%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : NUN088+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 08:42:56 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUN088+2 : TPTP v9.2.1. Released v7.3.0. % 0.11/0.13 % 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 12:44:07 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.37/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort $$unsorted 0) % 0.37/0.56 (declare-const tptp.r4 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.r3 (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.r2 (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.r1 (-> $$unsorted Bool)) % 0.37/0.56 (define @t1 () (@var "Y24" $$unsorted)) % 0.37/0.56 (define @t2 () (@var "X19" $$unsorted)) % 0.37/0.56 (define @t3 () (= @t2 @t1)) % 0.37/0.56 (define @t4 () (tptp.r1 @t2)) % 0.37/0.56 (define @t5 () (@var "Y21" $$unsorted)) % 0.37/0.56 (define @t6 () (@var "X12" $$unsorted)) % 0.37/0.56 (define @t7 () (= @t6 @t5)) % 0.37/0.56 (define @t8 () (@var "X11" $$unsorted)) % 0.37/0.56 (define @t9 () (tptp.r2 @t8 @t6)) % 0.37/0.56 (define @t10 () (@var "Y22" $$unsorted)) % 0.37/0.56 (define @t11 () (@var "X15" $$unsorted)) % 0.37/0.56 (define @t12 () (= @t11 @t10)) % 0.37/0.56 (define @t13 () (@var "X14" $$unsorted)) % 0.37/0.56 (define @t14 () (@var "X13" $$unsorted)) % 0.37/0.56 (define @t15 () (tptp.r3 @t14 @t13 @t11)) % 0.37/0.56 (define @t16 () (@var "Y23" $$unsorted)) % 0.37/0.56 (define @t17 () (@var "X18" $$unsorted)) % 0.37/0.56 (define @t18 () (= @t17 @t16)) % 0.37/0.56 (define @t19 () (@var "X17" $$unsorted)) % 0.37/0.56 (define @t20 () (@var "X16" $$unsorted)) % 0.37/0.56 (define @t21 () (tptp.r4 @t20 @t19 @t17)) % 0.37/0.56 (define @t22 () (@var "Y7" $$unsorted)) % 0.37/0.56 (define @t23 () (@var "X8" $$unsorted)) % 0.37/0.56 (define @t24 () (@var "X1" $$unsorted)) % 0.37/0.56 (define @t25 () (@var "Y4" $$unsorted)) % 0.37/0.56 (define @t26 () (@var "Y5" $$unsorted)) % 0.37/0.56 (define @t27 () (@var "Y15" $$unsorted)) % 0.37/0.56 (define @t28 () (@var "Y6" $$unsorted)) % 0.37/0.56 (define @t29 () (@var "X9" $$unsorted)) % 0.37/0.56 (define @t30 () (@var "X2" $$unsorted)) % 0.37/0.56 (define @t31 () (@var "Y2" $$unsorted)) % 0.37/0.56 (define @t32 () (@var "Y3" $$unsorted)) % 0.37/0.56 (define @t33 () (@var "Y14" $$unsorted)) % 0.37/0.56 (define @t34 () (@list @t32)) % 0.37/0.56 (define @t35 () (@list @t31)) % 0.37/0.56 (define @t36 () (@var "X10" $$unsorted)) % 0.37/0.56 (define @t37 () (@var "X3" $$unsorted)) % 0.37/0.56 (define @t38 () (@var "Y12" $$unsorted)) % 0.37/0.56 (define @t39 () (@var "Y13" $$unsorted)) % 0.37/0.56 (define @t40 () (@var "X4" $$unsorted)) % 0.37/0.56 (define @t41 () (@var "Y9" $$unsorted)) % 0.37/0.56 (define @t42 () (@var "Y16" $$unsorted)) % 0.37/0.56 (define @t43 () (@var "Y18" $$unsorted)) % 0.37/0.56 (define @t44 () (@var "Y8" $$unsorted)) % 0.37/0.56 (define @t45 () (@var "Y17" $$unsorted)) % 0.37/0.56 (define @t46 () (@var "X5" $$unsorted)) % 0.37/0.56 (define @t47 () (@var "Y11" $$unsorted)) % 0.37/0.56 (define @t48 () (@var "X6" $$unsorted)) % 0.37/0.56 (define @t49 () (@var "Y1" $$unsorted)) % 0.37/0.56 (define @t50 () (@var "Y19" $$unsorted)) % 0.37/0.56 (define @t51 () (@var "Y10" $$unsorted)) % 0.37/0.56 (define @t52 () (@var "X7" $$unsorted)) % 