%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO263^5 : 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 : n012.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 09:12:19 AM UTC 2026 % Result : Theorem 0.52s 0.75s % Output : Proof 0.52s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SYO263^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.25 % Computer : n012.cluster.edu % 0.09/0.25 % Model : x86_64 x86_64 % 0.09/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.25 % Memory : 8042.1875MB % 0.09/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.09/0.25 % CPULimit : 300 % 0.09/0.25 % WCLimit : 300 % 0.09/0.25 % DateTime : Wed Jun 3 00:01:48 EDT 2026 % 0.09/0.25 % CPUTime : % 0.17/0.33 %----Proving TH0 % 0.52/0.75 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.52/0.75 % SZS status Theorem % 0.52/0.75 % SZS output start Proof % 0.52/0.75 ( % 0.52/0.75 (declare-sort $$unsorted 0) % 0.52/0.75 (define @t1 () (@var "Xx" $$unsorted)) % 0.52/0.75 (define @t2 () (@var "P" (-> $$unsorted Bool))) % 0.52/0.75 (define @t3 () (_ @t2 @t1)) % 0.52/0.75 (define @t4 () (not @t3)) % 0.52/0.75 (define @t5 () (@var "Xn" (-> $$unsorted Bool))) % 0.52/0.75 (define @t6 () (_ @t5 @t1)) % 0.52/0.75 (define @t7 () (= @t6 @t4)) % 0.52/0.75 (define @t8 () (@list @t1)) % 0.52/0.75 (define @t9 () (forall @t8 @t7)) % 0.52/0.75 (define @t10 () (@var "Xc" $$unsorted)) % 0.52/0.75 (define @t11 () (_ @t2 @t10)) % 0.52/0.75 (define @t12 () (not @t11)) % 0.52/0.75 (define @t13 () (@var "Xm" (-> $$unsorted Bool))) % 0.52/0.75 (define @t14 () (_ @t13 @t10)) % 0.52/0.75 (define @t15 () (or @t14 @t12)) % 0.52/0.75 (define @t16 () (@var "Xb" $$unsorted)) % 0.52/0.75 (define @t17 () (_ @t5 @t16)) % 0.52/0.75 (define @t18 () (_ @t2 @t16)) % 0.52/0.75 (define @t19 () (or @t18 @t17)) % 0.52/0.75 (define @t20 () (@var "Xa" $$unsorted)) % 0.52/0.75 (define @t21 () (_ @t13 @t20)) % 0.52/0.75 (define @t22 () (_ @t5 @t20)) % 0.52/0.75 (define @t23 () (or @t22 @t21)) % 0.52/0.75 (define @t24 () (and @t23 @t19 @t15 @t9)) % 0.52/0.75 (define @t25 () (@list @t13 @t5)) % 0.52/0.75 (define @t26 () (exists @t25 @t24)) % 0.52/0.75 (define @t27 () (@list @t20 @t16 @t10 @t2)) % 0.52/0.75 (define @t28 () (forall @t27 @t26)) % 0.52/0.75 (define @t29 () (not @t28)) % 0.52/0.75 (define @t30 () (_ @t2 @t1)) % 0.52/0.75 (define @t31 () (_ @t5 @t1)) % 0.52/0.75 (define @t32 () (forall @t8 (= @t31 (not @t30)))) % 0.52/0.75 (define @t33 () (not @t32)) % 0.52/0.75 (define @t34 () (_ @t2 @t10)) % 0.52/0.75 (define @t35 () (_ @t13 @t10)) % 0.52/0.75 (define @t36 () (not @t14)) % 0.52/0.75 (define @t37 () (and @t36 @t11)) % 0.52/0.75 (define @t38 () (_ @t5 @t16)) % 0.52/0.75 (define @t39 () (not @t17)) % 0.52/0.75 (define @t40 () (_ @t2 @t16)) % 0.52/0.75 (define @t41 () (not @t18)) % 0.52/0.75 (define @t42 () (and @t41 @t39)) % 0.52/0.75 (define @t43 () (_ @t13 @t20)) % 0.52/0.75 (define @t44 () (not @t21)) % 0.52/0.75 (define @t45 () (_ @t5 @t20)) % 0.52/0.75 (define @t46 () (not @t22)) % 0.52/0.75 (define @t47 () (and @t46 @t44)) % 0.52/0.75 (define @t48 () (or @t47 @t42 @t37 @t33)) % 0.52/0.75 (define @t49 () (not @t15)) % 0.52/0.75 (define @t50 () (not @t19)) % 0.52/0.75 (define @t51 () (not @t23)) % 0.52/0.75 (define @t52 () (or @t51 @t50 @t49 @t33)) % 0.52/0.75 (define @t53 () (and @t23 @t19 @t15 @t32)) % 0.52/0.75 (define @t54 () (forall @t25 (not @t53))) % 0.52/0.75 (define @t55 () (not @t54)) % 0.52/0.75 (define @t56 () (forall @t27 (not (forall @t25 (or (and (not @t45) (not @t43)) (and (not @t40) (not @t38)) (and (not @t35) @t34) @t33))))) % 0.52/0.75 (define @t57 () (@quantifiers_skolemize @t56 3)) % 0.52/0.75 (define @t58 () (not (_ @t57 @t1))) % 0.52/0.75 (define @t59 () (@quantifiers_skolemize @t56 2)) % 0.52/0.75 (define @t60 () (_ @t57 @t59)) % 0.52/0.75 (define @t61 () (@quantifiers_skolemize @t56 1)) % 0.52/0.75 (define @t62 () (_ @t57 @t61)) % 0.52/0.75 (define @t63 () (not @t62)) % 0.52/0.75 (define @t64 () (@quantifiers_skolemize @t56 0)) % 0.52/0.75 (define @t65 () (forall @t25 (or (and (not (_ @t5 @t64)) (not (_ @t13 @t64))) (and @t63 (not (_ @t5 @t61))) (and (not (_ @t13 @t59)) @t60) (not (forall @t8 (= @t31 @t58)))))) % 0.52/0.75 (define @t66 () (not @t56)) % 0.52/0.75 (define @t67 () (not (not @t65))) % 0.52/0.75 (define @t68 () (and @t63 @t62)) % 0.52/0.75 (define @t69 () (@var "BOUND_VARIABLE_21882" $$unsorted)) % 0.52/0.75 (define @t70 () (lambda (@list @t69) (not (_ @t57 @t69)))) % 0.52/0.75 (define @t71 () (_ @t70 @t1)) % 0.52/0.75 (define @t72 () (= @t71 @t58)) % 0.52/0.75 (define @t73 () (forall @t8 @t72)) % 0.52/0.75 (define @t74 () (not @t73)) % 0.52/0.75 (define @t75 () (lambda (@list (@var "BOUND_VARIABLE_21655" $$unsorted)) true)) % 0.52/0.75 (define @t76 () (_ @t75 @t59)) % 0.52/0.75 (define @t77 () (not @t76)) % 0.52/0.75 (define @t78 () (and @t77 @t60)) % 0.52/0.75 (define @t79 () (_ @t70 @t61)) % 0.52/0.75 (define @t80 () (not @t79)) % 0.52/0.75 (define @t81 () (and @t63 @t80)) % 0.52/0.75 (define @t82 () (_ @t57 @t64)) % 0.52/0.75 (define @t83 () (_ @t75 @t64)) % 0.52/0.75 (define @t84 () (not @t83)) % 0.52/0.75 (define @t85 () (_ @t70 @t64)) % 0.52/0.75 (define @t86 () (not @t85)) % 0.52/0.75 (define @t87 () (and @t86 @t84)) % 0.52/0.75 (define @t88 () (or @t87 @t81 @t78 @t74)) % 0.52/0.75 (define @t89 () (@list false)) % 0.52/0.75 (define @t90 () (not @t68)) % 0.52/0.75 (assume @p1 @t29) % 0.52/0.75 (assume @p2 true) % 0.52/0.75 (step @p3 :rule refl :args (@t33)) % 0.52/0.75 (step @p4 :rule refl :args (@t34)) % 0.52/0.75 (step @p5 :rule refl :args (@t11)) % 0.52/0.75 (step @p6 :rule cong :premises (@p5 @p4) :args ((= @t11 @t34))) % 0.52/0.75 (step @p7 :rule symm :premises (@p6)) % 0.52/0.75 (step @p8 :rule eq_resolve :premises (@p5 @p7)) % 0.52/0.75 (step @p9 :rule refl :args (@t35)) % 0.52/0.75 (step @p10 :rule refl :args (@t14)) % 0.52/0.75 (step @p11 :rule cong :premises (@p10 @p9) :args ((= @t14 @t35))) % 0.52/0.75 (step @p12 :rule symm :premises (@p11)) % 0.52/0.75 (step @p13 :rule eq_resolve :premises (@p10 @p12)) % 0.52/0.75 (step @p14 :rule cong :premises (@p13) :args (@t36)) % 0.52/0.75 (step @p15 :rule nary_cong :premises (@p14 @p8) :args (@t37)) % 0.52/0.75 (step @p16 :rule refl :args (@t38)) % 0.52/0.75 (step @p17 :rule refl :args (@t17)) % 