%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET657^3 : 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 : n022.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 08:48:22 AM UTC 2026 % Result : Theorem 0.36s 0.59s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET657^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n022.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:06:08 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.36/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.59 % SZS status Theorem % 0.36/0.59 % SZS output start Proof % 0.36/0.59 ( % 0.36/0.59 (declare-sort $$unsorted 0) % 0.36/0.59 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.59 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.59 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.36/0.59 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.36/0.59 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.36/0.59 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.59 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.36/0.59 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.59 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.36/0.59 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.59 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.36/0.59 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.36/0.59 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.36/0.59 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.36/0.59 (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)))))))) % 0.36/0.59 (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)))))))) % 0.36/0.59 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.36/0.59 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.59 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$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 $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.36/0.59 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.36/0.59 (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))))) % 0.36/0.59 (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 $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.36/0.59 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.59 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.36/0.59 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.59 (define tptp.transitive () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.36/0.59 (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))))) % 0.36/0.59 (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))))))) % 0.36/0.59 (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))))))) % 0.36/0.59 (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)))))) % 0.36/0.59 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.36/0.59 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.36/0.59 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.36/0.59 (define tptp.well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.36/0.59 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.36/0.59 (define @t1 () (@var "X" $$unsorted)) % 0.36/0.59 (define @t2 () (@list @t1)) % 0.36/0.59 (define @t3 () (lambda @t2 true)) % 0.36/0.59 (define @t4 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.59 (define @t5 () (@list @t4)) % 0.36/0.59 (define @t6 () (forall @t5 (_ (_ tptp.subset (_ tptp.rel_field @t4)) (_ (_ tptp.union @t3) @t3)))) % 0.36/0.59 (define @t7 () (not @t6)) % 0.36/0.59 (define @t8 () (@var "M" (-> $$unsorted Bool))) % 0.36/0.59 (define @t9 () (lambda (@list @t1 @t8) (_ @t8 @t1))) % 0.36/0.59 (define @t10 () (lambda @t2 false)) % 0.36/0.59 (define @t11 () (@var "Y" $$unsorted)) % 0.36/0.59 (define @t12 () (@var "U" $$unsorted)) % 0.36/0.59 (define @t13 () (= @t12 @t1)) % 0.36/0.59 (define @t14 () (lambda (@list @t1 @t11 @t12) (or @t13 (= @t12 @t11)))) % 0.36/0.59 (define @t15 () (lambda (@list @t1 @t12) @t13)) % 0.36/0.59 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.59 (define @t17 () (_ @t16 @t12)) % 0.36/0.59 (define @t18 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.59 (define @t19 () (_ @t18 @t12)) % 0.36/0.59 (define @t20 () (@list @t18 @t16 @t12)) % 0.36/0.59 (define @t21 () (lambda @t20 (or @t19 @t17))) % 0.36/0.59 (define @t22 () (not @t19)) % 0.36/0.59 (define @t23 () (and @t19 (not @t17))) % 0.36/0.59 (define @t24 () (lambda @t20 (or @t23 (and @t22 @t17)))) % 0.36/0.59 (define @t25 () (and @t19 @t17)) % 0.36/0.59 (define @t26 () (lambda @t20 @t25)) % 0.36/0.59 (define @t27 () (lambda @t20 @t23)) % 0.36/0.59 (define @t28 () (lambda (@list @t18 @t12) @t22)) % 0.36/0.59 (define @t29 () (@list @t18 @t16)) % 0.36/0.59 (define @t30 () (lambda @t29 (= (_ (_ tptp.intersection @t18) @t16) tptp.emptyset))) % 0.36/0.59 (define @t31 () (@list @t12)) % 0.36/0.59 (define @t32 () (forall @t31 (=> @t19 @t17))) % 0.36/0.59 (define @t33 () (lambda @t29 @t32)) % 0.36/0.59 (define @t34 () (exists @t31 @t25)) % 0.36/0.59 (define @t35 () (lambda @t29 @t34)) % 0.36/0.59 (define @t36 () (lambda @t29 (not @t34))) % 0.36/0.59 (define @t37 () (@var "V" $$unsorted)) % 0.36/0.59 (define @t38 () (lambda (@list @t18 @t16 @t12 @t37) (and @t19 (_ @t16 @t37)))) % 0.36/0.59 (define @t39 () (lambda (@list @t1 @t11 @t12 @t37) (or @t13 (= @t37 @t11)))) % 0.36/0.59 (define @t40 () (= @t1 @t11)) % 0.36/0.59 (define @t41 () (@var "S" (-> $$unsorted Bool))) % 0.36/0.59 (define @t42 () (_ @t41 @t1)) % 0.36/0.59 (define @t43 () (lambda (@list @t41 @t1 @t11) (and @t42 @t40))) % 0.36/0.59 (define @t44 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.36/0.59 (define @t45 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.36/0.59 (define @t46 () (_ (_ @t45 @t1) @t11)) % 0.36/0.59 (define @t47 () (@list @t1 @t11)) % 0.36/0.59 (define @t48 () (lambda (@list @t45 @t44) (forall @t47 (=> @t46 (_ (_ @t44 @t1) @t11))))) % 0.36/0.59 (define @t49 () (@var "B" (-> $$unsorted Bool))) % 0.36/0.59 (define @t50 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.59 (define @t51 () (_ @t4 @t1)) % 0.36/0.59 (define @t52 () (_ @t51 @t11)) % 0.36/0.59 (define @t53 () (lambda (@list @t4 @t50 @t49) (forall @t47 (=> @t52 (and (_ @t50 @t1) (_ @t49 @t11)))))) % 0.36/0.59 (define @t54 () (@list @t4 @t41 @t1 @t11)) % 0.36/0.59 (define @t55 () (lambda @t54 (and @t42 @t52))) % 0.36/0.59 (define @t56 () (lambda @t47 @t40)) % 0.36/0.59 (define @t57 () (@var "Z" $$unsorted)) % 0.36/0.59 (define @t58 () (@list @t11)) % 0.36/0.59 (define @t59 () (lambda (@list @t45 @t44 @t1 @t57) (exists @t58 (and @t46 (_ (_ @t44 @t11) @t57))))) % 0.36/0.59 (define @t60 () (_ @t51 @t1)) % 0.36/0.59 (define @t61 () (lambda @t5 (forall @t2 @t60))) % 0.36/0.59 (define @t62 () (lambda @t5 (forall @t2 (not @t60)))) % 0.36/0.59 (define @t63 () (_ @t4 @t11)) % 0.36/0.59 (define @t64 () (_ @t63 @t1)) % 0.36/0.59 (define @t65 () (lambda @t5 (forall @t47 (=> @t52 @t64)))) % 0.36/0.59 (define @t66 () (lambda @t5 (forall (@list @t1 @t11 @t57) (=> (and @t52 (_ @t63 @t57)) (_ @t51 @t57))))) % 0.36/0.59 (define @t67 () (lambda @t5 (and (_ tptp.reflexive @t4) (_ tptp.symmetric @t4) (_ tptp.transitive @t4)))) % 0.36/0.59 (define @t68 () (exists @t2 @t52)) % 0.36/0.59 (define @t69 () (@list @t4 @t11)) % 0.36/0.59 (define @t70 () (lambda @t69 @t68)) % 0.36/0.59 (define @t71 () (exists @t58 @t52)) % 0.36/0.59 (define @t72 () (@list @t4 @t1)) % 0.36/0.59 (define @t73 () (lambda @t72 @t71)) % 0.36/0.59 (define @t74 () (lambda (@list @t4 @t1 @t11) @t64)) % 0.36/0.59 (define @t75 () (@var "S1" (-> $$unsorted Bool))) % 0.36/0.59 (define @t76 () (lambda (@list @t4 @t75) (exists @t2 (and (_ @t75 @t1) (forall @t58 (= (_ @t75 @t11) @t52)))))) % 0.36/0.59 (define @t77 () (lambda @t54 (and (_ @t41 @t11) @t52))) % 0.36/0.59 (define @t78 () (or (_ (_ tptp.rel_domain @t4) @t1) (_ (_ tptp.rel_codomain @t4) @t1))) % 0.36/0.59 (define @t79 () (lambda @t72 @t78)) % 0.36/0.59 (define @t80 () (@var "W" $$unsorted)) % 0.36/0.59 (define @t81 () (not (_ @t18 @t80))) % 0.36/0.59 (define @t82 () (@list @t80)) % 0.36/0.59 (define @t83 () (_ @t18 @t11)) % 0.36/0.59 (define @t84 () (_ @t18 @t57)) % 0.36/0.59 (define @t85 () (@list @t18 @t57)) % 0.36/0.59 (define @t86 () (lambda @t5 (forall @t85 (=> @t84 (exists @t58 (and @t83 (forall @t82 (=> (_ @t63 @t80) @t81)))))))) % 0.36/0.59 (define @t87 () (lambda @t5 (forall @t85 (=> @t84 (exists @t58 (and @t83 (forall @t82 (=> (_ @t63 @t11) @t81)))))))) % 0.36/0.59 (define @t88 () (@var "BOUND_VARIABLE_8186" $$unsorted)) % 0.36/0.59 (define @t89 () (@var "BOUND_VARIABLE_8182" $$unsorted)) % 0.36/0.59 (define @t90 () (@list @t12 @t89 @t88)) % 0.36/0.59 (define @t91 () (not (_ @t4 @t88 @t12))) % 0.36/0.59 (define @t92 () (not (_ @t4 @t12 @t89))) % 0.36/0.59 (define @t93 () (and @t92 @t91)) % 0.36/0.59 (define @t94 () (@var "BOUND_VARIABLE_8201" $$unsorted)) % 0.36/0.59 (define @t95 () (lambda (@list @t94) true)) % 0.36/0.59 (define @t96 () (_ @t95 @t12)) % 0.36/0.59 (define @t97 () (or @t93 @t96)) % 0.36/0.59 (define @t98 () (forall @t90 @t97)) % 0.36/0.59 (define @t99 () (_ @t16 @t12)) % 0.36/0.59 (define @t100 () (or @t93 @t99)) % 0.36/0.59 (define @t101 () (forall @t90 @t100)) % 0.36/0.59 (define @t102 () (@list @t16)) % 0.36/0.59 (define @t103 () (@var "BOUND_VARIABLE_8213" $$unsorted)) % 0.36/0.59 (define @t104 () (lambda (@list @t103) true)) % 0.36/0.59 (define @t105 () (@list @t94)) % 0.36/0.59 (define @t106 () (@var "BOUND_VARIABLE_8211" (-> $$unsorted Bool))) % 0.36/0.59 (define @t107 () (lambda (@list @t106 @t103) true)) % 0.36/0.59 (define @t108 () (@list @t1)) % 0.36/0.59 (define @t109 () (@list @t16 @t12)) % 0.36/0.59 (define @t110 () (_ @t95 @t12)) % 0.36/0.59 (define @t111 () (or @t110 @t17)) % 0.36/0.59 (define @t112 () (lambda @t109 @t111)) % 0.36/0.59 (define @t113 () (@list @t89 @t88)) % 0.36/0.59 (define @t114 () (forall @t113 @t100)) % 0.36/0.59 (define @t115 () (forall (@list @t88) @t91)) % 0.36/0.59 (define @t116 () (@var "BOUND_VARIABLE_7916" $$unsorted)) % 0.36/0.59 (define @t117 () (@list @t116)) % 0.36/0.59 (define @t118 () (forall @t113 @t91)) % 0.36/0.59 (define @t119 () (forall (@list @t89) @t92)) % 0.36/0.59 (define @t120 () (forall @t113 @t92)) % 0.36/0.59 (define @t121 () (and @t120 @t118)) % 0.36/0.59 (define @t122 () (forall @t113 @t93)) % 0.36/0.59 (define @t123 () (or @t122 @t99)) % 0.36/0.59 (define @t124 () (@list @t116)) % 0.36/0.59 (define @t125 () (forall @t124 (not (_ @t4 @t116 @t12)))) % 0.36/0.59 (define @t126 () (forall @t58 (not (_ @t4 @t12 @t11)))) % 0.36/0.59 (define @t127 () (not @t125)) % 0.36/0.59 (define @t128 () (not @t126)) % 0.36/0.59 (define @t129 () (or @t128 @t127)) % 0.36/0.59 (define @t130 () (or (not @t129) @t99)) % 0.36/0.59 (define @t131 () (not (forall @t124 (not (_ @t4 @t116 @t1))))) % 0.36/0.59 (define @t132 () (_ @t4 @t1 @t11)) % 0.36/0.59 (define @t133 () (not @t132)) % 0.36/0.59 (define @t134 () (not (forall @t58 @t133))) % 0.36/0.59 (define @t135 () (or @t134 @t131)) % 0.36/0.59 (define @t136 () (lambda @t2 @t135)) % 0.36/0.59 (define @t137 () (_ @t136 @t12)) % 0.36/0.59 (define @t138 () (not @t137)) % 0.36/0.59 (define @t139 () (or @t138 @t99)) % 0.36/0.59 (define @t140 () (forall @t31 @t139)) % 0.36/0.59 (define @t141 () (lambda @t102 @t140)) % 0.36/0.59 (define @t142 () (_ @t18 @t12)) % 0.36/0.59 (define @t143 () (lambda @t29 (forall @t31 (or (not @t142) @t99)))) % 0.36/0.59 (define @t144 () (_ (lambda @t72 @t135) @t4)) % 0.36/0.59 (define @t145 () (forall @t5 (_ (_ @t143 @t144) (_ (_ @t21 @t3) @t3)))) % 0.36/0.59 (define @t146 () (forall @t2 @t133)) % 0.36/0.59 (define @t147 () (not @t146)) % 0.36/0.59 (define @t148 () (lambda @t58 @t147)) % 0.36/0.59 (define @t149 () (_ (lambda @t69 @t147) @t4)) % 0.36/0.59 (define @t150 () (lambda @t2 @t134)) % 0.36/0.59 (define @t151 () (_ (lambda @t72 @t134) @t4)) % 0.36/0.59 (define @t152 () (not @t52)) % 0.36/0.59 (define @t153 () (forall @t2 @t152)) % 0.36/0.59 (define @t154 () (not @t153)) % 0.36/0.59 (define @t155 () (forall @t58 @t152)) % 0.36/0.59 (define @t156 () (not @t155)) % 0.36/0.59 (define @t157 () (or @t22 @t17)) % 0.36/0.59 (assume @p1 @t7) % 0.36/0.59 (assume @p2 true) % 0.36/0.59 (step @p3 (= tptp.in @t9) :rule refl :args (@t9)) % 0.36/0.59 (step @p4 (= tptp.is_a @t9) :rule refl :args (@t9)) % 0.36/0.59 (step @p5 (= tptp.emptyset @t10) :rule refl :args (@t10)) % 0.36/0.59 (step @p6 (= tptp.unord_pair @t14) :rule refl :args (@t14)) % 0.36/0.59 (step @p7 (= tptp.singleton @t15) :rule refl :args (@t15)) % 0.36/0.59 (step @p8 (= tptp.union @t21) :rule refl :args (@t21)) % 0.36/0.59 (step @p9 (= tptp.excl_union @t24) :rule refl :args (@t24)) % 0.36/0.59 (step @p10 (= tptp.intersection @t26) :rule refl :args (@t26)) % 0.36/0.59 (step @p11 (= tptp.setminus @t27) :rule refl :args (@t27)) % 0.36/0.59 (step @p12 (= tptp.complement @t28) :rule refl :args (@t28)) % 0.36/0.59 (step @p13 (= tptp.disjoint @t30) :rule refl :args (@t30)) % 0.36/0.59 (step @p14 (= tptp.subset @t33) :rule refl :args (@t33)) % 0.36/0.59 (step @p15 (= tptp.meets @t35) :rule refl :args (@t35)) % 0.36/0.59 (step @p16 (= tptp.misses @t36) :rule refl :args (@t36)) % 0.36/0.59 (step @p17 (= tptp.cartesian_product @t38) :rule refl :args (@t38)) % 0.36/0.59 (step @p18 (= tptp.pair_rel @t39) :rule refl :args (@t39)) % 0.36/0.59 (step @p19 (= tptp.id_rel @t43) :rule refl :args (@t43)) % 0.36/0.59 (step @p20 (= tptp.sub_rel @t48) :rule refl :args (@t48)) % 0.36/0.59 (step @p21 (= tptp.is_rel_on @t53) :rule refl :args (@t53)) % 0.36/0.59 (step @p22 (= tptp.restrict_rel_domain @t55) :rule refl :args (@t55)) % 0.36/0.59 (step @p23 (= tptp.rel_diagonal @t56) :rule refl :args (@t56)) % 0.36/0.59 (step @p24 (= tptp.rel_composition @t59) :rule refl :args (@t59)) % 0.36/0.59 (step @p25 (= tptp.reflexive @t61) :rule refl :args (@t61)) % 0.36/0.59 (step @p26 (= tptp.irreflexive @t62) :rule refl :args (@t62)) % 0.36/0.59 (step @p27 (= tptp.symmetric @t65) :rule refl :args (@t65)) % 0.36/0.59 (step @p28 (= tptp.transitive @t66) :rule refl :args (@t66)) % 0.36/0.59 (step @p29 (= tptp.equiv_rel @t67) :rule refl :args (@t67)) % 0.36/0.59 (step @p30 (= tptp.rel_codomain @t70) :rule refl :args (@t70)) % 0.36/0.59 (step @p31 (= tptp.rel_domain @t73) :rule refl :args (@t73)) % 0.36/0.59 (step @p32 (= tptp.rel_inverse @t74) :rule refl :args (@t74)) % 0.36/0.59 (step @p33 (= tptp.equiv_classes @t76) :rule refl :args (@t76)) % 0.36/0.59 (step @p34 (= tptp.restrict_rel_codomain @t77) :rule refl :args (@t77)) % 0.36/0.59 (step @p35 (= tptp.rel_field @t79) :rule refl :args (@t79)) % 0.36/0.59 (step @p36 (= tptp.well_founded @t86) :rule refl :args (@t86)) % 0.36/0.59 (step @p37 (= tptp.upwards_well_founded @t87) :rule refl :args (@t87)) % 0.36/0.59 (step @p38 :rule evaluate :args ((not true))) % 0.36/0.59 (step @p39 :rule quant-unused-vars :args ((= (forall @t5 true) true))) % 0.36/0.59 (step @p40 :rule quant-unused-vars :args ((= (forall @t90 true) true))) % 0.36/0.59 (step @p41 :rule absorb :args ((= (or @t93 true) true))) % 0.36/0.59 (step @p42 :rule beta-reduce :args ((= @t96 true))) % 0.36/0.59 (step @p43 :rule refl :args (@t93)) % 0.36/0.59 (step @p44 :rule nary_cong :premises (@p43 @p42) :args (@t97)) % 0.36/0.59 (step @p45 :rule trans :premises (@p44 @p41)) % 0.36/0.59 (step @p46 :rule cong :premises (@p45) :args (@t98)) % 0.36/0.59 (step @p47 :rule trans :premises (@p46 @p40)) % 0.36/0.59 (step @p48 :rule beta-reduce :args ((= (_ (lambda @t102 @t101) @t95) @t98))) % 0.36/0.59 (step @p49 :rule trans :premises (@p48 @p47)) % 0.36/0.59 (step @p50 :rule refl :args (@t95)) % 