%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET640^3 : 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 : 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 08:48:20 AM UTC 2026 % Result : Theorem 0.38s 0.60s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET640^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n027.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:05:51 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.52 %----Proving TH0 % 0.38/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.60 % SZS status Theorem % 0.38/0.60 % SZS output start Proof % 0.38/0.60 ( % 0.38/0.60 (declare-sort $$unsorted 0) % 0.38/0.60 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.60 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.60 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.60 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.38/0.60 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.38/0.60 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.60 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.38/0.60 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.60 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.60 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.38/0.60 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.38/0.60 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.38/0.60 (define tptp.cartesian_product () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3 _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.pair_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "V" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1 _let_4 _let_2) (or (= _let_4 _let_3) (= _let_2 _let_1)))))))) % 0.38/0.60 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.38/0.60 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.38/0.60 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.38/0.60 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 0.38/0.60 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.60 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.60 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.38/0.60 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.transitive () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.38/0.60 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 0.38/0.60 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.60 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.38/0.60 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S1" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.60 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.60 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.38/0.60 (define tptp.well_founded () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "Z" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.38/0.60 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "Z" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.38/0.60 (define @t1 () (@var "X" $$unsorted)) % 0.38/0.60 (define @t2 () (@list @t1)) % 0.38/0.60 (define @t3 () (lambda @t2 true)) % 0.38/0.60 (define @t4 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t5 () (_ tptp.sub_rel @t4)) % 0.38/0.60 (define @t6 () (@var "Q" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t7 () (=> (_ @t5 @t6) (_ @t5 (_ (_ tptp.cartesian_product @t3) @t3)))) % 0.38/0.60 (define @t8 () (@list @t4 @t6)) % 0.38/0.60 (define @t9 () (forall @t8 @t7)) % 0.38/0.60 (define @t10 () (not @t9)) % 0.38/0.60 (define @t11 () (@var "M" (-> $$unsorted Bool))) % 0.38/0.60 (define @t12 () (lambda (@list @t1 @t11) (_ @t11 @t1))) % 0.38/0.60 (define @t13 () (lambda @t2 false)) % 0.38/0.60 (define @t14 () (@var "Y" $$unsorted)) % 0.38/0.60 (define @t15 () (@var "U" $$unsorted)) % 0.38/0.60 (define @t16 () (= @t15 @t1)) % 0.38/0.60 (define @t17 () (lambda (@list @t1 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.38/0.60 (define @t18 () (lambda (@list @t1 @t15) @t16)) % 0.38/0.60 (define @t19 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.60 (define @t20 () (_ @t19 @t15)) % 0.38/0.60 (define @t21 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.60 (define @t22 () (_ @t21 @t15)) % 0.38/0.60 (define @t23 () (@list @t21 @t19 @t15)) % 0.38/0.60 (define @t24 () (lambda @t23 (or @t22 @t20))) % 0.38/0.60 (define @t25 () (not @t22)) % 0.38/0.60 (define @t26 () (and @t22 (not @t20))) % 0.38/0.60 (define @t27 () (lambda @t23 (or @t26 (and @t25 @t20)))) % 0.38/0.60 (define @t28 () (and @t22 @t20)) % 0.38/0.60 (define @t29 () (lambda @t23 @t28)) % 0.38/0.60 (define @t30 () (lambda @t23 @t26)) % 0.38/0.60 (define @t31 () (lambda (@list @t21 @t15) @t25)) % 0.38/0.60 (define @t32 () (@list @t21 @t19)) % 0.38/0.60 (define @t33 () (lambda @t32 (= (_ (_ tptp.intersection @t21) @t19) tptp.emptyset))) % 0.38/0.60 (define @t34 () (@list @t15)) % 0.38/0.60 (define @t35 () (lambda @t32 (forall @t34 (=> @t22 @t20)))) % 0.38/0.60 (define @t36 () (exists @t34 @t28)) % 0.38/0.60 (define @t37 () (lambda @t32 @t36)) % 0.38/0.60 (define @t38 () (lambda @t32 (not @t36))) % 0.38/0.60 (define @t39 () (@var "V" $$unsorted)) % 0.38/0.60 (define @t40 () (_ @t19 @t39)) % 0.38/0.60 (define @t41 () (lambda (@list @t21 @t19 @t15 @t39) (and @t22 @t40))) % 0.38/0.60 (define @t42 () (lambda (@list @t1 @t14 @t15 @t39) (or @t16 (= @t39 @t14)))) % 0.38/0.60 (define @t43 () (= @t1 @t14)) % 0.38/0.60 (define @t44 () (@var "S" (-> $$unsorted Bool))) % 0.38/0.60 (define @t45 () (_ @t44 @t1)) % 0.38/0.60 (define @t46 () (lambda (@list @t44 @t1 @t14) (and @t45 @t43))) % 0.38/0.60 (define @t47 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t48 () (_ (_ @t47 @t1) @t14)) % 0.38/0.60 (define @t49 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.38/0.60 (define @t50 () (_ (_ @t49 @t1) @t14)) % 0.38/0.60 (define @t51 () (@list @t1 @t14)) % 0.38/0.60 (define @t52 () (forall @t51 (=> @t50 @t48))) % 0.38/0.60 (define @t53 () (@list @t49 @t47)) % 0.38/0.60 (define @t54 () (lambda @t53 @t52)) % 0.38/0.60 (define @t55 () (@var "B" (-> $$unsorted Bool))) % 0.38/0.60 (define @t56 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.60 (define @t57 () (_ @t4 @t1)) % 0.38/0.60 (define @t58 () (_ @t57 @t14)) % 0.38/0.60 (define @t59 () (lambda (@list @t4 @t56 @t55) (forall @t51 (=> @t58 (and (_ @t56 @t1) (_ @t55 @t14)))))) % 0.38/0.60 (define @t60 () (@list @t4 @t44 @t1 @t14)) % 0.38/0.60 (define @t61 () (lambda @t60 (and @t45 @t58))) % 0.38/0.60 (define @t62 () (lambda @t51 @t43)) % 0.38/0.60 (define @t63 () (@var "Z" $$unsorted)) % 0.38/0.60 (define @t64 () (@list @t14)) % 0.38/0.60 (define @t65 () (lambda (@list @t49 @t47 @t1 @t63) (exists @t64 (and @t50 (_ (_ @t47 @t14) @t63))))) % 0.38/0.60 (define @t66 () (_ @t57 @t1)) % 0.38/0.60 (define @t67 () (@list @t4)) % 0.38/0.60 (define @t68 () (lambda @t67 (forall @t2 @t66))) % 0.38/0.60 (define @t69 () (lambda @t67 (forall @t2 (not @t66)))) % 0.38/0.60 (define @t70 () (_ @t4 @t14)) % 0.38/0.60 (define @t71 () (_ @t70 @t1)) % 0.38/0.60 (define @t72 () (lambda @t67 (forall @t51 (=> @t58 @t71)))) % 0.38/0.60 (define @t73 () (lambda @t67 (forall (@list @t1 @t14 @t63) (=> (and @t58 (_ @t70 @t63)) (_ @t57 @t63))))) % 0.38/0.60 (define @t74 () (lambda @t67 (and (_ tptp.reflexive @t4) (_ tptp.symmetric @t4) (_ tptp.transitive @t4)))) % 0.38/0.60 (define @t75 () (lambda (@list @t4 @t14) (exists @t2 @t58))) % 0.38/0.60 (define @t76 () (@list @t4 @t1)) % 0.38/0.60 (define @t77 () (lambda @t76 (exists @t64 @t58))) % 0.38/0.60 (define @t78 () (lambda (@list @t4 @t1 @t14) @t71)) % 0.38/0.60 (define @t79 () (@var "S1" (-> $$unsorted Bool))) % 0.38/0.60 (define @t80 () (lambda (@list @t4 @t79) (exists @t2 (and (_ @t79 @t1) (forall @t64 (= (_ @t79 @t14) @t58)))))) % 0.38/0.60 (define @t81 () (lambda @t60 (and (_ @t44 @t14) @t58))) % 0.38/0.60 (define @t82 () (lambda @t76 (or (_ (_ tptp.rel_domain @t4) @t1) (_ (_ tptp.rel_codomain @t4) @t1)))) % 0.38/0.60 (define @t83 () (@var "W" $$unsorted)) % 0.38/0.60 (define @t84 () (not (_ @t21 @t83))) % 0.38/0.60 (define @t85 () (@list @t83)) % 0.38/0.60 (define @t86 () (_ @t21 @t14)) % 0.38/0.60 (define @t87 () (_ @t21 @t63)) % 0.38/0.60 (define @t88 () (@list @t21 @t63)) % 0.38/0.60 (define @t89 () (lambda @t67 (forall @t88 (=> @t87 (exists @t64 (and @t86 (forall @t85 (=> (_ @t70 @t83) @t84)))))))) % 0.38/0.60 (define @t90 () (lambda @t67 (forall @t88 (=> @t87 (exists @t64 (and @t86 (forall @t85 (=> (_ @t70 @t14) @t84)))))))) % 0.38/0.60 (define @t91 () (not (_ @t4 @t1 @t14))) % 0.38/0.60 (define @t92 () (forall @t51 (or @t91 (_ @t6 @t1 @t14)))) % 0.38/0.60 (define @t93 () (@var "BOUND_VARIABLE_8195" $$unsorted)) % 0.38/0.60 (define @t94 () (@var "BOUND_VARIABLE_8193" $$unsorted)) % 0.38/0.60 (define @t95 () (lambda (@list @t94 @t93) true)) % 0.38/0.60 (define @t96 () (_ @t95 @t1 @t14)) % 0.38/0.60 (define @t97 () (or @t91 @t96)) % 0.38/0.60 (define @t98 () (forall @t51 @t97)) % 0.38/0.60 (define @t99 () (_ @t47 @t1 @t14)) % 0.38/0.60 (define @t100 () (lambda (@list @t47) (forall @t51 (or @t91 @t99)))) % 0.38/0.60 (define @t101 () (@list @t15 @t39)) % 0.38/0.60 (define @t102 () (@var "BOUND_VARIABLE_8177" $$unsorted)) % 0.38/0.60 (define @t103 () (lambda (@list @t102) true)) % 0.38/0.60 (define @t104 () (_ @t103 @t39)) % 0.38/0.60 (define @t105 () (lambda @t101 @t104)) % 0.38/0.60 (define @t106 () (@list @t19 @t15 @t39)) % 0.38/0.60 (define @t107 () (_ @t103 @t15)) % 0.38/0.60 (define @t108 () (and @t107 @t40)) % 0.38/0.60 (define @t109 () (lambda @t106 @t108)) % 0.38/0.60 (define @t110 () (_ @t49 @t1 @t14)) % 0.38/0.60 (define @t111 () (_ (lambda @t53 (forall @t51 (or (not @t110) @t99))) @t4)) % 0.38/0.60 (define @t112 () (=> (_ @t111 @t6) (_ @t111 (_ (_ @t41 @t3) @t3)))) % 0.38/0.60 (define @t113 () (forall @t8 @t112)) % 0.38/0.60 (define @t114 () (not @t50)) % 0.38/0.60 (define @t115 () (or @t114 @t48)) % 0.38/0.60 (assume @p1 @t10) % 0.38/0.60 (assume @p2 true) % 0.38/0.60 (step @p3 (= tptp.in @t12) :rule refl :args (@t12)) % 0.38/0.60 (step @p4 (= tptp.is_a @t12) :rule refl :args (@t12)) % 0.38/0.60 (step @p5 (= tptp.emptyset @t13) :rule refl :args (@t13)) % 0.38/0.60 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.38/0.60 (step @p7 (= tptp.singleton @t18) :rule refl :args (@t18)) % 0.38/0.60 (step @p8 (= tptp.union @t24) :rule refl :args (@t24)) % 0.38/0.60 (step @p9 (= tptp.excl_union @t27) :rule refl :args (@t27)) % 0.38/0.60 (step @p10 (= tptp.intersection @t29) :rule refl :args (@t29)) % 0.38/0.60 (step @p11 (= tptp.setminus @t30) :rule refl :args (@t30)) % 0.38/0.60 (step @p12 (= tptp.complement @t31) :rule refl :args (@t31)) % 0.38/0.60 (step @p13 (= tptp.disjoint @t33) :rule refl :args (@t33)) % 