%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET671^3 : 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 : n010.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 08:48:24 AM UTC 2026 % Result : Theorem 0.36s 0.58s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET671^3 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n010.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 16:05:55 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.36/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.58 % SZS status Theorem % 0.36/0.58 % SZS output start Proof % 0.36/0.58 ( % 0.36/0.58 (declare-sort $$unsorted 0) % 0.36/0.58 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.58 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.58 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.36/0.58 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.36/0.58 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.36/0.58 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.58 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.36/0.58 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.58 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.36/0.58 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.58 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.36/0.58 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.36/0.58 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.36/0.58 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.36/0.58 (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)))))))) % 0.36/0.58 (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)))))))) % 0.36/0.58 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.36/0.58 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.36/0.59 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.59 (define @t2 () (@var "Z" (-> $$unsorted Bool))) % 0.36/0.59 (define @t3 () (= (_ (_ tptp.restrict_rel_domain @t1) @t2) @t1)) % 0.36/0.59 (define @t4 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.59 (define @t5 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.59 (define @t6 () (and (_ (_ (_ tptp.is_rel_on @t1) @t4) @t5) (_ (_ tptp.subset @t4) @t2))) % 0.36/0.59 (define @t7 () (=> @t6 @t3)) % 0.36/0.59 (define @t8 () (@list @t2 @t1 @t4 @t5)) % 0.36/0.59 (define @t9 () (forall @t8 @t7)) % 0.36/0.59 (define @t10 () (not @t9)) % 0.36/0.59 (define @t11 () (@var "X" $$unsorted)) % 0.36/0.59 (define @t12 () (@var "M" (-> $$unsorted Bool))) % 0.36/0.59 (define @t13 () (lambda (@list @t11 @t12) (_ @t12 @t11))) % 0.36/0.59 (define @t14 () (@list @t11)) % 0.36/0.59 (define @t15 () (lambda @t14 false)) % 0.36/0.59 (define @t16 () (@var "Y" $$unsorted)) % 0.36/0.59 (define @t17 () (@var "U" $$unsorted)) % 0.36/0.59 (define @t18 () (= @t17 @t11)) % 0.36/0.59 (define @t19 () (lambda (@list @t11 @t16 @t17) (or @t18 (= @t17 @t16)))) % 0.36/0.59 (define @t20 () (lambda (@list @t11 @t17) @t18)) % 0.36/0.59 (define @t21 () (_ @t5 @t17)) % 