%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU644^2 : TPTP v9.2.1. Released v3.7.0. % 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 08:52:33 AM UTC 2026 % Result : Theorem 0.37s 0.56s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU644^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n009.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 17:43:59 EDT 2026 % 0.15/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.37/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.56 % SZS status Theorem % 0.37/0.56 % SZS output start Proof % 0.37/0.56 ( % 0.37/0.56 (declare-sort $$unsorted 0) % 0.37/0.56 (declare-const tptp.emptyset $$unsorted) % 0.37/0.56 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.56 (declare-const tptp.setunionsingleton Bool) % 0.37/0.56 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 0.37/0.56 (declare-const tptp.eqinunit Bool) % 0.37/0.56 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.37/0.56 (define @t1 () (@var "Xy" $$unsorted)) % 0.37/0.56 (define @t2 () (_ (_ tptp.setadjoin @t1) tptp.emptyset)) % 0.37/0.56 (define @t3 () (@var "Xx" $$unsorted)) % 0.37/0.56 (define @t4 () (_ tptp.in @t3)) % 0.37/0.56 (define @t5 () (_ @t4 @t2)) % 0.37/0.56 (define @t6 () (= @t3 @t1)) % 0.37/0.56 (define @t7 () (@list @t3 @t1)) % 0.37/0.56 (define @t8 () (forall @t7 (=> @t6 @t5))) % 0.37/0.56 (define @t9 () (= tptp.eqinunit @t8)) % 0.37/0.56 (define @t10 () (_ (_ tptp.setadjoin @t3) tptp.emptyset)) % 0.37/0.56 (define @t11 () (_ tptp.setunion @t10)) % 0.37/0.56 (define @t12 () (@list @t3)) % 0.37/0.56 (define @t13 () (forall @t12 (= @t11 @t3))) % 0.37/0.56 (define @t14 () (= tptp.setunionsingleton @t13)) % 0.37/0.56 (define @t15 () (@var "X" $$unsorted)) % 0.37/0.56 (define @t16 () (_ tptp.setunion @t15)) % 0.37/0.56 (define @t17 () (_ (_ tptp.in @t16) @t15)) % 0.37/0.56 (define @t18 () (=> (_ tptp.singleton @t15) @t17)) % 0.37/0.56 (define @t19 () (@list @t15)) % 0.37/0.56 (define @t20 () (forall @t19 @t18)) % 0.37/0.56 (define @t21 () (=> tptp.setunionsingleton @t20)) % 0.37/0.56 (define @t22 () (=> tptp.eqinunit @t21)) % 0.37/0.56 (define @t23 () (not @t22)) % 0.37/0.56 (define @t24 () (@var "A" $$unsorted)) % 0.37/0.56 (define @t25 () (_ @t4 @t24)) % 0.37/0.56 (define @t26 () (and @t25 (= @t24 @t10))) % 0.37/0.56 (define @t27 () (exists @t12 @t26)) % 0.37/0.56 (define @t28 () (@list @t24)) % 0.37/0.56 (define @t29 () (lambda @t28 @t27)) % 0.37/0.56 (define @t30 () (@var "BOUND_VARIABLE_7540" $$unsorted)) % 0.37/0.56 (define @t31 () (tptp.setadjoin @t30 tptp.emptyset)) % 0.37/0.56 (define @t32 () (not (tptp.in @t30 @t31))) % 0.37/0.56 (define @t33 () (tptp.in (tptp.setunion @t31) @t31)) % 0.37/0.56 (define @t34 () (or @t33 @t32)) % 0.37/0.56 (define @t35 () (@list @t30)) % 0.37/0.56 (define @t36 () (forall @t35 @t34)) % 0.37/0.56 (define @t37 () (tptp.setadjoin @t3 tptp.emptyset)) % 0.37/0.56 (define @t38 () (tptp.setunion @t37)) % 0.37/0.56 (define @t39 () (= @t3 @t11)) % 0.37/0.56 (define @t40 () (=> tptp.setunionsingleton @t36)) % 0.37/0.56 (define @t41 () (tptp.setadjoin @t1 tptp.emptyset)) % 0.37/0.56 (define @t42 () (tptp.in @t1 @t41)) % 0.37/0.56 (define @t43 () (not (= @t1 @t1))) % 0.37/0.56 (define @t44 () (or @t43 @t42)) % 0.37/0.56 (define @t45 () (@list @t1)) % 0.37/0.56 (define @t46 () (tptp.in @t3 @t41)) % 0.37/0.56 (define @t47 () (not @t6)) % 0.37/0.56 (define @t48 () (or @t47 @t47 @t46)) % 0.37/0.56 (define @t49 () (or @t47 @t46)) % 0.37/0.56 (define @t50 () (forall @t12 @t49)) % 0.37/0.56 (define @t51 () (forall @t45 @t50)) % 0.37/0.56 (define @t52 () (forall (@list @t1 @t3) @t49)) % 0.37/0.56 (define @t53 () (or @t47 @t5)) % 0.37/0.56 (define @t54 () (=> tptp.eqinunit @t40)) % 0.37/0.56 (define @t55 () (not (= @t31 @t31))) % 0.37/0.56 (define @t56 () (or @t33 @t32 @t55)) % 0.37/0.56 (define @t57 () (not (= @t15 @t31))) % 0.37/0.56 (define @t58 () (not (tptp.in @t30 @t15))) % 0.37/0.56 (define @t59 () (tptp.setunion @t15)) % 0.37/0.56 (define @t60 () (tptp.in @t59 @t15)) % 0.37/0.56 (define @t61 () (or @t57 @t60 @t58 @t57)) % 0.37/0.56 (define @t62 () (or @t60 @t58 @t57)) % 0.37/0.56 (define @t63 () (forall @t19 @t62)) % 0.37/0.56 (define @t64 () (forall @t35 @t63)) % 0.37/0.56 (define @t65 () (forall (@list @t30 @t15) @t62)) % 0.37/0.56 (define @t66 () (@list @t15 @t30)) % 0.37/0.56 (define @t67 () (not (= @t31 @t15))) % 0.37/0.56 (define @t68 () (or @t60 @t58 @t67)) % 0.37/0.56 (define @t69 () (or @t58 @t67)) % 0.37/0.56 (define @t70 () (or @t69 @t60)) % 0.37/0.56 (define @t71 () (forall @t66 @t70)) % 0.37/0.56 (define @t72 () (forall @t35 @t70)) % 0.37/0.56 (define @t73 () (forall @t35 @t69)) % 0.37/0.56 (define @t74 () (or @t73 @t60)) % 0.37/0.56 (define @t75 () (not (tptp.in @t3 @t15))) % 0.37/0.56 (define @t76 () (forall @t12 (or @t75 (not (= @t37 @t15))))) % 0.37/0.56 (define @t77 () (or @t76 @t17)) % 0.37/0.56 (define @t78 () (not @t76)) % 0.37/0.56 (define @t79 () (not (= @t15 @t37))) % 0.37/0.56 (define @t80 () (or @t75 @t79)) % 0.37/0.56 (define @t81 () (forall @t12 @t80)) % 0.37/0.56 (define @t82 () (not @t81)) % 0.37/0.56 (define @t83 () (tptp.in @t3 @t24)) % 0.37/0.56 (define @t84 () (not @t83)) % 0.37/0.56 (define @t85 () (_ (lambda @t28 (not (forall @t12 (or @t84 (not (= @t24 @t37)))))) @t15)) % 0.37/0.56 (define @t86 () (=> @t85 @t17)) % 0.37/0.56 (define @t87 () (forall @t19 @t86)) % 0.37/0.56 (define @t88 () (=> tptp.setunionsingleton @t87)) % 0.37/0.56 (define @t89 () (=> tptp.eqinunit @t88)) % 0.37/0.56 (define @t90 () (not (= @t37 @t24))) % 0.37/0.56 (define @t91 () (or @t84 @t90)) % 0.37/0.56 (define @t92 () (= @t10 @t24)) % 0.37/0.56 (define @t93 () (not @t92)) % 0.37/0.56 (define @t94 () (not @t25)) % 0.37/0.56 (define @t95 () (or @t94 @t93)) % 0.37/0.56 (define @t96 () (and @t25 @t92)) % 0.37/0.56 (define @t97 () (forall @t12 (not @t96))) % 0.37/0.56 (define @t98 () (not @t97)) % 0.37/0.56 (define @t99 () (@quantifiers_skolemize @t36 0)) % 0.37/0.56 (define @t100 () (tptp.setadjoin @t99 tptp.emptyset)) % 0.37/0.56 (define @t101 () (tptp.in @t99 @t100)) % 0.37/0.56 (define @t102 () (not @t101)) % 0.37/0.56 (define @t103 () (tptp.in (tptp.setunion @t100) @t100)) % 0.37/0.56 (define @t104 () (or @t103 @t102)) % 0.37/0.56 (define @t105 () (@list true)) % 0.37/0.56 (define @t106 () (@list @t104)) % 0.37/0.56 (assume @p1 @t9) % 0.37/0.56 (assume @p2 @t14) % 0.37/0.56 (assume @p3 @t23) % 0.37/0.56 (assume @p4 true) % 0.37/0.56 (step @p5 (= tptp.singleton @t29) :rule refl :args (@t29)) % 0.37/0.56 (step @p6 :rule evaluate :args ((= true false))) % 0.37/0.56 (step @p7 :rule refl :args (@t36)) % 0.37/0.56 (step @p8 :rule refl :args ((tptp.setunion @t10))) % 0.37/0.56 (step @p9 :rule refl :args (@t37)) % 0.37/0.56 (step @p10 :rule cong :premises (@p9) :args (@t38)) % 0.37/0.56 (step @p11 :rule trans :premises (@p10 @p8)) % 0.37/0.56 (step @p12 :rule refl :args (tptp.setunion)) % 0.37/0.56 (step @p13 :rule ho_cong :premises (@p12 @p9)) % 0.37/0.56 (step @p14 :rule cong :premises (@p13 @p11) :args ((= (_ tptp.setunion @t37) @t38))) % 0.37/0.56 (step @p15 :rule symm :premises (@p14)) % 0.37/0.56 (step @p16 :rule refl :args (@t11)) % 0.37/0.56 (step @p17 :rule eq_resolve :premises (@p16 @p15)) % 0.37/0.56 (step @p18 :rule refl :args (@t10)) % 0.37/0.56 (step @p19 :rule cong :premises (@p18 @p9) :args ((= @t10 @t37))) % 0.37/0.56 (step @p20 :rule symm :premises (@p19)) % 0.37/0.56 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.37/0.56 (step @p22 :rule ho_cong :premises (@p12 @p21)) % 0.37/0.56 (step @p23 :rule trans :premises (@p22 @p17)) % 0.37/0.56 (step @p24 :rule refl :args (@t3)) % 0.37/0.56 (step @p25 :rule cong :premises (@p24 @p23) :args (@t39)) % 0.37/0.56 (step @p26 :rule cong :premises (@p25) :args ((forall @t12 @t39))) % 0.37/0.56 (step @p27 :rule eq-symm :args (@t11 @t3)) % 0.37/0.56 (step @p28 :rule cong :premises (@p27) :args (@t13)) % 0.37/0.56 (step @p29 :rule trans :premises (@p28 @p26)) % 0.37/0.56 (step @p30 :rule refl :args (tptp.setunionsingleton)) % 0.37/0.56 (step @p31 :rule cong :premises (@p30 @p29) :args (@t14)) % 0.37/0.56 (step @p32 :rule eq_resolve :premises (@p2 @p31)) % 0.37/0.56 (step @p33 :rule cong :premises (@p32 @p7) :args (@t40)) % 0.37/0.56 (step @p34 :rule aci_norm :args ((= (or false @t42) @t42))) % 0.37/0.56 (step @p35 :rule refl :args (@t42)) % 0.37/0.56 (step @p36 :rule evaluate :args ((not true))) % 0.37/0.56 (step @p37 :rule eq-refl :args (@t1)) % 0.37/0.56 (step @p38 :rule cong :premises (@p37) :args (@t43)) % 0.37/0.56 (step @p39 :rule trans :premises (@p38 @p36)) % 0.37/0.56 (step @p40 :rule nary_cong :premises (@p39 @p35) :args (@t44)) % 0.37/0.56 (step @p41 :rule trans :premises (@p40 @p34)) % 0.37/0.56 (step @p42 :rule cong :premises (@p41) :args ((forall @t45 @t44))) % 0.37/0.56 (step @p43 :rule quant-var-elim-eq :args ((= (forall @t12 @t48) @t44))) % 0.37/0.56 (step @p44 :rule aci_norm :args ((= @t49 @t48))) % 0.37/0.56 (step @p45 :rule cong :premises (@p44) :args (@t50)) % 0.37/0.56 (step @p46 :rule trans :premises (@p45 @p43)) % 0.37/0.56 (step @p47 :rule cong :premises (@p46) :args (@t51)) % 0.37/0.56 (step @p48 :rule quant-merge-prenex :args ((= @t51 @t52))) % 0.37/0.56 (step @p49 :rule symm :premises (@p48)) % 0.37/0.56 (step @p50 :rule quant_var_reordering :args ((= (forall @t7 @t49) @t52))) % 0.37/0.56 (step @p51 :rule trans :premises (@p50 @p49 @p47)) % 0.37/0.56 (step @p52 :rule trans :premises (@p51 @p42)) % 0.37/0.56 (step @p53 :rule refl :args ((tptp.in @t3 @t2))) % 0.37/0.56 (step @p54 :rule refl :args (@t41)) % 0.37/0.56 (step @p55 :rule cong :premises (@p24 @p54) :args (@t46)) % 0.37/0.56 (step @p56 :rule trans :premises (@p55 @p53)) % 0.37/0.56 (step @p57 :rule refl :args (@t4)) % 0.37/0.56 (step @p58 :rule ho_cong :premises (@p57 @p54)) % 0.37/0.56 (step @p59 :rule cong :premises (@p58 @p56) :args ((= (_ @t4 @t41) @t46))) % 0.37/0.56 (step @p60 :rule symm :premises (@p59)) % 0.37/0.56 (step @p61 :rule refl :args (@t5)) % 0.37/0.56 (step @p62 :rule eq_resolve :premises (@p61 @p60)) % 0.37/0.56 (step @p63 :rule refl :args (@t2)) % 0.37/0.56 (step @p64 :rule cong :premises (@p63 @p54) :args ((= @t2 @t41))) % 0.37/0.56 (step @p65 :rule symm :premises (@p64)) % 0.37/0.56 (step @p66 :rule eq_resolve :premises (@p63 @p65)) % 0.37/0.56 (step @p67 :rule ho_cong :premises (@p57 @p66)) % 0.37/0.56 (step @p68 :rule trans :premises (@p67 @p62)) % 0.37/0.56 (step @p69 :rule refl :args (@t47)) % 0.37/0.56 (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t53)) % 0.37/0.56 (step @p71 :rule cong :premises (@p70) :args ((forall @t7 @t53))) % 0.37/0.56 (step @p72 :rule trans :premises (@p71 @p52)) % 0.37/0.56 (step @p73 :rule bool-impl-elim :args (@t6 @t5)) % 0.37/0.56 (step @p74 :rule cong :premises (@p73) :args (@t8)) % 0.37/0.56 (step @p75 :rule trans :premises (@p74 @p72)) % 0.37/0.56 (step @p76 :rule refl :args (tptp.eqinunit)) % 0.37/0.56 (step @p77 :rule cong :premises (@p76 @p75) :args (@t9)) % 0.37/0.56 (step @p78 :rule eq_resolve :premises (@p1 @p77)) % 0.37/0.56 (step @p79 :rule cong :premises (@p78 @p33) :args (@t54)) % 0.37/0.56 (step @p80 :rule cong :premises (@p79) :args ((not @t54))) % 0.37/0.56 (step @p81 :rule aci_norm :args ((= (or @t33 @t32 false) @t34))) % 0.37/0.56 (step @p82 :rule eq-refl :args (@t31)) % 0.37/0.56 (step @p83 :rule cong :premises (@p82) :args (@t55)) % 0.37/0.56 (step @p84 :rule trans :premises (@p83 @p36)) % 0.37/0.56 (step @p85 :rule refl :args (@t32)) % 0.37/0.56 (step @p86 :rule refl :args (@t33)) % 0.37/0.56 (step @p87 :rule nary_cong :premises (@p86 @p85 @p84) :args (@t56)) % 0.37/0.56 (step @p88 :rule trans :premises (@p87 @p81)) % 0.37/0.56 (step @p89 :rule cong :premises (@p88) :args ((forall @t35 @t56))) % 0.37/0.56 (step @p90 :rule quant-var-elim-eq :args ((= (forall @t19 @t61) @t56))) % 0.37/0.56 (step @p91 :rule aci_norm :args ((= @t62 @t61))) % 0.37/0.56 (step @p92 :rule cong :premises (@p91) :args (@t63)) % 0.37/0.56 (step @p93 :rule trans :premises (@p92 @p90)) % 0.37/0.56 (step @p94 :rule cong :premises (@p93) :args (@t64)) % 0.37/0.56 (step @p95 :rule quant-merge-prenex :args ((= @t64 @t65))) % 0.37/0.56 (step @p96 :rule symm :premises (@p95)) % 0.37/0.56 (step @p97 :rule quant_var_reordering :args ((= (forall @t66 @t62) @t65))) % 0.37/0.56 (step @p98 :rule trans :premises (@p97 @p96 @p94)) % 0.37/0.56 (step @p99 :rule trans :premises (@p98 @p89)) % 0.37/0.56 (step @p100 :rule eq-symm :args (@t31 @t15)) % 0.37/0.56 (step @p101 :rule cong :premises (@p100) :args (@t67)) % 0.37/0.56 (step @p102 :rule refl :args (@t58)) % 0.37/0.56 (step @p103 :rule refl :args (@t60)) % 0.37/0.56 (step @p104 :rule nary_cong :premises (@p103 @p102 @p101) :args (@t68)) % 0.37/0.56 (step @p105 :rule aci_norm :args ((= @t70 @t68))) % 0.37/0.56 (step @p106 :rule trans :premises (@p105 @p104)) % 0.37/0.56 (step @p107 :rule cong :premises (@p106) :args (@t71)) % 0.37/0.56 (step @p108 :rule trans :premises (@p107 @p99)) % 0.37/0.56 (step @p109 :rule quant-merge-prenex :args ((= (forall @t19 @t72) @t71))) % 0.37/0.56 (step @p110 :rule refl :args (@t60)) % 0.37/0.56 (step @p111 :rule alpha_equiv :args (@t73 (@list @t30) (@list @t3))) % 0.37/0.56 (step @p112 :rule nary_cong :premises (@p111 @p110) :args (@t74)) % 0.37/0.56 (step @p113 :rule quant-miniscope-or :args ((= @t72 @t74))) % 0.37/0.56 (step @p114 :rule trans :premises (@p113 @p112)) % 0.37/0.56 (step @p115 :rule symm :premises (@p114)) % 0.37/0.56 (step @p116 :rule cong :premises (@p115) :args ((forall @t19 (or @t76 @t60)))) % 0.37/0.56 (step @p117 :rule trans :premises (@p116 @p109)) % 0.37/0.56 (step @p118 :rule trans :premises (@p117 @p108)) % 0.37/0.56 (step @p119 :rule refl :args ((tptp.in @t16 @t15))) % 0.37/0.56 (step @p120 :rule refl :args (@t15)) % 0.37/0.56 (step @p121 :rule refl :args (@t59)) % 0.37/0.56 (step @p122 :rule cong :premises (@p121 @p120) :args (@t60)) % 0.37/0.56 (step @p123 :rule trans :premises (@p122 @p119)) % 0.37/0.56 (step @p124 :rule refl :args (tptp.in)) % 0.37/0.56 (step @p125 :rule ho_cong :premises (@p124 @p121)) % 0.37/0.56 (step @p126 :rule ho_cong :premises (@p125 @p120)) % 0.37/0.56 (step @p127 :rule cong :premises (@p126 @p123) :args ((= (_ (_ tptp.in @t59) @t15) @t60))) % 0.37/0.56 (step @p128 :rule symm :premises (@p127)) % 0.37/0.56 (step @p129 :rule refl :args (@t17)) % 0.37/0.56 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 0.37/0.56 (step @p131 :rule refl :args (@t16)) % 0.37/0.56 (step @p132 :rule cong :premises (@p131 @p121) :args ((= @t16 @t59))) % 0.37/0.56 (step @p133 :rule symm :premises (@p132)) % 0.37/0.56 (step @p134 :rule eq_resolve :premises (@p131 @p133)) % 0.37/0.56 (step @p135 :rule ho_cong :premises (@p124 @p134)) % 0.37/0.56 (step @p136 :rule ho_cong :premises (@p135 @p120)) % 0.37/0.56 (step @p137 :rule