%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 09:07:23 AM UTC 2026 % Result : Theorem 0.62s 0.81s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n003.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:09:59 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.62/0.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.62/0.81 % SZS status Theorem % 0.62/0.81 % SZS output start Proof % 0.62/0.81 ( % 0.62/0.81 (declare-sort $$unsorted 0) % 0.62/0.81 (declare-const tptp.x (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.double (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.cons (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.suc (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.head (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.half (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.tail (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.evenNat (-> $$unsorted Bool)) % 0.62/0.81 (declare-const tptp.rd (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.append (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.nil $$unsorted) % 0.62/0.81 (declare-const tptp.proj1Suc (-> $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.zero $$unsorted) % 0.62/0.81 (declare-const tptp.o $$unsorted) % 0.62/0.81 (declare-const tptp.addNat (-> $$unsorted $$unsorted $$unsorted)) % 0.62/0.81 (declare-const tptp.i $$unsorted) % 0.62/0.81 (declare-const tptp.shw (-> $$unsorted $$unsorted)) % 0.62/0.81 (define @t1 () (@var "X" $$unsorted)) % 0.62/0.81 (define @t2 () (@var "X2" $$unsorted)) % 0.62/0.81 (define @t3 () (tptp.cons @t1 @t2)) % 0.62/0.81 (define @t4 () (@list @t1 @t2)) % 0.62/0.81 (define @t5 () (tptp.suc @t1)) % 0.62/0.81 (define @t6 () (tptp.proj1Suc @t5)) % 0.62/0.81 (define @t7 () (@list @t1)) % 0.62/0.81 (define @t8 () (forall @t7 (= @t6 @t1))) % 0.62/0.81 (define @t9 () (tptp.half tptp.zero)) % 0.62/0.81 (define @t10 () (tptp.suc tptp.zero)) % 0.62/0.81 (define @t11 () (tptp.half @t10)) % 0.62/0.81 (define @t12 () (@var "N" $$unsorted)) % 0.62/0.81 (define @t13 () (tptp.suc @t12)) % 0.62/0.81 (define @t14 () (@list @t12)) % 0.62/0.81 (define @t15 () (tptp.evenNat tptp.zero)) % 0.62/0.81 (define @t16 () (forall @t14 (= (tptp.evenNat @t13) (not (tptp.evenNat @t12))))) % 0.62/0.81 (define @t17 () (tptp.shw tptp.zero)) % 0.62/0.81 (define @t18 () (@var "Y" $$unsorted)) % 0.62/0.81 (define @t19 () (tptp.suc @t18)) % 0.62/0.81 (define @t20 () (tptp.shw (tptp.half @t19))) % 0.62/0.81 (define @t21 () (tptp.shw @t19)) % 0.62/0.81 (define @t22 () (= @t21 (tptp.cons tptp.o @t20))) % 0.62/0.81 (define @t23 () (tptp.evenNat @t19)) % 0.62/0.81 (define @t24 () (@list @t18)) % 0.62/0.81 (define @t25 () (forall @t24 (=> @t23 @t22))) % 0.62/0.81 (define @t26 () (= @t21 (tptp.cons tptp.i @t20))) % 0.62/0.81 (define @t27 () (not @t23)) % 0.62/0.81 (define @t28 () (forall @t24 (=> @t27 @t26))) % 0.62/0.81 (define @t29 () (tptp.append tptp.nil @t18)) % 0.62/0.81 (define @t30 () (forall @t24 (= @t29 @t18))) % 0.62/0.81 (define @t31 () (@var "Xs" $$unsorted)) % 0.62/0.81 (define @t32 () (@var "Z" $$unsorted)) % 0.62/0.81 (define @t33 () (tptp.addNat