%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM843+2 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 08:40:48 AM UTC 2026 % Result : Theorem 0.38s 0.59s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM843+2 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n009.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 12:29:14 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.59 % SZS status Theorem % 0.38/0.59 % SZS output start Proof % 0.38/0.59 ( % 0.38/0.59 (declare-sort $$unsorted 0) % 0.38/0.59 (declare-const tptp.vskolem2 (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.vsucc (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.less (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.vplus (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.v1 $$unsorted) % 0.38/0.59 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.vd390 $$unsorted) % 0.38/0.59 (declare-const tptp.vd391 $$unsorted) % 0.38/0.59 (define @t1 () (tptp.greater tptp.vd390 tptp.vd391)) % 0.38/0.59 (define @t2 () (tptp.leq tptp.vd390 tptp.vd391)) % 0.38/0.59 (define @t3 () (@var "Vd376" $$unsorted)) % 0.38/0.59 (define @t4 () (@var "Vd375" $$unsorted)) % 0.38/0.59 (define @t5 () (@var "Vd369" $$unsorted)) % 0.38/0.59 (define @t6 () (@var "Vd366" $$unsorted)) % 0.38/0.59 (define @t7 () (@var "Vd363" $$unsorted)) % 0.38/0.59 (define @t8 () (@var "Vd365" $$unsorted)) % 0.38/0.59 (define @t9 () (@var "Vd362" $$unsorted)) % 0.38/0.59 (define @t10 () (@var "Vd356" $$unsorted)) % 0.38/0.59 (define @t11 () (@var "Vd354" $$unsorted)) % 0.38/0.59 (define @t12 () (@var "Vd355" $$unsorted)) % 0.38/0.59 (define @t13 () (@var "Vd353" $$unsorted)) % 0.38/0.59 (define @t14 () (@var "Vd341" $$unsorted)) % 0.38/0.59 (define @t15 () (@var "Vd338" $$unsorted)) % 0.38/0.59 (define @t16 () (@var "Vd340" $$unsorted)) % 0.38/0.59 (define @t17 () (@var "Vd337" $$unsorted)) % 0.38/0.59 (define @t18 () (@var "Vd329" $$unsorted)) % 0.38/0.59 (define @t19 () (@var "Vd328" $$unsorted)) % 0.38/0.59 (define @t20 () (@var "Vd330" $$unsorted)) % 0.38/0.59 (define @t21 () (tptp.vplus @t18 @t20)) % 0.38/0.59 (define @t22 () (tptp.vplus @t19 @t20)) % 0.38/0.59 (define @t23 () (@list @t19 @t18 @t20)) % 0.38/0.59 (define @t24 () (@var "Vd303" $$unsorted)) % 0.38/0.59 (define @t25 () (@var "Vd302" $$unsorted)) % 0.38/0.59 (define @t26 () (tptp.vplus @t25 @t24)) % 0.38/0.59 (define @t27 () (@var "Vd301" $$unsorted)) % 0.38/0.59 (define @t28 () (tptp.vplus @t27 @t24)) % 0.38/0.59 (define @t29 () (@list @t27 @t25 @t24)) % 0.38/0.59 (define @t30 () (@var "Vd295" $$unsorted)) % 0.38/0.59 (define @t31 () (@var "Vd296" $$unsorted)) % 0.38/0.59 (define @t32 () (@var "Vd292" $$unsorted)) % 0.38/0.59 (define @t33 () (@var "Vd289" $$unsorted)) % 0.38/0.59 (define @t34 () (@var "Vd290" $$unsorted)) % 0.38/0.59 (define @t35 () (@var "Vd283" $$unsorted)) % 0.38/0.59 (define @t36 () (@var "Vd281" $$unsorted)) % 0.38/0.59 (define @t37 () (@var "Vd282" $$unsorted)) % 0.38/0.59 (define @t38 () (@var "Vd265" $$unsorted)) % 0.38/0.59 (define @t39 () (@var "Vd262" $$unsorted)) % 0.38/0.59 (define @t40 () (@var "Vd263" $$unsorted)) % 0.38/0.59 (define @t41 () (@var "Vd258" $$unsorted)) % 0.38/0.59 (define @t42 () (@var "Vd259" $$unsorted)) % 0.38/0.59 (define @t43 () (@var "Vd254" $$unsorted)) % 0.38/0.59 (define @t44 () (@var "Vd255" $$unsorted)) % 0.38/0.59 (define @t45 () (@var "Vd249" $$unsorted)) % 0.38/0.59 (define @t46 () (@var "Vd250" $$unsorted)) % 0.38/0.59 (define @t47 () (tptp.less @t46 @t45)) % 0.38/0.59 (define @t48 () (or @t47 (= @t46 @t45))) % 0.38/0.59 (define @t49 () (tptp.leq @t46 @t45)) % 0.38/0.59 (define @t50 () (= @t49 @t48)) % 0.38/0.59 (define @t51 () (@list @t45 @t46)) % 0.38/0.59 (define @t52 () (forall @t51 @t50)) % 0.38/0.59 (define @t53 () (@var "Vd244" $$unsorted)) % 0.38/0.59 (define @t54 () (@var "Vd245" $$unsorted)) % 0.38/0.59 (define @t55 () (@var "Vd226" $$unsorted)) % 0.38/0.59 (define @t56 () (@var "Vd227" $$unsorted)) % 0.38/0.59 (define @t57 () (@var "Vd208" $$unsorted)) % 0.38/0.59 (define @t58 () (@var "Vd209" $$unsorted)) % 0.38/0.59 (define @t59 () (@var "Vd204" $$unsorted)) % 0.38/0.59 (define @t60 () (@var "Vd203" $$unsorted)) % 0.38/0.59 (define @t61 () (tptp.less @t60 @t59)) % 0.38/0.59 (define @t62 () (tptp.greater @t60 @t59)) % 0.38/0.59 (define @t63 () (= @t60 @t59)) % 0.38/0.59 (define @t64 () (@list @t60 @t59)) % 0.38/0.59 (define @t65 () (not @t61)) % 0.38/0.59 (define @t66 () (not @t63)) % 0.38/0.59 (define @t67 () (not @t62)) % 0.38/0.59 (define @t68 () (@var "Vd201" $$unsorted)) % 0.38/0.59 (define @t69 () (@var "Vd199" $$unsorted)) % 0.38/0.59 (define @t70 () (@var "Vd198" $$unsorted)) % 0.38/0.59 (define @t71 () (@var "Vd196" $$unsorted)) % 0.38/0.59 (define @t72 () (@var "Vd193" $$unsorted)) % 0.38/0.59 (define @t73 () (@var "Vd194" $$unsorted)) % 0.38/0.59 (define @t74 () (@var "Vd125" $$unsorted)) % 0.38/0.59 (define @t75 () (@var "Vd120" $$unsorted)) % 0.38/0.59 (define @t76 () (@var "Vd121" $$unsorted)) % 0.38/0.59 (define @t77 () (exists (@list @t74) (= @t76 (tptp.vplus @t75 @t74)))) % 0.38/0.59 (define @t78 () (@var "Vd123" $$unsorted)) % 0.38/0.59 (define @t79 () (exists (@list @t78) (= @t75 (tptp.vplus @t76 @t78)))) % 0.38/0.59 (define @t80 () (= @t75 @t76)) % 0.38/0.59 (define @t81 () (@list @t75 @t76)) % 0.38/0.59 (define @t82 () (not @t77)) % 0.38/0.59 (define @t83 () (not @t80)) % 0.38/0.59 (define @t84 () (not @t79)) % 0.38/0.59 (define @t85 () (@var "Vd105" $$unsorted)) % 0.38/0.59 (define @t86 () (@var "Vd107" $$unsorted)) % 0.38/0.59 (define @t87 () (@var "Vd104" $$unsorted)) % 0.38/0.59 (define @t88 () (@var "Vd93" $$unsorted)) % 0.38/0.59 (define @t89 () (@var "Vd92" $$unsorted)) % 0.38/0.59 (define @t90 () (@var "Vd79" $$unsorted)) % 0.38/0.59 (define @t91 () (@var "Vd78" $$unsorted)) % 0.38/0.59 (define @t92 () (@var "Vd69" $$unsorted)) % 0.38/0.59 (define @t93 () (@var "Vd68" $$unsorted)) % 0.38/0.59 (define @t94 () (@var "Vd59" $$unsorted)) % 0.38/0.59 (define @t95 () (@var "Vd48" $$unsorted)) % 0.38/0.59 (define @t96 () (@var "Vd47" $$unsorted)) % 0.38/0.59 (define @t97 () (@var "Vd46" $$unsorted)) % 0.38/0.59 (define @t98 () (@var "Vd42" $$unsorted)) % 0.38/0.59 (define @t99 () (@var "Vd43" $$unsorted)) % 0.38/0.59 (define @t100 () (@var "Vd24" $$unsorted)) % 0.38/0.59 (define @t101 () (@var "Vd16" $$unsorted)) % 0.38/0.59 (define @t102 () (@var "Vd8" $$unsorted)) % 0.38/0.59 (define @t103 () (@var "Vd7" $$unsorted)) % 0.38/0.59 (define @t104 () (@var "Vd4" $$unsorted)) % 0.38/0.59 (define @t105 () (@var "Vd3" $$unsorted)) % 0.38/0.59 (define @t106 () (@var "Vd1" $$unsorted)) % 0.38/0.59 (define @t107 () (tptp.less tptp.vd390 tptp.vd391)) % 0.38/0.59 (define @t108 () (or @t107 (= tptp.vd391 tptp.vd390))) % 0.38/0.59 (define @t109 () (= @t2 @t108)) % 0.38/0.59 (define @t110 () (forall @t51 (= @t49 (or @t47 (= @t45 @t46))))) % 0.38/0.59 (define @t111 () (= tptp.vd390 tptp.vd391)) % 0.38/0.59 (define @t112 () (or @t107 @t111)) % 0.38/0.59 (define @t113 () (= @t2 @t112)) % 0.38/0.59 (define @t114 () (not @t112)) % 0.38/0.59 (define @t115 () (@list true)) % 0.38/0.59 (define @t116 () (@list @t112)) % 0.38/0.59 (define @t117 () (or @t111 @t1 @t107)) % 0.38/0.59 (assume @p1 (not @t1)) % 0.38/0.59 (assume @p2 (not @t2)) % 0.38/0.59 (assume @p3 (tptp.less tptp.vd390 (tptp.vplus tptp.vd391 tptp.v1))) % 0.38/0.59 (assume @p4 (forall (@list @t4 @t3) (=> (tptp.greater @t4 @t3) (tptp.geq @t4 (tptp.vplus @t3 tptp.v1))))) % 0.38/0.59 (assume @p5 (forall (@list @t5) (tptp.geq @t5 tptp.v1))) % 0.38/0.59 (assume @p6 (forall (@list @t9 @t7 @t8 @t6) (=> (and (tptp.geq @t8 @t6) (tptp.geq @t9 @t7)) (tptp.geq (tptp.vplus @t9 @t8) (tptp.vplus @t7 @t6))))) % 0.38/0.59 (assume @p7 (forall (@list @t13 @t11 @t12 @t10) (=> (or (and (tptp.greater @t12 @t10) (tptp.geq @t13 @t11)) (and (tptp.geq @t12 @t10) (tptp.greater @t13 @t11))) (tptp.greater (tptp.vplus @t13 @t12) (tptp.vplus @t11 @t10))))) % 0.38/0.59 (assume @p8 (forall (@list @t17 @t15 @t16 @t14) (=> (and (tptp.greater @t16 @t14) (tptp.greater @t17 @t15)) (tptp.greater (tptp.vplus @t17 @t16) (tptp.vplus @t15 @t14))))) % 0.38/0.59 (assume @p9 (forall @t23 (=> (tptp.less @t22 @t21) (tptp.less @t19 @t18)))) % 0.38/0.59 (assume @p10 (forall @t23 (=> (= @t22 @t21) (= @t19 @t18)))) % 0.38/0.59 (assume @p11 (forall @t23 (=> (tptp.greater @t22 @t21) (tptp.greater @t19 @t18)))) % 0.38/0.59 (assume @p12 (forall @t29 (=> (tptp.less @t27 @t25) (tptp.less @t28 @t26)))) % 0.38/0.59 (assume @p13 (forall @t29 (=> (= @t27 @t25) (= @t28 @t26)))) % 0.38/0.59 (assume @p14 (forall @t29 (=> (tptp.greater @t27 @t25) (tptp.greater @t28 @t26)))) % 0.38/0.59 (assume @p15 (forall (@list @t30 @t31) (tptp.greater (tptp.vplus @t30 @t31) @t30))) % 0.38/0.59 (assume @p16 (forall (@list @t33 @t34 @t32) (=> (and (tptp.leq @t34 @t32) (tptp.leq @t33 @t34)) (tptp.leq @t33 @t32)))) % 0.38/0.59 (assume @p17 (forall (@list @t36 @t37 @t35) (=> (or (and (tptp.less @t37 @t35) (tptp.leq @t36 @t37)) (and (tptp.leq @t37 @t35) (tptp.less @t36 @t37))) (tptp.less @t36 @t35)))) % 0.38/0.59 (assume @p18 (forall (@list @t39 @t40 @t38) (=> (and (tptp.less @t40 @t38) (tptp.less @t39 @t40)) (tptp.less @t39 @t38)))) % 0.38/0.59 (assume @p19 (forall (@list @t41 @t42) (=> (tptp.leq @t41 @t42) (tptp.geq @t42 @t41)))) % 0.38/0.59 (assume @p20 (forall (@list @t43 @t44) (=> (tptp.geq @t43 @t44) (tptp.leq @t44 @t43)))) % 0.38/0.59 (assume @p21 @t52) % 0.38/0.59 (assume @p22 (forall (@list @t53 @t54) (= (tptp.geq @t54 @t53) (or (tptp.greater @t54 @t53) (= @t54 @t53))))) % 0.38/0.59 (assume @p23 (forall (@list @t55 @t56) (=> (tptp.less @t55 @t56) (tptp.greater @t56 @t55)))) % 0.38/0.59 (assume @p24 (forall (@list @t57 @t58) (=> (tptp.greater @t57 @t58) (tptp.less @t58 @t57)))) % 0.38/0.59 (assume @p25 (forall @t64 (or @t63 @t62 @t61))) % 0.38/0.59 (assume @p26 (forall @t64 (or @t66 @t65))) % 0.38/0.59 (assume @p27 (forall @t64 (or @t67 @t65))) % 0.38/0.59 (assume @p28 (forall @t64 (or @t66 @t67))) % 0.38/0.59 (assume @p29 (forall (@list @t70 @t69) (= (tptp.less @t69 @t70) (exists (@list @t68) (= @t70 (tptp.vplus @t69 @t68)))))) % 0.38/0.59 (assume @p30 (forall (@list @t72 @t73) (= (tptp.greater @t73 @t72) (exists (@list @t71) (= @t73 (tptp.vplus @t72 @t71)))))) % 0.38/0.59 (assume @p31 (forall @t81 (or @t80 @t79 @t77))) % 0.38/0.59 (assume @p32 (forall @t81 (or @t83 @t82))) % 0.38/0.59 (assume @p33 (forall @t81 (or @t84 @t82))) % 0.38/0.59 (assume @p34 (forall @t81 (or @t83 @t84))) % 0.38/0.59 (assume @p35 (forall (@list @t87 @t85) (=> (not (= @t87 @t85)) (forall (@list @t86) (not (= (tptp.vplus @t86 @t87) (tptp.vplus @t86 @t85))))))) % 0.38/0.59 (assume @p36 (forall (@list @t89 @t88) (not (= @t88 (tptp.vplus @t89 @t88))))) % 0.38/0.59 (assume @p37 (forall (@list @t91 @t90) (= (tptp.vplus @t90 @t91) (tptp.vplus @t91 @t90)))) % 0.38/0.59 (assume @p38 (forall (@list @t93 @t92) (= (tptp.vplus (tptp.vsucc @t93) @t92) (tptp.vsucc (tptp.vplus @t93 @t92))))) % 0.38/0.59 (assume @p39 (forall (@list @t94) (= (tptp.vplus tptp.v1 @t94) (tptp.vsucc @t94)))) % 0.38/0.59 (assume @p40 (forall (@list @t97 @t96 @t95) (= (tptp.vplus (tptp.vplus @t97 @t96) @t95) (tptp.vplus @t97 (tptp.vplus @t96 @t95))))) % 0.38/0.59 (assume @p41 (forall (@list @t98 @t99) (and (= (tptp.vplus @t98 (tptp.vsucc @t99)) (tptp.vsucc (tptp.vplus @t98 @t99))) (= (tptp.vplus @t98 tptp.v1) (tptp.vsucc @t98))))) % 0.38/0.59 (assume @p42 (forall (@list @t100) (=> (not (= @t100 tptp.v1)) (= @t100 (tptp.vsucc (tptp.vskolem2 @t100)))))) % 0.38/0.59 (assume @p43 (forall (@list @t101) (not (= (tptp.vsucc @t101) @t101)))) % 