%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG044+1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n023.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 08:45:29 AM UTC 2026 % Result : Theorem 0.34s 0.59s % Output : Proof 0.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG044+1 : TPTP v9.2.1. Released v4.0.0. % 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 : n023.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 14:04:28 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.34/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.34/0.59 % SZS status Theorem % 0.34/0.59 % SZS output start Proof % 0.34/0.59 ( % 0.34/0.59 (declare-sort $$unsorted 0) % 0.34/0.59 (declare-const tptp.xy $$unsorted) % 0.34/0.59 (declare-const tptp.xu $$unsorted) % 0.34/0.59 (declare-const tptp.xv $$unsorted) % 0.34/0.59 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.34/0.59 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.59 (declare-const tptp.xx $$unsorted) % 0.34/0.59 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.34/0.59 (declare-const tptp.sz0z00 $$unsorted) % 0.34/0.59 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.34/0.59 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.34/0.59 (declare-const tptp.aScalar0 (-> $$unsorted Bool)) % 0.34/0.59 (declare-const tptp.sz00 $$unsorted) % 0.34/0.59 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.34/0.59 (define @t1 () (@var "W0" $$unsorted)) % 0.34/0.59 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.34/0.59 (define @t3 () (@list @t1)) % 0.34/0.59 (define @t4 () (tptp.szszuzczcdt0 @t1)) % 0.34/0.59 (define @t5 () (@var "W1" $$unsorted)) % 0.34/0.59 (define @t6 () (tptp.szszuzczcdt0 @t5)) % 0.34/0.59 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 0.34/0.59 (define @t8 () (and @t2 @t7)) % 0.34/0.59 (define @t9 () (@list @t1 @t5)) % 0.34/0.59 (define @t10 () (tptp.aScalar0 @t1)) % 0.34/0.59 (define @t11 () (tptp.sdtpldt0 @t1 @t5)) % 0.34/0.59 (define @t12 () (tptp.aScalar0 @t11)) % 0.34/0.59 (define @t13 () (tptp.aScalar0 @t5)) % 0.34/0.59 (define @t14 () (and @t10 @t13)) % 0.34/0.59 (define @t15 () (forall @t9 (=> @t14 @t12))) % 0.34/0.59 (define @t16 () (tptp.sdtasdt0 @t1 @t5)) % 0.34/0.59 (define @t17 () (tptp.smndt0 @t1)) % 0.34/0.59 (define @t18 () (@var "W2" $$unsorted)) % 0.34/0.59 (define @t19 () (tptp.sdtasdt0 @t5 @t18)) % 0.34/0.59 (define @t20 () (tptp.sdtpldt0 @t5 @t18)) % 0.34/0.59 (define @t21 () (tptp.aScalar0 @t18)) % 0.34/0.59 (define @t22 () (and @t10 @t13 @t21)) % 0.34/0.59 (define @t23 () (@list @t1 @t5 @t18)) % 0.34/0.59 (define @t24 () (tptp.sdtasdt0 @t1 @t18)) % 0.34/0.59 (define @t25 () (and (= (tptp.sdtasdt0 @t1 @t20) (tptp.sdtpldt0 @t16 @t24)) (= (tptp.sdtasdt0 @t11 @t18) (tptp.sdtpldt0 @t24 @t19)))) % 0.34/0.59 (define @t26 () (forall @t23 (=> @t22 @t25))) % 0.34/0.59 (define @t27 () (tptp.aScalar0 tptp.xv)) % 0.34/0.59 (define @t28 () (tptp.aScalar0 tptp.xu)) % 0.34/0.59 (define @t29 () (tptp.aScalar0 tptp.xy)) % 