0.36/0.59 (step @p51 :rule symm :premises (@p50)) % 0.36/0.59 (step @p52 :rule alpha_equiv :args (@t104 (@list @t103) @t105)) % 0.36/0.59 (step @p53 :rule trans :premises (@p52 @p51)) % 0.36/0.59 (step @p54 :rule beta-reduce :args ((= (_ @t107 @t95) @t104))) % 0.36/0.59 (step @p55 :rule trans :premises (@p54 @p53)) % 0.36/0.59 (step @p56 :rule alpha_equiv :args (@t3 @t108 @t105)) % 0.36/0.59 (step @p57 :rule trans :premises (@p56 @p51)) % 0.36/0.59 (step @p58 :rule refl :args (@t107)) % 0.36/0.59 (step @p59 :rule symm :premises (@p58)) % 0.36/0.59 (step @p60 :rule alpha_equiv :args ((lambda @t109 true) (@list @t16 @t12) (@list @t106 @t103))) % 0.36/0.59 (step @p61 :rule trans :premises (@p60 @p59)) % 0.36/0.59 (step @p62 :rule absorb :args ((= (or true @t17) true))) % 0.36/0.59 (step @p63 :rule refl :args (@t17)) % 0.36/0.59 (step @p64 :rule beta-reduce :args ((= @t110 true))) % 0.36/0.59 (step @p65 :rule nary_cong :premises (@p64 @p63) :args (@t111)) % 0.36/0.59 (step @p66 :rule trans :premises (@p65 @p62)) % 0.36/0.59 (step @p67 :rule cong :premises (@p66) :args (@t112)) % 0.36/0.59 (step @p68 :rule trans :premises (@p67 @p61)) % 0.36/0.59 (step @p69 :rule beta-reduce :args ((= (_ @t21 @t95) @t112))) % 0.36/0.59 (step @p70 :rule trans :premises (@p69 @p68)) % 0.36/0.59 (step @p71 :rule refl :args (@t21)) % 0.36/0.59 (step @p72 :rule ho_cong :premises (@p71 @p57)) % 0.36/0.59 (step @p73 :rule trans :premises (@p72 @p70)) % 0.36/0.59 (step @p74 :rule ho_cong :premises (@p73 @p57)) % 0.36/0.59 (step @p75 :rule trans :premises (@p74 @p55)) % 0.36/0.59 (step @p76 :rule quant-merge-prenex :args ((= (forall @t31 @t114) @t101))) % 0.36/0.59 (step @p77 :rule refl :args (@t99)) % 0.36/0.59 (step @p78 :rule alpha_equiv :args (@t115 (@list @t88) @t117)) % 0.36/0.59 (step @p79 :rule quant-unused-vars :args ((= @t118 @t115))) % 0.36/0.59 (step @p80 :rule trans :premises (@p79 @p78)) % 0.36/0.59 (step @p81 :rule alpha_equiv :args (@t119 (@list @t89) (@list @t11))) % 0.36/0.59 (step @p82 :rule quant-unused-vars :args ((= @t120 @t119))) % 0.36/0.59 (step @p83 :rule trans :premises (@p82 @p81)) % 0.36/0.59 (step @p84 :rule nary_cong :premises (@p83 @p80) :args (@t121)) % 0.36/0.59 (step @p85 :rule quant-miniscope-and :args ((= @t122 @t121))) % 0.36/0.59 (step @p86 :rule trans :premises (@p85 @p84)) % 0.36/0.59 (step @p87 :rule nary_cong :premises (@p86 @p77) :args (@t123)) % 0.36/0.59 (step @p88 :rule quant-miniscope-or :args ((= @t114 @t123))) % 0.36/0.59 (step @p89 :rule trans :premises (@p88 @p87)) % 0.36/0.59 (step @p90 :rule symm :premises (@p89)) % 0.36/0.59 (step @p91 :rule cong :premises (@p90) :args ((forall @t31 (or (and @t126 @t125) @t99)))) % 0.36/0.59 (step @p92 :rule trans :premises (@p91 @p76)) % 0.36/0.59 (step @p93 :rule bool-double-not-elim :args (@t125)) % 0.36/0.59 (step @p94 :rule bool-double-not-elim :args (@t126)) % 0.36/0.59 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((and (not @t128) (not @t127)))) % 0.36/0.59 (step @p96 :rule bool-or-de-morgan :args (@t128 @t127 false)) % 0.36/0.59 (step @p97 :rule trans :premises (@p96 @p95)) % 0.36/0.59 (step @p98 :rule nary_cong :premises (@p97 @p77) :args (@t130)) % 0.36/0.59 (step @p99 :rule cong :premises (@p98) :args ((forall @t31 @t130))) % 0.36/0.59 (step @p100 :rule trans :premises (@p99 @p92)) % 0.36/0.59 (step @p101 :rule refl :args (@t99)) % 0.36/0.59 (step @p102 :rule beta-reduce :args ((= @t137 @t129))) % 0.36/0.59 (step @p103 :rule cong :premises (@p102) :args (@t138)) % 0.36/0.59 (step @p104 :rule nary_cong :premises (@p103 @p101) :args (@t139)) % 0.36/0.59 (step @p105 :rule cong :premises (@p104) :args (@t140)) % 0.36/0.59 (step @p106 :rule trans :premises (@p105 @p100)) % 0.36/0.59 (step @p107 :rule cong :premises (@p106) :args (@t141)) % 0.36/0.59 (step @p108 :rule beta-reduce :args ((= (_ @t143 @t136) @t141))) % 0.36/0.59 (step @p109 :rule trans :premises (@p108 @p107)) % 0.36/0.59 (step @p110 :rule beta-reduce :args ((= @t144 @t136))) % 0.36/0.59 (step @p111 :rule refl :args (@t143)) % 0.36/0.59 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.36/0.59 (step @p113 :rule trans :premises (@p112 @p109)) % 0.36/0.59 (step @p114 :rule ho_cong :premises (@p113 @p75)) % 0.36/0.59 (step @p115 :rule trans :premises (@p114 @p49)) % 0.36/0.59 (step @p116 :rule cong :premises (@p115) :args (@t145)) % 0.36/0.59 (step @p117 :rule trans :premises (@p116 @p39)) % 0.36/0.59 (step @p118 :rule cong :premises (@p117) :args ((not @t145))) % 0.36/0.59 (step @p119 :rule trans :premises (@p118 @p38)) % 0.36/0.59 (step @p120 :rule refl :args (@t3)) % 0.36/0.59 (step @p121 :rule ho_cong :premises (@p8 @p120)) % 0.36/0.59 (step @p122 :rule ho_cong :premises (@p121 @p120)) % 0.36/0.59 (step @p123 :rule refl :args (@t4)) % 0.36/0.59 (step @p124 :rule beta-reduce :args ((= (_ (lambda @t58 (not (forall @t124 (not (_ @t4 @t116 @t11))))) @t1) @t131))) % 0.36/0.59 (step @p125 :rule refl :args (@t1)) % 0.36/0.59 (step @p126 :rule alpha_equiv :args (@t146 @t108 @t117)) % 0.36/0.59 (step @p127 :rule cong :premises (@p126) :args (@t147)) % 0.36/0.59 (step @p128 :rule cong :premises (@p127) :args (@t148)) % 0.36/0.59 (step @p129 :rule ho_cong :premises (@p128 @p125)) % 0.36/0.59 (step @p130 :rule trans :premises (@p129 @p124)) % 0.36/0.59 (step @p131 :rule refl :args (@t1)) % 0.36/0.59 (step @p132 :rule beta-reduce :args ((= @t149 @t148))) % 0.36/0.59 (step @p133 :rule ho_cong :premises (@p132 @p131)) % 0.36/0.59 (step @p134 :rule trans :premises (@p133 @p130)) % 0.36/0.59 (step @p135 :rule beta-reduce :args ((= (_ @t150 @t1) @t134))) % 0.36/0.59 (step @p136 :rule beta-reduce :args ((= @t151 @t150))) % 0.36/0.59 (step @p137 :rule ho_cong :premises (@p136 @p131)) % 0.36/0.59 (step @p138 :rule trans :premises (@p137 @p135)) % 0.36/0.59 (step @p139 :rule nary_cong :premises (@p138 @p134) :args ((or (_ @t151 @t1) (_ @t149 @t1)))) % 0.36/0.59 (step @p140 :rule refl :args (@t132)) % 0.36/0.59 (step @p141 :rule refl :args (@t52)) % 0.36/0.59 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t52 @t132))) % 0.36/0.59 (step @p143 :rule symm :premises (@p142)) % 0.36/0.59 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.36/0.59 (step @p145 :rule cong :premises (@p144) :args (@t152)) % 0.36/0.60 (step @p146 :rule cong :premises (@p145) :args (@t153)) % 0.36/0.60 (step @p147 :rule cong :premises (@p146) :args (@t154)) % 0.36/0.60 (step @p148 :rule exists-elim :args ((= @t68 @t154))) % 0.36/0.60 (step @p149 :rule trans :premises (@p148 @p147)) % 0.36/0.60 (step @p150 :rule cong :premises (@p149) :args (@t70)) % 0.36/0.60 (step @p151 :rule trans :premises (@p30 @p150)) % 0.36/0.60 (step @p152 :rule ho_cong :premises (@p151 @p123)) % 0.36/0.60 (step @p153 :rule ho_cong :premises (@p152 @p131)) % 0.36/0.60 (step @p154 :rule cong :premises (@p145) :args (@t155)) % 0.36/0.60 (step @p155 :rule cong :premises (@p154) :args (@t156)) % 0.36/0.60 (step @p156 :rule exists-elim :args ((= @t71 @t156))) % 0.36/0.60 (step @p157 :rule trans :premises (@p156 @p155)) % 0.36/0.60 (step @p158 :rule cong :premises (@p157) :args (@t73)) % 0.36/0.60 (step @p159 :rule trans :premises (@p31 @p158)) % 0.36/0.60 (step @p160 :rule ho_cong :premises (@p159 @p123)) % 0.36/0.60 (step @p161 :rule ho_cong :premises (@p160 @p131)) % 0.36/0.60 (step @p162 :rule nary_cong :premises (@p161 @p153) :args (@t78)) % 0.36/0.60 (step @p163 :rule trans :premises (@p162 @p139)) % 0.36/0.60 (step @p164 :rule cong :premises (@p163) :args (@t79)) % 0.36/0.60 (step @p165 :rule trans :premises (@p35 @p164)) % 0.36/0.60 (step @p166 :rule ho_cong :premises (@p165 @p123)) % 0.36/0.60 (step @p167 :rule refl :args (@t99)) % 0.36/0.60 (step @p168 :rule refl :args (@t17)) % 0.36/0.60 (step @p169 :rule cong :premises (@p168 @p167) :args ((= @t17 @t99))) % 0.36/0.60 (step @p170 :rule symm :premises (@p169)) % 0.36/0.60 (step @p171 :rule eq_resolve :premises (@p168 @p170)) % 0.36/0.60 (step @p172 :rule refl :args (@t142)) % 0.36/0.60 (step @p173 :rule refl :args (@t19)) % 0.36/0.60 (step @p174 :rule cong :premises (@p173 @p172) :args ((= @t19 @t142))) % 0.36/0.60 (step @p175 :rule symm :premises (@p174)) % 0.36/0.60 (step @p176 :rule eq_resolve :premises (@p173 @p175)) % 0.36/0.60 (step @p177 :rule cong :premises (@p176) :args (@t22)) % 0.36/0.60 (step @p178 :rule nary_cong :premises (@p177 @p171) :args (@t157)) % 0.36/0.60 (step @p179 :rule cong :premises (@p178) :args ((forall @t31 @t157))) % 0.36/0.60 (step @p180 :rule bool-impl-elim :args (@t19 @t17)) % 0.36/0.60 (step @p181 :rule cong :premises (@p180) :args (@t32)) % 0.36/0.60 (step @p182 :rule trans :premises (@p181 @p179)) % 0.36/0.60 (step @p183 :rule cong :premises (@p182) :args (@t33)) % 0.36/0.60 (step @p184 :rule trans :premises (@p14 @p183)) % 0.36/0.60 (step @p185 :rule ho_cong :premises (@p184 @p166)) % 0.36/0.60 (step @p186 :rule ho_cong :premises (@p185 @p122)) % 0.36/0.60 (step @p187 :rule cong :premises (@p186) :args (@t6)) % 0.36/0.60 (step @p188 :rule cong :premises (@p187) :args (@t7)) % 0.36/0.60 (step @p189 :rule trans :premises (@p188 @p119)) % 0.36/0.60 (step @p190 false :rule eq_resolve :premises (@p1 @p189)) % 0.36/0.60 ) % 0.36/0.60 % SZS output end Proof % 0.36/0.60 % cvc5 exiting %------------------------------------------------------------------------------