%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET067^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n023.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 08:47:14 AM UTC 2026 % Result : Theorem 0.39s 0.57s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET067^1 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n023.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 14:51:13 EDT 2026 % 0.17/0.35 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.39/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.57 % SZS status Theorem % 0.39/0.57 % SZS output start Proof % 0.39/0.57 ( % 0.39/0.57 (declare-sort $$unsorted 0) % 0.39/0.57 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.39/0.57 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.39/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.39/0.57 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.39/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.39/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.57 (define tptp.excl_union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.39/0.57 (define tptp.intersection () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.57 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.39/0.57 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.39/0.57 (define tptp.subset () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.39/0.57 (define tptp.misses () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))) % 0.39/0.57 (define @t1 () (@var "X" $$unsorted)) % 0.39/0.57 (define @t2 () (@var "Y" $$unsorted)) % 0.39/0.57 (define @t3 () (@list @t1 @t2)) % 0.39/0.57 (define @t4 () (forall @t3 (_ (_ tptp.subset (_ (_ tptp.unord_pair @t1) @t2)) (_ (_ tptp.unord_pair @t2) @t1)))) % 0.39/0.57 (define @t5 () (not @t4)) % 0.39/0.57 (define @t6 () (@var "M" (-> $$unsorted Bool))) % 0.39/0.57 (define @t7 () (lambda (@list @t1 @t6) (_ @t6 @t1))) % 0.39/0.57 (define @t8 () (lambda (@list @t1) false)) % 0.39/0.57 (define @t9 () (@var "U" $$unsorted)) % 0.39/0.57 (define @t10 () (= @t9 @t1)) % 0.39/0.57 (define @t11 () (or @t10 (= @t9 @t2))) % 0.39/0.57 (define @t12 () (@list @t1 @t2 @t9)) % 0.39/0.57 (define @t13 () (lambda @t12 @t11)) % 0.39/0.57 (define @t14 () (lambda (@list @t1 @t9) @t10)) % 0.39/0.57 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.57 (define @t16 () (_ @t15 @t9)) % 0.39/0.57 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.57 (define @t18 () (_ @t17 @t9)) % 0.39/0.57 (define @t19 () (@list @t17 @t15 @t9)) % 0.39/0.57 (define @t20 () (lambda @t19 (or @t18 @t16))) % 0.39/0.57 (define @t21 () (not @t18)) % 0.39/0.57 (define @t22 () (and @t18 (not @t16))) % 0.39/0.57 (define @t23 () (lambda @t19 (or @t22 (and @t21 @t16)))) % 0.39/0.57 (define @t24 () (and @t18 @t16)) % 0.39/0.57 (define @t25 () (lambda @t19 @t24)) % 0.39/0.57 (define @t26 () (lambda @t19 @t22)) % 0.39/0.57 (define @t27 () (lambda (@list @t17 @t9) @t21)) % 0.39/0.57 (define @t28 () (@list @t17 @t15)) % 0.39/0.57 (define @t29 () (lambda @t28 (= (_ (_ tptp.intersection @t17) @t15) tptp.emptyset))) % 0.39/0.57 (define @t30 () (@list @t9)) % 0.39/0.57 (define @t31 () (forall @t30 (=> @t18 @t16))) % 0.39/0.57 (define @t32 () (lambda @t28 @t31)) % 0.39/0.57 (define @t33 () (exists @t30 @t24)) % 0.39/0.57 (define @t34 () (lambda @t28 @t33)) % 0.39/0.57 (define @t35 () (lambda @t28 (not @t33))) % 0.39/0.57 (define @t36 () (= @t1 @t2)) % 0.39/0.57 (define @t37 () (= @t2 @t2)) % 0.39/0.57 (define @t38 () (or @t37 @t36)) % 0.39/0.57 (define @t39 () (= @t1 @t9)) % 0.39/0.57 (define @t40 () (= @t2 @t9)) % 0.39/0.57 (define @t41 () (lambda @t30 (or @t40 @t39))) % 0.39/0.57 (define @t42 () (_ @t41 @t2)) % 0.39/0.57 (define @t43 () (= @t1 @t1)) % 0.39/0.57 (define @t44 () (or (= @t2 @t1) @t43)) % 0.39/0.57 (define @t45 () (_ @t41 @t1)) % 0.39/0.57 (define @t46 () (and @t45 @t42)) % 0.39/0.57 (define @t47 () (_ @t15 @t2)) % 0.39/0.57 (define @t48 () (_ @t15 @t1)) % 0.39/0.57 (define @t49 () (@list @t15)) % 0.39/0.57 (define @t50 () (or @t40 @t10)) % 0.39/0.57 (define @t51 () (lambda @t30 @t50)) % 0.39/0.57 (define @t52 () (@var "BOUND_VARIABLE_7682" $$unsorted)) % 0.39/0.57 (define @t53 () (= @t9 @t52)) % 0.39/0.57 (define @t54 () (lambda (@list @t52 @t9) (or @t40 @t53))) % 0.39/0.57 (define @t55 () (@list @t1 @t52 @t9)) % 0.39/0.57 (define @t56 () (or @t39 (= @t52 @t9))) % 0.39/0.57 (define @t57 () (or @t39 @t40)) % 0.39/0.57 (define @t58 () (lambda @t12 @t57)) % 0.39/0.57 (define @t59 () (not @t37)) % 0.39/0.57 (define @t60 () (or @t59 @t47)) % 0.39/0.57 (define @t61 () (@var "BOUND_VARIABLE_7661" $$unsorted)) % 0.39/0.57 (define @t62 () (_ @t15 @t61)) % 0.39/0.57 (define @t63 () (not (= @t2 @t61))) % 0.39/0.57 (define @t64 () (@list @t61)) % 0.39/0.57 (define @t65 () (or @t63 @t63 @t62)) % 0.39/0.57 (define @t66 () (or @t63 @t62)) % 0.39/0.57 (define @t67 () (forall @t64 @t66)) % 0.39/0.57 (define @t68 () (not @t43)) % 0.39/0.57 (define @t69 () (or @t68 @t48)) % 0.39/0.57 (define @t70 () (@var "BOUND_VARIABLE_7653" $$unsorted)) % 0.39/0.57 (define @t71 () (_ @t15 @t70)) % 0.39/0.57 (define @t72 () (not (= @t1 @t70))) % 0.39/0.57 (define @t73 () (@list @t70)) % 0.39/0.57 (define @t74 () (or @t72 @t72 @t71)) % 0.39/0.57 (define @t75 () (or @t72 @t71)) % 0.39/0.57 (define @t76 () (forall @t73 @t75)) % 0.39/0.57 (define @t77 () (_ @t15 @t9)) % 0.39/0.57 (define @t78 () (not @t40)) % 0.39/0.57 (define @t79 () (or @t78 @t77)) % 0.39/0.57 (define @t80 () (forall @t30 @t79)) % 0.39/0.57 (define @t81 () (@list @t9)) % 0.39/0.57 (define @t82 () (not @t39)) % 0.39/0.57 (define @t83 () (or @t82 @t77)) % 0.39/0.57 (define @t84 () (forall @t30 @t83)) % 0.39/0.57 (define @t85 () (and @t84 @t80)) % 0.39/0.57 (define @t86 () (or (not @t57) @t77)) % 0.39/0.57 (define @t87 () (lambda @t30 @t57)) % 0.39/0.57 (define @t88 () (_ @t87 @t9)) % 0.39/0.57 (define @t89 () (not @t88)) % 0.39/0.57 (define @t90 () (or @t89 @t77)) % 0.39/0.57 (define @t91 () (forall @t30 @t90)) % 0.39/0.57 (define @t92 () (lambda @t49 @t91)) % 0.39/0.57 (define @t93 () (_ @t17 @t9)) % 0.39/0.57 (define @t94 () (lambda @t28 (forall @t30 (or (not @t93) @t77)))) % 0.39/0.57 (define @t95 () (lambda (@list @t2 @t9) @t57)) % 0.39/0.57 (define @t96 () (_ @t58 @t1)) % 0.39/0.57 (define @t97 () (forall @t3 (_ (_ @t94 (_ @t96 @t2)) (_ (_ @t58 @t2) @t1)))) % 0.39/0.57 (define @t98 () (or @t21 @t16)) % 0.39/0.57 (assume @p1 @t5) % 0.39/0.57 (assume @p2 true) % 0.39/0.57 (step @p3 (= tptp.in @t7) :rule refl :args (@t7)) % 0.39/0.57 (step @p4 (= tptp.is_a @t7) :rule refl :args (@t7)) % 0.39/0.57 (step @p5 (= tptp.emptyset @t8) :rule refl :args (@t8)) % 0.39/0.57 (step @p6 (= tptp.unord_pair @t13) :rule refl :args (@t13)) % 0.39/0.57 (step @p7 (= tptp.singleton @t14) :rule refl :args (@t14)) % 0.39/0.57 (step @p8 (= tptp.union @t20) :rule refl :args (@t20)) % 0.39/0.57 (step @p9 (= tptp.excl_union @t23) :rule refl :args (@t23)) % 0.39/0.57 (step @p10 (= tptp.intersection @t25) :rule refl :args (@t25)) % 0.39/0.57 (step @p11 (= tptp.setminus @t26) :rule refl :args (@t26)) % 0.39/0.57 (step @p12 (= tptp.complement @t27) :rule refl :args (@t27)) % 0.39/0.57 (step @p13 (= tptp.disjoint @t29) :rule refl :args (@t29)) % 0.39/0.57 (step @p14 (= tptp.subset @t32) :rule refl :args (@t32)) % 0.39/0.57 (step @p15 (= tptp.meets @t34) :rule refl :args (@t34)) % 0.39/0.57 (step @p16 (= tptp.misses @t35) :rule refl :args (@t35)) % 0.39/0.57 (step @p17 :rule evaluate :args ((not true))) % 0.39/0.57 (step @p18 :rule quant-unused-vars :args ((= (forall @t3 true) true))) % 0.39/0.57 (step @p19 :rule evaluate :args ((and true true))) % 0.39/0.57 (step @p20 :rule absorb :args ((= (or true @t36) true))) % 0.39/0.57 (step @p21 :rule refl :args (@t36)) % 0.39/0.57 (step @p22 :rule eq-refl :args (@t2)) % 0.39/0.57 (step @p23 :rule nary_cong :premises (@p22 @p21) :args (@t38)) % 0.39/0.57 (step @p24 :rule trans :premises (@p23 @p20)) % 0.39/0.57 (step @p25 :rule beta-reduce :args ((= @t42 @t38))) % 0.39/0.57 (step @p26 :rule trans :premises (@p25 @p24)) % 0.39/0.57 (step @p27 :rule absorb :args ((= (or @t36 true) true))) % 0.39/0.57 (step @p28 :rule eq-refl :args (@t1)) % 0.39/0.57 (step @p29 :rule eq-symm :args (@t2 @t1)) % 0.39/0.57 (step @p30 :rule nary_cong :premises (@p29 @p28) :args (@t44)) % 0.39/0.57 (step @p31 :rule trans :premises (@p30 @p27)) % 0.39/0.57 (step @p32 :rule beta-reduce :args ((= @t45 @t44))) % 0.39/0.57 (step @p33 :rule trans :premises (@p32 @p31)) % 0.39/0.57 (step @p34 :rule nary_cong :premises (@p33 @p26) :args (@t46)) % 0.39/0.57 (step @p35 :rule trans :premises (@p34 @p19)) % 0.39/0.57 (step @p36 :rule beta-reduce :args ((= (_ (lambda @t49 (and @t48 @t47)) @t41) @t46))) % 0.39/0.57 (step @p37 :rule trans :premises (@p36 @p35)) % 0.39/0.57 (step @p38 :rule eq-symm :args (@t9 @t1)) % 0.39/0.57 (step @p39 :rule refl :args (@t40)) % 0.39/0.57 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t50)) % 0.39/0.57 (step @p41 :rule cong :premises (@p40) :args (@t51)) % 0.39/0.57 (step @p42 :rule beta-reduce :args ((= (_ @t54 @t1) @t51))) % 0.39/0.57 (step @p43 :rule trans :premises (@p42 @p41)) % 0.39/0.57 (step @p44 :rule refl :args (@t1)) % 0.39/0.57 (step @p45 :rule beta-reduce :args ((= (_ (lambda @t55 (or @t39 @t53)) @t2) @t54))) % 0.39/0.57 (step @p46 :rule refl :args (@t2)) % 0.39/0.57 (step @p47 :rule eq-symm :args (@t52 @t9)) % 0.39/0.57 (step @p48 :rule refl :args (@t39)) % 0.39/0.57 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t56)) % 0.39/0.57 (step @p50 :rule cong :premises (@p49) :args ((lambda @t55 @t56))) % 0.39/0.57 (step @p51 :rule ho_cong :premises (@p50 @p46)) % 0.39/0.57 (step @p52 :rule trans :premises (@p51 @p45)) % 0.39/0.57 (step @p53 :rule refl :args (@t2)) % 0.39/0.57 (step @p54 :rule alpha_equiv :args (@t58 (@list @t2) (@list @t52))) % 0.39/0.57 (step @p55 :rule ho_cong :premises (@p54 @p53)) % 0.39/0.57 (step @p56 :rule trans :premises (@p55 @p52)) % 0.39/0.57 (step @p57 :rule ho_cong :premises (@p56 @p44)) % 0.39/0.57 (step @p58 :rule trans :premises (@p57 @p43)) % 0.39/0.57 (step @p59 :rule aci_norm :args ((= (or false @t47) @t47))) % 0.39/0.57 (step @p60 :rule refl :args (@t47)) % 0.39/0.57 (step @p61 :rule cong :premises (@p22) :args (@t59)) % 0.39/0.57 (step @p62 :rule trans :premises (@p61 @p17)) % 0.39/0.57 (step @p63 :rule nary_cong :premises (@p62 @p60) :args (@t60)) % 0.39/0.57 (step @p64 :rule trans :premises (@p63 @p59)) % 0.39/0.57 (step @p65 :rule quant-var-elim-eq :args ((= (forall @t64 (or (not (= @t61 @t2)) @t63 @t62)) @t60))) % 0.39/0.57 (step @p66 :rule refl :args (@t62)) % 0.39/0.57 (step @p67 :rule refl :args (@t63)) % 0.39/0.57 (step @p68 :rule eq-symm :args (@t2 @t61)) % 0.39/0.57 (step @p69 :rule cong :premises (@p68) :args (@t63)) % 0.39/0.57 (step @p70 :rule nary_cong :premises (@p69 @p67 @p66) :args (@t65)) % 0.39/0.57 (step @p71 :rule aci_norm :args ((= @t66 @t65))) % 0.39/0.57 (step @p72 :rule trans :premises (@p71 @p70)) % 0.39/0.57 (step @p73 :rule cong :premises (@p72) :args (@t67)) % 0.39/0.57 (step @p74 :rule trans :premises (@p73 @p65)) % 0.39/0.57 (step @p75 :rule trans :premises (@p74 @p64)) % 0.39/0.57 (step @p76 :rule aci_norm :args ((= (or false @t48) @t48))) % 0.39/0.57 (step @p77 :rule refl :args (@t48)) % 0.39/0.57 (step @p78 :rule cong :premises (@p28) :args (@t68)) % 0.39/0.57 (step @p79 :rule trans :premises (@p78 @p17)) % 0.39/0.57 (step @p80 :rule nary_cong :premises (@p79 @p77) :args (@t69)) % 0.39/0.57 (step @p81 :rule trans :premises (@p80 @p76)) % 0.39/0.57 (step @p82 :rule quant-var-elim-eq :args ((= (forall @t73 (or (not (= @t70 @t1)) @t72 @t71)) @t69))) % 0.39/0.57 (step @p83 :rule refl :args (@t71)) % 0.39/0.57 (step @p84 :rule refl :args (@t72)) % 0.39/0.57 (step @p85 :rule eq-symm :args (@t1 @t70)) % 0.39/0.57 (step @p86 :rule cong :premises (@p85) :args (@t72)) % 0.39/0.57 (step @p87 :rule nary_cong :premises (@p86 @p84 @p83) :args (@t74)) % 0.39/0.57 (step @p88 :rule aci_norm :args ((= @t75 @t74))) % 0.39/0.57 (step @p89 :rule trans :premises (@p88 @p87)) % 0.39/0.57 (step @p90 :rule cong :premises (@p89) :args (@t76)) % 0.39/0.57 (step @p91 :rule trans :premises (@p90 @p82)) % 0.39/0.57 (step @p92 :rule trans :premises (@p91 @p81)) % 0.39/0.57 (step @p93 :rule nary_cong :premises (@p92 @p75) :args ((and @t76 @t67))) % 0.39/0.57 (step @p94 :rule alpha_equiv :args (@t80 @t81 (@list @t61))) % 0.39/0.57 (step @p95 :rule alpha_equiv :args (@t84 @t81 (@list @t70))) % 0.39/0.57 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t85)) % 0.39/0.57 (step @p97 :rule quant-miniscope-and :args ((= (forall @t30 (and @t83 @t79)) @t85))) % 0.39/0.57 (step @p98 :rule trans :premises (@p97 @p96)) % 0.39/0.57 (step @p99 :rule trans :premises (@p98 @p93)) % 0.39/0.57 (step @p100 :rule bool-or-and-distrib :args (@t82 @t78 true @t77 false)) % 0.39/0.57 (step @p101 :rule cong :premises (@p100) :args ((forall @t30 (or (and @t82 @t78) @t77)))) % 0.39/0.57 (step @p102 :rule trans :premises (@p101 @p99)) % 0.39/0.58 (step @p103 :rule refl :args (@t77)) % 0.39/0.58 (step @p104 :rule bool-or-de-morgan :args (@t39 @t40 false)) % 0.39/0.58 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t86)) % 0.39/0.58 (step @p106 :rule cong :premises (@p105) :args ((forall @t30 @t86))) % 0.39/0.58 (step @p107 :rule trans :premises (@p106 @p102)) % 0.39/0.58 (step @p108 :rule refl :args (@t77)) % 0.39/0.58 (step @p109 :rule beta-reduce :args ((= @t88 @t57))) % 0.39/0.58 (step @p110 :rule cong :premises (@p109) :args (@t89)) % 0.39/0.58 (step @p111 :rule nary_cong :premises (@p110 @p108) :args (@t90)) % 0.39/0.58 (step @p112 :rule cong :premises (@p111) :args (@t91)) % 0.39/0.58 (step @p113 :rule trans :premises (@p112 @p107)) % 0.39/0.58 (step @p114 :rule cong :premises (@p113) :args (@t92)) % 0.39/0.58 (step @p115 :rule beta-reduce :args ((= (_ @t94 @t87) @t92))) % 0.39/0.58 (step @p116 :rule trans :premises (@p115 @p114)) % 0.39/0.58 (step @p117 :rule beta-reduce :args ((= (_ @t95 @t2) @t87))) % 0.39/0.58 (step @p118 :rule beta-reduce :args ((= @t96 @t95))) % 0.39/0.58 (step @p119 :rule ho_cong :premises (@p118 @p46)) % 0.39/0.58 (step @p120 :rule trans :premises (@p119 @p117)) % 0.39/0.58 (step @p121 :rule refl :args (@t94)) % 0.39/0.58 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.39/0.58 (step @p123 :rule trans :premises (@p122 @p116)) % 0.39/0.58 (step @p124 :rule ho_cong :premises (@p123 @p58)) % 0.39/0.58 (step @p125 :rule trans :premises (@p124 @p37)) % 0.39/0.58 (step @p126 :rule cong :premises (@p125) :args (@t97)) % 0.39/0.58 (step @p127 :rule trans :premises (@p126 @p18)) % 0.39/0.58 (step @p128 :rule cong :premises (@p127) :args ((not @t97))) % 0.39/0.58 (step @p129 :rule trans :premises (@p128 @p17)) % 0.39/0.58 (step @p130 :rule eq-symm :args (@t9 @t2)) % 0.39/0.58 (step @p131 :rule nary_cong :premises (@p38 @p130) :args (@t11)) % 0.39/0.58 (step @p132 :rule cong :premises (@p131) :args (@t13)) % 0.39/0.58 (step @p133 :rule trans :premises (@p6 @p132)) % 0.39/0.58 (step @p134 :rule ho_cong :premises (@p133 @p46)) % 0.39/0.58 (step @p135 :rule ho_cong :premises (@p134 @p44)) % 0.39/0.58 (step @p136 :rule ho_cong :premises (@p133 @p44)) % 0.39/0.58 (step @p137 :rule ho_cong :premises (@p136 @p46)) % 0.39/0.58 (step @p138 :rule refl :args (@t77)) % 0.39/0.58 (step @p139 :rule refl :args (@t16)) % 0.39/0.58 (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t16 @t77))) % 0.39/0.58 (step @p141 :rule symm :premises (@p140)) % 0.39/0.58 (step @p142 :rule eq_resolve :premises (@p139 @p141)) % 0.39/0.58 (step @p143 :rule refl :args (@t93)) % 0.39/0.58 (step @p144 :rule refl :args (@t18)) % 0.39/0.58 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t18 @t93))) % 0.39/0.58 (step @p146 :rule symm :premises (@p145)) % 0.39/0.58 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.39/0.58 (step @p148 :rule cong :premises (@p147) :args (@t21)) % 0.39/0.58 (step @p149 :rule nary_cong :premises (@p148 @p142) :args (@t98)) % 0.39/0.58 (step @p150 :rule cong :premises (@p149) :args ((forall @t30 @t98))) % 0.39/0.58 (step @p151 :rule bool-impl-elim :args (@t18 @t16)) % 0.39/0.58 (step @p152 :rule cong :premises (@p151) :args (@t31)) % 0.39/0.58 (step @p153 :rule trans :premises (@p152 @p150)) % 0.39/0.58 (step @p154 :rule cong :premises (@p153) :args (@t32)) % 0.39/0.58 (step @p155 :rule trans :premises (@p14 @p154)) % 0.39/0.58 (step @p156 :rule ho_cong :premises (@p155 @p137)) % 0.39/0.58 (step @p157 :rule ho_cong :premises (@p156 @p135)) % 0.39/0.58 (step @p158 :rule cong :premises (@p157) :args (@t4)) % 0.39/0.58 (step @p159 :rule cong :premises (@p158) :args (@t5)) % 0.39/0.58 (step @p160 :rule trans :premises (@p159 @p129)) % 0.39/0.58 (step @p161 false :rule eq_resolve :premises (@p1 @p160)) % 0.39/0.58 ) % 0.39/0.58 % SZS output end Proof % 0.39/0.58 % cvc5 exiting %------------------------------------------------------------------------------