%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV084^5 : 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 : n028.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 08:55:25 AM UTC 2026 % Result : Theorem 1.84s 2.09s % Output : Proof 1.84s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV084^5 : 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 : n028.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 18:12:20 EDT 2026 % 0.17/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 1.84/2.09 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.84/2.09 % SZS status Theorem % 1.84/2.09 % SZS output start Proof % 1.84/2.09 ( % 1.84/2.09 (declare-sort $$unsorted 0) % 1.84/2.09 (declare-const tptp.cP Bool) % 1.84/2.09 (define @t1 () (@var "Xz" (-> $$unsorted Bool))) % 1.84/2.09 (define @t2 () (@var "Xx" (-> $$unsorted Bool))) % 1.84/2.09 (define @t3 () (@var "R" (-> (-> $$unsorted Bool) (-> $$unsorted Bool) Bool))) % 1.84/2.09 (define @t4 () (_ @t3 @t2)) % 1.84/2.09 (define @t5 () (_ @t4 @t1)) % 1.84/2.09 (define @t6 () (@var "Xy" (-> $$unsorted Bool))) % 1.84/2.09 (define @t7 () (_ (_ @t3 @t6) @t1)) % 1.84/2.09 (define @t8 () (_ @t4 @t6)) % 1.84/2.09 (define @t9 () (and @t8 @t7)) % 1.84/2.09 (define @t10 () (@list @t2 @t6 @t1)) % 1.84/2.09 (define @t11 () (forall @t10 (=> @t9 @t5))) % 1.84/2.09 (define @t12 () (_ @t4 @t2)) % 1.84/2.09 (define @t13 () (@list @t2)) % 1.84/2.09 (define @t14 () (forall @t13 @t12)) % 1.84/2.09 (define @t15 () (not tptp.cP)) % 1.84/2.09 (define @t16 () (and tptp.cP @t15)) % 1.84/2.09 (define @t17 () (@list (@var "Xx" $$unsorted))) % 1.84/2.09 (define @t18 () (lambda @t17 @t16)) % 1.84/2.09 (define @t19 () (or tptp.cP @t15)) % 1.84/2.09 (define @t20 () (lambda @t17 @t19)) % 1.84/2.09 (define @t21 () (_ (_ @t3 @t20) @t18)) % 1.84/2.09 (define @t22 () (not @t21)) % 1.84/2.09 (define @t23 () (and @t22 @t14 @t11)) % 1.84/2.09 (define @t24 () (@list @t3)) % 1.84/2.09 (define @t25 () (exists @t24 @t23)) % 1.84/2.09 (define @t26 () (not @t25)) % 1.84/2.09 (define @t27 () (_ @t3 @t2 @t1)) % 1.84/2.09 (define @t28 () (_ @t3 @t6 @t1)) % 1.84/2.09 (define @t29 () (_ @t3 @t2 @t6)) % 1.84/2.09 (define @t30 () (forall @t10 (or (not @t29) (not @t28) @t27))) % 1.84/2.09 (define @t31 () (not @t30)) % 1.84/2.09 (define @t32 () (_ @t3 @t2 @t2)) % 1.84/2.09 (define @t33 () (forall @t13 @t32)) % 1.84/2.09 (define @t34 () (not @t33)) % 1.84/2.09 (define @t35 () (_ @t3 @t20 @t18)) % 1.84/2.09 (define @t36 () (forall @t24 (or @t35 @t34 @t31))) % 1.84/2.09 (define @t37 () (or @t21 @t34 @t31)) % 1.84/2.09 (define @t38 () (not @t22)) % 1.84/2.09 (define @t39 () (or @t38 @t34 @t31)) % 1.84/2.09 (define @t40 () (and @t22 @t33 @t30)) % 1.84/2.09 (define @t41 () (forall @t24 (not @t40))) % 1.84/2.09 (define @t42 () (not @t41)) % 1.84/2.09 (define @t43 () (not @t7)) % 1.84/2.09 (define @t44 () (not @t8)) % 1.84/2.09 (define @t45 () (or @t44 @t43 @t5)) % 1.84/2.09 (define @t46 () (@purify @t20)) % 1.84/2.09 (define @t47 () (@purify @t18)) % 1.84/2.09 (define @t48 () (= @t20 @t18)) % 1.84/2.09 (define @t49 () (@list @t6 @t1)) % 1.84/2.09 (define @t50 () (= @t6 @t1)) % 1.84/2.09 (define @t51 () (not @t50)) % 1.84/2.09 (define @t52 () (or @t51 @t50)) % 1.84/2.09 (define @t53 () (not (= @t6 @t6))) % 1.84/2.09 (define @t54 () (or @t53 @t51 @t50)) % 1.84/2.09 (define @t55 () (= @t2 @t1)) % 1.84/2.09 (define @t56 () (= @t2 @t6)) % 1.84/2.09 (define @t57 () (not @t56)) % 1.84/2.09 (define @t58 () (or @t57 @t57 @t51 @t55)) % 1.84/2.09 (define @t59 () (or @t57 @t51 @t55)) % 1.84/2.09 (define @t60 () (forall @t13 @t59)) % 1.84/2.09 (define @t61 () (forall @t49 @t60)) % 1.84/2.09 (define @t62 () (forall (@list @t6 @t1 @t2) @t59)) % 1.84/2.09 (define @t63 () (@var "BOUND_VARIABLE_532637" (-> $$unsorted Bool))) % 1.84/2.09 (define @t64 () (@var "BOUND_VARIABLE_532636" (-> $$unsorted Bool))) % 1.84/2.09 (define @t65 () (lambda (@list @t64 @t63) (= @t64 @t63))) % 1.84/2.09 (define @t66 () (_ @t65 @t2 @t1)) % 1.84/2.09 (define @t67 () (_ @t65 @t6 @t1)) % 1.84/2.09 (define @t68 () (not @t67)) % 1.84/2.09 (define @t69 () (_ @t65 @t2 @t6)) % 1.84/2.09 (define @t70 () (not @t69)) % 1.84/2.09 (define @t71 () (or @t70 @t68 @t66)) % 1.84/2.09 (define @t72 () (forall @t10 @t71)) % 1.84/2.09 (define @t73 () (not @t72)) % 1.84/2.09 (define @t74 () (_ @t65 @t2 @t2)) % 1.84/2.09 (define @t75 () (forall @t13 @t74)) % 1.84/2.09 (define @t76 () (not @t75)) % 1.84/2.09 (define @t77 () (_ @t65 @t20 @t18)) % 1.84/2.09 (define @t78 () (or @t77 @t76 @t73)) % 1.84/2.09 (define @t79 () (= @t47 @t46)) % 1.84/2.09 (define @t80 () (@list false)) % 1.84/2.09 (define @t81 () (= true false)) % 1.84/2.09 (define @t82 () (= @t19 @t16)) % 1.84/2.09 (define @t83 () (forall @t17 (= @t16 @t19))) % 1.84/2.09 (define @t84 () (=> @t79 @t83)) % 1.84/2.09 (assume @p1 @t26) % 1.84/2.09 (assume @p2 true) % 1.84/2.09 (step @p3 :rule bool-double-not-elim :args (@t36)) % 1.84/2.09 (step @p4 :rule refl :args (@t31)) % 1.84/2.09 (step @p5 :rule refl :args (@t34)) % 1.84/2.09 (step @p6 :rule refl :args (@t35)) % 1.84/2.09 (step @p7 :rule refl :args (@t21)) % 1.84/2.09 (step @p8 :rule cong :premises (@p7 @p6) :args ((= @t21 @t35))) % 1.84/2.09 (step @p9 :rule symm :premises (@p8)) % 1.84/2.09 (step @p10 :rule eq_resolve :premises (@p7 @p9)) % 1.84/2.09 (step @p11 :rule nary_cong :premises (@p10 @p5 @p4) :args (@t37)) % 1.84/2.09 (step @p12 :rule cong :premises (@p11) :args ((forall @t24 @t37))) % 1.84/2.09 (step @p13 :rule bool-double-not-elim :args (@t21)) % 1.84/2.09 (step @p14 :rule nary_cong :premises (@p13 @p5 @p4) :args (@t39)) % 1.84/2.09 (step @p15 :rule aci_norm :args ((= (or @t38 (or @t34 @t31)) @t39))) % 1.84/2.09 (step @p16 :rule trans :premises (@p15 @p14)) % 1.84/2.09 (step @p17 :rule bool-and-de-morgan :args (@t33 @t30 true)) % 1.84/2.09 (step @p18 :rule refl :args (@t38)) % 1.84/2.09 (step @p19 :rule nary_cong :premises (@p18 @p17) :args ((or @t38 (not (and @t33 @t30))))) % 1.84/2.09 (step @p20 :rule bool-and-de-morgan :args (@t22 @t33 (and @t30))) % 1.84/2.09 (step @p21 :rule trans :premises (@p20 @p19)) % 1.84/2.09 (step @p22 :rule