97 @p94 @p93) :args (@t55)) % 0.94/1.16 (step @p99 :rule refl :args (@t56)) % 0.94/1.16 (step @p100 :rule cong :premises (@p99 @p98) :args ((=> @t56 @t55))) % 0.94/1.16 (assume-push @p256 @t56) % 0.94/1.16 (step @p102 :rule instantiate :premises (@p91) :args ((@list tptp.z tptp.y tptp.x))) % 0.94/1.16 (step-pop @p257 :rule scope :premises (@p102)) % 0.94/1.16 (step @p103 :rule process_scope :premises (@p257) :args (@t55)) % 0.94/1.16 (step @p105 :rule eq_resolve :premises (@p103 @p100)) % 0.94/1.16 (step @p106 :rule implies_elim :premises (@p105)) % 0.94/1.16 (step @p107 :rule chain_m_resolution :premises (@p106 @p91) :args (@t60 @t61 (@list @t56))) % 0.94/1.16 (step @p108 :rule refl :args (@t63)) % 0.94/1.16 (step @p109 :rule refl :args (@t64)) % 0.94/1.16 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t64 @t63))) % 0.94/1.16 (step @p111 :rule symm :premises (@p110)) % 0.94/1.16 (step @p112 :rule eq_resolve :premises (@p109 @p111)) % 0.94/1.16 (step @p113 :rule eq-refl :args (@t6)) % 0.94/1.16 (step @p114 :rule skolem_intro :args (@t62)) % 0.94/1.16 (step @p115 :rule refl :args (@t6)) % 0.94/1.16 (step @p116 :rule cong :premises (@p115 @p114) :args ((= @t6 @t62))) % 0.94/1.16 (step @p117 :rule trans :premises (@p116 @p113)) % 0.94/1.16 (step @p118 :rule true_elim :premises (@p117)) % 0.94/1.16 (step @p119 :rule refl :args (tptp.some)) % 0.94/1.16 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.94/1.16 (step @p121 :rule trans :premises (@p120 @p112)) % 0.94/1.16 (step @p122 :rule eq_resolve :premises (@p2 @p121)) % 0.94/1.16 (step @p123 :rule true_intro :premises (@p122)) % 0.94/1.16 (step @p124 :rule eq-symm :args (@t65 @t66)) % 0.94/1.16 (step @p125 :rule cong :premises (@p124) :args ((forall @t5 (= @t65 @t66)))) % 0.94/1.16 (step @p126 :rule refl :args (@t66)) % 0.94/1.16 (step @p127 :rule refl :args (@t65)) % 0.94/1.16 (step @p128 :rule refl :args (@t4)) % 0.94/1.16 (step @p129 :rule cong :premises (@p128 @p127) :args ((= @t4 @t65))) % 0.94/1.16 (step @p130 :rule symm :premises (@p129)) % 0.94/1.16 (step @p131 :rule eq_resolve :premises (@p128 @p130)) % 0.94/1.16 (step @p132 :rule cong :premises (@p131 @p126) :args (@t67)) % 0.94/1.16 (step @p133 :rule cong :premises (@p132) :args ((forall @t5 @t67))) % 0.94/1.16 (step @p134 :rule trans :premises (@p133 @p125)) % 0.94/1.16 (step @p135 :rule eq-symm :args (@t66 @t4)) % 0.94/1.16 (step @p136 :rule beta-reduce :args ((= @t68 @t4))) % 0.94/1.16 (step @p137 :rule refl :args (@t66)) % 0.94/1.16 (step @p138 :rule cong :premises (@p137 @p136) :args (@t69)) % 0.94/1.16 (step @p139 :rule trans :premises (@p138 @p135)) % 0.94/1.16 (step @p140 :rule cong :premises (@p139) :args (@t70)) % 0.94/1.16 (step @p141 :rule trans :premises (@p140 @p134)) % 0.94/1.16 (step @p142 :rule eq-refl :args (@t68)) % 0.94/1.16 (step @p143 :rule cong :premises (@p142) :args ((forall @t5 (= @t68 @t68)))) % 0.94/1.16 (step @p144 :rule trans :premises (@p143 @p25)) % 0.94/1.16 (step @p145 :rule refl :args (@t68)) % 0.94/1.16 (step @p146 :rule ho_cong :premises (@p114 @p30)) % 0.94/1.16 (step @p147 :rule cong :premises (@p146 @p145) :args (@t69)) % 0.94/1.16 (step @p148 :rule cong :premises (@p147) :args (@t70)) % 0.94/1.16 (step @p149 :rule trans :premises (@p148 @p144)) % 0.94/1.16 (step @p150 :rule true_elim :premises (@p149)) % 0.94/1.16 (step @p151 :rule eq_resolve :premises (@p150 @p141)) % 0.94/1.16 (step @p152 :rule eq-symm :args (@t72 @t73)) % 0.94/1.16 (step @p153 :rule refl :args (@t74)) % 0.94/1.16 (step @p154 :rule cong :premises (@p153 @p152) :args ((=> @t74 @t75))) % 0.94/1.16 (assume-push @p258 @t74) % 0.94/1.16 (step @p156 :rule instantiate :premises (@p151) :args ((@list @t71))) % 0.94/1.16 (step-pop @p259 :rule scope :premises (@p156)) % 0.94/1.16 (step @p157 :rule process_scope :premises (@p259) :args (@t75)) % 0.94/1.16 (step @p159 :rule eq_resolve :premises (@p157 @p154)) % 0.94/1.16 (step @p160 :rule implies_elim :premises (@p159)) % 0.94/1.16 (step @p161 :rule chain_m_resolution :premises (@p160 @p151) :args (@t76 @t61 (@list @t74))) % 0.94/1.16 ; WARNING: add trust step for TRUST % 0.94/1.16 ; trust TRUST THEORY_LEMMA % 0.94/1.16 (step @p162 :rule trust :premises () :args ((or @t78 @t77))) % 0.94/1.16 (step @p163 :rule reordering :premises (@p162) :args ((or @t77 @t78))) % 0.94/1.16 (step @p164 :rule chain_m_resolution :premises (@p163 @p161) :args (@t78 @t61 (@list @t76))) % 0.94/1.16 (step @p165 :rule cong :premises (@p164) :args (@t58)) % 0.94/1.16 (step @p166 :rule trans :premises (@p165 @p123)) % 0.94/1.16 (step @p167 :rule true_elim :premises (@p166)) % 0.94/1.16 (step @p168 :rule refl :args (@t79)) % 0.94/1.16 (step @p169 :rule refl :args (@t23)) % 0.94/1.16 (step @p170 :rule cong :premises (@p169 @p168) :args ((= @t23 @t79))) % 0.94/1.16 (step @p171 :rule symm :premises (@p170)) % 0.94/1.16 (step @p172 :rule eq_resolve :premises (@p169 @p171)) % 0.94/1.16 (step @p173 :rule refl :args (@t80)) % 0.94/1.16 (step @p174 :rule refl :args (@t24)) % 0.94/1.16 (step @p175 :rule cong :premises (@p174 @p173) :args ((= @t24 @t80))) % 0.94/1.16 (step @p176 :rule symm :premises (@p175)) % 0.94/1.16 (step @p177 :rule eq_resolve :premises (@p174 @p176)) % 0.94/1.16 (step @p178 :rule cong :premises (@p177) :args (@t81)) % 0.94/1.16 (step @p179 :rule nary_cong :premises (@p178 @p172) :args (@t82)) % 0.94/1.16 (step @p180 :rule cong :premises (@p179) :args ((forall @t25 @t82))) % 0.94/1.16 (step @p181 :rule bool-impl-elim :args (@t24 @t23)) % 0.94/1.16 (step @p182 :rule cong :premises (@p181) :args (@t26)) % 0.94/1.16 (step @p183 :rule trans :premises (@p182 @p180)) % 0.94/1.16 (step @p184 :rule eq_resolve :premises (@p4 @p183)) % 0.94/1.16 (step @p185 :rule instantiate :premises (@p184) :args ((@list tptp.x tptp.y))) % 0.94/1.16 (step @p186 :rule refl :args (@t83)) % 0.94/1.16 (step @p187 :rule refl :args (@t1)) % 0.94/1.16 (step @p188 :rule cong :premises (@p187 @p186) :args ((= @t1 @t83))) % 0.94/1.16 (step @p189 :rule symm :premises (@p188)) % 0.94/1.16 (step @p190 :rule eq_resolve :premises (@p187 @p189)) % 0.94/1.16 (step @p191 :rule eq_resolve :premises (@p1 @p190)) % 0.94/1.16 (step @p192 :rule cnf_or_pos :args (@t85)) % 0.94/1.16 (step @p193 :rule reordering :premises (@p192) :args ((or @t84 @t50 (not @t85)))) % 0.94/1.16 (step @p194 :rule chain_m_resolution :premises (@p193 @p191 @p185) :args (@t50 (@list false false) (@list @t83 @t85))) % 0.94/1.16 (step @p195 :rule cnf_or_pos :args (@t60)) % 0.94/1.16 (step @p196 :rule reordering :premises (@p195) :args ((or @t51 @t57 @t59 (not @t60)))) % 0.94/1.16 (step @p197 :rule chain_m_resolution :premises (@p196 @p194 @p167 @p107) :args (@t57 (@list false false false) (@list @t50 @t58 @t60))) % 0.94/1.16 (step @p198 :rule refl :args (@t86)) % 0.94/1.16 (step @p199 :rule refl :args (@t87)) % 0.94/1.16 (step @p200 :rule cong :premises (@p199 @p198) :args ((= @t87 @t86))) % 0.94/1.16 (step @p201 :rule symm :premises (@p200)) % 0.94/1.16 (step @p202 :rule eq_resolve :premises (@p199 @p201)) % 0.94/1.16 (step @p203 :rule eq-refl :args (@t29)) % 