%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUM850+2 : 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 : n017.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 0.36s 0.58s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : NUM850+2 : TPTP v9.2.1. Released v4.1.0. % 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n017.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 12:28:31 EDT 2026 % 0.16/0.34 % CPUTime : % 0.25/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.58 % SZS status Theorem % 0.36/0.58 % SZS output start Proof % 0.36/0.58 ( % 0.36/0.58 (declare-sort $$unsorted 0) % 0.36/0.58 (declare-const tptp.geq (-> $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.less (-> $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.v1 $$unsorted) % 0.36/0.58 (declare-const tptp.vsucc (-> $$unsorted $$unsorted)) % 0.36/0.58 (declare-const tptp.vmul (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.58 (declare-const tptp.greater (-> $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.vd470 $$unsorted) % 0.36/0.58 (declare-const tptp.leq (-> $$unsorted $$unsorted Bool)) % 0.36/0.58 (declare-const tptp.vplus (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.58 (declare-const tptp.vskolem2 (-> $$unsorted $$unsorted)) % 0.36/0.58 (declare-const tptp.vd471 $$unsorted) % 0.36/0.58 (define @t1 () (@var "Vd473" $$unsorted)) % 0.36/0.58 (define @t2 () (= tptp.vd470 (tptp.vplus tptp.vd471 @t1))) % 0.36/0.58 (define @t3 () (@list @t1)) % 0.36/0.58 (define @t4 () (exists @t3 @t2)) % 0.36/0.58 (define @t5 () (not @t4)) % 0.36/0.58 (define @t6 () (tptp.greater tptp.vd470 tptp.vd471)) % 0.36/0.58 (define @t7 () (@var "Vd446" $$unsorted)) % 0.36/0.58 (define @t8 () (@var "Vd445" $$unsorted)) % 0.36/0.58 (define @t9 () (@var "Vd444" $$unsorted)) % 0.36/0.58 (define @t10 () (@var "Vd434" $$unsorted)) % 0.36/0.58 (define @t11 () (@var "Vd432" $$unsorted)) % 0.36/0.58 (define @t12 () (@var "Vd433" $$unsorted)) % 0.36/0.58 (define @t13 () (@var "Vd418" $$unsorted)) % 0.36/0.58 (define @t14 () (@var "Vd419" $$unsorted)) % 0.36/0.58 (define @t15 () (@var "Vd409" $$unsorted)) % 0.36/0.58 (define @t16 () (@var "Vd408" $$unsorted)) % 0.36/0.58 (define @t17 () (@var "Vd400" $$unsorted)) % 0.36/0.58 (define @t18 () (@var "Vd396" $$unsorted)) % 0.36/0.58 (define @t19 () (@var "Vd397" $$unsorted)) % 0.36/0.58 (define @t20 () (@var "Vd387" $$unsorted)) % 0.36/0.58 (define @t21 () (@var "Vd386" $$unsorted)) % 0.36/0.58 (define @t22 () (@var "Vd376" $$unsorted)) % 0.36/0.58 (define @t23 () (@var "Vd375" $$unsorted)) % 0.36/0.58 (define @t24 () (@var "Vd369" $$unsorted)) % 0.36/0.58 (define @t25 () (@var "Vd366" $$unsorted)) % 0.36/0.58 (define @t26 () (@var "Vd363" $$unsorted)) % 0.36/0.58 (define @t27 () (@var "Vd365" $$unsorted)) % 0.36/0.58 (define @t28 () (@var "Vd362" $$unsorted)) % 0.36/0.58 (define @t29 () (@var "Vd356" $$unsorted)) % 0.36/0.58 (define @t30 () (@var "Vd354" $$unsorted)) % 0.36/0.58 (define @t31 () (@var "Vd355" $$unsorted)) % 