%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET609^3 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n008.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 08:48:12 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 : SET609^3 : TPTP v9.2.1. Released v3.6.0. % 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 : n008.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 16:04:48 EDT 2026 % 0.16/0.34 % CPUTime : % 0.32/0.50 %----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 $$unsorted 0) % 0.37/0.57 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.37/0.57 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.37/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.57 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.37/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.37/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.57 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.37/0.57 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.57 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.37/0.57 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.57 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.37/0.57 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.37/0.57 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.57 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.37/0.57 (define @t1 () (@var "Z" (-> $$unsorted Bool))) % 0.37/0.57 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.57 (define @t3 () (_ tptp.intersection @t2)) % 0.37/0.57 (define @t4 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.57 (define @t5 () (_ tptp.setminus @t2)) % 0.37/0.57 (define @t6 () (= (_ @t5 (_ (_ tptp.setminus @t4) @t1)) (_ (_ tptp.union (_ @t5 @t4)) (_ @t3 @t1)))) % 0.37/0.57 (define @t7 () (@list @t2 @t4 @t1)) % 0.37/0.57 (define @t8 () (forall @t7 @t6)) % 0.37/0.57 (define @t9 () (not @t8)) % 0.37/0.57 (define @t10 () (@var "X" $$unsorted)) % 0.37/0.57 (define @t11 () (@var "M" (-> $$unsorted Bool))) % 0.37/0.57 (define @t12 () (lambda (@list @t10 @t11) (_ @t11 @t10))) % 0.37/0.57 (define @t13 () (lambda (@list @t10) false)) % 0.37/0.57 (define @t14 () (@var "Y" $$unsorted)) % 0.37/0.57 (define @t15 () (@var "U" $$unsorted)) % 0.37/0.57 (define @t16 () (= @t15 @t10)) % 0.37/0.57 (define @t17 () (lambda (@list @t10 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.37/0.57 (define @t18 () (lambda (@list @t10 @t15) @t16)) % 0.37/0.57 (define @t19 () (_ @t4 @t15)) % 0.37/0.57 (define @t20 () (_ @t2 @t15)) % 0.37/0.57 (define @t21 () (@list @t2 @t4 @t15)) % 0.37/0.57 (define @t22 () (lambda @t21 (or @t20 @t19))) % 0.37/0.57 (define @t23 () (not @t20)) % 0.37/0.57 (define @t24 () (not @t19)) % 0.37/0.57 (define @t25 () (and @t20 @t24)) % 0.37/0.57 (define @t26 () (lambda @t21 (or @t25 (and @t23 @t19)))) % 0.37/0.57 (define @t27 () (and @t20 @t19)) % 0.37/0.57 (define @t28 () (lambda @t21 @t27)) % 0.37/0.57 (define @t29 () (lambda @t21 @t25)) % 0.37/0.57 (define @t30 () (lambda (@list @t2 @t15) @t23)) % 0.37/0.57 (define @t31 () (@list @t2 @t4)) % 0.37/0.57 (define @t32 () (lambda @t31 (= (_ @t3 @t4) tptp.emptyset))) % 0.37/0.57 (define @t33 () (@list @t15)) % 0.37/0.57 (define @t34 () (lambda @t31 (forall @t33 (=> @t20 @t19)))) % 0.37/0.57 (define @t35 () (exists @t33 @t27)) % 0.37/0.57 (define @t36 () (lambda @t31 @t35)) % 0.37/0.57 (define @t37 () (lambda @t31 (not @t35))) % 0.37/0.57 (define @t38 () (@const 0 $$unsorted)) % 0.37/0.57 (define @t39 () (_ @t1 @t15)) % 0.37/0.57 (define @t40 () (_ @t2 @t15)) % 0.37/0.57 (define @t41 () (_ @t4 @t15)) % 0.37/0.57 (define @t42 () (forall @t7 (= (lambda @t33 (and @t40 (not (and @t41 (not @t39))))) (lambda @t33 (or (and @t40 (not @t41)) (and @t40 @t39)))))) % 0.37/0.57 (define @t43 () (@quantifiers_skolemize @t42 2)) % 0.37/0.57 (define @t44 () (_ @t43 @t38)) % 0.37/0.57 (define @t45 () (not @t44)) % 0.37/0.57 (define @t46 () (@quantifiers_skolemize @t42 1)) % 0.37/0.57 (define @t47 () (_ @t46 @t38)) % 0.37/0.57 (define @t48 () (and @t47 @t45)) % 0.37/0.57 (define @t49 () (not @t48)) % 0.37/0.57 (define @t50 () (@quantifiers_skolemize @t42 0)) % 0.37/0.57 (define @t51 () (_ @t50 @t38)) % 0.37/0.57 (define @t52 () (not @t51)) % 0.37/0.57 (define @t53 () (not @t47)) % 0.37/0.57 (define @t54 () (and @t51 @t53)) % 0.37/0.57 (define @t55 () (and @t51 @t49)) % 0.37/0.57 (define @t56 () (and @t51 @t44)) % 0.37/0.57 (define @t57 () (or @t54 @t56)) % 0.37/0.57 (define @t58 () (_ @t1 @t15)) % 0.37/0.57 (define @t59 () (and @t20 @t58)) % 0.37/0.57 (define @t60 () (or @t25 @t59)) % 0.37/0.57 (define @t61 () (lambda @t33 @t60)) % 0.37/0.57 (define @t62 () (not @t58)) % 0.37/0.57 (define @t63 () (and @t19 @t62)) % 0.37/0.57 (define @t64 () (not @t63)) % 0.37/0.57 (define @t65 () (and @t20 @t64)) % 0.37/0.57 (define @t66 () (lambda @t33 @t65)) % 0.37/0.57 (define @t67 () (= @t66 @t61)) % 0.37/0.57 (define @t68 () (lambda @t33 @t59)) % 0.37/0.57 (define @t69 () (_ @t68 @t15)) % 0.37/0.57 (define @t70 () (or @t25 @t69)) % 0.37/0.57 (define @t71 () (lambda @t33 @t70)) % 0.37/0.57 (define @t72 () (@var "BOUND_VARIABLE_7669" (-> $$unsorted Bool))) % 0.37/0.57 (define @t73 () (_ @t72 @t15)) % 0.37/0.57 (define @t74 () (@list @t72 @t15)) % 0.37/0.57 (define @t75 () (@list @t4 @t15)) % 0.37/0.57 (define @t76 () (lambda @t75 @t27)) % 0.37/0.57 (define @t77 () (_ @t28 @t2)) % 0.37/0.57 (define @t78 () (lambda @t33 @t25)) % 0.37/0.57 (define @t79 () (_ @t78 @t15)) % 0.37/0.57 (define @t80 () (or @t79 @t73)) % 0.37/0.57 (define @t81 () (lambda @t74 @t80)) % 0.37/0.57 (define @t82 () (@list @t4)) % 0.37/0.57 (define @t83 () (lambda @t75 @t25)) % 0.37/0.57 (define @t84 () (_ @t29 @t2)) % 0.37/0.57 (define @t85 () (lambda @t33 @t63)) % 0.37/0.57 (define @t86 () (_ @t85 @t15)) % 0.37/0.57 (define @t87 () (not @t86)) % 0.37/0.57 (define @t88 () (and @t20 @t87)) % 0.37/0.57 (define @t89 () (lambda @t33 @t88)) % 0.37/0.57 (define @t90 () (@var "BOUND_VARIABLE_7639" (-> $$unsorted Bool))) % 0.37/0.57 (define @t91 () (not (_ @t90 @t15))) % 0.37/0.57 (define @t92 () (lambda (@list @t90 @t15) (and @t19 @t91))) % 0.37/0.57 (define @t93 () (= (_ @t84 (_ (_ @t29 @t4) @t1)) (_ (_ @t22 (_ @t84 @t4)) (_ @t77 @t1)))) % 0.37/0.57 (define @t94 () (forall @t7 @t93)) % 0.37/0.57 (define @t95 () (_ @t43 @t15)) % 0.37/0.57 (define @t96 () (_ @t46 @t15)) % 0.37/0.57 (define @t97 () (_ @t50 @t15)) % 0.37/0.57 (define @t98 () (lambda @t33 (and @t97 (not (and @t96 (not @t95)))))) % 0.37/0.57 (define @t99 () (@purify @t98)) % 0.37/0.57 (define @t100 () (lambda @t33 (or (and @t97 (not @t96)) (and @t97 @t95)))) % 0.37/0.57 (define @t101 () (@purify @t100)) % 0.37/0.57 (define @t102 () (= @t101 @t99)) % 0.37/0.57 (define @t103 () (not @t102)) % 0.37/0.57 (define @t104 () (not @t42)) % 0.37/0.57 (define @t105 () (= @t98 @t100)) % 0.37/0.57 (define @t106 () (not @t105)) % 0.37/0.57 (define @t107 () (@list true)) % 0.37/0.57 (define @t108 () (= (_ @t98 @t38) @t55)) % 0.37/0.57 (define @t109 () (_ @t99 @t38)) % 0.37/0.57 (define @t110 () (= (_ @t100 @t38) @t57)) % 0.37/0.57 (define @t111 () (_ @t101 @t38)) % 0.37/0.57 (define @t112 () (= @t111 @t109)) % 0.37/0.57 (define @t113 () (not @t112)) % 0.37/0.57 (define @t114 () (or @t102 @t113)) % 0.37/0.57 (define @t115 () (= @t55 @t57)) % 0.37/0.57 (define @t116 () (@list true false false false true)) % 0.37/0.57 (define @t117 () (not @t54)) % 0.37/0.57 (define @t118 () (not @t56)) % 0.37/0.57 (define @t119 () (not @t55)) % 0.37/0.57 (define @t120 () (@list @t51)) % 0.37/0.57 (assume @p1 @t9) % 0.37/0.57 (assume @p2 true) % 0.37/0.57 (step @p3 (= tptp.in @t12) :rule refl :args (@t12)) % 0.37/0.57 (step @p4 (= tptp.is_a @t12) :rule refl :args (@t12)) % 0.37/0.57 (step @p5 (= tptp.emptyset @t13) :rule refl :args (@t13)) % 0.37/0.57 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.37/0.57 (step @p7 (= tptp.singleton @t18) :rule refl :args (@t18)) % 0.37/0.57 (step @p8 (= tptp.union @t22) :rule refl :args (@t22)) % 0.37/0.57 (step @p9 (= tptp.excl_union @t26) :rule refl :args (@t26)) % 0.37/0.57 (step @p10 (= tptp.intersection @t28) :rule refl :args (@t28)) % 0.37/0.57 (step @p11 (= tptp.setminus @t29) :rule refl :args (@t29)) % 0.37/0.57 (step @p12 (= tptp.complement @t30) :rule refl :args (@t30)) % 0.37/0.57 (step @p13 (= tptp.disjoint @t32) :rule refl :args (@t32)) % 0.37/0.57 (step @p14 (= tptp.subset @t34) :rule refl :args (@t34)) % 0.37/0.57 (step @p15 (= tptp.meets @t36) :rule refl :args (@t36)) % 0.37/0.57 (step @p16 (= tptp.misses @t37) :rule refl :args (@t37)) % 0.37/0.57 (step @p17 :rule cnf_and_pos :args (@t48 0)) % 0.37/0.57 (step @p18 :rule reordering :premises (@p17) :args ((or @t47 @t49))) % 0.37/0.57 (step @p19 :rule bool-double-not-elim :args (@t47)) % 0.37/0.57 (step @p20 :rule refl :args (@t52)) % 0.37/0.57 (step @p21 :rule refl :args (@t54)) % 0.37/0.57 (step @p22 :rule nary_cong :premises (@p21 @p20 @p19) :args ((or @t54 @t52 (not @t53)))) % 0.37/0.57 (step @p23 :rule cnf_and_neg :args (@t54)) % 0.37/0.57 (step @p24 :rule eq_resolve :premises (@p23 @p22)) % 0.37/0.57 (step @p25 :rule reordering :premises (@p24) :args ((or @t47 @t54 @t52))) % 0.37/0.57 (step @p26 :rule bool-double-not-elim :args (@t48)) % 0.37/0.57 (step @p27 :rule refl :args (@t55)) % 0.37/0.57 (step @p28 :rule nary_cong :premises (@p27 @p20 @p26) :args ((or @t55 @t52 (not @t49)))) % 0.37/0.57 (step @p29 :rule cnf_and_neg :args (@t55)) % 0.37/0.57 (step @p30 :rule eq_resolve :premises (@p29 @p28)) % 0.37/0.57 (step @p31 :rule reordering :premises (@p30) :args ((or @t48 @t55 @t52))) % 0.37/0.57 (step @p32 :rule cnf_or_neg :args (@t57 0)) % 0.37/0.57 (step @p33 :rule refl :args (@t39)) % 0.37/0.57 (step @p34 :rule refl :args (@t58)) % 0.37/0.57 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t58 @t39))) % 0.37/0.57 (step @p36 :rule symm :premises (@p35)) % 0.37/0.57 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.37/0.57 (step @p38 :rule refl :args (@t40)) % 0.37/0.57 (step @p39 :rule refl :args (@t20)) % 0.37/0.57 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t20 @t40))) % 0.37/0.57 (step @p41 :rule symm :premises (@p40)) % 0.37/0.57 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.37/0.57 (step @p43 :rule nary_cong :premises (@p42 @p37) :args (@t59)) % 0.37/0.57 (step @p44 :rule refl :args (@t41)) % 0.37/0.57 (step @p45 :rule refl :args (@t19)) % 0.37/0.57 (step @p46 :rule cong :premises (@p45 @p44) :args ((= @t19 @t41))) % 0.37/0.57 (step @p47 :rule symm :premises (@p46)) % 0.37/0.57 (step @p48 :rule eq_resolve :premises (@p45 @p47)) % 0.37/0.57 (step @p49 :rule cong :premises (@p48) :args (@t24)) % 0.37/0.57 (step @p50 :rule nary_cong :premises (@p42 @p49) :args (@t25)) % 0.37/0.57 (step @p51 :rule nary_cong :premises (@p50 @p43) :args (@t60)) % 0.37/0.57 (step @p52 :rule cong :premises (@p51) :args (@t61)) % 0.37/0.57 (step @p53 :rule cong :premises (@p37) :args (@t62)) % 0.37/0.57 (step @p54 :rule nary_cong :premises (@p48 @p53) :args (@t63)) % 0.37/0.57 (step @p55 :rule cong :premises (@p54) :args (@t64)) % 0.37/0.57 (step @p56 :rule nary_cong :premises (@p42 @p55) :args (@t65)) % 0.37/0.57 (step @p57 :rule cong :premises (@p56) :args (@t66)) % 0.37/0.57 (step @p58 :rule cong :premises (@p57 @p52) :args (@t67)) % 0.37/0.57 (step @p59 :rule cong :premises (@p58) :args ((forall @t7 @t67))) % 