%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET684^3 : 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 : n004.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 08:48:26 AM UTC 2026 % Result : Theorem 0.38s 0.59s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET684^3 : TPTP v9.2.1. Released v3.6.0. % 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n004.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:08:22 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.38/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.59 % SZS status Theorem % 0.38/0.59 % SZS output start Proof % 0.38/0.59 ( % 0.38/0.59 (declare-sort $$unsorted 0) % 0.38/0.59 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.59 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.59 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.59 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.38/0.59 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.38/0.59 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.59 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.38/0.59 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.59 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.38/0.59 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.59 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.38/0.59 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.38/0.59 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.59 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.38/0.59 (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)))))))) % 0.38/0.59 (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)))))))) % 0.38/0.59 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.38/0.59 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.38/0.59 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$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 $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.38/0.59 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.38/0.59 (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))))) % 0.38/0.59 (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 $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.59 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.59 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.38/0.59 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.59 (define tptp.transitive () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.38/0.59 (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))))) % 0.38/0.59 (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))))))) % 0.38/0.59 (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))))))) % 0.38/0.59 (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)))))) % 0.38/0.59 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.59 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.38/0.59 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.38/0.59 (define tptp.well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.38/0.59 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.38/0.59 (define @t1 () (@var "Z" $$unsorted)) % 0.38/0.59 (define @t2 () (@var "Y" $$unsorted)) % 0.38/0.59 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.59 (define @t4 () (_ @t3 @t2)) % 0.38/0.59 (define @t5 () (_ @t4 @t1)) % 0.38/0.59 (define @t6 () (@var "X" $$unsorted)) % 0.38/0.59 (define @t7 () (@var "P" (-> $$unsorted $$unsorted Bool))) % 0.38/0.59 (define @t8 () (_ (_ @t7 @t6) @t2)) % 