%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM436+3 : 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 : n009.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 08:39:24 AM UTC 2026 % Result : Theorem 0.45s 0.68s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM436+3 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n009.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 11:18:29 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.45/0.68 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.45/0.68 % SZS status Theorem % 0.45/0.68 % SZS output start Proof % 0.45/0.68 ( % 0.45/0.68 (declare-sort $$unsorted 0) % 0.45/0.68 (declare-const tptp.xa $$unsorted) % 0.45/0.68 (declare-const tptp.xb $$unsorted) % 0.45/0.68 (declare-const tptp.xq $$unsorted) % 0.45/0.68 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.xp $$unsorted) % 0.45/0.68 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.45/0.68 (declare-const tptp.xm $$unsorted) % 0.45/0.68 (declare-const tptp.sz10 $$unsorted) % 0.45/0.68 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.sz00 $$unsorted) % 0.45/0.68 (declare-const tptp.aDivisorOf0 (-> $$unsorted $$unsorted Bool)) % 0.45/0.68 (declare-const tptp.aInteger0 (-> $$unsorted Bool)) % 0.45/0.68 (define @t1 () (@var "W0" $$unsorted)) % 0.45/0.68 (define @t2 () (tptp.aInteger0 @t1)) % 0.45/0.68 (define @t3 () (@list @t1)) % 0.45/0.68 (define @t4 () (tptp.smndt0 @t1)) % 0.45/0.68 (define @t5 () (@var "W1" $$unsorted)) % 0.45/0.68 (define @t6 () (tptp.sdtpldt0 @t1 @t5)) % 0.45/0.68 (define @t7 () (tptp.aInteger0 @t5)) % 0.45/0.68 (define @t8 () (and @t2 @t7)) % 0.45/0.68 (define @t9 () (@list @t1 @t5)) % 0.45/0.68 (define @t10 () (tptp.sdtasdt0 @t1 @t5)) % 0.45/0.68 (define @t11 () (tptp.aInteger0 @t10)) % 0.45/0.68 (define @t12 () (forall @t9 (=> @t8 @t11))) % 0.45/0.68 (define @t13 () (@var "W2" $$unsorted)) % 0.45/0.68 (define @t14 () (tptp.sdtpldt0 @t5 @t13)) % 0.45/0.68 (define @t15 () (tptp.aInteger0 @t13)) % 0.45/0.68 (define @t16 () (and @t2 @t7 @t15)) % 0.45/0.68 (define @t17 () (@list @t1 @t5 @t13)) % 0.45/0.68 (define @t18 () (tptp.sdtasdt0 @t5 @t13)) % 0.45/0.68 (define @t19 () (tptp.sdtasdt0 @t1 @t13)) % 0.45/0.68 (define @t20 () (tptp.smndt0 tptp.sz10)) % 0.45/0.68 (define @t21 () (= @t5 tptp.sz00)) % 0.45/0.68 (define @t22 () (not @t21)) % 0.45/0.68 (define @t23 () (tptp.sdteqdtlpzmzozddtrp0 @t1 @t5 @t13)) % 0.45/0.68 (define @t24 () (not (= @t13 tptp.sz00))) % 0.45/0.68 (define @t25 () (and @t2 @t7 @t15 @t24)) % 0.45/0.68 (define @t26 () (@var "W3" $$unsorted)) % 0.45/0.68 (define @t27 () (tptp.aInteger0 tptp.xq)) % 0.45/0.68 (define @t28 () (tptp.aInteger0 tptp.xp)) % 0.45/0.68 (define @t29 () (tptp.sdtasdt0 tptp.xp tptp.xq)) % 0.45/0.68 (define @t30 () (tptp.sdtpldt0 tptp.xa (tptp.smndt0 tptp.xb))) % 0.45/0.68 (define @t31 () (tptp.aInteger0 tptp.xm)) % 