%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET614^3 : 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 : n012.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 08:48:14 AM UTC 2026 % Result : Theorem 0.16s 0.36s % Output : Proof 0.16s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET614^3 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 16:04:48 EDT 2026 % 0.07/0.25 % CPUTime : % 0.16/0.33 %----Proving TH0 % 0.16/0.36 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.16/0.36 % SZS status Theorem % 0.16/0.36 % SZS output start Proof % 0.16/0.36 ( % 0.16/0.36 (declare-sort $$unsorted 0) % 0.16/0.36 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.16/0.36 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.16/0.36 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.16/0.36 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.16/0.36 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.16/0.36 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.16/0.36 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.16/0.36 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.16/0.36 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.16/0.36 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.16/0.36 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.16/0.36 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.16/0.36 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.16/0.36 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.16/0.36 (define @t1 () (@var "Z" (-> $$unsorted Bool))) % 0.16/0.36 (define @t2 () (@var "Y" (-> $$unsorted Bool))) % 0.16/0.36 (define @t3 () (@var "X" (-> $$unsorted Bool))) % 0.16/0.36 (define @t4 () (_ tptp.setminus @t3)) % 0.16/0.36 (define @t5 () (= (_ (_ tptp.setminus (_ @t4 @t2)) @t1) (_ @t4 (_ (_ tptp.union @t2) @t1)))) % 0.16/0.36 (define @t6 () (@list @t3 @t2 @t1)) % 0.16/0.36 (define @t7 () (forall @t6 @t5)) % 0.16/0.36 (define @t8 () (not @t7)) % 0.16/0.36 (define @t9 () (@var "X" $$unsorted)) % 0.16/0.36 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.16/0.36 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.16/0.36 (define @t12 () (lambda (@list @t9) false)) % 0.16/0.36 (define @t13 () (@var "Y" $$unsorted)) % 0.16/0.36 (define @t14 () (@var "U" $$unsorted)) % 0.16/0.36 (define @t15 () (= @t14 @t9)) % 0.16/0.36 (define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13)))) % 0.16/0.36 (define @t17 () (lambda (@list @t9 @t14) @t15)) % 0.16/0.36 (define @t18 () (_ @t2 @t14)) % 0.16/0.36 (define @t19 () (_ @t3 @t14)) % 0.16/0.36 (define @t20 () (@list @t3 @t2 @t14)) % 0.16/0.36 (define @t21 () (lambda @t20 (or @t19 @t18))) % 0.16/0.36 (define @t22 () (not @t19)) % 0.16/0.36 (define @t23 () (not @t18)) % 0.16/0.36 (define @t24 () (and @t19 @t23)) % 0.16/0.36 (define @t25 () (lambda @t20 (or @t24 (and @t22 @t18)))) % 0.16/0.36 (define @t26 () (and @t19 @t18)) % 0.16/0.36 (define @t27 () (lambda @t20 @t26)) % 0.16/0.36 (define @t28 () (lambda @t20 @t24)) % 0.16/0.36 (define @t29 () (lambda (@list @t3 @t14) @t22)) % 0.16/0.36 (define @t30 () (@list @t3 @t2)) % 0.16/0.36 (define @t31 () (lambda @t30 (= (_ (_ tptp.intersection @t3) @t2) tptp.emptyset))) % 0.16/0.36 (define @t32 () (@list @t14)) % 0.16/0.36 (define @t33 () (lambda @t30 (forall @t32 (=> @t19 @t18)))) % 0.16/0.36 (define @t34 () (exists @t32 @t26)) % 0.16/0.36 (define @t35 () (lambda @t30 @t34)) % 0.16/0.36 (define @t36 () (lambda @t30 (not @t34))) % 0.16/0.36 (define @t37 () (@const 0 $$unsorted)) % 0.16/0.36 (define @t38 () (_ @t1 @t14)) % 0.16/0.36 (define @t39 () (_ @t2 @t14)) % 0.16/0.36 (define @t40 () (_ @t3 @t14)) % 0.16/0.36 (define @t41 () (forall @t6 (= (lambda @t32 (and (not @t38) @t40 (not @t39))) (lambda @t32 (and @t40 (not (or @t39 @t38))))))) % 0.16/0.36 (define @t42 () (@quantifiers_skolemize @t41 1)) % 0.16/0.36 (define @t43 () (_ @t42 @t37)) % 0.16/0.36 (define @t44 () (not @t43)) % 0.16/0.36 (define @t45 () (@quantifiers_skolemize @t41 0)) % 0.16/0.36 (define @t46 () (_ @t45 @t37)) % 0.16/0.36 (define @t47 () (@quantifiers_skolemize @t41 2)) % 0.16/0.36 (define @t48 () (_ @t47 @t37)) % 0.16/0.36 (define @t49 () (not @t48)) % 0.16/0.36 (define @t50 () (and @t49 @t46 @t44)) % 0.16/0.36 (define @t51 () (not @t50)) % 0.16/0.36 (define @t52 () (or @t43 @t48)) % 0.16/0.36 (define @t53 () (not @t52)) % 0.16/0.36 (define @t54 () (and @t46 @t53)) % 0.16/0.36 (define @t55 () (not @t54)) % 0.16/0.36 (define @t56 () (_ @t1 @t14)) % 0.16/0.36 (define @t57 () (or @t18 @t56)) % 0.16/0.36 (define @t58 () (not @t57)) % 0.16/0.36 (define @t59 () (and @t19 @t58)) % 0.16/0.36 (define @t60 () (lambda @t32 @t59)) % 0.16/0.36 (define @t61 () (not @t56)) % 0.16/0.36 (define @t62 () (and @t61 @t19 @t23)) % 0.16/0.36 (define @t63 () (lambda @t32 @t62)) % 0.16/0.36 (define @t64 () (= @t63 @t60)) % 0.16/0.36 (define @t65 () (lambda @t32 @t57)) % 0.16/0.36 (define @t66 () (_ @t65 @t14)) % 0.16/0.36 (define @t67 () (not @t66)) % 0.16/0.36 (define @t68 () (and @t19 @t67)) % 0.16/0.36 (define @t69 () (lambda @t32 @t68)) % 0.16/0.36 (define @t70 () (lambda (@list @t2 @t14) @t24)) % 0.16/0.36 (define @t71 () (@var "BOUND_VARIABLE_7663" (-> $$unsorted Bool))) % 0.16/0.36 (define @t72 () (_ @t71 @t14)) % 0.16/0.36 (define @t73 () (lambda (@list @t71 @t14) (or @t18 @t72))) % 0.16/0.36 (define @t74 () (@list @t2)) % 0.16/0.36 (define @t75 () (_ @t28 @t3)) % 0.16/0.36 (define @t76 () (@var "BOUND_VARIABLE_7640" (-> $$unsorted Bool))) % 0.16/0.36 (define @t77 () (not (_ @t76 @t14))) % 0.16/0.36 (define @t78 () (and @t77 @t19 @t23)) % 0.16/0.36 (define @t79 () (@list @t76 @t14)) % 0.16/0.36 (define @t80 () (lambda @t32 @t24)) % 0.16/0.36 (define @t81 () (_ @t80 @t14)) % 0.16/0.36 (define @t82 () (and @t81 @t77)) % 0.16/0.36 (define @t83 () (lambda @t79 @t82)) % 0.16/0.36 (define @t84 () (= (_ (_ @t28 (_ @t75 @t2)) @t1) (_ @t75 (_ (_ @t21 @t2) @t1)))) % 0.16/0.36 (define @t85 () (forall @t6 @t84)) % 0.16/0.36 (define @t86 () (_ @t42 @t14)) % 0.16/0.36 (define @t87 () (_ @t45 @t14)) % 0.16/0.36 (define @t88 () (_ @t47 @t14)) % 0.16/0.36 (define @t89 () (lambda @t32 (and (not @t88) @t87 (not @t86)))) % 0.16/0.36 (define @t90 () (@purify @t89)) % 0.16/0.36 (define @t91 () (lambda @t32 (and @t87 (not (or @t86 @t88))))) % 0.16/0.36 (define @t92 () (@purify @t91)) % 0.16/0.36 (define @t93 () (= @t92 @t90)) % 0.16/0.36 (define @t94 () (not @t93)) % 0.16/0.36 (define @t95 () (not @t41)) % 0.16/0.36 (define @t96 () (= @t89 @t91)) % 0.16/0.36 (define @t97 () (not @t96)) % 0.16/0.36 (define @t98 () (@list true)) % 0.16/0.36 (define @t99 () (= (_ @t89 @t37) @t50)) % 0.16/0.36 (define @t100 () (_ @t90 @t37)) % 0.16/0.36 (define @t101 () (= (_ @t91 @t37) @t54)) % 0.16/0.36 (define @t102 () (_ @t92 @t37)) % 0.16/0.36 (define @t103 () (= @t102 @t100)) % 0.16/0.36 (define @t104 () (not @t103)) % 0.16/0.36 (define @t105 () (or @t93 @t104)) % 0.16/0.36 (define @t106 () (= @t50 @t54)) % 0.16/0.36 (define @t107 () (not @t46)) % 0.16/0.36 (define @t108 () (@list false)) % 0.16/0.36 (define @t109 () (@list @t48)) % 0.16/0.36 (assume @p1 @t8) % 0.16/0.36 (assume @p2 true) % 0.16/0.36 (step @p3 (= tptp.in @t11) :rule refl :args (@t11)) % 0.16/0.36 (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11)) % 0.16/0.36 (step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12)) % 0.16/0.36 (step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16)) % 0.16/0.36 (step @p7 (= tptp.singleton @t17) :rule refl :args (@t17)) % 0.16/0.36 (step @p8 (= tptp.union @t21) :rule refl :args (@t21)) % 0.16/0.36 (step @p9 (= tptp.excl_union @t25) :rule refl :args (@t25)) % 0.16/0.36 (step @p10 (= tptp.intersection @t27) :rule refl :args (@t27)) % 0.16/0.36 (step @p11 (= tptp.setminus @t28) :rule refl :args (@t28)) % 0.16/0.36 (step @p12 (= tptp.complement @t29) :rule refl :args (@t29)) % 0.16/0.36 (step @p13 (= tptp.disjoint @t31) :rule refl :args (@t31)) % 0.16/0.36 (step @p14 (= tptp.subset @t33) :rule refl :args (@t33)) % 0.16/0.36 (step @p15 (= tptp.meets @t35) :rule refl :args (@t35)) % 0.16/0.36 (step @p16 (= tptp.misses @t36) :rule refl :args (@t36)) % 0.16/0.36 (step @p17 :rule cnf_and_pos :args (@t50 1)) % 0.16/0.36 (step @p18 :rule reordering :premises (@p17) :args ((or @t46 @t51))) % 0.16/0.36 (step @p19 :rule cnf_and_pos :args (@t54 0)) % 0.16/0.36 (step @p20 :rule reordering :premises (@p19) :args ((or @t46 @t55))) % 0.16/0.36 (step @p21 :rule refl :args (@t38)) % 0.16/0.36 (step @p22 :rule refl :args (@t56)) % 0.16/0.36 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t56 @t38))) % 0.16/0.36 (step @p24 :rule symm :premises (@p23)) % 0.16/0.36 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.16/0.36 (step @p26 :rule refl :args (@t39)) % 0.16/0.36 (step @p27 :rule refl :args (@t18)) % 0.16/0.36 (step @p28 :rule cong :premises (@p27 @p26) :args ((= @t18 @t39))) % 0.16/0.36 (step @p29 :rule symm :premises (@p28)) % 0.16/0.36 (step @p30 :rule eq_resolve :premises (@p27 @p29)) % 0.16/0.36 (step @p31 :rule nary_cong :premises (@p30 @p25) :args (@t57)) % 0.16/0.36 (step @p32 :rule cong :premises (@p31) :args (@t58)) % 0.16/0.36 (step @p33 :rule refl :args (@t40)) % 0.16/0.36 (step @p34 :rule refl :args (@t19)) % 0.16/0.36 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t19 @t40))) % 0.16/0.36 (step @p36 :rule symm :premises (@p35)) % 0.16/0.36 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.16/0.36 (step @p38 :rule nary_cong :premises (@p37 @p32) :args (@t59)) % 0.16/0.36 (step @p39 :rule cong :premises (@p38) :args (@t60)) % 0.16/0.36 (step @p40 :rule cong :premises (@p30) :args (@t23)) % 0.16/0.36 (step @p41 :rule cong :premises (@p25) :args (@t61)) % 0.16/0.36 (step @p42 :rule nary_cong :premises (@p41 @p37 @p40) :args (@t62)) % 0.16/0.36 (step @p43 :rule cong :premises (@p42) :args (@t63)) % 0.16/0.36 (step @p44 :rule cong :premises (@p43 @p39) :args (@t64)) % 0.16/0.36 (step @p45 :rule cong :premises (@p44) :args ((forall @t6 @t64))) % 0.16/0.36 (step @p46 :rule beta-reduce :args ((= @t66 @t57))) % 0.16/0.36 (step @p47 :rule cong :premises (@p46) :args (@t67)) % 0.16/0.36 (step @p48 :rule refl :args (@t19)) % 0.16/0.36 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t68)) % 0.16/0.36 (step @p50 :rule cong :premises (@p49) :args (@t69)) % 0.16/0.36 (step @p51 :rule beta-reduce :args ((= (_ @t70 @t65) @t69))) % 0.16/0.36 (step @p52 :rule trans :premises (@p51 @p50)) % 0.16/0.36 (step @p53 :rule beta-reduce :args ((= (_ @t73 @t1) @t65))) % 0.16/0.36 (step @p54 :rule refl :args (@t1)) % 0.16/0.36 (step @p55 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t71 @t14) (or @t19 @t72)) @t2) @t73))) % 0.16/0.36 (step @p56 :rule refl :args (@t2)) % 0.16/0.36 (step @p57 :rule alpha_equiv :args (@t21 @t74 (@list @t71))) % 0.16/0.36 (step @p58 :rule ho_cong :premises (@p57 @p56)) % 0.16/0.36 (step @p59 :rule trans :premises (@p58 @p55)) % 0.16/0.36 (step @p60 :rule ho_cong :premises (@p59 @p54)) % 0.16/0.36 (step @p61 :rule trans :premises (@p60 @p53)) % 0.16/0.36 (step @p62 :rule beta-reduce :args ((= @t75 @t70))) % 0.16/0.36 (step @p63 :rule ho_cong :premises (@p62 @p61)) % 0.16/0.36 (step @p64 :rule trans :premises (@p63 @p52)) % 0.16/0.36 (step @p65 :rule beta-reduce :args ((= (_ (lambda @t79 @t78) @t1) @t63))) % 0.16/0.36 (step @p66 :rule aci_norm :args ((= (and @t24 @t77) @t78))) % 0.16/0.36 (step @p67 :rule refl :args (@t77)) % 0.16/0.36 (step @p68 :rule beta-reduce :args ((= @t81 @t24))) % 0.16/0.36 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t82)) % 0.16/0.36 (step @p70 :rule trans :premises (@p69 @p66)) % 0.16/0.36 (step @p71 :rule cong :premises (@p70) :args (@t83)) % 0.16/0.36 (step @p72 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t76 @t14) (and @t19 @t77)) @t80) @t83))) % 0.16/0.36 (step @p73 :rule trans :premises (@p72 @p71)) % 0.16/0.36 (step @p74 :rule refl :args (@t80)) % 0.16/0.36 (step @p75 :rule alpha_equiv :args (@t28 @t74 (@list @t76))) % 0.16/0.36 (step @p76 :rule ho_cong :premises (@p75 @p74)) % 0.16/0.36 (step @p77 :rule trans :premises (@p76 @p73)) % 0.16/0.36 (step @p78 :rule beta-reduce :args ((= (_ @t70 @t2) @t80))) % 0.16/0.36 (step @p79 :rule refl :args (@t2)) % 0.16/0.36 (step @p80 :rule ho_cong :premises (@p62 @p79)) % 0.16/0.36 (step @p81 :rule trans :premises (@p80 @p78)) % 0.16/0.36 (step @p82 :rule refl :args (@t28)) % 0.16/0.36 (step @p83 :rule ho_cong :premises (@p82 @p81)) % 0.16/0.36 (step @p84 :rule trans :premises (@p83 @p77)) % 0.16/0.36 (step @p85 :rule ho_cong :premises (@p84 @p54)) % 0.16/0.36 (step @p86 :rule trans :premises (@p85 @p65)) % 0.16/0.36 (step @p87 :rule cong :premises (@p86 @p64) :args (@t84)) % 0.16/0.36 (step @p88 :rule cong :premises (@p87) :args (@t85)) % 0.16/0.36 (step @p89 :rule trans :premises (@p88 @p45)) % 0.16/0.36 (step @p90 :rule cong :premises (@p89) :args ((not @t85))) % 0.16/0.36 (step @p91 :rule ho_cong :premises (@p8 @p79)) % 0.16/0.36 (step @p92 :rule ho_cong :premises (@p91 @p54)) % 0.16/0.36 (step @p93 :rule refl :args (@t3)) % 0.16/0.36 (step @p94 :rule ho_cong :premises (@p11 @p93)) % 0.16/0.36 (step @p95 :rule ho_cong :premises (@p94 @p92)) % 0.16/0.36 (step @p96 :rule ho_cong :premises (@p94 @p79)) % 0.16/0.36 (step @p97 :rule ho_cong :premises (@p11 @p96)) % 0.16/0.36 (step @p98 :rule ho_cong :premises (@p97 @p54)) % 0.16/0.36 (step @p99 :rule cong :premises (@p98 @p95) :args (@t5)) % 0.16/0.36 (step @p100 :rule cong :premises (@p99) :args (@t7)) % 0.16/0.36 (step @p101 :rule cong :premises (@p100) :args (@t8)) % 0.16/0.36 (step @p102 :rule trans :premises (@p101 @p90)) % 0.16/0.36 (step @p103 :rule eq_resolve :premises (@p1 @p102)) % 0.16/0.36 (step @p104 :rule refl :args (@t94)) % 0.16/0.36 (step @p105 :rule bool-double-not-elim :args (@t41)) % 0.16/0.36 (step @p106 :rule nary_cong :premises (@p105 @p104) :args ((or (not @t95) @t94))) % 0.16/0.36 (step @p107 :rule eq-symm :args (@t90 @t92)) % 0.16/0.36 (step @p108 :rule eq-refl :args (@t91)) % 0.16/0.36 (step @p109 :rule skolem_intro :args (@t92)) % 0.16/0.36 (step @p110 :rule refl :args (@t91)) % 0.16/0.36 (step @p111 :rule cong :premises (@p110 @p109) :args ((= @t91 @t92))) % 0.16/0.36 (step @p112 :rule trans :premises (@p111 @p108)) % 0.16/0.36 (step @p113 :rule true_elim :premises (@p112)) % 0.16/0.36 (step @p114 :rule eq-refl :args (@t89)) % 0.16/0.36 (step @p115 :rule skolem_intro :args (@t90)) % 0.16/0.36 (step @p116 :rule refl :args (@t89)) % 0.16/0.36 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t89 @t90))) % 0.16/0.36 (step @p118 :rule trans :premises (@p117 @p114)) % 0.16/0.36 (step @p119 :rule true_elim :premises (@p118)) % 0.16/0.36 (step @p120 :rule cong :premises (@p119 @p113) :args (@t96)) % 0.16/0.36 (step @p121 :rule trans :premises (@p120 @p107)) % 0.16/0.36 (step @p122 :rule cong :premises (@p121) :args (@t97)) % 0.16/0.36 (step @p123 :rule refl :args (@t95)) % 0.16/0.36 (step @p124 :rule cong :premises (@p123 @p122) :args ((=> @t95 @t97))) % 0.16/0.36 (assume-push @p196 @t95) % 0.16/0.36 (step @p126 :rule skolemize :premises (@p103)) % 0.16/0.36 (step-pop @p197 :rule scope :premises (@p126)) % 0.16/0.36 (step @p127 :rule process_scope :premises (@p197) :args (@t97)) % 0.16/0.36 (step @p129 :rule eq_resolve :premises (@p127 @p124)) % 0.16/0.36 (step @p130 :rule implies_elim :premises (@p129)) % 0.16/0.36 (step @p131 :rule eq_resolve :premises (@p130 @p106)) % 0.16/0.36 (step @p132 :rule chain_m_resolution :premises (@p131 @p103) :args (@t94 @t98 (@list @t41))) % 0.16/0.36 (step @p133 :rule eq-symm :args (@t54 @t50)) % 0.16/0.36 (step @p134 :rule eq-refl :args (@t50)) % 0.16/0.36 (step @p135 :rule refl :args (@t50)) % 0.16/0.36 (step @p136 :rule beta-reduce :args (@t99)) % 0.16/0.36 (step @p137 :rule cong :premises (@p136 @p135) :args (@t99)) % 0.16/0.36 (step @p138 :rule trans :premises (@p137 @p134)) % 0.16/0.36 (step @p139 :rule refl :args (@t37)) % 0.16/0.36 (step @p140 :rule ho_cong :premises (@p115 @p139)) % 0.16/0.36 (step @p141 :rule cong :premises (@p140 @p135) :args ((= @t100 @t50))) % 0.16/0.36 (step @p142 :rule trans :premises (@p141 @p138)) % 0.16/0.36 (step @p143 :rule true_elim :premises (@p142)) % 0.16/0.36 (step @p144 :rule eq-refl :args (@t54)) % 0.16/0.36 (step @p145 :rule refl :args (@t54)) % 0.16/0.36 (step @p146 :rule beta-reduce :args (@t101)) % 0.16/0.36 (step @p147 :rule cong :premises (@p146 @p145) :args (@t101)) % 0.16/0.36 (step @p148 :rule trans :premises (@p147 @p144)) % 0.16/0.36 (step @p149 :rule ho_cong :premises (@p109 @p139)) % 0.16/0.36 (step @p150 :rule cong :premises (@p149 @p145) :args ((= @t102 @t54))) % 0.16/0.36 (step @p151 :rule trans :premises (@p150 @p148)) % 0.16/0.36 (step @p152 :rule true_elim :premises (@p151)) % 0.16/0.36 (step @p153 :rule cong :premises (@p152 @p143) :args (@t103)) % 0.16/0.36 (step @p154 :rule trans :premises (@p153 @p133)) % 0.16/0.37 (step @p155 :rule cong :premises (@p154) :args (@t104)) % 0.16/0.37 (step @p156 :rule refl :args (@t93)) % 0.16/0.37 (step @p157 :rule nary_cong :premises (@p156 @p155) :args (@t105)) % 0.16/0.37 ; WARNING: add trust step for TRUST % 0.16/0.37 ; trust TRUST THEORY_LEMMA % 0.16/0.37 (step @p158 :rule trust :premises () :args (@t105)) % 0.16/0.37 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 0.16/0.37 (step @p160 :rule chain_m_resolution :premises (@p159 @p132) :args ((not @t106) @t98 (@list @t93))) % 0.16/0.37 (step @p161 :rule cnf_equiv_neg1 :args (@t106)) % 0.16/0.37 (step @p162 :rule reordering :premises (@p161) :args ((or @t50 @t54 @t106))) % 0.16/0.37 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p20 @p18) :args (@t46 (@list true true