%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU940^5 : 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 : 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 08:53:34 AM UTC 2026 % Result : Theorem 0.83s 1.10s % Output : Proof 0.83s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU940^5 : TPTP v9.2.1. Released v4.0.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 18:01:03 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.33 %----Proving TH0 % 0.83/1.10 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.83/1.10 % SZS status Theorem % 0.83/1.10 % SZS output start Proof % 0.83/1.10 ( % 0.83/1.10 (declare-sort $$unsorted 0) % 0.83/1.10 (define @t1 () (@var "Y" $$unsorted)) % 0.83/1.10 (define @t2 () (@var "G" (-> $$unsorted $$unsorted))) % 0.83/1.10 (define @t3 () (_ @t2 @t1)) % 0.83/1.10 (define @t4 () (@var "P" (-> $$unsorted Bool))) % 0.83/1.10 (define @t5 () (_ @t4 @t3)) % 0.83/1.10 (define @t6 () (_ @t4 @t1)) % 0.83/1.10 (define @t7 () (@list @t1)) % 0.83/1.10 (define @t8 () (forall @t7 (=> @t6 @t5))) % 0.83/1.10 (define @t9 () (@var "Xx" $$unsorted)) % 0.83/1.10 (define @t10 () (@var "H" (-> $$unsorted $$unsorted))) % 0.83/1.10 (define @t11 () (_ @t10 @t9)) % 0.83/1.10 (define @t12 () (_ @t2 @t11)) % 0.83/1.10 (define @t13 () (@list @t9)) % 0.83/1.10 (define @t14 () (lambda @t13 @t12)) % 0.83/1.10 (define @t15 () (@var "M" (-> (-> $$unsorted $$unsorted) Bool))) % 0.83/1.10 (define @t16 () (_ @t15 @t14)) % 0.83/1.10 (define @t17 () (and @t16 @t8)) % 0.83/1.10 (define @t18 () (_ @t15 @t10)) % 0.83/1.10 (define @t19 () (_ @t15 @t2)) % 0.83/1.10 (define @t20 () (and @t19 @t18)) % 0.83/1.10 (define @t21 () (=> @t20 @t17)) % 0.83/1.10 (define @t22 () (@list @t2 @t10)) % 0.83/1.10 (define @t23 () (forall @t22 @t21)) % 0.83/1.10 (define @t24 () (lambda @t13 @t9)) % 0.83/1.10 (define @t25 () (_ @t15 @t24)) % 0.83/1.10 (define @t26 () (and @t25 @t23)) % 0.83/1.10 (define @t27 () (@list @t15)) % 0.83/1.10 (define @t28 () (exists @t27 @t26)) % 0.83/1.10 (define @t29 () (@list @t4)) % 0.83/1.10 (define @t30 () (forall @t29 @t28)) % 0.83/1.10 (define @t31 () (not @t30)) % 0.83/1.10 (define @t32 () (@var "BOUND_VARIABLE_7473" $$unsorted)) % 0.83/1.10 (define @t33 () (_ @t2 @t32)) % 0.83/1.10 (define @t34 () (or (not (_ @t4 @t32)) (_ @t4 @t33))) % 0.83/1.10 (define @t35 () (_ @t10 @t9)) % 0.83/1.10 (define @t36 () (_ @t2 @t35)) % 0.83/1.10 (define @t37 () (lambda @t13 @t36)) % 0.83/1.10 (define @t38 () (_ @t15 @t37)) % 0.83/1.10 (define @t39 () (and @t38 @t34)) % 0.83/1.10 (define @t40 () (_ @t15 @t10)) % 0.83/1.10 (define @t41 () (not @t40)) % 0.83/1.10 (define @t42 () (_ @t15 @t2)) % 0.83/1.10 (define @t43 () (not @t42)) % 0.83/1.10 (define @t44 () (or @t43 @t41 @t39)) % 0.83/1.10 (define @t45 () (@list @t2 @t10 @t32)) % 0.83/1.10 (define @t46 () (forall @t45 @t44)) % 0.83/1.10 (define @t47 () (not @t46)) % 0.83/1.10 (define @t48 () (_ @t15 @t24)) % 0.83/1.10 (define @t49 () (not @t25)) % 