0.45/0.68 (define @t32 () (tptp.sdtasdt0 tptp.xp tptp.xm)) % 0.45/0.68 (define @t33 () (= @t30 (tptp.sdtasdt0 tptp.xq @t32))) % 0.45/0.68 (define @t34 () (tptp.sdtasdt0 tptp.xq tptp.xm)) % 0.45/0.68 (define @t35 () (tptp.sdtasdt0 tptp.xp @t34)) % 0.45/0.68 (define @t36 () (tptp.sdteqdtlpzmzozddtrp0 tptp.xa tptp.xb tptp.xq)) % 0.45/0.68 (define @t37 () (tptp.aDivisorOf0 tptp.xq @t30)) % 0.45/0.68 (define @t38 () (tptp.sdtasdt0 tptp.xq @t1)) % 0.45/0.68 (define @t39 () (and @t2 (= @t38 @t30))) % 0.45/0.68 (define @t40 () (exists @t3 @t39)) % 0.45/0.68 (define @t41 () (or @t40 @t37 @t36)) % 0.45/0.68 (define @t42 () (tptp.sdteqdtlpzmzozddtrp0 tptp.xa tptp.xb tptp.xp)) % 0.45/0.68 (define @t43 () (tptp.aDivisorOf0 tptp.xp @t30)) % 0.45/0.68 (define @t44 () (tptp.sdtasdt0 tptp.xp @t1)) % 0.45/0.68 (define @t45 () (and @t2 (= @t44 @t30))) % 0.45/0.68 (define @t46 () (exists @t3 @t45)) % 0.45/0.68 (define @t47 () (or @t46 @t43 @t42)) % 0.45/0.68 (define @t48 () (and @t47 @t41)) % 0.45/0.68 (define @t49 () (not @t48)) % 0.45/0.68 (define @t50 () (not @t7)) % 0.45/0.68 (define @t51 () (not @t2)) % 0.45/0.68 (define @t52 () (tptp.aInteger0 @t32)) % 0.45/0.68 (define @t53 () (not @t31)) % 0.45/0.68 (define @t54 () (not @t28)) % 0.45/0.68 (define @t55 () (or @t54 @t53 @t52)) % 0.45/0.68 (define @t56 () (@list false false false)) % 0.45/0.68 (define @t57 () (not @t33)) % 0.45/0.68 (define @t58 () (not @t52)) % 0.45/0.68 (define @t59 () (or @t58 @t57)) % 0.45/0.68 (define @t60 () (not @t59)) % 0.45/0.68 (define @t61 () (@list false false)) % 0.45/0.68 (define @t62 () (= @t30 @t38)) % 0.45/0.68 (define @t63 () (forall @t3 (or @t51 (not @t62)))) % 0.45/0.68 (define @t64 () (not @t63)) % 0.45/0.68 (define @t65 () (@list true)) % 0.45/0.68 (define @t66 () (or @t64 @t37 @t36)) % 0.45/0.68 (define @t67 () (and @t2 @t62)) % 0.45/0.68 (define @t68 () (forall @t3 (not @t67))) % 0.45/0.68 (define @t69 () (not @t68)) % 0.45/0.68 (define @t70 () (= @t30 @t44)) % 0.45/0.68 (define @t71 () (and @t2 @t70)) % 0.45/0.68 (define @t72 () (forall @t3 (not @t71))) % 0.45/0.68 (define @t73 () (not @t72)) % 0.45/0.68 (define @t74 () (forall @t3 (or @t51 (not @t70)))) % 0.45/0.68 (define @t75 () (not @t74)) % 0.45/0.68 (define @t76 () (or @t75 @t43 @t42)) % 0.45/0.68 (define @t77 () (tptp.aInteger0 @t34)) % 0.45/0.68 (define @t78 () (not @t27)) % 0.45/0.68 (define @t79 () (or @t78 @t53 @t77)) % 0.45/0.68 (define @t80 () (= @t30 @t35)) % 0.45/0.68 (define @t81 () (not @t80)) % 0.45/0.68 (define @t82 () (not @t77)) % 0.45/0.68 (define @t83 () (or @t82 @t81)) % 0.45/0.68 (define @t84 () (not @t83)) % 0.45/0.68 (assume @p1 (forall @t3 (=> @t2 true))) % 0.45/0.68 (assume @p2 (tptp.aInteger0 tptp.sz00)) % 0.45/0.68 (assume @p3 (tptp.aInteger0 tptp.sz10)) % 0.45/0.68 (assume @p4 (forall @t3 (=> @t2 (tptp.aInteger0 @t4)))) % 0.45/0.68 (assume @p5 (forall @t9 (=> @t8 (tptp.aInteger0 @t6)))) % 0.45/0.68 (assume @p6 @t12) % 0.45/0.68 (assume @p7 (forall @t17 (=> @t16 (= (tptp.sdtpldt0 @t1 @t14) (tptp.sdtpldt0 @t6 @t13))))) % 0.45/0.68 (assume @p8 (forall @t9 (=> @t8 (= @t6 (tptp.sdtpldt0 @t5 @t1))))) % 0.45/0.68 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.45/0.68 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t4) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t4 @t1)))))) % 0.45/0.68 (assume @p11 (forall @t17 (=> @t16 (= (tptp.sdtasdt0 @t1 @t18) (tptp.sdtasdt0 @t10 @t13))))) % 0.45/0.68 (assume @p12 (forall @t9 (=> @t8 (= @t10 (tptp.sdtasdt0 @t5 @t1))))) % 0.45/0.68 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.45/0.68 (assume @p14 (forall @t17 (=> @t16 (and (= (tptp.sdtasdt0 @t1 @t14) (tptp.sdtpldt0 @t10 @t19)) (= (tptp.sdtasdt0 @t6 @t13) (tptp.sdtpldt0 @t19 @t18)))))) % 0.45/0.68 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.45/0.68 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t20 @t1) @t4) (= @t4 (tptp.sdtasdt0 @t1 @t20)))))) % 0.45/0.68 (assume @p17 (forall @t9 (=> @t8 (=> (= @t10 tptp.sz00) (or (= @t1 tptp.sz00) @t21))))) % 0.45/0.68 (assume @p18 (forall @t3 (=> @t2 (forall (@list @t5) (= (tptp.aDivisorOf0 @t5 @t1) (and @t7 @t22 (exists (@list @t13) (and @t15 (= @t18 @t1))))))))) % 0.45/0.68 (assume @p19 (forall @t17 (=> @t25 (= @t23 (tptp.aDivisorOf0 @t13 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t5))))))) % 0.45/0.68 (assume @p20 (forall @t9 (=> (and @t2 @t7 @t22) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t1 @t5)))) % 0.45/0.68 (assume @p21 (forall @t17 (=> @t25 (=> @t23 (tptp.sdteqdtlpzmzozddtrp0 @t5 @t1 @t13))))) % 0.45/0.68 (assume @p22 (forall (@list @t1 @t5 @t13 @t26) (=> (and @t2 @t7 @t15 @t24 (tptp.aInteger0 @t26)) (=> (and @t23 (tptp.sdteqdtlpzmzozddtrp0 @t5 @t26 @t13)) (tptp.sdteqdtlpzmzozddtrp0 @t1 @t26 @t13))))) % 0.45/0.68 (assume @p23 (and (tptp.aInteger0 tptp.xa) (tptp.aInteger0 tptp.xb) @t28 (not (= tptp.xp tptp.sz00)) @t27 (not (= tptp.xq tptp.sz00)))) % 0.45/0.68 (assume @p24 (and (not (= @t29 tptp.sz00)) (exists @t3 (and @t2 (= (tptp.sdtasdt0 @t29 @t1) @t30))) (tptp.aDivisorOf0 @t29 @t30) (tptp.sdteqdtlpzmzozddtrp0 tptp.xa tptp.xb @t29))) % 0.45/0.68 (assume @p25 (and @t31 (= (tptp.sdtasdt0 @t29 tptp.xm) @t30))) % 0.45/0.68 (assume @p26 (and (= @t35 @t30) @t33)) % 0.45/0.68 (assume @p27 @t49) % 0.45/0.68 (assume @p28 true) % 0.45/0.68 (step @p29 :rule aci_norm :args ((= (or (or @t51 @t50) @t11) (or @t51 @t50 @t11)))) % 0.45/0.68 (step @p30 :rule refl :args (@t11)) % 0.45/0.68 (step @p31 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.45/0.68 (step @p32 :rule nary_cong :premises (@p31 @p30) :args ((or (not @t8) @t11))) % 0.45/0.68 (step @p33 :rule trans :premises (@p32 @p29)) % 0.45/0.68 (step @p34 :rule bool-impl-elim :args (@t8 @t11)) % 0.45/0.68 (step @p35 :rule trans :premises (@p34 @p33)) % 0.45/0.68 (step @p36 :rule cong :premises (@p35) :args (@t12)) % 0.45/0.68 (step @p37 :rule eq_resolve :premises (@p6 @p36)) % 0.45/0.68 (step @p38 :rule instantiate :premises (@p37) :args ((@list tptp.xp tptp.xm))) % 0.45/0.68 (step @p39 :rule and_elim :premises (@p25) :args (0)) % 0.45/0.68 (step @p40 :rule and_elim :premises (@p23) :args (2)) % 0.45/0.68 (step @p41 :rule cnf_or_pos :args (@t55)) % 0.45/0.68 (step @p42 :rule reordering :premises (@p41) :args ((or @t54 @t53 @t52 (not @t55)))) % 0.45/0.68 (step @p43 :rule chain_m_resolution :premises (@p42 @p40 @p39 @p38) :args (@t52 @t56 (@list @t28 @t31 @t55))) % 0.45/0.68 (step @p44 :rule and_elim :premises (@p26) :args (1)) % 0.45/0.68 (step @p45 :rule cnf_or_pos :args (@t59)) % 0.45/0.68 (step @p46 :rule reordering :premises (@p45) :args ((or @t57 @t58 @t60))) % 0.45/0.68 (step @p47 :rule chain_m_resolution :premises (@p46 @p44 @p43) :args (@t60 @t61 (@list @t33 @t52))) % 0.45/0.68 (assume-push @p114 @t63) % 0.45/0.68 (step @p49 :rule instantiate :premises (@p114) :args ((@list @t32))) % 0.45/0.68 (step-pop @p115 :rule scope :premises (@p49)) % 0.45/0.68 (step @p50 :rule process_scope :premises (@p115) :args (@t59)) % 0.45/0.68 (step @p52 :rule implies_elim :premises (@p50)) % 0.45/0.68 (step @p53 :rule chain_m_resolution :premises (@p52 @p47) :args (@t64 @t65 (@list @t59))) % 0.45/0.68 (step @p54 :rule bool-double-not-elim :args (@t63)) % 0.45/0.68 (step @p55 :rule refl :args (@t66)) % 0.45/0.68 (step @p56 :rule nary_cong :premises (@p55 @p54) :args ((or @t66 (not @t64)))) % 0.45/0.69 (step @p57 :rule cnf_or_neg :args (@t66 0)) % 0.45/0.69 (step @p58 :rule eq_resolve :premises (@p57 @p56)) % 0.45/0.69 (step @p59 :rule reordering :premises (@p58) :args ((or @t63 @t66))) % 0.45/0.69 (step @p60 :rule chain_m_resolution :premises (@p59 @p53) :args (@t66 @t65 (@list @t63))) % 0.45/0.69 (step @p61 :rule refl :args (@t36)) % 0.45/0.69 (step @p62 :rule refl :args (@t37)) % 0.45/0.69 (step @p63 :rule bool-and-de-morgan :args (@t2 @t62 true)) % 0.45/0.69 (step @p64 :rule cong :premises (@p63) :args (@t68)) % 0.45/0.69 (step @p65 :rule cong :premises (@p64) :args (@t69)) % 0.45/0.69 (step @p66 :rule exists-elim :args ((= (exists @t3 @t67) @t69))) % 0.45/0.69 (step @p67 :rule trans :premises (@p66 @p65)) % 0.45/0.69 (step @p68 :rule eq-symm :args (@t38 @t30)) % 0.45/0.69 (step @p69 :rule refl :args (@t2)) % 0.45/0.69 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t39)) % 0.45/0.69 (step @p71 :rule cong :premises (@p70) :args (@t40)) % 0.45/0.69 (step @p72 :rule trans :premises (@p71 @p67)) % 0.45/0.69 (step @p73 :rule nary_cong :premises (@p72 @p62 @p61) :args (@t41)) % 0.45/0.69 (step @p74 :rule refl :args (@t42)) % 0.45/0.69 (step @p75 :rule refl :args (@t43)) % 0.45/0.69 (step @p76 :rule bool-and-de-morgan :args (@t2 @t70 true)) % 0.45/0.69 (step @p77 :rule