0.37/0.56 (define @t53 () (not (tptp.r2 @t52 @t51))) % 0.37/0.56 (define @t54 () (@var "Y20" $$unsorted)) % 0.37/0.56 (define @t55 () (not (= @t54 @t51))) % 0.37/0.56 (define @t56 () (not (tptp.r1 @t54))) % 0.37/0.56 (define @t57 () (or @t56 @t55)) % 0.37/0.56 (define @t58 () (@list @t54)) % 0.37/0.56 (define @t59 () (forall @t58 @t57)) % 0.37/0.56 (define @t60 () (or @t59 @t53)) % 0.37/0.56 (define @t61 () (@list @t52 @t51)) % 0.37/0.56 (define @t62 () (forall @t61 @t60)) % 0.37/0.56 (define @t63 () (forall @t34 (or (not (tptp.r1 @t32)) (not (tptp.r2 @t32 @t49))))) % 0.37/0.56 (define @t64 () (not (= @t31 @t49))) % 0.37/0.56 (define @t65 () (not (tptp.r1 @t31))) % 0.37/0.56 (define @t66 () (or @t65 @t64)) % 0.37/0.56 (define @t67 () (forall @t35 @t66)) % 0.37/0.56 (define @t68 () (or @t67 @t63)) % 0.37/0.56 (define @t69 () (@list @t49)) % 0.37/0.56 (define @t70 () (forall @t69 @t68)) % 0.37/0.56 (define @t71 () (not @t70)) % 0.37/0.56 (define @t72 () (not (tptp.r1 @t51))) % 0.37/0.56 (define @t73 () (not (= @t51 @t51))) % 0.37/0.56 (define @t74 () (or @t72 @t73)) % 0.37/0.56 (define @t75 () (not (= @t51 @t54))) % 0.37/0.56 (define @t76 () (or @t75 @t56 @t75)) % 0.37/0.56 (define @t77 () (or @t56 @t75)) % 0.37/0.56 (define @t78 () (@var "BOUND_VARIABLE_8138" $$unsorted)) % 0.37/0.56 (define @t79 () (not (tptp.r2 @t78 @t49))) % 0.37/0.56 (define @t80 () (not (tptp.r1 @t78))) % 0.37/0.56 (define @t81 () (not (tptp.r1 @t49))) % 0.37/0.56 (define @t82 () (or @t81 @t80 @t79)) % 0.37/0.56 (define @t83 () (or @t80 @t79)) % 0.37/0.56 (define @t84 () (or @t81 @t83)) % 0.37/0.56 (define @t85 () (@list @t49 @t78)) % 0.37/0.56 (define @t86 () (forall @t85 @t84)) % 0.37/0.56 (define @t87 () (@list @t78)) % 0.37/0.56 (define @t88 () (forall @t87 @t84)) % 0.37/0.56 (define @t89 () (forall @t87 @t83)) % 0.37/0.56 (define @t90 () (or @t81 @t89)) % 0.37/0.56 (define @t91 () (not (= @t49 @t49))) % 0.37/0.56 (define @t92 () (or @t81 @t91)) % 0.37/0.56 (define @t93 () (or @t64 @t65 @t64)) % 0.37/0.56 (define @t94 () (forall @t85 @t82)) % 0.37/0.56 (define @t95 () (@quantifiers_skolemize @t94 0)) % 0.37/0.56 (define @t96 () (@quantifiers_skolemize @t94 1)) % 0.37/0.56 (define @t97 () (tptp.r2 @t96 @t95)) % 0.37/0.56 (define @t98 () (not @t97)) % 0.37/0.56 (define @t99 () (tptp.r1 @t95)) % 0.37/0.56 (define @t100 () (not @t99)) % 0.37/0.56 (define @t101 () (or @t100 (not (tptp.r1 @t96)) @t98)) % 0.37/0.56 (define @t102 () (@list true)) % 0.37/0.56 (define @t103 () (@list @t101)) % 0.37/0.56 (define @t104 () (or @t100 @t98)) % 0.37/0.56 (define @t105 () (not @t104)) % 0.37/0.56 (define @t106 () (forall @t61 (or @t72 @t53))) % 0.37/0.56 (assume @p1 (exists (@list @t1) (forall (@list @t2) (or (and (not @t4) (not @t3)) (and @t4 @t3))))) % 0.37/0.56 (assume @p2 (forall (@list @t8) (exists (@list @t5) (forall (@list @t6) (or (and (not @t9) (not @t7)) (and @t9 @t7)))))) % 0.37/0.56 (assume @p3 (forall (@list @t14 @t13) (exists (@list @t10) (forall (@list @t11) (or (and (not @t15) (not @t12)) (and @t15 @t12)))))) % 0.37/0.56 (assume @p4 (forall (@list @t20 @t19) (exists (@list @t16) (forall (@list @t17) (or (and (not @t21) (not @t18)) (and @t21 @t18)))))) % 0.37/0.56 (assume @p5 (forall (@list @t24 @t23) (exists (@list @t25) (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))))))) % 