tptp.zero @t18)) % 0.62/0.81 (define @t34 () (forall @t24 (= @t33 @t18))) % 0.62/0.81 (define @t35 () (tptp.double (tptp.rd @t31))) % 0.62/0.81 (define @t36 () (@list @t31)) % 0.62/0.81 (define @t37 () (tptp.rd (tptp.cons tptp.o @t31))) % 0.62/0.81 (define @t38 () (forall @t36 (= @t37 @t35))) % 0.62/0.81 (define @t39 () (tptp.x @t1 @t18)) % 0.62/0.81 (define @t40 () (@list @t1 @t18)) % 0.62/0.81 (define @t41 () (= @t39 (tptp.x @t18 @t1))) % 0.62/0.81 (define @t42 () (not @t41)) % 0.62/0.81 (define @t43 () (exists @t40 @t42)) % 0.62/0.81 (define @t44 () (not @t43)) % 0.62/0.81 (define @t45 () (tptp.suc @t10)) % 0.62/0.81 (define @t46 () (@list @t45)) % 0.62/0.81 (define @t47 () (tptp.evenNat @t45)) % 0.62/0.81 (define @t48 () (tptp.evenNat @t10)) % 0.62/0.81 (define @t49 () (not @t48)) % 0.62/0.81 (define @t50 () (= @t47 @t49)) % 0.62/0.81 (define @t51 () (@list @t10)) % 0.62/0.81 (define @t52 () (= @t49 @t47)) % 0.62/0.81 (define @t53 () (@list false)) % 0.62/0.81 (define @t54 () (@list @t16)) % 0.62/0.81 (define @t55 () (not @t15)) % 0.62/0.81 (define @t56 () (= @t48 @t55)) % 0.62/0.81 (define @t57 () (@list tptp.zero)) % 0.62/0.81 (define @t58 () (= @t55 @t48)) % 0.62/0.81 (define @t59 () (@list false false)) % 0.62/0.81 (define @t60 () (not @t52)) % 0.62/0.81 (define @t61 () (@list true false)) % 0.62/0.81 (define @t62 () (not @t47)) % 0.62/0.81 (define @t63 () (tptp.suc @t45)) % 0.62/0.81 (define @t64 () (tptp.evenNat @t63)) % 0.62/0.81 (define @t65 () (= @t64 @t62)) % 0.62/0.81 (define @t66 () (not @t64)) % 0.62/0.81 (define @t67 () (tptp.shw @t11)) % 0.62/0.81 (define @t68 () (tptp.rd @t67)) % 0.62/0.81 (define @t69 () (@list @t68)) % 0.62/0.81 (define @t70 () (tptp.suc (tptp.double @t68))) % 0.62/0.81 (define @t71 () (tptp.cons tptp.i @t67)) % 0.62/0.81 (define @t72 () (tptp.shw @t10)) % 0.62/0.81 (define @t73 () (= @t72 @t71)) % 0.62/0.81 (define @t74 () (or @t48 @t73)) % 0.62/0.81 (define @t75 () (tptp.shw (tptp.half @t45))) % 0.62/0.81 (define @t76 () (tptp.rd @t75)) % 0.62/0.81 (define @t77 () (@list @t76)) % 0.62/0.81 (define @t78 () (tptp.addNat tptp.zero @t76)) % 0.62/0.81 (define @t79 () (tptp.suc @t78)) % 0.62/0.81 (define @t80 () (tptp.double @t76)) % 0.62/0.81 (define @t81 () (tptp.suc @t80)) % 0.62/0.81 (define @t82 () (@list @t75)) % 0.62/0.81 (define @t83 () (tptp.half @t63)) % 0.62/0.81 (define @t84 () (tptp.shw @t83)) % 0.62/0.81 (define @t85 () (tptp.cons tptp.i @t84)) % 0.62/0.81 (define @t86 () (= (tptp.shw @t63) @t85)) % 0.62/0.81 (define @t87 () (or @t64 @t86)) % 0.62/0.81 (define @t88 () (tptp.suc (tptp.suc @t63))) % 0.62/0.81 (define @t89 () (tptp.half @t88)) % 0.62/0.81 (define @t90 () (tptp.shw (tptp.half (tptp.suc (tptp.suc @t88))))) % 0.62/0.81 (define @t91 () (tptp.rd @t90)) % 0.62/0.81 (define @t92 () (@list @t91)) % 0.62/0.81 (define @t93 () (tptp.addNat tptp.zero @t91)) % 0.62/0.81 (define @t94 () (tptp.shw @t70)) % 0.62/0.81 (define @t95 () (tptp.append @t67 @t94)) % 0.62/0.81 (define @t96 () (tptp.append @t94 @t94)) % 0.62/0.81 (define @t97 () (tptp.cons tptp.o @t75)) % 0.62/0.81 (define @t98 () (tptp.shw @t45)) % 0.62/0.81 (define @t99 () (= @t98 @t97)) % 