0.34/0.59 (define @t30 () (tptp.aScalar0 tptp.xx)) % 0.34/0.59 (define @t31 () (tptp.sdtasdt0 tptp.xy tptp.xv)) % 0.34/0.59 (define @t32 () (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xu) @t31)) % 0.34/0.59 (define @t33 () (tptp.sdtasdt0 tptp.xx tptp.xv)) % 0.34/0.59 (define @t34 () (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xx tptp.xu) @t33)) % 0.34/0.59 (define @t35 () (tptp.sdtpldt0 tptp.xu tptp.xv)) % 0.34/0.59 (define @t36 () (tptp.sdtasdt0 (tptp.sdtpldt0 tptp.xx tptp.xy) @t35)) % 0.34/0.59 (define @t37 () (= @t36 (tptp.sdtpldt0 @t34 @t32))) % 0.34/0.59 (define @t38 () (not @t37)) % 0.34/0.59 (define @t39 () (not @t21)) % 0.34/0.59 (define @t40 () (not @t13)) % 0.34/0.59 (define @t41 () (not @t10)) % 0.34/0.59 (define @t42 () (or @t41 @t40 @t39 @t25)) % 0.34/0.59 (define @t43 () (or @t41 @t40 @t39)) % 0.34/0.59 (define @t44 () (tptp.sdtasdt0 tptp.xu tptp.xv)) % 0.34/0.59 (define @t45 () (= (tptp.sdtasdt0 (tptp.sdtpldt0 tptp.xy tptp.xu) tptp.xv) (tptp.sdtpldt0 @t31 @t44))) % 0.34/0.59 (define @t46 () (tptp.sdtasdt0 tptp.xy @t35)) % 0.34/0.59 (define @t47 () (and (= @t46 @t32) @t45)) % 0.34/0.59 (define @t48 () (not @t27)) % 0.34/0.59 (define @t49 () (not @t28)) % 0.34/0.59 (define @t50 () (not @t29)) % 0.34/0.59 (define @t51 () (or @t50 @t49 @t48 @t47)) % 0.34/0.59 (define @t52 () (forall @t23 @t42)) % 0.34/0.59 (define @t53 () (= @t32 @t46)) % 0.34/0.59 (define @t54 () (and @t53 @t45)) % 0.34/0.59 (define @t55 () (or @t50 @t49 @t48 @t54)) % 0.34/0.59 (define @t56 () (@list false)) % 0.34/0.59 (define @t57 () (@list @t52)) % 0.34/0.59 (define @t58 () (@list false false false false)) % 0.34/0.59 (define @t59 () (= (tptp.sdtasdt0 (tptp.sdtpldt0 tptp.xx tptp.xu) tptp.xv) (tptp.sdtpldt0 @t33 @t44))) % 0.34/0.59 (define @t60 () (tptp.sdtasdt0 tptp.xx @t35)) % 0.34/0.59 (define @t61 () (and (= @t60 @t34) @t59)) % 0.34/0.59 (define @t62 () (not @t30)) % 0.34/0.59 (define @t63 () (or @t62 @t49 @t48 @t61)) % 0.34/0.59 (define @t64 () (= @t34 @t60)) % 0.34/0.59 (define @t65 () (and @t64 @t59)) % 0.34/0.59 (define @t66 () (or @t62 @t49 @t48 @t65)) % 0.34/0.59 (define @t67 () (tptp.aScalar0 @t35)) % 0.34/0.59 (define @t68 () (or @t49 @t48 @t67)) % 0.34/0.59 (define @t69 () (tptp.sdtpldt0 @t60 @t46)) % 0.34/0.59 (define @t70 () (= @t36 @t69)) % 0.34/0.59 (define @t71 () (and (= (tptp.sdtasdt0 tptp.xx (tptp.sdtpldt0 tptp.xy @t35)) (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xx tptp.xy) @t60)) @t70)) % 0.34/0.59 (define @t72 () (not @t67)) % 0.34/0.59 (define @t73 () (or @t62 @t50 @t72 @t71)) % 0.34/0.59 (define @t74 () (not @t70)) % 0.34/0.59 (define @t75 () (not @t64)) % 0.34/0.59 (define @t76 () (not @t53)) % 0.34/0.59 (define @t77 () (and @t38 @t53 @t64)) % 0.34/0.59 (assume @p1 (forall @t3 (=> @t2 true))) % 0.34/0.59 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.34/0.59 (assume @p3 (forall @t3 (=> @t2 (and (tptp.aNaturalNumber0 @t4) (not (= @t4 tptp.sz00)))))) % 0.34/0.59 (assume @p4 (forall @t3 (=> (and @t2 (not (= @t1 tptp.sz00))) (exists (@list @t5) (and @t7 (= @t1 @t6)))))) % 0.34/0.59 (assume @p5 (forall @t9 (=> @t8 (=> (= @t4 @t6) (= @t1 @t5))))) % 0.34/0.59 (assume @p6 (forall @t9 (=> @t8 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.34/0.59 (assume @p7 (forall @t3 (=> @t2 (tptp.iLess0 @t1 @t4)))) % 0.34/0.59 (assume @p8 (forall @t3 (=> @t10 true))) % 0.34/0.59 (assume @p9 (tptp.aScalar0 tptp.sz0z00)) % 0.34/0.59 (assume @p10 @t15) % 0.34/0.59 (assume @p11 (forall @t9 (=> @t14 (tptp.aScalar0 @t16)))) % 0.34/0.59 (assume @p12 (forall @t3 (=> @t10 (tptp.aScalar0 @t17)))) % 0.34/0.59 (assume @p13 (forall @t3 (=> @t10 (and (= (tptp.sdtpldt0 @t1 tptp.sz0z00) @t1) (= (tptp.sdtpldt0 tptp.sz0z00 @t1) @t1) (= (tptp.sdtasdt0 @t1 tptp.sz0z00) tptp.sz0z00) (= (tptp.sdtasdt0 tptp.sz0z00 @t1) tptp.sz0z00) (= (tptp.sdtpldt0 @t1 @t17) tptp.sz0z00) (= (tptp.sdtpldt0 @t17 @t1) tptp.sz0z00) (= (tptp.smndt0 @t17) @t1) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) % 0.34/0.59 (assume @p14 (forall @t23 (=> @t22 (and (= (tptp.sdtpldt0 @t11 @t18) (tptp.sdtpldt0 @t1 @t20)) (= @t11 (tptp.sdtpldt0 @t5 @t1)) (= (tptp.sdtasdt0 @t16 @t18) (tptp.sdtasdt0 @t1 @t19)) (= @t16 (tptp.sdtasdt0 @t5 @t1)))))) % 0.34/0.59 (assume @p15 @t26) % 0.34/0.59 (assume @p16 (and @t30 @t29 @t28 @t27)) % 0.34/0.59 (assume @p17 @t38) % 0.34/0.59 (assume @p18 true) % 0.34/0.59 (step @p19 :rule aci_norm :args ((= (or @t43 @t25) @t42))) % 0.34/0.59 (step @p20 :rule refl :args (@t25)) % 0.34/0.59 (step @p21 :rule aci_norm :args ((= (or @t41 (or @t40 @t39)) @t43))) % 0.34/0.59 (step @p22 :rule bool-and-de-morgan :args (@t13 @t21 true)) % 0.34/0.59 (step @p23 :rule refl :args (@t41)) % 0.34/0.59 (step @p24 :rule nary_cong :premises (@p23 @p22) :args ((or @t41 (not (and @t13 @t21))))) % 0.34/0.59 (step @p25 :rule bool-and-de-morgan :args (@t10 @t13 (and @t21))) % 0.34/0.59 (step @p26 :rule trans :premises (@p25 @p24)) % 0.34/0.59 (step @p27 :rule trans :premises (@p26 @p21)) % 0.34/0.59 (step @p28 :rule nary_cong :premises (@p27 @p20) :args ((or (not @t22) @t25))) % 0.34/0.59 (step @p29 :rule trans :premises (@p28 @p19)) % 0.34/0.59 (step @p30 :rule bool-impl-elim :args (@t22 @t25)) % 0.34/0.59 (step @p31 :rule trans :premises (@p30 @p29)) % 0.34/0.59 (step @p32 :rule cong :premises (@p31) :args (@t26)) % 0.34/0.59 (step @p33 :rule eq_resolve :premises (@p15 @p32)) % 0.34/0.59 (step @p34 :rule refl :args (@t45)) % 0.34/0.59 (step @p35 :rule eq-symm :args (@t46 @t32)) % 0.34/0.59 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t47)) % 0.34/0.59 (step @p37 :rule refl :args (@t48)) % 0.34/0.59 (step @p38 :rule refl :args (@t49)) % 0.34/0.59 (step @p39 :rule refl :args (@t50)) % 0.34/0.59 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37 @p36) :args (@t51)) % 0.34/0.59 (step @p41 :rule refl :args (@t52)) % 0.34/0.59 (step @p42 :rule cong :premises (@p41 @p40) :args ((=> @t52 @t51))) % 0.34/0.59 (assume-push @p124 @t52) % 0.34/0.59 (step @p44 :rule instantiate :premises (@p33) :args ((@list tptp.xy tptp.xu tptp.xv))) % 0.34/0.59 (step-pop @p125 :rule scope :premises (@p44)) % 0.34/0.59 (step @p45 :rule process_scope :premises (@p125) :args (@t51)) % 0.34/0.59 (step @p47 :rule eq_resolve :premises (@p45 @p42)) % 0.34/0.59 (step @p48 :rule implies_elim :premises (@p47)) % 0.34/0.59 (step @p49 :rule chain_m_resolution :premises (@p48 @p33) :args (@t55 @t56 @t57)) % 0.34/0.59 (step @p50 :rule and_elim :premises (@p16) :args (3)) % 0.34/0.59 (step @p51 :rule and_elim :premises (@p16) :args (2)) % 0.34/0.59 (step @p52 :rule and_elim :premises (@p16) :args (1)) % 0.34/0.59 (step @p53 :rule cnf_or_pos :args (@t55)) % 0.34/0.59 (step @p54 :rule reordering :premises (@p53) :args ((or @t50 @t49 @t48 @t54 (not @t55)))) % 0.34/0.59 (step @p55 :rule chain_m_resolution :premises (@p54 @p52 @p51 @p50 @p49) :args (@t54 @t58 (@list @t29 @t28 @t27 @t55))) % 0.34/0.59 (step @p56 :rule cnf_and_pos :args (@t54 0)) % 0.34/0.59 (step @p57 :rule reordering :premises (@p56) :args ((or @t53 (not @t54)))) % 0.34/0.59 (step @p58 :rule chain_m_resolution :premises (@p57 @p55) :args (@t53 @t56 (@list @t54))) % 0.34/0.59 (step @p59 :rule refl :args (@t59)) % 0.34/0.59 (step @p60 :rule eq-symm :args (@t60 @t34)) % 0.34/0.59 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t61)) % 0.34/0.59 (step @p62 :rule refl :args (@t62)) % 0.34/0.59 (step @p63 :rule nary_cong :premises (@p62 @p38 @p37 @p61) :args (@t63)) % 0.34/0.59 (step @p64 :rule cong :premises (@p41 @p63) :args ((=> @t52 @t63))) % 0.34/0.59 (assume-push @p126 @t52) % 0.34/0.59 (step @p66 :rule instantiate :premises (@p33) :args ((@list tptp.xx tptp.xu tptp.xv))) % 0.34/0.59 (step-pop @p127 :rule scope :premises (@p66)) % 0.34/0.59 (step @p67 :rule process_scope :premises (@p127) :args (@t63)) % 0.34/0.59 (step @p69 :rule eq_resolve :premises (@p67 @p64)) % 0.34/0.59 (step @p70 :rule implies_elim :premises (@p69)) % 0.34/0.59 (step @p71 :rule chain_m_resolution :premises (@p70 @p33) :args (@t66 @t56 @t57)) % 0.34/0.59 (step @p72 :rule and_elim :premises (@p16) :args (0)) % 0.34/0.59 (step @p73 :rule cnf_or_pos :args (@t66)) % 0.34/0.59 (step @p74 :rule reordering :premises (@p73) :args ((or @t62 @t49 @t48 @t65 (not @t66)))) % 0.34/0.59 (step @p75 :rule chain_m_resolution :premises (@p74 @p72 @p51 @p50 @p71) :args (@t65 @t58 (@list @t30 @t28 @t27 @t66))) % 0.34/0.59 (step @p76 :rule cnf_and_pos :args (@t65 0)) % 0.34/0.59 (step @p77 :rule reordering :premises (@p76) :args ((or @t64 (not @t65)))) % 0.34/0.59 (step @p78 :rule chain_m_resolution :premises (@p77 @p75) :args (@t64 @t56 (@list @t65))) % 0.34/0.59 (step @p79 :rule instantiate :premises (@p33) :args ((@list tptp.xx tptp.xy @t35))) % 0.34/0.59 (step @p80 :rule aci_norm :args ((= (or (or @t41 @t40) @t12) (or @t41 @t40 @t12)))) % 0.34/0.59 (step @p81 :rule refl :args (@t12)) % 0.34/0.59 (step @p82 :rule bool-and-de-morgan :args (@t10 @t13 true)) % 0.34/0.59 (step @p83 :rule nary_cong :premises (@p82 @p81) :args ((or (not @t14) @t12))) % 0.34/0.59 (step @p84 :rule trans :premises (@p83 @p80)) % 0.34/0.59 (step @p85 :rule bool-impl-elim :args (@t14 @t12)) % 0.34/0.59 (step @p86 :rule trans :premises (@p85 @p84)) % 0.34/0.59 (step @p87 :rule cong :premises (@p86) :args (@t15)) % 0.34/0.59 (step @p88 :rule eq_resolve :premises (@p10 @p87)) % 0.34/0.59 (step @p89 :rule instantiate :premises (@p88) :args ((@list tptp.xu tptp.xv))) % 0.34/0.59 (step @p90 :rule cnf_or_pos :args (@t68)) % 0.34/0.59 (step @p91 :rule reordering :premises (@p90) :args ((or @t49 @t48 @t67 (not @t68)))) % 0.34/0.59 (step @p92 :rule chain_m_resolution :premises (@p91 @p51 @p50 @p89) :args (@t67 (@list false false false) (@list @t28 @t27 @t68))) % 0.34/0.59 (step @p93 :rule cnf_or_pos :args (@t73)) % 0.34/0.59 (step @p94 :rule reordering :premises (@p93) :args ((or @t62 @t50 @t72 @t71 (not @t73)))) % 0.34/0.59 (step @p95 :rule chain_m_resolution :premises (@p94 @p72 @p52 @p92 @p79) :args (@t71 @t58 (@list @t30 @t29 @t67 @t73))) % 0.34/0.59 (step @p96 :rule cnf_and_pos :args (@t71 1)) % 0.34/0.59 (step @p97 :rule reordering :premises (@p96) :args ((or @t70 (not @t71)))) % 0.34/0.59 (step @p98 :rule chain_m_resolution :premises (@p97 @p95) :args (@t70 @t56 (@list @t71))) % 0.34/0.59 (step @p99 :rule refl :args (@t74)) % 0.34/0.59 (step @p100 :rule refl :args (@t75)) % 0.34/0.59 (step @p101 :rule refl :args (@t76)) % 0.34/0.59 (step @p102 :rule bool-double-not-elim :args (@t37)) % 0.34/0.59 (step @p103 :rule nary_cong :premises (@p102 @p101 @p100 @p99) :args ((or (not @t38) @t76 @t75 @t74))) % 0.34/0.59 (assume-push @p128 @t38) % 0.34/0.59 (assume-push @p129 @t53) % 0.34/0.59 (assume-push @p130 @t64) % 0.34/0.59 (step @p107 :rule false_intro :premises (@p17)) % 0.34/0.59 (step @p108 :rule symm :premises (@p58)) % 0.34/0.59 (step @p109 :rule symm :premises (@p78)) % 0.34/0.59 (step @p110 :rule cong :premises (@p109 @p108) :args (@t69)) % 0.34/0.59 (step @p111 :rule refl :args (@t36)) % 0.34/0.59 (step @p112 :rule cong :premises (@p111 @p110) :args (@t70)) % 0.34/0.59 (step @p113 :rule trans :premises (@p112 @p107)) % 0.34/0.59 (step @p114 :rule false_elim :premises (@p113)) % 0.34/0.59 (step-pop @p131 :rule scope :premises (@p114)) % 0.34/0.59 (step-pop @p132 :rule scope :premises (@p131)) % 0.34/0.59 (step-pop @p133 :rule scope :premises (@p132)) % 0.34/0.59 (step @p115 :rule process_scope :premises (@p133) :args (@t74)) % 0.34/0.59 (step @p119 :rule implies_elim :premises (@p115)) % 0.34/0.59 (step @p120 :rule cnf_and_neg :args (@t77)) % 0.34/0.59 (step @p121 :rule resolution :premises (@p120 @p119) :args (true @t77)) % 0.34/0.59 (step @p122 :rule eq_resolve :premises (@p121 @p103)) % 0.34/0.59 (step @p123 false :rule chain_m_resolution :premises (@p122 @p98 @p78 @p58 @p17) :args (false (@list false false false true) (@list @t70 @t64 @t53 @t37))) % 0.34/0.59 ) % 0.34/0.59 % SZS output end Proof % 0.34/0.59 % cvc5 exiting %------------------------------------------------------------------------------