0.38/0.60 (step @p14 (= tptp.subset @t35) :rule refl :args (@t35)) % 0.38/0.60 (step @p15 (= tptp.meets @t37) :rule refl :args (@t37)) % 0.38/0.60 (step @p16 (= tptp.misses @t38) :rule refl :args (@t38)) % 0.38/0.60 (step @p17 (= tptp.cartesian_product @t41) :rule refl :args (@t41)) % 0.38/0.60 (step @p18 (= tptp.pair_rel @t42) :rule refl :args (@t42)) % 0.38/0.60 (step @p19 (= tptp.id_rel @t46) :rule refl :args (@t46)) % 0.38/0.60 (step @p20 (= tptp.sub_rel @t54) :rule refl :args (@t54)) % 0.38/0.60 (step @p21 (= tptp.is_rel_on @t59) :rule refl :args (@t59)) % 0.38/0.60 (step @p22 (= tptp.restrict_rel_domain @t61) :rule refl :args (@t61)) % 0.38/0.60 (step @p23 (= tptp.rel_diagonal @t62) :rule refl :args (@t62)) % 0.38/0.60 (step @p24 (= tptp.rel_composition @t65) :rule refl :args (@t65)) % 0.38/0.60 (step @p25 (= tptp.reflexive @t68) :rule refl :args (@t68)) % 0.38/0.60 (step @p26 (= tptp.irreflexive @t69) :rule refl :args (@t69)) % 0.38/0.60 (step @p27 (= tptp.symmetric @t72) :rule refl :args (@t72)) % 0.38/0.60 (step @p28 (= tptp.transitive @t73) :rule refl :args (@t73)) % 0.38/0.60 (step @p29 (= tptp.equiv_rel @t74) :rule refl :args (@t74)) % 0.38/0.60 (step @p30 (= tptp.rel_codomain @t75) :rule refl :args (@t75)) % 0.38/0.60 (step @p31 (= tptp.rel_domain @t77) :rule refl :args (@t77)) % 0.38/0.60 (step @p32 (= tptp.rel_inverse @t78) :rule refl :args (@t78)) % 0.38/0.60 (step @p33 (= tptp.equiv_classes @t80) :rule refl :args (@t80)) % 0.38/0.60 (step @p34 (= tptp.restrict_rel_codomain @t81) :rule refl :args (@t81)) % 0.38/0.60 (step @p35 (= tptp.rel_field @t82) :rule refl :args (@t82)) % 0.38/0.60 (step @p36 (= tptp.well_founded @t89) :rule refl :args (@t89)) % 0.38/0.60 (step @p37 (= tptp.upwards_well_founded @t90) :rule refl :args (@t90)) % 0.38/0.60 (step @p38 :rule evaluate :args ((not true))) % 0.38/0.60 (step @p39 :rule quant-unused-vars :args ((= (forall @t8 true) true))) % 0.38/0.60 (step @p40 :rule bool-impl-true1 :args (@t92)) % 0.38/0.60 (step @p41 :rule quant-unused-vars :args ((= (forall @t51 true) true))) % 0.38/0.60 (step @p42 :rule absorb :args ((= (or @t91 true) true))) % 0.38/0.60 (step @p43 :rule beta-reduce :args ((= @t96 true))) % 0.38/0.60 (step @p44 :rule refl :args (@t91)) % 0.38/0.60 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t97)) % 0.38/0.60 (step @p46 :rule trans :premises (@p45 @p42)) % 0.38/0.60 (step @p47 :rule cong :premises (@p46) :args (@t98)) % 0.38/0.60 (step @p48 :rule trans :premises (@p47 @p41)) % 0.38/0.60 (step @p49 :rule beta-reduce :args ((= (_ @t100 @t95) @t98))) % 0.38/0.60 (step @p50 :rule trans :premises (@p49 @p48)) % 0.38/0.60 (step @p51 :rule refl :args (@t95)) % 0.38/0.60 (step @p52 :rule symm :premises (@p51)) % 0.38/0.60 (step @p53 :rule alpha_equiv :args ((lambda @t101 true) (@list @t15 @t39) (@list @t94 @t93))) % 0.38/0.60 (step @p54 :rule trans :premises (@p53 @p52)) % 0.38/0.60 (step @p55 :rule beta-reduce :args ((= @t104 true))) % 0.38/0.60 (step @p56 :rule cong :premises (@p55) :args (@t105)) % 0.38/0.60 (step @p57 :rule trans :premises (@p56 @p54)) % 0.38/0.60 (step @p58 :rule beta-reduce :args ((= (_ (lambda @t106 @t40) @t103) @t105))) % 0.38/0.60 (step @p59 :rule trans :premises (@p58 @p57)) % 0.38/0.60 (step @p60 :rule refl :args (@t103)) % 0.38/0.60 (step @p61 :rule symm :premises (@p60)) % 0.38/0.60 (step @p62 :rule alpha_equiv :args (@t3 (@list @t1) (@list @t102))) % 0.38/0.60 (step @p63 :rule trans :premises (@p62 @p61)) % 0.38/0.60 (step @p64 :rule aci_norm :args ((= (and true @t40) @t40))) % 0.38/0.60 (step @p65 :rule refl :args (@t40)) % 0.38/0.60 (step @p66 :rule beta-reduce :args ((= @t107 true))) % 0.38/0.60 (step @p67 :rule nary_cong :premises (@p66 @p65) :args (@t108)) % 0.38/0.60 (step @p68 :rule trans :premises (@p67 @p64)) % 0.38/0.60 (step @p69 :rule cong :premises (@p68) :args (@t109)) % 0.38/0.60 (step @p70 :rule beta-reduce :args ((= (_ @t41 @t103) @t109))) % 0.38/0.60 (step @p71 :rule trans :premises (@p70 @p69)) % 0.38/0.60 (step @p72 :rule refl :args (@t41)) % 0.38/0.60 (step @p73 :rule ho_cong :premises (@p72 @p63)) % 0.38/0.60 (step @p74 :rule trans :premises (@p73 @p71)) % 0.38/0.60 (step @p75 :rule ho_cong :premises (@p74 @p63)) % 0.38/0.60 (step @p76 :rule trans :premises (@p75 @p59)) % 0.38/0.60 (step @p77 :rule beta-reduce :args ((= @t111 @t100))) % 0.38/0.60 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 0.38/0.60 (step @p79 :rule trans :premises (@p78 @p50)) % 0.38/0.60 (step @p80 :rule beta-reduce :args ((= (_ @t100 @t6) @t92))) % 0.38/0.60 (step @p81 :rule refl :args (@t6)) % 0.38/0.60 (step @p82 :rule ho_cong :premises (@p77 @p81)) % 0.38/0.60 (step @p83 :rule trans :premises (@p82 @p80)) % 0.38/0.60 (step @p84 :rule cong :premises (@p83 @p79) :args (@t112)) % 0.38/0.60 (step @p85 :rule trans :premises (@p84 @p40)) % 0.38/0.60 (step @p86 :rule cong :premises (@p85) :args (@t113)) % 0.38/0.60 (step @p87 :rule trans :premises (@p86 @p39)) % 0.38/0.60 (step @p88 :rule cong :premises (@p87) :args ((not @t113))) % 0.38/0.60 (step @p89 :rule trans :premises (@p88 @p38)) % 0.38/0.60 (step @p90 :rule refl :args (@t3)) % 0.38/0.60 (step @p91 :rule ho_cong :premises (@p17 @p90)) % 0.38/0.60 (step @p92 :rule ho_cong :premises (@p91 @p90)) % 0.38/0.60 (step @p93 :rule refl :args (@t4)) % 0.38/0.60 (step @p94 :rule refl :args (@t99)) % 0.38/0.60 (step @p95 :rule refl :args (@t48)) % 0.38/0.60 (step @p96 :rule cong :premises (@p95 @p94) :args ((= @t48 @t99))) % 0.38/0.60 (step @p97 :rule symm :premises (@p96)) % 0.38/0.60 (step @p98 :rule eq_resolve :premises (@p95 @p97)) % 0.38/0.60 (step @p99 :rule refl :args (@t110)) % 0.38/0.60 (step @p100 :rule refl :args (@t50)) % 0.38/0.60 (step @p101 :rule cong :premises (@p100 @p99) :args ((= @t50 @t110))) % 0.38/0.60 (step @p102 :rule symm :premises (@p101)) % 0.38/0.60 (step @p103 :rule eq_resolve :premises (@p100 @p102)) % 0.38/0.60 (step @p104 :rule cong :premises (@p103) :args (@t114)) % 0.38/0.60 (step @p105 :rule nary_cong :premises (@p104 @p98) :args (@t115)) % 0.38/0.60 (step @p106 :rule cong :premises (@p105) :args ((forall @t51 @t115))) % 0.38/0.60 (step @p107 :rule bool-impl-elim :args (@t50 @t48)) % 0.38/0.60 (step @p108 :rule cong :premises (@p107) :args (@t52)) % 0.38/0.60 (step @p109 :rule trans :premises (@p108 @p106)) % 0.38/0.60 (step @p110 :rule cong :premises (@p109) :args (@t54)) % 0.38/0.60 (step @p111 :rule trans :premises (@p20 @p110)) % 0.38/0.60 (step @p112 :rule ho_cong :premises (@p111 @p93)) % 0.38/0.60 (step @p113 :rule ho_cong :premises (@p112 @p92)) % 0.38/0.60 (step @p114 :rule ho_cong :premises (@p112 @p81)) % 0.38/0.60 (step @p115 :rule cong :premises (@p114 @p113) :args (@t7)) % 0.38/0.60 (step @p116 :rule cong :premises (@p115) :args (@t9)) % 0.38/0.60 (step @p117 :rule cong :premises (@p116) :args (@t10)) % 0.38/0.60 (step @p118 :rule trans :premises (@p117 @p89)) % 0.38/0.60 (step @p119 false :rule eq_resolve :premises (@p1 @p118)) % 0.38/0.60 ) % 0.38/0.60 % SZS output end Proof % 0.38/0.60 % cvc5 exiting %------------------------------------------------------------------------------