0.62/0.81 (define @t100 () (or @t62 @t99)) % 0.62/0.81 (define @t101 () (tptp.append @t98 @t72)) % 0.62/0.81 (define @t102 () (forall @t40 (not @t42))) % 0.62/0.81 (define @t103 () (not @t102)) % 0.62/0.81 (define @t104 () (@list @t10 @t45)) % 0.62/0.81 (define @t105 () (tptp.shw @t89)) % 0.62/0.81 (define @t106 () (tptp.cons tptp.i @t105)) % 0.62/0.81 (define @t107 () (tptp.rd @t105)) % 0.62/0.81 (define @t108 () (tptp.double @t107)) % 0.62/0.81 (define @t109 () (@list @t107)) % 0.62/0.81 (define @t110 () (tptp.addNat @t78 @t107)) % 0.62/0.81 (assume @p1 (forall @t4 (= (tptp.head @t3) @t1))) % 0.62/0.81 (assume @p2 (forall @t4 (= (tptp.tail @t3) @t2))) % 0.62/0.81 (assume @p3 (forall @t4 (not (= tptp.nil @t3)))) % 0.62/0.81 (assume @p4 @t8) % 0.62/0.81 (assume @p5 (forall @t7 (not (= tptp.zero @t5)))) % 0.62/0.81 (assume @p6 (not (= tptp.i tptp.o))) % 0.62/0.81 (assume @p7 (= @t9 tptp.zero)) % 0.62/0.81 (assume @p8 (= @t11 tptp.zero)) % 0.62/0.81 (assume @p9 (forall @t14 (= (tptp.half (tptp.suc @t13)) (tptp.suc (tptp.half @t12))))) % 0.62/0.81 (assume @p10 @t15) % 0.62/0.81 (assume @p11 @t16) % 0.62/0.81 (assume @p12 (= @t17 tptp.nil)) % 0.62/0.81 (assume @p13 @t25) % 0.62/0.81 (assume @p14 @t28) % 0.62/0.81 (assume @p15 @t30) % 0.62/0.81 (assume @p16 (forall (@list @t18 @t32 @t31) (= (tptp.append (tptp.cons @t32 @t31) @t18) (tptp.cons @t32 (tptp.append @t31 @t18))))) % 0.62/0.81 (assume @p17 @t34) % 0.62/0.81 (assume @p18 (forall (@list @t18 @t32) (= (tptp.addNat (tptp.suc @t32) @t18) (tptp.suc (tptp.addNat @t32 @t18))))) % 0.62/0.81 (assume @p19 (forall @t7 (= (tptp.double @t1) (tptp.addNat @t1 @t1)))) % 0.62/0.81 (assume @p20 (= (tptp.rd tptp.nil) tptp.zero)) % 0.62/0.81 (assume @p21 (forall @t36 (= (tptp.rd (tptp.cons tptp.i @t31)) (tptp.suc @t35)))) % 0.62/0.81 (assume @p22 @t38) % 0.62/0.81 (assume @p23 (forall @t40 (= @t39 (tptp.rd (tptp.append (tptp.shw @t1) (tptp.shw @t18)))))) % 0.62/0.81 (assume @p24 @t44) % 0.62/0.81 (assume @p25 true) % 0.62/0.81 (step @p26 :rule evaluate :args ((= true false))) % 0.62/0.81 (step @p27 :rule instantiate :premises (@p11) :args (@t46)) % 0.62/0.81 (step @p28 :rule eq-symm :args (@t47 @t49)) % 0.62/0.81 (step @p29 :rule refl :args (@t16)) % 0.62/0.81 (step @p30 :rule cong :premises (@p29 @p28) :args ((=> @t16 @t50))) % 0.62/0.81 (assume-push @p263 @t16) % 0.62/0.81 (step @p32 :rule instantiate :premises (@p11) :args (@t51)) % 0.62/0.81 (step-pop @p264 :rule scope :premises (@p32)) % 0.62/0.81 (step @p33 :rule process_scope :premises (@p264) :args (@t50)) % 0.62/0.81 (step @p35 :rule eq_resolve :premises (@p33 @p30)) % 0.62/0.81 (step @p36 :rule implies_elim :premises (@p35)) % 0.62/0.81 (step @p37 :rule chain_m_resolution :premises (@p36 @p11) :args (@t52 @t53 @t54)) % 0.62/0.81 (step @p38 :rule eq-symm :args (@t48 @t55)) % 0.62/0.81 (step @p39 :rule cong :premises (@p29 @p38) :args ((=> @t16 @t56))) % 0.62/0.81 (assume-push @p265 @t16) % 0.62/0.81 (step @p41 :rule instantiate :premises (@p11) :args (@t57)) % 0.62/0.81 (step-pop @p266 :rule scope :premises (@p41)) % 0.62/0.81 (step @p42 :rule process_scope :premises (@p266) :args (@t56)) % 