trans :premises (@p21 @p16)) % 1.84/2.09 (step @p23 :rule cong :premises (@p22) :args (@t41)) % 1.84/2.09 (step @p24 :rule trans :premises (@p23 @p12)) % 1.84/2.09 (step @p25 :rule cong :premises (@p24) :args (@t42)) % 1.84/2.09 (step @p26 :rule exists-elim :args ((= (exists @t24 @t40) @t42))) % 1.84/2.09 (step @p27 :rule trans :premises (@p26 @p25)) % 1.84/2.09 (step @p28 :rule refl :args (@t27)) % 1.84/2.09 (step @p29 :rule refl :args (@t5)) % 1.84/2.09 (step @p30 :rule cong :premises (@p29 @p28) :args ((= @t5 @t27))) % 1.84/2.09 (step @p31 :rule symm :premises (@p30)) % 1.84/2.09 (step @p32 :rule eq_resolve :premises (@p29 @p31)) % 1.84/2.09 (step @p33 :rule refl :args (@t28)) % 1.84/2.09 (step @p34 :rule refl :args (@t7)) % 1.84/2.09 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t7 @t28))) % 1.84/2.09 (step @p36 :rule symm :premises (@p35)) % 1.84/2.09 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 1.84/2.09 (step @p38 :rule cong :premises (@p37) :args (@t43)) % 1.84/2.09 (step @p39 :rule refl :args (@t29)) % 1.84/2.09 (step @p40 :rule refl :args (@t8)) % 1.84/2.09 (step @p41 :rule cong :premises (@p40 @p39) :args ((= @t8 @t29))) % 1.84/2.09 (step @p42 :rule symm :premises (@p41)) % 1.84/2.09 (step @p43 :rule eq_resolve :premises (@p40 @p42)) % 1.84/2.09 (step @p44 :rule cong :premises (@p43) :args (@t44)) % 1.84/2.09 (step @p45 :rule nary_cong :premises (@p44 @p38 @p32) :args (@t45)) % 1.84/2.09 (step @p46 :rule cong :premises (@p45) :args ((forall @t10 @t45))) % 1.84/2.09 (step @p47 :rule aci_norm :args ((= (or (or @t44 @t43) @t5) @t45))) % 1.84/2.09 (step @p48 :rule bool-and-de-morgan :args (@t8 @t7 true)) % 1.84/2.09 (step @p49 :rule nary_cong :premises (@p48 @p29) :args ((or (not @t9) @t5))) % 1.84/2.09 (step @p50 :rule trans :premises (@p49 @p47)) % 1.84/2.09 (step @p51 :rule bool-impl-elim :args (@t9 @t5)) % 1.84/2.09 (step @p52 :rule trans :premises (@p51 @p50)) % 1.84/2.09 (step @p53 :rule cong :premises (@p52) :args (@t11)) % 1.84/2.09 (step @p54 :rule trans :premises (@p53 @p46)) % 1.84/2.09 (step @p55 :rule refl :args (@t32)) % 1.84/2.09 (step @p56 :rule refl :args (@t12)) % 1.84/2.09 (step @p57 :rule cong :premises (@p56 @p55) :args ((= @t12 @t32))) % 1.84/2.09 (step @p58 :rule symm :premises (@p57)) % 1.84/2.09 (step @p59 :rule eq_resolve :premises (@p56 @p58)) % 1.84/2.09 (step @p60 :rule cong :premises (@p59) :args (@t14)) % 1.84/2.09 (step @p61 :rule refl :args (@t22)) % 1.84/2.09 (step @p62 :rule nary_cong :premises (@p61 @p60 @p54) :args (@t23)) % 1.84/2.09 (step @p63 :rule cong :premises (@p62) :args (@t25)) % 1.84/2.09 (step @p64 :rule trans :premises (@p63 @p27)) % 1.84/2.09 (step @p65 :rule cong :premises (@p64) :args (@t26)) % 1.84/2.09 (step @p66 :rule trans :premises (@p65 @p3)) % 1.84/2.09 (step @p67 :rule eq_resolve :premises (@p1 @p66)) % 1.84/2.09 (step @p68 :rule eq-symm :args (@t46 @t47)) % 1.84/2.09 (step @p69 :rule eq-refl :args (@t18)) % 1.84/2.09 (step @p70 :rule skolem_intro :args (@t47)) % 1.84/2.09 (step @p71 :rule refl :args (@t18)) % 1.84/2.09 (step @p72 :rule cong :premises (@p71 @p70) :args ((= @t18 @t47))) % 1.84/2.09 (step @p73 :rule trans :premises (@p72 @p69)) % 1.84/2.09 (step @p74 :rule true_elim :premises (@p73)) % 1.84/2.09 (step @p75 :rule eq-refl :args (@t20)) % 1.84/2.09 (step @p76 :rule skolem_intro :args (@t46)) % 1.84/2.09 (step @p77 :rule refl :args (@t20)) % 1.84/2.09 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t20 @t46))) % 1.84/2.09 (step @p79 :rule trans :premises (@p78 @p75)) % 1.84/2.09 (step @p80 :rule true_elim :premises (@p79)) % 1.84/2.09 (step @p81 :rule cong :premises (@p80 @p74) :args (@t48)) % 1.84/2.09 (step @p82 :rule trans :premises (@p81 @p68)) % 1.84/2.09 (step @p83 :rule refl :args (@t36)) % 1.84/2.09 (step @p84 :rule cong :premises (@p83 @p82) :args ((=> @t36 @t48))) % 1.84/2.09 (step @p85 :rule aci_norm :args ((= (or @t48 false false) @t48))) % 1.84/2.09 (step @p86 :rule evaluate :args ((not true))) % 1.84/2.09 (step @p87 :rule quant-unused-vars :args ((= (forall @t49 true) true))) % 1.84/2.09 (step @p88 :rule bool-or-taut2 :args (false @t50 false false)) % 1.84/2.09 (step @p89 :rule cong :premises (@p88) :args ((forall @t49 @t52))) % 1.84/2.09 (step @p90 :rule trans :premises (@p89 @p87)) % 1.84/2.09 (step @p91 :rule aci_norm :args ((= (or false @t51 @t50) @t52))) % 1.84/2.09 (step @p92 :rule refl :args (@t50)) % 1.84/2.09 (step @p93 :rule refl :args (@t51)) % 1.84/2.09 (step @p94 :rule eq-refl :args (@t6)) % 1.84/2.09 (step @p95 :rule cong :premises (@p94) :args (@t53)) % 1.84/2.09 (step @p96 :rule trans :premises (@p95 @p86)) % 1.84/2.09 (step @p97 :rule nary_cong :premises (@p96 @p93 @p92) :args (@t54)) % 1.84/2.09 (step @p98 :rule trans :premises (@p97 @p91)) % 1.84/2.10 (step @p99 :rule cong :premises (@p98) :args ((forall @t49 @t54))) % 1.84/2.10 (step @p100 :rule trans :premises (@p99 @p90)) % 1.84/2.10 (step @p101 :rule quant-var-elim-eq :args ((= (forall @t13 @t58) @t54))) % 1.84/2.10 (step @p102 :rule aci_norm :args ((= @t59 @t58))) % 1.84/2.10 (step @p103 :rule cong :premises (@p102) :args (@t60)) % 1.84/2.10 (step @p104 :rule trans :premises (@p103 @p101)) % 1.84/2.10 (step @p105 :rule cong :premises (@p104) :args (@t61)) % 1.84/2.10 (step @p106 :rule quant-merge-prenex :args ((= @t61 @t62))) % 1.84/2.10 (step @p107 :rule symm :premises (@p106)) % 1.84/2.10 (step @p108 :rule quant_var_reordering :args ((= (forall @t10 @t59) @t62))) % 1.84/2.10 (step @p109 :rule trans :premises (@p108 @p107 @p105)) % 1.84/2.10 (step @p110 :rule trans :premises (@p109 @p100)) % 1.84/2.10 (step @p111 :rule beta-reduce :args ((= @t66 @t55))) % 1.84/2.10 (step @p112 :rule beta-reduce :args ((= @t67 @t50))) % 1.84/2.10 (step @p113 :rule cong :premises (@p112) :args (@t68)) % 1.84/2.10 (step @p114 :rule beta-reduce :args ((= @t69 @t56))) % 1.84/2.10 (step @p115 :rule cong :premises (@p114) :args (@t70)) % 1.84/2.10 (step @p116 :rule nary_cong :premises (@p115 @p113 @p111) :args (@t71)) % 1.84/2.10 (step @p117 :rule cong :premises (@p116) :args (@t72)) % 1.84/2.10 (step @p118 :rule trans :premises (@p117 @p110)) % 1.84/2.10 (step @p119 :rule cong :premises (@p118) :args (@t73)) % 1.84/2.10 (step @p120 :rule trans :premises (@p119 @p86)) % 1.84/2.10 (step @p121 :rule quant-unused-vars :args ((= (forall @t13 true) true))) % 1.84/2.10 (step @p122 :rule eq-refl :args (@t2)) % 1.84/2.10 (step @p123 :rule beta-reduce :args ((= @t74 (= @t2 @t2)))) % 1.84/2.10 (step @p124 :rule trans :premises (@p123 @p122)) % 1.84/2.10 (step @p125 :rule cong :premises (@p124) :args (@t75)) % 1.84/2.10 (step @p126 :rule trans :premises (@p125 @p121)) % 1.84/2.10 (step @p127 :rule cong :premises (@p126) :args (@t76)) % 1.84/2.10 (step @p128 :rule trans :premises (@p127 @p86)) % 1.84/2.10 (step @p129 :rule beta-reduce :args ((= @t77 @t48))) % 1.84/2.10 (step @p130 :rule nary_cong :premises (@p129 @p128 @p120) :args (@t78)) % 1.84/2.10 (step @p131 :rule trans :premises (@p130 @p85)) % 1.84/2.10 (step @p132 :rule cong :premises (@p83 @p131) :args ((=> @t36 @t78))) % 1.84/2.10 (assume-push @p160 @t36) % 1.84/2.10 (step @p134 :rule instantiate :premises (@p67) :args ((@list @t65))) % 1.84/2.10 (step-pop @p161 :rule scope :premises (@p134)) % 1.84/2.10 (step @p135 :rule process_scope :premises (@p161) :args (@t78)) % 1.84/2.10 (step @p137 :rule eq_resolve :premises (@p135 @p132)) % 1.84/2.10 (step @p138 :rule eq_resolve :premises (@p137 @p84)) % 1.84/2.10 (step @p139 :rule implies_elim :premises (@p138)) % 1.84/2.10 (step @p140 :rule chain_m_resolution :premises (@p139 @p67) :args (@t79 @t80 (@list @t36))) % 1.84/2.10 (step @p141 :rule bool-impl-false1 :args (@t79)) % 1.84/2.10 (step @p142 :rule quant-unused-vars :args ((= (forall @t17 false) false))) % 1.84/2.10 (step @p143 :rule evaluate :args (@t81)) % 1.84/2.10 (step @p144 :rule cong :premises (@p143) :args ((forall @t17 @t81))) % 1.84/2.10 (step @p145 :rule trans :premises (@p144 @p142)) % 1.84/2.10 (step @p146 :rule bool-and-conf :args (true tptp.cP true true)) % 1.84/2.10 (step @p147 :rule bool-or-taut :args (false tptp.cP false false)) % 1.84/2.10 (step @p148 :rule cong :premises (@p147 @p146) :args (@t82)) % 1.84/2.10 (step @p149 :rule cong :premises (@p148) :args ((forall @t17 @t82))) % 1.84/2.10 (step @p150 :rule trans :premises (@p149 @p145)) % 1.84/2.10 (step @p151 :rule eq-symm :args (@t16 @t19)) % 1.84/2.10 (step @p152 :rule cong :premises (@p151) :args (@t83)) % 1.84/2.10 (step @p153 :rule trans :premises (@p152 @p150)) % 1.84/2.10 (step @p154 :rule refl :args (@t79)) % 1.84/2.10 (step @p155 :rule cong :premises (@p154 @p153) :args (@t84)) % 1.84/2.10 (step @p156 :rule trans :premises (@p155 @p141)) % 1.84/2.10 ; WARNING: add trust step for TRUST % 1.84/2.10 ; trust TRUST THEORY_LEMMA % 1.84/2.10 (step @p157 :rule trust :premises () :args (@t84)) % 1.84/2.10 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 1.84/2.10 (step @p159 false :rule chain_m_resolution :premises (@p158 @p140) :args (false @t80 (@list @t79))) % 1.84/2.10 ) % 1.84/2.10 % SZS output end Proof % 1.84/2.10 % cvc5 exiting %------------------------------------------------------------------------------