%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : RNG095+2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n024.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 08:45:39 AM UTC 2026 % Result : Theorem 0.16s 0.37s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : RNG095+2 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.06/0.24 % Computer : n024.cluster.edu % 0.06/0.24 % Model : x86_64 x86_64 % 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.06/0.24 % Memory : 8042.1875MB % 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64 % 0.06/0.24 % CPULimit : 300 % 0.06/0.24 % WCLimit : 300 % 0.06/0.24 % DateTime : Tue Jun 2 09:06:45 EDT 2026 % 0.06/0.25 % CPUTime : % 0.06/0.32 %----Proving TF0_NAR, FOF, or CNF % 0.16/0.37 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.16/0.37 % SZS status Theorem % 0.16/0.37 % SZS output start Proof % 0.16/0.37 ( % 0.16/0.37 (declare-sort $$unsorted 0) % 0.16/0.37 (declare-const tptp.xx $$unsorted) % 0.16/0.37 (declare-const tptp.xI $$unsorted) % 0.16/0.37 (declare-const tptp.aElement0 (-> $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.sz00 $$unsorted) % 0.16/0.37 (declare-const tptp.sz10 $$unsorted) % 0.16/0.37 (declare-const tptp.smndt0 (-> $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.sdtpldt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.xy $$unsorted) % 0.16/0.37 (declare-const tptp.sdtasasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.aIdeal0 (-> $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.sdtasdt0 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.xJ $$unsorted) % 0.16/0.37 (declare-const tptp.aSet0 (-> $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.sdtpldt1 (-> $$unsorted $$unsorted $$unsorted)) % 0.16/0.37 (declare-const tptp.aElementOf0 (-> $$unsorted $$unsorted Bool)) % 0.16/0.37 (declare-const tptp.sdteqdtlpzmzozddtrp0 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.16/0.37 (define @t1 () (@var "W0" $$unsorted)) % 0.16/0.37 (define @t2 () (tptp.aElement0 @t1)) % 0.16/0.37 (define @t3 () (@list @t1)) % 0.16/0.37 (define @t4 () (tptp.aElement0 tptp.sz10)) % 0.16/0.37 (define @t5 () (tptp.smndt0 @t1)) % 0.16/0.37 (define @t6 () (@var "W1" $$unsorted)) % 0.16/0.37 (define @t7 () (tptp.sdtpldt0 @t1 @t6)) % 0.16/0.37 (define @t8 () (tptp.aElement0 @t6)) % 0.16/0.37 (define @t9 () (and @t2 @t8)) % 0.16/0.37 (define @t10 () (@list @t1 @t6)) % 0.16/0.37 (define @t11 () (tptp.sdtasdt0 @t1 @t6)) % 0.16/0.37 (define @t12 () (@var "W2" $$unsorted)) % 0.16/0.37 (define @t13 () (tptp.sdtpldt0 @t6 @t12)) % 0.16/0.37 (define @t14 () (tptp.aElement0 @t12)) % 0.16/0.37 (define @t15 () (and @t2 @t8 @t14)) % 0.16/0.37 (define @t16 () (@list @t1 @t6 @t12)) % 0.16/0.37 (define @t17 () (tptp.sdtasdt0 @t6 @t1)) % 0.16/0.37 (define @t18 () (tptp.smndt0 tptp.sz10)) % 0.16/0.37 (define @t19 () (tptp.aSet0 @t1)) % 0.16/0.37 (define @t20 () (tptp.aElementOf0 @t6 @t1)) % 0.16/0.37 (define @t21 () (@list @t6)) % 0.16/0.37 (define @t22 () (tptp.aElementOf0 @t12 @t1)) % 0.16/0.37 (define @t23 () (tptp.aElementOf0 @t12 @t6)) % 0.16/0.37 (define @t24 () (@list @t12)) % 0.16/0.37 (define @t25 () (and @t19 (tptp.aSet0 @t6))) % 0.16/0.37 (define @t26 () (@var "W3" $$unsorted)) % 0.16/0.37 (define @t27 () (@var "W5" $$unsorted)) % 0.16/0.37 (define @t28 () (@var "W4" $$unsorted)) % 0.16/0.37 (define @t29 () (tptp.aElementOf0 @t26 @t12)) % 0.16/0.37 (define @t30 () (@list @t26)) % 0.16/0.37 (define @t31 () (tptp.aSet0 @t12)) % 0.16/0.37 (define @t32 () (tptp.sdtpldt1 @t1 @t6)) % 0.16/0.37 (define @t33 () (tptp.sdtasasdt0 @t1 @t6)) % 0.16/0.37 (define @t34 () (tptp.aIdeal0 @t1)) % 0.16/0.37 (define @t35 () (and @t34 (tptp.aIdeal0 @t6))) % 0.16/0.37 (define @t36 () (tptp.aElementOf0 @t6 tptp.xJ)) % 0.16/0.37 (define @t37 () (tptp.aElementOf0 @t6 tptp.xI)) % 0.16/0.37 (define @t38 () (tptp.aElementOf0 @t1 tptp.xI)) % 0.16/0.37 (define @t39 () (tptp.sdtpldt1 tptp.xI tptp.xJ)) % 0.16/0.37 (define @t40 () (tptp.aElementOf0 @t1 @t39)) % 0.16/0.37 (define @t41 () (tptp.aElementOf0 @t12 tptp.xJ)) % 0.16/0.37 (define @t42 () (and @t37 @t41 (= @t13 @t1))) % 0.16/0.37 (define @t43 () (@list @t6 @t12)) % 0.16/0.37 (define @t44 () (exists @t43 @t42)) % 0.16/0.37 (define @t45 () (and @t44 @t40)) % 0.16/0.37 (define @t46 () (=> @t2 @t45)) % 0.16/0.37 (define @t47 () (forall @t3 @t46)) % 0.16/0.37 (define @t48 () (and @t38 @t36 (= @t7 tptp.sz10))) % 0.16/0.37 (define @t49 () (exists @t10 @t48)) % 0.16/0.37 (define @t50 () (not @t49)) % 0.16/0.37 (define @t51 () (= @t1 @t13)) % 0.16/0.37 (define @t52 () (not @t51)) % 0.16/0.37 (define @t53 () (not @t41)) % 0.16/0.37 (define @t54 () (not @t37)) % 0.16/0.37 (define @t55 () (or @t54 @t53 @t52)) % 0.16/0.37 (define @t56 () (and (not (forall @t43 @t55)) @t40)) % 0.16/0.37 (define @t57 () (and @t37 @t41 @t51)) % 0.16/0.37 (define @t58 () (forall @t43 (not @t57))) % 0.16/0.37 (define @t59 () (not @t58)) % 0.16/0.37 (define @t60 () (= tptp.sz10 @t7)) % 0.16/0.37 (define @t61 () (not @t60)) % 0.16/0.37 (define @t62 () (not @t36)) % 0.16/0.37 (define @t63 () (not @t38)) % 0.16/0.37 (define @t64 () (or @t63 @t62 @t61)) % 0.16/0.37 (define @t65 () (forall @t10 @t64)) % 0.16/0.37 (define @t66 () (and @t38 @t36 @t60)) % 0.16/0.37 (define @t67 () (forall @t10 (not @t66))) % 0.16/0.37 (define @t68 () (not @t67)) % 0.16/0.37 (define @t69 () (@var "BOUND_VARIABLE_9705" $$unsorted)) % 0.16/0.37 (define @t70 () (@var "BOUND_VARIABLE_9704" $$unsorted)) % 0.16/0.37 (define @t71 () (@list @t70 @t69)) % 0.16/0.37 (define @t72 () (forall @t43 (or @t54 @t53 (not (= tptp.sz10 @t13))))) % 0.16/0.37 (define @t73 () (@list false)) % 0.16/0.37 (define @t74 () (not @t72)) % 0.16/0.37 (define @t75 () (and @t74 (tptp.aElementOf0 tptp.sz10 @t39))) % 0.16/0.37 (define @t76 () (not @t75)) % 0.16/0.37 (define @t77 () (not @t4)) % 0.16/0.37 (define @t78 () (or @t77 @t75)) % 0.16/0.37 (assume @p1 (forall @t3 (=> @t2 true))) % 0.16/0.37 (assume @p2 (tptp.aElement0 tptp.sz00)) % 0.16/0.37 (assume @p3 @t4) % 0.16/0.37 (assume @p4 (forall @t3 (=> @t2 (tptp.aElement0 @t5)))) % 0.16/0.37 (assume @p5 (forall @t10 (=> @t9 (tptp.aElement0 @t7)))) % 0.16/0.37 (assume @p6 (forall @t10 (=> @t9 (tptp.aElement0 @t11)))) % 0.16/0.37 (assume @p7 (forall @t10 (=> @t9 (= @t7 (tptp.sdtpldt0 @t6 @t1))))) % 0.16/0.37 (assume @p8 (forall @t16 (=> @t15 (= (tptp.sdtpldt0 @t7 @t12) (tptp.sdtpldt0 @t1 @t13))))) % 0.16/0.37 (assume @p9 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 tptp.sz00) @t1) (= @t1 (tptp.sdtpldt0 tptp.sz00 @t1)))))) % 0.16/0.37 (assume @p10 (forall @t3 (=> @t2 (and (= (tptp.sdtpldt0 @t1 @t5) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 @t5 @t1)))))) % 0.16/0.37 (assume @p11 (forall @t10 (=> @t9 (= @t11 @t17)))) % 0.16/0.37 (assume @p12 (forall @t16 (=> @t15 (= (tptp.sdtasdt0 @t11 @t12) (tptp.sdtasdt0 @t1 (tptp.sdtasdt0 @t6 @t12)))))) % 0.16/0.37 (assume @p13 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz10) @t1) (= @t1 (tptp.sdtasdt0 tptp.sz10 @t1)))))) % 0.16/0.37 (assume @p14 (forall @t16 (=> @t15 (and (= (tptp.sdtasdt0 @t1 @t13) (tptp.sdtpldt0 @t11 (tptp.sdtasdt0 @t1 @t12))) (= (tptp.sdtasdt0 @t13 @t1) (tptp.sdtpldt0 @t17 (tptp.sdtasdt0 @t12 @t1))))))) % 0.16/0.37 (assume @p15 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t18 @t1) @t5) (= @t5 (tptp.sdtasdt0 @t1 @t18)))))) % 0.16/0.37 (assume @p16 (forall @t3 (=> @t2 (and (= (tptp.sdtasdt0 @t1 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 @t1)))))) % 0.16/0.37 (assume @p17 (forall @t10 (=> @t9 (=> (= @t11 tptp.sz00) (or (= @t1 tptp.sz00) (= @t6 tptp.sz00)))))) % 0.16/0.37 (assume @p18 (not (= tptp.sz10 tptp.sz00))) % 0.16/0.37 (assume @p19 (forall @t3 (=> @t19 true))) % 0.16/0.37 (assume @p20 (forall @t3 (=> @t19 (forall @t21 (=> @t20 @t8))))) % 0.16/0.37 (assume @p21 (forall @t10 (=> @t25 (=> (and (forall @t24 (=> @t22 @t23)) (forall @t24 (=> @t23 @t22))) (= @t1 @t6))))) % 0.16/0.37 (assume @p22 (forall @t10 (=> @t25 (forall @t24 (= (= @t12 @t32) (and @t31 (forall @t30 (= @t29 (exists (@list @t28 @t27) (and (tptp.aElementOf0 @t28 @t1) (tptp.aElementOf0 @t27 @t6) (= (tptp.sdtpldt0 @t28 @t27) @t26))))))))))) % 0.16/0.37 (assume @p23 (forall @t10 (=> @t25 (forall @t24 (= (= @t12 @t33) (and @t31 (forall @t30 (= @t29 (and (tptp.aElementOf0 @t26 @t1) (tptp.aElementOf0 @t26 @t6)))))))))) % 0.16/0.37 (assume @p24 (forall @t3 (= @t34 (and @t19 (forall @t21 (=> @t20 (and (forall @t24 (=> @t22 (tptp.aElementOf0 @t13 @t1))) (forall @t24 (=> @t14 (tptp.aElementOf0 (tptp.sdtasdt0 @t12 @t6) @t1)))))))))) % 0.16/0.37 (assume @p25 (forall @t10 (=> @t35 (tptp.aIdeal0 @t32)))) % 0.16/0.37 (assume @p26 (forall @t10 (=> @t35 (tptp.aIdeal0 @t33)))) % 0.16/0.37 (assume @p27 (forall @t16 (=> (and @t2 @t8 (tptp.aIdeal0 @t12)) (= (tptp.sdteqdtlpzmzozddtrp0 @t1 @t6 @t12) (tptp.aElementOf0 (tptp.sdtpldt0 @t1 (tptp.smndt0 @t6)) @t12))))) % 0.16/0.37 (assume @p28 (and (tptp.aSet0 tptp.xI) (forall @t3 (=> @t38 (and (forall @t21 (=> @t37 (tptp.aElementOf0 @t7 tptp.xI))) (forall @t21 (=> @t8 (tptp.aElementOf0 @t17 tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall @t3 (=> (tptp.aElementOf0 @t1 tptp.xJ) (and (forall @t21 (=> @t36 (tptp.aElementOf0 @t7 tptp.xJ))) (forall @t21 (=> @t8 (tptp.aElementOf0 @t17 tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ))) % 0.16/0.37 (assume @p29 @t47) % 0.16/0.37 (assume @p30 (and (tptp.aElement0 tptp.xx) (tptp.aElement0 tptp.xy))) % 0.16/0.37 (assume @p31 @t50) % 0.16/0.37 (assume @p32 true) % 0.16/0.37 (step @p33 :rule bool-impl-elim :args (@t2 @t56)) % 0.16/0.37 (step @p34 :rule cong :premises (@p33) :args ((forall @t3 (=> @t2 @t56)))) % 0.16/0.37 (step @p35 :rule refl :args (@t40)) % 0.16/0.37 (step @p36 :rule aci_norm :args ((= (or @t54 (or @t53 @t52)) @t55))) % 0.16/0.37 (step @p37 :rule bool-and-de-morgan :args (@t41 @t51 true)) % 0.16/0.37 (step @p38 :rule refl :args (@t54)) % 0.16/0.37 (step @p39 :rule nary_cong :premises (@p38 @p37) :args ((or @t54 (not (and @t41 @t51))))) % 0.16/0.37 (step @p40 :rule bool-and-de-morgan :args (@t37 @t41 (and @t51))) % 0.16/0.37 (step @p41 :rule trans :premises (@p40 @p39)) % 0.16/0.37 (step @p42 :rule trans :premises (@p41 @p36)) % 0.16/0.37 (step @p43 :rule cong :premises (@p42) :args (@t58)) % 0.16/0.37 (step @p44 :rule cong :premises (@p43) :args (@t59)) % 0.16/0.37 (step @p45 :rule exists-elim :args ((= (exists @t43 @t57) @t59))) % 0.16/0.37 (step @p46 :rule trans :premises (@p45 @p44)) % 0.16/0.37 (step @p47 :rule eq-symm :args (@t13 @t1)) % 0.16/0.37 (step @p48 :rule refl :args (@t41)) % 0.16/0.37 (step @p49 :rule refl :args (@t37)) % 0.16/0.37 (step @p50 :rule nary_cong :premises (@p49 @p48 @p47) :args (@t42)) % 0.16/0.37 (step @p51 :rule cong :premises (@p50) :args (@t44)) % 0.16/0.37 (step @p52 :rule trans :premises (@p51 @p46)) % 0.16/0.37 (step @p53 :rule nary_cong :premises (@p52 @p35) :args (@t45)) % 0.16/0.37 (step @p54 :rule refl :args (@t2)) % 0.16/0.37 (step @p55 :rule cong :premises (@p54 @p53) :args (@t46)) % 0.16/0.37 (step @p56 :rule cong :premises (@p55) :args (@t47)) % 0.16/0.37 (step @p57 :rule trans :premises (@p56 @p34)) % 0.16/0.37 (step @p58 :rule eq_resolve :premises (@p29 @p57)) % 0.16/0.37 (step @p59 :rule instantiate :premises (@p58) :args ((@list tptp.sz10))) % 0.16/0.37 (step @p60 :rule bool-double-not-elim :args (@t65)) % 0.16/0.37 (step @p61 :rule aci_norm :args ((= (or @t63 (or @t62 @t61)) @t64))) % 0.16/0.37 (step @p62 :rule bool-and-de-morgan :args (@t36 @t60 true)) % 0.16/0.37 (step @p63 :rule refl :args (@t63)) % 0.16/0.37 (step @p64 :rule nary_cong :premises (@p63 @p62) :args ((or @t63 (not (and @t36 @t60))))) % 0.16/0.37 (step @p65 :rule bool-and-de-morgan :args (@t38 @t36 (and @t60))) % 0.16/0.37 (step @p66 :rule trans :premises (@p65 @p64)) % 0.16/0.37 (step @p67 :rule trans :premises (@p66 @p61)) % 0.16/0.37 (step @p68 :rule cong :premises (@p67) :args (@t67)) % 0.16/0.37 (step @p69 :rule cong :premises (@p68) :args (@t68)) % 0.16/0.37 (step @p70 :rule exists-elim :args ((= (exists @t10 @t66) @t68))) % 0.16/0.37 (step @p71 :rule trans :premises (@p70 @p69)) % 0.16/0.37 (step @p72 :rule eq-symm :args (@t7 tptp.sz10)) % 0.16/0.37 (step @p73 :rule refl :args (@t36)) % 0.16/0.37 (step @p74 :rule refl :args (@t38)) % 0.16/0.37 (step @p75 :rule nary_cong :premises (@p74 @p73 @p72) :args (@t48)) % 0.16/0.37 (step @p76 :rule cong :premises (@p75) :args (@t49)) % 0.16/0.37 (step @p77 :rule trans :premises (@p76 @p71)) % 0.16/0.37 (step @p78 :rule cong :premises (@p77) :args (@t50)) % 0.16/0.37 (step @p79 :rule trans :premises (@p78 @p60)) % 0.16/0.37 (step @p80 :rule eq_resolve :premises (@p31 @p79)) % 0.16/0.37 (step @p81 :rule alpha_equiv :args ((forall (@list @t70 @t69) (or (not (tptp.aElementOf0 @t70 tptp.xI)) (not (tptp.aElementOf0 @t69 tptp.xJ)) (not (= tptp.sz10 (tptp.sdtpldt0 @t70 @t69))))) @t71 (@list @t6 @t12))) % 0.16/0.37 (step @p82 :rule alpha_equiv :args (@t65 (@list @t1 @t6) @t71)) % 0.16/0.37 (step @p83 :rule trans :premises (@p82 @p81)) % 0.16/0.37 (step @p84 :rule equiv_elim1 :premises (@p83)) % 0.16/0.37 (step @p85 :rule chain_m_resolution :premises (@p84 @p80) :args (@t72 @t73 (@list @t65))) % 0.16/0.37 (step @p86 :rule cnf_and_pos :args (@t75 0)) % 0.16/0.37 (step @p87 :rule reordering :premises (@p86) :args ((or @t74 @t76))) % 0.16/0.37 (step @p88 :rule chain_m_resolution :premises (@p87 @p85) :args (@t76 @t73 (@list @t72))) % 0.16/0.37 (step @p89 :rule cnf_or_pos :args (@t78)) % 0.16/0.37 (step @p90 :rule reordering :premises (@p89) :args ((or @t77 @t75 (not @t78)))) % 0.16/0.37 (step @p91 false :rule chain_m_resolution :premises (@p90 @p88 @p59 @p3) :args (false (@list true false false) (@list @t75 @t78 @t4))) % 0.16/0.37 ) % 0.16/0.37 % SZS output end Proof % 0.16/0.37 % cvc5 exiting %------------------------------------------------------------------------------