%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM836+1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n025.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 08:40:46 AM UTC 2026 % Result : Theorem 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM836+1 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n025.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 12:28:46 EDT 2026 % 0.15/0.35 % CPUTime : % 0.29/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.57 % SZS status Theorem % 0.36/0.57 % SZS output start Proof % 0.36/0.57 ( % 0.36/0.57 (declare-sort $$unsorted 0) % 0.36/0.57 (declare-const tptp.vskolem2 (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.v1 $$unsorted) % 0.36/0.57 (declare-const tptp.vsucc (-> $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.vplus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.57 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.less (-> $$unsorted $$unsorted Bool)) % 0.36/0.57 (declare-const tptp.vd203 $$unsorted) % 0.36/0.57 (declare-const tptp.vd204 $$unsorted) % 0.36/0.57 (define @t1 () (tptp.less tptp.vd203 tptp.vd204)) % 0.36/0.57 (define @t2 () (not @t1)) % 0.36/0.57 (define @t3 () (tptp.greater tptp.vd203 tptp.vd204)) % 0.36/0.57 (define @t4 () (not @t3)) % 0.36/0.57 (define @t5 () (@var "Vd201" $$unsorted)) % 0.36/0.57 (define @t6 () (@var "Vd199" $$unsorted)) % 0.36/0.57 (define @t7 () (@var "Vd198" $$unsorted)) % 0.36/0.57 (define @t8 () (= @t7 (tptp.vplus @t6 @t5))) % 0.36/0.57 (define @t9 () (@list @t5)) % 0.36/0.57 (define @t10 () (exists @t9 @t8)) % 0.36/0.57 (define @t11 () (tptp.less @t6 @t7)) % 0.36/0.57 (define @t12 () (= @t11 @t10)) % 0.36/0.57 (define @t13 () (forall (@list @t7 @t6) @t12)) % 0.36/0.57 (define @t14 () (@var "Vd196" $$unsorted)) % 0.36/0.57 (define @t15 () (@var "Vd193" $$unsorted)) % 0.36/0.57 (define @t16 () (@var "Vd194" $$unsorted)) % 0.36/0.57 (define @t17 () (= @t16 (tptp.vplus @t15 @t14))) % 0.36/0.57 (define @t18 () (@list @t14)) % 0.36/0.57 (define @t19 () (exists @t18 @t17)) % 0.36/0.57 (define @t20 () (tptp.greater @t16 @t15)) % 0.36/0.57 (define @t21 () (= @t20 @t19)) % 0.36/0.57 (define @t22 () (forall (@list @t15 @t16) @t21)) % 0.36/0.57 (define @t23 () (@var "Vd125" $$unsorted)) % 0.36/0.57 (define @t24 () (@var "Vd120" $$unsorted)) % 0.36/0.57 (define @t25 () (@var "Vd121" $$unsorted)) % 0.36/0.57 (define @t26 () (= @t25 (tptp.vplus @t24 @t23))) % 0.36/0.57 (define @t27 () (@list @t23)) % 0.36/0.57 (define @t28 () (exists @t27 @t26)) % 0.36/0.57 (define @t29 () (@var "Vd123" $$unsorted)) % 0.36/0.57 (define @t30 () (= @t24 (tptp.vplus @t25 @t29))) % 0.36/0.57 (define @t31 () (@list @t29)) % 0.36/0.57 (define @t32 () (exists @t31 @t30)) % 0.36/0.57 (define @t33 () (= @t24 @t25)) % 0.36/0.57 (define @t34 () (@list @t24 @t25)) % 0.36/0.57 (define @t35 () (not @t28)) % 0.36/0.57 (define @t36 () (not @t33)) % 0.36/0.57 (define @t37 () (not @t32)) % 0.36/0.57 (define @t38 () (or @t37 @t35)) % 0.36/0.57 (define @t39 () (forall @t34 @t38)) % 