%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM851+1 : 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 : n013.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 08:40:49 AM UTC 2026 % Result : Theorem 0.40s 0.59s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM851+1 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n013.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 12:29:45 EDT 2026 % 0.17/0.34 % CPUTime : % 0.32/0.50 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.59 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.59 % SZS status Theorem % 0.40/0.59 % SZS output start Proof % 0.40/0.59 ( % 0.40/0.59 (declare-sort $$unsorted 0) % 0.40/0.59 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.v1 $$unsorted) % 0.40/0.59 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.less (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.vd470 $$unsorted) % 0.40/0.59 (declare-const tptp.vplus (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.vskolem2 (-> $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.vd471 $$unsorted) % 0.40/0.59 (declare-const tptp.vsucc (-> $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.vmul (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.59 (declare-const tptp.vd473 $$unsorted) % 0.40/0.59 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.40/0.59 (declare-const tptp.vd469 $$unsorted) % 0.40/0.59 (define @t1 () (tptp.vplus tptp.vd471 tptp.vd473)) % 0.40/0.59 (define @t2 () (tptp.vmul @t1 tptp.vd469)) % 0.40/0.59 (define @t3 () (@var "Vd446" $$unsorted)) % 0.40/0.59 (define @t4 () (@var "Vd445" $$unsorted)) % 0.40/0.59 (define @t5 () (@var "Vd444" $$unsorted)) % 0.40/0.59 (define @t6 () (@var "Vd434" $$unsorted)) % 0.40/0.59 (define @t7 () (@var "Vd432" $$unsorted)) % 0.40/0.59 (define @t8 () (@var "Vd433" $$unsorted)) % 0.40/0.59 (define @t9 () (forall (@list @t7 @t8 @t6) (= (tptp.vmul @t7 (tptp.vplus @t8 @t6)) (tptp.vplus (tptp.vmul @t7 @t8) (tptp.vmul @t7 @t6))))) % 0.40/0.59 (define @t10 () (@var "Vd418" $$unsorted)) % 0.40/0.59 (define @t11 () (@var "Vd419" $$unsorted)) % 0.40/0.59 (define @t12 () (@var "Vd409" $$unsorted)) % 0.40/0.59 (define @t13 () (@var "Vd408" $$unsorted)) % 0.40/0.59 (define @t14 () (@var "Vd400" $$unsorted)) % 0.40/0.59 (define @t15 () (@var "Vd396" $$unsorted)) % 0.40/0.59 (define @t16 () (@var "Vd397" $$unsorted)) % 0.40/0.59 (define @t17 () (@var "Vd387" $$unsorted)) % 0.40/0.59 (define @t18 () (@var "Vd386" $$unsorted)) % 0.40/0.59 (define @t19 () (@var "Vd376" $$unsorted)) % 0.40/0.59 (define @t20 () (@var "Vd375" $$unsorted)) % 0.40/0.59 (define @t21 () (@var "Vd369" $$unsorted)) % 0.40/0.59 (define @t22 () (@var "Vd366" $$unsorted)) % 0.40/0.59 (define @t23 () (@var "Vd363" $$unsorted)) % 0.40/0.59 (define @t24 () (@var "Vd365" $$unsorted)) % 0.40/0.59 (define @t25 () (@var "Vd362" $$unsorted)) % 0.40/0.59 (define @t26 () (@var "Vd356" $$unsorted)) % 0.40/0.59 (define @t27 () (@var "Vd354" $$unsorted)) % 0.40/0.59 (define @t28 () (@var "Vd355" $$unsorted)) % 0.40/0.59 (define @t29 () (@var "Vd353" $$unsorted)) % 0.40/0.59 (define @t30 () (@var "Vd341" $$unsorted)) % 0.40/0.59 (define @t31 () (@var "Vd338" $$unsorted)) % 0.40/0.59 (define @t32 () (@var "Vd340" $$unsorted)) % 0.40/0.59 (define @t33 () (@var "Vd337" $$unsorted)) % 0.40/0.59 (define @t34 () (@var "Vd329" $$unsorted)) % 0.40/0.59 (define @t35 () (@var "Vd328" $$unsorted)) % 0.40/0.59 (define @t36 () (@var "Vd330" $$unsorted)) % 0.40/0.59 (define @t37 () (tptp.vplus @t34 @t36)) % 0.40/0.59 (define @t38 () (tptp.vplus @t35 @t36)) % 0.40/0.59 (define @t39 () (@list @t35 @t34 @t36)) % 0.40/0.59 (define @t40 () (@var "Vd303" $$unsorted)) % 0.40/0.59 (define @t41 () (@var "Vd302" $$unsorted)) % 0.40/0.59 (define @t42 () (tptp.vplus @t41 @t40)) % 0.40/0.59 (define @t43 () (@var "Vd301" $$unsorted)) % 0.40/0.59 (define @t44 () (tptp.vplus @t43 @t40)) % 0.40/0.59 (define @t45 () (@list @t43 @t41 @t40)) % 0.40/0.59 (define @t46 () (@var "Vd295" $$unsorted)) % 0.40/0.59 (define @t47 () (@var "Vd296" $$unsorted)) % 0.40/0.59 (define @t48 () (@var "Vd292" $$unsorted)) % 0.40/0.59 (define @t49 () (@var "Vd289" $$unsorted)) % 0.40/0.59 (define @t50 () (@var "Vd290" $$unsorted)) % 0.40/0.59 (define @t51 () (@var "Vd283" $$unsorted)) % 0.40/0.59 (define @t52 () (@var "Vd281" $$unsorted)) % 0.40/0.59 (define @t53 () (@var "Vd282" $$unsorted)) % 0.40/0.59 (define @t54 () (@var "Vd265" $$unsorted)) % 0.40/0.59 (define @t55 () (@var "Vd262" $$unsorted)) % 0.40/0.59 (define @t56 () (@var "Vd263" $$unsorted)) % 0.40/0.59 (define @t57 () (@var "Vd258" $$unsorted)) % 0.40/0.59 (define @t58 () (@var "Vd259" $$unsorted)) % 0.40/0.59 (define @t59 () (@var "Vd254" $$unsorted)) % 0.40/0.59 (define @t60 () (@var "Vd255" $$unsorted)) % 0.40/0.59 (define @t61 () (@var "Vd249" $$unsorted)) % 0.40/0.59 (define @t62 () (@var "Vd250" $$unsorted)) % 0.40/0.59 (define @t63 () (@var "Vd244" $$unsorted)) % 0.40/0.59 (define @t64 () (@var "Vd245" $$unsorted)) % 0.40/0.59 (define @t65 () (@var "Vd226" $$unsorted)) % 0.40/0.59 (define @t66 () (@var "Vd227" $$unsorted)) % 0.40/0.59 (define @t67 () (@var "Vd208" $$unsorted)) % 0.40/0.59 (define @t68 () (@var "Vd209" $$unsorted)) % 0.40/0.59 (define @t69 () (@var "Vd204" $$unsorted)) % 0.40/0.59 (define @t70 () (@var "Vd203" $$unsorted)) % 0.40/0.59 (define @t71 () (tptp.less @t70 @t69)) % 0.40/0.59 (define @t72 () (tptp.greater @t70 @t69)) % 0.40/0.59 (define @t73 () (= @t70 @t69)) % 0.40/0.59 (define @t74 () (@list @t70 @t69)) % 0.40/0.59 (define @t75 () (not @t71)) % 0.40/0.59 (define @t76 () (not @t73)) % 0.40/0.59 (define @t77 () (not @t72)) % 0.40/0.59 (define @t78 () (@var "Vd201" $$unsorted)) % 0.40/0.59 (define @t79 () (@var "Vd199" $$unsorted)) % 0.40/0.59 (define @t80 () (@var "Vd198" $$unsorted)) % 0.40/0.59 (define @t81 () (@var "Vd196" $$unsorted)) % 0.40/0.59 (define @t82 () (@var "Vd193" $$unsorted)) % 0.40/0.59 (define @t83 () (@var "Vd194" $$unsorted)) % 0.40/0.59 (define @t84 () (@var "Vd125" $$unsorted)) % 0.40/0.59 (define @t85 () (@var "Vd120" $$unsorted)) % 0.40/0.59 (define @t86 () (@var "Vd121" $$unsorted)) % 0.40/0.59 (define @t87 () (exists (@list @t84) (= @t86 (tptp.vplus @t85 @t84)))) % 0.40/0.59 (define @t88 () (@var "Vd123" $$unsorted)) % 0.40/0.59 (define @t89 () (exists (@list @t88) (= @t85 (tptp.vplus @t86 @t88)))) % 0.40/0.59 (define @t90 () (= @t85 @t86)) % 0.40/0.59 (define @t91 () (@list @t85 @t86)) % 0.40/0.59 (define @t92 () (not @t87)) % 0.40/0.59 (define @t93 () (not @t90)) % 0.40/0.59 (define @t94 () (not @t89)) % 0.40/0.59 (define @t95 () (@var "Vd105" $$unsorted)) % 0.40/0.59 (define @t96 () (@var "Vd107" $$unsorted)) % 0.40/0.59 (define @t97 () (@var "Vd104" $$unsorted)) % 0.40/0.59 (define @t98 () (@var "Vd93" $$unsorted)) % 0.40/0.59 (define @t99 () (@var "Vd92" $$unsorted)) % 0.40/0.59 (define @t100 () (@var "Vd79" $$unsorted)) % 0.40/0.59 (define @t101 () (@var "Vd78" $$unsorted)) % 0.40/0.59 (define @t102 () (@var "Vd69" $$unsorted)) % 0.40/0.59 (define @t103 () (@var "Vd68" $$unsorted)) % 0.40/0.59 (define @t104 () (@var "Vd59" $$unsorted)) % 0.40/0.59 (define @t105 () (@var "Vd48" $$unsorted)) % 0.40/0.59 (define @t106 () (@var "Vd47" $$unsorted)) % 0.40/0.59 (define @t107 () (@var "Vd46" $$unsorted)) % 0.40/0.59 (define @t108 () (@var "Vd42" $$unsorted)) % 0.40/0.59 (define @t109 () (@var "Vd43" $$unsorted)) % 0.40/0.59 (define @t110 () (@var "Vd24" $$unsorted)) % 0.40/0.59 (define @t111 () (@var "Vd16" $$unsorted)) % 0.40/0.59 (define @t112 () (@var "Vd8" $$unsorted)) % 0.40/0.59 (define @t113 () (@var "Vd7" $$unsorted)) % 0.40/0.59 (define @t114 () (@var "Vd4" $$unsorted)) % 0.40/0.59 (define @t115 () (@var "Vd3" $$unsorted)) % 0.40/0.59 (define @t116 () (@var "Vd1" $$unsorted)) % 0.40/0.59 (define @t117 () (tptp.vplus (tptp.vmul tptp.vd469 tptp.vd471) (tptp.vmul tptp.vd469 tptp.vd473))) % 0.40/0.59 (define @t118 () (= (tptp.vmul tptp.vd469 @t1) @t117)) % 0.40/0.59 (assume @p1 (not (= @t2 (tptp.vplus (tptp.vmul tptp.vd471 tptp.vd469) (tptp.vmul tptp.vd473 tptp.vd469))))) % 0.40/0.59 (assume @p2 (= (tptp.vmul tptp.vd470 tptp.vd469) @t2)) % 0.40/0.59 (assume @p3 (= tptp.vd470 @t1)) % 0.40/0.59 (assume @p4 (tptp.greater tptp.vd470 tptp.vd471)) % 0.40/0.59 (assume @p5 (forall (@list @t5 @t4 @t3) (= (tptp.vmul (tptp.vmul @t5 @t4) @t3) (tptp.vmul @t5 (tptp.vmul @t4 @t3))))) % 0.40/0.59 (assume @p6 @t9) % 0.40/0.59 (assume @p7 (forall (@list @t10 @t11) (= (tptp.vmul @t10 @t11) (tptp.vmul @t11 @t10)))) % 0.40/0.59 (assume @p8 (forall (@list @t13 @t12) (= (tptp.vmul (tptp.vsucc @t13) @t12) (tptp.vplus (tptp.vmul @t13 @t12) @t12)))) % 0.40/0.59 (assume @p9 (forall (@list @t14) (= (tptp.vmul tptp.v1 @t14) @t14))) % 0.40/0.59 (assume @p10 (forall (@list @t15 @t16) (and (= (tptp.vmul @t15 (tptp.vsucc @t16)) (tptp.vplus (tptp.vmul @t15 @t16) @t15)) (= (tptp.vmul @t15 tptp.v1) @t15)))) % 0.40/0.59 (assume @p11 (forall (@list @t18 @t17) (=> (tptp.less @t18 (tptp.vplus @t17 tptp.v1)) (tptp.leq @t18 @t17)))) % 0.40/0.59 (assume @p12 (forall (@list @t20 @t19) (=> (tptp.greater @t20 @t19) (tptp.geq @t20 (tptp.vplus @t19 tptp.v1))))) % 0.40/0.59 (assume @p13 (forall (@list @t21) (tptp.geq @t21 tptp.v1))) % 0.40/0.59 (assume @p14 (forall (@list @t25 @t23 @t24 @t22) (=> (and (tptp.geq @t24 @t22) (tptp.geq @t25 @t23)) (tptp.geq (tptp.vplus @t25 @t24) (tptp.vplus @t23 @t22))))) % 0.40/0.59 (assume @p15 (forall (@list @t29 @t27 @t28 @t26) (=> (or (and (tptp.greater @t28 @t26) (tptp.geq @t29 @t27)) (and (tptp.geq @t28 @t26) (tptp.greater @t29 @t27))) (tptp.greater (tptp.vplus @t29 @t28) (tptp.vplus @t27 @t26))))) % 0.40/0.59 (assume @p16 (forall (@list @t33 @t31 @t32 @t30) (=> (and (tptp.greater @t32 @t30) (tptp.greater @t33 @t31)) (tptp.greater (tptp.vplus @t33 @t32) (tptp.vplus @t31 @t30))))) % 0.40/0.59 (assume @p17 (forall @t39 (=> (tptp.less @t38 @t37) (tptp.less @t35 @t34)))) % 0.40/0.59 (assume @p18 (forall @t39 (=> (= @t38 @t37) (= @t35 @t34)))) % 0.40/0.59 (assume @p19 (forall @t39 (=> (tptp.greater @t38 @t37) (tptp.greater @t35 @t34)))) % 0.40/0.59 (assume @p20 (forall @t45 (=> (tptp.less @t43 @t41) (tptp.less @t44 @t42)))) % 0.40/0.59 (assume @p21 (forall @t45 (=> (= @t43 @t41) (= @t44 @t42)))) % 0.40/0.59 (assume @p22 (forall @t45 (=> (tptp.greater @t43 @t41) (tptp.greater @t44 @t42)))) % 0.40/0.59 (assume @p23 (forall (@list @t46 @t47) (tptp.greater (tptp.vplus @t46 @t47) @t46))) % 0.40/0.59 (assume @p24 (forall (@list @t49 @t50 @t48) (=> (and (tptp.leq @t50 @t48) (tptp.leq @t49 @t50)) (tptp.leq @t49 @t48)))) % 0.40/0.59 (assume @p25 (forall (@list @t52 @t53 @t51) (=> (or (and (tptp.less @t53 @t51) (tptp.leq @t52 @t53)) (and (tptp.leq @t53 @t51) (tptp.less @t52 @t53))) (tptp.less @t52 @t51)))) % 0.40/0.59 (assume @p26 (forall (@list @t55 @t56 @t54) (=> (and (tptp.less @t56 @t54) (tptp.less @t55 @t56)) (tptp.less @t55 @t54)))) % 0.40/0.59 (assume @p27 (forall (@list @t57 @t58) (=> (tptp.leq @t57 @t58) (tptp.geq @t58 @t57)))) % 0.40/0.59 (assume @p28 (forall (@list @t59 @t60) (=> (tptp.geq @t59 @t60) (tptp.leq @t60 @t59)))) % 0.40/0.59 (assume @p29 (forall (@list @t61 @t62) (= (tptp.leq @t62 @t61) (or (tptp.less @t62 @t61) (= @t62 @t61))))) % 0.40/0.59 (assume @p30 (forall (@list @t63 @t64) (= (tptp.geq @t64 @t63) (or (tptp.greater @t64 @t63) (= @t64 @t63))))) % 0.40/0.59 (assume @p31 (forall (@list @t65 @t66) (=> (tptp.less @t65 @t66) (tptp.greater @t66 @t65)))) % 0.40/0.59 (assume @p32 (forall (@list @t67 @t68) (=> (tptp.greater @t67 @t68) (tptp.less @t68 @t67)))) % 0.40/0.59 (assume @p33 (forall @t74 (or @t73 @t72 @t71))) % 0.40/0.59 (assume @p34 (forall @t74 (or @t76 @t75))) % 0.40/0.59 (assume @p35 (forall @t74 (or @t77 @t75))) % 0.40/0.59 (assume @p36 (forall @t74 (or @t76 @t77))) % 0.40/0.59 (assume @p37 (forall (@list @t80 @t79) (= (tptp.less @t79 @t80) (exists (@list @t78) (= @t80 (tptp.vplus @t79 @t78)))))) % 0.40/0.59 (assume @p38 (forall (@list @t82 @t83) (= (tptp.greater @t83 @t82) (exists (@list @t81) (= @t83 (tptp.vplus @t82 @t81)))))) % 0.40/0.59 (assume @p39 (forall @t91 (or @t90 @t89 @t87))) % 0.40/0.59 (assume @p40 (forall @t91 (or @t93 @t92))) % 0.40/0.59 (assume @p41 (forall @t91 (or @t94 @t92))) % 0.40/0.59 (assume @p42 (forall @t91 (or @t93 @t94))) % 0.40/0.59 (assume @p43 (forall (@list @t97 @t95) (=> (not (= @t97 @t95)) (forall (@list @t96) (not (= (tptp.vplus @t96 @t97) (tptp.vplus @t96 @t95))))))) % 0.40/0.59 (assume @p44 (forall (@list @t99 @t98) (not (= @t98 (tptp.vplus @t99 @t98))))) % 0.40/0.59 (assume @p45 (forall (@list @t101 @t100) (= (tptp.vplus @t100 @t101) (tptp.vplus @t101 @t100)))) % 0.40/0.59 (assume @p46 (forall (@list @t103 @t102) (= (tptp.vplus (tptp.vsucc @t103) @t102) (tptp.vsucc (tptp.vplus @t103 @t102))))) % 0.40/0.59 (assume @p47 (forall (@list @t104) (= (tptp.vplus tptp.v1 @t104) (tptp.vsucc @t104)))) % 0.40/0.59 (assume @p48 (forall (@list @t107 @t106 @t105) (= (tptp.vplus (tptp.vplus @t107 @t106) @t105) (tptp.vplus @t107 (tptp.vplus @t106 @t105))))) % 0.40/0.59 (assume @p49 (forall (@list @t108 @t109) (and (= (tptp.vplus @t108 (tptp.vsucc @t109)) (tptp.vsucc (tptp.vplus @t108 @t109))) (= (tptp.vplus @t108 tptp.v1) (tptp.vsucc @t108))))) % 0.40/0.59 (assume @p50 (forall (@list @t110) (=> (not (= @t110 tptp.v1)) (= @t110 (tptp.vsucc (tptp.vskolem2 @t110)))))) % 0.40/0.59 (assume @p51 (forall (@list @t111) (not (= (tptp.vsucc @t111) @t111)))) % 0.40/0.59 (assume @p52 (forall (@list @t113 @t112) (=> (not (= @t113 @t112)) (not (= (tptp.vsucc @t113) (tptp.vsucc @t112)))))) % 0.40/0.59 (assume @p53 (forall (@list @t115 @t114) (=> (= (tptp.vsucc @t115) (tptp.vsucc @t114)) (= @t115 @t114)))) % 0.40/0.59 (assume @p54 (forall (@list @t116) (not (= (tptp.vsucc @t116) tptp.v1)))) % 0.40/0.59 (assume @p55 true) % 0.40/0.59 (step @p56 :rule false_intro :premises (@p1)) % 0.40/0.59 (step @p57 :rule instantiate :premises (@p7) :args ((@list tptp.vd473 tptp.vd469))) % 0.40/0.59 (step @p58 :rule symm :premises (@p57)) % 0.40/0.59 (step @p59 :rule instantiate :premises (@p7) :args ((@list tptp.vd471 tptp.vd469))) % 0.40/0.59 (step @p60 :rule symm :premises (@p59)) % 0.40/0.59 (step @p61 :rule cong :premises (@p60 @p58) :args (@t117)) % 0.40/0.59 (step @p62 :rule instantiate :premises (@p7) :args ((@list @t1 tptp.vd469))) % 0.40/0.59 (step @p63 :rule symm :premises (@p62)) % 0.40/0.59 (step @p64 :rule cong :premises (@p63 @p61) :args (@t118)) % 0.40/0.59 (step @p65 :rule trans :premises (@p64 @p56)) % 0.40/0.59 (step @p66 :rule false_elim :premises (@p65)) % 0.40/0.59 (assume-push @p73 @t9) % 0.40/0.59 (step @p68 :rule instantiate :premises (@p6) :args ((@list tptp.vd469 tptp.vd471 tptp.vd473))) % 0.40/0.59 (step-pop @p74 :rule scope :premises (@p68)) % 0.40/0.59 (step @p69 :rule process_scope :premises (@p74) :args (@t118)) % 0.40/0.59 (step @p71 :rule implies_elim :premises (@p69)) % 0.40/0.59 (step @p72 false :rule chain_m_resolution :premises (@p71 @p66 @p6) :args (false (@list true false) (@list @t118 @t9))) % 0.40/0.59 ) % 0.40/0.59 % SZS output end Proof % 0.40/0.59 % cvc5 exiting %------------------------------------------------------------------------------