%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET144^5 : 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 : n009.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 08:47:30 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 : SET144^5 : 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 : n009.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 15:01:29 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.49 %----Proving TH0 % 0.38/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.56 % SZS status Theorem % 0.38/0.56 % SZS output start Proof % 0.38/0.56 ( % 0.38/0.56 (declare-sort tptp.a 0) % 0.38/0.56 (define @t1 () (@var "Xx" tptp.a)) % 0.38/0.56 (define @t2 () (@var "Z" (-> tptp.a Bool))) % 0.38/0.56 (define @t3 () (_ @t2 @t1)) % 0.38/0.56 (define @t4 () (@var "Y" (-> tptp.a Bool))) % 0.38/0.56 (define @t5 () (_ @t4 @t1)) % 0.38/0.56 (define @t6 () (@var "X" (-> tptp.a Bool))) % 0.38/0.56 (define @t7 () (_ @t6 @t1)) % 0.38/0.56 (define @t8 () (or @t7 @t5)) % 0.38/0.56 (define @t9 () (and @t8 @t3)) % 0.38/0.56 (define @t10 () (@list @t1)) % 0.38/0.56 (define @t11 () (lambda @t10 @t9)) % 0.38/0.56 (define @t12 () (@var "Xz" tptp.a)) % 0.38/0.56 (define @t13 () (_ @t2 @t12)) % 0.38/0.56 (define @t14 () (_ @t4 @t12)) % 0.38/0.56 (define @t15 () (and @t14 @t13)) % 0.38/0.56 (define @t16 () (_ @t6 @t12)) % 0.38/0.56 (define @t17 () (or @t16 @t15)) % 0.38/0.56 (define @t18 () (@list @t12)) % 0.38/0.56 (define @t19 () (lambda @t18 @t17)) % 0.38/0.56 (define @t20 () (= @t19 @t11)) % 0.38/0.56 (define @t21 () (forall @t10 (=> @t7 @t3))) % 0.38/0.56 (define @t22 () (=> @t21 @t20)) % 0.38/0.56 (define @t23 () (@list @t6 @t4 @t2)) % 0.38/0.56 (define @t24 () (forall @t23 @t22)) % 0.38/0.56 (define @t25 () (not @t24)) % 0.38/0.56 (define @t26 () (_ @t2 @t1)) % 0.38/0.56 (define @t27 () (_ @t4 @t1)) % 0.38/0.56 (define @t28 () (_ @t6 @t1)) % 0.38/0.56 (define @t29 () (_ @t2 @t12)) % 0.38/0.56 (define @t30 () (_ @t4 @t12)) % 0.38/0.56 (define @t31 () (_ @t6 @t12)) % 0.38/0.56 (define @t32 () (forall @t10 (or (not @t28) @t26))) % 0.38/0.56 (define @t33 () (not @t32)) % 0.38/0.56 (define @t34 () (or @t33 @t20)) % 0.38/0.56 (define @t35 () (not @t7)) % 0.38/0.56 (define @t36 () (or @t35 @t3)) % 0.38/0.56 (define @t37 () (forall @t23 (or @t33 (= (lambda @t18 (or @t31 (and @t30 @t29))) (lambda @t10 (and (or @t28 @t27) @t26)))))) % 0.38/0.56 (define @t38 () (@quantifiers_skolemize @t37 2)) % 0.38/0.56 (define @t39 () (@quantifiers_skolemize @t37 1)) % 0.38/0.56 (define @t40 () (@quantifiers_skolemize @t37 0)) % 0.38/0.56 (define @t41 () (lambda @t18 (or (_ @t40 @t12) (and (_ @t39 @t12) (_ @t38 @t12))))) % 0.38/0.56 (define @t42 () (@purify @t41)) % 0.38/0.56 (define @t43 () (_ @t38 @t1)) % 0.38/0.56 (define @t44 () (_ @t40 @t1)) % 0.38/0.56 (define @t45 () (lambda @t10 (and (or @t44 (_ @t39 @t1)) @t43))) % 0.38/0.56 (define @t46 () (@purify @t45)) % 0.38/0.56 (define @t47 () (= @t46 @t42)) % 0.38/0.56 (define @t48 () (forall @t10 (or (not @t44) @t43))) % 0.38/0.56 (define @t49 () (not @t48)) % 0.38/0.56 (define @t50 () (or @t49 @t47)) % 0.38/0.56 (define @t51 () (not @t50)) % 0.38/0.56 (define @t52 () (not @t37)) % 0.38/0.56 (define @t53 () (= @t41 @t45)) % 0.38/0.56 (define @t54 () (or @t49 @t53)) % 0.38/0.56 (define @t55 () (not @t54)) % 0.38/0.56 (define @t56 () (@list true)) % 0.38/0.56 (define @t57 () (@list @t50)) % 0.38/0.56 (define @t58 () (@const 0 tptp.a)) % 0.38/0.56 (define @t59 () (_ @t38 @t58)) % 0.38/0.56 (define @t60 () (_ @t39 @t58)) % 0.38/0.56 (define @t61 () (_ @t40 @t58)) % 0.38/0.56 (define @t62 () (or @t61 @t60)) % 0.38/0.56 (define @t63 () (and @t62 @t59)) % 0.38/0.56 (define @t64 () (and @t60 @t59)) % 0.38/0.56 (define @t65 () (or @t61 @t64)) % 0.38/0.56 (define @t66 () (= (_ @t41 @t58) @t65)) % 0.38/0.56 (define @t67 () (_ @t42 @t58)) % 0.38/0.56 (define @t68 () (= (_ @t45 @t58) @t63)) % 0.38/0.56 (define @t69 () (_ @t46 @t58)) % 0.38/0.56 (define @t70 () (= @t69 @t67)) % 0.38/0.56 (define @t71 () (not @t70)) % 0.38/0.56 (define @t72 () (or @t47 @t71)) % 0.38/0.56 (define @t73 () (= @t65 @t63)) % 0.38/0.56 (define @t74 () (not @t64)) % 0.38/0.56 (define @t75 () (not @t63)) % 0.38/0.56 (define @t76 () (not @t61)) % 0.38/0.56 (define @t77 () (or @t76 @t59)) % 0.38/0.56 (define @t78 () (not @t62)) % 0.38/0.56 (define @t79 () (not @t59)) % 0.38/0.56 (define @t80 () (not @t65)) % 0.38/0.56 (define @t81 () (not @t60)) % 0.38/0.56 (define @t82 () (@list true true)) % 0.38/0.56 (assume @p1 @t25) % 0.38/0.56 (assume @p2 true) % 0.38/0.56 (step @p3 :rule refl :args (@t26)) % 0.38/0.56 (step @p4 :rule refl :args (@t3)) % 0.38/0.56 (step @p5 :rule cong :premises (@p4 @p3) :args ((= @t3 @t26))) % 0.38/0.56 (step @p6 :rule symm :premises (@p5)) % 0.38/0.56 (step @p7 :rule eq_resolve :premises (@p4 @p6)) % 0.38/0.56 (step @p8 :rule refl :args (@t27)) % 0.38/0.56 (step @p9 :rule refl :args (@t5)) % 0.38/0.56 (step @p10 :rule cong :premises (@p9 @p8) :args ((= @t5 @t27))) % 0.38/0.56 (step @p11 :rule symm :premises (@p10)) % 0.38/0.56 (step @p12 :rule eq_resolve :premises (@p9 @p11)) % 0.38/0.56 (step @p13 :rule refl :args (@t28)) % 0.38/0.56 (step @p14 :rule refl :args (@t7)) % 0.38/0.56 (step @p15 :rule cong :premises (@p14 @p13) :args ((= @t7 @t28))) % 0.38/0.56 (step @p16 :rule symm :premises (@p15)) % 0.38/0.56 (step @p17 :rule eq_resolve :premises (@p14 @p16)) % 0.38/0.56 (step @p18 :rule nary_cong :premises (@p17 @p12) :args (@t8)) % 0.38/0.56 (step @p19 :rule nary_cong :premises (@p18 @p7) :args (@t9)) % 0.38/0.56 (step @p20 :rule cong :premises (@p19) :args (@t11)) % 0.38/0.56 (step @p21 :rule refl :args (@t29)) % 0.38/0.56 (step @p22 :rule refl :args (@t13)) % 0.38/0.56 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t13 @t29))) % 0.38/0.56 (step @p24 :rule symm :premises (@p23)) % 0.38/0.56 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.38/0.56 (step @p26 :rule refl :args (@t30)) % 0.38/0.56 (step @p27 :rule refl :args (@t14)) % 0.38/0.56 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t14 @t30))) % 0.38/0.56 (step @p29 :rule symm :premises (@p28)) % 0.38/0.56 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.38/0.56 (step @p31 :rule nary_cong :premises (@p30 @p25) :args (@t15)) % 0.38/0.56 (step @p32 :rule refl :args (@t31)) % 0.38/0.56 (step @p33 :rule refl :args (@t16)) % 0.38/0.56 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t16 @t31))) % 0.38/0.56 (step @p35 :rule symm :premises (@p34)) % 0.38/0.56 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.38/0.56 (step @p37 :rule nary_cong :premises (@p36 @p31) :args (@t17)) % 0.38/0.56 (step @p38 :rule cong :premises (@p37) :args (@t19)) % 0.38/0.56 (step @p39 :rule cong :premises (@p38 @p20) :args (@t20)) % 0.38/0.56 (step @p40 :rule refl :args (@t33)) % 0.38/0.56 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t34)) % 0.38/0.56 (step @p42 :rule cong :premises (@p41) :args ((forall @t23 @t34))) % 0.38/0.56 (step @p43 :rule bool-impl-elim :args (@t32 @t20)) % 0.38/0.56 (step @p44 :rule cong :premises (@p43) :args ((forall @t23 (=> @t32 @t20)))) % 0.38/0.56 (step @p45 :rule trans :premises (@p44 @p42)) % 0.38/0.56 (step @p46 :rule refl :args (@t20)) % 0.38/0.56 (step @p47 :rule cong :premises (@p17) :args (@t35)) % 0.38/0.56 (step @p48 :rule nary_cong :premises (@p47 @p7) :args (@t36)) % 0.38/0.56 (step @p49 :rule cong :premises (@p48) :args ((forall @t10 @t36))) % 0.38/0.56 (step @p50 :rule bool-impl-elim :args (@t7 @t3)) % 0.38/0.56 (step @p51 :rule cong :premises (@p50) :args (@t21)) % 0.38/0.56 (step @p52 :rule trans :premises (@p51 @p49)) % 0.38/0.56 (step @p53 :rule cong :premises (@p52 @p46) :args (@t22)) % 0.38/0.56 (step @p54 :rule cong :premises (@p53) :args (@t24)) % 0.38/0.56 (step @p55 :rule trans :premises (@p54 @p45)) % 0.38/0.56 (step @p56 :rule cong :premises (@p55) :args (@t25)) % 0.38/0.56 (step @p57 :rule eq_resolve :premises (@p1 @p56)) % 0.38/0.56 (step @p58 :rule refl :args (@t51)) % 0.38/0.56 (step @p59 :rule bool-double-not-elim :args (@t37)) % 0.38/0.56 (step @p60 :rule nary_cong :premises (@p59 @p58) :args ((or (not @t52) @t51))) % 0.38/0.56 (step @p61 :rule eq-symm :args (@t42 @t46)) % 0.38/0.56 (step @p62 :rule eq-refl :args (@t45)) % 0.38/0.56 (step @p63 :rule skolem_intro :args (@t46)) % 0.38/0.56 (step @p64 :rule refl :args (@t45)) % 0.38/0.56 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t45 @t46))) % 0.38/0.56 (step @p66 :rule trans :premises (@p65 @p62)) % 0.38/0.56 (step @p67 :rule true_elim :premises (@p66)) % 0.38/0.56 (step @p68 :rule eq-refl :args (@t41)) % 0.38/0.56 (step @p69 :rule skolem_intro :args (@t42)) % 0.38/0.56 (step @p70 :rule refl :args (@t41)) % 0.38/0.56 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t41 @t42))) % 0.38/0.56 (step @p72 :rule trans :premises (@p71 @p68)) % 0.38/0.56 (step @p73 :rule true_elim :premises (@p72)) % 0.38/0.56 (step @p74 :rule cong :premises (@p73 @p67) :args (@t53)) % 0.38/0.56 (step @p75 :rule trans :premises (@p74 @p61)) % 0.38/0.56 (step @p76 :rule refl :args (@t49)) % 0.38/0.56 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t54)) % 0.38/0.56 (step @p78 :rule cong :premises (@p77) :args (@t55)) % 0.38/0.56 (step @p79 :rule refl :args (@t52)) % 0.38/0.56 (step @p80 :rule cong :premises (@p79 @p78) :args ((=> @t52 @t55))) % 0.38/0.56 (assume-push @p160 @t52) % 0.38/0.56 (step @p82 :rule skolemize :premises (@p57)) % 0.38/0.56 (step-pop @p161 :rule scope :premises (@p82)) % 0.38/0.56 (step @p83 :rule process_scope :premises (@p161) :args (@t55)) % 0.38/0.56 (step @p85 :rule eq_resolve :premises (@p83 @p80)) % 0.38/0.56 (step @p86 :rule implies_elim :premises (@p85)) % 0.38/0.56 (step @p87 :rule eq_resolve :premises (@p86 @p60)) % 0.38/0.56 (step @p88 :rule chain_m_resolution :premises (@p87 @p57) :args (@t51 @t56 (@list @t37))) % 0.38/0.56 (step @p89 :rule cnf_or_neg :args (@t50 1)) % 0.38/0.56 (step @p90 :rule chain_m_resolution :premises (@p89 @p88) :args ((not @t47) @t56 @t57)) % 0.38/0.56 (step @p91 :rule eq-symm :args (@t63 @t65)) % 0.38/0.56 (step @p92 :rule eq-refl :args (@t65)) % 0.38/0.56 (step @p93 :rule refl :args (@t65)) % 0.38/0.56 (step @p94 :rule beta-reduce :args (@t66)) % 0.38/0.56 (step @p95 :rule cong :premises (@p94 @p93) :args (@t66)) % 0.38/0.56 (step @p96 :rule trans :premises (@p95 @p92)) % 0.38/0.56 (step @p97 :rule refl :args (@t58)) % 0.38/0.56 (step @p98 :rule ho_cong :premises (@p69 @p97)) % 0.38/0.56 (step @p99 :rule cong :premises (@p98 @p93) :args ((= @t67 @t65))) % 0.38/0.56 (step @p100 :rule trans :premises (@p99 @p96)) % 0.38/0.56 (step @p101 :rule true_elim :premises (@p100)) % 0.38/0.56 (step @p102 :rule eq-refl :args (@t63)) % 0.38/0.56 (step @p103 :rule refl :args (@t63)) % 0.38/0.56 (step @p104 :rule beta-reduce :args (@t68)) % 0.38/0.56 (step @p105 :rule cong :premises (@p104 @p103) :args (@t68)) % 0.38/0.56 (step @p106 :rule trans :premises (@p105 @p102)) % 0.38/0.56 (step @p107 :rule ho_cong :premises (@p63 @p97)) % 0.38/0.56 (step @p108 :rule cong :premises (@p107 @p103) :args ((= @t69 @t63))) % 0.38/0.56 (step @p109 :rule trans :premises (@p108 @p106)) % 0.38/0.56 (step @p110 :rule true_elim :premises (@p109)) % 0.38/0.56 (step @p111 :rule cong :premises (@p110 @p101) :args (@t70)) % 0.38/0.56 (step @p112 :rule trans :premises (@p111 @p91)) % 0.38/0.56 (step @p113 :rule cong :premises (@p112) :args (@t71)) % 0.38/0.56 (step @p114 :rule refl :args (@t47)) % 0.38/0.56 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t72)) % 0.38/0.56 ; WARNING: add trust step for TRUST % 0.38/0.56 ; trust TRUST THEORY_LEMMA % 0.38/0.56 (step @p116 :rule trust :premises () :args (@t72)) % 0.38/0.56 (step @p117 :rule eq_resolve :premises (@p116 @p115)) % 0.38/0.56 (step @p118 :rule chain_m_resolution :premises (@p117 @p90) :args ((not @t73) @t56 (@list @t47))) % 0.38/0.56 (step @p119 :rule cnf_and_pos :args (@t64 1)) % 0.38/0.56 (step @p120 :rule reordering :premises (@p119) :args ((or @t59 @t74))) % 0.38/0.56 (step @p121 :rule cnf_and_pos :args (@t63 1)) % 0.38/0.56 (step @p122 :rule reordering :premises (@p121) :args ((or @t59 @t75))) % 0.38/0.56 (step @p123 :rule cnf_or_neg :args (@t65 0)) % 0.38/0.56 (step @p124 :rule cnf_or_neg :args (@t62 0)) % 0.38/0.56 (step @p125 :rule bool-double-not-elim :args (@t48)) % 0.38/0.56 (step @p126 :rule refl :args (@t50)) % 0.38/0.56 