%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN089+2 : TPTP v9.2.1. Released v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.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 08:42:57 AM UTC 2026 % Result : Theorem 0.38s 0.56s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN089+2 : TPTP v9.2.1. Released v7.3.0. % 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 : n004.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 12:44:37 EDT 2026 % 0.17/0.34 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.38/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.38/0.56 % SZS status Theorem % 0.38/0.56 % SZS output start Proof % 0.38/0.56 ( % 0.38/0.56 (declare-sort $$unsorted 0) % 0.38/0.56 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.56 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.38/0.56 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.38/0.56 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.38/0.56 (define @t1 () (@var "Y24" $$unsorted)) % 0.38/0.56 (define @t2 () (@var "X19" $$unsorted)) % 0.38/0.56 (define @t3 () (= @t2 @t1)) % 0.38/0.56 (define @t4 () (tptp.r1 @t2)) % 0.38/0.56 (define @t5 () (@var "Y21" $$unsorted)) % 0.38/0.56 (define @t6 () (@var "X12" $$unsorted)) % 0.38/0.56 (define @t7 () (= @t6 @t5)) % 0.38/0.56 (define @t8 () (@var "X11" $$unsorted)) % 0.38/0.56 (define @t9 () (tptp.r2 @t8 @t6)) % 0.38/0.56 (define @t10 () (@var "Y22" $$unsorted)) % 0.38/0.56 (define @t11 () (@var "X15" $$unsorted)) % 0.38/0.56 (define @t12 () (= @t11 @t10)) % 0.38/0.56 (define @t13 () (@var "X14" $$unsorted)) % 0.38/0.56 (define @t14 () (@var "X13" $$unsorted)) % 0.38/0.56 (define @t15 () (tptp.r3 @t14 @t13 @t11)) % 0.38/0.56 (define @t16 () (@var "Y23" $$unsorted)) % 0.38/0.56 (define @t17 () (@var "X18" $$unsorted)) % 0.38/0.56 (define @t18 () (= @t17 @t16)) % 0.38/0.56 (define @t19 () (@var "X17" $$unsorted)) % 0.38/0.56 (define @t20 () (@var "X16" $$unsorted)) % 0.38/0.56 (define @t21 () (tptp.r4 @t20 @t19 @t17)) % 0.38/0.56 (define @t22 () (@var "Y7" $$unsorted)) % 0.38/0.56 (define @t23 () (@var "X8" $$unsorted)) % 0.38/0.56 (define @t24 () (@var "X1" $$unsorted)) % 0.38/0.56 (define @t25 () (@var "Y4" $$unsorted)) % 0.38/0.56 (define @t26 () (@var "Y5" $$unsorted)) % 0.38/0.56 (define @t27 () (@var "Y15" $$unsorted)) % 0.38/0.56 (define @t28 () (@list @t25)) % 0.38/0.56 (define @t29 () (@var "Y6" $$unsorted)) % 0.38/0.56 (define @t30 () (@var "X9" $$unsorted)) % 0.38/0.56 (define @t31 () (@var "X2" $$unsorted)) % 0.38/0.56 (define @t32 () (@var "Y2" $$unsorted)) % 0.38/0.56 (define @t33 () (@var "Y3" $$unsorted)) % 0.38/0.56 (define @t34 () (@var "Y14" $$unsorted)) % 0.38/0.56 (define @t35 () (@list @t33)) % 0.38/0.56 (define @t36 () (@list @t32)) % 0.38/0.56 (define @t37 () (@var "X10" $$unsorted)) % 0.38/0.56 (define @t38 () (@var "X3" $$unsorted)) % 0.38/0.56 (define @t39 () (@var "Y12" $$unsorted)) % 0.38/0.56 (define @t40 () (@var "Y13" $$unsorted)) % 0.38/0.56 (define @t41 () (@var "X4" $$unsorted)) % 0.38/0.56 (define @t42 () (@var "Y9" $$unsorted)) % 0.38/0.56 (define @t43 () (@var "Y16" $$unsorted)) % 0.38/0.56 (define @t44 () (@var "Y18" $$unsorted)) % 0.38/0.56 (define @t45 () (@var "Y8" $$unsorted)) % 0.38/0.56 (define @t46 () (@var "Y17" $$unsorted)) % 0.38/0.56 (define @t47 () (@var "X5" $$unsorted)) % 0.38/0.56 (define @t48 () (@var "Y11" $$unsorted)) % 0.38/0.56 (define @t49 () (@var "X6" $$unsorted)) % 0.38/0.56 (define @t50 () (@var "Y1" $$unsorted)) % 0.38/0.56 (define @t51 () (@var "Y19" $$unsorted)) % 0.38/0.56 (define @t52 () (@var "Y10" $$unsorted)) % 0.38/0.56 (define @t53 () (@var "X7" $$unsorted)) % 0.38/0.56 (define @t54 () (not (tptp.r2 @t53 @t52))) % 0.38/0.56 (define @t55 () (@var "Y20" $$unsorted)) % 0.38/0.56 (define @t56 () (not (= @t55 @t52))) % 0.38/0.56 (define @t57 () (not (tptp.r1 @t55))) % 0.38/0.56 (define @t58 () (or @t57 @t56)) % 0.38/0.56 (define @t59 () (@list @t55)) % 0.38/0.56 (define @t60 () (forall @t59 @t58)) % 0.38/0.56 (define @t61 () (or @t60 @t54)) % 0.38/0.56 (define @t62 () (@list @t53 @t52)) % 0.38/0.56 (define @t63 () (forall @t62 @t61)) % 0.38/0.56 (define @t64 () (not (tptp.r1 @t25))) % 0.38/0.56 (define @t65 () (not (= @t25 @t50))) % 0.38/0.56 (define @t66 () (or @t65 @t64)) % 0.38/0.56 (define @t67 () (forall @t28 @t66)) % 0.38/0.56 (define @t68 () (not (tptp.r2 @t32 @t50))) % 0.38/0.56 (define @t69 () (forall @t36 (or (forall @t35 (or (not (tptp.r1 @t33)) (not (tptp.r2 @t33 @t32)))) @t68))) % 0.38/0.56 (define @t70 () (or @t69 @t67)) % 0.38/0.56 (define @t71 () (@list @t50)) % 0.38/0.56 (define @t72 () (forall @t71 @t70)) % 0.38/0.56 (define @t73 () (not @t72)) % 0.38/0.56 (define @t74 () (not (tptp.r1 @t52))) % 0.38/0.56 (define @t75 () (not (= @t52 @t52))) % 0.38/0.56 (define @t76 () (or @t74 @t75)) % 0.38/0.56 (define @t77 () (not (= @t52 @t55))) % 0.38/0.56 (define @t78 () (or @t77 @t57 @t77)) % 0.38/0.56 (define @t79 () (or @t57 @t77)) % 0.38/0.56 (define @t80 () (@var "BOUND_VARIABLE_8154" $$unsorted)) % 0.38/0.56 (define @t81 () (@var "BOUND_VARIABLE_8156" $$unsorted)) % 0.38/0.56 (define @t82 () (not (tptp.r2 @t81 @t80))) % 0.38/0.56 (define @t83 () (not (tptp.r1 @t81))) % 0.38/0.56 (define @t84 () (not (tptp.r2 @t80 @t50))) % 0.38/0.56 (define @t85 () (not (tptp.r1 @t50))) % 0.38/0.56 (define @t86 () (or @t85 @t84 @t83 @t82)) % 0.38/0.56 (define @t87 () (or @t84 @t83 @t82)) % 0.38/0.56 (define @t88 () (or @t87 @t85)) % 0.38/0.56 (define @t89 () (@list @t50 @t80 @t81)) % 0.38/0.56 (define @t90 () (forall @t89 @t88)) % 0.38/0.56 (define @t91 () (@list @t80 @t81)) % 0.38/0.56 (define @t92 () (forall @t91 @t88)) % 0.38/0.56 (define @t93 () (forall @t91 @t87)) % 0.38/0.56 (define @t94 () (@var "BOUND_VARIABLE_8134" $$unsorted)) % 0.38/0.56 (define @t95 () (or @t93 @t85)) % 0.38/0.56 (define @t96 () (not (tptp.r2 @t94 @t32))) % 0.38/0.56 (define @t97 () (not (tptp.r1 @t94))) % 0.38/0.56 (define @t98 () (or @t68 @t97 @t96)) % 0.38/0.56 (define @t99 () (@list @t32 @t94)) % 0.38/0.56 (define @t100 () (not (= @t50 @t50))) % 0.38/0.56 (define @t101 () (or @t100 @t85)) % 0.38/0.56 (define @t102 () (or @t65 @t65 @t64)) % 0.38/0.56 (define @t103 () (or @t97 @t96)) % 0.38/0.56 (define @t104 () (or @t103 @t68)) % 0.38/0.56 (define @t105 () (forall @t99 @t104)) % 0.38/0.56 (define @t106 () (@list @t94)) % 0.38/0.56 (define @t107 () (forall @t106 @t104)) % 0.38/0.56 (define @t108 () (forall @t106 @t103)) % 0.38/0.56 (define @t109 () (or @t108 @t68)) % 0.38/0.56 (define @t110 () (forall @t89 @t86)) % 0.38/0.56 (define @t111 () (@quantifiers_skolemize @t110 0)) % 0.38/0.56 (define @t112 () (@quantifiers_skolemize @t110 1)) % 0.38/0.56 (define @t113 () (tptp.r2 @t112 @t111)) % 0.38/0.56 (define @t114 () (@quantifiers_skolemize @t110 2)) % 0.38/0.56 (define @t115 () (not @t113)) % 0.38/0.56 (define @t116 () (tptp.r1 @t111)) % 0.38/0.56 (define @t117 () (not @t116)) % 0.38/0.56 (define @t118 () (or @t117 @t115 (not (tptp.r1 @t114)) (not (tptp.r2 @t114 @t112)))) % 0.38/0.56 (define @t119 () (@list true)) % 0.38/0.56 (define @t120 () (@list @t118)) % 0.38/0.56 (define @t121 () (or @t117 @t115)) % 0.38/0.56 (define @t122 () (not @t121)) % 0.38/0.56 (define @t123 () (forall @t62 (or @t74 @t54))) % 0.38/0.56 (assume @p1 (exists (@list @t1) (forall (@list @t2) (or (and (not @t4) (not @t3)) (and @t4 @t3))))) % 0.38/0.56 (assume @p2 (forall (@list @t8) (exists (@list @t5) (forall (@list @t6) (or (and (not @t9) (not @t7)) (and @t9 @t7)))))) % 0.38/0.56 (assume @p3 (forall (@list @t14 @t13) (exists (@list @t10) (forall (@list @t11) (or (and (not @t15) (not @t12)) (and @t15 @t12)))))) % 0.38/0.56 (assume @p4 (forall (@list @t20 @t19) (exists (@list @t16) (forall (@list @t17) (or (and (not @t21) (not @t18)) (and @t21 @t18)))))) % 0.38/0.56 (assume @p5 (forall (@list @t24 @t23) (exists @t28 (and (exists (@list @t26) (and (exists (@list @t27) (and (tptp.r2 @t23 @t27) (tptp.r3 @t24 @t27 @t26))) (= @t26 @t25))) (exists (@list @t22) (and (tptp.r2 @t22 @t25) (tptp.r3 @t24 @t23 @t22))))))) % 0.38/0.56 (assume @p6 (forall (@list @t31 @t30) (exists @t36 (and (exists @t35 (and (exists (@list @t34) (and (tptp.r2 @t30 @t34) (tptp.r4 @t31 @t34 @t33))) (= @t33 @t32))) (exists (@list @t29) (and (tptp.r3 @t29 @t31 @t32) (tptp.r4 @t31 @t30 @t29))))))) % 0.38/0.56 (assume @p7 (forall (@list @t38 @t37) (or (forall (@list @t39) (or (forall (@list @t40) (or (not (tptp.r2 @t38 @t40)) (not (= @t40 @t39)))) (not (tptp.r2 @t37 @t39)))) (= @t38 @t37)))) % 0.38/0.56 (assume @p8 (forall (@list @t41) (exists (@list @t42) (and (exists (@list @t43) (and (tptp.r1 @t43) (tptp.r3 @t41 @t43 @t42))) (= @t42 @t41))))) % 0.38/0.56 (assume @p9 (forall (@list @t47) (exists (@list @t45) (and (exists (@list @t46) (and (tptp.r1 @t46) (tptp.r4 @t47 @t46 @t45))) (exists (@list @t44) (and (tptp.r1 @t44) (= @t45 @t44))))))) % 0.38/0.56 (assume @p10 (forall (@list @t49) (or (exists (@list @t51) (and (tptp.r1 @t51) (= @t49 @t51))) (exists (@list @t50 @t48) (and (tptp.r2 @t50 @t48) (= @t49 @t48)))))) % 0.38/0.56 (assume @p11 @t63) % 0.38/0.56 (assume @p12 @t73) % 0.38/0.56 (assume @p13 true) % 0.38/0.56 (step @p14 :rule refl :args (@t54)) % 0.38/0.56 (step @p15 :rule aci_norm :args ((= (or @t74 false) @t74))) % 0.38/0.56 (step @p16 :rule evaluate :args ((not true))) % 0.38/0.56 (step @p17 :rule eq-refl :args (@t52)) % 0.38/0.56 (step @p18 :rule cong :premises (@p17) :args (@t75)) % 0.38/0.56 (step @p19 :rule trans :premises (@p18 @p16)) % 0.38/0.56 (step @p20 :rule refl :args (@t74)) % 0.38/0.56 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t76)) % 0.38/0.56 (step @p22 :rule trans :premises (@p21 @p15)) % 0.38/0.56 (step @p23 :rule quant-var-elim-eq :args ((= (forall @t59 (or @t56 @t57 @t77)) @t76))) % 0.38/0.56 (step @p24 :rule refl :args (@t77)) % 0.38/0.56 (step @p25 :rule refl :args (@t57)) % 0.38/0.56 (step @p26 :rule eq-symm :args (@t52 @t55)) % 0.38/0.56 (step @p27 :rule cong :premises (@p26) :args (@t77)) % 0.38/0.56 (step @p28 :rule nary_cong :premises (@p27 @p25 @p24) :args (@t78)) % 0.38/0.56 (step @p29 :rule aci_norm :args ((= @t79 @t78))) % 0.38/0.56 (step @p30 :rule trans :premises (@p29 @p28)) % 0.38/0.56 (step @p31 :rule cong :premises (@p30) :args ((forall @t59 @t79))) % 0.38/0.56 (step @p32 :rule trans :premises (@p31 @p23)) % 0.38/0.56 (step @p33 :rule trans :premises (@p32 @p22)) % 0.38/0.56 (step @p34 :rule eq-symm :args (@t55 @t52)) % 0.38/0.56 (step @p35 :rule cong :premises (@p34) :args (@t56)) % 0.38/0.56 (step @p36 :rule refl :args (@t57)) % 0.38/0.56 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t58)) % 0.38/0.56 (step @p38 :rule cong :premises (@p37) :args (@t60)) % 0.38/0.57 (step @p39 :rule trans :premises (@p38 @p33)) % 0.38/0.57 (step @p40 :rule nary_cong :premises (@p39 @p14) :args (@t61)) % 0.38/0.57 (step @p41 :rule cong :premises (@p40) :args (@t63)) % 0.38/0.57 (step @p42 :rule eq_resolve :premises (@p11 @p41)) % 0.38/0.57 (step @p43 :rule aci_norm :args ((= @t88 @t86))) % 0.38/0.57 (step @p44 :rule cong :premises (@p43) :args (@t90)) % 0.38/0.57 (step @p45 :rule quant-merge-prenex :args ((= (forall @t71 @t92) @t90))) % 0.38/0.57 (step @p46 :rule refl :args (@t85)) % 0.38/0.57 (step @p47 :rule alpha_equiv :args (@t93 (@list @t80 @t81) (@list @t32 @t94))) % 0.38/0.57 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t95)) % 0.38/0.57 (step @p49 :rule quant-miniscope-or :args ((= @t92 @t95))) % 0.38/0.57 (step @p50 :rule trans :premises (@p49 @p48)) % 0.38/0.57 (step @p51 :rule symm :premises (@p50)) % 0.38/0.57 (step @p52 :rule cong :premises (@p51) :args ((forall @t71 (or (forall @t99 @t98) @t85)))) % 0.38/0.57 (step @p53 :rule trans :premises (@p52 @p45)) % 0.38/0.57 (step @p54 :rule trans :premises (@p53 @p44)) % 0.38/0.57 (step @p55 :rule aci_norm :args ((= (or false @t85) @t85))) % 0.38/0.57 (step @p56 :rule refl :args (@t85)) % 0.38/0.57 (step @p57 :rule eq-refl :args (@t50)) % 0.38/0.57 (step @p58 :rule cong :premises (@p57) :args (@t100)) % 0.38/0.57 (step @p59 :rule trans :premises (@p58 @p16)) % 0.38/0.57 (step @p60 :rule nary_cong :premises (@p59 @p56) :args (@t101)) % 0.38/0.57 (step @p61 :rule trans :premises (@p60 @p55)) % 0.38/0.57 (step @p62 :rule quant-var-elim-eq :args ((= (forall @t28 @t102) @t101))) % 0.38/0.57 (step @p63 :rule aci_norm :args ((= @t66 @t102))) % 0.38/0.57 (step @p64 :rule cong :premises (@p63) :args (@t67)) % 0.38/0.57 (step @p65 :rule trans :premises (@p64 @p62)) % 0.38/0.57 (step @p66 :rule trans :premises (@p65 @p61)) % 0.38/0.57 (step @p67 :rule aci_norm :args ((= @t104 @t98))) % 0.38/0.57 (step @p68 :rule cong :premises (@p67) :args (@t105)) % 0.38/0.57 (step @p69 :rule quant-merge-prenex :args ((= (forall @t36 @t107) @t105))) % 0.38/0.57 (step @p70 :rule refl :args (@t68)) % 0.38/0.57 (step @p71 :rule alpha_equiv :args (@t108 (@list @t94) (@list @t33))) % 0.38/0.57 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t109)) % 0.38/0.57 (step @p73 :rule quant-miniscope-or :args ((= @t107 @t109))) % 0.38/0.57 (step @p74 :rule trans :premises (@p73 @p72)) % 0.38/0.57 (step @p75 :rule symm :premises (@p74)) % 0.38/0.57 (step @p76 :rule cong :premises (@p75) :args (@t69)) % 0.38/0.57 (step @p77 :rule trans :premises (@p76 @p69)) % 0.38/0.57 (step @p78 :rule trans :premises (@p77 @p68)) % 0.38/0.57 (step @p79 :rule nary_cong :premises (@p78 @p66) :args (@t70)) % 0.38/0.57 (step @p80 :rule cong :premises (@p79) :args (@t72)) % 0.38/0.57 (step @p81 :rule trans :premises (@p80 @p54)) % 0.38/0.57 (step @p82 :rule cong :premises (@p81) :args (@t73)) % 0.38/0.57 (step @p83 :rule eq_resolve :premises (@p12 @p82)) % 0.38/0.57 (step @p84 :rule skolemize :premises (@p83)) % 0.38/0.57 (step @p85 :rule bool-double-not-elim :args (@t113)) % 0.38/0.57 (step @p86 :rule refl :args (@t118)) % 0.38/0.57 (step @p87 :rule nary_cong :premises (@p86 @p85) :args ((or @t118 (not @t115)))) % 0.38/0.57 (step @p88 :rule cnf_or_neg :args (@t118 1)) % 0.38/0.57 (step @p89 :rule eq_resolve :premises (@p88 @p87)) % 0.38/0.57 (step @p90 :rule reordering :premises (@p89) :args ((or @t113 @t118))) % 0.38/0.57 (step @p91 :rule chain_m_resolution :premises (@p90 @p84) :args (@t113 @t119 @t120)) % 0.38/0.57 (step @p92 :rule bool-double-not-elim :args (@t116)) % 0.38/0.57 (step @p93 :rule nary_cong :premises (@p86 @p92) :args ((or @t118 (not @t117)))) % 0.38/0.57 (step @p94 :rule cnf_or_neg :args (@t118 0)) % 0.38/0.57 (step @p95 :rule eq_resolve :premises (@p94 @p93)) % 0.38/0.57 (step @p96 :rule reordering :premises (@p95) :args ((or @t116 @t118))) % 0.38/0.57 (step @p97 :rule chain_m_resolution :premises (@p96 @p84) :args (@t116 @t119 @t120)) % 0.38/0.57 (step @p98 :rule cnf_or_pos :args (@t121)) % 0.38/0.57 (step @p99 :rule reordering :premises (@p98) :args ((or @t117 @t115 @t122))) % 0.38/0.57 (step @p100 :rule chain_m_resolution :premises (@p99 @p97 @p91) :args (@t122 (@list false false) (@list @t116 @t113))) % 0.38/0.57 (assume-push @p107 @t123) % 0.38/0.57 (step @p102 :rule instantiate :premises (@p42) :args ((@list @t112 @t111))) % 0.38/0.57 (step-pop @p108 :rule scope :premises (@p102)) % 0.38/0.57 (step @p103 :rule process_scope :premises (@p108) :args (@t121)) % 0.38/0.57 (step @p105 :rule implies_elim :premises (@p103)) % 0.38/0.57 (step @p106 false :rule chain_m_resolution :premises (@p105 @p100 @p42) :args (false (@list true false) (@list @t121 @t123))) % 0.38/0.57 ) % 0.38/0.57 % SZS output end Proof % 0.38/0.57 % cvc5 exiting %------------------------------------------------------------------------------