%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU801^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 08:53:15 AM UTC 2026 % Result : Theorem 0.37s 0.57s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU801^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n017.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:51:16 EDT 2026 % 0.16/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.37/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.57 % SZS status Theorem % 0.37/0.57 % SZS output start Proof % 0.37/0.57 ( % 0.37/0.57 (declare-sort $$unsorted 0) % 0.37/0.57 (declare-const tptp.ap (-> $$unsorted $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.37/0.57 (declare-const tptp.funcSet (-> $$unsorted $$unsorted $$unsorted)) % 0.37/0.57 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.37/0.57 (declare-const tptp.dsetconstrEL Bool) % 0.37/0.57 (define tptp.surjective () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xf" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_3) (forall (@list _let_1) (=> (_ (_ tptp.in _let_1) _let_4) (exists (@list _let_2) (and (_ (_ tptp.in _let_2) _let_5) (= (_ (_ (_ (_ tptp.ap _let_5) _let_4) _let_3) _let_2) _let_1)))))))))))) % 0.37/0.57 (define tptp.surjFuncSet () (let ((_let_1 (@var "Xf" $$unsorted))) (let ((_let_2 (@var "B" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ (_ tptp.dsetconstr (_ (_ tptp.funcSet _let_3) _let_2)) (lambda (@list _let_1) (_ (_ (_ tptp.surjective _let_3) _let_2) _let_1)))))))) % 0.37/0.57 (define @t1 () (@var "A" $$unsorted)) % 0.37/0.57 (define @t2 () (@var "Xx" $$unsorted)) % 0.37/0.57 (define @t3 () (_ tptp.in @t2)) % 0.37/0.57 (define @t4 () (_ @t3 @t1)) % 0.37/0.57 (define @t5 () (@var "Xy" $$unsorted)) % 0.37/0.57 (define @t6 () (@var "Xphi" (-> $$unsorted Bool))) % 0.37/0.57 (define @t7 () (_ @t6 @t5)) % 0.37/0.57 (define @t8 () (@list @t5)) % 0.37/0.57 (define @t9 () (lambda @t8 @t7)) % 0.37/0.57 (define @t10 () (_ tptp.dsetconstr @t1)) % 0.37/0.57 (define @t11 () (_ @t10 @t9)) % 0.37/0.57 (define @t12 () (_ @t3 @t11)) % 0.37/0.57 (define @t13 () (@list @t1 @t6 @t2)) % 0.37/0.57 (define @t14 () (forall @t13 (=> @t12 @t4))) % 0.37/0.57 (define @t15 () (= tptp.dsetconstrEL @t14)) % 0.37/0.57 (define @t16 () (@var "B" $$unsorted)) % 0.37/0.57 (define @t17 () (_ (_ tptp.funcSet @t1) @t16)) % 0.37/0.57 (define @t18 () (@var "Xf" $$unsorted)) % 0.37/0.57 (define @t19 () (_ tptp.in @t18)) % 0.37/0.57 (define @t20 () (_ @t19 @t17)) % 0.37/0.57 (define @t21 () (=> (_ @t19 (_ (_ tptp.surjFuncSet @t1) @t16)) @t20)) % 0.37/0.57 (define @t22 () (@list @t1 @t16 @t18)) % 0.37/0.57 (define @t23 () (forall @t22 @t21)) % 0.37/0.57 (define @t24 () (=> tptp.dsetconstrEL @t23)) % 0.37/0.57 (define @t25 () (not @t24)) % 0.37/0.57 (define @t26 () (_ (_ tptp.ap @t1) @t16)) % 0.37/0.57 (define @t27 () (_ (_ @t26 @t18) @t5)) % 0.37/0.57 (define @t28 () (_ (_ tptp.in @t5) @t1)) % 