0.38/0.59 (define @t9 () (and @t8 @t5)) % 0.38/0.59 (define @t10 () (@list @t2)) % 0.38/0.59 (define @t11 () (exists @t10 @t9)) % 0.38/0.59 (define @t12 () (= (_ (_ (_ (_ tptp.rel_composition @t7) @t3) @t6) @t1) @t11)) % 0.38/0.59 (define @t13 () (@list @t7 @t3 @t6 @t1)) % 0.38/0.59 (define @t14 () (forall @t13 @t12)) % 0.38/0.59 (define @t15 () (not @t14)) % 0.38/0.59 (define @t16 () (@var "M" (-> $$unsorted Bool))) % 0.38/0.59 (define @t17 () (lambda (@list @t6 @t16) (_ @t16 @t6))) % 0.38/0.59 (define @t18 () (@list @t6)) % 0.38/0.59 (define @t19 () (lambda @t18 false)) % 0.38/0.59 (define @t20 () (@var "U" $$unsorted)) % 0.38/0.59 (define @t21 () (= @t20 @t6)) % 0.38/0.59 (define @t22 () (lambda (@list @t6 @t2 @t20) (or @t21 (= @t20 @t2)))) % 0.38/0.59 (define @t23 () (lambda (@list @t6 @t20) @t21)) % 0.38/0.59 (define @t24 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.59 (define @t25 () (_ @t24 @t20)) % 0.38/0.59 (define @t26 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.59 (define @t27 () (_ @t26 @t20)) % 0.38/0.59 (define @t28 () (@list @t26 @t24 @t20)) % 0.38/0.59 (define @t29 () (lambda @t28 (or @t27 @t25))) % 0.38/0.59 (define @t30 () (not @t27)) % 0.38/0.59 (define @t31 () (and @t27 (not @t25))) % 0.38/0.59 (define @t32 () (lambda @t28 (or @t31 (and @t30 @t25)))) % 0.38/0.59 (define @t33 () (and @t27 @t25)) % 0.38/0.59 (define @t34 () (lambda @t28 @t33)) % 0.38/0.59 (define @t35 () (lambda @t28 @t31)) % 0.38/0.59 (define @t36 () (lambda (@list @t26 @t20) @t30)) % 0.38/0.59 (define @t37 () (@list @t26 @t24)) % 0.38/0.59 (define @t38 () (lambda @t37 (= (_ (_ tptp.intersection @t26) @t24) tptp.emptyset))) % 0.38/0.59 (define @t39 () (@list @t20)) % 0.38/0.59 (define @t40 () (lambda @t37 (forall @t39 (=> @t27 @t25)))) % 0.38/0.59 (define @t41 () (exists @t39 @t33)) % 0.38/0.59 (define @t42 () (lambda @t37 @t41)) % 0.38/0.59 (define @t43 () (lambda @t37 (not @t41))) % 0.38/0.59 (define @t44 () (@var "V" $$unsorted)) % 0.38/0.59 (define @t45 () (lambda (@list @t26 @t24 @t20 @t44) (and @t27 (_ @t24 @t44)))) % 0.38/0.59 (define @t46 () (lambda (@list @t6 @t2 @t20 @t44) (or @t21 (= @t44 @t2)))) % 0.38/0.59 (define @t47 () (= @t6 @t2)) % 0.38/0.59 (define @t48 () (@var "S" (-> $$unsorted Bool))) % 0.38/0.59 (define @t49 () (_ @t48 @t6)) % 0.38/0.59 (define @t50 () (lambda (@list @t48 @t6 @t2) (and @t49 @t47))) % 0.38/0.59 (define @t51 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.38/0.59 (define @t52 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.38/0.59 (define @t53 () (_ (_ @t52 @t6) @t2)) % 0.38/0.59 (define @t54 () (@list @t6 @t2)) % 0.38/0.59 (define @t55 () (lambda (@list @t52 @t51) (forall @t54 (=> @t53 (_ (_ @t51 @t6) @t2))))) % 0.38/0.59 (define @t56 () (@var "B" (-> $$unsorted Bool))) % 0.38/0.59 (define @t57 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.59 (define @t58 () (_ @t3 @t6)) % 0.38/0.59 (define @t59 () (_ @t58 @t2)) % 0.38/0.59 (define @t60 () (lambda (@list @t3 @t57 @t56) (forall @t54 (=> @t59 (and (_ @t57 @t6) (_ @t56 @t2)))))) % 0.38/0.59 (define @t61 () (@list @t3 @t48 @t6 @t2)) % 0.38/0.59 (define @t62 () (lambda @t61 (and @t49 @t59))) % 0.38/0.59 (define @t63 () (lambda @t54 @t47)) % 0.38/0.59 (define @t64 () (_ (_ @t51 @t2) @t1)) % 0.38/0.59 (define @t65 () (and @t53 @t64)) % 0.38/0.59 (define @t66 () (exists @t10 @t65)) % 0.38/0.59 (define @t67 () (@list @t52 @t51 @t6 @t1)) % 0.38/0.59 (define @t68 () (lambda @t67 @t66)) % 0.38/0.59 (define @t69 () (_ @t58 @t6)) % 0.38/0.59 (define @t70 () (@list @t3)) % 0.38/0.59 (define @t71 () (lambda @t70 (forall @t18 @t69))) % 0.38/0.59 (define @t72 () (lambda @t70 (forall @t18 (not @t69)))) % 0.38/0.59 (define @t73 () (_ @t4 @t6)) % 0.38/0.59 (define @t74 () (lambda @t70 (forall @t54 (=> @t59 @t73)))) % 0.38/0.59 (define @t75 () (lambda @t70 (forall (@list @t6 @t2 @t1) (=> (and @t59 @t5) (_ @t58 @t1))))) % 0.38/0.59 (define @t76 () (lambda @t70 (and (_ tptp.reflexive @t3) (_ tptp.symmetric @t3) (_ tptp.transitive @t3)))) % 0.38/0.59 (define @t77 () (lambda (@list @t3 @t2) (exists @t18 @t59))) % 0.38/0.59 (define @t78 () (@list @t3 @t6)) % 0.38/0.59 (define @t79 () (lambda @t78 (exists @t10 @t59))) % 0.38/0.59 (define @t80 () (lambda (@list @t3 @t6 @t2) @t73)) % 0.38/0.59 (define @t81 () (@var "S1" (-> $$unsorted Bool))) % 0.38/0.59 (define @t82 () (lambda (@list @t3 @t81) (exists @t18 (and (_ @t81 @t6) (forall @t10 (= (_ @t81 @t2) @t59)))))) % 0.38/0.59 (define @t83 () (lambda @t61 (and (_ @t48 @t2) @t59))) % 0.38/0.59 (define @t84 () (lambda @t78 (or (_ (_ tptp.rel_domain @t3) @t6) (_ (_ tptp.rel_codomain @t3) @t6)))) % 0.38/0.59 (define @t85 () (@var "W" $$unsorted)) % 0.38/0.59 (define @t86 () (not (_ @t26 @t85))) % 0.38/0.59 (define @t87 () (@list @t85)) % 0.38/0.59 (define @t88 () (_ @t26 @t2)) % 0.38/0.59 (define @t89 () (_ @t26 @t1)) % 0.38/0.59 (define @t90 () (@list @t26 @t1)) % 0.38/0.59 (define @t91 () (lambda @t70 (forall @t90 (=> @t89 (exists @t10 (and @t88 (forall @t87 (=> (_ @t4 @t85) @t86)))))))) % 0.38/0.59 (define @t92 () (lambda @t70 (forall @t90 (=> @t89 (exists @t10 (and @t88 (forall @t87 (=> (_ @t4 @t2) @t86)))))))) % 0.38/0.59 (define @t93 () (_ @t3 @t2 @t1)) % 0.38/0.59 (define @t94 () (_ @t7 @t6 @t2)) % 0.38/0.59 (define @t95 () (not @t94)) % 0.38/0.59 (define @t96 () (not (forall @t10 (or @t95 (not @t93))))) % 0.38/0.59 (define @t97 () (lambda (@list @t1) @t96)) % 0.38/0.59 (define @t98 () (lambda (@list @t6 @t1) @t96)) % 0.38/0.59 (define @t99 () (_ @t51 @t2 @t1)) % 0.38/0.59 (define @t100 () (not @t99)) % 0.38/0.59 (define @t101 () (lambda (@list @t51 @t6 @t1) (not (forall @t10 (or @t95 @t100))))) % 0.38/0.59 (define @t102 () (_ @t52 @t6 @t2)) % 0.38/0.59 (define @t103 () (_ (lambda @t67 (not (forall @t10 (or (not @t102) @t100)))) @t7)) % 0.38/0.59 (define @t104 () (not @t5)) % 0.38/0.59 (define @t105 () (not @t8)) % 0.38/0.59 (define @t106 () (or @t105 @t104)) % 0.38/0.59 (define @t107 () (forall @t10 (not @t9))) % 0.38/0.59 (define @t108 () (not @t107)) % 0.38/0.59 (define @t109 () (_ (_ (_ @t103 @t3) @t6) @t1)) % 0.38/0.59 (define @t110 () (forall @t13 (= @t109 @t11))) % 0.38/0.59 (define @t111 () (not @t64)) % 0.38/0.59 (define @t112 () (not @t53)) % 0.38/0.59 (define @t113 () (or @t112 @t111)) % 0.38/0.59 (define @t114 () (forall @t10 (not @t65))) % 0.38/0.59 (define @t115 () (not @t114)) % 0.38/0.59 (assume @p1 @t15) % 0.38/0.59 (assume @p2 true) % 0.38/0.59 (step @p3 (= tptp.in @t17) :rule refl :args (@t17)) % 0.38/0.59 (step @p4 (= tptp.is_a @t17) :rule refl :args (@t17)) % 0.38/0.59 (step @p5 (= tptp.emptyset @t19) :rule refl :args (@t19)) % 0.38/0.59 (step @p6 (= tptp.unord_pair @t22) :rule refl :args (@t22)) % 0.38/0.59 (step @p7 (= tptp.singleton @t23) :rule refl :args (@t23)) % 0.38/0.59 (step @p8 (= tptp.union @t29) :rule refl :args (@t29)) % 0.38/0.59 (step @p9 (= tptp.excl_union @t32) :rule refl :args (@t32)) % 0.38/0.59 (step @p10 (= tptp.intersection @t34) :rule