%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU956^5 : 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 : n019.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 08:53:35 AM UTC 2026 % Result : Theorem 0.37s 0.58s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU956^5 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n019.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 18:02:04 EDT 2026 % 0.18/0.36 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.37/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.58 % SZS status Theorem % 0.37/0.58 % SZS output start Proof % 0.37/0.58 ( % 0.37/0.58 (declare-sort $$unsorted 0) % 0.37/0.58 (define @t1 () (@var "Xy" $$unsorted)) % 0.37/0.58 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.58 (define @t3 () (= @t2 @t1)) % 0.37/0.58 (define @t4 () (@var "Y" $$unsorted)) % 0.37/0.58 (define @t5 () (@list @t4)) % 0.37/0.58 (define @t6 () (= (lambda @t5 (= @t2 @t4)) (lambda @t5 (= @t1 @t4)))) % 0.37/0.58 (define @t7 () (@list @t2 @t1)) % 0.37/0.58 (define @t8 () (forall @t7 (=> @t6 @t3))) % 0.37/0.58 (define @t9 () (@var "X" $$unsorted)) % 0.37/0.58 (define @t10 () (@var "R" (-> $$unsorted Bool))) % 0.37/0.58 (define @t11 () (_ @t10 @t9)) % 0.37/0.58 (define @t12 () (@var "S" (-> $$unsorted Bool))) % 0.37/0.58 (define @t13 () (_ @t12 @t9)) % 0.37/0.58 (define @t14 () (@list @t9)) % 0.37/0.58 (define @t15 () (forall @t14 (=> @t13 @t11))) % 0.37/0.58 (define @t16 () (= @t10 @t12)) % 0.37/0.58 (define @t17 () (=> @t16 @t15)) % 0.37/0.58 (define @t18 () (@list @t10 @t12)) % 0.37/0.58 (define @t19 () (forall @t18 @t17)) % 0.37/0.58 (define @t20 () (=> @t19 @t8)) % 0.37/0.58 (define @t21 () (not @t20)) % 0.37/0.58 (define @t22 () (forall @t7 (or (not @t6) @t3))) % 0.37/0.58 (define @t23 () (@var "BOUND_VARIABLE_7447" $$unsorted)) % 0.37/0.58 (define @t24 () (@list @t12 @t23)) % 0.37/0.58 (define @t25 () (_ @t12 @t23)) % 0.37/0.58 (define @t26 () (not @t25)) % 0.37/0.58 (define @t27 () (or @t26 @t25)) % 0.37/0.58 (define @t28 () (not (= @t12 @t12))) % 0.37/0.58 (define @t29 () (or @t28 @t26 @t25)) % 0.37/0.58 (define @t30 () (_ @t10 @t23)) % 0.37/0.58 (define @t31 () (not @t16)) % 0.37/0.58 (define @t32 () (or @t31 @t31 @t26 @t30)) % 0.37/0.58 (define @t33 () (@list @t10)) % 0.37/0.58 (define @t34 () (or @t31 @t26 @t30)) % 0.37/0.58 (define @t35 () (forall @t33 @t34)) % 0.37/0.58 (define @t36 () (forall @t24 @t35)) % 0.37/0.58 (define @t37 () (forall (@list @t12 @t23 @t10) @t34)) % 0.37/0.58 (define @t38 () (@list @t10 @t12 @t23)) % 0.37/0.58 (define @t39 () (or @t26 @t30)) % 0.37/0.58 (define @t40 () (or @t31 @t39)) % 0.37/0.58 (define @t41 () (forall @t38 @t40)) % 0.37/0.58 (define @t42 () (@list @t23)) % 0.37/0.58 (define @t43 () (forall @t42 @t40)) % 0.37/0.58 (define @t44 () (forall @t42 @t39)) % 0.37/0.58 (define @t45 () (or @t31 @t44)) % 0.37/0.58 (define @t46 () (_ @t10 @t9)) % 0.37/0.58 (define @t47 () (_ @t12 @t9)) % 0.37/0.58 (define @t48 () (forall @t14 (or (not @t47) @t46))) % 0.37/0.58 (define @t49 () (not @t13)) % 0.37/0.58 (define @t50 () (or @t49 @t11)) % 0.37/0.58 (define @t51 () (@quantifiers_skolemize @t22 1)) % 0.37/0.58 (define @t52 () (@quantifiers_skolemize @t22 0)) % 0.37/0.58 (define @t53 () (= @t52 @t51)) % 0.37/0.58 (define @t54 () (= @t4 @t52)) % 0.37/0.58 (define @t55 () (lambda @t5 @t54)) % 0.37/0.58 (define @t56 () (@purify @t55)) % 0.37/0.58 (define @t57 () (= @t4 @t51)) % 0.37/0.58 (define @t58 () (lambda @t5 @t57)) % 0.37/0.58 (define @t59 () (@purify @t58)) % 0.37/0.58 (define @t60 () (= @t59 @t56)) % 0.37/0.58 (define @t61 () (not @t60)) % 0.37/0.58 (define @t62 () (or @t61 @t53)) % 0.37/0.58 (define @t63 () (not @t62)) % 0.37/0.58 (define @t64 () (not @t22)) % 0.37/0.58 (define @t65 () (= @t55 @t58)) % 0.37/0.58 (define @t66 () (not @t65)) % 0.37/0.58 (define @t67 () (or @t66 @t53)) % 0.37/0.58 (define @t68 () (not @t67)) % 0.37/0.58 (define @t69 () (lambda @t5 (= @t51 @t4))) % 0.37/0.58 (define @t70 () (lambda @t5 (= @t52 @t4))) % 0.37/0.58 (define @t71 () (= @t70 @t69)) % 0.37/0.58 (define @t72 () (not @t71)) % 0.37/0.58 (define @t73 () (or @t72 @t53)) % 0.37/0.58 (define @t74 () (not @t73)) % 0.37/0.58 (define @t75 () (@list true)) % 0.37/0.58 (define @t76 () (@list @t62)) % 0.37/0.58 (define @t77 () (forall @t5 (= @t57 @t54))) % 0.37/0.58 (define @t78 () (=> @t60 @t77)) % 0.37/0.58 (define @t79 () (forall @t5 (= @t54 @t57))) % 0.37/0.58 (define @t80 () (= (= @t51 @t52) (= @t51 @t51))) % 0.37/0.58 (assume @p1 @t21) % 0.37/0.58 (assume @p2 true) % 0.37/0.58 (step @p3 :rule bool-impl-true2 :args (@t22)) % 0.37/0.58 (step @p4 :rule bool-impl-elim :args (@t6 @t3)) % 0.37/0.58 (step @p5 :rule cong :premises (@p4) :args (@t8)) % 0.37/0.58 (step @p6 :rule quant-unused-vars :args ((= (forall @t24 true) true))) % 0.37/0.58 (step @p7 :rule bool-or-taut2 :args (false @t25 false false)) % 0.37/0.58 (step @p8 :rule cong :premises (@p7) :args ((forall @t24 @t27))) % 0.37/0.58 (step @p9 :rule trans :premises (@p8 @p6)) % 0.37/0.58 (step @p10 :rule aci_norm :args ((= (or false @t26 @t25) @t27))) % 0.37/0.58 (step @p11 :rule refl :args (@t25)) % 0.37/0.58 (step @p12 :rule refl :args (@t26)) % 0.37/0.58 (step @p13 :rule evaluate :args ((not true))) % 0.37/0.58 (step @p14 :rule eq-refl :args (@t12)) % 0.37/0.58 (step @p15 :rule cong :premises (@p14) :args (@t28)) % 0.37/0.58 (step @p16 :rule trans :premises (@p15 @p13)) % 0.37/0.58 (step @p17 :rule nary_cong :premises (@p16 @p12 @p11) :args (@t29)) % 0.37/0.58 (step @p18 :rule trans :premises (@p17 @p10)) % 0.37/0.58 (step @p19 :rule cong :premises (@p18) :args ((forall @t24 @t29))) % 0.37/0.58 (step @p20 :rule trans :premises (@p19 @p9)) % 0.37/0.58 (step @p21 :rule quant-var-elim-eq :args ((= (forall @t33 @t32) @t29))) % 0.37/0.58 (step @p22 :rule aci_norm :args ((= @t34 @t32))) % 0.37/0.58 (step @p23 :rule cong :premises (@p22) :args (@t35)) % 0.37/0.58 (step @p24 :rule trans :premises (@p23 @p21)) % 0.37/0.58 (step @p25 :rule cong :premises (@p24) :args (@t36)) % 0.37/0.58 (step @p26 :rule quant-merge-prenex :args ((= @t36 @t37))) % 0.37/0.58 (step @p27 :rule symm :premises (@p26)) % 0.37/0.58 (step @p28 :rule quant_var_reordering :args ((= (forall @t38 @t34) @t37))) % 0.37/0.58 (step @p29 :rule trans :premises (@p28 @p27 @p25)) % 0.37/0.58 (step @p30 :rule trans :premises (@p29 @p20)) % 0.37/0.58 (step @p31 :rule aci_norm :args ((= @t40 @t34))) % 0.37/0.58 (step @p32 :rule cong :premises (@p31) :args (@t41)) % 0.37/0.58 (step @p33 :rule trans :premises (@p32 @p30)) % 0.37/0.58 (step @p34 :rule quant-merge-prenex :args ((= (forall @t18 @t43) @t41))) % 0.37/0.58 (step @p35 :rule alpha_equiv :args (@t44 (@list @t23) (@list @t9))) % 0.37/0.58 (step @p36 :rule refl :args (@t31)) % 0.37/0.58 (step @p37 :rule nary_cong :premises (@p36 @p35) :args (@t45)) % 0.37/0.58 (step @p38 :rule quant-miniscope-or :args ((= @t43 @t45))) % 0.37/0.58 (step @p39 :rule trans :premises (@p38 @p37)) % 0.37/0.58 (step @p40 :rule symm :premises (@p39)) % 0.37/0.58 (step @p41 :rule cong :premises (@p40) :args ((forall @t18 (or @t31 @t48)))) % 0.37/0.58 (step @p42 :rule trans :premises (@p41 @p34)) % 0.37/0.58 (step @p43 :rule trans :premises (@p42 @p33)) % 0.37/0.58 (step @p44 :rule bool-impl-elim :args (@t16 @t48)) % 0.37/0.58 (step @p45 :rule cong :premises (@p44) :args ((forall @t18 (=> @t16 @t48)))) % 0.37/0.58 (step @p46 :rule trans :premises (@p45 @p43)) % 0.37/0.58 (step @p47 :rule refl :args (@t46)) % 0.37/0.58 (step @p48 :rule refl :args (@t11)) % 0.37/0.58 (step @p49 :rule cong :premises (@p48 @p47) :args ((= @t11 @t46))) % 0.37/0.58 (step @p50 :rule symm :premises (@p49)) % 0.37/0.58 (step @p51 :rule eq_resolve :premises (@p48 @p50)) % 0.37/0.58 (step @p52 :rule refl :args (@t47)) % 0.37/0.58 (step @p53 :rule refl :args (@t13)) % 0.37/0.58 (step @p54 :rule cong :premises (@p53 @p52) :args ((= @t13 @t47))) % 0.37/0.58 (step @p55 :rule symm :premises (@p54)) % 0.37/0.58 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.37/0.58 (step @p57 :rule cong :premises (@p56) :args (@t49)) % 0.37/0.58 (step @p58 :rule nary_cong :premises (@p57 @p51) :args (@t50)) % 0.37/0.58 (step @p59 :rule cong :premises (@p58) :args ((forall @t14 @t50))) % 0.37/0.58 (step @p60 :rule bool-impl-elim :args (@t13 @t11)) % 0.37/0.58 (step @p61 :rule cong :premises (@p60) :args (@t15)) % 0.37/0.58 (step @p62 :rule trans :premises (@p61 @p59)) % 0.37/0.58 (step @p63 :rule refl :args (@t16)) % 0.37/0.58 (step @p64 :rule cong :premises (@p63 @p62) :args (@t17)) % 0.37/0.58 (step @p65 :rule cong :premises (@p64) :args (@t19)) % 0.37/0.58 (step @p66 :rule trans :premises (@p65 @p46)) % 0.37/0.58 (step @p67 :rule cong :premises (@p66 @p5) :args (@t20)) % 0.37/0.58 (step @p68 :rule trans :premises (@p67 @p3)) % 0.37/0.58 (step @p69 :rule cong :premises (@p68) :args (@t21)) % 0.37/0.58 (step @p70 :rule eq_resolve :premises (@p1 @p69)) % 0.37/0.58 (step @p71 :rule refl :args (@t63)) % 0.37/0.58 (step @p72 :rule bool-double-not-elim :args (@t22)) % 0.37/0.58 (step @p73 :rule nary_cong :premises (@p72 @p71) :args ((or (not @t64) @t63))) % 0.37/0.58 (step @p74 :rule refl :args (@t53)) % 0.37/0.58 (step @p75 :rule eq-symm :args (@t56 @t59)) % 0.37/0.58 (step @p76 :rule eq-refl :args (@t58)) % 0.37/0.58 (step @p77 :rule skolem_intro :args (@t59)) % 0.37/0.58 (step @p78 :rule refl :args (@t58)) % 0.37/0.58 (step @p79 :rule cong :premises (@p78 @p77) :args ((= @t58 @t59))) % 0.37/0.58 (step @p80 :rule trans :premises (@p79 @p76)) % 0.37/0.58 (step @p81 :rule true_elim :premises (@p80)) % 0.37/0.58 (step @p82 :rule eq-refl :args (@t55)) % 0.37/0.58 (step @p83 :rule skolem_intro :args (@t56)) % 0.37/0.58 (step @p84 :rule refl :args (@t55)) % 0.37/0.58 (step @p85 :rule cong :premises (@p84 @p83) :args ((= @t55 @t56))) % 0.37/0.58 (step @p86 :rule trans :premises (@p85 @p82)) % 0.37/0.58 (step @p87 :rule true_elim :premises (@p86)) % 0.37/0.58 (step @p88 :rule cong :premises (@p87 @p81) :args (@t65)) % 0.37/0.58 (step @p89 :rule trans :premises (@p88 @p75)) % 0.37/0.58 (step @p90 :rule cong :premises (@p89) :args (@t66)) % 0.37/0.58 (step @p91 :rule nary_cong :premises (@p90 @p74) :args (@t67)) % 0.37/0.58 (step @p92 :rule cong :premises (@p91) :args (@t68)) % 0.37/0.58 (step @p93 :rule refl :args (@t64)) % 0.37/0.58 (step @p94 :rule cong :premises (@p93 @p92) :args ((=> @t64 @t68))) % 0.37/0.58 (step @p95 :rule eq-symm :args (@t51 @t4)) % 0.37/0.58 (step @p96 :rule cong :premises (@p95) :args (@t69)) % 0.37/0.58 (step @p97 :rule eq-symm :args (@t52 @t4)) % 0.37/0.58 (step @p98 :rule cong :premises (@p97) :args (@t70)) % 0.37/0.58 (step @p99 :rule cong :premises (@p98 @p96) :args (@t71)) % 0.37/0.58 (step @p100 :rule cong :premises (@p99) :args (@t72)) % 0.37/0.58 (step @p101 :rule nary_cong :premises (@p100 @p74) :args (@t73)) % 0.37/0.58 (step @p102 :rule cong :premises (@p101) :args (@t74)) % 0.37/0.58 (step @p103 :rule cong :premises (@p93 @p102) :args ((=> @t64 @t74))) % 0.37/0.58 (step @p104 :rule trans :premises (@p103 @p94)) % 0.37/0.58 (assume-push @p145 @t64) % 0.37/0.58 (step @p106 :rule skolemize :premises (@p70)) % 0.37/0.58 (step-pop @p146 :rule scope :premises (@p106)) % 0.37/0.58 (step @p107 :rule process_scope :premises (@p146) :args (@t74)) % 0.37/0.58 (step @p109 :rule eq_resolve :premises (@p107 @p104)) % 0.37/0.58 (step @p110 :rule implies_elim :premises (@p109)) % 0.37/0.58 (step @p111 :rule eq_resolve :premises (@p110 @p73)) % 0.37/0.58 (step @p112 :rule chain_m_resolution :premises (@p111 @p70) :args (@t63 @t75 (@list @t22))) % 0.37/0.58 (step @p113 :rule cnf_or_neg :args (@t62 1)) % 0.37/0.58 (step @p114 :rule chain_m_resolution :premises (@p113 @p112) :args ((not @t53) @t75 @t76)) % 0.37/0.58 (step @p115 :rule bool-double-not-elim :args (@t60)) % 0.37/0.58 (step @p116 :rule refl :args (@t62)) % 0.37/0.58 (step @p117 :rule nary_cong :premises (@p116 @p115) :args ((or @t62 (not @t61)))) % 0.37/0.58 (step @p118 :rule cnf_or_neg :args (@t62 0)) % 0.37/0.58 (step @p119 :rule eq_resolve :premises (@p118 @p117)) % 0.37/0.58 (step @p120 :rule reordering :premises (@p119) :args ((or @t60 @t62))) % 0.37/0.58 (step @p121 :rule chain_m_resolution :premises (@p120 @p112) :args (@t60 @t75 @t76)) % 0.37/0.58 (step @p122 :rule eq-symm :args (@t57 @t54)) % 0.37/0.58 (step @p123 :rule cong :premises (@p122) :args (@t77)) % 0.37/0.58 (step @p124 :rule refl :args (@t60)) % 0.37/0.58 (step @p125 :rule cong :premises (@p124 @p123) :args (@t78)) % 0.37/0.58 ; WARNING: add trust step for TRUST % 0.37/0.58 ; trust TRUST THEORY_LEMMA % 0.37/0.58 (step @p126 :rule trust :premises () :args (@t78)) % 0.37/0.58 (step @p127 :rule eq_resolve :premises (@p126 @p125)) % 0.37/0.58 (step @p128 :rule implies_elim :premises (@p127)) % 0.37/0.58 (step @p129 :rule chain_m_resolution :premises (@p128 @p121) :args (@t79 (@list false) (@list @t60))) % 0.37/0.58 (step @p130 :rule bool-eq-true :args (@t53)) % 0.37/0.58 (step @p131 :rule eq-refl :args (@t51)) % 0.37/0.58 (step @p132 :rule eq-symm :args (@t51 @t52)) % 0.37/0.58 (step @p133 :rule cong :premises (@p132 @p131) :args (@t80)) % 0.37/0.58 (step @p134 :rule trans :premises (@p133 @p130)) % 0.37/0.58 (step @p135 :rule refl :args (@t79)) % 0.37/0.58 (step @p136 :rule cong :premises (@p135 @p134) :args ((=> @t79 @t80))) % 0.37/0.58 (assume-push @p147 @t79) % 0.37/0.58 (step @p138 :rule instantiate :premises (@p129) :args ((@list @t51))) % 0.37/0.58 (step-pop @p148 :rule scope :premises (@p138)) % 0.37/0.58 (step @p139 :rule process_scope :premises (@p148) :args (@t80)) % 0.37/0.58 (step @p141 :rule eq_resolve :premises (@p139 @p136)) % 0.37/0.58 (step @p142 :rule implies_elim :premises (@p141)) % 0.37/0.58 (step @p143 :rule reordering :premises (@p142) :args ((or @t53 (not @t79)))) % 0.37/0.58 (step @p144 false :rule chain_m_resolution :premises (@p143 @p129 @p114) :args (false (@list false true) (@list @t79 @t53))) % 0.37/0.58 ) % 0.37/0.58 % SZS output end Proof % 0.37/0.58 % cvc5 exiting %------------------------------------------------------------------------------