%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET143^3 : 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 : n001.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 08:47:30 AM UTC 2026 % Result : Theorem 0.36s 0.56s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET143^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.15/0.34 % Computer : n001.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Tue Jun 2 15:04:20 EDT 2026 % 0.15/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.36/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.56 % SZS status Theorem % 0.36/0.56 % SZS output start Proof % 0.36/0.56 ( % 0.36/0.56 (declare-sort $$unsorted 0) % 0.36/0.56 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.56 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.56 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.36/0.56 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.36/0.56 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.36/0.56 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.56 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.36/0.56 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.56 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.36/0.56 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.56 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.36/0.56 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.36/0.56 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.36/0.56 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.36/0.56 (define @t1 () (@var "Z" (-> $$unsorted Bool))) % 0.36/0.56 (define @t2 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.56 (define @t3 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.56 (define @t4 () (_ tptp.intersection @t3)) % 0.36/0.56 (define @t5 () (_ @t4 @t2)) % 0.36/0.56 (define @t6 () (= (_ (_ tptp.intersection @t5) @t1) (_ @t4 (_ (_ tptp.intersection @t2) @t1)))) % 0.36/0.56 (define @t7 () (@list @t3 @t2 @t1)) % 0.36/0.56 (define @t8 () (forall @t7 @t6)) % 0.36/0.56 (define @t9 () (not @t8)) % 0.36/0.56 (define @t10 () (@var "X" $$unsorted)) % 0.36/0.56 (define @t11 () (@var "M" (-> $$unsorted Bool))) % 0.36/0.56 (define @t12 () (lambda (@list @t10 @t11) (_ @t11 @t10))) % 0.36/0.56 (define @t13 () (lambda (@list @t10) false)) % 0.36/0.56 (define @t14 () (@var "Y" $$unsorted)) % 0.36/0.56 (define @t15 () (@var "U" $$unsorted)) % 0.36/0.56 (define @t16 () (= @t15 @t10)) % 0.36/0.56 (define @t17 () (lambda (@list @t10 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.36/0.56 (define @t18 () (lambda (@list @t10 @t15) @t16)) % 0.36/0.56 (define @t19 () (_ @t2 @t15)) % 0.36/0.56 (define @t20 () (_ @t3 @t15)) % 0.36/0.57 (define @t21 () (@list @t3 @t2 @t15)) % 0.36/0.57 (define @t22 () (lambda @t21 (or @t20 @t19))) % 0.36/0.57 (define @t23 () (not @t20)) % 0.36/0.57 (define @t24 () (and @t20 (not @t19))) % 0.36/0.57 (define @t25 () (lambda @t21 (or @t24 (and @t23 @t19)))) % 0.36/0.57 (define @t26 () (and @t20 @t19)) % 0.36/0.57 (define @t27 () (lambda @t21 @t26)) % 0.36/0.57 (define @t28 () (lambda @t21 @t24)) % 0.36/0.57 (define @t29 () (lambda (@list @t3 @t15) @t23)) % 0.36/0.57 (define @t30 () (@list @t3 @t2)) % 0.36/0.57 (define @t31 () (lambda @t30 (= @t5 tptp.emptyset))) % 0.36/0.57 (define @t32 () (@list @t15)) % 0.36/0.57 (define @t33 () (lambda @t30 (forall @t32 (=> @t20 @t19)))) % 0.36/0.57 (define @t34 () (exists @t32 @t26)) % 0.36/0.57 (define @t35 () (lambda @t30 @t34)) % 0.36/0.57 (define @t36 () (lambda @t30 (not @t34))) % 0.36/0.57 (define @t37 () (_ @t1 @t15)) % 0.36/0.57 (define @t38 () (_ @t1 @t15)) % 0.36/0.57 (define @t39 () (_ @t2 @t15)) % 0.36/0.57 (define @t40 () (_ @t3 @t15)) % 0.36/0.57 (define @t41 () (and @t20 @t19 @t38)) % 0.36/0.57 (define @t42 () (lambda @t32 @t41)) % 0.36/0.57 (define @t43 () (and @t38 @t20 @t19)) % 0.36/0.57 (define @t44 () (lambda @t32 @t43)) % 0.36/0.57 (define @t45 () (= @t44 @t42)) % 0.36/0.57 (define @t46 () (and @t19 @t38)) % 0.36/0.57 (define @t47 () (lambda @t32 @t46)) % 0.36/0.57 (define @t48 () (_ @t47 @t15)) % 0.36/0.57 (define @t49 () (and @t20 @t48)) % 0.36/0.57 (define @t50 () (lambda @t32 @t49)) % 0.36/0.57 (define @t51 () (lambda (@list @t2 @t15) @t26)) % 0.36/0.57 (define @t52 () (@var "BOUND_VARIABLE_7653" (-> $$unsorted Bool))) % 0.36/0.57 (define @t53 () (_ @t52 @t15)) % 0.36/0.57 (define @t54 () (lambda (@list @t52 @t15) (and @t19 @t53))) % 0.36/0.57 (define @t55 () (@list @t2)) % 0.36/0.57 (define @t56 () (_ @t27 @t3)) % 0.36/0.57 (define @t57 () (@var "BOUND_VARIABLE_7633" (-> $$unsorted Bool))) % 0.36/0.57 (define @t58 () (_ @t57 @t15)) % 0.36/0.57 (define @t59 () (and @t58 @t20 @t19)) % 0.36/0.57 (define @t60 () (@list @t57 @t15)) % 0.36/0.57 (define @t61 () (lambda @t32 @t26)) % 0.36/0.57 (define @t62 () (_ @t61 @t15)) % 0.36/0.57 (define @t63 () (and @t62 @t58)) % 0.36/0.57 (define @t64 () (lambda @t60 @t63)) % 0.36/0.57 (define @t65 () (= (_ (_ @t27 (_ @t56 @t2)) @t1) (_ @t56 (_ (_ @t27 @t2) @t1)))) % 0.36/0.57 (define @t66 () (forall @t7 @t65)) % 0.36/0.57 (define @t67 () (forall @t7 (= (lambda @t32 (and @t37 @t40 @t39)) (lambda @t32 (and @t40 @t39 @t37))))) % 0.36/0.57 (define @t68 () (@quantifiers_skolemize @t67 1)) % 0.36/0.57 (define @t69 () (_ @t68 @t15)) % 0.36/0.57 (define @t70 () (@quantifiers_skolemize @t67 0)) % 0.36/0.57 (define @t71 () (_ @t70 @t15)) % 0.36/0.57 (define @t72 () (@quantifiers_skolemize @t67 2)) % 0.36/0.57 (define @t73 () (_ @t72 @t15)) % 0.36/0.57 (define @t74 () (lambda @t32 (and @t73 @t71 @t69))) % 0.36/0.57 (define @t75 () (@purify @t74)) % 0.36/0.57 (define @t76 () (lambda @t32 (and @t71 @t69 @t73))) % 0.36/0.57 (define @t77 () (@purify @t76)) % 0.36/0.57 (define @t78 () (= @t77 @t75)) % 0.36/0.57 (define @t79 () (not @t78)) % 0.36/0.57 (define @t80 () (not @t67)) % 0.36/0.57 (define @t81 () (= @t74 @t76)) % 0.36/0.57 (define @t82 () (not @t81)) % 0.36/0.57 (define @t83 () (@list true)) % 0.36/0.57 (define @t84 () (@const 0 $$unsorted)) % 0.36/0.57 (define @t85 () (_ @t72 @t84)) % 0.36/0.57 (define @t86 () (_ @t68 @t84)) % 0.36/0.57 (define @t87 () (_ @t70 @t84)) % 0.36/0.57 (define @t88 () (and @t87 @t86 @t85)) % 0.36/0.57 (define @t89 () (and @t85 @t87 @t86)) % 0.36/0.57 (define @t90 () (= @t89 @t88)) % 0.36/0.57 (define @t91 () (= (_ @t74 @t84) @t89)) % 0.36/0.57 (define @t92 () (_ @t75 @t84)) % 