%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG047+2 : 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 : n026.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 08:45:29 AM UTC 2026 % Result : Theorem 0.46s 0.69s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : RNG047+2 : 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 % 0.17/0.34 % Computer : n026.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 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 14:04:10 EDT 2026 % 0.17/0.35 % CPUTime : % 0.32/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.46/0.69 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.46/0.69 % SZS status Theorem % 0.46/0.69 % SZS output start Proof % 0.46/0.69 ( % 0.46/0.69 (declare-sort $$unsorted 0) % 0.46/0.69 (declare-const tptp.xs $$unsorted) % 0.46/0.69 (declare-const tptp.sziznziztdt0 (-> $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.aScalar0 (-> $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.szszuzczcdt0 (-> $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.iLess0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.sz0z00 $$unsorted) % 0.46/0.69 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.xt $$unsorted) % 0.46/0.69 (declare-const tptp.sdtlbdtrb0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.aNaturalNumber0 (-> $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.sz00 $$unsorted) % 0.46/0.69 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.46/0.69 (declare-const tptp.sdtlseqdt0 (-> $$unsorted $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.aVector0 (-> $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.aDimensionOf0 (-> $$unsorted $$unsorted)) % 0.46/0.69 (define @t1 () (@var "W0" $$unsorted)) % 0.46/0.69 (define @t2 () (tptp.aNaturalNumber0 @t1)) % 0.46/0.69 (define @t3 () (@list @t1)) % 0.46/0.69 (define @t4 () (tptp.szszuzczcdt0 @t1)) % 0.46/0.69 (define @t5 () (@var "W1" $$unsorted)) % 0.46/0.69 (define @t6 () (tptp.szszuzczcdt0 @t5)) % 0.46/0.69 (define @t7 () (tptp.aNaturalNumber0 @t5)) % 0.46/0.69 (define @t8 () (@list @t5)) % 0.46/0.69 (define @t9 () (= @t1 @t5)) % 0.46/0.69 (define @t10 () (= @t4 @t6)) % 0.46/0.69 (define @t11 () (=> @t10 @t9)) % 0.46/0.69 (define @t12 () (and @t2 @t7)) % 0.46/0.69 (define @t13 () (@list @t1 @t5)) % 0.46/0.69 (define @t14 () (forall @t13 (=> @t12 @t11))) % 0.46/0.69 (define @t15 () (tptp.aScalar0 @t1)) % 0.46/0.69 (define @t16 () (tptp.sdtpldt0 @t1 @t5)) % 0.46/0.69 (define @t17 () (tptp.aScalar0 @t5)) % 0.46/0.69 (define @t18 () (and @t15 @t17)) % 0.46/0.69 (define @t19 () (tptp.sdtasdt0 @t1 @t5)) % 0.46/0.69 (define @t20 () (tptp.smndt0 @t1)) % 0.46/0.69 (define @t21 () (@var "W2" $$unsorted)) % 0.46/0.69 (define @t22 () (tptp.sdtasdt0 @t5 @t21)) % 0.46/0.69 (define @t23 () (tptp.sdtpldt0 @t5 @t21)) % 0.46/0.69 (define @t24 () (tptp.aScalar0 @t21)) % 0.46/0.69 (define @t25 () (and @t15 @t17 @t24)) % 0.46/0.69 (define @t26 () (@list @t1 @t5 @t21)) % 0.46/0.69 (define @t27 () (tptp.sdtasdt0 @t1 @t21)) % 0.46/0.69 (define @t28 () (@var "W3" $$unsorted)) % 0.46/0.69 (define @t29 () (tptp.sdtasdt0 @t5 @t28)) % 0.46/0.69 (define @t30 () (and @t15 @t17 @t24 (tptp.aScalar0 @t28))) % 0.46/0.69 (define @t31 () (@list @t1 @t5 @t21 @t28)) % 0.46/0.69 (define @t32 () (tptp.smndt0 @t19)) % 0.46/0.69 (define @t33 () (tptp.smndt0 @t5)) % 0.46/0.69 (define @t34 () (tptp.sdtlseqdt0 @t1 @t5)) % 0.46/0.69 (define @t35 () (tptp.sdtlseqdt0 @t5 @t1)) % 0.46/0.69 (define @t36 () (tptp.sdtlseqdt0 @t21 @t28)) % 0.46/0.69 (define @t37 () (tptp.sdtlseqdt0 tptp.sz0z00 @t5)) % 0.46/0.69 (define @t38 () (tptp.sdtlseqdt0 tptp.sz0z00 @t1)) % 0.46/0.69 (define @t39 () (tptp.sdtasdt0 @t1 @t1)) % 0.46/0.69 (define @t40 () (tptp.aVector0 @t1)) % 0.46/0.69 (define @t41 () (tptp.aDimensionOf0 @t1)) % 0.46/0.69 (define @t42 () (tptp.aNaturalNumber0 @t41)) % 0.46/0.69 (define @t43 () (forall @t3 (=> @t40 @t42))) % 0.46/0.69 (define @t44 () (tptp.aDimensionOf0 tptp.xt)) % 0.46/0.69 (define @t45 () (tptp.aDimensionOf0 tptp.xs)) % 0.46/0.69 (define @t46 () (tptp.sziznziztdt0 tptp.xt)) % 0.46/0.69 (define @t47 () (tptp.aDimensionOf0 @t46)) % 0.46/0.69 (define @t48 () (tptp.sziznziztdt0 tptp.xs)) % 0.46/0.69 (define @t49 () (tptp.aDimensionOf0 @t48)) % 0.46/0.69 (define @t50 () (= (tptp.sdtlbdtrb0 @t46 @t1) (tptp.sdtlbdtrb0 tptp.xt @t1))) % 0.46/0.69 (define @t51 () (forall @t3 (=> @t2 @t50))) % 0.46/0.69 (define @t52 () (tptp.szszuzczcdt0 @t47)) % 0.46/0.69 (define @t53 () (tptp.aVector0 @t46)) % 0.46/0.69 (define @t54 () (and @t53 (= @t52 @t44) @t51)) % 0.46/0.69 (define @t55 () (=> @t54 (= @t49 @t47))) % 0.46/0.69 (define @t56 () (= (tptp.sdtlbdtrb0 @t48 @t1) (tptp.sdtlbdtrb0 tptp.xs @t1))) % 0.46/0.69 (define @t57 () (forall @t3 (=> @t2 @t56))) % 0.46/0.69 (define @t58 () (tptp.szszuzczcdt0 @t49)) % 0.46/0.69 (define @t59 () (tptp.aVector0 @t48)) % 0.46/0.69 (define @t60 () (and @t59 (= @t58 @t45) @t57)) % 0.46/0.69 (define @t61 () (=> @t60 @t55)) % 0.46/0.69 (define @t62 () (not @t61)) % 0.46/0.69 (define @t63 () (not @t10)) % 0.46/0.69 (define @t64 () (not @t7)) % 0.46/0.69 (define @t65 () (not @t2)) % 0.46/0.69 (define @t66 () (or @t65 @t64 @t63 @t9)) % 0.46/0.69 (define @t67 () (= @t47 @t49)) % 0.46/0.69 (define @t68 () (not (= @t52 @t58))) % 0.46/0.69 (define @t69 () (tptp.aNaturalNumber0 @t49)) % 0.46/0.69 (define @t70 () (not @t69)) % 0.46/0.69 (define @t71 () (tptp.aNaturalNumber0 @t47)) % 0.46/0.69 (define @t72 () (not @t71)) % 0.46/0.69 (define @t73 () (or @t72 @t70 @t68 @t67)) % 0.46/0.69 (define @t74 () (forall @t13 @t66)) % 0.46/0.69 (define @t75 () (not (= @t58 @t52))) % 0.46/0.69 (define @t76 () (or @t72 @t70 @t75 @t67)) % 0.46/0.69 (define @t77 () (not @t59)) % 0.46/0.69 (define @t78 () (or @t77 @t69)) % 0.46/0.69 (define @t79 () (@list false false)) % 0.46/0.69 (define @t80 () (not @t53)) % 0.46/0.69 (define @t81 () (or @t80 @t71)) % 0.46/0.69 (assume @p1 (forall @t3 (=> @t2 true))) % 0.46/0.69 (assume @p2 (tptp.aNaturalNumber0 tptp.sz00)) % 0.46/0.69 (assume @p3 (forall @t3 (=> @t2 (and (tptp.aNaturalNumber0 @t4) (not (= @t4 tptp.sz00)))))) % 0.46/0.69 (assume @p4 (forall @t3 (=> (and @t2 (not (= @t1 tptp.sz00))) (exists @t8 (and @t7 (= @t1 @t6)))))) % 0.46/0.69 (assume @p5 @t14) % 0.46/0.69 (assume @p6 (forall @t13 (=> @t12 (=> (tptp.iLess0 @t1 @t5) true)))) % 0.46/0.69 (assume @p7 (forall @t3 (=> @t2 (tptp.iLess0 @t1 @t4)))) % 0.46/0.69 (assume @p8 (forall @t3 (=> @t15 true))) % 0.46/0.69 (assume @p9 (tptp.aScalar0 tptp.sz0z00)) % 0.46/0.69 (assume @p10 (forall @t13 (=> @t18 (tptp.aScalar0 @t16)))) % 0.46/0.69 (assume @p11 (forall @t13 (=> @t18 (tptp.aScalar0 @t19)))) % 0.46/0.69 (assume @p12 (forall @t3 (=> @t15 (tptp.aScalar0 @t20)))) % 0.46/0.69 (assume @p13 (forall @t3 (=> @t15 (and (= (tptp.sdtpldt0 @t1 tptp.sz0z00) @t1) (= (tptp.sdtpldt0 tptp.sz0z00 @t1) @t1) (= (tptp.sdtasdt0 @t1 tptp.sz0z00) tptp.sz0z00) (= (tptp.sdtasdt0 tptp.sz0z00 @t1) tptp.sz0z00) (= (tptp.sdtpldt0 @t1 @t20) tptp.sz0z00) (= (tptp.sdtpldt0 @t20 @t1) tptp.sz0z00) (= (tptp.smndt0 @t20) @t1) (= (tptp.smndt0 tptp.sz0z00) tptp.sz0z00))))) % 0.46/0.69 (assume @p14 (forall @t26 (=> @t25 (and (= (tptp.sdtpldt0 @t16 @t21) (tptp.sdtpldt0 @t1 @t23)) (= @t16 (tptp.sdtpldt0 @t5 @t1)) (= (tptp.sdtasdt0 @t19 @t21) (tptp.sdtasdt0 @t1 @t22)) (= @t19 (tptp.sdtasdt0 @t5 @t1)))))) % 0.46/0.69 (assume @p15 (forall @t26 (=> @t25 (and (= (tptp.sdtasdt0 @t1 @t23) (tptp.sdtpldt0 @t19 @t27)) (= (tptp.sdtasdt0 @t16 @t21) (tptp.sdtpldt0 @t27 @t22)))))) % 0.46/0.69 (assume @p16 (forall @t31 (=> @t30 (= (tptp.sdtasdt0 @t16 (tptp.sdtpldt0 @t21 @t28)) (tptp.sdtpldt0 (tptp.sdtpldt0 @t27 (tptp.sdtasdt0 @t1 @t28)) (tptp.sdtpldt0 @t22 @t29)))))) % 0.46/0.69 (assume @p17 (forall @t13 (=> @t18 (and (= (tptp.sdtasdt0 @t1 @t33) @t32) (= (tptp.sdtasdt0 @t20 @t5) @t32))))) % 0.46/0.69 (assume @p18 (forall @t13 (=> @t18 (= (tptp.sdtasdt0 @t20 @t33) @t19)))) % 0.46/0.69 (assume @p19 (forall @t13 (=> @t18 (=> @t34 true)))) % 0.46/0.69 (assume @p20 (forall @t3 (=> @t15 (tptp.sdtlseqdt0 @t1 @t1)))) % 0.46/0.69 (assume @p21 (forall @t13 (=> @t18 (=> (and @t34 @t35) @t9)))) % 0.46/0.69 (assume @p22 (forall @t26 (=> @t25 (=> (and @t34 (tptp.sdtlseqdt0 @t5 @t21)) (tptp.sdtlseqdt0 @t1 @t21))))) % 0.46/0.69 (assume @p23 (forall @t31 (=> @t30 (=> (and @t34 @t36) (tptp.sdtlseqdt0 (tptp.sdtpldt0 @t1 @t21) (tptp.sdtpldt0 @t5 @t28)))))) % 0.46/0.69 (assume @p24 (forall @t31 (=> @t30 (=> (and @t34 (tptp.sdtlseqdt0 tptp.sz0z00 @t21) @t36) (tptp.sdtlseqdt0 @t27 @t29))))) % 0.46/0.69 (assume @p25 (forall @t13 (=> @t18 (or @t34 @t35)))) % 0.46/0.69 (assume @p26 (forall @t13 (=> @t18 (=> (and @t38 @t37) (and (tptp.sdtlseqdt0 tptp.sz0z00 @t16) (tptp.sdtlseqdt0 tptp.sz0z00 @t19)))))) % 0.46/0.69 (assume @p27 (forall @t3 (=> @t15 (tptp.sdtlseqdt0 tptp.sz0z00 @t39)))) % 0.46/0.69 (assume @p28 (forall @t13 (=> @t18 (=> (and @t38 @t37 (= @t39 (tptp.sdtasdt0 @t5 @t5))) @t9)))) % 0.46/0.69 (assume @p29 (forall @t3 (=> @t40 true))) % 0.46/0.69 (assume @p30 @t43) % 0.46/0.69 (assume @p31 (forall @t13 (=> (and @t40 @t7) (tptp.aScalar0 (tptp.sdtlbdtrb0 @t1 @t5))))) % 0.46/0.69 (assume @p32 (forall @t3 (=> @t40 (=> (not (= @t41 tptp.sz00)) (forall @t8 (= (= @t5 (tptp.sziznziztdt0 @t1)) (and (tptp.aVector0 @t5) (= (tptp.szszuzczcdt0 (tptp.aDimensionOf0 @t5)) @t41) (forall (@list @t21) (=> (tptp.aNaturalNumber0 @t21) (= (tptp.sdtlbdtrb0 @t5 @t21) (tptp.sdtlbdtrb0 @t1 @t21))))))))))) % 0.46/0.69 (assume @p33 (and (tptp.aVector0 tptp.xs) (tptp.aVector0 tptp.xt))) % 0.46/0.69 (assume @p34 (and (= @t45 @t44) (not (= @t44 tptp.sz00)))) % 0.46/0.69 (assume @p35 @t62) % 0.46/0.69 (assume @p36 true) % 0.46/0.69 (step @p37 :rule evaluate :args ((= true false))) % 0.46/0.69 (step @p38 :rule aci_norm :args ((= (or (or @t65 @t64) (or @t63 @t9)) @t66))) % 0.46/0.69 (step @p39 :rule bool-impl-elim :args (@t10 @t9)) % 0.46/0.69 (step @p40 :rule bool-and-de-morgan :args (@t2 @t7 true)) % 0.46/0.69 (step @p41 :rule nary_cong :premises (@p40 @p39) :args ((or (not @t12) @t11))) % 0.46/0.69 (step @p42 :rule trans :premises (@p41 @p38)) % 0.46/0.69 (step @p43 :rule bool-impl-elim :args (@t12 @t11)) % 0.46/0.69 (step @p44 :rule trans :premises (@p43 @p42)) % 0.46/0.69 (step @p45 :rule cong :premises (@p44) :args (@t14)) % 0.46/0.69 (step @p46 :rule eq_resolve :premises (@p5 @p45)) % 0.46/0.69 (step @p47 :rule refl :args (@t67)) % 0.46/0.69 (step @p48 :rule eq-symm :args (@t52 @t58)) % 0.46/0.69 (step @p49 :rule cong :premises (@p48) :args (@t68)) % 0.46/0.69 (step @p50 :rule refl :args (@t70)) % 0.46/0.69 (step @p51 :rule refl :args (@t72)) % 0.46/0.69 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49 @p47) :args (@t73)) % 0.46/0.69 (step @p53 :rule refl :args (@t74)) % 0.46/0.69 (step @p54 :rule cong :premises (@p53 @p52) :args ((=> @t74 @t73))) % 0.46/0.69 (assume-push @p110 @t74) % 0.46/0.69 (step @p56 :rule instantiate :premises (@p46) :args ((@list @t47 @t49))) % 0.46/0.69 (step-pop @p111 :rule scope :premises (@p56)) % 0.46/0.69 (step @p57 :rule process_scope :premises (@p111) :args (@t73)) % 0.46/0.69 (step @p59 :rule eq_resolve :premises (@p57 @p54)) % 0.46/0.69 (step @p60 :rule implies_elim :premises (@p59)) % 0.46/0.69 (step @p61 :rule chain_m_resolution :premises (@p60 @p46) :args (@t76 (@list false) (@list @t74))) % 0.46/0.69 (step @p62 :rule bool-impl-elim :args (@t40 @t42)) % 0.46/0.69 (step @p63 :rule cong :premises (@p62) :args (@t43)) % 0.46/0.69 (step @p64 :rule eq_resolve :premises (@p30 @p63)) % 0.46/0.69 (step @p65 :rule instantiate :premises (@p64) :args ((@list @t48))) % 0.46/0.69 (step @p66 :rule eq-symm :args (@t49 @t47)) % 0.46/0.69 (step @p67 :rule bool-impl-elim :args (@t2 @t50)) % 0.46/0.69 (step @p68 :rule cong :premises (@p67) :args (@t51)) % 0.46/0.69 (step @p69 :rule eq-symm :args (@t52 @t44)) % 0.46/0.69 (step @p70 :rule refl :args (@t53)) % 0.46/0.69 (step @p71 :rule nary_cong :premises (@p70 @p69 @p68) :args (@t54)) % 0.46/0.69 (step @p72 :rule cong :premises (@p71 @p66) :args (@t55)) % 0.46/0.69 (step @p73 :rule bool-impl-elim :args (@t2 @t56)) % 0.46/0.69 (step @p74 :rule cong :premises (@p73) :args (@t57)) % 0.46/0.69 (step @p75 :rule eq-symm :args (@t58 @t45)) % 0.46/0.69 (step @p76 :rule refl :args (@t59)) % 0.46/0.69 (step @p77 :rule nary_cong :premises (@p76 @p75 @p74) :args (@t60)) % 0.46/0.69 (step @p78 :rule cong :premises (@p77 @p72) :args (@t61)) % 0.46/0.69 (step @p79 :rule cong :premises (@p78) :args (@t62)) % 0.46/0.69 (step @p80 :rule eq_resolve :premises (@p35 @p79)) % 0.46/0.69 (step @p81 :rule not_implies_elim1 :premises (@p80)) % 0.46/0.69 (step @p82 :rule and_elim :premises (@p81) :args (0)) % 0.46/0.69 (step @p83 :rule cnf_or_pos :args (@t78)) % 0.46/0.69 (step @p84 :rule reordering :premises (@p83) :args ((or @t77 @t69 (not @t78)))) % 0.46/0.69 (step @p85 :rule chain_m_resolution :premises (@p84 @p82 @p65) :args (@t69 @t79 (@list @t59 @t78))) % 0.46/0.69 (step @p86 :rule instantiate :premises (@p64) :args ((@list @t46))) % 0.46/0.69 (step @p87 :rule not_implies_elim2 :premises (@p80)) % 0.46/0.69 (step @p88 :rule not_implies_elim1 :premises (@p87)) % 0.46/0.69 (step @p89 :rule and_elim :premises (@p88) :args (0)) % 0.46/0.69 (step @p90 :rule cnf_or_pos :args (@t81)) % 0.46/0.69 (step @p91 :rule reordering :premises (@p90) :args ((or @t80 @t71 (not @t81)))) % 0.46/0.69 (step @p92 :rule chain_m_resolution :premises (@p91 @p89 @p86) :args (@t71 @t79 (@list @t53 @t81))) % 0.46/0.69 (step @p93 :rule not_implies_elim2 :premises (@p87)) % 0.46/0.69 (step @p94 :rule cnf_or_pos :args (@t76)) % 0.46/0.69 (step @p95 :rule reordering :premises (@p94) :args ((or @t67 @t72 @t70 @t75 (not @t76)))) % 0.46/0.69 (step @p96 :rule chain_m_resolution :premises (@p95 @p93 @p92 @p85 @p61) :args (@t75 (@list true false false false) (@list @t67 @t71 @t69 @t76))) % 0.46/0.69 (step @p97 :rule false_intro :premises (@p96)) % 0.46/0.69 (step @p98 :rule and_elim :premises (@p88) :args (1)) % 0.46/0.69 (step @p99 :rule and_elim :premises (@p34) :args (0)) % 0.46/0.69 (step @p100 :rule trans :premises (@p99 @p98)) % 0.46/0.69 (step @p101 :rule symm :premises (@p99)) % 0.46/0.69 (step @p102 :rule and_elim :premises (@p81) :args (1)) % 0.46/0.69 (step @p103 :rule trans :premises (@p101 @p102)) % 0.46/0.69 (step @p104 :rule symm :premises (@p103)) % 0.46/0.69 (step @p105 :rule trans :premises (@p104 @p101 @p100)) % 0.46/0.69 (step @p106 :rule true_intro :premises (@p105)) % 0.46/0.69 (step @p107 :rule symm :premises (@p106)) % 0.46/0.69 (step @p108 :rule trans :premises (@p107 @p97)) % 0.46/0.69 (step @p109 false :rule eq_resolve :premises (@p108 @p37)) % 0.46/0.69 ) % 0.46/0.69 % SZS output end Proof % 0.46/0.69 % cvc5 exiting %------------------------------------------------------------------------------