trans :premises (@p136 @p130)) % 0.37/0.56 (step @p138 :rule refl :args (@t76)) % 0.37/0.56 (step @p139 :rule nary_cong :premises (@p138 @p137) :args (@t77)) % 0.37/0.56 (step @p140 :rule cong :premises (@p139) :args ((forall @t19 @t77))) % 0.37/0.56 (step @p141 :rule trans :premises (@p140 @p118)) % 0.37/0.56 (step @p142 :rule bool-double-not-elim :args (@t76)) % 0.37/0.56 (step @p143 :rule nary_cong :premises (@p142 @p129) :args ((or (not @t78) @t17))) % 0.37/0.56 (step @p144 :rule bool-impl-elim :args (@t78 @t17)) % 0.37/0.56 (step @p145 :rule trans :premises (@p144 @p143)) % 0.37/0.56 (step @p146 :rule cong :premises (@p145) :args ((forall @t19 (=> @t78 @t17)))) % 0.37/0.56 (step @p147 :rule trans :premises (@p146 @p141)) % 0.37/0.56 (step @p148 :rule refl :args (@t17)) % 0.37/0.56 (step @p149 :rule eq-symm :args (@t15 @t37)) % 0.37/0.56 (step @p150 :rule cong :premises (@p149) :args (@t79)) % 0.37/0.56 (step @p151 :rule refl :args (@t75)) % 0.37/0.56 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t80)) % 0.37/0.56 (step @p153 :rule cong :premises (@p152) :args (@t81)) % 0.37/0.56 (step @p154 :rule cong :premises (@p153) :args (@t82)) % 0.37/0.56 (step @p155 :rule beta-reduce :args ((= @t85 @t82))) % 0.37/0.56 (step @p156 :rule trans :premises (@p155 @p154)) % 0.37/0.56 (step @p157 :rule cong :premises (@p156 @p148) :args (@t86)) % 0.37/0.56 (step @p158 :rule cong :premises (@p157) :args (@t87)) % 0.37/0.56 (step @p159 :rule trans :premises (@p158 @p147)) % 0.37/0.56 (step @p160 :rule cong :premises (@p30 @p159) :args (@t88)) % 0.37/0.56 (step @p161 :rule cong :premises (@p76 @p160) :args (@t89)) % 0.37/0.56 (step @p162 :rule cong :premises (@p161) :args ((not @t89))) % 0.37/0.56 (step @p163 :rule refl :args (@t15)) % 0.37/0.56 (step @p164 :rule eq-symm :args (@t37 @t24)) % 0.37/0.56 (step @p165 :rule cong :premises (@p164) :args (@t90)) % 0.37/0.56 (step @p166 :rule refl :args (@t84)) % 0.37/0.56 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t91)) % 0.37/0.56 (step @p168 :rule cong :premises (@p167) :args ((forall @t12 @t91))) % 0.37/0.56 (step @p169 :rule refl :args (@t24)) % 0.37/0.56 (step @p170 :rule cong :premises (@p21 @p169) :args (@t92)) % 0.37/0.56 (step @p171 :rule cong :premises (@p170) :args (@t93)) % 0.37/0.56 (step @p172 :rule refl :args (@t83)) % 0.37/0.56 (step @p173 :rule refl :args (@t25)) % 0.37/0.56 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t25 @t83))) % 0.37/0.56 (step @p175 :rule symm :premises (@p174)) % 0.37/0.56 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 0.37/0.56 (step @p177 :rule cong :premises (@p176) :args (@t94)) % 0.37/0.56 (step @p178 :rule nary_cong :premises (@p177 @p171) :args (@t95)) % 0.37/0.56 (step @p179 :rule cong :premises (@p178) :args ((forall @t12 @t95))) % 0.37/0.56 (step @p180 :rule trans :premises (@p179 @p168)) % 0.37/0.56 (step @p181 :rule bool-and-de-morgan :args (@t25 @t92 true)) % 0.37/0.56 (step @p182 :rule cong :premises (@p181) :args (@t97)) % 0.37/0.56 (step @p183 :rule trans :premises (@p182 @p180)) % 0.37/0.56 (step @p184 :rule cong :premises (@p183) :args (@t98)) % 0.37/0.56 (step @p185 :rule exists-elim :args ((= (exists @t12 @t96) @t98))) % 0.37/0.56 (step @p186 :rule trans :premises (@p185 @p184)) % 0.37/0.56 (step @p187 :rule eq-symm :args (@t24 @t10)) % 0.37/0.56 (step @p188 :rule refl :args (@t25)) % 0.37/0.56 (step @p189 :rule nary_cong :premises (@p188 @p187) :args (@t26)) % 0.37/0.56 (step @p190 :rule cong :premises (@p189) :args (@t27)) % 0.37/0.56 (step @p191 :rule trans :premises (@p190 @p186)) % 0.37/0.56 (step @p192 :rule cong :premises (@p191) :args (@t29)) % 0.37/0.56 (step @p193 :rule trans :premises (@p5 @p192)) % 0.37/0.56 (step @p194 :rule ho_cong :premises (@p193 @p163)) % 0.37/0.56 (step @p195 :rule cong :premises (@p194 @p148) :args (@t18)) % 0.37/0.56 (step @p196 :rule cong :premises (@p195) :args (@t20)) % 0.37/0.56 (step @p197 :rule cong :premises (@p30 @p196) :args (@t21)) % 0.37/0.56 (step @p198 :rule cong :premises (@p76 @p197) :args (@t22)) % 0.37/0.56 (step @p199 :rule cong :premises (@p198) :args (@t23)) % 0.37/0.56 (step @p200 :rule trans :premises (@p199 @p162)) % 0.37/0.56 (step @p201 :rule trans :premises (@p200 @p80)) % 0.37/0.56 (step @p202 :rule eq_resolve :premises (@p3 @p201)) % 0.37/0.56 (step @p203 :rule not_implies_elim2 :premises (@p202)) % 0.37/0.56 (step @p204 :rule not_implies_elim2 :premises (@p203)) % 0.37/0.56 (step @p205 :rule skolemize :premises (@p204)) % 0.37/0.56 (step @p206 :rule cnf_or_neg :args (@t104 0)) % 0.37/0.56 (step @p207 :rule chain_m_resolution :premises (@p206 @p205) :args ((not @t103) @t105 @t106)) % 0.37/0.56 (step @p208 :rule false_intro :premises (@p207)) % 0.37/0.56 (step @p209 :rule refl :args (@t100)) % 0.37/0.56 (step @p210 :rule not_implies_elim1 :premises (@p203)) % 0.37/0.56 (step @p211 :rule instantiate :premises (@p210) :args ((@list @t99))) % 0.37/0.56 (step @p212 :rule cong :premises (@p211 @p209) :args (@t101)) % 0.37/0.56 (step @p213 :rule bool-double-not-elim :args (@t101)) % 0.37/0.56 (step @p214 :rule refl :args (@t104)) % 0.37/0.56 (step @p215 :rule nary_cong :premises (@p214 @p213) :args ((or @t104 (not @t102)))) % 0.37/0.56 (step @p216 :rule cnf_or_neg :args (@t104 1)) % 0.37/0.56 (step @p217 :rule eq_resolve :premises (@p216 @p215)) % 0.37/0.56 (step @p218 :rule reordering :premises (@p217) :args ((or @t101 @t104))) % 0.37/0.56 (step @p219 :rule chain_m_resolution :premises (@p218 @p205) :args (@t101 @t105 @t106)) % 0.37/0.56 (step @p220 :rule true_intro :premises (@p219)) % 0.37/0.56 (step @p221 :rule symm :premises (@p220)) % 0.37/0.56 (step @p222 :rule trans :premises (@p221 @p212 @p208)) % 0.37/0.56 (step @p223 false :rule eq_resolve :premises (@p222 @p6)) % 0.37/0.56 ) % 0.37/0.56 % SZS output end Proof % 0.37/0.56 % cvc5 exiting %------------------------------------------------------------------------------