0.36/0.57 (define @t93 () (= (_ @t76 @t84) @t88)) % 0.36/0.57 (define @t94 () (_ @t77 @t84)) % 0.36/0.57 (define @t95 () (= @t94 @t92)) % 0.36/0.57 (define @t96 () (not @t95)) % 0.36/0.57 (define @t97 () (or @t78 @t96)) % 0.36/0.57 (define @t98 () (not @t89)) % 0.36/0.57 (define @t99 () (not @t88)) % 0.36/0.57 (define @t100 () (@list true true true)) % 0.36/0.57 (define @t101 () (@list @t90 @t88 @t89)) % 0.36/0.57 (define @t102 () (not @t86)) % 0.36/0.57 (define @t103 () (not @t87)) % 0.36/0.57 (define @t104 () (not @t85)) % 0.36/0.57 (define @t105 () (@list @t85)) % 0.36/0.57 (assume @p1 @t9) % 0.36/0.57 (assume @p2 true) % 0.36/0.57 (step @p3 (= tptp.in @t12) :rule refl :args (@t12)) % 0.36/0.57 (step @p4 (= tptp.is_a @t12) :rule refl :args (@t12)) % 0.36/0.57 (step @p5 (= tptp.emptyset @t13) :rule refl :args (@t13)) % 0.36/0.57 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.36/0.57 (step @p7 (= tptp.singleton @t18) :rule refl :args (@t18)) % 0.36/0.57 (step @p8 (= tptp.union @t22) :rule refl :args (@t22)) % 0.36/0.57 (step @p9 (= tptp.excl_union @t25) :rule refl :args (@t25)) % 0.36/0.57 (step @p10 (= tptp.intersection @t27) :rule refl :args (@t27)) % 0.36/0.57 (step @p11 (= tptp.setminus @t28) :rule refl :args (@t28)) % 0.36/0.57 (step @p12 (= tptp.complement @t29) :rule refl :args (@t29)) % 0.36/0.57 (step @p13 (= tptp.disjoint @t31) :rule refl :args (@t31)) % 0.36/0.57 (step @p14 (= tptp.subset @t33) :rule refl :args (@t33)) % 0.36/0.57 (step @p15 (= tptp.meets @t35) :rule refl :args (@t35)) % 0.36/0.57 (step @p16 (= tptp.misses @t36) :rule refl :args (@t36)) % 0.36/0.57 (step @p17 :rule refl :args (@t37)) % 0.36/0.57 (step @p18 :rule refl :args (@t38)) % 0.36/0.57 (step @p19 :rule cong :premises (@p18 @p17) :args ((= @t38 @t37))) % 0.36/0.57 (step @p20 :rule symm :premises (@p19)) % 0.36/0.57 (step @p21 :rule eq_resolve :premises (@p18 @p20)) % 0.36/0.57 (step @p22 :rule refl :args (@t39)) % 0.36/0.57 (step @p23 :rule refl :args (@t19)) % 0.36/0.57 (step @p24 :rule cong :premises (@p23 @p22) :args ((= @t19 @t39))) % 0.36/0.57 (step @p25 :rule symm :premises (@p24)) % 0.36/0.57 (step @p26 :rule eq_resolve :premises (@p23 @p25)) % 0.36/0.57 (step @p27 :rule refl :args (@t40)) % 0.36/0.57 (step @p28 :rule refl :args (@t20)) % 0.36/0.57 (step @p29 :rule cong :premises (@p28 @p27) :args ((= @t20 @t40))) % 0.36/0.57 (step @p30 :rule symm :premises (@p29)) % 0.36/0.57 (step @p31 :rule eq_resolve :premises (@p28 @p30)) % 0.36/0.57 (step @p32 :rule nary_cong :premises (@p31 @p26 @p21) :args (@t41)) % 0.36/0.57 (step @p33 :rule cong :premises (@p32) :args (@t42)) % 0.36/0.57 (step @p34 :rule nary_cong :premises (@p21 @p31 @p26) :args (@t43)) % 0.36/0.57 (step @p35 :rule cong :premises (@p34) :args (@t44)) % 0.36/0.57 (step @p36 :rule cong :premises (@p35 @p33) :args (@t45)) % 0.36/0.57 (step @p37 :rule cong :premises (@p36) :args ((forall @t7 @t45))) % 0.36/0.57 (step @p38 :rule aci_norm :args ((= (and @t20 @t46) @t41))) % 0.36/0.57 (step @p39 :rule beta-reduce :args ((= @t48 @t46))) % 0.36/0.57 (step @p40 :rule refl :args (@t20)) % 0.36/0.57 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t49)) % 0.36/0.57 (step @p42 :rule trans :premises (@p41 @p38)) % 0.36/0.57 (step @p43 :rule cong :premises (@p42) :args (@t50)) % 0.36/0.57 (step @p44 :rule beta-reduce :args ((= (_ @t51 @t47) @t50))) % 0.36/0.57 (step @p45 :rule trans :premises (@p44 @p43)) % 0.36/0.57 (step @p46 :rule beta-reduce :args ((= (_ @t54 @t1) @t47))) % 0.36/0.57 (step @p47 :rule refl :args (@t1)) % 0.36/0.57 (step @p48 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t52 @t15) (and @t20 @t53)) @t2) @t54))) % 0.36/0.57 (step @p49 :rule refl :args (@t2)) % 0.36/0.57 (step @p50 :rule alpha_equiv :args (@t27 @t55 (@list @t52))) % 0.36/0.57 (step @p51 :rule ho_cong :premises (@p50 @p49)) % 0.36/0.57 (step @p52 :rule trans :premises (@p51 @p48)) % 0.36/0.57 (step @p53 :rule ho_cong :premises (@p52 @p47)) % 0.36/0.57 (step @p54 :rule trans :premises (@p53 @p46)) % 0.36/0.57 (step @p55 :rule beta-reduce :args ((= @t56 @t51))) % 0.36/0.57 (step @p56 :rule ho_cong :premises (@p55 @p54)) % 0.36/0.57 (step @p57 :rule trans :premises (@p56 @p45)) % 0.36/0.57 (step @p58 :rule beta-reduce :args ((= (_ (lambda @t60 @t59) @t1) @t44))) % 0.36/0.57 (step @p59 :rule aci_norm :args ((= (and @t26 @t58) @t59))) % 0.36/0.57 (step @p60 :rule refl :args (@t58)) % 0.36/0.57 (step @p61 :rule beta-reduce :args ((= @t62 @t26))) % 0.36/0.57 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t63)) % 0.36/0.57 (step @p63 :rule trans :premises (@p62 @p59)) % 0.36/0.57 (step @p64 :rule cong :premises (@p63) :args (@t64)) % 0.36/0.57 (step @p65 :rule beta-reduce :args ((= (_ (lambda (@list @t3 @t57 @t15) (and @t20 @t58)) @t61) @t64))) % 0.36/0.57 (step @p66 :rule trans :premises (@p65 @p64)) % 0.36/0.57 (step @p67 :rule refl :args (@t61)) % 0.36/0.57 (step @p68 :rule alpha_equiv :args (@t27 @t55 (@list @t57))) % 0.36/0.57 (step @p69 :rule ho_cong :premises (@p68 @p67)) % 0.36/0.57 (step @p70 :rule trans :premises (@p69 @p66)) % 0.36/0.57 (step @p71 :rule beta-reduce :args ((= (_ @t51 @t2) @t61))) % 0.36/0.57 (step @p72 :rule refl :args (@t2)) % 0.36/0.57 (step @p73 :rule ho_cong :premises (@p55 @p72)) % 0.36/0.57 (step @p74 :rule trans :premises (@p73 @p71)) % 0.36/0.57 (step @p75 :rule refl :args (@t27)) % 0.36/0.57 (step @p76 :rule ho_cong :premises (@p75 @p74)) % 0.36/0.57 (step @p77 :rule trans :premises (@p76 @p70)) % 0.36/0.57 (step @p78 :rule ho_cong :premises (@p77 @p47)) % 0.36/0.57 (step @p79 :rule trans :premises (@p78 @p58)) % 0.36/0.57 (step @p80 :rule cong :premises (@p79 @p57) :args (@t65)) % 0.36/0.57 (step @p81 :rule cong :premises (@p80) :args (@t66)) % 0.36/0.57 (step @p82 :rule trans :premises (@p81 @p37)) % 0.36/0.57 (step @p83 :rule cong :premises (@p82) :args ((not @t66))) % 0.36/0.57 (step @p84 :rule ho_cong :premises (@p10 @p72)) % 0.36/0.57 (step @p85 :rule ho_cong :premises (@p84 @p47)) % 0.36/0.57 (step @p86 :rule refl :args (@t3)) % 0.36/0.57 (step @p87 :rule ho_cong :premises (@p10 @p86)) % 0.36/0.57 (step @p88 :rule ho_cong :premises (@p87 @p85)) % 0.36/0.57 (step @p89 :rule ho_cong :premises (@p87 @p72)) % 0.36/0.57 (step @p90 :rule ho_cong :premises (@p10 @p89)) % 0.36/0.57 (step @p91 :rule ho_cong :premises (@p90 @p47)) % 0.36/0.57 (step @p92 :rule cong :premises (@p91 @p88) :args (@t6)) % 0.36/0.57 (step @p93 :rule cong :premises (@p92) :args (@t8)) % 0.36/0.57 (step @p94 :rule cong :premises (@p93) :args (@t9)) % 0.36/0.57 (step @p95 :rule trans :premises (@p94 @p83)) % 0.36/0.57 (step @p96 :rule eq_resolve :premises (@p1 @p95)) % 0.36/0.57 (step @p97 :rule refl :args (@t79)) % 0.36/0.57 (step @p98 :rule bool-double-not-elim :args (@t67)) % 0.36/0.57 (step @p99 :rule nary_cong :premises (@p98 @p97) :args ((or (not @t80) @t79))) % 0.36/0.57 (step @p100 :rule eq-symm :args (@t75 @t77)) % 0.36/0.57 (step @p101 :rule eq-refl :args (@t76)) % 0.36/0.57 (step @p102 :rule skolem_intro :args (@t77)) % 0.36/0.57 (step @p103 :rule refl :args (@t76)) % 0.36/0.57 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t76 @t77))) % 0.36/0.57 (step @p105 :rule trans :premises (@p104 @p101)) % 0.36/0.57 (step @p106 :rule true_elim :premises (@p105)) % 0.36/0.57 (step @p107 :rule eq-refl :args (@t74)) % 0.36/0.57 (step @p108 :rule skolem_intro :args (@t75)) % 0.36/0.57 (step @p109 :rule refl :args (@t74)) % 0.36/0.57 (step @p110 :rule cong :premises (@p109 @p108) :args ((= @t74 @t75))) % 0.36/0.57 (step @p111 :rule trans :premises (@p110 @p107)) % 0.36/0.57 (step @p112 :rule true_elim :premises (@p111)) % 0.36/0.57 (step @p113 :rule cong :premises (@p112 @p106) :args (@t81)) % 0.36/0.57 (step @p114 :rule trans :premises (@p113 @p100)) % 0.36/0.57 (step @p115 :rule cong :premises (@p114) :args (@t82)) % 0.36/0.57 (step @p116 :rule refl :args (@t80)) % 0.36/0.57 (step @p117 :rule cong :premises (@p116 @p115) :args ((=> @t80 @t82))) % 0.36/0.57 (assume-push @p181 @t80) % 0.36/0.57 (step @p119 :rule skolemize :premises (@p96)) % 0.36/0.57 (step-pop @p182 :rule scope :premises (@p119)) % 0.36/0.57 (step @p120 :rule process_scope :premises (@p182) :args (@t82)) % 0.36/0.57 (step @p122 :rule eq_resolve :premises (@p120 @p117)) % 0.36/0.57 (step @p123 :rule implies_elim :premises (@p122)) % 0.36/0.57 (step @p124 :rule eq_resolve :premises (@p123 @p99)) % 0.36/0.57 (step @p125 :rule chain_m_resolution :premises (@p124 @p96) :args (@t79 @t83 (@list @t67))) % 0.36/0.57 (step @p126 :rule aci_norm :args (@t90)) % 0.36/0.57 (step @p127 :rule symm :premises (@p126)) % 0.36/0.57 (step @p128 :rule cong :premises (@p127 @p126) :args ((= @t88 @t89))) % 0.36/0.57 (step @p129 :rule eq-refl :args (@t89)) % 0.36/0.57 (step @p130 :rule refl :args (@t89)) % 0.36/0.57 (step @p131 :rule beta-reduce :args (@t91)) % 0.36/0.57 (step @p132 :rule cong :premises (@p131 @p130) :args (@t91)) % 0.36/0.57 (step @p133 :rule trans :premises (@p132 @p129)) % 0.36/0.57 (step @p134 :rule refl :args (@t84)) % 0.36/0.57 (step @p135 :rule ho_cong :premises (@p108 @p134)) % 0.36/0.57 (step @p136 :rule cong :premises (@p135 @p130) :args ((= @t92 @t89))) % 0.36/0.57 (step @p137 :rule trans :premises (@p136 @p133)) % 0.36/0.57 (step @p138 :rule true_elim :premises (@p137)) % 0.36/0.57 (step @p139 :rule eq-refl :args (@t88)) % 0.36/0.57 (step @p140 :rule refl :args (@t88)) % 0.36/0.57 (step @p141 :rule beta-reduce :args (@t93)) % 0.36/0.57 (step @p142 :rule cong :premises (@p141 @p140) :args (@t93)) % 0.36/0.57 (step @p143 :rule trans :premises (@p142 @p139)) % 0.36/0.57 (step @p144 :rule ho_cong :premises (@p102 @p134)) % 0.36/0.57 (step @p145 :rule cong :premises (@p144 @p140) :args ((= @t94 @t88))) % 0.36/0.57 (step @p146 :rule trans :premises (@p145 @p143)) % 0.36/0.57 (step @p147 :rule true_elim :premises (@p146)) % 0.36/0.57 (step @p148 :rule cong :premises (@p147 @p138) :args (@t95)) % 0.36/0.57 (step @p149 :rule trans :premises (@p148 @p128)) % 0.36/0.57 (step @p150 :rule cong :premises (@p149) :args (@t96)) % 0.36/0.57 (step @p151 :rule refl :args (@t78)) % 0.36/0.57 (step @p152 :rule nary_cong :premises (@p151 @p150) :args (@t97)) % 0.36/0.57 ; WARNING: add trust step for TRUST % 0.36/0.57 ; trust TRUST THEORY_LEMMA % 0.36/0.57 (step @p153 :rule trust :premises () :args (@t97)) % 0.36/0.57 (step @p154 :rule eq_resolve :premises (@p153 @p152)) % 0.36/0.57 (step @p155 :rule chain_m_resolution :premises (@p154 @p125) :args ((not @t90) @t83 (@list @t78))) % 0.36/0.57 (step @p156 :rule cnf_and_pos :args (@t89 2)) % 0.36/0.57 (step @p157 :rule reordering :premises (@p156) :args ((or @t86 @t98))) % 0.36/0.57 (step @p158 :rule cnf_and_pos :args (@t88 1)) % 0.36/0.57 (step @p159 :rule reordering :premises (@p158) :args ((or @t86 @t99))) % 0.36/0.57 (step @p160 :rule cnf_equiv_neg1 :args (@t90)) % 0.36/0.57 (step @p161 :rule reordering :premises (@p160) :args ((or @t89 @t88 @t90))) % 0.36/0.57 (step @p162 :rule chain_m_resolution :premises (@p161 @p155 @p159 @p157) :args (@t86 @t100 @t101)) % 0.36/0.57 (step @p163 :rule cnf_and_pos :args (@t89 1)) % 0.36/0.57 (step @p164 :rule reordering :premises (@p163) :args ((or @t87 @t98))) % 0.36/0.57 (step @p165 :rule cnf_and_pos :args (@t88 0)) % 0.36/0.57 (step @p166 :rule reordering :premises (@p165) :args ((or @t87 @t99))) % 0.36/0.57 (step @p167 :rule chain_m_resolution :premises (@p161 @p155 @p166 @p164) :args (@t87 @t100 @t101)) % 0.36/0.57 (step @p168 :rule cnf_and_neg :args (@t89)) % 0.36/0.57 (step @p169 :rule cnf_and_neg :args (@t88)) % 0.36/0.57 (step @p170 :rule reordering :premises (@p169) :args ((or @t88 @t104 @t103 @t102))) % 0.36/0.57 (step @p171 :rule cnf_equiv_neg2 :args (@t90)) % 0.36/0.57 (step @p172 :rule chain_m_resolution :premises (@p171 @p155 @p170 @p168) :args ((or @t104 @t103 @t102) (@list true false false) @t101)) % 0.36/0.57 (step @p173 :rule chain_m_resolution :premises (@p172 @p167 @p162) :args (@t104 (@list false false) (@list @t87 @t86))) % 0.36/0.57 (step @p174 :rule cnf_and_pos :args (@t89 0)) % 0.36/0.57 (step @p175 :rule reordering :premises (@p174) :args ((or @t85 @t98))) % 0.36/0.57 (step @p176 :rule chain_m_resolution :premises (@p175 @p173) :args (@t98 @t83 @t105)) % 0.36/0.57 (step @p177 :rule cnf_and_pos :args (@t88 2)) % 0.36/0.57 (step @p178 :rule reordering :premises (@p177) :args ((or @t85 @t99))) % 0.36/0.57 (step @p179 :rule chain_m_resolution :premises (@p178 @p173) :args (@t99 @t83 @t105)) % 0.36/0.57 (step @p180 false :rule chain_m_resolution :premises (@p161 @p179 @p176 @p155) :args (false @t100 (@list @t88 @t89 @t90))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.57 % cvc5 exiting %------------------------------------------------------------------------------