refl :args (@t34)) % 0.38/0.59 (step @p11 (= tptp.setminus @t35) :rule refl :args (@t35)) % 0.38/0.59 (step @p12 (= tptp.complement @t36) :rule refl :args (@t36)) % 0.38/0.59 (step @p13 (= tptp.disjoint @t38) :rule refl :args (@t38)) % 0.38/0.59 (step @p14 (= tptp.subset @t40) :rule refl :args (@t40)) % 0.38/0.59 (step @p15 (= tptp.meets @t42) :rule refl :args (@t42)) % 0.38/0.59 (step @p16 (= tptp.misses @t43) :rule refl :args (@t43)) % 0.38/0.59 (step @p17 (= tptp.cartesian_product @t45) :rule refl :args (@t45)) % 0.38/0.59 (step @p18 (= tptp.pair_rel @t46) :rule refl :args (@t46)) % 0.38/0.59 (step @p19 (= tptp.id_rel @t50) :rule refl :args (@t50)) % 0.38/0.59 (step @p20 (= tptp.sub_rel @t55) :rule refl :args (@t55)) % 0.38/0.59 (step @p21 (= tptp.is_rel_on @t60) :rule refl :args (@t60)) % 0.38/0.59 (step @p22 (= tptp.restrict_rel_domain @t62) :rule refl :args (@t62)) % 0.38/0.59 (step @p23 (= tptp.rel_diagonal @t63) :rule refl :args (@t63)) % 0.38/0.59 (step @p24 (= tptp.rel_composition @t68) :rule refl :args (@t68)) % 0.38/0.59 (step @p25 (= tptp.reflexive @t71) :rule refl :args (@t71)) % 0.38/0.59 (step @p26 (= tptp.irreflexive @t72) :rule refl :args (@t72)) % 0.38/0.59 (step @p27 (= tptp.symmetric @t74) :rule refl :args (@t74)) % 0.38/0.59 (step @p28 (= tptp.transitive @t75) :rule refl :args (@t75)) % 0.38/0.59 (step @p29 (= tptp.equiv_rel @t76) :rule refl :args (@t76)) % 0.38/0.59 (step @p30 (= tptp.rel_codomain @t77) :rule refl :args (@t77)) % 0.38/0.59 (step @p31 (= tptp.rel_domain @t79) :rule refl :args (@t79)) % 0.38/0.59 (step @p32 (= tptp.rel_inverse @t80) :rule refl :args (@t80)) % 0.38/0.59 (step @p33 (= tptp.equiv_classes @t82) :rule refl :args (@t82)) % 0.38/0.59 (step @p34 (= tptp.restrict_rel_codomain @t83) :rule refl :args (@t83)) % 0.38/0.59 (step @p35 (= tptp.rel_field @t84) :rule refl :args (@t84)) % 0.38/0.59 (step @p36 (= tptp.well_founded @t91) :rule refl :args (@t91)) % 0.38/0.59 (step @p37 (= tptp.upwards_well_founded @t92) :rule refl :args (@t92)) % 0.38/0.59 (step @p38 :rule evaluate :args ((not true))) % 0.38/0.59 (step @p39 :rule quant-unused-vars :args ((= (forall @t13 true) true))) % 0.38/0.59 (step @p40 :rule eq-refl :args (@t96)) % 0.38/0.59 (step @p41 :rule beta-reduce :args ((= (_ @t97 @t1) @t96))) % 0.38/0.59 (step @p42 :rule refl :args (@t1)) % 0.38/0.59 (step @p43 :rule beta-reduce :args ((= (_ @t98 @t6) @t97))) % 0.38/0.59 (step @p44 :rule refl :args (@t6)) % 0.38/0.59 (step @p45 :rule beta-reduce :args ((= (_ @t101 @t3) @t98))) % 0.38/0.59 (step @p46 :rule refl :args (@t3)) % 0.38/0.59 (step @p47 :rule beta-reduce :args ((= @t103 @t101))) % 0.38/0.59 (step @p48 :rule ho_cong :premises (@p47 @p46)) % 0.38/0.59 (step @p49 :rule trans :premises (@p48 @p45)) % 0.38/0.59 (step @p50 :rule ho_cong :premises (@p49 @p44)) % 0.38/0.59 (step @p51 :rule trans :premises (@p50 @p43)) % 0.38/0.59 (step @p52 :rule ho_cong :premises (@p51 @p42)) % 0.38/0.59 (step @p53 :rule trans :premises (@p52 @p41)) % 0.38/0.59 (step @p54 :rule refl :args (@t93)) % 0.38/0.59 (step @p55 :rule refl :args (@t5)) % 0.38/0.59 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t5 @t93))) % 0.38/0.59 (step @p57 :rule symm :premises (@p56)) % 0.38/0.59 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.38/0.59 (step @p59 :rule cong :premises (@p58) :args (@t104)) % 0.38/0.59 (step @p60 :rule refl :args (@t94)) % 0.38/0.59 (step @p61 :rule refl :args (@t8)) % 0.38/0.59 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t8 @t94))) % 0.38/0.59 (step @p63 :rule symm :premises (@p62)) % 0.38/0.59 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.38/0.59 (step @p65 :rule cong :premises (@p64) :args (@t105)) % 0.38/0.59 (step @p66 :rule nary_cong :premises (@p65 @p59) :args (@t106)) % 0.38/0.59 (step @p67 :rule cong :premises (@p66) :args ((forall @t10 @t106))) % 0.38/0.59 (step @p68 :rule bool-and-de-morgan :args (@t8 @t5 true)) % 0.38/0.59 (step @p69 :rule cong :premises (@p68) :args (@t107)) % 0.38/0.59 (step @p70 :rule trans :premises (@p69 @p67)) % 0.38/0.59 (step @p71 :rule cong :premises (@p70) :args (@t108)) % 0.38/0.59 (step @p72 :rule exists-elim :args ((= @t11 @t108))) % 0.38/0.59 (step @p73 :rule trans :premises (@p72 @p71)) % 0.38/0.59 (step @p74 :rule cong :premises (@p73 @p53) :args ((= @t11 @t109))) % 0.38/0.59 (step @p75 :rule trans :premises (@p74 @p40)) % 0.38/0.59 (step @p76 :rule eq-symm :args (@t109 @t11)) % 0.38/0.59 (step @p77 :rule trans :premises (@p76 @p75)) % 0.38/0.59 (step @p78 :rule cong :premises (@p77) :args (@t110)) % 0.38/0.59 (step @p79 :rule trans :premises (@p78 @p39)) % 0.38/0.59 (step @p80 :rule cong :premises (@p79) :args ((not @t110))) % 0.38/0.59 (step @p81 :rule trans :premises (@p80 @p38)) % 0.38/0.59 (step @p82 :rule refl :args (@t11)) % 0.38/0.59 (step @p83 :rule refl :args (@t7)) % 0.38/0.59 (step @p84 :rule refl :args (@t99)) % 0.38/0.59 (step @p85 :rule refl :args (@t64)) % 0.38/0.59 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t64 @t99))) % 0.38/0.59 (step @p87 :rule symm :premises (@p86)) % 0.38/0.59 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.38/0.59 (step @p89 :rule cong :premises (@p88) :args (@t111)) % 0.38/0.59 (step @p90 :rule refl :args (@t102)) % 0.38/0.59 (step @p91 :rule refl :args (@t53)) % 0.38/0.59 (step @p92 :rule cong :premises (@p91 @p90) :args ((= @t53 @t102))) % 0.38/0.59 (step @p93 :rule symm :premises (@p92)) % 0.38/0.59 (step @p94 :rule eq_resolve :premises (@p91 @p93)) % 0.38/0.59 (step @p95 :rule cong :premises (@p94) :args (@t112)) % 0.38/0.59 (step @p96 :rule nary_cong :premises (@p95 @p89) :args (@t113)) % 0.38/0.59 (step @p97 :rule cong :premises (@p96) :args ((forall @t10 @t113))) % 0.38/0.59 (step @p98 :rule bool-and-de-morgan :args (@t53 @t64 true)) % 0.38/0.59 (step @p99 :rule cong :premises (@p98) :args (@t114)) % 0.38/0.59 (step @p100 :rule trans :premises (@p99 @p97)) % 0.38/0.59 (step @p101 :rule cong :premises (@p100) :args (@t115)) % 0.38/0.59 (step @p102 :rule exists-elim :args ((= @t66 @t115))) % 0.38/0.59 (step @p103 :rule trans :premises (@p102 @p101)) % 0.38/0.59 (step @p104 :rule cong :premises (@p103) :args (@t68)) % 0.38/0.59 (step @p105 :rule trans :premises (@p24 @p104)) % 0.38/0.59 (step @p106 :rule ho_cong :premises (@p105 @p83)) % 0.38/0.59 (step @p107 :rule ho_cong :premises (@p106 @p46)) % 0.38/0.59 (step @p108 :rule ho_cong :premises (@p107 @p44)) % 0.38/0.59 (step @p109 :rule ho_cong :premises (@p108 @p42)) % 0.38/0.59 (step @p110 :rule cong :premises (@p109 @p82) :args (@t12)) % 0.38/0.59 (step @p111 :rule cong :premises (@p110) :args (@t14)) % 0.38/0.59 (step @p112 :rule cong :premises (@p111) :args (@t15)) % 0.38/0.59 (step @p113 :rule trans :premises (@p112 @p81)) % 0.38/0.59 (step @p114 false :rule eq_resolve :premises (@p1 @p113)) % 0.38/0.59 ) % 0.38/0.59 % SZS output end Proof % 0.38/0.59 % cvc5 exiting %------------------------------------------------------------------------------