0.37/0.57 (step @p60 :rule beta-reduce :args ((= @t69 @t59))) % 0.37/0.57 (step @p61 :rule refl :args (@t25)) % 0.37/0.57 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t70)) % 0.37/0.57 (step @p63 :rule cong :premises (@p62) :args (@t71)) % 0.37/0.57 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t74 (or @t25 @t73)) @t68) @t71))) % 0.37/0.57 (step @p65 :rule trans :premises (@p64 @p63)) % 0.37/0.57 (step @p66 :rule beta-reduce :args ((= (_ @t76 @t1) @t68))) % 0.37/0.57 (step @p67 :rule refl :args (@t1)) % 0.37/0.57 (step @p68 :rule beta-reduce :args ((= @t77 @t76))) % 0.37/0.57 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.37/0.57 (step @p70 :rule trans :premises (@p69 @p66)) % 0.37/0.57 (step @p71 :rule refl :args (@t73)) % 0.37/0.57 (step @p72 :rule beta-reduce :args ((= @t79 @t25))) % 0.37/0.57 (step @p73 :rule nary_cong :premises (@p72 @p71) :args (@t80)) % 0.37/0.57 (step @p74 :rule cong :premises (@p73) :args (@t81)) % 0.37/0.57 (step @p75 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t72 @t15) (or @t20 @t73)) @t78) @t81))) % 0.37/0.57 (step @p76 :rule trans :premises (@p75 @p74)) % 0.37/0.57 (step @p77 :rule refl :args (@t78)) % 0.37/0.57 (step @p78 :rule alpha_equiv :args (@t22 @t82 (@list @t72))) % 0.37/0.57 (step @p79 :rule ho_cong :premises (@p78 @p77)) % 0.37/0.57 (step @p80 :rule trans :premises (@p79 @p76)) % 0.37/0.57 (step @p81 :rule beta-reduce :args ((= (_ @t83 @t4) @t78))) % 0.37/0.57 (step @p82 :rule refl :args (@t4)) % 0.37/0.57 (step @p83 :rule beta-reduce :args ((= @t84 @t83))) % 0.37/0.57 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.37/0.57 (step @p85 :rule trans :premises (@p84 @p81)) % 0.37/0.57 (step @p86 :rule refl :args (@t22)) % 0.37/0.57 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 0.37/0.57 (step @p88 :rule trans :premises (@p87 @p80)) % 0.37/0.57 (step @p89 :rule ho_cong :premises (@p88 @p70)) % 0.37/0.57 (step @p90 :rule trans :premises (@p89 @p65)) % 0.37/0.57 (step @p91 :rule beta-reduce :args ((= @t86 @t63))) % 0.37/0.57 (step @p92 :rule cong :premises (@p91) :args (@t87)) % 0.37/0.57 (step @p93 :rule refl :args (@t20)) % 0.37/0.57 (step @p94 :rule nary_cong :premises (@p93 @p92) :args (@t88)) % 0.37/0.57 (step @p95 :rule cong :premises (@p94) :args (@t89)) % 0.37/0.57 (step @p96 :rule beta-reduce :args ((= (_ @t83 @t85) @t89))) % 0.37/0.57 (step @p97 :rule trans :premises (@p96 @p95)) % 0.37/0.57 (step @p98 :rule beta-reduce :args ((= (_ @t92 @t1) @t85))) % 0.37/0.57 (step @p99 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t90 @t15) (and @t20 @t91)) @t4) @t92))) % 0.37/0.57 (step @p100 :rule refl :args (@t4)) % 0.37/0.57 (step @p101 :rule alpha_equiv :args (@t29 @t82 (@list @t90))) % 0.37/0.57 (step @p102 :rule ho_cong :premises (@p101 @p100)) % 0.37/0.57 (step @p103 :rule trans :premises (@p102 @p99)) % 0.37/0.57 (step @p104 :rule ho_cong :premises (@p103 @p67)) % 0.37/0.57 (step @p105 :rule trans :premises (@p104 @p98)) % 0.37/0.57 (step @p106 :rule ho_cong :premises (@p83 @p105)) % 0.37/0.57 (step @p107 :rule trans :premises (@p106 @p97)) % 0.37/0.57 (step @p108 :rule cong :premises (@p107 @p90) :args (@t93)) % 0.37/0.57 (step @p109 :rule cong :premises (@p108) :args (@t94)) % 0.37/0.57 (step @p110 :rule trans :premises (@p109 @p59)) % 0.37/0.57 (step @p111 :rule cong :premises (@p110) :args ((not @t94))) % 0.37/0.57 (step @p112 :rule refl :args (@t2)) % 0.37/0.57 (step @p113 :rule ho_cong :premises (@p10 @p112)) % 0.37/0.57 (step @p114 :rule ho_cong :premises (@p113 @p67)) % 0.37/0.57 (step @p115 :rule ho_cong :premises (@p11 @p112)) % 0.37/0.57 (step @p116 :rule ho_cong :premises (@p115 @p82)) % 0.37/0.57 (step @p117 :rule ho_cong :premises (@p8 @p116)) % 0.37/0.57 (step @p118 :rule ho_cong :premises (@p117 @p114)) % 0.37/0.57 (step @p119 :rule ho_cong :premises (@p11 @p82)) % 0.37/0.57 (step @p120 :rule ho_cong :premises (@p119 @p67)) % 0.37/0.57 (step @p121 :rule ho_cong :premises (@p115 @p120)) % 0.37/0.57 (step @p122 :rule cong :premises (@p121 @p118) :args (@t6)) % 0.37/0.57 (step @p123 :rule cong :premises (@p122) :args (@t8)) % 0.37/0.57 (step @p124 :rule cong :premises (@p123) :args (@t9)) % 0.37/0.57 (step @p125 :rule trans :premises (@p124 @p111)) % 0.37/0.57 (step @p126 :rule eq_resolve :premises (@p1 @p125)) % 0.37/0.57 (step @p127 :rule refl :args (@t103)) % 0.37/0.57 (step @p128 :rule bool-double-not-elim :args (@t42)) % 0.37/0.57 (step @p129 :rule nary_cong :premises (@p128 @p127) :args ((or (not @t104) @t103))) % 0.37/0.57 (step @p130 :rule eq-symm :args (@t99 @t101)) % 0.37/0.57 (step @p131 :rule eq-refl :args (@t100)) % 0.37/0.57 (step @p132 :rule skolem_intro :args (@t101)) % 0.37/0.57 (step @p133 :rule refl :args (@t100)) % 0.37/0.57 (step @p134 :rule cong :premises (@p133 @p132) :args ((= @t100 @t101))) % 0.37/0.57 (step @p135 :rule trans :premises (@p134 @p131)) % 0.37/0.57 (step @p136 :rule true_elim :premises (@p135)) % 0.37/0.57 (step @p137 :rule eq-refl :args (@t98)) % 0.37/0.57 (step @p138 :rule skolem_intro :args (@t99)) % 0.37/0.57 (step @p139 :rule refl :args (@t98)) % 0.37/0.57 (step @p140 :rule cong :premises (@p139 @p138) :args ((= @t98 @t99))) % 0.37/0.57 (step @p141 :rule trans :premises (@p140 @p137)) % 0.37/0.57 (step @p142 :rule true_elim :premises (@p141)) % 0.37/0.57 (step @p143 :rule cong :premises (@p142 @p136) :args (@t105)) % 0.37/0.57 (step @p144 :rule trans :premises (@p143 @p130)) % 0.37/0.57 (step @p145 :rule cong :premises (@p144) :args (@t106)) % 0.37/0.57 (step @p146 :rule refl :args (@t104)) % 0.37/0.57 (step @p147 :rule cong :premises (@p146 @p145) :args ((=> @t104 @t106))) % 0.37/0.57 (assume-push @p220 @t104) % 0.37/0.57 (step @p149 :rule skolemize :premises (@p126)) % 0.37/0.57 (step-pop @p221 :rule scope :premises (@p149)) % 0.37/0.57 (step @p150 :rule process_scope :premises (@p221) :args (@t106)) % 0.37/0.57 (step @p152 :rule eq_resolve :premises (@p150 @p147)) % 0.37/0.57 (step @p153 :rule implies_elim :premises (@p152)) % 0.37/0.57 (step @p154 :rule eq_resolve :premises (@p153 @p129)) % 0.37/0.57 (step @p155 :rule chain_m_resolution :premises (@p154 @p126) :args (@t103 @t107 (@list @t42))) % 0.37/0.57 (step @p156 :rule eq-symm :args (@t57 @t55)) % 0.37/0.57 (step @p157 :rule eq-refl :args (@t55)) % 0.37/0.57 (step @p158 :rule beta-reduce :args (@t108)) % 0.37/0.57 (step @p159 :rule cong :premises (@p158 @p27) :args (@t108)) % 0.37/0.57 (step @p160 :rule trans :premises (@p159 @p157)) % 0.37/0.57 (step @p161 :rule refl :args (@t38)) % 0.37/0.57 (step @p162 :rule ho_cong :premises (@p138 @p161)) % 0.37/0.57 (step @p163 :rule cong :premises (@p162 @p27) :args ((= @t109 @t55))) % 0.37/0.57 (step @p164 :rule trans :premises (@p163 @p160)) % 0.37/0.57 (step @p165 :rule true_elim :premises (@p164)) % 0.37/0.57 (step @p166 :rule eq-refl :args (@t57)) % 0.37/0.57 (step @p167 :rule refl :args (@t57)) % 0.37/0.57 (step @p168 :rule beta-reduce :args (@t110)) % 0.37/0.57 (step @p169 :rule cong :premises (@p168 @p167) :args (@t110)) % 0.37/0.57 (step @p170 :rule trans :premises (@p169 @p166)) % 0.37/0.57 (step @p171 :rule ho_cong :premises (@p132 @p161)) % 0.37/0.57 (step @p172 :rule cong :premises (@p171 @p167) :args ((= @t111 @t57))) % 0.37/0.57 (step @p173 :rule trans :premises (@p172 @p170)) % 0.37/0.57 (step @p174 :rule true_elim :premises (@p173)) % 0.37/0.57 (step @p175 :rule cong :premises (@p174 @p165) :args (@t112)) % 0.37/0.57 (step @p176 :rule trans :premises (@p175 @p156)) % 0.37/0.57 (step @p177 :rule cong :premises (@p176) :args (@t113)) % 0.37/0.57 (step @p178 :rule refl :args (@t102)) % 0.37/0.57 (step @p179 :rule nary_cong :premises (@p178 @p177) :args (@t114)) % 0.37/0.57 ; WARNING: add trust step for TRUST % 0.37/0.57 ; trust TRUST THEORY_LEMMA % 0.37/0.57 (step @p180 :rule trust :premises () :args (@t114)) % 0.37/0.57 (step @p181 :rule eq_resolve :premises (@p180 @p179)) % 0.37/0.57 (step @p182 :rule chain_m_resolution :premises (@p181 @p155) :args ((not @t115) @t107 (@list @t102))) % 0.37/0.57 (step @p183 :rule cnf_equiv_neg2 :args (@t115)) % 0.37/0.57 (step @p184 :rule chain_m_resolution :premises (@p183 @p182 @p32 @p31 @p25 @p18) :args ((or @t47 @t52) @t116 (@list @t115 @t57 @t55 @t54 @t48))) % 0.37/0.57 (step @p185 :rule cnf_and_pos :args (@t54 1)) % 0.37/0.57 (step @p186 :rule reordering :premises (@p185) :args ((or @t53 @t117))) % 0.37/0.57 (step @p187 :rule cnf_and_pos :args (@t48 1)) % 0.37/0.57 (step @p188 :rule reordering :premises (@p187) :args ((or @t45 @t49))) % 0.37/0.57 (step @p189 :rule cnf_and_neg :args (@t56)) % 0.37/0.57 (step @p190 :rule reordering :premises (@p189) :args ((or @t45 @t56 @t52))) % 0.37/0.57 (step @p191 :rule cnf_or_neg :args (@t57 1)) % 0.37/0.57 (step @p192 :rule chain_m_resolution :premises (@p183 @p182 @p191 @p31 @p190 @p188) :args ((or @t45 @t52) @t116 (@list @t115 @t57 @t55 @t56 @t48))) % 0.37/0.57 (step @p193 :rule bool-double-not-elim :args (@t44)) % 0.37/0.57 (step @p194 :rule refl :args (@t53)) % 0.37/0.57 (step @p195 :rule refl :args (@t48)) % 0.37/0.57 (step @p196 :rule nary_cong :premises (@p195 @p194 @p193) :args ((or @t48 @t53 (not @t45)))) % 0.37/0.57 (step @p197 :rule cnf_and_neg :args (@t48)) % 0.37/0.57 (step @p198 :rule eq_resolve :premises (@p197 @p196)) % 0.37/0.57 (step @p199 :rule reordering :premises (@p198) :args ((or @t44 @t48 @t53))) % 0.37/0.57 (step @p200 :rule cnf_and_pos :args (@t56 1)) % 0.37/0.57 (step @p201 :rule reordering :premises (@p200) :args ((or @t44 @t118))) % 0.37/0.57 (step @p202 :rule cnf_and_pos :args (@t55 1)) % 0.37/0.57 (step @p203 :rule reordering :premises (@p202) :args ((or @t49 @t119))) % 0.37/0.57 (step @p204 :rule cnf_or_pos :args (@t57)) % 0.37/0.57 (step @p205 :rule reordering :premises (@p204) :args ((or @t54 @t56 (not @t57)))) % 0.37/0.57 (step @p206 :rule cnf_equiv_neg1 :args (@t115)) % 0.37/0.57 (step @p207 :rule reordering :premises (@p206) :args ((or @t55 @t57 @t115))) % 0.37/0.57 (step @p208 :rule chain_m_resolution :premises (@p207 @p182 @p205 @p203 @p201 @p199 @p192 @p186 @p184) :args (@t52 (@list true true true true false true true false) (@list @t115 @t57 @t55 @t56 @t48 @t44 @t54 @t47))) % 0.37/0.57 (step @p209 :rule cnf_and_pos :args (@t54 0)) % 0.37/0.57 (step @p210 :rule reordering :premises (@p209) :args ((or @t51 @t117))) % 0.37/0.57 (step @p211 :rule chain_m_resolution :premises (@p210 @p208) :args (@t117 @t107 @t120)) % 0.37/0.57 (step @p212 :rule cnf_and_pos :args (@t56 0)) % 0.37/0.57 (step @p213 :rule reordering :premises (@p212) :args ((or @t51 @t118))) % 0.37/0.57 (step @p214 :rule chain_m_resolution :premises (@p213 @p208) :args (@t118 @t107 @t120)) % 0.37/0.57 (step @p215 :rule cnf_and_pos :args (@t55 0)) % 0.37/0.57 (step @p216 :rule reordering :premises (@p215) :args ((or @t51 @t119))) % 0.37/0.57 (step @p217 :rule chain_m_resolution :premises (@p216 @p208) :args (@t119 @t107 @t120)) % 0.37/0.57 (step @p218 :rule chain_m_resolution :premises (@p207 @p217 @p182) :args (@t57 (@list true true) (@list @t55 @t115))) % 0.37/0.57 (step @p219 false :rule chain_m_resolution :premises (@p205 @p218 @p214 @p211) :args (false (@list false true true) (@list @t57 @t56 @t54))) % 0.37/0.57 ) % 0.37/0.57 % SZS output end Proof % 0.37/0.57 % cvc5 exiting %------------------------------------------------------------------------------