%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU769^2 : 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 : n017.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 08:53:07 AM UTC 2026 % Result : Theorem 0.38s 0.59s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU769^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.19/0.35 % Computer : n017.cluster.edu % 0.19/0.35 % Model : x86_64 x86_64 % 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.19/0.35 % Memory : 8042.1875MB % 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.19/0.35 % CPULimit : 300 % 0.19/0.35 % WCLimit : 300 % 0.19/0.35 % DateTime : Tue Jun 2 17:49:46 EDT 2026 % 0.19/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.38/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.59 % SZS status Theorem % 0.38/0.59 % SZS output start Proof % 0.38/0.59 ( % 0.38/0.59 (declare-sort $$unsorted 0) % 0.38/0.59 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.38/0.59 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.38/0.59 (declare-const tptp.dsetconstrER Bool) % 0.38/0.59 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.38/0.59 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.38/0.59 (define tptp.breln1 () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2 _let_1) (_ (_ (_ tptp.breln _let_2) _let_2) _let_1))))) % 0.38/0.59 (define tptp.breln1Set () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (_ (_ tptp.dsetconstr (_ tptp.powerset (_ (_ tptp.cartprod _let_2) _let_2))) (lambda (@list _let_1) (_ (_ tptp.breln1 _let_2) _let_1))))))) % 0.38/0.59 (define @t1 () (@var "Xx" $$unsorted)) % 0.38/0.59 (define @t2 () (@var "Xphi" (-> $$unsorted Bool))) % 0.38/0.59 (define @t3 () (_ @t2 @t1)) % 0.38/0.59 (define @t4 () (@var "Xy" $$unsorted)) % 0.38/0.59 (define @t5 () (_ @t2 @t4)) % 0.38/0.59 (define @t6 () (@list @t4)) % 0.38/0.59 (define @t7 () (lambda @t6 @t5)) % 0.38/0.59 (define @t8 () (@var "A" $$unsorted)) % 0.38/0.59 (define @t9 () (_ tptp.dsetconstr @t8)) % 0.38/0.59 (define @t10 () (_ @t9 @t7)) % 0.38/0.59 (define @t11 () (_ tptp.in @t1)) % 0.38/0.59 (define @t12 () (_ @t11 @t10)) % 0.38/0.59 (define @t13 () (@list @t8 @t2 @t1)) % 0.38/0.59 (define @t14 () (forall @t13 (=> @t12 @t3))) % 0.38/0.59 (define @t15 () (= tptp.dsetconstrER @t14)) % 0.38/0.59 (define @t16 () (@var "R" $$unsorted)) % 0.38/0.59 (define @t17 () (_ (_ tptp.breln1 @t8) @t16)) % 0.38/0.59 (define @t18 () (_ tptp.in @t16)) % 0.38/0.59 (define @t19 () (=> (_ @t18 (_ tptp.breln1Set @t8)) @t17)) % 0.38/0.59 (define @t20 () (@list @t8 @t16)) % 0.38/0.59 (define @t21 () (forall @t20 @t19)) % 0.38/0.59 (define @t22 () (=> tptp.dsetconstrER @t21)) % 0.38/0.59 (define @t23 () (not @t22)) % 0.38/0.59 (define @t24 () (@var "B" $$unsorted)) % 0.38/0.59 (define @t25 () (_ tptp.cartprod @t8)) % 0.38/0.59 (define @t26 () (@var "C" $$unsorted)) % 0.38/0.59 (define @t27 () (_ tptp.subset @t26)) % 0.38/0.59 (define @t28 () (_ @t27 (_ @t25 @t24))) % 0.38/0.59 (define @t29 () (lambda (@list @t8 @t24 @t26) @t28)) % 0.38/0.59 (define @t30 () (lambda @t20 (_ (_ (_ tptp.breln @t8) @t8) @t16))) % 0.38/0.59 (define @t31 () (@list @t16)) % 0.38/0.59 (define @t32 () (lambda @t31 @t17)) % 0.38/0.59 (define @t33 () (_ @t25 @t8)) % 0.38/0.59 (define @t34 () (_ tptp.powerset @t33)) % 0.38/0.59 (define @t35 () (_ tptp.dsetconstr @t34)) % 0.38/0.59 (define @t36 () (@list @t8)) % 0.38/0.59 (define @t37 () (lambda @t36 (_ @t35 @t32))) % 0.38/0.59 (define @t38 () (tptp.cartprod @t8 @t8)) % 0.38/0.59 (define @t39 () (tptp.subset @t16 @t38)) % 0.38/0.59 (define @t40 () (@var "BOUND_VARIABLE_7548" $$unsorted)) % 0.38/0.59 (define @t41 () (tptp.subset @t40 @t38)) % 0.38/0.59 (define @t42 () (@list @t40)) % 0.38/0.59 (define @t43 () (lambda @t42 @t41)) % 0.38/0.59 (define @t44 () (tptp.powerset @t38)) % 0.38/0.59 (define @t45 () (tptp.dsetconstr @t44 @t43)) % 0.38/0.59 (define @t46 () (tptp.in @t16 @t45)) % 0.38/0.59 (define @t47 () (forall @t20 (or (not @t46) @t39))) % 0.38/0.59 (define @t48 () (_ @t2 @t1)) % 0.38/0.59 (define @t49 () (_ @t2 @t4)) % 0.38/0.59 (define @t50 () (lambda @t6 @t49)) % 0.38/0.59 (define @t51 () (tptp.dsetconstr @t8 @t50)) % 0.38/0.59 (define @t52 () (tptp.in @t1 @t51)) % 0.38/0.59 (define @t53 () (not @t52)) % 0.38/0.59 (define @t54 () (or @t53 @t48)) % 0.38/0.59 (define @t55 () (not @t12)) % 0.38/0.59 (define @t56 () (or @t55 @t3)) % 0.38/0.59 (define @t57 () (=> tptp.dsetconstrER @t47)) % 0.38/0.59 (define @t58 () (_ tptp.subset @t16)) % 0.38/0.59 (define @t59 () (_ @t58 @t33)) % 0.38/0.59 (define @t60 () (_ tptp.subset @t40)) % 0.38/0.59 (define @t61 () (_ @t60 @t33)) % 0.38/0.59 (define @t62 () (lambda @t42 @t61)) % 0.38/0.59 (define @t63 () (_ @t35 @t62)) % 0.38/0.59 (define @t64 () (_ @t18 @t63)) % 0.38/0.59 (define @t65 () (not @t64)) % 0.38/0.59 (define @t66 () (or @t65 @t59)) % 0.38/0.59 (define @t67 () (lambda @t31 @t59)) % 0.38/0.59 (define @t68 () (_ @t35 @t67)) % 0.38/0.59 (define @t69 () (=> (_ @t18 @t68) @t59)) % 0.38/0.59 (define @t70 () (_ (lambda @t20 @t59) @t8)) % 0.38/0.59 (define @t71 () (_ (lambda @t36 @t68) @t8)) % 0.38/0.59 (define @t72 () (_ @t70 @t16)) % 0.38/0.59 (define @t73 () (=> (_ @t18 @t71) @t72)) % 0.38/0.59 (define @t74 () (forall @t20 @t73)) % 0.38/0.59 (define @t75 () (=> tptp.dsetconstrER @t74)) % 0.38/0.59 (define @t76 () (lambda (@list @t26) (_ @t27 @t33))) % 0.38/0.59 (define @t77 () (lambda (@list @t24 @t26) @t28)) % 0.38/0.59 (define @t78 () (@quantifiers_skolemize @t47 0)) % 0.38/0.59 (define @t79 () (tptp.cartprod @t78 @t78)) % 0.38/0.59 (define @t80 () (@quantifiers_skolemize @t47 1)) % 0.38/0.59 (define @t81 () (tptp.subset @t80 @t79)) % 0.38/0.59 (define @t82 () (tptp.subset @t40 @t79)) % 0.38/0.59 (define @t83 () (lambda @t42 @t82)) % 0.38/0.59 (define @t84 () (@purify @t83)) % 0.38/0.59 (define @t85 () (tptp.powerset @t79)) % 0.38/0.59 (define @t86 () (tptp.in @t80 (tptp.dsetconstr @t85 @t84))) % 0.38/0.59 (define @t87 () (not @t86)) % 0.38/0.59 (define @t88 () (or @t87 @t81)) % 0.38/0.59 (define @t89 () (not @t88)) % 0.38/0.59 (define @t90 () (not @t47)) % 0.38/0.59 (define @t91 () (tptp.dsetconstr @t85 @t83)) % 0.38/0.59 (define @t92 () (tptp.in @t80 @t91)) % 0.38/0.59 (define @t93 () (not @t92)) % 0.38/0.59 (define @t94 () (or @t93 @t81)) % 0.38/0.59 (define @t95 () (not @t94)) % 0.38/0.59 (define @t96 () (@list true)) % 0.38/0.59 (define @t97 () (@list @t88)) % 0.38/0.59 (define @t98 () (_ @t84 @t40)) % 0.38/0.59 (define @t99 () (_ @t83 @t40)) % 0.38/0.59 (define @t100 () (= @t98 @t99)) % 0.38/0.59 (define @t101 () (forall @t42 @t100)) % 0.38/0.59 (define @t102 () (_ @t84 @t80)) % 0.38/0.59 (define @t103 () (or @t87 @t102)) % 0.38/0.59 (define @t104 () (= @t81 @t102)) % 0.38/0.59 (assume @p1 @t15) % 0.38/0.59 (assume @p2 @t23) % 0.38/0.59 (assume @p3 true) % 0.38/0.59 (step @p4 (= tptp.breln @t29) :rule refl :args (@t29)) % 0.38/0.59 (step @p5 (= tptp.breln1 @t30) :rule refl :args (@t30)) % 0.38/0.59 (step @p6 (= tptp.breln1Set @t37) :rule refl :args (@t37)) % 0.38/0.59 (step @p7 :rule refl :args (@t47)) % 0.38/0.59 (step @p8 :rule refl :args (@t48)) % 0.38/0.59 (step @p9 :rule lambda-elim :args ((= @t50 @t2))) % 0.38/0.59 (step @p10 :rule refl :args (@t8)) % 0.38/0.59 (step @p11 :rule cong :premises (@p10 @p9) :args (@t51)) % 0.38/0.59 (step @p12 :rule refl :args (@t1)) % 0.38/0.59 (step @p13 :rule cong :premises (@p12 @p11) :args (@t52)) % 0.38/0.59 (step @p14 :rule cong :premises (@p13) :args (@t53)) % 0.38/0.59 (step @p15 :rule nary_cong :premises (@p14 @p8) :args (@t54)) % 0.38/0.59 (step @p16 :rule cong :premises (@p15) :args ((forall @t13 @t54))) % 0.38/0.59 (step @p17 :rule refl :args (@t48)) % 0.38/0.59 (step @p18 :rule refl :args (@t3)) % 0.38/0.59 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t3 @t48))) % 0.38/0.59 (step @p20 :rule symm :premises (@p19)) % 0.38/0.59 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.38/0.59 (step @p22 :rule refl :args ((tptp.in @t1 @t10))) % 0.38/0.59 (step @p23 :rule refl :args ((tptp.dsetconstr @t8 @t7))) % 0.38/0.59 (step @p24 :rule refl :args (@t49)) % 0.38/0.59 (step @p25 :rule cong :premises (@p24) :args (@t50)) % 0.38/0.59 (step @p26 :rule refl :args (@t8)) % 0.38/0.59 (step @p27 :rule cong :premises (@p26 @p25) :args (@t51)) % 0.38/0.59 (step @p28 :rule trans :premises (@p27 @p23)) % 0.38/0.59 (step @p29 :rule refl :args (@t1)) % 0.38/0.59 (step @p30 :rule cong :premises (@p29 @p28) :args (@t52)) % 0.38/0.59 (step @p31 :rule trans :premises (@p30 @p22)) % 0.38/0.59 (step @p32 :rule refl :args (@t11)) % 0.38/0.59 (step @p33 :rule ho_cong :premises (@p32 @p28)) % 0.38/0.59 (step @p34 :rule cong :premises (@p33 @p31) :args ((= (_ @t11 @t51) @t52))) % 0.38/0.59 (step @p35 :rule symm :premises (@p34)) % 0.38/0.59 (step @p36 :rule refl :args (@t12)) % 0.38/0.59 (step @p37 :rule eq_resolve :premises (@p36 @p35)) % 0.38/0.59 (step @p38 :rule refl :args (@t9)) % 0.38/0.59 (step @p39 :rule ho_cong :premises (@p38 @p25)) % 0.38/0.59 (step @p40 :rule cong :premises (@p39 @p28) :args ((= (_ @t9 @t50) @t51))) % 0.38/0.59 (step @p41 :rule symm :premises (@p40)) % 0.38/0.59 (step @p42 :rule refl :args (@t10)) % 0.38/0.59 (step @p43 :rule eq_resolve :premises (@p42 @p41)) % 0.38/0.59 (step @p44 :rule refl :args (@t5)) % 0.38/0.59 (step @p45 :rule cong :premises (@p44 @p24) :args ((= @t5 @t49))) % 0.38/0.59 (step @p46 :rule symm :premises (@p45)) % 0.38/0.59 (step @p47 :rule eq_resolve :premises (@p44 @p46)) % 0.38/0.59 (step @p48 :rule cong :premises (@p47) :args (@t7)) % 0.38/0.59 (step @p49 :rule ho_cong :premises (@p38 @p48)) % 0.38/0.59 (step @p50 :rule trans :premises (@p49 @p43)) % 0.38/0.59 (step @p51 :rule ho_cong :premises (@p32 @p50)) % 0.38/0.59 (step @p52 :rule trans :premises (@p51 @p37)) % 0.38/0.59 (step @p53 :rule cong :premises (@p52) :args (@t55)) % 0.38/0.59 (step @p54 :rule nary_cong :premises (@p53 @p21) :args (@t56)) % 0.38/0.59 (step @p55 :rule cong :premises (@p54) :args ((forall @t13 @t56))) % 0.38/0.59 (step @p56 :rule trans :premises (@p55 @p16)) % 0.38/0.59 (step @p57 :rule bool-impl-elim :args (@t12 @t3)) % 0.38/0.59 (step @p58 :rule cong :premises (@p57) :args (@t14)) % 0.38/0.59 (step @p59 :rule trans :premises (@p58 @p56)) % 0.38/0.59 (step @p60 :rule refl :args (tptp.dsetconstrER)) % 0.38/0.59 (step @p61 :rule cong :premises (@p60 @p59) :args (@t15)) % 0.38/0.59 (step @p62 :rule eq_resolve :premises (@p1 @p61)) % 0.38/0.59 (step @p63 :rule cong :premises (@p62 @p7) :args (@t57)) % 0.38/0.59 (step @p64 :rule cong :premises (@p63) :args ((not @t57))) % 0.38/0.59 (step @p65 :rule refl :args ((tptp.subset @t16 @t33))) % 0.38/0.59 (step @p66 :rule refl :args (@t38)) % 0.38/0.59 (step @p67 :rule refl :args (@t16)) % 0.38/0.59 (step @p68 :rule cong :premises (@p67 @p66) :args (@t39)) % 0.38/0.59 (step @p69 :rule trans :premises (@p68 @p65)) % 0.38/0.59 (step @p70 :rule refl :args (@t58)) % 0.38/0.59 (step @p71 :rule ho_cong :premises (@p70 @p66)) % 0.38/0.59 (step @p72 :rule cong :premises (@p71 @p69) :args ((= (_ @t58 @t38) @t39))) % 0.38/0.59 (step @p73 :rule symm :premises (@p72)) % 0.38/0.59 (step @p74 :rule refl :args (@t59)) % 0.38/0.59 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.38/0.59 (step @p76 :rule refl :args (@t33)) % 0.38/0.59 (step @p77 :rule cong :premises (@p76 @p66) :args ((= @t33 @t38))) % 0.38/0.59 (step @p78 :rule symm :premises (@p77)) % 0.38/0.59 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.38/0.59 (step @p80 :rule ho_cong :premises (@p70 @p79)) % 0.38/0.59 (step @p81 :rule trans :premises (@p80 @p75)) % 0.38/0.59 (step @p82 :rule refl :args ((tptp.in @t16 @t63))) % 0.38/0.59 (step @p83 :rule refl :args ((tptp.dsetconstr @t34 @t62))) % 0.38/0.59 (step @p84 :rule refl :args ((tptp.subset @t40 @t33))) % 0.38/0.59 (step @p85 :rule refl :args (@t40)) % 0.38/0.59 (step @p86 :rule cong :premises (@p85 @p66) :args (@t41)) % 0.38/0.59 (step @p87 :rule trans :premises (@p86 @p84)) % 0.38/0.59 (step @p88 :rule cong :premises (@p87) :args (@t43)) % 0.38/0.59 (step @p89 :rule refl :args ((tptp.powerset @t33))) % 0.38/0.59 (step @p90 :rule cong :premises (@p66) :args (@t44)) % 0.38/0.59 (step @p91 :rule trans :premises (@p90 @p89)) % 0.38/0.59 (step @p92 :rule cong :premises (@p91 @p88) :args (@t45)) % 0.38/0.59 (step @p93 :rule trans :premises (@p92 @p83)) % 0.38/0.59 (step @p94 :rule cong :premises (@p67 @p93) :args (@t46)) % 0.38/0.59 (step @p95 :rule trans :premises (@p94 @p82)) % 0.38/0.59 (step @p96 :rule refl :args (@t18)) % 0.38/0.59 (step @p97 :rule ho_cong :premises (@p96 @p93)) % 0.38/0.59 (step @p98 :rule cong :premises (@p97 @p95) :args ((= (_ @t18 @t45) @t46))) % 0.38/0.59 (step @p99 :rule symm :premises (@p98)) % 0.38/0.59 (step @p100 :rule refl :args (@t64)) % 0.38/0.59 (step @p101 :rule eq_resolve :premises (@p100 @p99)) % 0.38/0.59 (step @p102 :rule refl :args (tptp.dsetconstr)) % 0.38/0.59 (step @p103 :rule ho_cong :premises (@p102 @p91)) % 0.38/0.59 (step @p104 :rule ho_cong :premises (@p103 @p88)) % 0.38/0.59 (step @p105 :rule cong :premises (@p104 @p93) :args ((= (_ (_ tptp.dsetconstr @t44) @t43) @t45))) % 0.38/0.59 (step @p106 :rule symm :premises (@p105)) % 0.38/0.59 (step @p107 :rule refl :args (@t63)) % 0.38/0.59 (step @p108 :rule eq_resolve :premises (@p107 @p106)) % 0.38/0.59 (step @p109 :rule refl :args (@t60)) % 0.38/0.59 (step @p110 :rule ho_cong :premises (@p109 @p66)) % 0.38/0.59 (step @p111 :rule cong :premises (@p110 @p87) :args ((= (_ @t60 @t38) @t41))) % 0.38/0.59 (step @p112 :rule symm :premises (@p111)) % 0.38/0.59 (step @p113 :rule refl :args (@t61)) % 0.38/0.59 (step @p114 :rule eq_resolve :premises (@p113 @p112)) % 0.38/0.59 (step @p115 :rule ho_cong :premises (@p109 @p79)) % 0.38/0.59 (step @p116 :rule trans :premises (@p115 @p114)) % 0.38/0.59 (step @p117 :rule cong :premises (@p116) :args (@t62)) % 0.38/0.59 (step @p118 :rule refl :args (tptp.powerset)) % 0.38/0.59 (step @p119 :rule ho_cong :premises (@p118 @p66)) % 0.38/0.59 (step @p120 :rule cong :premises (@p119 @p91) :args ((= (_ tptp.powerset @t38) @t44))) % 0.38/0.59 (step @p121 :rule symm :premises (@p120)) % 0.38/0.59 (step @p122 :rule refl :args (@t34)) % 0.38/0.59 (step @p123 :rule eq_resolve :premises (@p122 @p121)) % 0.38/0.59 (step @p124 :rule ho_cong :premises (@p118 @p79)) % 0.38/0.59 (step @p125 :rule trans :premises (@p124 @p123)) % 0.38/0.59 (step @p126 :rule ho_cong :premises (@p102 @p125)) % 0.38/0.59 (step @p127 :rule ho_cong :premises (@p126 @p117)) % 0.38/0.59 (step @p128 :rule trans :premises (@p127 @p108)) % 0.38/0.59 (step @p129 :rule ho_cong :premises (@p96 @p128)) % 0.38/0.59 (step @p130 :rule trans :premises (@p129 @p101)) % 0.38/0.59 (step @p131 :rule cong :premises (@p130) :args (@t65)) % 0.38/0.59 (step @p132 :rule nary_cong :premises (@p131 @p81) :args (@t66)) % 0.38/0.59 (step @p133 :rule cong :premises (@p132) :args ((forall @t20 @t66))) % 0.38/0.59 (step @p134 :rule bool-impl-elim :args (@t64 @t59)) % 0.38/0.59 (step @p135 :rule cong :premises (@p134) :args ((forall @t20 (=> @t64 @t59)))) % 0.38/0.59 (step @p136 :rule trans :premises (@p135 @p133)) % 0.38/0.59 (step @p137 :rule alpha_equiv :args (@t67 (@list @t16) (@list @t40))) % 0.38/0.59 (step @p138 :rule refl :args (@t35)) % 0.38/0.59 (step @p139 :rule ho_cong :premises (@p138 @p137)) % 0.38/0.59 (step @p140 :rule ho_cong :premises (@p96 @p139)) % 0.38/0.59 (step @p141 :rule cong :premises (@p140 @p74) :args (@t69)) % 0.38/0.59 (step @p142 :rule cong :premises (@p141) :args ((forall @t20 @t69))) % 0.38/0.59 (step @p143 :rule trans :premises (@p142 @p136)) % 0.38/0.59 (step @p144 :rule beta-reduce :args ((= (_ @t67 @t16) @t59))) % 0.38/0.59 (step @p145 :rule refl :args (@t16)) % 0.38/0.59 (step @p146 :rule beta-reduce :args ((= @t70 @t67))) % 0.38/0.59 (step @p147 :rule ho_cong :premises (@p146 @p145)) % 0.38/0.59 (step @p148 :rule trans :premises (@p147 @p144)) % 0.38/0.59 (step @p149 :rule beta-reduce :args ((= @t71 @t68))) % 0.38/0.59 (step @p150 :rule refl :args (@t18)) % 0.38/0.59 (step @p151 :rule ho_cong :premises (@p150 @p149)) % 0.38/0.59 (step @p152 :rule cong :premises (@p151 @p148) :args (@t73)) % 0.38/0.59 (step @p153 :rule cong :premises (@p152) :args (@t74)) % 0.38/0.59 (step @p154 :rule trans :premises (@p153 @p143)) % 0.38/0.59 (step @p155 :rule cong :premises (@p60 @p154) :args (@t75)) % 0.38/0.59 (step @p156 :rule cong :premises (@p155) :args ((not @t75))) % 0.38/0.59 (step @p157 :rule beta-reduce :args ((= (_ @t76 @t16) @t59))) % 0.38/0.59 (step @p158 :rule beta-reduce :args ((= (_ @t77 @t8) @t76))) % 0.38/0.59 (step @p159 :rule beta-reduce :args ((= (_ @t29 @t8) @t77))) % 0.38/0.59 (step @p160 :rule ho_cong :premises (@p159 @p10)) % 0.38/0.59 (step @p161 :rule trans :premises (@p160 @p158)) % 0.38/0.59 (step @p162 :rule ho_cong :premises (@p161 @p145)) % 0.38/0.59 (step @p163 :rule trans :premises (@p162 @p157)) % 0.38/0.59 (step @p164 :rule ho_cong :premises (@p4 @p10)) % 0.38/0.59 (step @p165 :rule ho_cong :premises (@p164 @p10)) % 0.38/0.59 (step @p166 :rule ho_cong :premises (@p165 @p145)) % 0.38/0.59 (step @p167 :rule trans :premises (@p166 @p163)) % 0.38/0.59 (step @p168 :rule cong :premises (@p167) :args (@t30)) % 0.38/0.59 (step @p169 :rule trans :premises (@p5 @p168)) % 0.38/0.59 (step @p170 :rule ho_cong :premises (@p169 @p10)) % 0.38/0.59 (step @p171 :rule ho_cong :premises (@p170 @p145)) % 0.38/0.59 (step @p172 :rule cong :premises (@p148) :args ((lambda @t31 @t72))) % 0.38/0.59 (step @p173 :rule refl :args (@t35)) % 0.38/0.59 (step @p174 :rule ho_cong :premises (@p173 @p172)) % 0.38/0.59 (step @p175 :rule cong :premises (@p171) :args (@t32)) % 0.38/0.59 (step @p176 :rule ho_cong :premises (@p173 @p175)) % 0.38/0.59 (step @p177 :rule trans :premises (@p176 @p174)) % 0.38/0.59 (step @p178 :rule cong :premises (@p177) :args (@t37)) % 0.38/0.59 (step @p179 :rule trans :premises (@p6 @p178)) % 0.38/0.59 (step @p180 :rule ho_cong :premises (@p179 @p10)) % 0.38/0.59 (step @p181 :rule ho_cong :premises (@p150 @p180)) % 0.38/0.59 (step @p182 :rule cong :premises (@p181 @p171) :args (@t19)) % 0.38/0.59 (step @p183 :rule cong :premises (@p182) :args (@t21)) % 0.38/0.59 (step @p184 :rule cong :premises (@p60 @p183) :args (@t22)) % 0.38/0.59 (step @p185 :rule cong :premises (@p184) :args (@t23)) % 0.38/0.59 (step @p186 :rule trans :premises (@p185 @p156)) % 0.38/0.59 (step @p187 :rule trans :premises (@p186 @p64)) % 0.38/0.59 (step @p188 :rule eq_resolve :premises (@p2 @p187)) % 0.38/0.59 (step @p189 :rule not_implies_elim2 :premises (@p188)) % 0.38/0.59 (step @p190 :rule refl :args (@t89)) % 0.38/0.59 (step @p191 :rule bool-double-not-elim :args (@t47)) % 0.38/0.59 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or (not @t90) @t89))) % 0.38/0.59 (step @p193 :rule refl :args (@t81)) % 0.38/0.59 (step @p194 :rule eq-refl :args (@t83)) % 0.38/0.59 (step @p195 :rule skolem_intro :args (@t84)) % 0.38/0.59 (step @p196 :rule refl :args (@t83)) % 0.38/0.59 (step @p197 :rule cong :premises (@p196 @p195) :args ((= @t83 @t84))) % 0.38/0.59 (step @p198 :rule trans :premises (@p197 @p194)) % 0.38/0.59 (step @p199 :rule true_elim :premises (@p198)) % 0.38/0.59 (step @p200 :rule refl :args (@t85)) % 0.38/0.59 (step @p201 :rule cong :premises (@p200 @p199) :args (@t91)) % 0.38/0.59 (step @p202 :rule refl :args (@t80)) % 0.38/0.59 (step @p203 :rule cong :premises (@p202 @p201) :args (@t92)) % 0.38/0.59 (step @p204 :rule cong :premises (@p203) :args (@t93)) % 0.38/0.59 (step @p205 :rule nary_cong :premises (@p204 @p193) :args (@t94)) % 0.38/0.59 (step @p206 :rule cong :premises (@p205) :args (@t95)) % 0.38/0.59 (step @p207 :rule refl :args (@t90)) % 0.38/0.59 (step @p208 :rule cong :premises (@p207 @p206) :args ((=> @t90 @t95))) % 0.38/0.59 (assume-push @p253 @t90) % 0.38/0.59 (step @p210 :rule skolemize :premises (@p189)) % 0.38/0.59 (step-pop @p254 :rule scope :premises (@p210)) % 0.38/0.59 (step @p211 :rule process_scope :premises (@p254) :args (@t95)) % 0.38/0.59 (step @p213 :rule eq_resolve :premises (@p211 @p208)) % 0.38/0.59 (step @p214 :rule implies_elim :premises (@p213)) % 0.38/0.59 (step @p215 :rule eq_resolve :premises (@p214 @p192)) % 0.38/0.59 (step @p216 :rule chain_m_resolution :premises (@p215 @p189) :args (@t89 @t96 (@list @t47))) % 0.38/0.59 (step @p217 :rule cnf_or_neg :args (@t88 1)) % 0.38/0.59 (step @p218 :rule chain_m_resolution :premises (@p217 @p216) :args ((not @t81) @t96 @t97)) % 0.38/0.59 (step @p219 :rule eq-symm :args (@t98 @t82)) % 0.38/0.59 (step @p220 :rule beta-reduce :args ((= @t99 @t82))) % 0.38/0.59 (step @p221 :rule refl :args (@t98)) % 0.38/0.59 (step @p222 :rule cong :premises (@p221 @p220) :args (@t100)) % 0.38/0.59 (step @p223 :rule trans :premises (@p222 @p219)) % 0.38/0.59 (step @p224 :rule cong :premises (@p223) :args (@t101)) % 0.38/0.59 (step @p225 :rule quant-unused-vars :args ((= (forall @t42 true) true))) % 0.38/0.59 (step @p226 :rule eq-refl :args (@t99)) % 0.38/0.59 (step @p227 :rule cong :premises (@p226) :args ((forall @t42 (= @t99 @t99)))) % 0.38/0.59 (step @p228 :rule trans :premises (@p227 @p225)) % 0.38/0.59 (step @p229 :rule refl :args (@t99)) % 0.38/0.59 (step @p230 :rule refl :args (@t40)) % 0.38/0.59 (step @p231 :rule ho_cong :premises (@p195 @p230)) % 0.38/0.59 (step @p232 :rule cong :premises (@p231 @p229) :args (@t100)) % 0.38/0.59 (step @p233 :rule cong :premises (@p232) :args (@t101)) % 0.38/0.59 (step @p234 :rule trans :premises (@p233 @p228)) % 0.38/0.59 (step @p235 :rule true_elim :premises (@p234)) % 0.38/0.59 (step @p236 :rule eq_resolve :premises (@p235 @p224)) % 0.38/0.59 (step @p237 :rule instantiate :premises (@p236) :args ((@list @t80))) % 0.38/0.59 (step @p238 :rule not_implies_elim1 :premises (@p188)) % 0.38/0.59 (step @p239 :rule instantiate :premises (@p238) :args ((@list @t85 @t84 @t80))) % 0.38/0.59 (step @p240 :rule bool-double-not-elim :args (@t86)) % 0.38/0.59 (step @p241 :rule refl :args (@t88)) % 0.38/0.59 (step @p242 :rule nary_cong :premises (@p241 @p240) :args ((or @t88 (not @t87)))) % 0.38/0.59 (step @p243 :rule cnf_or_neg :args (@t88 0)) % 0.38/0.59 (step @p244 :rule eq_resolve :premises (@p243 @p242)) % 0.38/0.59 (step @p245 :rule reordering :premises (@p244) :args ((or @t86 @t88))) % 0.38/0.59 (step @p246 :rule chain_m_resolution :premises (@p245 @p216) :args (@t86 @t96 @t97)) % 0.38/0.59 (step @p247 :rule cnf_or_pos :args (@t103)) % 0.38/0.59 (step @p248 :rule reordering :premises (@p247) :args ((or @t87 @t102 (not @t103)))) % 0.38/0.59 (step @p249 :rule chain_m_resolution :premises (@p248 @p246 @p239) :args (@t102 (@list false false) (@list @t86 @t103))) % 0.38/0.59 (step @p250 :rule cnf_equiv_pos2 :args (@t104)) % 0.38/0.59 (step @p251 :rule reordering :premises (@p250) :args ((or @t81 (not @t102) (not @t104)))) % 0.38/0.59 (step @p252 false :rule chain_m_resolution :premises (@p251 @p249 @p237 @p218) :args (false (@list false false true) (@list @t102 @t104 @t81))) % 0.38/0.59 ) % 0.38/0.59 % SZS output end Proof % 0.38/0.59 % cvc5 exiting %------------------------------------------------------------------------------