0.38/0.59 (assume @p44 (forall (@list @t103 @t102) (=> (not (= @t103 @t102)) (not (= (tptp.vsucc @t103) (tptp.vsucc @t102)))))) % 0.38/0.59 (assume @p45 (forall (@list @t105 @t104) (=> (= (tptp.vsucc @t105) (tptp.vsucc @t104)) (= @t105 @t104)))) % 0.38/0.59 (assume @p46 (forall (@list @t106) (not (= (tptp.vsucc @t106) tptp.v1)))) % 0.38/0.59 (assume @p47 true) % 0.38/0.59 (step @p48 :rule instantiate :premises (@p25) :args ((@list tptp.vd390 tptp.vd391))) % 0.38/0.59 (step @p49 :rule eq-symm :args (@t46 @t45)) % 0.38/0.59 (step @p50 :rule refl :args (@t47)) % 0.38/0.59 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t48)) % 0.38/0.59 (step @p52 :rule refl :args (@t49)) % 0.38/0.59 (step @p53 :rule cong :premises (@p52 @p51) :args (@t50)) % 0.38/0.59 (step @p54 :rule cong :premises (@p53) :args (@t52)) % 0.38/0.59 (step @p55 :rule eq_resolve :premises (@p21 @p54)) % 0.38/0.59 (step @p56 :rule eq-symm :args (tptp.vd391 tptp.vd390)) % 0.38/0.59 (step @p57 :rule refl :args (@t107)) % 0.38/0.59 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t108)) % 0.38/0.59 (step @p59 :rule refl :args (@t2)) % 0.38/0.59 (step @p60 :rule cong :premises (@p59 @p58) :args (@t109)) % 0.38/0.59 (step @p61 :rule refl :args (@t110)) % 0.38/0.59 (step @p62 :rule cong :premises (@p61 @p60) :args ((=> @t110 @t109))) % 0.38/0.59 (assume-push @p80 @t110) % 0.38/0.59 (step @p64 :rule instantiate :premises (@p55) :args ((@list tptp.vd391 tptp.vd390))) % 0.38/0.59 (step-pop @p81 :rule scope :premises (@p64)) % 0.38/0.59 (step @p65 :rule process_scope :premises (@p81) :args (@t109)) % 0.38/0.59 (step @p67 :rule eq_resolve :premises (@p65 @p62)) % 0.38/0.59 (step @p68 :rule implies_elim :premises (@p67)) % 0.38/0.59 (step @p69 :rule chain_m_resolution :premises (@p68 @p55) :args (@t113 (@list false) (@list @t110))) % 0.38/0.59 (step @p70 :rule cnf_equiv_pos2 :args (@t113)) % 0.38/0.59 (step @p71 :rule reordering :premises (@p70) :args ((or @t2 @t114 (not @t113)))) % 0.38/0.59 (step @p72 :rule chain_m_resolution :premises (@p71 @p2 @p69) :args (@t114 (@list true false) (@list @t2 @t113))) % 0.38/0.59 (step @p73 :rule cnf_or_neg :args (@t112 0)) % 0.38/0.59 (step @p74 :rule chain_m_resolution :premises (@p73 @p72) :args ((not @t107) @t115 @t116)) % 0.38/0.59 (step @p75 :rule cnf_or_neg :args (@t112 1)) % 0.38/0.59 (step @p76 :rule chain_m_resolution :premises (@p75 @p72) :args ((not @t111) @t115 @t116)) % 0.38/0.59 (step @p77 :rule cnf_or_pos :args (@t117)) % 0.38/0.59 (step @p78 :rule reordering :premises (@p77) :args ((or @t1 @t107 @t111 (not @t117)))) % 0.38/0.59 (step @p79 false :rule chain_m_resolution :premises (@p78 @p76 @p74 @p48 @p1) :args (false (@list true true false true) (@list @t111 @t107 @t117 @t1))) % 0.38/0.59 ) % 0.38/0.59 % SZS output end Proof % 0.38/0.59 % cvc5 exiting %------------------------------------------------------------------------------