0.37/0.57 (define @t29 () (and @t28 (= @t27 @t2))) % 0.37/0.57 (define @t30 () (exists @t8 @t29)) % 0.37/0.57 (define @t31 () (_ @t3 @t16)) % 0.37/0.57 (define @t32 () (=> @t31 @t30)) % 0.37/0.57 (define @t33 () (@list @t2)) % 0.37/0.57 (define @t34 () (forall @t33 @t32)) % 0.37/0.57 (define @t35 () (lambda @t22 @t34)) % 0.37/0.57 (define @t36 () (@list @t18)) % 0.37/0.57 (define @t37 () (lambda @t36 (_ (_ (_ tptp.surjective @t1) @t16) @t18))) % 0.37/0.57 (define @t38 () (_ tptp.dsetconstr @t17)) % 0.37/0.57 (define @t39 () (@list @t1 @t16)) % 0.37/0.57 (define @t40 () (lambda @t39 (_ @t38 @t37))) % 0.37/0.57 (define @t41 () (tptp.funcSet @t1 @t16)) % 0.37/0.57 (define @t42 () (tptp.in @t18 @t41)) % 0.37/0.57 (define @t43 () (@var "BOUND_VARIABLE_7570" $$unsorted)) % 0.37/0.57 (define @t44 () (tptp.ap @t1 @t16 @t43 @t5)) % 0.37/0.57 (define @t45 () (= @t2 @t44)) % 0.37/0.57 (define @t46 () (not @t45)) % 0.37/0.57 (define @t47 () (tptp.in @t5 @t1)) % 0.37/0.57 (define @t48 () (not @t47)) % 0.37/0.57 (define @t49 () (or @t48 @t46)) % 0.37/0.57 (define @t50 () (forall @t8 @t49)) % 0.37/0.57 (define @t51 () (not @t50)) % 0.37/0.57 (define @t52 () (tptp.in @t2 @t16)) % 0.37/0.57 (define @t53 () (not @t52)) % 0.37/0.57 (define @t54 () (or @t53 @t51)) % 0.37/0.57 (define @t55 () (forall @t33 @t54)) % 0.37/0.57 (define @t56 () (@list @t43)) % 0.37/0.57 (define @t57 () (lambda @t56 @t55)) % 0.37/0.57 (define @t58 () (tptp.dsetconstr @t41 @t57)) % 0.37/0.57 (define @t59 () (tptp.in @t18 @t58)) % 0.37/0.57 (define @t60 () (forall @t22 (or (not @t59) @t42))) % 0.37/0.57 (define @t61 () (tptp.in @t2 @t1)) % 0.37/0.57 (define @t62 () (_ @t6 @t5)) % 0.37/0.57 (define @t63 () (lambda @t8 @t62)) % 0.37/0.57 (define @t64 () (tptp.dsetconstr @t1 @t63)) % 0.37/0.57 (define @t65 () (tptp.in @t2 @t64)) % 0.37/0.57 (define @t66 () (not @t65)) % 0.37/0.57 (define @t67 () (or @t66 @t61)) % 0.37/0.57 (define @t68 () (not @t12)) % 0.37/0.57 (define @t69 () (or @t68 @t4)) % 0.37/0.57 (define @t70 () (=> tptp.dsetconstrEL @t60)) % 0.37/0.57 (define @t71 () (not @t28)) % 0.37/0.57 (define @t72 () (not @t31)) % 0.37/0.57 (define @t73 () (lambda @t56 (forall @t33 (or @t72 (not (forall @t8 (or @t71 (not (= @t2 (_ (_ @t26 @t43) @t5)))))))))) % 0.37/0.57 (define @t74 () (_ @t38 @t73)) % 0.37/0.57 (define @t75 () (_ @t19 (_ @t38 @t57))) % 0.37/0.57 (define @t76 () (not @t75)) % 0.37/0.57 (define @t77 () (or @t76 @t20)) % 0.37/0.57 (define @t78 () (tptp.ap @t1 @t16 @t18 @t5)) % 0.37/0.57 (define @t79 () (not (forall @t8 (or @t48 (not (= @t2 @t78)))))) % 0.37/0.57 (define @t80 () (forall @t33 (or @t53 @t79))) % 0.37/0.57 (define @t81 () (lambda @t36 @t80)) % 0.37/0.57 (define @t82 () (_ @t38 @t81)) % 0.37/0.57 (define @t83 () (=> (_ @t19 @t82) @t20)) % 0.37/0.57 (define @t84 () (lambda (@list @t16) @t82)) % 0.37/0.57 (define @t85 () (_ (lambda @t39 @t82) @t1)) % 0.37/0.57 (define @t86 () (=> (_ @t19 (_ @t85 @t16)) @t20)) % 0.37/0.57 (define @t87 () (forall @t22 @t86)) % 0.37/0.57 (define @t88 () (=> tptp.dsetconstrEL @t87)) % 0.37/0.57 (define @t89 () (lambda (@list @t16 @t18) @t80)) % 0.37/0.57 (define @t90 () (_ (lambda @t22 @t80) @t1)) % 0.37/0.57 (define @t91 () (or @t72 @t79)) % 0.37/0.57 (define @t92 () (= @t2 @t27)) % 0.37/0.57 (define @t93 () (not @t92)) % 0.37/0.57 (define @t94 () (or @t71 @t93)) % 0.37/0.57 (define @t95 () (and @t28 @t92)) % 0.37/0.57 (define @t96 () (forall @t8 (not @t95))) % 0.37/0.57 (define @t97 () (not @t96)) % 0.37/0.57 (define @t98 () (@quantifiers_skolemize @t60 1)) % 0.37/0.57 (define @t99 () (@quantifiers_skolemize @t60 0)) % 0.37/0.57 (define @t100 () (tptp.funcSet @t99 @t98)) % 0.37/0.57 (define @t101 () (@quantifiers_skolemize @t60 2)) % 0.37/0.57 (define @t102 () (tptp.in @t101 @t100)) % 0.37/0.57 (define @t103 () (lambda @t56 (forall @t33 (or (not (tptp.in @t2 @t98)) (not (forall @t8 (or (not (tptp.in @t5 @t99)) (not (= @t2 (tptp.ap @t99 @t98 @t43 @t5)))))))))) % 0.37/0.57 (define @t104 () (@purify @t103)) % 0.37/0.57 (define @t105 () (or (not (tptp.in @t101 (tptp.dsetconstr @t100 @t104))) @t102)) % 0.37/0.57 (define @t106 () (not @t105)) % 0.37/0.57 (define @t107 () (not @t60)) % 0.37/0.57 (define @t108 () (tptp.dsetconstr @t100 @t103)) % 0.37/0.57 (define @t109 () (tptp.in @t101 @t108)) % 0.37/0.57 (define @t110 () (not @t109)) % 0.37/0.57 (define @t111 () (or @t110 @t102)) % 0.37/0.57 (define @t112 () (not @t111)) % 0.37/0.57 (define @t113 () (forall @t13 (or (not (tptp.in @t2 (tptp.dsetconstr @t1 @t6))) @t61))) % 0.37/0.57 (assume @p1 @t15) % 0.37/0.57 (assume @p2 @t25) % 0.37/0.57 (assume @p3 true) % 0.37/0.57 (step @p4 (= tptp.surjective @t35) :rule refl :args (@t35)) % 0.37/0.57 (step @p5 (= tptp.surjFuncSet @t40) :rule refl :args (@t40)) % 0.37/0.57 (step @p6 :rule refl :args (@t60)) % 0.37/0.57 (step @p7 :rule refl :args (@t61)) % 0.37/0.57 (step @p8 :rule lambda-elim :args ((= @t63 @t6))) % 0.37/0.57 (step @p9 :rule refl :args (@t1)) % 0.37/0.57 (step @p10 :rule cong :premises (@p9 @p8) :args (@t64)) % 0.37/0.57 (step @p11 :rule refl :args (@t2)) % 0.37/0.57 (step @p12 :rule cong :premises (@p11 @p10) :args (@t65)) % 0.37/0.57 (step @p13 :rule cong :premises (@p12) :args (@t66)) % 0.37/0.57 (step @p14 :rule nary_cong :premises (@p13 @p7) :args (@t67)) % 0.37/0.57 (step @p15 :rule cong :premises (@p14) :args ((forall @t13 @t67))) % 0.37/0.57 (step @p16 :rule refl :args (@t61)) % 0.37/0.57 (step @p17 :rule refl :args (@t4)) % 0.37/0.57 (step @p18 :rule cong :premises (@p17 @p16) :args ((= @t4 @t61))) % 0.37/0.57 (step @p19 :rule symm :premises (@p18)) % 0.37/0.57 (step @p20 :rule eq_resolve :premises (@p17 @p19)) % 0.37/0.57 (step @p21 :rule refl :args ((tptp.in @t2 @t11))) % 0.37/0.57 (step @p22 :rule refl :args ((tptp.dsetconstr @t1 @t9))) % 0.37/0.57 (step @p23 :rule refl :args (@t62)) % 0.37/0.57 (step @p24 :rule cong :premises (@p23) :args (@t63)) % 0.37/0.57 (step @p25 :rule refl :args (@t1)) % 0.37/0.57 (step @p26 :rule cong :premises (@p25 @p24) :args (@t64)) % 0.37/0.57 (step @p27 :rule trans :premises (@p26 @p22)) % 0.37/0.57 (step @p28 :rule refl :args (@t2)) % 0.37/0.57 (step @p29 :rule cong :premises (@p28 @p27) :args (@t65)) % 0.37/0.57 (step @p30 :rule trans :premises (@p29 @p21)) % 0.37/0.57 (step @p31 :rule refl :args (@t3)) % 0.37/0.57 (step @p32 :rule ho_cong :premises (@p31 @p27)) % 0.37/0.57 (step @p33 :rule cong :premises (@p32 @p30) :args ((= (_ @t3 @t64) @t65))) % 0.37/0.57 (step @p34 :rule symm :premises (@p33)) % 0.37/0.57 (step @p35 :rule refl :args (@t12)) % 0.37/0.57 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 0.37/0.57 (step @p37 :rule refl :args (@t10)) % 0.37/0.57 (step @p38 :rule ho_cong :premises (@p37 @p24)) % 0.37/0.57 (step @p39 :rule cong :premises (@p38 @p27) :args ((= (_ @t10 @t63) @t64))) % 0.37/0.57 (step @p40 :rule symm :premises (@p39)) % 0.37/0.57 (step @p41 :rule refl :args (@t11)) % 0.37/0.57 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.37/0.57 (step @p43 :rule refl :args (@t7)) % 0.37/0.57 (step @p44 :rule cong :premises (@p43 @p23) :args ((= @t7 @t62))) % 0.37/0.57 (step @p45 :rule symm :premises (@p44)) % 0.37/0.57 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.37/0.57 (step @p47 :rule cong :premises (@p46) :args (@t9)) % 0.37/0.57 (step @p48 :rule ho_cong :premises (@p37 @p47)) % 0.37/0.57 (step @p49 :rule trans :premises (@p48 @p42)) % 0.37/0.57 (step @p50 :rule ho_cong :premises (@p31 @p49)) % 0.37/0.57 (step @p51 :rule trans :premises (@p50 @p36)) % 0.37/0.57 (step @p52 :rule cong :premises (@p51) :args (@t68)) % 0.37/0.57 (step @p53 :rule nary_cong :premises (@p52 @p20) :args (@t69)) % 0.37/0.57 (step @p54 :rule cong :premises (@p53) :args ((forall @t13 @t69))) % 0.37/0.57 (step @p55 :rule trans :premises (@p54 @p15)) % 0.37/0.57 (step @p56 :rule bool-impl-elim :args (@t12 @t4)) % 0.37/0.57 (step @p57 :rule cong :premises (@p56) :args (@t14)) % 0.37/0.57 (step @p58 :rule trans :premises (@p57 @p55)) % 0.37/0.57 (step @p59 :rule refl :args (tptp.dsetconstrEL)) % 0.37/0.57 (step @p60 :rule cong :premises (@p59 @p58) :args (@t15)) % 0.37/0.57 (step @p61 :rule eq_resolve :premises (@p1 @p60)) % 0.37/0.57 (step @p62 :rule cong :premises (@p61 @p6) :args (@t70)) % 0.37/0.57 (step @p63 :rule cong :premises (@p62) :args ((not @t70))) % 0.37/0.57 (step @p64 :rule refl :args ((tptp.in @t18 @t17))) % 0.37/0.57 (step @p65 :rule refl :args (@t41)) % 0.37/0.57 (step @p66 :rule refl :args (@t18)) % 0.37/0.57 (step @p67 :rule cong :premises (@p66 @p65) :args (@t42)) % 0.37/0.57 (step @p68 :rule trans :premises (@p67 @p64)) % 0.37/0.57 (step @p69 :rule refl :args (@t19)) % 0.37/0.57 (step @p70 :rule ho_cong :premises (@p69 @p65)) % 0.37/0.57 (step @p71 :rule cong :premises (@p70 @p68) :args ((= (_ @t19 @t41) @t42))) % 0.37/0.57 (step @p72 :rule symm :premises (@p71)) % 0.37/0.57 (step @p73 :rule refl :args (@t20)) % 0.37/0.57 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.37/0.57 (step @p75 :rule refl :args (@t17)) % 0.37/0.57 (step @p76 :rule cong :premises (@p75 @p65) :args ((= @t17 @t41))) % 0.37/0.57 (step @p77 :rule symm :premises (@p76)) % 0.37/0.57 (step @p78 :rule eq_resolve :premises (@p75 @p77)) % 0.37/0.57 (step @p79 :rule ho_cong :premises (@p69 @p78)) % 0.37/0.57 (step @p80 :rule trans :premises (@p79 @p74)) % 0.37/0.57 (step @p81 :rule refl :args ((tptp.in @t18 @t74))) % 0.37/0.57 (step @p82 :rule refl :args ((tptp.dsetconstr @t17 @t73))) % 0.37/0.57 (step @p83 :rule refl :args (@t44)) % 0.37/0.57 (step @p84 :rule cong :premises (@p28 @p83) :args (@t45)) % 0.37/0.57 (step @p85 :rule cong :premises (@p84) :args (@t46)) % 0.37/0.57 (step @p86 :rule refl :args (@t47)) % 0.37/0.57 (step @p87 :rule cong :premises (@p86) :args (@t48)) % 0.37/0.57 (step @p88 :rule nary_cong :premises (@p87 @p85) :args (@t49)) % 0.37/0.57 (step @p89 :rule cong :premises (@p88) :args (@t50)) % 0.37/0.57 (step @p90 :rule cong :premises (@p89) :args (@t51)) % 0.37/0.57 (step @p91 :rule refl :args (@t52)) % 0.37/0.57 (step @p92 :rule cong :premises (@p91) :args (@t53)) % 0.37/0.57 (step @p93 :rule nary_cong :premises (@p92 @p90) :args (@t54)) % 0.37/0.57 (step @p94 :rule cong :premises (@p93) :args (@t55)) % 0.37/0.57 (step @p95 :rule cong :premises (@p94) :args (@t57)) % 0.37/0.57 (step @p96 :rule cong :premises (@p65 @p95) :args (@t58)) % 0.37/0.57 (step @p97 :rule trans :premises (@p96 @p82)) % 0.37/0.57 (step @p98 :rule cong :premises (@p66 @p97) :args (@t59)) % 0.37/0.57 (step @p99 :rule trans :premises (@p98 @p81)) % 0.37/0.57 (step @p100 :rule ho_cong :premises (@p69 @p97)) % 0.37/0.57 (step @p101 :rule cong :premises (@p100 @p99) :args ((= (_ @t19 @t58) @t59))) % 0.37/0.57 (step @p102 :rule symm :premises (@p101)) % 0.37/0.57 (step @p103 :rule refl :args ((_ @t19 @t74))) % 0.37/0.57 (step @p104 :rule eq_resolve :premises (@p103 @p102)) % 0.37/0.57 (step @p105 :rule refl :args (tptp.dsetconstr)) % 0.37/0.57 (step @p106 :rule ho_cong :premises (@p105 @p65)) % 0.37/0.57 (step @p107 :rule ho_cong :premises (@p106 @p95)) % 0.37/0.57 (step @p108 :rule cong :premises (@p107 @p97) :args ((= (_ (_ tptp.dsetconstr @t41) @t57) @t58))) % 0.37/0.57 (step @p109 :rule symm :premises (@p108)) % 0.37/0.57 (step @p110 :rule refl :args (@t74)) % 0.37/0.57 (step @p111 :rule eq_resolve :premises (@p110 @p109)) % 0.37/0.57 (step @p112 :rule refl :args (@t57)) % 0.37/0.57 (step @p113 :rule ho_cong :premises (@p105 @p78)) % 0.37/0.57 (step @p114 :rule ho_cong :premises (@p113 @p112)) % 0.37/0.57 (step @p115 :rule trans :premises (@p114 @p111)) % 0.37/0.57 (step @p116 :rule ho_cong :premises (@p69 @p115)) % 0.37/0.57 (step @p117 :rule trans :premises (@p116 @p104)) % 0.37/0.57 (step @p118 :rule