0.94/1.16 (step @p204 :rule refl :args (@t29)) % 0.94/1.16 (step @p205 :rule cong :premises (@p204 @p31) :args ((= @t29 @t32))) % 0.94/1.16 (step @p206 :rule trans :premises (@p205 @p203)) % 0.94/1.16 (step @p207 :rule true_elim :premises (@p206)) % 0.94/1.16 (step @p208 :rule ho_cong :premises (@p119 @p207)) % 0.94/1.16 (step @p209 :rule trans :premises (@p208 @p202)) % 0.94/1.16 (step @p210 :rule cong :premises (@p209) :args (@t30)) % 0.94/1.16 (step @p211 :rule eq_resolve :premises (@p5 @p210)) % 0.94/1.16 (step @p212 :rule refl :args (@t89)) % 0.94/1.16 (step @p213 :rule refl :args (@t90)) % 0.94/1.16 (step @p214 :rule bool-double-not-elim :args (@t86)) % 0.94/1.16 (step @p215 :rule nary_cong :premises (@p214 @p213 @p212) :args ((or (not @t91) @t90 @t89))) % 0.94/1.16 (assume-push @p260 @t57) % 0.94/1.16 (assume-push @p261 @t88) % 0.94/1.16 (assume-push @p262 @t91) % 0.94/1.16 (step @p219 :rule evaluate :args ((= false true))) % 0.94/1.16 (step @p220 :rule true_intro :premises (@p197)) % 0.94/1.16 (step @p221 :rule symm :premises (@p261)) % 0.94/1.16 (step @p222 :rule cong :premises (@p221) :args (@t86)) % 0.94/1.16 (step @p223 :rule false_intro :premises (@p211)) % 0.94/1.16 (step @p224 :rule symm :premises (@p223)) % 0.94/1.16 (step @p225 :rule trans :premises (@p224 @p222 @p220)) % 0.94/1.16 (step @p226 false :rule eq_resolve :premises (@p225 @p219)) % 0.94/1.16 (step-pop @p263 :rule scope :premises (@p226)) % 0.94/1.16 (step-pop @p264 :rule scope :premises (@p263)) % 0.94/1.16 (step-pop @p265 :rule scope :premises (@p264)) % 0.94/1.16 (step @p227 :rule process_scope :premises (@p265) :args (false)) % 0.94/1.16 (assume-push @p266 @t91) % 0.94/1.16 (assume-push @p267 @t57) % 0.94/1.16 (assume-push @p268 @t88) % 0.94/1.16 (step @p234 :rule and_intro :premises (@p197 @p268 @p211)) % 0.94/1.16 (step-pop @p269 :rule scope :premises (@p234)) % 0.94/1.16 (step-pop @p270 :rule scope :premises (@p269)) % 0.94/1.16 (step-pop @p271 :rule scope :premises (@p270)) % 0.94/1.16 (step @p235 :rule process_scope :premises (@p271) :args (@t92)) % 0.94/1.16 (step @p239 :rule implies_elim :premises (@p235)) % 0.94/1.16 (step @p240 :rule resolution :premises (@p239 @p227) :args (true @t92)) % 0.94/1.16 (step @p241 :rule not_and :premises (@p240)) % 0.94/1.16 (step @p242 :rule eq_resolve :premises (@p241 @p215)) % 0.94/1.16 (step @p243 :rule chain_m_resolution :premises (@p242 @p211 @p197) :args (@t89 @t93 (@list @t86 @t57))) % 0.94/1.16 ; trust TRUST THEORY_LEMMA % 0.94/1.16 (step @p244 :rule trust :premises () :args ((or @t88 @t98))) % 0.94/1.16 (step @p245 :rule chain_m_resolution :premises (@p244 @p243) :args (@t98 (@list true) (@list @t88))) % 0.94/1.16 (step @p246 :rule eq-symm :args (@t95 @t96)) % 0.94/1.16 (step @p247 :rule refl :args (@t99)) % 0.94/1.16 (step @p248 :rule cong :premises (@p247 @p246) :args ((=> @t99 @t100))) % 0.94/1.16 (assume-push @p272 @t99) % 0.94/1.16 (step @p250 :rule instantiate :premises (@p37) :args ((@list @t94))) % 0.94/1.16 (step-pop @p273 :rule scope :premises (@p250)) % 0.94/1.16 (step @p251 :rule process_scope :premises (@p273) :args (@t100)) % 0.94/1.16 (step @p253 :rule eq_resolve :premises (@p251 @p248)) % 0.94/1.16 (step @p254 :rule implies_elim :premises (@p253)) % 0.94/1.16 (step @p255 false :rule chain_m_resolution :premises (@p254 @p245 @p37) :args (false @t93 (@list @t97 @t99))) % 0.94/1.16 ) % 0.94/1.16 % SZS output end Proof % 0.94/1.16 % cvc5 exiting %------------------------------------------------------------------------------