true) (@list @t106 @t54 @t50))) % 0.16/0.37 (step @p164 :rule cnf_and_pos :args (@t50 2)) % 0.16/0.37 (step @p165 :rule reordering :premises (@p164) :args ((or @t44 @t51))) % 0.16/0.37 (step @p166 :rule cnf_or_neg :args (@t52 0)) % 0.16/0.37 (step @p167 :rule reordering :premises (@p166) :args ((or @t44 @t52))) % 0.16/0.37 (step @p168 :rule cnf_and_pos :args (@t54 1)) % 0.16/0.37 (step @p169 :rule reordering :premises (@p168) :args ((or @t53 @t55))) % 0.16/0.37 (step @p170 :rule chain_m_resolution :premises (@p169 @p162 @p160 @p167 @p165) :args (@t44 (@list false true false true) (@list @t54 @t106 @t52 @t50))) % 0.16/0.37 (step @p171 :rule cnf_or_pos :args (@t52)) % 0.16/0.37 (step @p172 :rule reordering :premises (@p171) :args ((or @t48 @t43 @t53))) % 0.16/0.37 (step @p173 :rule bool-double-not-elim :args (@t43)) % 0.16/0.37 (step @p174 :rule refl :args (@t107)) % 0.16/0.37 (step @p175 :rule bool-double-not-elim :args (@t48)) % 0.16/0.37 (step @p176 :rule nary_cong :premises (@p135 @p175 @p174 @p173) :args ((or @t50 (not @t49) @t107 (not @t44)))) % 0.16/0.37 (step @p177 :rule cnf_and_neg :args (@t50)) % 0.16/0.37 (step @p178 :rule eq_resolve :premises (@p177 @p176)) % 0.16/0.37 (step @p179 :rule reordering :premises (@p178) :args ((or @t48 @t43 @t50 @t107))) % 0.16/0.37 (step @p180 :rule bool-double-not-elim :args (@t52)) % 0.16/0.37 (step @p181 :rule nary_cong :premises (@p145 @p174 @p180) :args ((or @t54 @t107 (not @t53)))) % 0.16/0.37 (step @p182 :rule cnf_and_neg :args (@t54)) % 0.16/0.37 (step @p183 :rule eq_resolve :premises (@p182 @p181)) % 0.16/0.37 (step @p184 :rule reordering :premises (@p183) :args ((or @t52 @t54 @t107))) % 0.16/0.37 (step @p185 :rule cnf_equiv_neg2 :args (@t106)) % 0.16/0.37 (step @p186 :rule chain_m_resolution :premises (@p185 @p160 @p184 @p179 @p172) :args ((or @t48 @t43 @t107) (@list true false false true) (@list @t106 @t54 @t50 @t52))) % 0.16/0.37 (step @p187 :rule chain_m_resolution :premises (@p186 @p170 @p163) :args (@t48 (@list true false) (@list @t43 @t46))) % 0.16/0.37 (step @p188 :rule cnf_or_neg :args (@t52 1)) % 0.16/0.37 (step @p189 :rule reordering :premises (@p188) :args ((or @t49 @t52))) % 0.16/0.37 (step @p190 :rule chain_m_resolution :premises (@p189 @p187) :args (@t52 @t108 @t109)) % 0.16/0.37 (step @p191 :rule cnf_and_pos :args (@t50 0)) % 0.16/0.37 (step @p192 :rule reordering :premises (@p191) :args ((or @t49 @t51))) % 0.16/0.37 (step @p193 :rule chain_m_resolution :premises (@p192 @p187) :args (@t51 @t108 @t109)) % 0.16/0.37 (step @p194 :rule chain_m_resolution :premises (@p162 @p193 @p160) :args (@t54 (@list true true) (@list @t50 @t106))) % 0.16/0.37 (step @p195 false :rule chain_m_resolution :premises (@p169 @p194 @p190) :args (false (@list false false) (@list @t54 @t52))) % 0.16/0.37 ) % 0.16/0.37 % SZS output end Proof % 0.16/0.37 % cvc5 exiting %------------------------------------------------------------------------------