0.36/0.58 (define @t32 () (@var "Vd353" $$unsorted)) % 0.36/0.58 (define @t33 () (@var "Vd341" $$unsorted)) % 0.36/0.58 (define @t34 () (@var "Vd338" $$unsorted)) % 0.36/0.58 (define @t35 () (@var "Vd340" $$unsorted)) % 0.36/0.58 (define @t36 () (@var "Vd337" $$unsorted)) % 0.36/0.58 (define @t37 () (@var "Vd329" $$unsorted)) % 0.36/0.58 (define @t38 () (@var "Vd328" $$unsorted)) % 0.36/0.58 (define @t39 () (@var "Vd330" $$unsorted)) % 0.36/0.58 (define @t40 () (tptp.vplus @t37 @t39)) % 0.36/0.58 (define @t41 () (tptp.vplus @t38 @t39)) % 0.36/0.58 (define @t42 () (@list @t38 @t37 @t39)) % 0.36/0.58 (define @t43 () (@var "Vd303" $$unsorted)) % 0.36/0.58 (define @t44 () (@var "Vd302" $$unsorted)) % 0.36/0.58 (define @t45 () (tptp.vplus @t44 @t43)) % 0.36/0.58 (define @t46 () (@var "Vd301" $$unsorted)) % 0.36/0.58 (define @t47 () (tptp.vplus @t46 @t43)) % 0.36/0.58 (define @t48 () (@list @t46 @t44 @t43)) % 0.36/0.58 (define @t49 () (@var "Vd295" $$unsorted)) % 0.36/0.58 (define @t50 () (@var "Vd296" $$unsorted)) % 0.36/0.58 (define @t51 () (@var "Vd292" $$unsorted)) % 0.36/0.58 (define @t52 () (@var "Vd289" $$unsorted)) % 0.36/0.58 (define @t53 () (@var "Vd290" $$unsorted)) % 0.36/0.58 (define @t54 () (@var "Vd283" $$unsorted)) % 0.36/0.58 (define @t55 () (@var "Vd281" $$unsorted)) % 0.36/0.58 (define @t56 () (@var "Vd282" $$unsorted)) % 0.36/0.58 (define @t57 () (@var "Vd265" $$unsorted)) % 0.36/0.58 (define @t58 () (@var "Vd262" $$unsorted)) % 0.36/0.58 (define @t59 () (@var "Vd263" $$unsorted)) % 0.36/0.58 (define @t60 () (@var "Vd258" $$unsorted)) % 0.36/0.58 (define @t61 () (@var "Vd259" $$unsorted)) % 0.36/0.58 (define @t62 () (@var "Vd249" $$unsorted)) % 0.36/0.58 (define @t63 () (@var "Vd250" $$unsorted)) % 0.36/0.58 (define @t64 () (@var "Vd244" $$unsorted)) % 0.36/0.58 (define @t65 () (@var "Vd245" $$unsorted)) % 0.36/0.58 (define @t66 () (@var "Vd226" $$unsorted)) % 0.36/0.58 (define @t67 () (@var "Vd227" $$unsorted)) % 0.36/0.58 (define @t68 () (@var "Vd208" $$unsorted)) % 0.36/0.58 (define @t69 () (@var "Vd209" $$unsorted)) % 0.36/0.58 (define @t70 () (@var "Vd204" $$unsorted)) % 0.36/0.58 (define @t71 () (@var "Vd203" $$unsorted)) % 0.36/0.58 (define @t72 () (tptp.less @t71 @t70)) % 0.36/0.58 (define @t73 () (tptp.greater @t71 @t70)) % 0.36/0.58 (define @t74 () (= @t71 @t70)) % 0.36/0.58 (define @t75 () (@list @t71 @t70)) % 0.36/0.58 (define @t76 () (not @t72)) % 0.36/0.58 (define @t77 () (not @t74)) % 0.36/0.58 (define @t78 () (not @t73)) % 0.36/0.58 (define @t79 () (@var "Vd201" $$unsorted)) % 0.36/0.58 (define @t80 () (@var "Vd199" $$unsorted)) % 0.36/0.58 (define @t81 () (@var "Vd198" $$unsorted)) % 0.36/0.58 (define @t82 () (@var "Vd196" $$unsorted)) % 0.36/0.58 (define @t83 () (@var "Vd193" $$unsorted)) % 0.36/0.58 (define @t84 () (@var "Vd194" $$unsorted)) % 0.36/0.58 (define @t85 () (= @t84 (tptp.vplus @t83 @t82))) % 0.36/0.58 (define @t86 () (@list @t82)) % 0.36/0.58 (define @t87 () (exists @t86 @t85)) % 0.36/0.58 (define @t88 () (tptp.greater @t84 @t83)) % 0.36/0.58 (define @t89 () (= @t88 @t87)) % 0.36/0.58 (define @t90 () (forall (@list @t83 @t84) @t89)) % 0.36/0.58 (define @t91 () (@var "Vd125" $$unsorted)) % 0.36/0.58 (define @t92 () (@var "Vd120" $$unsorted)) % 0.36/0.58 (define @t93 () (@var "Vd121" $$unsorted)) % 0.36/0.58 (define @t94 () (exists (@list @t91) (= @t93 (tptp.vplus @t92 @t91)))) % 0.36/0.58 (define @t95 () (@var "Vd123" $$unsorted)) % 0.36/0.58 (define @t96 () (exists (@list @t95) (= @t92 (tptp.vplus @t93 @t95)))) % 0.36/0.58 (define @t97 () (= @t92 @t93)) % 0.36/0.58 (define @t98 () (@list @t92 @t93)) % 0.36/0.58 (define @t99 () (not @t94)) % 0.36/0.58 (define @t100 () (not @t97)) % 0.36/0.58 (define @t101 () (not @t96)) % 0.36/0.58 (define @t102 () (@var "Vd105" $$unsorted)) % 0.36/0.58 (define @t103 () (@var "Vd107" $$unsorted)) % 0.36/0.58 (define @t104 () (@var "Vd104" $$unsorted)) % 0.36/0.58 (define @t105 () (@var "Vd93" $$unsorted)) % 0.36/0.58 (define @t106 () (@var "Vd92" $$unsorted)) % 0.36/0.58 (define @t107 () (@var "Vd79" $$unsorted)) % 0.36/0.58 (define @t108 () (@var "Vd78" $$unsorted)) % 0.36/0.58 (define @t109 () (@var "Vd69" $$unsorted)) % 0.36/0.58 (define @t110 () (@var "Vd68" $$unsorted)) % 0.36/0.58 (define @t111 () (@var "Vd59" $$unsorted)) % 0.36/0.58 (define @t112 () (@var "Vd48" $$unsorted)) % 0.36/0.58 (define @t113 () (@var "Vd47" $$unsorted)) % 0.36/0.58 (define @t114 () (@var "Vd46" $$unsorted)) % 0.36/0.58 (define @t115 () (@var "Vd42" $$unsorted)) % 0.36/0.58 (define @t116 () (@var "Vd43" $$unsorted)) % 0.36/0.58 (define @t117 () (@var "Vd24" $$unsorted)) % 0.36/0.58 (define @t118 () (@var "Vd16" $$unsorted)) % 0.36/0.58 (define @t119 () (@var "Vd8" $$unsorted)) % 0.36/0.58 (define @t120 () (@var "Vd7" $$unsorted)) % 0.36/0.58 (define @t121 () (@var "Vd4" $$unsorted)) % 0.36/0.58 (define @t122 () (@var "Vd3" $$unsorted)) % 0.36/0.58 (define @t123 () (@var "Vd1" $$unsorted)) % 0.36/0.58 (define @t124 () (forall @t3 (not @t2))) % 0.36/0.58 (define @t125 () (forall @t86 (not (= tptp.vd470 (tptp.vplus tptp.vd471 @t82))))) % 0.36/0.58 (define @t126 () (not @t125)) % 0.36/0.58 (define @t127 () (= @t6 @t126)) % 0.36/0.58 (assume @p1 @t5) % 0.36/0.58 (assume @p2 @t6) % 0.36/0.58 (assume @p3 (forall (@list @t9 @t8 @t7) (= (tptp.vmul (tptp.vmul @t9 @t8) @t7) (tptp.vmul @t9 (tptp.vmul @t8 @t7))))) % 0.36/0.58 (assume @p4 (forall (@list @t11 @t12 @t10) (= (tptp.vmul @t11 (tptp.vplus @t12 @t10)) (tptp.vplus (tptp.vmul @t11 @t12) (tptp.vmul @t11 @t10))))) % 0.36/0.58 (assume @p5 (forall (@list @t13 @t14) (= (tptp.vmul @t13 @t14) (tptp.vmul @t14 @t13)))) % 0.36/0.58 (assume @p6 (forall (@list @t16 @t15) (= (tptp.vmul (tptp.vsucc @t16) @t15) (tptp.vplus (tptp.vmul @t16 @t15) @t15)))) % 0.36/0.58 (assume @p7 (forall (@list @t17) (= (tptp.vmul tptp.v1 @t17) @t17))) % 0.36/0.58 (assume @p8 (forall (@list @t18 @t19) (and (= (tptp.vmul @t18 (tptp.vsucc @t19)) (tptp.vplus (tptp.vmul @t18 @t19) @t18)) (= (tptp.vmul @t18 tptp.v1) @t18)))) % 0.36/0.58 (assume @p9 (forall (@list @t21 @t20) (=> (tptp.less @t21 (tptp.vplus @t20 tptp.v1)) (tptp.leq @t21 @t20)))) % 0.36/0.58 (assume @p10 (forall (@list @t23 @t22) (=> (tptp.greater @t23 @t22) (tptp.geq @t23 (tptp.vplus @t22 tptp.v1))))) % 0.36/0.58 (assume @p11 (forall (@list @t24) (tptp.geq @t24 tptp.v1))) % 0.36/0.58 (assume @p12 (forall (@list @t28 @t26 @t27 @t25) (=> (and (tptp.geq @t27 @t25) (tptp.geq @t28 @t26)) (tptp.geq (tptp.vplus @t28 @t27) (tptp.vplus @t26 @t25))))) % 0.36/0.58 (assume @p13 (forall (@list @t32 @t30 @t31 @t29) (=> (or (and (tptp.greater @t31 @t29) (tptp.geq @t32 @t30)) (and (tptp.geq @t31 @t29) (tptp.greater @t32 @t30))) (tptp.greater (tptp.vplus @t32 @t31) (tptp.vplus @t30 @t29))))) % 0.36/0.58 (assume @p14 (forall (@list @t36 @t34 @t35 @t33) (=> (and (tptp.greater @t35 @t33) (tptp.greater @t36 @t34)) (tptp.greater (tptp.vplus @t36 @t35) (tptp.vplus @t34 @t33))))) % 0.36/0.58 (assume @p15 (forall @t42 (=> (tptp.less @t41 @t40) (tptp.less @t38 @t37)))) % 0.36/0.58 (assume @p16 (forall @t42 (=> (= @t41 @t40) (= @t38 @t37)))) % 0.36/0.58 (assume @p17 (forall @t42 (=> (tptp.greater @t41 @t40) (tptp.greater @t38 @t37)))) % 0.36/0.58 (assume @p18 (forall @t48 (=> (tptp.less @t46 @t44) (tptp.less @t47 @t45)))) % 0.36/0.58 (assume @p19 (forall @t48 (=> (= @t46 @t44) (= @t47 @t45)))) % 0.36/0.58 (assume @p20 (forall @t48 (=> (tptp.greater @t46 @t44) (tptp.greater @t47 @t45)))) % 0.36/0.58 (assume @p21 (forall (@list @t49 @t50) (tptp.greater (tptp.vplus @t49 @t50) @t49))) % 0.36/0.58 (assume @p22 (forall (@list @t52 @t53 @t51) (=> (and (tptp.leq @t53 @t51) (tptp.leq @t52 @t53)) (tptp.leq @t52 @t51)))) % 0.36/0.58 (assume @p23 (forall (@list @t55 @t56 @t54) (=> (or (and (tptp.less @t56 @t54) (tptp.leq @t55 @t56)) (and (tptp.leq @t56 @t54) (tptp.less @t55 @t56))) (tptp.less @t55 @t54)))) % 0.36/0.58 (assume @p24 (forall (@list @t58 @t59 @t57) (=> (and (tptp.less @t59 @t57) (tptp.less @t58 @t59)) (tptp.less @t58 @t57)))) % 0.36/0.58 (assume @p25 (forall (@list @t60 @t61) (=> (tptp.leq @t60 @t61) (tptp.geq @t61 @t60)))) % 0.36/0.58 (assume @p26 (forall (@list @t62 @t63) (= (tptp.leq @t63 @t62) (or (tptp.less @t63 @t62) (= @t63 @t62))))) % 0.36/0.58 (assume @p27 (forall (@list @t64 @t65) (= (tptp.geq @t65 @t64) (or (tptp.greater @t65 @t64) (= @t65 @t64))))) % 0.36/0.58 (assume @p28 (forall (@list @t66 @t67) (=> (tptp.less @t66 @t67) (tptp.greater @t67 @t66)))) % 0.36/0.58 (assume @p29 (forall (@list @t68 @t69) (=> (tptp.greater @t68 @t69) (tptp.less @t69 @t68)))) % 0.36/0.58 (assume @p30 (forall @t75 (or @t74 @t73 @t72))) % 0.36/0.58 (assume @p31 (forall @t75 (or @t77 @t76))) % 0.36/0.58 (assume @p32 (forall @t75 (or @t78 @t76))) % 0.36/0.58 (assume @p33 (forall @t75 (or @t77 @t78))) % 0.36/0.58 (assume @p34 (forall (@list @t81 @t80) (= (tptp.less @t80 @t81) (exists (@list @t79) (= @t81 (tptp.vplus @t80 @t79)))))) % 0.36/0.58 (assume @p35 @t90) % 0.36/0.58 (assume @p36 (forall @t98 (or @t97 @t96 @t94))) % 0.36/0.58 (assume @p37 (forall @t98 (or @t100 @t99))) % 0.36/0.58 (assume @p38 (forall @t98 (or @t101 @t99))) % 0.36/0.58 (assume @p39 (forall @t98 (or @t100 @t101))) % 0.36/0.58 (assume @p40 (forall (@list @t104 @t102) (=> (not (= @t104 @t102)) (forall (@list @t103) (not (= (tptp.vplus @t103 @t104) (tptp.vplus @t103 @t102))))))) % 0.36/0.58 (assume @p41 (forall (@list @t106 @t105) (not (= @t105 (tptp.vplus @t106 @t105))))) % 0.36/0.58 (assume @p42 (forall (@list @t108 @t107) (= (tptp.vplus @t107 @t108) (tptp.vplus @t108 @t107)))) % 0.36/0.58 (assume @p43 (forall (@list @t110 @t109) (= (tptp.vplus (tptp.vsucc @t110) @t109) (tptp.vsucc (tptp.vplus @t110 @t109))))) % 0.36/0.58 (assume @p44 (forall (@list @t111) (= (tptp.vplus tptp.v1 @t111) (tptp.vsucc @t111)))) % 0.36/0.58 (assume @p45 (forall (@list @t114 @t113 @t112) (= (tptp.vplus (tptp.vplus @t114 @t113) @t112) (tptp.vplus @t114 (tptp.vplus @t113 @t112))))) % 0.36/0.58 (assume @p46 (forall (@list @t115 @t116) (and (= (tptp.vplus @t115 (tptp.vsucc @t116)) (tptp.vsucc (tptp.vplus @t115 @t116))) (= (tptp.vplus @t115 tptp.v1) (tptp.vsucc @t115))))) % 0.36/0.58 (assume @p47 (forall (@list @t117) (=> (not (= @t117 tptp.v1)) (= @t117 (tptp.vsucc (tptp.vskolem2 @t117)))))) % 0.36/0.58 (assume @p48 (forall (@list @t118) (not (= (tptp.vsucc @t118) @t118)))) % 0.36/0.58 (assume @p49 (forall (@list @t120 @t119) (=> (not (= @t120 @t119)) (not (= (tptp.vsucc @t120) (tptp.vsucc @t119)))))) % 0.36/0.58 (assume @p50 (forall (@list @t122 @t121) (=> (= (tptp.vsucc @t122) (tptp.vsucc @t121)) (= @t122 @t121)))) % 0.36/0.58 (assume @p51 (forall (@list @t123) (not (= (tptp.vsucc @t123) tptp.v1)))) % 0.36/0.58 (assume @p52 true) % 0.36/0.58 (step @p53 :rule bool-double-not-elim :args (@t124)) % 0.36/0.58 (step @p54 :rule exists-elim :args ((= @t4 (not @t124)))) % 0.36/0.58 (step @p55 :rule cong :premises (@p54) :args (@t5)) % 0.36/0.58 (step @p56 :rule trans :premises (@p55 @p53)) % 0.36/0.58 (step @p57 :rule eq_resolve :premises (@p1 @p56)) % 0.36/0.58 (step @p58 :rule alpha_equiv :args (@t124 (@list @t1) (@list @t82))) % 0.36/0.58 (step @p59 :rule equiv_elim1 :premises (@p58)) % 0.36/0.58 (step @p60 :rule chain_m_resolution :premises (@p59 @p57) :args (@t125 (@list false) (@list @t124))) % 0.36/0.58 (step @p61 :rule exists-elim :args ((= @t87 (not (forall @t86 (not @t85)))))) % 0.36/0.58 (step @p62 :rule refl :args (@t88)) % 0.36/0.58 (step @p63 :rule cong :premises (@p62 @p61) :args (@t89)) % 0.36/0.58 (step @p64 :rule cong :premises (@p63) :args (@t90)) % 0.36/0.58 (step @p65 :rule eq_resolve :premises (@p35 @p64)) % 0.36/0.58 (step @p66 :rule instantiate :premises (@p65) :args ((@list tptp.vd471 tptp.vd470))) % 0.36/0.58 (step @p67 :rule cnf_equiv_pos1 :args (@t127)) % 0.36/0.58 (step @p68 :rule reordering :premises (@p67) :args ((or (not @t6) @t126 (not @t127)))) % 0.36/0.58 (step @p69 false :rule chain_m_resolution :premises (@p68 @p66 @p60 @p2) :args (false (@list false false false) (@list @t127 @t125 @t6))) % 0.36/0.58 ) % 0.36/0.58 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------