0.62/0.81 (step @p44 :rule eq_resolve :premises (@p42 @p39)) % 0.62/0.81 (step @p45 :rule implies_elim :premises (@p44)) % 0.62/0.81 (step @p46 :rule chain_m_resolution :premises (@p45 @p11) :args (@t58 @t53 @t54)) % 0.62/0.81 (step @p47 :rule cnf_equiv_pos2 :args (@t58)) % 0.62/0.81 (step @p48 :rule reordering :premises (@p47) :args ((or @t55 @t49 (not @t58)))) % 0.62/0.81 (step @p49 :rule chain_m_resolution :premises (@p48 @p10 @p46) :args (@t49 @t59 (@list @t15 @t58))) % 0.62/0.81 (step @p50 :rule refl :args (@t47)) % 0.62/0.81 (step @p51 :rule bool-double-not-elim :args (@t48)) % 0.62/0.81 (step @p52 :rule refl :args (@t60)) % 0.62/0.81 (step @p53 :rule nary_cong :premises (@p52 @p51 @p50) :args ((or @t60 (not @t49) @t47))) % 0.62/0.81 (step @p54 :rule cnf_equiv_pos1 :args (@t52)) % 0.62/0.81 (step @p55 :rule eq_resolve :premises (@p54 @p53)) % 0.62/0.81 (step @p56 :rule reordering :premises (@p55) :args ((or @t48 @t47 @t60))) % 0.62/0.81 (step @p57 :rule chain_m_resolution :premises (@p56 @p49 @p37) :args (@t47 @t61 (@list @t48 @t52))) % 0.62/0.81 (step @p58 :rule cnf_equiv_pos1 :args (@t65)) % 0.62/0.81 (step @p59 :rule reordering :premises (@p58) :args ((or @t62 @t66 (not @t65)))) % 0.62/0.81 (step @p60 :rule chain_m_resolution :premises (@p59 @p57 @p27) :args (@t66 @t59 (@list @t47 @t65))) % 0.62/0.81 (step @p61 :rule false_intro :premises (@p60)) % 0.62/0.81 (step @p62 :rule cong :premises (@p8) :args (@t67)) % 0.62/0.81 (step @p63 :rule trans :premises (@p62 @p12)) % 0.62/0.81 (step @p64 :rule cong :premises (@p63) :args (@t68)) % 0.62/0.81 (step @p65 :rule eq-symm :args (@t33 @t18)) % 0.62/0.81 (step @p66 :rule cong :premises (@p65) :args (@t34)) % 0.62/0.81 (step @p67 :rule eq_resolve :premises (@p17 @p66)) % 0.62/0.81 (step @p68 :rule instantiate :premises (@p67) :args (@t69)) % 0.62/0.81 (step @p69 :rule symm :premises (@p68)) % 0.62/0.81 (step @p70 :rule refl :args (@t68)) % 0.62/0.81 (step @p71 :rule trans :premises (@p64 @p20)) % 0.62/0.81 (step @p72 :rule cong :premises (@p71 @p70) :args ((tptp.addNat @t68 @t68))) % 0.62/0.81 (step @p73 :rule instantiate :premises (@p19) :args (@t69)) % 0.62/0.81 (step @p74 :rule trans :premises (@p73 @p72 @p69 @p64 @p20)) % 0.62/0.81 (step @p75 :rule cong :premises (@p74) :args (@t70)) % 0.62/0.81 (step @p76 :rule instantiate :premises (@p21) :args ((@list @t67))) % 0.62/0.81 (step @p77 :rule refl :args (@t26)) % 0.62/0.81 (step @p78 :rule bool-double-not-elim :args (@t23)) % 0.62/0.81 (step @p79 :rule nary_cong :premises (@p78 @p77) :args ((or (not @t27) @t26))) % 0.62/0.81 (step @p80 :rule bool-impl-elim :args (@t27 @t26)) % 0.62/0.81 (step @p81 :rule trans :premises (@p80 @p79)) % 0.62/0.81 (step @p82 :rule cong :premises (@p81) :args (@t28)) % 0.62/0.81 (step @p83 :rule eq_resolve :premises (@p14 @p82)) % 0.62/0.81 (step @p84 :rule instantiate :premises (@p83) :args (@t57)) % 0.62/0.81 (step @p85 :rule cnf_or_pos :args (@t74)) % 0.62/0.81 (step @p86 :rule reordering :premises (@p85) :args ((or @t48 @t73 (not @t74)))) % 0.62/0.81 (step @p87 :rule chain_m_resolution :premises (@p86 @p49 @p84) :args (@t73 @t61 (@list @t48 @t74))) % 0.62/0.81 (step @p88 :rule cong :premises (@p7) :args ((tptp.suc @t9))) % 0.62/0.81 (step @p89 :rule instantiate :premises (@p9) :args (@t57)) % 0.62/0.81 (step @p90 :rule trans :premises (@p89 @p88)) % 0.62/0.81 (step @p91 :rule cong :premises (@p90) :args (@t75)) % 0.62/0.81 (step @p92 :rule trans :premises (@p91 @p87)) % 0.62/0.81 (step @p93 :rule cong :premises (@p92) :args (@t76)) % 0.62/0.81 (step @p94 :rule instantiate :premises (@p67) :args (@t77)) % 0.62/0.81 (step @p95 :rule symm :premises (@p94)) % 0.62/0.81 (step @p96 :rule trans :premises (@p95 @p93 @p76 @p75)) % 0.62/0.81 (step @p97 :rule cong :premises (@p96) :args (@t79)) % 0.62/0.81 (step @p98 :rule instantiate :premises (@p18) :args ((@list @t76 tptp.zero))) % 0.62/0.81 (step @p99 :rule refl :args (@t76)) % 0.62/0.81 (step @p100 :rule cong :premises (@p71) :args ((tptp.suc @t68))) % 0.62/0.81 (step @p101 :rule symm :premises (@p100)) % 0.62/0.81 (step @p102 :rule trans :premises (@p93 @p76 @p75 @p101)) % 0.62/0.81 (step @p103 :rule trans :premises (@p102 @p100)) % 0.62/0.81 (step @p104 :rule cong :premises (@p103 @p99) :args ((tptp.addNat @t76 @t76))) % 0.62/0.81 (step @p105 :rule instantiate :premises (@p19) :args (@t77)) % 0.62/0.81 (step @p106 :rule trans :premises (@p105 @p104 @p98 @p97)) % 0.62/0.81 (step @p107 :rule cong :premises (@p106) :args (@t81)) % 0.62/0.81 (step @p108 :rule cong :premises (@p107) :args ((tptp.evenNat @t81))) % 0.62/0.81 (step @p109 :rule instantiate :premises (@p21) :args (@t82)) % 0.62/0.81 (step @p110 :rule symm :premises (@p91)) % 0.62/0.81 (step @p111 :rule cong :premises (@p8) :args ((tptp.suc @t11))) % 0.62/0.81 (step @p112 :rule instantiate :premises (@p9) :args (@t51)) % 0.62/0.81 (step @p113 :rule trans :premises (@p112 @p111)) % 0.62/0.81 (step @p114 :rule cong :premises (@p113) :args (@t84)) % 0.62/0.81 (step @p115 :rule trans :premises (@p114 @p110)) % 0.62/0.81 (step @p116 :rule refl :args (tptp.i)) % 0.62/0.81 (step @p117 :rule cong :premises (@p116 @p115) :args (@t85)) % 0.62/0.81 (step @p118 :rule instantiate :premises (@p83) :args (@t46)) % 0.62/0.81 (step @p119 :rule cnf_or_pos :args (@t87)) % 0.62/0.81 (step @p120 :rule reordering :premises (@p119) :args ((or @t64 @t86 (not @t87)))) % 0.62/0.81 (step @p121 :rule chain_m_resolution :premises (@p120 @p60 @p118) :args (@t86 @t61 (@list @t64 @t87))) % 0.62/0.81 (step @p122 :rule cong :premises (@p113) :args ((tptp.suc @t83))) % 0.62/0.81 (step @p123 :rule instantiate :premises (@p9) :args ((@list @t63))) % 0.62/0.81 (step @p124 :rule trans :premises (@p123 @p122)) % 0.62/0.81 (step @p125 :rule cong :premises (@p124) :args ((tptp.suc @t89))) % 0.62/0.81 (step @p126 :rule instantiate :premises (@p9) :args ((@list @t88))) % 0.62/0.81 (step @p127 :rule trans :premises (@p126 @p125)) % 0.62/0.81 (step @p128 :rule cong :premises (@p127) :args (@t90)) % 0.62/0.81 (step @p129 :rule trans :premises (@p128 @p121 @p117)) % 0.62/0.81 (step @p130 :rule cong :premises (@p129) :args (@t91)) % 0.62/0.81 (step @p131 :rule instantiate :premises (@p67) :args (@t92)) % 0.62/0.81 (step @p132 :rule symm :premises (@p131)) % 0.62/0.81 (step @p133 :rule