cong :premises (@p117) :args (@t76)) % 0.37/0.57 (step @p119 :rule nary_cong :premises (@p118 @p80) :args (@t77)) % 0.37/0.57 (step @p120 :rule cong :premises (@p119) :args ((forall @t22 @t77))) % 0.37/0.57 (step @p121 :rule bool-impl-elim :args (@t75 @t20)) % 0.37/0.57 (step @p122 :rule cong :premises (@p121) :args ((forall @t22 (=> @t75 @t20)))) % 0.37/0.57 (step @p123 :rule trans :premises (@p122 @p120)) % 0.37/0.57 (step @p124 :rule alpha_equiv :args (@t81 (@list @t18) (@list @t43))) % 0.37/0.57 (step @p125 :rule refl :args (@t38)) % 0.37/0.57 (step @p126 :rule ho_cong :premises (@p125 @p124)) % 0.37/0.57 (step @p127 :rule ho_cong :premises (@p69 @p126)) % 0.37/0.57 (step @p128 :rule cong :premises (@p127 @p73) :args (@t83)) % 0.37/0.57 (step @p129 :rule cong :premises (@p128) :args ((forall @t22 @t83))) % 0.37/0.57 (step @p130 :rule trans :premises (@p129 @p123)) % 0.37/0.57 (step @p131 :rule refl :args (@t20)) % 0.37/0.57 (step @p132 :rule beta-reduce :args ((= (_ @t84 @t16) @t82))) % 0.37/0.57 (step @p133 :rule refl :args (@t16)) % 0.37/0.57 (step @p134 :rule beta-reduce :args ((= @t85 @t84))) % 0.37/0.57 (step @p135 :rule ho_cong :premises (@p134 @p133)) % 0.37/0.57 (step @p136 :rule trans :premises (@p135 @p132)) % 0.37/0.57 (step @p137 :rule refl :args (@t19)) % 0.37/0.57 (step @p138 :rule ho_cong :premises (@p137 @p136)) % 0.37/0.57 (step @p139 :rule cong :premises (@p138 @p131) :args (@t86)) % 0.37/0.57 (step @p140 :rule cong :premises (@p139) :args (@t87)) % 0.37/0.57 (step @p141 :rule trans :premises (@p140 @p130)) % 0.37/0.57 (step @p142 :rule cong :premises (@p59 @p141) :args (@t88)) % 0.37/0.57 (step @p143 :rule cong :premises (@p142) :args ((not @t88))) % 0.37/0.57 (step @p144 :rule beta-reduce :args ((= (_ @t81 @t18) @t80))) % 0.37/0.57 (step @p145 :rule refl :args (@t18)) % 0.37/0.57 (step @p146 :rule beta-reduce :args ((= (_ @t89 @t16) @t81))) % 0.37/0.57 (step @p147 :rule beta-reduce :args ((= @t90 @t89))) % 0.37/0.57 (step @p148 :rule ho_cong :premises (@p147 @p133)) % 0.37/0.57 (step @p149 :rule trans :premises (@p148 @p146)) % 0.37/0.57 (step @p150 :rule ho_cong :premises (@p149 @p145)) % 0.37/0.57 (step @p151 :rule trans :premises (@p150 @p144)) % 0.37/0.57 (step @p152 :rule cong :premises (@p151) :args ((lambda @t36 (_ (_ @t90 @t16) @t18)))) % 0.37/0.57 (step @p153 :rule refl :args (@t38)) % 0.37/0.57 (step @p154 :rule ho_cong :premises (@p153 @p152)) % 0.37/0.57 (step @p155 :rule refl :args (@t79)) % 0.37/0.57 (step @p156 :rule refl :args (@t31)) % 0.37/0.57 (step @p157 :rule cong :premises (@p156 @p91) :args ((= @t31 @t52))) % 0.37/0.57 (step @p158 :rule symm :premises (@p157)) % 0.37/0.57 (step @p159 :rule eq_resolve :premises (@p156 @p158)) % 0.37/0.57 (step @p160 :rule cong :premises (@p159) :args (@t72)) % 0.37/0.57 (step @p161 :rule nary_cong :premises (@p160 @p155) :args (@t91)) % 0.37/0.57 (step @p162 :rule cong :premises (@p161) :args ((forall @t33 @t91))) % 0.37/0.57 (step @p163 :rule bool-impl-elim :args (@t31 @t79)) % 0.37/0.57 (step @p164 :rule cong :premises (@p163) :args ((forall @t33 (=> @t31 @t79)))) % 0.37/0.57 (step @p165 :rule trans :premises (@p164 @p162)) % 0.37/0.57 (step @p166 :rule refl :args (@t78)) % 0.37/0.57 (step @p167 :rule refl :args (@t27)) % 0.37/0.57 (step @p168 :rule cong :premises (@p167 @p166) :args ((= @t27 @t78))) % 0.37/0.57 (step @p169 :rule symm :premises (@p168)) % 0.37/0.57 (step @p170 :rule eq_resolve :premises (@p167 @p169)) % 0.37/0.57 (step @p171 :rule cong :premises (@p28 @p170) :args (@t92)) % 0.37/0.57 (step @p172 :rule cong :premises (@p171) :args (@t93)) % 0.37/0.57 (step @p173 :rule refl :args (@t28)) % 0.37/0.57 (step @p174 :rule cong :premises (@p173 @p86) :args ((= @t28 @t47))) % 0.37/0.57 (step @p175 :rule symm :premises (@p174)) % 0.37/0.57 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 0.37/0.57 (step @p177 :rule cong :premises (@p176) :args (@t71)) % 0.37/0.57 (step @p178 :rule nary_cong :premises (@p177 @p172) :args (@t94)) % 0.37/0.57 (step @p179 :rule cong :premises (@p178) :args ((forall @t8 @t94))) % 0.37/0.57 (step @p180 :rule bool-and-de-morgan :args (@t28 @t92 true)) % 0.37/0.57 (step @p181 :rule cong :premises (@p180) :args (@t96)) % 0.37/0.57 (step @p182 :rule trans :premises (@p181 @p179)) % 0.37/0.57 (step @p183 :rule cong :premises (@p182) :args (@t97)) % 0.37/0.57 (step @p184 :rule exists-elim :args ((= (exists @t8 @t95) @t97))) % 0.37/0.57 (step @p185 :rule trans :premises (@p184 @p183)) % 0.37/0.57 (step @p186 :rule eq-symm :args (@t27 @t2)) % 0.37/0.57 (step @p187 :rule refl :args (@t28)) % 0.37/0.57 (step @p188 :rule nary_cong :premises (@p187 @p186) :args (@t29)) % 0.37/0.57 (step @p189 :rule cong :premises (@p188) :args (@t30)) % 0.37/0.57 (step @p190 :rule trans :premises (@p189 @p185)) % 0.37/0.57 (step @p191 :rule refl :args (@t31)) % 0.37/0.57 (step @p192 :rule cong :premises (@p191 @p190) :args (@t32)) % 0.37/0.57 (step @p193 :rule cong :premises (@p192) :args (@t34)) % 0.37/0.57 (step @p194 :rule trans :premises (@p193 @p165)) % 0.37/0.57 (step @p195 :rule cong :premises (@p194) :args (@t35)) % 0.37/0.57 (step @p196 :rule trans :premises (@p4 @p195)) % 0.37/0.57 (step @p197 :rule ho_cong :premises (@p196 @p9)) % 0.37/0.57 (step @p198 :rule ho_cong :premises (@p197 @p133)) % 0.37/0.57 (step @p199 :rule ho_cong :premises (@p198 @p145)) % 0.37/0.57 (step @p200 :rule cong :premises (@p199) :args (@t37)) % 0.37/0.57 (step @p201 :rule ho_cong :premises (@p153 @p200)) % 0.37/0.57 (step @p202 :rule trans :premises (@p201 @p154)) % 0.37/0.57 (step @p203 :rule cong :premises (@p202) :args (@t40)) % 0.37/0.57 (step @p204 :rule trans :premises (@p5 @p203)) % 0.37/0.57 (step @p205 :rule ho_cong :premises (@p204 @p9)) % 0.37/0.57 (step @p206 :rule ho_cong :premises (@p205 @p133)) % 0.37/0.57 (step @p207 :rule ho_cong :premises (@p137 @p206)) % 0.37/0.57 (step @p208 :rule cong :premises (@p207 @p131) :args (@t21)) % 0.37/0.57 (step @p209 :rule cong :premises (@p208) :args (@t23)) % 0.37/0.57 (step @p210 :rule cong :premises (@p59 @p209) :args (@t24)) % 0.37/0.57 (step @p211 :rule cong :premises (@p210) :args (@t25)) % 0.37/0.57 (step @p212 :rule trans :premises (@p211 @p143)) % 0.37/0.57 (step @p213 :rule trans :premises (@p212 @p63)) % 0.37/0.57 (step @p214 :rule eq_resolve :premises (@p2 @p213)) % 0.37/0.57 (step @p215 :rule not_implies_elim1 :premises (@p214)) % 0.37/0.57 (step @p216 :rule not_implies_elim2 :premises (@p214)) % 0.37/0.57 (step @p217 :rule refl :args (@t106)) % 0.37/0.57 (step @p218 :rule bool-double-not-elim :args (@t60)) % 0.37/0.57 (step @p219 :rule nary_cong :premises (@p218 @p217) :args ((or (not @t107) @t106))) % 0.37/0.57 (step @p220 :rule refl :args (@t102)) % 0.37/0.57 (step @p221 :rule eq-refl :args (@t103)) % 0.37/0.57 (step @p222 :rule skolem_intro :args (@t104)) % 0.37/0.57 (step @p223 :rule refl :args (@t103)) % 0.37/0.57 (step @p224 :rule cong :premises (@p223 @p222) :args ((= @t103 @t104))) % 0.37/0.57 (step @p225 :rule trans :premises (@p224 @p221)) % 0.37/0.57 (step @p226 :rule true_elim :premises (@p225)) % 0.37/0.57 (step @p227 :rule refl :args (@t100)) % 0.37/0.57 (step @p228 :rule cong :premises (@p227 @p226) :args (@t108)) % 0.37/0.57 (step @p229 :rule refl :args (@t101)) % 0.37/0.57 (step @p230 :rule cong :premises (@p229 @p228) :args (@t109)) % 0.37/0.57 (step @p231 :rule cong :premises (@p230) :args (@t110)) % 0.37/0.57 (step @p232 :rule nary_cong :premises (@p231 @p220) :args (@t111)) % 0.37/0.57 (step @p233 :rule cong :premises (@p232) :args (@t112)) % 0.37/0.57 (step @p234 :rule refl :args (@t107)) % 0.37/0.57 (step @p235 :rule cong :premises (@p234 @p233) :args ((=> @t107 @t112))) % 0.37/0.57 (assume-push @p250 @t107) % 0.37/0.57 (step @p237 :rule skolemize :premises (@p216)) % 0.37/0.57 (step-pop @p251 :rule scope :premises (@p237)) % 0.37/0.57 (step @p238 :rule process_scope :premises (@p251) :args (@t112)) % 0.37/0.57 (step @p240 :rule eq_resolve :premises (@p238 @p235)) % 0.37/0.57 (step @p241 :rule implies_elim :premises (@p240)) % 0.37/0.57 (step @p242 :rule eq_resolve :premises (@p241 @p219)) % 0.37/0.57 (step @p243 :rule chain_m_resolution :premises (@p242 @p216) :args (@t106 (@list true) (@list @t60))) % 0.37/0.57 (assume-push @p252 @t113) % 0.37/0.57 (step @p245 :rule instantiate :premises (@p215) :args ((@list @t100 @t104 @t101))) % 0.37/0.57 (step-pop @p253 :rule scope :premises (@p245)) % 0.37/0.57 (step @p246 :rule process_scope :premises (@p253) :args (@t105)) % 0.37/0.57 (step @p248 :rule implies_elim :premises (@p246)) % 0.37/0.57 (step @p249 false :rule chain_m_resolution :premises (@p248 @p243 @p215) :args (false (@list true false) (@list @t105 @t113))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------