0.52/0.75 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t17 @t38))) % 0.52/0.75 (step @p19 :rule symm :premises (@p18)) % 0.52/0.75 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.52/0.75 (step @p21 :rule cong :premises (@p20) :args (@t39)) % 0.52/0.75 (step @p22 :rule refl :args (@t40)) % 0.52/0.75 (step @p23 :rule refl :args (@t18)) % 0.52/0.75 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t18 @t40))) % 0.52/0.75 (step @p25 :rule symm :premises (@p24)) % 0.52/0.75 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.52/0.75 (step @p27 :rule cong :premises (@p26) :args (@t41)) % 0.52/0.75 (step @p28 :rule nary_cong :premises (@p27 @p21) :args (@t42)) % 0.52/0.75 (step @p29 :rule refl :args (@t43)) % 0.52/0.75 (step @p30 :rule refl :args (@t21)) % 0.52/0.75 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t21 @t43))) % 0.52/0.75 (step @p32 :rule symm :premises (@p31)) % 0.52/0.75 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.52/0.75 (step @p34 :rule cong :premises (@p33) :args (@t44)) % 0.52/0.75 (step @p35 :rule refl :args (@t45)) % 0.52/0.75 (step @p36 :rule refl :args (@t22)) % 0.52/0.75 (step @p37 :rule cong :premises (@p36 @p35) :args ((= @t22 @t45))) % 0.52/0.75 (step @p38 :rule symm :premises (@p37)) % 0.52/0.75 (step @p39 :rule eq_resolve :premises (@p36 @p38)) % 0.52/0.75 (step @p40 :rule cong :premises (@p39) :args (@t46)) % 0.52/0.75 (step @p41 :rule nary_cong :premises (@p40 @p34) :args (@t47)) % 0.52/0.75 (step @p42 :rule nary_cong :premises (@p41 @p28 @p15 @p3) :args (@t48)) % 0.52/0.75 (step @p43 :rule cong :premises (@p42) :args ((forall @t25 @t48))) % 0.52/0.75 (step @p44 :rule bool-double-not-elim :args (@t11)) % 0.52/0.75 (step @p45 :rule refl :args (@t36)) % 0.52/0.75 (step @p46 :rule nary_cong :premises (@p45 @p44) :args ((and @t36 (not @t12)))) % 0.52/0.75 (step @p47 :rule bool-or-de-morgan :args (@t14 @t12 false)) % 0.52/0.75 (step @p48 :rule trans :premises (@p47 @p46)) % 0.52/0.75 (step @p49 :rule bool-or-de-morgan :args (@t18 @t17 false)) % 0.52/0.75 (step @p50 :rule bool-or-de-morgan :args (@t22 @t21 false)) % 0.52/0.75 (step @p51 :rule nary_cong :premises (@p50 @p49 @p48 @p3) :args (@t52)) % 0.52/0.75 (step @p52 :rule aci_norm :args ((= (or @t51 (or @t50 (or @t49 @t33))) @t52))) % 0.52/0.75 (step @p53 :rule bool-and-de-morgan :args (@t15 @t32 true)) % 0.52/0.75 (step @p54 :rule refl :args (@t50)) % 0.52/0.75 (step @p55 :rule nary_cong :premises (@p54 @p53) :args ((or @t50 (not (and @t15 @t32))))) % 0.52/0.75 (step @p56 :rule bool-and-de-morgan :args (@t19 @t15 (and @t32))) % 0.52/0.75 (step @p57 :rule trans :premises (@p56 @p55)) % 0.52/0.75 (step @p58 :rule refl :args (@t51)) % 0.52/0.75 (step @p59 :rule nary_cong :premises (@p58 @p57) :args ((or @t51 (not (and @t19 @t15 @t32))))) % 0.52/0.75 (step @p60 :rule bool-and-de-morgan :args (@t23 @t19 (and @t15 @t32))) % 0.52/0.75 (step @p61 :rule trans :premises (@p60 @p59)) % 0.52/0.75 (step @p62 :rule trans :premises (@p61 @p52)) % 0.52/0.75 (step @p63 :rule trans :premises (@p62 @p51)) % 0.52/0.75 (step @p64 :rule cong :premises (@p63) :args (@t54)) % 0.52/0.75 (step @p65 :rule trans :premises (@p64 @p43)) % 0.52/0.75 (step @p66 :rule cong :premises (@p65) :args (@t55)) % 0.52/0.75 (step @p67 :rule exists-elim :args ((= (exists @t25 @t53) @t55))) % 0.52/0.75 (step @p68 :rule trans :premises (@p67 @p66)) % 0.52/0.75 (step @p69 :rule refl :args (@t30)) % 0.52/0.75 (step @p70 :rule refl :args (@t3)) % 0.52/0.75 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t3 @t30))) % 0.52/0.75 (step @p72 :rule symm :premises (@p71)) % 0.52/0.75 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.52/0.75 (step @p74 :rule cong :premises (@p73) :args (@t4)) % 0.52/0.75 (step @p75 :rule refl :args (@t31)) % 0.52/0.75 (step @p76 :rule refl :args (@t6)) % 0.52/0.75 (step @p77 :rule cong :premises (@p76 @p75) :args ((= @t6 @t31))) % 0.52/0.75 (step @p78 :rule symm :premises (@p77)) % 0.52/0.75 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.52/0.75 (step @p80 :rule cong :premises (@p79 @p74) :args (@t7)) % 0.52/0.75 (step @p81 :rule cong :premises (@p80) :args (@t9)) % 0.52/0.75 (step @p82 :rule refl :args (@t15)) % 0.52/0.75 (step @p83 :rule refl :args (@t19)) % 0.52/0.75 (step @p84 :rule refl :args (@t23)) % 0.52/0.75 (step @p85 :rule nary_cong :premises (@p84 @p83 @p82 @p81) :args (@t24)) % 0.52/0.75 (step @p86 :rule cong :premises (@p85) :args (@t26)) % 0.52/0.75 (step @p87 :rule trans :premises (@p86 @p68)) % 0.52/0.75 (step @p88 :rule cong :premises (@p87) :args (@t28)) % 0.52/0.75 (step @p89 :rule cong :premises (@p88) :args (@t29)) % 0.52/0.75 (step @p90 :rule eq_resolve :premises (@p1 @p89)) % 0.52/0.75 (step @p91 :rule refl :args (@t65)) % 0.52/0.75 (step @p92 :rule bool-double-not-elim :args (@t56)) % 0.52/0.75 (step @p93 :rule nary_cong :premises (@p92 @p91) :args ((or (not @t66) @t65))) % 0.52/0.75 (step @p94 :rule bool-double-not-elim :args (@t65)) % 0.52/0.75 (step @p95 :rule refl :args (@t66)) % 0.52/0.75 (step @p96 :rule cong :premises (@p95 @p94) :args ((=> @t66 @t67))) % 0.52/0.75 (assume-push @p158 @t66) % 0.52/0.75 (step @p98 :rule skolemize :premises (@p90)) % 0.52/0.75 (step-pop @p159 :rule scope :premises (@p98)) % 0.52/0.75 (step @p99 :rule process_scope :premises (@p159) :args (@t67)) % 0.52/0.75 (step @p101 :rule eq_resolve :premises (@p99 @p96)) % 0.52/0.75 (step @p102 :rule implies_elim :premises (@p101)) % 0.52/0.75 (step @p103 :rule eq_resolve :premises (@p102 @p93)) % 0.52/0.75 (step @p104 :rule chain_m_resolution :premises (@p103 @p90) :args (@t65 (@list true) (@list @t56))) % 0.52/0.75 (step @p105 :rule aci_norm :args ((= (or false @t68 false false) @t68))) % 0.52/0.75 (step @p106 :rule evaluate :args ((not true))) % 0.52/0.75 (step @p107 :rule quant-unused-vars :args ((= (forall @t8 true) true))) % 0.52/0.75 (step @p108 :rule eq-refl :args (@t58)) % 0.52/0.75 (step @p109 :rule beta-reduce :args (@t72)) % 0.52/0.75 (step @p110 :rule refl :args (@t58)) % 0.52/0.75 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t58 @t71))) % 0.52/0.75 (step @p112 :rule trans :premises (@p111 @p108)) % 0.52/0.75 (step @p113 :rule eq-symm :args (@t71 @t58)) % 0.52/0.75 (step @p114 :rule trans :premises (@p113 @p112)) % 0.52/0.75 (step @p115 :rule