cong :premises (@p76) :args (@t72)) % 0.45/0.69 (step @p78 :rule cong :premises (@p77) :args (@t73)) % 0.45/0.69 (step @p79 :rule exists-elim :args ((= (exists @t3 @t71) @t73))) % 0.45/0.69 (step @p80 :rule trans :premises (@p79 @p78)) % 0.45/0.69 (step @p81 :rule eq-symm :args (@t44 @t30)) % 0.45/0.69 (step @p82 :rule nary_cong :premises (@p69 @p81) :args (@t45)) % 0.45/0.69 (step @p83 :rule cong :premises (@p82) :args (@t46)) % 0.45/0.69 (step @p84 :rule trans :premises (@p83 @p80)) % 0.45/0.69 (step @p85 :rule nary_cong :premises (@p84 @p75 @p74) :args (@t47)) % 0.45/0.69 (step @p86 :rule nary_cong :premises (@p85 @p73) :args (@t48)) % 0.45/0.69 (step @p87 :rule cong :premises (@p86) :args (@t49)) % 0.45/0.69 (step @p88 :rule eq_resolve :premises (@p27 @p87)) % 0.45/0.69 (step @p89 :rule not_and :premises (@p88)) % 0.45/0.69 (step @p90 :rule chain_m_resolution :premises (@p89 @p60) :args ((not @t76) (@list false) (@list @t66))) % 0.45/0.69 (step @p91 :rule bool-double-not-elim :args (@t74)) % 0.45/0.69 (step @p92 :rule refl :args (@t76)) % 0.45/0.69 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or @t76 (not @t75)))) % 0.45/0.69 (step @p94 :rule cnf_or_neg :args (@t76 0)) % 0.45/0.69 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.45/0.69 (step @p96 :rule reordering :premises (@p95) :args ((or @t74 @t76))) % 0.45/0.69 (step @p97 :rule chain_m_resolution :premises (@p96 @p90) :args (@t74 @t65 (@list @t76))) % 0.45/0.69 (step @p98 :rule instantiate :premises (@p37) :args ((@list tptp.xq tptp.xm))) % 0.45/0.69 (step @p99 :rule and_elim :premises (@p23) :args (4)) % 0.45/0.69 (step @p100 :rule cnf_or_pos :args (@t79)) % 0.45/0.69 (step @p101 :rule reordering :premises (@p100) :args ((or @t78 @t53 @t77 (not @t79)))) % 0.45/0.69 (step @p102 :rule chain_m_resolution :premises (@p101 @p99 @p39 @p98) :args (@t77 @t56 (@list @t27 @t31 @t79))) % 0.45/0.69 (step @p103 :rule and_elim :premises (@p26) :args (0)) % 0.45/0.69 (step @p104 :rule symm :premises (@p103)) % 0.45/0.69 (step @p105 :rule cnf_or_pos :args (@t83)) % 0.45/0.69 (step @p106 :rule reordering :premises (@p105) :args ((or @t81 @t82 @t84))) % 0.45/0.69 (step @p107 :rule chain_m_resolution :premises (@p106 @p104 @p102) :args (@t84 @t61 (@list @t80 @t77))) % 0.45/0.69 (assume-push @p116 @t74) % 0.45/0.69 (step @p109 :rule instantiate :premises (@p116) :args ((@list @t34))) % 0.45/0.69 (step-pop @p117 :rule scope :premises (@p109)) % 0.45/0.69 (step @p110 :rule process_scope :premises (@p117) :args (@t83)) % 0.45/0.69 (step @p112 :rule implies_elim :premises (@p110)) % 0.45/0.69 (step @p113 false :rule chain_m_resolution :premises (@p112 @p107 @p97) :args (false (@list true false) (@list @t83 @t74))) % 0.45/0.69 ) % 0.45/0.69 % SZS output end Proof % 0.45/0.69 % cvc5 exiting %------------------------------------------------------------------------------