trans :premises (@p132 @p130 @p109)) % 0.62/0.81 (step @p134 :rule cong :premises (@p133) :args ((tptp.evenNat @t93))) % 0.62/0.81 (step @p135 :rule eq-symm :args (@t6 @t1)) % 0.62/0.81 (step @p136 :rule cong :premises (@p135) :args (@t8)) % 0.62/0.81 (step @p137 :rule eq_resolve :premises (@p4 @p136)) % 0.62/0.81 (step @p138 :rule instantiate :premises (@p137) :args ((@list @t93))) % 0.62/0.81 (step @p139 :rule symm :premises (@p138)) % 0.62/0.81 (step @p140 :rule instantiate :premises (@p18) :args ((@list @t91 tptp.zero))) % 0.62/0.81 (step @p141 :rule instantiate :premises (@p137) :args ((@list (tptp.addNat @t10 @t91)))) % 0.62/0.81 (step @p142 :rule symm :premises (@p141)) % 0.62/0.81 (step @p143 :rule instantiate :premises (@p18) :args ((@list @t91 @t10))) % 0.62/0.81 (step @p144 :rule instantiate :premises (@p137) :args ((@list (tptp.addNat @t45 @t91)))) % 0.62/0.81 (step @p145 :rule symm :premises (@p144)) % 0.62/0.81 (step @p146 :rule instantiate :premises (@p18) :args ((@list @t91 @t45))) % 0.62/0.81 (step @p147 :rule refl :args (@t91)) % 0.62/0.81 (step @p148 :rule trans :premises (@p130 @p109 @p107)) % 0.62/0.81 (step @p149 :rule cong :premises (@p148 @p147) :args ((tptp.addNat @t91 @t91))) % 0.62/0.81 (step @p150 :rule instantiate :premises (@p19) :args (@t92)) % 0.62/0.81 (step @p151 :rule eq-symm :args (@t37 @t35)) % 0.62/0.81 (step @p152 :rule cong :premises (@p151) :args (@t38)) % 0.62/0.81 (step @p153 :rule eq_resolve :premises (@p22 @p152)) % 0.62/0.81 (step @p154 :rule instantiate :premises (@p153) :args ((@list @t90))) % 0.62/0.81 (step @p155 :rule symm :premises (@p154)) % 0.62/0.81 (step @p156 :rule symm :premises (@p128)) % 0.62/0.81 (step @p157 :rule symm :premises (@p121)) % 0.62/0.81 (step @p158 :rule symm :premises (@p114)) % 0.62/0.81 (step @p159 :rule eq-symm :args (@t29 @t18)) % 0.62/0.81 (step @p160 :rule cong :premises (@p159) :args (@t30)) % 0.62/0.81 (step @p161 :rule eq_resolve :premises (@p15 @p160)) % 0.62/0.81 (step @p162 :rule instantiate :premises (@p161) :args ((@list @t72))) % 0.62/0.81 (step @p163 :rule symm :premises (@p162)) % 0.62/0.81 (step @p164 :rule refl :args (@t72)) % 0.62/0.81 (step @p165 :rule cong :premises (@p12 @p164) :args ((tptp.append @t17 @t72))) % 0.62/0.81 (step @p166 :rule cong :premises (@p75) :args (@t94)) % 0.62/0.81 (step @p167 :rule cong :premises (@p62 @p166) :args (@t95)) % 0.62/0.81 (step @p168 :rule trans :premises (@p167 @p165 @p163 @p158)) % 0.62/0.81 (step @p169 :rule cong :premises (@p116 @p168) :args ((tptp.cons tptp.i @t95))) % 0.62/0.81 (step @p170 :rule instantiate :premises (@p16) :args ((@list @t94 tptp.i @t67))) % 0.62/0.81 (step @p171 :rule refl :args (@t94)) % 0.62/0.81 (step @p172 :rule trans :premises (@p166 @p87)) % 0.62/0.81 (step @p173 :rule cong :premises (@p172 @p171) :args (@t96)) % 0.62/0.81 (step @p174 :rule trans :premises (@p173 @p170 @p169 @p157 @p156)) % 0.62/0.81 (step @p175 :rule refl :args (tptp.o)) % 0.62/0.81 (step @p176 :rule cong :premises (@p175 @p174) :args ((tptp.cons tptp.o @t96))) % 0.62/0.81 (step @p177 :rule instantiate :premises (@p16) :args ((@list @t94 tptp.o @t94))) % 0.62/0.81 (step @p178 :rule symm :premises (@p166)) % 0.62/0.81 (step @p179 :rule trans :premises (@p114 @p178)) % 0.62/0.81 (step @p180 :rule cong :premises (@p175 @p179) :args ((tptp.cons tptp.o @t84))) % 0.62/0.81 (step @p181 :rule symm :premises (@p115)) % 0.62/0.81 (step @p182 :rule cong :premises (@p175 @p181) :args (@t97)) % 0.62/0.81 (step @p183 :rule bool-impl-elim :args (@t23 @t22)) % 0.62/0.81 (step @p184 :rule cong :premises (@p183) :args (@t25)) % 0.62/0.81 (step @p185 :rule eq_resolve :premises (@p13 @p184)) % 0.62/0.81 (step @p186 :rule instantiate :premises (@p185) :args (@t51)) % 0.62/0.81 (step @p187 :rule cnf_or_pos :args (@t100)) % 0.62/0.81 (step @p188 :rule reordering :premises (@p187) :args ((or @t62 @t99 (not @t100)))) % 0.62/0.81 (step @p189 :rule chain_m_resolution :premises (@p188 @p57 @p186) :args (@t99 @t59 (@list @t47 @t100))) % 0.62/0.81 (step @p190 :rule trans :premises (@p189 @p182 @p180)) % 0.62/0.81 (step @p191 :rule cong :premises (@p190 @p178) :args (@t101)) % 0.62/0.81 (step @p192 :rule trans :premises (@p191 @p177 @p176)) % 0.62/0.81 (step @p193 :rule cong :premises (@p192) :args ((tptp.rd @t101))) % 0.62/0.81 (step @p194 :rule instantiate :premises (@p23) :args ((@list @t45 @t10))) % 0.62/0.81 (step @p195 :rule bool-double-not-elim :args ((forall @t40 @t41))) % 0.62/0.81 (step @p196 :rule bool-double-not-elim :args (@t41)) % 0.62/0.81 (step @p197 :rule cong :premises (@p196) :args (@t102)) % 0.62/0.81 (step @p198 :rule cong :premises (@p197) :args (@t103)) % 0.62/0.81 (step @p199 :rule exists-elim :args ((= @t43 @t103))) % 0.62/0.81 (step @p200 :rule trans :premises (@p199 @p198)) % 0.62/0.82 (step @p201 :rule cong :premises (@p200) :args (@t44)) % 0.62/0.82 (step @p202 :rule trans :premises (@p201 @p195)) % 0.62/0.82 (step @p203 :rule eq_resolve :premises (@p24 @p202)) % 0.62/0.82 (step @p204 :rule instantiate :premises (@p203) :args (@t104)) % 0.62/0.82 (step @p205 :rule instantiate :premises (@p23) :args (@t104)) % 0.62/0.82 (step @p206 :rule symm :premises (@p205)) % 0.62/0.82 (step @p207 :rule refl :args (@t98)) % 0.62/0.82 (step @p208 :rule cong :premises (@p91 @p207) :args ((tptp.append @t75 @t98))) % 0.62/0.82 (step @p209 :rule symm :premises (@p92)) % 0.62/0.82 (step @p210 :rule cong :premises (@p209 @p207) :args ((tptp.append @t71 @t98))) % 0.62/0.82 (step @p211 :rule instantiate :premises (@p16) :args ((@list @t98 tptp.i @t67))) % 0.62/0.82 (step @p212 :rule symm :premises (@p211)) % 0.62/0.82 (step @p213 :rule symm :premises (@p62)) % 0.62/0.82 (step @p214 :rule cong :premises (@p213 @p207) :args ((tptp.append @t17 @t98))) % 0.62/0.82 (step @p215 :rule symm :premises (@p12)) % 0.62/0.82 (step @p216 :rule cong :premises (@p215 @p207) :args ((tptp.append tptp.nil @t98))) % 0.62/0.82 (step @p217 :rule instantiate :premises (@p161) :args ((@list @t98))) % 0.62/0.82 (step @p218 :rule cong :premises (@p124) :args (@t105)) % 0.62/0.82 (step @p219 :rule trans :premises (@p218 @p217 @p216 @p214)) % 0.62/0.82 (step @p220 :rule cong :premises (@p116 @p219) :args (@t106)) % 0.62/0.82 (step @p221 :rule trans :premises (@p220 @p212 @p210 @p208)) % 0.62/0.82 (step @p222 :rule cong :premises (@p221) :args ((tptp.rd @t106))) % 0.62/0.82 (step @p223 :rule instantiate :premises (@p21) :args ((@list @t105))) % 0.62/0.82 (step @p224 :rule symm :premises (@p223)) % 0.62/0.82 (step @p225 :rule trans :premises (@p224 @p222 @p206 @p204 @p194 @p193 @p155 @p150 @p149 @p146)) % 0.62/0.82 (step @p226 :rule cong :premises (@p225) :args ((tptp.proj1Suc (tptp.suc @t108)))) % 0.62/0.82 (step @p227 :rule instantiate :premises (@p137) :args ((@list @t108))) % 0.62/0.82 (step @p228 :rule instantiate :premises (@p19) :args (@t109)) % 0.62/0.82 (step @p229 :rule symm :premises (@p228)) % 0.62/0.82 (step @p230 :rule refl :args (@t107)) % 0.62/0.82 (step @p231 :rule symm :premises (@p218)) % 0.62/0.82 (step @p232 :rule symm :premises (@p189)) % 0.62/0.82 (step @p233 :rule trans :premises (@p232 @p231)) % 0.62/0.82 (step @p234 :rule cong :premises (@p233) :args ((tptp.rd @t97))) % 0.62/0.82 (step @p235 :rule instantiate :premises (@p153) :args (@t82)) % 0.62/0.82 (step @p236 :rule symm :premises (@p105)) % 0.62/0.82 (step @p237 :rule symm :premises (@p104)) % 0.62/0.82 (step @p238 :rule symm :premises (@p98)) % 0.62/0.82 (step @p239 :rule trans :premises (@p238 @p237 @p236 @p235 @p234)) % 0.62/0.82 (step @p240 :rule cong :premises (@p239 @p230) :args ((tptp.addNat @t79 @t107))) % 0.62/0.82 (step @p241 :rule instantiate :premises (@p18) :args ((@list @t107 @t78))) % 0.62/0.82 (step @p242 :rule symm :premises (@p241)) % 0.62/0.82 (step @p243 :rule trans :premises (@p242 @p240 @p229 @p227 @p226 @p145 @p143)) % 0.62/0.82 (step @p244 :rule cong :premises (@p243) :args ((tptp.proj1Suc (tptp.suc @t110)))) % 0.62/0.82 (step @p245 :rule instantiate :premises (@p137) :args ((@list @t110))) % 0.62/0.82 (step @p246 :rule symm :premises (@p96)) % 0.62/0.82 (step @p247 :rule cong :premises (@p246 @p230) :args ((tptp.addNat @t10 @t107))) % 0.62/0.82 (step @p248 :rule instantiate :premises (@p18) :args ((@list @t107 tptp.zero))) % 0.62/0.82 (step @p249 :rule symm :premises (@p248)) % 0.62/0.82 (step @p250 :rule instantiate :premises (@p67) :args (@t109)) % 0.62/0.82 (step @p251 :rule symm :premises (@p97)) % 0.62/0.82 (step @p252 :rule trans :premises (@p251 @p238 @p237 @p236 @p235 @p234 @p250)) % 0.62/0.82 (step @p253 :rule cong :premises (@p252) :args (@t63)) % 0.62/0.82 (step @p254 :rule trans :premises (@p107 @p253 @p249 @p247 @p245 @p244 @p142 @p140)) % 0.62/0.82 (step @p255 :rule cong :premises (@p254) :args ((tptp.proj1Suc @t81))) % 0.62/0.82 (step @p256 :rule instantiate :premises (@p137) :args ((@list @t80))) % 0.62/0.82 (step @p257 :rule trans :premises (@p251 @p238 @p237 @p236 @p256 @p255 @p139)) % 0.62/0.82 (step @p258 :rule cong :premises (@p257) :args (@t47)) % 0.62/0.82 (step @p259 :rule true_intro :premises (@p57)) % 0.62/0.82 (step @p260 :rule symm :premises (@p259)) % 0.62/0.82 (step @p261 :rule trans :premises (@p260 @p258 @p134 @p108 @p61)) % 0.62/0.82 (step @p262 false :rule eq_resolve :premises (@p261 @p26)) % 0.62/0.82 ) % 0.62/0.82 % SZS output end Proof % 0.62/0.82 % cvc5 exiting %------------------------------------------------------------------------------