%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET612^3 : 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 : n027.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 08:48:13 AM UTC 2026 % Result : Theorem 0.36s 0.57s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET612^3 : 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 % 0.16/0.34 % Computer : n027.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 16:05:06 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.50 %----Proving TH0 % 0.36/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.57 % SZS status Theorem % 0.36/0.57 % SZS output start Proof % 0.36/0.57 ( % 0.36/0.57 (declare-sort $$unsorted 0) % 0.36/0.57 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.57 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.57 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.36/0.57 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.36/0.57 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.36/0.57 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.57 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.36/0.57 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.57 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.36/0.57 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.57 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.36/0.57 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.36/0.57 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.36/0.57 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.36/0.57 (define @t1 () (@var "Z" (-> $$unsorted Bool))) % 0.36/0.57 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.57 (define @t3 () (_ tptp.setminus @t2)) % 0.36/0.57 (define @t4 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.57 (define @t5 () (= (_ @t3 (_ (_ tptp.union @t4) @t1)) (_ (_ tptp.intersection (_ @t3 @t4)) (_ @t3 @t1)))) % 0.36/0.57 (define @t6 () (@list @t2 @t4 @t1)) % 0.36/0.57 (define @t7 () (forall @t6 @t5)) % 0.36/0.57 (define @t8 () (not @t7)) % 0.36/0.57 (define @t9 () (@var "X" $$unsorted)) % 0.36/0.57 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.36/0.57 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.36/0.57 (define @t12 () (lambda (@list @t9) false)) % 0.36/0.57 (define @t13 () (@var "Y" $$unsorted)) % 0.36/0.57 (define @t14 () (@var "U" $$unsorted)) % 0.36/0.57 (define @t15 () (= @t14 @t9)) % 0.36/0.57 (define @t16 () (lambda (@list @t9 @t13 @t14) (or @t15 (= @t14 @t13)))) % 0.36/0.57 (define @t17 () (lambda (@list @t9 @t14) @t15)) % 0.36/0.57 (define @t18 () (_ @t4 @t14)) % 0.36/0.57 (define @t19 () (_ @t2 @t14)) % 0.36/0.57 (define @t20 () (@list @t2 @t4 @t14)) % 0.36/0.57 (define @t21 () (lambda @t20 (or @t19 @t18))) % 0.36/0.57 (define @t22 () (not @t19)) % 0.36/0.57 (define @t23 () (not @t18)) % 0.36/0.57 (define @t24 () (and @t19 @t23)) % 0.36/0.57 (define @t25 () (lambda @t20 (or @t24 (and @t22 @t18)))) % 0.36/0.57 (define @t26 () (and @t19 @t18)) % 0.36/0.57 (define @t27 () (lambda @t20 @t26)) % 0.36/0.57 (define @t28 () (lambda @t20 @t24)) % 0.36/0.57 (define @t29 () (lambda (@list @t2 @t14) @t22)) % 0.36/0.57 (define @t30 () (@list @t2 @t4)) % 0.36/0.57 (define @t31 () (lambda @t30 (= (_ (_ tptp.intersection @t2) @t4) tptp.emptyset))) % 0.36/0.57 (define @t32 () (@list @t14)) % 0.36/0.57 (define @t33 () (lambda @t30 (forall @t32 (=> @t19 @t18)))) % 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 @t14)) % 0.36/0.57 (define @t38 () (_ @t1 @t14)) % 0.36/0.57 (define @t39 () (not @t38)) % 0.36/0.57 (define @t40 () (_ @t4 @t14)) % 0.36/0.57 (define @t41 () (_ @t2 @t14)) % 0.36/0.57 (define @t42 () (and @t19 @t23 @t39)) % 0.36/0.57 (define @t43 () (lambda @t32 @t42)) % 0.36/0.57 (define @t44 () (or @t18 @t38)) % 0.36/0.57 (define @t45 () (not @t44)) % 0.36/0.57 (define @t46 () (and @t19 @t45)) % 0.36/0.57 (define @t47 () (lambda @t32 @t46)) % 0.36/0.57 (define @t48 () (= @t47 @t43)) % 0.36/0.57 (define @t49 () (and @t19 @t39)) % 0.36/0.57 (define @t50 () (lambda @t32 @t49)) % 0.36/0.57 (define @t51 () (_ @t50 @t14)) % 0.36/0.57 (define @t52 () (and @t51 @t19 @t23)) % 0.36/0.57 (define @t53 () (lambda @t32 @t52)) % 0.36/0.57 (define @t54 () (@var "BOUND_VARIABLE_7667" (-> $$unsorted Bool))) % 0.36/0.57 (define @t55 () (_ @t54 @t14)) % 0.36/0.57 (define @t56 () (and @t55 @t19 @t23)) % 0.36/0.57 (define @t57 () (@list @t54 @t14)) % 0.36/0.57 (define @t58 () (lambda (@list @t4 @t14) @t24)) % 0.36/0.57 (define @t59 () (_ @t28 @t2)) % 0.36/0.57 (define @t60 () (lambda @t32 @t24)) % 0.36/0.57 (define @t61 () (_ @t60 @t14)) % 0.36/0.57 (define @t62 () (and @t61 @t55)) % 0.36/0.57 (define @t63 () (lambda @t57 @t62)) % 0.36/0.57 (define @t64 () (@list @t4)) % 0.36/0.57 (define @t65 () (lambda @t32 @t44)) % 0.36/0.57 (define @t66 () (_ @t65 @t14)) % 0.36/0.57 (define @t67 () (not @t66)) % 0.36/0.57 (define @t68 () (and @t19 @t67)) % 0.36/0.57 (define @t69 () (lambda @t32 @t68)) % 0.36/0.57 (define @t70 () (@var "BOUND_VARIABLE_7640" (-> $$unsorted Bool))) % 0.36/0.57 (define @t71 () (_ @t70 @t14)) % 0.36/0.57 (define @t72 () (lambda (@list @t70 @t14) (or @t18 @t71))) % 0.36/0.57 (define @t73 () (= (_ @t59 (_ (_ @t21 @t4) @t1)) (_ (_ @t27 (_ @t59 @t4)) (_ @t59 @t1)))) % 0.36/0.57 (define @t74 () (forall @t6 @t73)) % 0.36/0.57 (define @t75 () (forall @t6 (= (lambda @t32 (and @t41 (not (or @t40 @t37)))) (lambda @t32 (and @t41 (not @t40) (not @t37)))))) % 0.36/0.57 (define @t76 () (@quantifiers_skolemize @t75 2)) % 0.36/0.57 (define @t77 () (_ @t76 @t14)) % 0.36/0.57 (define @t78 () (@quantifiers_skolemize @t75 1)) % 0.36/0.57 (define @t79 () (_ @t78 @t14)) % 0.36/0.57 (define @t80 () (@quantifiers_skolemize @t75 0)) % 0.36/0.57 (define @t81 () (_ @t80 @t14)) % 0.36/0.57 (define @t82 () (lambda @t32 (and @t81 (not (or @t79 @t77))))) % 0.36/0.57 (define @t83 () (@purify @t82)) % 0.36/0.57 (define @t84 () (lambda @t32 (and @t81 (not @t79) (not @t77)))) % 0.36/0.57 (define @t85 () (@purify @t84)) % 0.36/0.57 (define @t86 () (= @t85 @t83)) % 0.36/0.57 (define @t87 () (not @t86)) % 0.36/0.57 (define @t88 () (not @t75)) % 0.36/0.57 (define @t89 () (= @t82 @t84)) % 0.36/0.57 (define @t90 () (not @t89)) % 0.36/0.57 (define @t91 () (@list true)) % 0.36/0.57 (define @t92 () (@const 0 $$unsorted)) % 0.36/0.57 (define @t93 () (_ @t76 @t92)) % 0.36/0.57 (define @t94 () (not @t93)) % 0.36/0.57 (define @t95 () (_ @t78 @t92)) % 0.36/0.57 (define @t96 () (not @t95)) % 0.36/0.57 (define @t97 () (_ @t80 @t92)) % 0.36/0.57 (define @t98 () (and @t97 @t96 @t94)) % 0.36/0.57 (define @t99 () (or @t95 @t93)) % 0.36/0.57 (define @t100 () (not @t99)) % 0.36/0.57 (define @t101 () (and @t97 @t100)) % 0.36/0.57 (define @t102 () (= (_ @t82 @t92) @t101)) % 0.36/0.57 (define @t103 () (_ @t83 @t92)) % 0.36/0.57 (define @t104 () (= (_ @t84 @t92) @t98)) % 0.36/0.57 (define @t105 () (_ @t85 @t92)) % 0.36/0.57 (define @t106 () (= @t105 @t103)) % 0.36/0.57 (define @t107 () (not @t106)) % 0.36/0.57 (define @t108 () (or @t86 @t107)) % 0.36/0.57 (define @t109 () (= @t101 @t98)) % 0.36/0.57 (define @t110 () (not @t98)) % 0.36/0.57 (define @t111 () (not @t101)) % 0.36/0.57 (define @t112 () (@list true true true false)) % 0.36/0.57 (define @t113 () (@list @t109 @t101 @t98 @t99)) % 0.36/0.57 (define @t114 () (not @t97)) % 0.36/0.57 (define @t115 () (@list @t97)) % 0.36/0.57 (assume @p1 @t8) % 0.36/0.57 (assume @p2 true) % 0.36/0.57 (step @p3 (= tptp.in @t11) :rule refl :args (@t11)) % 0.36/0.57 (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11)) % 0.36/0.57 (step @p5 (= tptp.emptyset @t12) :rule refl :args (@t12)) % 0.36/0.57 (step @p6 (= tptp.unord_pair @t16) :rule refl :args (@t16)) % 0.36/0.57 (step @p7 (= tptp.singleton @t17) :rule refl :args (@t17)) % 0.36/0.57 (step @p8 (= tptp.union @t21) :rule refl :args (@t21)) % 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 cong :premises (@p21) :args (@t39)) % 0.36/0.57 (step @p23 :rule refl :args (@t40)) % 0.36/0.57 (step @p24 :rule refl :args (@t18)) % 0.36/0.57 (step @p25 :rule cong :premises (@p24 @p23) :args ((= @t18 @t40))) % 0.36/0.57 (step @p26 :rule symm :premises (@p25)) % 0.36/0.57 (step @p27 :rule eq_resolve :premises (@p24 @p26)) % 0.36/0.57 (step @p28 :rule cong :premises (@p27) :args (@t23)) % 0.36/0.57 (step @p29 :rule refl :args (@t41)) % 0.36/0.57 (step @p30 :rule refl :args (@t19)) % 0.36/0.57 (step @p31 :rule cong :premises (@p30 @p29) :args ((= @t19 @t41))) % 0.36/0.57 (step @p32 :rule symm :premises (@p31)) % 0.36/0.57 (step @p33 :rule eq_resolve :premises (@p30 @p32)) % 0.36/0.57 (step @p34 :rule nary_cong :premises (@p33 @p28 @p22) :args (@t42)) % 0.36/0.57 (step @p35 :rule cong :premises (@p34) :args (@t43)) % 0.36/0.57 (step @p36 :rule nary_cong :premises (@p27 @p21) :args (@t44)) % 0.36/0.57 (step @p37 :rule cong :premises (@p36) :args (@t45)) % 0.36/0.57 (step @p38 :rule nary_cong :premises (@p33 @p37) :args (@t46)) % 0.36/0.57 (step @p39 :rule cong :premises (@p38) :args (@t47)) % 0.36/0.57 (step @p40 :rule cong :premises (@p39 @p35) :args (@t48)) % 0.36/0.57 (step @p41 :rule cong :premises (@p40) :args ((forall @t6 @t48))) % 0.36/0.57 (step @p42 :rule aci_norm :args ((= (and @t49 @t19 @t23) @t42))) % 0.36/0.57 (step @p43 :rule refl :args (@t23)) % 0.36/0.57 (step @p44 :rule refl :args (@t19)) % 0.36/0.57 (step @p45 :rule beta-reduce :args ((= @t51 @t49))) % 0.36/0.57 (step @p46 :rule nary_cong :premises (@p45 @p44 @p43) :args (@t52)) % 0.36/0.57 (step @p47 :rule trans :premises (@p46 @p42)) % 0.36/0.57 (step @p48 :rule cong :premises (@p47) :args (@t53)) % 0.36/0.57 (step @p49 :rule beta-reduce :args ((= (_ (lambda @t57 @t56) @t50) @t53))) % 0.36/0.57 (step @p50 :rule trans :premises (@p49 @p48)) % 0.36/0.57 (step @p51 :rule beta-reduce :args ((= (_ @t58 @t1) @t50))) % 0.36/0.57 (step @p52 :rule refl :args (@t1)) % 0.36/0.57 (step @p53 :rule beta-reduce :args ((= @t59 @t58))) % 0.36/0.57 (step @p54 :rule ho_cong :premises (@p53 @p52)) % 0.36/0.57 (step @p55 :rule trans :premises (@p54 @p51)) % 0.36/0.57 (step @p56 :rule aci_norm :args ((= (and @t24 @t55) @t56))) % 0.36/0.57 (step @p57 :rule refl :args (@t55)) % 0.36/0.57 (step @p58 :rule beta-reduce :args ((= @t61 @t24))) % 0.36/0.57 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t62)) % 0.36/0.57 (step @p60 :rule trans :premises (@p59 @p56)) % 0.36/0.57 (step @p61 :rule cong :premises (@p60) :args (@t63)) % 0.36/0.57 (step @p62 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t54 @t14) (and @t19 @t55)) @t60) @t63))) % 0.36/0.57 (step @p63 :rule trans :premises (@p62 @p61)) % 0.36/0.57 (step @p64 :rule refl :args (@t60)) % 0.36/0.57 (step @p65 :rule alpha_equiv :args (@t27 @t64 (@list @t54))) % 0.36/0.57 (step @p66 :rule ho_cong :premises (@p65 @p64)) % 0.36/0.57 (step @p67 :rule trans :premises (@p66 @p63)) % 0.36/0.57 (step @p68 :rule beta-reduce :args ((= (_ @t58 @t4) @t60))) % 0.36/0.57 (step @p69 :rule refl :args (@t4)) % 0.36/0.57 (step @p70 :rule ho_cong :premises (@p53 @p69)) % 0.36/0.57 (step @p71 :rule trans :premises (@p70 @p68)) % 0.36/0.57 (step @p72 :rule refl :args (@t27)) % 0.36/0.57 (step @p73 :rule ho_cong :premises (@p72 @p71)) % 0.36/0.57 (step @p74 :rule trans :premises (@p73 @p67)) % 0.36/0.57 (step @p75 :rule ho_cong :premises (@p74 @p55)) % 0.36/0.57 (step @p76 :rule trans :premises (@p75 @p50)) % 0.36/0.57 (step @p77 :rule beta-reduce :args ((= @t66 @t44))) % 0.36/0.57 (step @p78 :rule cong :premises (@p77) :args (@t67)) % 0.36/0.57 (step @p79 :rule nary_cong :premises (@p44 @p78) :args (@t68)) % 0.36/0.57 (step @p80 :rule cong :premises (@p79) :args (@t69)) % 0.36/0.57 (step @p81 :rule beta-reduce :args ((= (_ @t58 @t65) @t69))) % 0.36/0.57 (step @p82 :rule trans :premises (@p81 @p80)) % 0.36/0.57 (step @p83 :rule beta-reduce :args ((= (_ @t72 @t1) @t65))) % 0.36/0.57 (step @p84 :rule beta-reduce :args ((= (_ (lambda (@list @t2 @t70 @t14) (or @t19 @t71)) @t4) @t72))) % 0.36/0.57 (step @p85 :rule refl :args (@t4)) % 0.36/0.57 (step @p86 :rule alpha_equiv :args (@t21 @t64 (@list @t70))) % 0.36/0.57 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 0.36/0.57 (step @p88 :rule trans :premises (@p87 @p84)) % 0.36/0.57 (step @p89 :rule ho_cong :premises (@p88 @p52)) % 0.36/0.57 (step @p90 :rule trans :premises (@p89 @p83)) % 0.36/0.57 (step @p91 :rule ho_cong :premises (@p53 @p90)) % 0.36/0.57 (step @p92 :rule trans :premises (@p91 @p82)) % 0.36/0.57 (step @p93 :rule cong :premises (@p92 @p76) :args (@t73)) % 0.36/0.57 (step @p94 :rule cong :premises (@p93) :args (@t74)) % 0.36/0.57 (step @p95 :rule trans :premises (@p94 @p41)) % 0.36/0.57 (step @p96 :rule cong :premises (@p95) :args ((not @t74))) % 0.36/0.57 (step @p97 :rule refl :args (@t2)) % 0.36/0.57 (step @p98 :rule ho_cong :premises (@p11 @p97)) % 0.36/0.57 (step @p99 :rule ho_cong :premises (@p98 @p52)) % 0.36/0.57 (step @p100 :rule ho_cong :premises (@p98 @p69)) % 0.36/0.57 (step @p101 :rule ho_cong :premises (@p10 @p100)) % 0.36/0.57 (step @p102 :rule ho_cong :premises (@p101 @p99)) % 0.36/0.57 (step @p103 :rule ho_cong :premises (@p8 @p69)) % 0.36/0.57 (step @p104 :rule ho_cong :premises (@p103 @p52)) % 0.36/0.57 (step @p105 :rule ho_cong :premises (@p98 @p104)) % 0.36/0.57 (step @p106 :rule cong :premises (@p105 @p102) :args (@t5)) % 0.36/0.57 (step @p107 :rule cong :premises (@p106) :args (@t7)) % 0.36/0.57 (step @p108 :rule cong :premises (@p107) :args (@t8)) % 0.36/0.57 (step @p109 :rule trans :premises (@p108 @p96)) % 0.36/0.57 (step @p110 :rule eq_resolve :premises (@p1 @p109)) % 0.36/0.57 (step @p111 :rule refl :args (@t87)) % 0.36/0.57 (step @p112 :rule bool-double-not-elim :args (@t75)) % 0.36/0.57 (step @p113 :rule nary_cong :premises (@p112 @p111) :args ((or (not @t88) @t87))) % 0.36/0.57 (step @p114 :rule eq-symm :args (@t83 @t85)) % 0.36/0.57 (step @p115 :rule eq-refl :args (@t84)) % 0.36/0.57 (step @p116 :rule skolem_intro :args (@t85)) % 0.36/0.57 (step @p117 :rule refl :args (@t84)) % 0.36/0.57 (step @p118 :rule cong :premises (@p117 @p116) :args ((= @t84 @t85))) % 0.36/0.57 (step @p119 :rule trans :premises (@p118 @p115)) % 0.36/0.57 (step @p120 :rule true_elim :premises (@p119)) % 0.36/0.57 (step @p121 :rule eq-refl :args (@t82)) % 0.36/0.57 (step @p122 :rule skolem_intro :args (@t83)) % 0.36/0.57 (step @p123 :rule refl :args (@t82)) % 0.36/0.57 (step @p124 :rule cong :premises (@p123 @p122) :args ((= @t82 @t83))) % 0.36/0.57 (step @p125 :rule trans :premises (@p124 @p121)) % 0.36/0.57 (step @p126 :rule true_elim :premises (@p125)) % 0.36/0.57 (step @p127 :rule cong :premises (@p126 @p120) :args (@t89)) % 0.36/0.57 (step @p128 :rule trans :premises (@p127 @p114)) % 0.36/0.57 (step @p129 :rule cong :premises (@p128) :args (@t90)) % 0.36/0.57 (step @p130 :rule refl :args (@t88)) % 0.36/0.57 (step @p131 :rule cong :premises (@p130 @p129) :args ((=> @t88 @t90))) % 0.36/0.57 (assume-push @p204 @t88) % 0.36/0.57 (step @p133 :rule skolemize :premises (@p110)) % 0.36/0.57 (step-pop @p205 :rule scope :premises (@p133)) % 0.36/0.57 (step @p134 :rule process_scope :premises (@p205) :args (@t90)) % 0.36/0.57 (step @p136 :rule eq_resolve :premises (@p134 @p131)) % 0.36/0.57 (step @p137 :rule implies_elim :premises (@p136)) % 0.36/0.57 (step @p138 :rule eq_resolve :premises (@p137 @p113)) % 0.36/0.57 (step @p139 :rule chain_m_resolution :premises (@p138 @p110) :args (@t87 @t91 (@list @t75))) % 0.36/0.57 (step @p140 :rule eq-symm :args (@t98 @t101)) % 0.36/0.57 (step @p141 :rule eq-refl :args (@t101)) % 0.36/0.57 (step @p142 :rule refl :args (@t101)) % 0.36/0.57 (step @p143 :rule beta-reduce :args (@t102)) % 0.36/0.57 (step @p144 :rule cong :premises (@p143 @p142) :args (@t102)) % 0.36/0.57 (step @p145 :rule trans :premises (@p144 @p141)) % 0.36/0.57 (step @p146 :rule refl :args (@t92)) % 0.36/0.57 (step @p147 :rule ho_cong :premises (@p122 @p146)) % 0.36/0.57 (step @p148 :rule cong :premises (@p147 @p142) :args ((= @t103 @t101))) % 0.36/0.57 (step @p149 :rule trans :premises (@p148 @p145)) % 0.36/0.57 (step @p150 :rule true_elim :premises (@p149)) % 0.36/0.57 (step @p151 :rule eq-refl :args (@t98)) % 0.36/0.57 (step @p152 :rule refl :args (@t98)) % 0.36/0.57 (step @p153 :rule beta-reduce :args (@t104)) % 0.36/0.57 (step @p154 :rule cong :premises (@p153 @p152) :args (@t104)) % 0.36/0.57 (step @p155 :rule trans :premises (@p154 @p151)) % 0.36/0.57 (step @p156 :rule ho_cong :premises (@p116 @p146)) % 0.36/0.57 (step @p157 :rule cong :premises (@p156 @p152) :args ((= @t105 @t98))) % 0.36/0.57 (step @p158 :rule trans :premises (@p157 @p155)) % 0.36/0.57 (step @p159 :rule true_elim :premises (@p158)) % 0.36/0.57 (step @p160 :rule cong :premises (@p159 @p150) :args (@t106)) % 0.36/0.57 (step @p161 :rule trans :premises (@p160 @p140)) % 0.36/0.57 (step @p162 :rule cong :premises (@p161) :args (@t107)) % 0.36/0.57 (step @p163 :rule refl :args (@t86)) % 0.36/0.57 (step @p164 :rule nary_cong :premises (@p163 @p162) :args (@t108)) % 0.36/0.57 ; WARNING: add trust step for TRUST % 0.36/0.57 ; trust TRUST THEORY_LEMMA % 0.36/0.57 (step @p165 :rule trust :premises () :args (@t108)) % 0.36/0.57 (step @p166 :rule eq_resolve :premises (@p165 @p164)) % 0.36/0.57 (step @p167 :rule chain_m_resolution :premises (@p166 @p139) :args ((not @t109) @t91 (@list @t86))) % 0.36/0.57 (step @p168 :rule cnf_or_neg :args (@t99 1)) % 0.36/0.57 (step @p169 :rule cnf_and_pos :args (@t98 2)) % 0.36/0.57 (step @p170 :rule reordering :premises (@p169) :args ((or @t94 @t110))) % 0.36/0.57 (step @p171 :rule cnf_and_pos :args (@t101 1)) % 0.36/0.57 (step @p172 :rule reordering :premises (@p171) :args ((or @t100 @t111))) % 0.36/0.57 (step @p173 :rule cnf_equiv_neg1 :args (@t109)) % 0.36/0.57 (step @p174 :rule reordering :premises (@p173) :args ((or @t101 @t98 @t109))) % 0.36/0.57 (step @p175 :rule chain_m_resolution :premises (@p174 @p167 @p172 @p170 @p168) :args (@t94 @t112 @t113)) % 0.36/0.57 (step @p176 :rule cnf_or_neg :args (@t99 0)) % 0.36/0.57 (step @p177 :rule cnf_and_pos :args (@t98 1)) % 0.36/0.57 (step @p178 :rule reordering :premises (@p177) :args ((or @t96 @t110))) % 0.36/0.57 (step @p179 :rule chain_m_resolution :premises (@p174 @p167 @p172 @p178 @p176) :args (@t96 @t112 @t113)) % 0.36/0.57 (step @p180 :rule cnf_or_pos :args (@t99)) % 0.36/0.57 (step @p181 :rule reordering :premises (@p180) :args ((or @t95 @t93 @t100))) % 0.36/0.57 (step @p182 :rule bool-double-not-elim :args (@t93)) % 0.36/0.57 (step @p183 :rule bool-double-not-elim :args (@t95)) % 0.36/0.57 (step @p184 :rule refl :args (@t114)) % 0.36/0.57 (step @p185 :rule nary_cong :premises (@p152 @p184 @p183 @p182) :args ((or @t98 @t114 (not @t96) (not @t94)))) % 0.36/0.57 (step @p186 :rule cnf_and_neg :args (@t98)) % 0.36/0.57 (step @p187 :rule eq_resolve :premises (@p186 @p185)) % 0.36/0.57 (step @p188 :rule reordering :premises (@p187) :args ((or @t95 @t93 @t98 @t114))) % 0.36/0.57 (step @p189 :rule bool-double-not-elim :args (@t99)) % 0.36/0.57 (step @p190 :rule nary_cong :premises (@p142 @p184 @p189) :args ((or @t101 @t114 (not @t100)))) % 0.36/0.57 (step @p191 :rule cnf_and_neg :args (@t101)) % 0.36/0.57 (step @p192 :rule eq_resolve :premises (@p191 @p190)) % 0.36/0.57 (step @p193 :rule reordering :premises (@p192) :args ((or @t99 @t101 @t114))) % 0.36/0.57 (step @p194 :rule cnf_equiv_neg2 :args (@t109)) % 0.36/0.57 (step @p195 :rule chain_m_resolution :premises (@p194 @p167 @p193 @p188 @p181) :args ((or @t95 @t93 @t114) (@list true false false true) @t113)) % 0.36/0.57 (step @p196 :rule chain_m_resolution :premises (@p195 @p179 @p175) :args (@t114 (@list true true) (@list @t95 @t93))) % 0.36/0.57 (step @p197 :rule cnf_and_pos :args (@t101 0)) % 0.36/0.57 (step @p198 :rule reordering :premises (@p197) :args ((or @t97 @t111))) % 0.36/0.57 (step @p199 :rule chain_m_resolution :premises (@p198 @p196) :args (@t111 @t91 @t115)) % 0.36/0.57 (step @p200 :rule cnf_and_pos :args (@t98 0)) % 0.36/0.57 (step @p201 :rule reordering :premises (@p200) :args ((or @t97 @t110))) % 0.36/0.57 (step @p202 :rule chain_m_resolution :premises (@p201 @p196) :args (@t110 @t91 @t115)) % 0.36/0.57 (step @p203 false :rule chain_m_resolution :premises (@p174 @p202 @p199 @p167) :args (false (@list true true true) (@list @t98 @t101 @t109))) % 0.36/0.57 ) % 0.36/0.57 % SZS output end Proof % 0.36/0.58 % cvc5 exiting %------------------------------------------------------------------------------