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or @t50 (not @t49)))) % 0.38/0.56 (step @p128 :rule cnf_or_neg :args (@t50 0)) % 0.38/0.56 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.38/0.56 (step @p130 :rule reordering :premises (@p129) :args ((or @t48 @t50))) % 0.38/0.56 (step @p131 :rule chain_m_resolution :premises (@p130 @p88) :args (@t48 @t56 @t57)) % 0.38/0.56 (step @p132 :rule instantiate :premises (@p131) :args ((@list @t58))) % 0.38/0.56 (step @p133 :rule cnf_or_pos :args (@t77)) % 0.38/0.56 (step @p134 :rule reordering :premises (@p133) :args ((or @t59 @t76 (not @t77)))) % 0.38/0.56 (step @p135 :rule cnf_equiv_neg2 :args (@t73)) % 0.38/0.56 (step @p136 :rule cnf_and_neg :args (@t63)) % 0.38/0.56 (step @p137 :rule reordering :premises (@p136) :args ((or @t63 @t79 @t78))) % 0.38/0.56 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p118 @p134 @p132 @p124 @p123) :args (@t76 (@list true true false false false false) (@list @t63 @t73 @t59 @t77 @t62 @t65))) % 0.38/0.56 (step @p139 :rule cnf_or_pos :args (@t65)) % 0.38/0.56 (step @p140 :rule reordering :premises (@p139) :args ((or @t61 @t64 @t80))) % 0.38/0.56 (step @p141 :rule cnf_equiv_neg1 :args (@t73)) % 0.38/0.56 (step @p142 :rule reordering :premises (@p141) :args ((or @t65 @t63 @t73))) % 0.38/0.56 (step @p143 :rule chain_m_resolution :premises (@p142 @p118 @p140 @p138 @p122 @p120) :args (@t59 (@list true true true true true) (@list @t73 @t65 @t61 @t63 @t64))) % 0.38/0.56 (step @p144 :rule cnf_or_neg :args (@t62 1)) % 0.38/0.56 (step @p145 :rule cnf_and_neg :args (@t64)) % 0.38/0.56 (step @p146 :rule cnf_or_neg :args (@t65 1)) % 0.38/0.56 (step @p147 :rule chain_m_resolution :premises (@p135 @p118 @p146 @p137 @p145 @p144) :args ((or @t81 @t79) (@list true false false false false) (@list @t73 @t65 @t63 @t64 @t62))) % 0.38/0.56 (step @p148 :rule chain_m_resolution :premises (@p147 @p143) :args (@t81 (@list false) (@list @t59))) % 0.38/0.56 (step @p149 :rule cnf_and_pos :args (@t64 0)) % 0.38/0.56 (step @p150 :rule reordering :premises (@p149) :args ((or @t60 @t74))) % 0.38/0.56 (step @p151 :rule chain_m_resolution :premises (@p150 @p148) :args (@t74 @t56 (@list @t60))) % 0.38/0.56 (step @p152 :rule chain_m_resolution :premises (@p140 @p138 @p151) :args (@t80 @t82 (@list @t61 @t64))) % 0.38/0.56 (step @p153 :rule cnf_or_pos :args (@t62)) % 0.38/0.56 (step @p154 :rule reordering :premises (@p153) :args ((or @t61 @t60 @t78))) % 0.38/0.56 (step @p155 :rule chain_m_resolution :premises (@p154 @p138 @p148) :args (@t78 @t82 (@list @t61 @t60))) % 0.38/0.56 (step @p156 :rule cnf_and_pos :args (@t63 0)) % 0.38/0.56 (step @p157 :rule reordering :premises (@p156) :args ((or @t62 @t75))) % 0.38/0.56 (step @p158 :rule chain_m_resolution :premises (@p157 @p155) :args (@t75 @t56 (@list @t62))) % 0.38/0.56 (step @p159 false :rule chain_m_resolution :premises (@p142 @p158 @p152 @p118) :args (false (@list true true true) (@list @t63 @t65 @t73))) % 0.38/0.56 ) % 0.38/0.56 % SZS output end Proof % 0.38/0.56 % cvc5 exiting %------------------------------------------------------------------------------