0.37/0.56 (assume @p6 (forall (@list @t30 @t29) (exists @t35 (and (exists @t34 (and (exists (@list @t33) (and (tptp.r2 @t29 @t33) (tptp.r4 @t30 @t33 @t32))) (= @t32 @t31))) (exists (@list @t28) (and (tptp.r3 @t28 @t30 @t31) (tptp.r4 @t30 @t29 @t28))))))) % 0.37/0.56 (assume @p7 (forall (@list @t37 @t36) (or (forall (@list @t38) (or (forall (@list @t39) (or (not (tptp.r2 @t37 @t39)) (not (= @t39 @t38)))) (not (tptp.r2 @t36 @t38)))) (= @t37 @t36)))) % 0.37/0.56 (assume @p8 (forall (@list @t40) (exists (@list @t41) (and (exists (@list @t42) (and (tptp.r1 @t42) (tptp.r3 @t40 @t42 @t41))) (= @t41 @t40))))) % 0.37/0.56 (assume @p9 (forall (@list @t46) (exists (@list @t44) (and (exists (@list @t45) (and (tptp.r1 @t45) (tptp.r4 @t46 @t45 @t44))) (exists (@list @t43) (and (tptp.r1 @t43) (= @t44 @t43))))))) % 0.37/0.56 (assume @p10 (forall (@list @t48) (or (exists (@list @t50) (and (tptp.r1 @t50) (= @t48 @t50))) (exists (@list @t49 @t47) (and (tptp.r2 @t49 @t47) (= @t48 @t47)))))) % 0.37/0.56 (assume @p11 @t62) % 0.37/0.56 (assume @p12 @t71) % 0.37/0.56 (assume @p13 true) % 0.37/0.56 (step @p14 :rule refl :args (@t53)) % 0.37/0.56 (step @p15 :rule aci_norm :args ((= (or @t72 false) @t72))) % 0.37/0.56 (step @p16 :rule evaluate :args ((not true))) % 0.37/0.56 (step @p17 :rule eq-refl :args (@t51)) % 0.37/0.56 (step @p18 :rule cong :premises (@p17) :args (@t73)) % 0.37/0.56 (step @p19 :rule trans :premises (@p18 @p16)) % 0.37/0.56 (step @p20 :rule refl :args (@t72)) % 0.37/0.56 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t74)) % 0.37/0.56 (step @p22 :rule trans :premises (@p21 @p15)) % 0.37/0.56 (step @p23 :rule quant-var-elim-eq :args ((= (forall @t58 (or @t55 @t56 @t75)) @t74))) % 0.37/0.56 (step @p24 :rule refl :args (@t75)) % 0.37/0.56 (step @p25 :rule refl :args (@t56)) % 0.37/0.56 (step @p26 :rule eq-symm :args (@t51 @t54)) % 0.37/0.56 (step @p27 :rule cong :premises (@p26) :args (@t75)) % 0.37/0.56 (step @p28 :rule nary_cong :premises (@p27 @p25 @p24) :args (@t76)) % 0.37/0.56 (step @p29 :rule aci_norm :args ((= @t77 @t76))) % 0.37/0.56 (step @p30 :rule trans :premises (@p29 @p28)) % 0.37/0.56 (step @p31 :rule cong :premises (@p30) :args ((forall @t58 @t77))) % 0.37/0.56 (step @p32 :rule trans :premises (@p31 @p23)) % 0.37/0.56 (step @p33 :rule trans :premises (@p32 @p22)) % 0.37/0.56 (step @p34 :rule eq-symm :args (@t54 @t51)) % 0.37/0.56 (step @p35 :rule cong :premises (@p34) :args (@t55)) % 0.37/0.56 (step @p36 :rule refl :args (@t56)) % 0.37/0.56 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t57)) % 0.37/0.56 (step @p38 :rule cong :premises (@p37) :args (@t59)) % 0.37/0.56 (step @p39 :rule trans :premises (@p38 @p33)) % 0.37/0.56 (step @p40 :rule nary_cong :premises (@p39 @p14) :args (@t60)) % 0.37/0.56 (step @p41 :rule cong :premises (@p40) :args (@t62)) % 0.37/0.56 (step @p42 :rule eq_resolve :premises (@p11 @p41)) % 0.37/0.56 (step @p43 :rule aci_norm :args ((= @t84 @t82))) % 0.37/0.56 (step @p44 :rule cong :premises (@p43) :args (@t86)) % 0.37/0.56 (step @p45 :rule quant-merge-prenex :args ((= (forall @t69 @t88) @t86))) % 0.37/0.56 (step @p46 :rule alpha_equiv :args (@t89 (@list @t78) (@list @t32))) % 0.37/0.56 (step @p47 :rule refl :args (@t81)) % 0.37/0.56 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t90)) % 