0.36/0.57 (define @t40 () (@var "Vd105" $$unsorted)) % 0.36/0.57 (define @t41 () (@var "Vd107" $$unsorted)) % 0.36/0.57 (define @t42 () (@var "Vd104" $$unsorted)) % 0.36/0.57 (define @t43 () (@var "Vd93" $$unsorted)) % 0.36/0.57 (define @t44 () (@var "Vd92" $$unsorted)) % 0.36/0.57 (define @t45 () (@var "Vd79" $$unsorted)) % 0.36/0.57 (define @t46 () (@var "Vd78" $$unsorted)) % 0.36/0.57 (define @t47 () (@var "Vd69" $$unsorted)) % 0.36/0.57 (define @t48 () (@var "Vd68" $$unsorted)) % 0.36/0.57 (define @t49 () (@var "Vd59" $$unsorted)) % 0.36/0.57 (define @t50 () (@var "Vd48" $$unsorted)) % 0.36/0.57 (define @t51 () (@var "Vd47" $$unsorted)) % 0.36/0.57 (define @t52 () (@var "Vd46" $$unsorted)) % 0.36/0.57 (define @t53 () (@var "Vd42" $$unsorted)) % 0.36/0.57 (define @t54 () (@var "Vd43" $$unsorted)) % 0.36/0.57 (define @t55 () (@var "Vd24" $$unsorted)) % 0.36/0.57 (define @t56 () (@var "Vd16" $$unsorted)) % 0.36/0.57 (define @t57 () (@var "Vd8" $$unsorted)) % 0.36/0.57 (define @t58 () (@var "Vd7" $$unsorted)) % 0.36/0.57 (define @t59 () (@var "Vd4" $$unsorted)) % 0.36/0.57 (define @t60 () (@var "Vd3" $$unsorted)) % 0.36/0.57 (define @t61 () (@var "Vd1" $$unsorted)) % 0.36/0.57 (define @t62 () (@var "BOUND_VARIABLE_7632" $$unsorted)) % 0.36/0.57 (define @t63 () (@var "BOUND_VARIABLE_7627" $$unsorted)) % 0.36/0.57 (define @t64 () (tptp.vplus @t25 @t63)) % 0.36/0.57 (define @t65 () (not (= @t25 (tptp.vplus @t64 @t62)))) % 0.36/0.57 (define @t66 () (not (= @t64 @t64))) % 0.36/0.57 (define @t67 () (or @t66 @t65)) % 0.36/0.57 (define @t68 () (@list @t25 @t63 @t62)) % 0.36/0.57 (define @t69 () (not (= @t25 (tptp.vplus @t24 @t62)))) % 0.36/0.57 (define @t70 () (not (= @t24 @t64))) % 0.36/0.57 (define @t71 () (or @t70 @t70 @t69)) % 0.36/0.57 (define @t72 () (@list @t24)) % 0.36/0.57 (define @t73 () (or @t70 @t69)) % 0.36/0.57 (define @t74 () (forall @t72 @t73)) % 0.36/0.57 (define @t75 () (forall @t68 @t74)) % 0.36/0.57 (define @t76 () (forall (@list @t25 @t63 @t62 @t24) @t73)) % 0.36/0.57 (define @t77 () (forall (@list @t24 @t25 @t63 @t62) @t73)) % 0.36/0.57 (define @t78 () (forall (@list @t63 @t62) @t73)) % 0.36/0.57 (define @t79 () (forall (@list @t62) @t69)) % 0.36/0.57 (define @t80 () (forall (@list @t63) @t70)) % 0.36/0.57 (define @t81 () (or @t80 @t79)) % 0.36/0.57 (define @t82 () (forall @t27 (not @t26))) % 0.36/0.57 (define @t83 () (forall @t31 (not @t30))) % 0.36/0.57 (define @t84 () (forall @t9 (not (= tptp.vd204 (tptp.vplus tptp.vd203 @t5))))) % 0.36/0.57 (define @t85 () (@quantifiers_skolemize @t84 0)) % 0.36/0.57 (define @t86 () (@list tptp.vd204 tptp.vd203)) % 0.36/0.57 (define @t87 () (forall @t18 (not (= tptp.vd203 (tptp.vplus tptp.vd204 @t14))))) % 0.36/0.57 (define @t88 () (not @t87)) % 0.36/0.57 (define @t89 () (= @t3 @t88)) % 0.36/0.57 (define @t90 () (@list false false)) % 0.36/0.57 (define @t91 () (@quantifiers_skolemize @t87 0)) % 0.36/0.57 (define @t92 () (tptp.vplus tptp.vd204 @t91)) % 0.36/0.57 (define @t93 () (= tptp.vd203 @t92)) % 0.36/0.57 (define @t94 () (not (not @t93))) % 0.36/0.57 (define @t95 () (@list true)) % 0.36/0.57 (define @t96 () (tptp.vplus tptp.vd203 @t85)) % 0.36/0.57 (define @t97 () (not @t84)) % 0.36/0.57 (define @t98 () (= @t1 @t97)) % 0.36/0.57 (define @t99 () (= tptp.vd204 @t96)) % 0.36/0.57 (define @t100 () (not (not @t99))) % 0.36/0.57 (define @t101 () (forall @t68 @t65)) % 0.36/0.57 (define @t102 () (= tptp.vd204 (tptp.vplus @t92 @t85))) % 0.36/0.57 (assume @p1 (not (or @t4 @t2))) % 0.36/0.57 (assume @p2 (or (not (= tptp.vd203 tptp.vd204)) @t4)) % 0.36/0.57 (assume @p3 @t13) % 0.36/0.57 (assume @p4 @t22) % 0.36/0.57 (assume @p5 (forall @t34 (or @t33 @t32 @t28))) % 0.36/0.57 (assume @p6 (forall @t34 (or @t36 @t35))) % 0.36/0.57 (assume @p7 @t39) % 0.36/0.57 (assume @p8 (forall @t34 (or @t36 @t37))) % 0.36/0.57 (assume @p9 (forall (@list @t42 @t40) (=> (not (= @t42 @t40)) (forall (@list @t41) (not (= (tptp.vplus @t41 @t42) (tptp.vplus @t41 @t40))))))) % 0.36/0.58 (assume @p10 (forall (@list @t44 @t43) (not (= @t43 (tptp.vplus @t44 @t43))))) % 0.36/0.58 (assume @p11 (forall (@list @t46 @t45) (= (tptp.vplus @t45 @t46) (tptp.vplus @t46 @t45)))) % 0.36/0.58 (assume @p12 (forall (@list @t48 @t47) (= (tptp.vplus (tptp.vsucc @t48) @t47) (tptp.vsucc (tptp.vplus @t48 @t47))))) % 0.36/0.58 (assume @p13 (forall (@list @t49) (= (tptp.vplus tptp.v1 @t49) (tptp.vsucc @t49)))) % 0.36/0.58 (assume @p14 (forall (@list @t52 @t51 @t50) (= (tptp.vplus (tptp.vplus @t52 @t51) @t50) (tptp.vplus @t52 (tptp.vplus @t51 @t50))))) % 0.36/0.58 (assume @p15 (forall (@list @t53 @t54) (and (= (tptp.vplus @t53 (tptp.vsucc @t54)) (tptp.vsucc (tptp.vplus @t53 @t54))) (= (tptp.vplus @t53 tptp.v1) (tptp.vsucc @t53))))) % 0.36/0.58 (assume @p16 (forall (@list @t55) (=> (not (= @t55 tptp.v1)) (= @t55 (tptp.vsucc (tptp.vskolem2 @t55)))))) % 0.36/0.58 (assume @p17 (forall (@list @t56) (not (= (tptp.vsucc @t56) @t56)))) % 0.36/0.58 (assume @p18 (forall (@list @t58 @t57) (=> (not (= @t58 @t57)) (not (= (tptp.vsucc @t58) (tptp.vsucc @t57)))))) % 0.36/0.58 (assume @p19 (forall (@list @t60 @t59) (=> (= (tptp.vsucc @t60) (tptp.vsucc @t59)) (= @t60 @t59)))) % 0.36/0.58 (assume @p20 (forall (@list @t61) (not (= (tptp.vsucc @t61) tptp.v1)))) % 0.36/0.58 (assume @p21 true) % 0.36/0.58 (step @p22 :rule aci_norm :args ((= (or false @t65) @t65))) % 0.36/0.58 (step @p23 :rule refl :args (@t65)) % 0.36/0.58 (step @p24 :rule evaluate :args ((not true))) % 0.36/0.58 (step @p25 :rule eq-refl :args (@t64)) % 0.36/0.58 (step @p26 :rule cong :premises (@p25) :args (@t66)) % 0.36/0.58 (step @p27 :rule trans :premises (@p26 @p24)) % 0.36/0.58 (step @p28 :rule nary_cong :premises (@p27 @p23) :args (@t67)) % 0.36/0.58 (step @p29 :rule trans :premises (@p28 @p22)) % 0.36/0.58 (step @p30 :rule cong :premises (@p29) :args ((forall @t68 @t67))) % 0.36/0.58 (step @p31 :rule quant-var-elim-eq :args ((= (forall @t72 @t71) @t67))) % 0.36/0.58 (step @p32 :rule aci_norm :args ((= @t73 @t71))) % 0.36/0.58 (step @p33 :rule cong :premises (@p32) :args (@t74)) % 0.36/0.58 (step @p34 :rule trans :premises (@p33 @p31)) % 0.36/0.58 (step @p35 :rule cong :premises (@p34) :args (@t75)) % 0.36/0.58 (step @p36 :rule quant-merge-prenex :args ((= @t75 @t76))) % 0.36/0.58 (step @p37 :rule symm :premises (@p36)) % 0.36/0.58 (step @p38 :rule quant_var_reordering :args ((= @t77 @t76))) % 0.36/0.58 (step @p39 :rule trans :premises (@p38 @p37 @p35)) % 0.36/0.58 (step @p40 :rule trans :premises (@p39 @p30)) % 0.36/0.58 (step @p41 :rule quant-merge-prenex :args ((= (forall @t34 @t78) @t77))) % 0.36/0.58 (step @p42 :rule alpha_equiv :args (@t79 (@list @t62) (@list @t23))) % 0.36/0.58 (step @p43 :rule alpha_equiv :args (@t80 (@list @t63) (@list @t29))) % 0.36/0.58 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t81)) % 0.36/0.58 (step @p45 :rule quant-miniscope-or :args ((= @t78 @t81))) % 0.36/0.58 (step @p46 :rule trans :premises (@p45 @p44)) % 0.36/0.58 (step @p47 :rule symm :premises (@p46)) % 0.36/0.58 (step @p48 :rule cong :premises (@p47) :args ((forall @t34 (or @t83 @t82)))) % 0.36/0.58 (step @p49 :rule trans :premises (@p48 @p41)) % 0.36/0.58 (step @p50 :rule trans :premises (@p49 @p40)) % 0.36/0.58 (step @p51 :rule bool-double-not-elim :args (@t82)) % 0.36/0.58 (step @p52 :rule exists-elim :args ((= @t28 (not @t82)))) % 0.36/0.58 (step @p53 :rule cong :premises (@p52) :args (@t35)) % 0.36/0.58 (step @p54 :rule trans :premises (@p53 @p51)) % 0.36/0.58 (step @p55 :rule bool-double-not-elim :args (@t83)) % 0.36/0.58 (step @p56 :rule exists-elim :args ((= @t32 (not @t83)))) % 0.36/0.58 (step @p57 :rule cong :premises (@p56) :args (@t37)) % 0.36/0.58 (step @p58 :rule trans :premises (@p57 @p55)) % 0.36/0.58 (step @p59 :rule nary_cong :premises (@p58 @p54) :args (@t38)) % 0.36/0.58 (step @p60 :rule cong :premises (@p59) :args (@t39)) % 0.36/0.58 (step @p61 :rule trans :premises (@p60 @p50)) % 0.36/0.58 (step @p62 :rule eq_resolve :premises (@p7 @p61)) % 0.36/0.58 (step @p63 :rule refl :args (@t85)) % 0.36/0.58 (step @p64 :rule exists-elim :args ((= @t19 (not (forall @t18 (not @t17)))))) % 0.36/0.58 (step @p65 :rule refl :args (@t20)) % 0.36/0.58 (step @p66 :rule cong :premises (@p65 @p64) :args (@t21)) % 0.36/0.58 (step @p67 :rule cong :premises (@p66) :args (@t22)) % 0.36/0.58 (step @p68 :rule eq_resolve :premises (@p4 @p67)) % 0.36/0.58 (step @p69 :rule instantiate :premises (@p68) :args (@t86)) % 0.36/0.58 (step @p70 :rule not_or_elim :premises (@p1) :args (0)) % 0.36/0.58 (step @p71 :rule not_not_elim :premises (@p70)) % 0.36/0.58 (step @p72 :rule cnf_equiv_pos1 :args (@t89)) % 0.36/0.58 (step @p73 :rule reordering :premises (@p72) :args ((or @t4 @t88 (not @t89)))) % 0.36/0.58 (step @p74 :rule chain_m_resolution :premises (@p73 @p71 @p69) :args (@t88 @t90 (@list @t3 @t89))) % 0.36/0.58 (step @p75 :rule refl :args (@t93)) % 0.36/0.58 (step @p76 :rule bool-double-not-elim :args (@t87)) % 0.36/0.58 (step @p77 :rule nary_cong :premises (@p76 @p75) :args ((or (not @t88) @t93))) % 0.36/0.58 (step @p78 :rule bool-double-not-elim :args (@t93)) % 0.36/0.58 (step @p79 :rule refl :args (@t88)) % 0.36/0.58 (step @p80 :rule cong :premises (@p79 @p78) :args ((=> @t88 @t94))) % 0.36/0.58 (assume-push @p122 @t88) % 0.36/0.58 (step @p82 :rule skolemize :premises (@p74)) % 0.36/0.58 (step-pop @p123 :rule scope :premises (@p82)) % 0.36/0.58 (step @p83 :rule process_scope :premises (@p123) :args (@t94)) % 0.36/0.58 (step @p85 :rule eq_resolve :premises (@p83 @p80)) % 0.36/0.58 (step @p86 :rule implies_elim :premises (@p85)) % 0.36/0.58 (step @p87 :rule eq_resolve :premises (@p86 @p77)) % 0.36/0.58 (step @p88 :rule chain_m_resolution :premises (@p87 @p74) :args (@t93 @t95 (@list @t87))) % 0.36/0.58 (step @p89 :rule cong :premises (@p88 @p63) :args (@t96)) % 0.36/0.58 (step @p90 :rule exists-elim :args ((= @t10 (not (forall @t9 (not @t8)))))) % 0.36/0.58 (step @p91 :rule refl :args (@t11)) % 0.36/0.58 (step @p92 :rule cong :premises (@p91 @p90) :args (@t12)) % 0.36/0.58 (step @p93 :rule cong :premises (@p92) :args (@t13)) % 0.36/0.58 (step @p94 :rule eq_resolve :premises (@p3 @p93)) % 0.36/0.58 (step @p95 :rule instantiate :premises (@p94) :args (@t86)) % 0.36/0.58 (step @p96 :rule not_or_elim :premises (@p1) :args (1)) % 0.36/0.58 (step @p97 :rule not_not_elim :premises (@p96)) % 0.36/0.58 (step @p98 :rule cnf_equiv_pos1 :args (@t98)) % 0.36/0.58 (step @p99 :rule reordering :premises (@p98) :args ((or @t2 @t97 (not @t98)))) % 0.36/0.58 (step @p100 :rule chain_m_resolution :premises (@p99 @p97 @p95) :args (@t97 @t90 (@list @t1 @t98))) % 0.36/0.58 (step @p101 :rule refl :args (@t99)) % 0.36/0.58 (step @p102 :rule bool-double-not-elim :args (@t84)) % 0.36/0.58 (step @p103 :rule nary_cong :premises (@p102 @p101) :args ((or (not @t97) @t99))) % 0.36/0.58 (step @p104 :rule bool-double-not-elim :args (@t99)) % 0.36/0.58 (step @p105 :rule refl :args (@t97)) % 0.36/0.58 (step @p106 :rule cong :premises (@p105 @p104) :args ((=> @t97 @t100))) % 0.36/0.58 (assume-push @p124 @t97) % 0.36/0.58 (step @p108 :rule skolemize :premises (@p100)) % 0.36/0.58 (step-pop @p125 :rule scope :premises (@p108)) % 0.36/0.58 (step @p109 :rule process_scope :premises (@p125) :args (@t100)) % 0.36/0.58 (step @p111 :rule eq_resolve :premises (@p109 @p106)) % 0.36/0.58 (step @p112 :rule implies_elim :premises (@p111)) % 0.36/0.58 (step @p113 :rule eq_resolve :premises (@p112 @p103)) % 0.36/0.58 (step @p114 :rule chain_m_resolution :premises (@p113 @p100) :args (@t99 @t95 (@list @t84))) % 0.36/0.58 (step @p115 :rule trans :premises (@p114 @p89)) % 0.36/0.58 (assume-push @p126 @t101) % 0.36/0.58 (step @p117 :rule instantiate :premises (@p62) :args ((@list tptp.vd204 @t91 @t85))) % 0.36/0.58 (step-pop @p127 :rule scope :premises (@p117)) % 0.36/0.58 (step @p118 :rule process_scope :premises (@p127) :args ((not @t102))) % 0.36/0.58 (step @p120 :rule implies_elim :premises (@p118)) % 0.36/0.58 (step @p121 false :rule chain_m_resolution :premises (@p120 @p115 @p62) :args (false @t90 (@list @t102 @t101))) % 0.36/0.58 ) % 0.36/0.58 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------