cong :premises (@p114) :args (@t73)) % 0.52/0.75 (step @p116 :rule trans :premises (@p115 @p107)) % 0.52/0.75 (step @p117 :rule cong :premises (@p116) :args (@t74)) % 0.52/0.75 (step @p118 :rule trans :premises (@p117 @p106)) % 0.52/0.75 (step @p119 :rule absorb :args ((= (and false @t60) false))) % 0.52/0.75 (step @p120 :rule refl :args (@t60)) % 0.52/0.75 (step @p121 :rule beta-reduce :args ((= @t76 true))) % 0.52/0.75 (step @p122 :rule cong :premises (@p121) :args (@t77)) % 0.52/0.75 (step @p123 :rule trans :premises (@p122 @p106)) % 0.52/0.75 (step @p124 :rule nary_cong :premises (@p123 @p120) :args (@t78)) % 0.52/0.75 (step @p125 :rule trans :premises (@p124 @p119)) % 0.52/0.75 (step @p126 :rule bool-double-not-elim :args (@t62)) % 0.52/0.75 (step @p127 :rule beta-reduce :args ((= @t79 @t63))) % 0.52/0.75 (step @p128 :rule cong :premises (@p127) :args (@t80)) % 0.52/0.75 (step @p129 :rule trans :premises (@p128 @p126)) % 0.52/0.75 (step @p130 :rule refl :args (@t63)) % 0.52/0.75 (step @p131 :rule nary_cong :premises (@p130 @p129) :args (@t81)) % 0.52/0.75 (step @p132 :rule absorb :args ((= (and @t82 false) false))) % 0.52/0.75 (step @p133 :rule beta-reduce :args ((= @t83 true))) % 0.52/0.75 (step @p134 :rule cong :premises (@p133) :args (@t84)) % 0.52/0.75 (step @p135 :rule trans :premises (@p134 @p106)) % 0.52/0.75 (step @p136 :rule bool-double-not-elim :args (@t82)) % 0.52/0.75 (step @p137 :rule beta-reduce :args ((= @t85 (not @t82)))) % 0.52/0.75 (step @p138 :rule cong :premises (@p137) :args (@t86)) % 0.52/0.75 (step @p139 :rule trans :premises (@p138 @p136)) % 0.52/0.75 (step @p140 :rule nary_cong :premises (@p139 @p135) :args (@t87)) % 0.52/0.75 (step @p141 :rule trans :premises (@p140 @p132)) % 0.52/0.75 (step @p142 :rule nary_cong :premises (@p141 @p131 @p125 @p118) :args (@t88)) % 0.52/0.75 (step @p143 :rule trans :premises (@p142 @p105)) % 0.52/0.75 (step @p144 :rule cong :premises (@p91 @p143) :args ((=> @t65 @t88))) % 0.52/0.75 (assume-push @p160 @t65) % 0.52/0.75 (step @p146 :rule instantiate :premises (@p104) :args ((@list @t75 @t70))) % 0.52/0.75 (step-pop @p161 :rule scope :premises (@p146)) % 0.52/0.75 (step @p147 :rule process_scope :premises (@p161) :args (@t88)) % 0.52/0.75 (step @p149 :rule eq_resolve :premises (@p147 @p144)) % 0.52/0.75 (step @p150 :rule implies_elim :premises (@p149)) % 0.52/0.75 (step @p151 :rule chain_m_resolution :premises (@p150 @p104) :args (@t68 @t89 (@list @t65))) % 0.52/0.75 (step @p152 :rule cnf_and_pos :args (@t68 0)) % 0.52/0.75 (step @p153 :rule reordering :premises (@p152) :args ((or @t63 @t90))) % 0.52/0.75 (step @p154 :rule chain_m_resolution :premises (@p153 @p151) :args (@t63 @t89 (@list @t68))) % 0.52/0.75 (step @p155 :rule cnf_and_pos :args (@t68 1)) % 0.52/0.75 (step @p156 :rule reordering :premises (@p155) :args ((or @t62 @t90))) % 0.52/0.75 (step @p157 false :rule chain_m_resolution :premises (@p156 @p154 @p151) :args (false (@list true false) (@list @t62 @t68))) % 0.52/0.75 ) % 0.52/0.75 % SZS output end Proof % 0.52/0.75 % cvc5 exiting %------------------------------------------------------------------------------