0.37/0.56 (step @p49 :rule quant-miniscope-or :args ((= @t88 @t90))) % 0.37/0.56 (step @p50 :rule trans :premises (@p49 @p48)) % 0.37/0.56 (step @p51 :rule symm :premises (@p50)) % 0.37/0.56 (step @p52 :rule cong :premises (@p51) :args ((forall @t69 (or @t81 @t63)))) % 0.37/0.57 (step @p53 :rule trans :premises (@p52 @p45)) % 0.37/0.57 (step @p54 :rule trans :premises (@p53 @p44)) % 0.37/0.57 (step @p55 :rule refl :args (@t63)) % 0.37/0.57 (step @p56 :rule aci_norm :args ((= (or @t81 false) @t81))) % 0.37/0.57 (step @p57 :rule eq-refl :args (@t49)) % 0.37/0.57 (step @p58 :rule cong :premises (@p57) :args (@t91)) % 0.37/0.57 (step @p59 :rule trans :premises (@p58 @p16)) % 0.37/0.57 (step @p60 :rule refl :args (@t81)) % 0.37/0.57 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t92)) % 0.37/0.57 (step @p62 :rule trans :premises (@p61 @p56)) % 0.37/0.57 (step @p63 :rule quant-var-elim-eq :args ((= (forall @t35 @t93) @t92))) % 0.37/0.57 (step @p64 :rule aci_norm :args ((= @t66 @t93))) % 0.37/0.57 (step @p65 :rule cong :premises (@p64) :args (@t67)) % 0.37/0.57 (step @p66 :rule trans :premises (@p65 @p63)) % 0.37/0.57 (step @p67 :rule trans :premises (@p66 @p62)) % 0.37/0.57 (step @p68 :rule nary_cong :premises (@p67 @p55) :args (@t68)) % 0.37/0.57 (step @p69 :rule cong :premises (@p68) :args (@t70)) % 0.37/0.57 (step @p70 :rule trans :premises (@p69 @p54)) % 0.37/0.57 (step @p71 :rule cong :premises (@p70) :args (@t71)) % 0.37/0.57 (step @p72 :rule eq_resolve :premises (@p12 @p71)) % 0.37/0.57 (step @p73 :rule skolemize :premises (@p72)) % 0.37/0.57 (step @p74 :rule bool-double-not-elim :args (@t97)) % 0.37/0.57 (step @p75 :rule refl :args (@t101)) % 0.37/0.57 (step @p76 :rule nary_cong :premises (@p75 @p74) :args ((or @t101 (not @t98)))) % 0.37/0.57 (step @p77 :rule cnf_or_neg :args (@t101 2)) % 0.37/0.57 (step @p78 :rule eq_resolve :premises (@p77 @p76)) % 0.37/0.57 (step @p79 :rule reordering :premises (@p78) :args ((or @t97 @t101))) % 0.37/0.57 (step @p80 :rule chain_m_resolution :premises (@p79 @p73) :args (@t97 @t102 @t103)) % 0.37/0.57 (step @p81 :rule bool-double-not-elim :args (@t99)) % 0.37/0.57 (step @p82 :rule nary_cong :premises (@p75 @p81) :args ((or @t101 (not @t100)))) % 0.37/0.57 (step @p83 :rule cnf_or_neg :args (@t101 0)) % 0.37/0.57 (step @p84 :rule eq_resolve :premises (@p83 @p82)) % 0.37/0.57 (step @p85 :rule reordering :premises (@p84) :args ((or @t99 @t101))) % 0.37/0.57 (step @p86 :rule chain_m_resolution :premises (@p85 @p73) :args (@t99 @t102 @t103)) % 0.37/0.57 (step @p87 :rule cnf_or_pos :args (@t104)) % 0.37/0.57 (step @p88 :rule reordering :premises (@p87) :args ((or @t100 @t98 @t105))) % 0.37/0.57 (step @p89 :rule chain_m_resolution :premises (@p88 @p86 @p80) :args (@t105 (@list false false) (@list @t99 @t97))) % 0.37/0.57 (assume-push @p96 @t106) % 0.37/0.57 (step @p91 :rule instantiate :premises (@p42) :args ((@list @t96 @t95))) % 0.37/0.57 (step-pop @p97 :rule scope :premises (@p91)) % 0.37/0.57 (step @p92 :rule process_scope :premises (@p97) :args (@t104)) % 0.37/0.57 (step @p94 :rule implies_elim :premises (@p92)) % 0.37/0.57 (step @p95 false :rule chain_m_resolution :premises (@p94 @p89 @p42) :args (false (@list true false) (@list @t104 @t106))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------