0.83/1.10 (define @t50 () (or @t49 @t47)) % 0.83/1.10 (define @t51 () (and @t25 @t46)) % 0.83/1.10 (define @t52 () (forall @t27 (not @t51))) % 0.83/1.10 (define @t53 () (not @t52)) % 0.83/1.10 (define @t54 () (@list @t32)) % 0.83/1.10 (define @t55 () (forall @t54 @t44)) % 0.83/1.10 (define @t56 () (forall @t54 @t34)) % 0.83/1.10 (define @t57 () (forall @t54 @t38)) % 0.83/1.10 (define @t58 () (and @t57 @t56)) % 0.83/1.10 (define @t59 () (forall @t54 @t39)) % 0.83/1.10 (define @t60 () (or @t43 @t41 @t59)) % 0.83/1.10 (define @t61 () (_ @t2 @t1)) % 0.83/1.10 (define @t62 () (_ @t4 @t61)) % 0.83/1.10 (define @t63 () (_ @t4 @t1)) % 0.83/1.10 (define @t64 () (forall @t7 (or (not @t63) @t62))) % 0.83/1.10 (define @t65 () (and @t16 @t64)) % 0.83/1.10 (define @t66 () (not @t18)) % 0.83/1.10 (define @t67 () (not @t19)) % 0.83/1.10 (define @t68 () (or @t67 @t66 @t65)) % 0.83/1.10 (define @t69 () (not @t6)) % 0.83/1.10 (define @t70 () (or @t69 @t5)) % 0.83/1.10 (define @t71 () (not @t48)) % 0.83/1.10 (define @t72 () (forall @t29 (not (forall @t27 (or @t71 @t47))))) % 0.83/1.10 (define @t73 () (@quantifiers_skolemize @t72 0)) % 0.83/1.10 (define @t74 () (_ @t73 @t32)) % 0.83/1.10 (define @t75 () (not @t74)) % 0.83/1.10 (define @t76 () (or @t75 (_ @t73 @t33))) % 0.83/1.10 (define @t77 () (forall @t27 (or @t71 (not (forall @t45 (or @t43 @t41 (and @t38 @t76))))))) % 0.83/1.10 (define @t78 () (not @t72)) % 0.83/1.10 (define @t79 () (not (not @t77))) % 0.83/1.10 (define @t80 () (@list @t10 @t32)) % 0.83/1.10 (define @t81 () (= @t24 @t10)) % 0.83/1.10 (define @t82 () (not @t81)) % 0.83/1.10 (define @t83 () (and @t81 true)) % 0.83/1.10 (define @t84 () (or @t82 @t83)) % 0.83/1.10 (define @t85 () (and @t81 (or @t75 @t74))) % 0.83/1.10 (define @t86 () (or @t82 @t85)) % 0.83/1.10 (define @t87 () (_ @t24 @t32)) % 0.83/1.10 (define @t88 () (_ @t73 @t87)) % 0.83/1.10 (define @t89 () (or @t75 @t88)) % 0.83/1.10 (define @t90 () (_ @t24 @t35)) % 0.83/1.10 (define @t91 () (lambda @t13 @t90)) % 0.83/1.10 (define @t92 () (= @t24 @t91)) % 0.83/1.10 (define @t93 () (and @t92 @t89)) % 0.83/1.10 (define @t94 () (= @t24 @t24)) % 0.83/1.10 (define @t95 () (not @t94)) % 0.83/1.10 (define @t96 () (or @t95 @t82 @t93)) % 0.83/1.10 (define @t97 () (= @t24 @t37)) % 0.83/1.10 (define @t98 () (and @t97 @t76)) % 0.83/1.10 (define @t99 () (= @t24 @t2)) % 0.83/1.10 (define @t100 () (not @t99)) % 0.83/1.10 (define @t101 () (@list @t2)) % 0.83/1.10 (define @t102 () (or @t100 @t100 @t82 @t98)) % 0.83/1.10 (define @t103 () (or @t100 @t82 @t98)) % 0.83/1.10 (define @t104 () (forall @t101 @t103)) % 0.83/1.10 (define @t105 () (forall @t80 @t104)) % 0.83/1.10 (define @t106 () (forall (@list @t10 @t32 @t2) @t103)) % 0.83/1.10 (define @t107 () (@var "BOUND_VARIABLE_29214" (-> $$unsorted $$unsorted))) % 0.83/1.10 (define @t108 () (lambda (@list @t107) (= @t24 @t107))) % 0.83/1.10 (define @t109 () (_ @t108 @t37)) % 0.83/1.10 (define @t110 () (and @t109 @t76)) % 0.83/1.10 (define @t111 () (_ @t108 @t10)) % 0.83/1.10 (define @t112 () (not @t111)) % 0.83/1.10 (define @t113 () (_ @t108 @t2)) % 0.83/1.10 (define @t114 () (not @t113)) % 0.83/1.10 (define @t115 () (or @t114 @t112 @t110)) % 0.83/1.10 (define @t116 () (forall @t45 @t115)) % 0.83/1.10 (define @t117 () (not @t116)) % 0.83/1.10 (define @t118 () (_ @t108 @t24)) % 0.83/1.10 (define @t119 () (not @t118)) % 0.83/1.10 (define @t120 () (or @t119 @t117)) % 0.83/1.10 (assume @p1 @t31) % 0.83/1.10 (assume @p2 true) % 0.83/1.10 (step @p3 :rule refl :args (@t47)) % 0.83/1.10 (step @p4 :rule refl :args (@t48)) % 0.83/1.10 (step @p5 :rule refl :args (@t25)) % 0.83/1.10 (step @p6 :rule cong :premises (@p5 @p4) :args ((= @t25 @t48))) % 0.83/1.10 (step @p7 :rule symm :premises (@p6)) % 0.83/1.10 (step @p8 :rule eq_resolve :premises (@p5 @p7)) % 0.83/1.10 (step @p9 :rule cong :premises (@p8) :args (@t49)) % 0.83/1.10 (step @p10 :rule nary_cong :premises (@p9 @p3) :args (@t50)) % 0.83/1.10 (step @p11 :rule cong :premises (@p10) :args ((forall @t27 @t50))) % 0.83/1.10 (step @p12 :rule bool-and-de-morgan :args (@t25 @t46 true)) % 0.83/1.10 (step @p13 :rule cong :premises (@p12) :args (@t52)) % 0.83/1.10 (step @p14 :rule trans :premises (@p13 @p11)) % 0.83/1.10 (step @p15 :rule cong :premises (@p14) :args (@t53)) % 0.83/1.10 (step @p16 :rule exists-elim :args ((= (exists @t27 @t51) @t53))) % 0.83/1.10 (step @p17 :rule trans :premises (@p16 @p15)) % 0.83/1.10 (step @p18 :rule quant-merge-prenex :args ((= (forall @t22 @t55) @t46))) % 0.83/1.10 (step @p19 :rule alpha_equiv :args (@t56 (@list @t32) (@list @t1))) % 0.83/1.10 (step @p20 :rule quant-unused-vars :args ((= @t57 @t38))) % 0.83/1.10 (step @p21 :rule nary_cong :premises (@p20 @p19) :args (@t58)) % 0.83/1.10 (step @p22 :rule quant-miniscope-and :args ((= @t59 @t58))) % 0.83/1.10 (step @p23 :rule trans :premises (@p22 @p21)) % 0.83/1.10 (step @p24 :rule refl :args (@t41)) % 0.83/1.10 (step @p25 :rule refl :args (@t43)) % 0.83/1.10 (step @p26 :rule nary_cong :premises (@p25 @p24 @p23) :args (@t60)) % 0.83/1.10 (step @p27 :rule quant-miniscope-or :args ((= @t55 @t60))) % 0.83/1.10 (step @p28 :rule trans :premises (@p27 @p26)) % 0.83/1.10 (step @p29 :rule symm :premises (@p28)) % 0.83/1.10 (step @p30 :rule cong :premises (@p29) :args ((forall @t22 (or @t43 @t41 (and @t38 @t64))))) % 0.83/1.10 (step @p31 :rule trans :premises (@p30 @p18)) % 0.83/1.10 (step @p32 :rule refl :args (@t64)) % 0.83/1.10 (step @p33 :rule refl :args ((_ @t15 @t14))) % 0.83/1.10 (step @p34 :rule refl :args ((_ @t2 @t11))) % 0.83/1.10 (step @p35 :rule refl :args (@t35)) % 0.83/1.10 (step @p36 :rule cong :premises (@p35) :args (@t36)) % 0.83/1.10 (step @p37 :rule trans :premises (@p36 @p34)) % 0.83/1.10 (step @p38 :rule cong :premises (@p37) :args (@t37)) % 0.83/1.10 (step @p39 :rule cong :premises (@p38) :args (@t38)) % 0.83/1.10 (step @p40 :rule trans :premises (@p39 @p33)) % 0.83/1.10 (step @p41 :rule refl :args (@t15)) % 0.83/1.10 (step @p42 :rule ho_cong :premises (@p41 @p38)) % 0.83/1.10 (step @p43 :rule cong :premises (@p42 @p40) :args ((= (_ @t15 @t37) @t38))) % 0.83/1.10 (step @p44 :rule symm :premises (@p43)) % 0.83/1.10 (step @p45 :rule refl :args (@t16)) % 0.83/1.10 (step @p46 :rule eq_resolve :premises (@p45 @p44)) % 0.83/1.10 (step @p47 :rule refl :args (@t2)) % 0.83/1.10 (step @p48 :rule ho_cong :premises (@p47 @p35)) % 0.83/1.10 (step @p49 :rule cong :premises (@p48 @p37) :args ((= (_ @t2 @t35) @t36))) % 0.83/1.10 (step @p50 :rule symm :premises (@p49)) % 0.83/1.10 (step @p51 :rule refl :args (@t12)) % 0.83/1.10 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 0.83/1.10 (step @p53 :rule refl :args (@t11)) % 0.83/1.10 (step @p54 :rule cong :premises (@p53 @p35) :args ((= @t11 @t35))) % 0.83/1.10 (step @p55 :rule symm :premises (@p54)) % 0.83/1.10 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.83/1.10 (step @p57 :rule ho_cong :premises (@p47 @p56)) % 0.83/1.10 (step @p58 :rule trans :premises (@p57 @p52)) % 0.83/1.10 (step @p59 :rule cong :premises (@p58) :args (@t14)) % 0.83/1.10 (step @p60 :rule ho_cong :premises (@p41 @p59)) % 0.83/1.10 (step @p61 :rule trans :premises (@p60 @p46)) % 0.83/1.10 (step @p62 :rule nary_cong :premises (@p61 @p32) :args (@t65)) % 0.83/1.10 (step @p63 :rule refl :args (@t40)) % 0.83/1.10 (step @p64 :rule refl :args (@t18)) % 0.83/1.10 (step @p65 :rule cong :premises (@p64 @p63) :args ((= @t18 @t40))) % 0.83/1.10 (step @p66 :rule symm :premises (@p65)) % 0.83/1.10 (step @p67 :rule eq_resolve :premises (@p64 @p66)) % 0.83/1.10 (step @p68 :rule cong :premises (@p67) :args (@t66)) % 0.83/1.10 (step @p69 :rule refl :args (@t42)) % 0.83/1.10 (step @p70 :rule refl :args (@t19)) % 0.83/1.10 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t19 @t42))) % 0.83/1.10 (step @p72 :rule symm :premises (@p71)) % 0.83/1.10 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.83/1.10 (step @p74 :rule cong :premises (@p73) :args (@t67)) % 0.83/1.10 (step @p75 :rule nary_cong :premises (@p74 @p68 @p62) :args (@t68)) % 0.83/1.10 (step @p76 :rule cong :premises (@p75) :args ((forall @t22 @t68))) % 0.83/1.10 (step @p77 :rule trans :premises (@p76 @p31)) % 0.83/1.10 (step @p78 :rule aci_norm :args ((= (or (or @t67 @t66) @t65) @t68))) % 0.83/1.10 (step @p79 :rule refl :args (@t65)) % 0.83/1.10 (step @p80 :rule bool-and-de-morgan :args (@t19 @t18 true)) % 0.83/1.10 (step @p81 :rule nary_cong :premises (@p80 @p79) :args ((or (not @t20) @t65))) % 0.83/1.10 (step @p82 :rule trans :premises (@p81 @p78)) % 0.83/1.10 (step @p83 :rule bool-impl-elim :args (@t20 @t65)) % 0.83/1.10 (step @p84 :rule trans :premises (@p83 @p82)) % 0.83/1.10 (step @p85 :rule cong :premises (@p84) :args ((forall @t22 (=> @t20 @t65)))) % 0.83/1.10 (step @p86 :rule trans :premises (@p85 @p77)) % 0.83/1.10 (step @p87 :rule refl :args ((_ @t4 @t3))) % 0.83/1.10 (step @p88 :rule refl :args (@t61)) % 0.83/1.10 (step @p89 :rule cong :premises (@p88) :args (@t62)) % 0.83/1.10 (step @p90 :rule trans :premises (@p89 @p87)) % 0.83/1.10 (step @p91 :rule refl :args (@t4)) % 0.83/1.10 (step @p92 :rule ho_cong :premises (@p91 @p88)) % 0.83/1.10 (step @p93 :rule cong :premises (@p92 @p90) :args ((= (_ @t4 @t61) @t62))) % 0.83/1.10 (step @p94 :rule symm :premises (@p93)) % 0.83/1.10 (step @p95 :rule refl :args (@t5)) % 0.83/1.10 (step @p96 :rule eq_resolve :premises (@p95 @p94)) % 0.83/1.10 (step @p97 :rule refl :args (@t3)) % 0.83/1.10 (step @p98 :rule cong :premises (@p97 @p88) :args ((= @t3 @t61))) % 0.83/1.10 (step @p99 :rule symm :premises (@p98)) % 0.83/1.10 (step @p100 :rule eq_resolve :premises (@p97 @p99)) % 0.83/1.10 (step @p101 :rule ho_cong :premises (@p91 @p100)) % 0.83/1.10 (step @p102 :rule trans :premises (@p101 @p96)) % 0.83/1.10 (step @p103 :rule refl :args (@t63)) % 0.83/1.10 (step @p104 :rule refl :args (@t6)) % 0.83/1.10 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t6 @t63))) % 0.83/1.10 (step @p106 :rule symm :premises (@p105)) % 0.83/1.10 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.83/1.10 (step @p108 :rule cong :premises (@p107) :args (@t69)) % 0.83/1.10 (step @p109 :rule nary_cong :premises (@p108 @p102) :args (@t70)) % 0.83/1.10 (step @p110 :rule cong :premises (@p109) :args ((forall @t7 @t70))) % 0.83/1.10 (step @p111 :rule bool-impl-elim :args (@t6 @t5)) % 0.83/1.10 (step @p112 :rule cong :premises (@p111) :args (@t8)) % 0.83/1.10 (step @p113 :rule trans :premises (@p112 @p110)) % 0.83/1.10 (step @p114 :rule refl :args (@t16)) % 0.83/1.10 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t17)) % 0.83/1.10 (step @p116 :rule refl :args (@t20)) % 0.83/1.10 (step @p117 :rule cong :premises (@p116 @p115) :args (@t21)) % 0.83/1.10 (step @p118 :rule cong :premises (@p117) :args (@t23)) % 0.83/1.10 (step @p119 :rule trans :premises (@p118 @p86)) % 0.83/1.10 (step @p120 :rule refl :args (@t25)) % 0.83/1.10 (step @p121 :rule nary_cong :premises (@p120 @p119) :args (@t26)) % 0.83/1.10 (step @p122 :rule cong :premises (@p121) :args (@t28)) % 0.83/1.10 (step @p123 :rule trans :premises (@p122 @p17)) % 0.83/1.10 (step @p124 :rule cong :premises (@p123) :args (@t30)) % 0.83/1.10 (step @p125 :rule cong :premises (@p124) :args (@t31)) % 0.83/1.10 (step @p126 :rule eq_resolve :premises (@p1 @p125)) % 0.83/1.10 (step @p127 :rule refl :args (@t77)) % 0.83/1.10 (step @p128 :rule bool-double-not-elim :args (@t72)) % 0.83/1.10 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or (not @t78) @t77))) % 0.83/1.10 (step @p130 :rule bool-double-not-elim :args (@t77)) % 0.83/1.10 (step @p131 :rule refl :args (@t78)) % 0.83/1.10 (step @p132 :rule cong :premises (@p131 @p130) :args ((=> @t78 @t79))) % 0.83/1.10 (assume-push @p221 @t78) % 0.83/1.10 (step @p134 :rule skolemize :premises (@p126)) % 0.83/1.10 (step-pop @p222 :rule scope :premises (@p134)) % 0.83/1.10 (step @p135 :rule process_scope :premises (@p222) :args (@t79)) % 0.83/1.10 (step @p137 :rule eq_resolve :premises (@p135 @p132)) % 0.83/1.10 (step @p138 :rule implies_elim :premises (@p137)) % 0.83/1.10 (step @p139 :rule eq_resolve :premises (@p138 @p129)) % 0.83/1.10 (step @p140 :rule chain_m_resolution :premises (@p139 @p126) :args (@t77 (@list true) (@list @t72))) % 0.83/1.10 (step @p141 :rule bool-impl-false1 :args (@t77)) % 0.83/1.10 (step @p142 :rule evaluate :args ((or false false))) % 0.83/1.10 (step @p143 :rule evaluate :args ((not true))) % 0.83/1.10 (step @p144 :rule quant-unused-vars :args ((= (forall @t80 true) true))) % 0.83/1.10 (step @p145 :rule bool-or-taut2 :args (false @t81 false false)) % 0.83/1.10 (step @p146 :rule cong :premises (@p145) :args ((forall @t80 (or @t82 @t81)))) % 0.83/1.10 (step @p147 :rule trans :premises (@p146 @p144)) % 0.83/1.10 (step @p148 :rule aci_norm :args ((= @t83 @t81))) % 0.83/1.10 (step @p149 :rule refl :args (@t82)) % 0.83/1.10 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t84)) % 0.83/1.10 (step @p151 :rule cong :premises (@p150) :args ((forall @t80 @t84))) % 0.83/1.10 (step @p152 :rule trans :premises (@p151 @p147)) % 0.83/1.10 (step @p153 :rule bool-or-taut2 :args (false @t74 false false)) % 0.83/1.10 (step @p154 :rule refl :args (@t81)) % 0.83/1.10 (step @p155 :rule nary_cong :premises (@p154 @p153) :args (@t85)) % 0.83/1.10 (step @p156 :rule refl :args (@t82)) % 0.83/1.10 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t86)) % 0.83/1.10 (step @p158 :rule cong :premises (@p157) :args ((forall @t80 @t86))) % 0.83/1.10 (step @p159 :rule trans :premises (@p158 @p152)) % 0.83/1.10 (step @p160 :rule aci_norm :args ((= (or false @t82 @t85) @t86))) % 0.83/1.10 (step @p161 :rule beta-reduce :args ((= @t87 @t32))) % 0.83/1.10 (step @p162 :rule cong :premises (@p161) :args (@t88)) % 0.83/1.10 (step @p163 :rule refl :args (@t75)) % 0.83/1.10 (step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t89)) % 0.83/1.10 (step @p165 :rule lambda-elim :args ((= (lambda @t13 @t35) @t10))) % 0.83/1.10 (step @p166 :rule beta-reduce :args ((= @t90 @t35))) % 0.83/1.10 (step @p167 :rule cong :premises (@p166) :args (@t91)) % 0.83/1.10 (step @p168 :rule trans :premises (@p167 @p165)) % 0.83/1.10 (step @p169 :rule refl :args (@t24)) % 0.83/1.10 (step @p170 :rule cong :premises (@p169 @p168) :args (@t92)) % 0.83/1.10 (step @p171 :rule nary_cong :premises (@p170 @p164) :args (@t93)) % 0.83/1.10 (step @p172 :rule eq-refl :args (@t24)) % 0.83/1.10 (step @p173 :rule cong :premises (@p172) :args (@t95)) % 0.83/1.10 (step @p174 :rule trans :premises (@p173 @p143)) % 0.83/1.10 (step @p175 :rule nary_cong :premises (@p174 @p149 @p171) :args (@t96)) % 0.83/1.10 (step @p176 :rule trans :premises (@p175 @p160)) % 0.83/1.10 (step @p177 :rule cong :premises (@p176) :args ((forall @t80 @t96))) % 0.83/1.10 (step @p178 :rule trans :premises (@p177 @p159)) % 0.83/1.10 (step @p179 :rule quant-var-elim-eq :args ((= (forall @t101 (or (not (= @t2 @t24)) @t100 @t82 @t98)) @t96))) % 0.83/1.10 (step @p180 :rule refl :args (@t98)) % 0.83/1.10 (step @p181 :rule refl :args (@t100)) % 0.83/1.10 (step @p182 :rule eq-symm :args (@t24 @t2)) % 0.83/1.10 (step @p183 :rule cong :premises (@p182) :args (@t100)) % 0.83/1.10 (step @p184 :rule nary_cong :premises (@p183 @p181 @p156 @p180) :args (@t102)) % 0.83/1.10 (step @p185 :rule aci_norm :args ((= @t103 @t102))) % 0.83/1.10 (step @p186 :rule trans :premises (@p185 @p184)) % 0.83/1.10 (step @p187 :rule cong :premises (@p186) :args (@t104)) % 0.83/1.10 (step @p188 :rule trans :premises (@p187 @p179)) % 0.83/1.10 (step @p189 :rule cong :premises (@p188) :args (@t105)) % 0.83/1.10 (step @p190 :rule quant-merge-prenex :args ((= @t105 @t106))) % 0.83/1.10 (step @p191 :rule symm :premises (@p190)) % 0.83/1.10 (step @p192 :rule quant_var_reordering :args ((= (forall @t45 @t103) @t106))) % 0.83/1.10 (step @p193 :rule trans :premises (@p192 @p191 @p189)) % 0.83/1.10 (step @p194 :rule trans :premises (@p193 @p178)) % 0.83/1.10 (step @p195 :rule refl :args (@t76)) % 0.83/1.10 (step @p196 :rule beta-reduce :args ((= @t109 @t97))) % 0.83/1.10 (step @p197 :rule nary_cong :premises (@p196 @p195) :args (@t110)) % 0.83/1.10 (step @p198 :rule beta-reduce :args ((= @t111 @t81))) % 0.83/1.10 (step @p199 :rule cong :premises (@p198) :args (@t112)) % 0.83/1.10 (step @p200 :rule beta-reduce :args ((= @t113 @t99))) % 0.83/1.10 (step @p201 :rule cong :premises (@p200) :args (@t114)) % 0.83/1.10 (step @p202 :rule nary_cong :premises (@p201 @p199 @p197) :args (@t115)) % 0.83/1.10 (step @p203 :rule cong :premises (@p202) :args (@t116)) % 0.83/1.10 (step @p204 :rule trans :premises (@p203 @p194)) % 0.83/1.10 (step @p205 :rule cong :premises (@p204) :args (@t117)) % 0.83/1.10 (step @p206 :rule trans :premises (@p205 @p143)) % 0.83/1.10 (step @p207 :rule beta-reduce :args ((= @t118 @t94))) % 0.83/1.10 (step @p208 :rule trans :premises (@p207 @p172)) % 0.83/1.10 (step @p209 :rule cong :premises (@p208) :args (@t119)) % 0.83/1.10 (step @p210 :rule trans :premises (@p209 @p143)) % 0.83/1.10 (step @p211 :rule nary_cong :premises (@p210 @p206) :args (@t120)) % 0.83/1.10 (step @p212 :rule trans :premises (@p211 @p142)) % 0.83/1.10 (step @p213 :rule cong :premises (@p127 @p212) :args ((=> @t77 @t120))) % 0.83/1.10 (step @p214 :rule trans :premises (@p213 @p141)) % 0.83/1.10 (assume-push @p223 @t77) % 0.83/1.10 (step @p216 :rule instantiate :premises (@p140) :args ((@list @t108))) % 0.83/1.10 (step-pop @p224 :rule scope :premises (@p216)) % 0.83/1.10 (step @p217 :rule process_scope :premises (@p224) :args (@t120)) % 0.83/1.10 (step @p219 :rule eq_resolve :premises (@p217 @p214)) % 0.83/1.10 (step @p220 false :rule chain_m_resolution :premises (@p219 @p140) :args (false (@list false) (@list @t77))) % 0.83/1.10 ) % 0.83/1.10 % SZS output end Proof % 0.83/1.10 % cvc5 exiting %------------------------------------------------------------------------------