0.36/0.59 (define @t22 () (_ @t4 @t17)) % 0.36/0.59 (define @t23 () (@list @t4 @t5 @t17)) % 0.36/0.59 (define @t24 () (lambda @t23 (or @t22 @t21))) % 0.36/0.59 (define @t25 () (not @t22)) % 0.36/0.59 (define @t26 () (and @t22 (not @t21))) % 0.36/0.59 (define @t27 () (lambda @t23 (or @t26 (and @t25 @t21)))) % 0.36/0.59 (define @t28 () (and @t22 @t21)) % 0.36/0.59 (define @t29 () (lambda @t23 @t28)) % 0.36/0.59 (define @t30 () (lambda @t23 @t26)) % 0.36/0.59 (define @t31 () (lambda (@list @t4 @t17) @t25)) % 0.36/0.59 (define @t32 () (@list @t4 @t5)) % 0.36/0.59 (define @t33 () (lambda @t32 (= (_ (_ tptp.intersection @t4) @t5) tptp.emptyset))) % 0.36/0.59 (define @t34 () (@list @t17)) % 0.36/0.59 (define @t35 () (forall @t34 (=> @t22 @t21))) % 0.36/0.59 (define @t36 () (lambda @t32 @t35)) % 0.36/0.59 (define @t37 () (exists @t34 @t28)) % 0.36/0.59 (define @t38 () (lambda @t32 @t37)) % 0.36/0.59 (define @t39 () (lambda @t32 (not @t37))) % 0.36/0.59 (define @t40 () (@var "V" $$unsorted)) % 0.36/0.59 (define @t41 () (lambda (@list @t4 @t5 @t17 @t40) (and @t22 (_ @t5 @t40)))) % 0.36/0.59 (define @t42 () (lambda (@list @t11 @t16 @t17 @t40) (or @t18 (= @t40 @t16)))) % 0.36/0.59 (define @t43 () (= @t11 @t16)) % 0.36/0.59 (define @t44 () (@var "S" (-> $$unsorted Bool))) % 0.36/0.59 (define @t45 () (_ @t44 @t11)) % 0.36/0.59 (define @t46 () (@list @t44 @t11 @t16)) % 0.36/0.59 (define @t47 () (lambda @t46 (and @t45 @t43))) % 0.36/0.59 (define @t48 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.36/0.59 (define @t49 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.36/0.59 (define @t50 () (_ (_ @t49 @t11) @t16)) % 0.36/0.59 (define @t51 () (@list @t11 @t16)) % 0.36/0.59 (define @t52 () (lambda (@list @t49 @t48) (forall @t51 (=> @t50 (_ (_ @t48 @t11) @t16))))) % 0.36/0.59 (define @t53 () (@var "B" (-> $$unsorted Bool))) % 0.36/0.59 (define @t54 () (_ @t53 @t16)) % 0.36/0.59 (define @t55 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.59 (define @t56 () (_ @t55 @t11)) % 0.36/0.59 (define @t57 () (and @t56 @t54)) % 0.36/0.59 (define @t58 () (_ @t1 @t11)) % 0.36/0.59 (define @t59 () (_ @t58 @t16)) % 0.36/0.59 (define @t60 () (forall @t51 (=> @t59 @t57))) % 0.36/0.59 (define @t61 () (@list @t1 @t55 @t53)) % 0.36/0.59 (define @t62 () (lambda @t61 @t60)) % 0.36/0.59 (define @t63 () (and @t45 @t59)) % 0.36/0.59 (define @t64 () (@list @t1 @t44 @t11 @t16)) % 0.36/0.59 (define @t65 () (lambda @t64 @t63)) % 0.36/0.59 (define @t66 () (lambda @t51 @t43)) % 0.36/0.59 (define @t67 () (@var "Z" $$unsorted)) % 0.36/0.59 (define @t68 () (@list @t16)) % 0.36/0.59 (define @t69 () (lambda (@list @t49 @t48 @t11 @t67) (exists @t68 (and @t50 (_ (_ @t48 @t16) @t67))))) % 0.36/0.59 (define @t70 () (_ @t58 @t11)) % 0.36/0.59 (define @t71 () (@list @t1)) % 0.36/0.59 (define @t72 () (lambda @t71 (forall @t14 @t70))) % 0.36/0.59 (define @t73 () (lambda @t71 (forall @t14 (not @t70)))) % 0.36/0.59 (define @t74 () (_ @t1 @t16)) % 0.36/0.59 (define @t75 () (_ @t74 @t11)) % 0.36/0.59 (define @t76 () (lambda @t71 (forall @t51 (=> @t59 @t75)))) % 0.36/0.59 (define @t77 () (lambda @t71 (forall (@list @t11 @t16 @t67) (=> (and @t59 (_ @t74 @t67)) (_ @t58 @t67))))) % 0.36/0.59 (define @t78 () (lambda @t71 (and (_ tptp.reflexive @t1) (_ tptp.symmetric @t1) (_ tptp.transitive @t1)))) % 0.36/0.59 (define @t79 () (lambda (@list @t1 @t16) (exists @t14 @t59))) % 0.36/0.59 (define @t80 () (@list @t1 @t11)) % 0.36/0.59 (define @t81 () (lambda @t80 (exists @t68 @t59))) % 0.36/0.59 (define @t82 () (lambda (@list @t1 @t11 @t16) @t75)) % 0.36/0.59 (define @t83 () (@var "S1" (-> $$unsorted Bool))) % 0.36/0.59 (define @t84 () (lambda (@list @t1 @t83) (exists @t14 (and (_ @t83 @t11) (forall @t68 (= (_ @t83 @t16) @t59)))))) % 0.36/0.59 (define @t85 () (lambda @t64 (and (_ @t44 @t16) @t59))) % 0.36/0.59 (define @t86 () (lambda @t80 (or (_ (_ tptp.rel_domain @t1) @t11) (_ (_ tptp.rel_codomain @t1) @t11)))) % 0.36/0.59 (define @t87 () (@var "W" $$unsorted)) % 0.36/0.59 (define @t88 () (not (_ @t4 @t87))) % 0.36/0.59 (define @t89 () (@list @t87)) % 0.36/0.59 (define @t90 () (_ @t4 @t16)) % 0.36/0.59 (define @t91 () (_ @t4 @t67)) % 0.36/0.59 (define @t92 () (@list @t4 @t67)) % 0.36/0.59 (define @t93 () (lambda @t71 (forall @t92 (=> @t91 (exists @t68 (and @t90 (forall @t89 (=> (_ @t74 @t87) @t88)))))))) % 0.36/0.59 (define @t94 () (lambda @t71 (forall @t92 (=> @t91 (exists @t68 (and @t90 (forall @t89 (=> (_ @t74 @t16) @t88)))))))) % 0.36/0.59 (define @t95 () (_ @t1 @t11 @t16)) % 0.36/0.59 (define @t96 () (_ @t2 @t11)) % 0.36/0.59 (define @t97 () (_ @t2 @t11)) % 0.36/0.59 (define @t98 () (and @t97 @t59)) % 0.36/0.59 (define @t99 () (lambda @t51 @t98)) % 0.36/0.59 (define @t100 () (= @t1 @t99)) % 0.36/0.59 (define @t101 () (_ @t4 @t17)) % 0.36/0.59 (define @t102 () (not @t101)) % 0.36/0.59 (define @t103 () (forall @t34 (or @t102 (_ @t2 @t17)))) % 0.36/0.59 (define @t104 () (not @t103)) % 0.36/0.59 (define @t105 () (_ @t4 @t11)) % 0.36/0.59 (define @t106 () (not @t95)) % 0.36/0.59 (define @t107 () (forall @t51 (or @t106 (and @t105 (_ @t5 @t16))))) % 0.36/0.59 (define @t108 () (not @t107)) % 0.36/0.59 (define @t109 () (or @t108 @t104 @t100)) % 0.36/0.59 (define @t110 () (and @t107 @t103)) % 0.36/0.59 (define @t111 () (lambda @t46 @t63)) % 0.36/0.59 (define @t112 () (_ @t65 @t1)) % 0.36/0.59 (define @t113 () (= (_ @t112 @t2) @t1)) % 0.36/0.59 (define @t114 () (_ @t5 @t17)) % 0.36/0.59 (define @t115 () (forall @t34 (or @t102 @t114))) % 0.36/0.59 (define @t116 () (lambda (@list @t5) @t115)) % 0.36/0.59 (define @t117 () (_ (lambda @t32 @t115) @t4)) % 0.36/0.59 (define @t118 () (_ @t53 @t16)) % 0.36/0.59 (define @t119 () (lambda (@list @t53) (forall @t51 (or @t106 (and @t105 @t118))))) % 0.36/0.59 (define @t120 () (_ @t55 @t11)) % 0.36/0.59 (define @t121 () (forall @t51 (or @t106 (and @t120 @t118)))) % 0.36/0.59 (define @t122 () (lambda (@list @t55 @t53) @t121)) % 0.36/0.59 (define @t123 () (_ (lambda @t61 @t121) @t1)) % 0.36/0.59 (define @t124 () (and (_ (_ @t123 @t4) @t5) (_ @t117 @t2))) % 0.36/0.59 (define @t125 () (=> @t124 @t113)) % 0.36/0.59 (define @t126 () (forall @t8 @t125)) % 0.36/0.59 (define @t127 () (or @t25 @t21)) % 0.36/0.59 (define @t128 () (not @t59)) % 0.36/0.59 (define @t129 () (or @t128 @t57)) % 0.36/0.59 (define @t130 () (forall @t8 (or @t108 @t104 (= @t1 (lambda @t51 (and @t96 @t95)))))) % 0.36/0.59 (define @t131 () (@quantifiers_skolemize @t130 1)) % 0.36/0.59 (define @t132 () (_ @t131 @t11 @t16)) % 0.36/0.59 (define @t133 () (@quantifiers_skolemize @t130 0)) % 0.36/0.59 (define @t134 () (lambda @t51 (and (_ @t133 @t11) @t132))) % 0.36/0.59 (define @t135 () (@purify @t134)) % 0.36/0.59 (define @t136 () (= @t131 @t135)) % 0.36/0.59 (define @t137 () (@quantifiers_skolemize @t130 2)) % 0.36/0.59 (define @t138 () (forall @t34 (or (not (_ @t137 @t17)) (_ @t133 @t17)))) % 0.36/0.59 (define @t139 () (not @t138)) % 0.36/0.59 (define @t140 () (@quantifiers_skolemize @t130 3)) % 0.36/0.59 (define @t141 () (forall @t51 (or (not @t132) (and (_ @t137 @t11) (_ @t140 @t16))))) % 0.36/0.59 (define @t142 () (not @t141)) % 0.36/0.59 (define @t143 () (or @t142 @t139 @t136)) % 0.36/0.59 (define @t144 () (not @t143)) % 0.36/0.59 (define @t145 () (not @t130)) % 0.36/0.59 (define @t146 () (= @t131 @t134)) % 0.36/0.59 (define @t147 () (or @t142 @t139 @t146)) % 0.36/0.59 (define @t148 () (not @t147)) % 0.36/0.59 (define @t149 () (@list true)) % 0.36/0.59 (define @t150 () (@list @t143)) % 0.36/0.59 (define @t151 () (@const 0 $$unsorted)) % 0.36/0.59 (define @t152 () (@const 1 $$unsorted)) % 0.36/0.59 (define @t153 () (_ @t131 @t152 @t151)) % 0.36/0.59 (define @t154 () (_ @t133 @t152)) % 0.36/0.59 (define @t155 () (and @t154 @t153)) % 0.36/0.59 (define @t156 () (= (_ @t134 @t152 @t151) @t155)) % 0.36/0.59 (define @t157 () (_ @t135 @t152 @t151)) % 0.36/0.59 (define @t158 () (= @t153 @t157)) % 0.36/0.59 (define @t159 () (not @t158)) % 0.36/0.59 (define @t160 () (or @t136 @t159)) % 0.36/0.59 (define @t161 () (= @t153 @t155)) % 0.36/0.59 (define @t162 () (_ @t137 @t152)) % 0.36/0.59 (define @t163 () (and @t162 (_ @t140 @t151))) % 0.36/0.59 (define @t164 () (not @t153)) % 0.36/0.59 (define @t165 () (or @t164 @t163)) % 0.36/0.59 (define @t166 () (not @t162)) % 0.36/0.59 (define @t167 () (or @t166 @t154)) % 0.36/0.59 (define @t168 () (not @t155)) % 0.36/0.59 (assume @p1 @t10) % 0.36/0.59 (assume @p2 true) % 0.36/0.59 (step @p3 (= tptp.in @t13) :rule refl :args (@t13)) % 0.36/0.59 (step @p4 (= tptp.is_a @t13) :rule refl :args (@t13)) % 0.36/0.59 (step @p5 (= tptp.emptyset @t15) :rule refl :args (@t15)) % 0.36/0.59 (step @p6 (= tptp.unord_pair @t19) :rule refl :args (@t19)) % 0.36/0.59 (step @p7 (= tptp.singleton @t20) :rule refl :args (@t20)) % 0.36/0.59 (step @p8 (= tptp.union @t24) :rule refl :args (@t24)) % 0.36/0.59 (step @p9 (= tptp.excl_union @t27) :rule refl :args (@t27)) % 0.36/0.59 (step @p10 (= tptp.intersection @t29) :rule refl :args (@t29)) % 0.36/0.59 (step @p11 (= tptp.setminus @t30) :rule refl :args (@t30)) % 0.36/0.59 (step @p12 (= tptp.complement @t31) :rule refl :args (@t31)) % 0.36/0.59 (step @p13 (= tptp.disjoint @t33) :rule refl :args (@t33)) % 0.36/0.59 (step @p14 (= tptp.subset @t36) :rule refl :args (@t36)) % 0.36/0.59 (step @p15 (= tptp.meets @t38) :rule refl :args (@t38)) % 0.36/0.59 (step @p16 (= tptp.misses @t39) :rule refl :args (@t39)) % 0.36/0.59 (step @p17 (= tptp.cartesian_product @t41) :rule refl :args (@t41)) % 0.36/0.59 (step @p18 (= tptp.pair_rel @t42) :rule refl :args (@t42)) % 0.36/0.59 (step @p19 (= tptp.id_rel @t47) :rule refl :args (@t47)) % 0.36/0.59 (step @p20 (= tptp.sub_rel @t52) :rule refl :args (@t52)) % 0.36/0.59 (step @p21 (= tptp.is_rel_on @t62) :rule refl :args (@t62)) % 0.36/0.59 (step @p22 (= tptp.restrict_rel_domain @t65) :rule refl :args (@t65)) % 0.36/0.59 (step @p23 (= tptp.rel_diagonal @t66) :rule refl :args (@t66)) % 0.36/0.59 (step @p24 (= tptp.rel_composition @t69) :rule refl :args (@t69)) % 0.36/0.59 (step @p25 (= tptp.reflexive @t72) :rule refl :args (@t72)) % 0.36/0.59 (step @p26 (= tptp.irreflexive @t73) :rule refl :args (@t73)) % 0.36/0.59 (step @p27 (= tptp.symmetric @t76) :rule refl :args (@t76)) % 0.36/0.59 (step @p28 (= tptp.transitive @t77) :rule refl :args (@t77)) % 0.36/0.59 (step @p29 (= tptp.equiv_rel @t78) :rule refl :args (@t78)) % 0.36/0.59 (step @p30 (= tptp.rel_codomain @t79) :rule refl :args (@t79)) % 0.36/0.59 (step @p31 (= tptp.rel_domain @t81) :rule refl :args (@t81)) % 0.36/0.59 (step @p32 (= tptp.rel_inverse @t82) :rule refl :args (@t82)) % 0.36/0.59 (step @p33 (= tptp.equiv_classes @t84) :rule refl :args (@t84)) % 0.36/0.59 (step @p34 (= tptp.restrict_rel_codomain @t85) :rule refl :args (@t85)) % 0.36/0.59 (step @p35 (= tptp.rel_field @t86) :rule refl :args (@t86)) % 0.36/0.59 (step @p36 (= tptp.well_founded @t93) :rule refl :args (@t93)) % 0.36/0.59 (step @p37 (= tptp.upwards_well_founded @t94) :rule refl :args (@t94)) % 0.36/0.59 (step @p38 :rule refl :args (@t95)) % 0.36/0.59 (step @p39 :rule refl :args (@t59)) % 0.36/0.59 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t59 @t95))) % 0.36/0.59 (step @p41 :rule symm :premises (@p40)) % 0.36/0.59 (step @p42 :rule eq_resolve 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@p65)) % 0.36/0.59 (step @p74 :rule beta-reduce :args ((= (_ @t116 @t2) @t103))) % 0.36/0.59 (step @p75 :rule beta-reduce :args ((= @t117 @t116))) % 0.36/0.59 (step @p76 :rule ho_cong :premises (@p75 @p68)) % 0.36/0.59 (step @p77 :rule trans :premises (@p76 @p74)) % 0.36/0.59 (step @p78 :rule beta-reduce :args ((= (_ @t119 @t5) @t107))) % 0.36/0.59 (step @p79 :rule refl :args (@t5)) % 0.36/0.59 (step @p80 :rule beta-reduce :args ((= (_ @t122 @t4) @t119))) % 0.36/0.59 (step @p81 :rule refl :args (@t4)) % 0.36/0.59 (step @p82 :rule beta-reduce :args ((= @t123 @t122))) % 0.36/0.59 (step @p83 :rule ho_cong :premises (@p82 @p81)) % 0.36/0.59 (step @p84 :rule trans :premises (@p83 @p80)) % 0.36/0.59 (step @p85 :rule ho_cong :premises (@p84 @p79)) % 0.36/0.59 (step @p86 :rule trans :premises (@p85 @p78)) % 0.36/0.59 (step @p87 :rule nary_cong :premises (@p86 @p77) :args (@t124)) % 0.36/0.59 (step @p88 :rule cong :premises (@p87 @p73) :args (@t125)) % 0.36/0.59 (step @p89 :rule cong :premises (@p88) :args (@t126)) % 0.36/0.59 (step @p90 :rule trans :premises (@p89 @p64)) % 0.36/0.59 (step @p91 :rule cong :premises (@p90) :args ((not @t126))) % 0.36/0.59 (step @p92 :rule ho_cong :premises (@p22 @p66)) % 0.36/0.59 (step @p93 :rule ho_cong :premises (@p92 @p68)) % 0.36/0.59 (step @p94 :rule cong :premises (@p93 @p66) :args (@t3)) % 0.36/0.59 (step @p95 :rule refl :args (@t114)) % 0.36/0.59 (step @p96 :rule refl :args (@t21)) % 0.36/0.59 (step @p97 :rule cong :premises (@p96 @p95) :args ((= @t21 @t114))) % 0.36/0.59 (step @p98 :rule symm :premises (@p97)) % 0.36/0.59 (step @p99 :rule eq_resolve :premises (@p96 @p98)) % 0.36/0.59 (step @p100 :rule refl :args (@t101)) % 0.36/0.59 (step @p101 :rule refl :args (@t22)) % 0.36/0.59 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t22 @t101))) % 0.36/0.59 (step @p103 :rule symm :premises (@p102)) % 0.36/0.59 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.36/0.59 (step @p105 :rule cong :premises (@p104) :args 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:premises (@p150)) % 0.36/0.59 (step @p152 :rule refl :args (@t131)) % 0.36/0.59 (step @p153 :rule cong :premises (@p152 @p151) :args (@t146)) % 0.36/0.59 (step @p154 :rule refl :args (@t139)) % 0.36/0.59 (step @p155 :rule refl :args (@t142)) % 0.36/0.59 (step @p156 :rule nary_cong :premises (@p155 @p154 @p153) :args (@t147)) % 0.36/0.59 (step @p157 :rule cong :premises (@p156) :args (@t148)) % 0.36/0.59 (step @p158 :rule refl :args (@t145)) % 0.36/0.59 (step @p159 :rule cong :premises (@p158 @p157) :args ((=> @t145 @t148))) % 0.36/0.59 (assume-push @p220 @t145) % 0.36/0.59 (step @p161 :rule skolemize :premises (@p142)) % 0.36/0.59 (step-pop @p221 :rule scope :premises (@p161)) % 0.36/0.59 (step @p162 :rule process_scope :premises (@p221) :args (@t148)) % 0.36/0.59 (step @p164 :rule eq_resolve :premises (@p162 @p159)) % 0.36/0.59 (step @p165 :rule implies_elim :premises (@p164)) % 0.36/0.59 (step @p166 :rule eq_resolve :premises (@p165 @p145)) % 0.36/0.59 (step @p167 :rule chain_m_resolution :premises (@p166 @p142) :args (@t144 @t149 (@list @t130))) % 0.36/0.59 (step @p168 :rule cnf_or_neg :args (@t143 2)) % 0.36/0.59 (step @p169 :rule chain_m_resolution :premises (@p168 @p167) :args ((not @t136) @t149 @t150)) % 0.36/0.59 (step @p170 :rule eq-refl :args (@t155)) % 0.36/0.59 (step @p171 :rule refl :args (@t155)) % 0.36/0.59 (step @p172 :rule beta-reduce :args (@t156)) % 0.36/0.59 (step @p173 :rule cong :premises (@p172 @p171) :args (@t156)) % 0.36/0.59 (step @p174 :rule trans :premises (@p173 @p170)) % 0.36/0.59 (step @p175 :rule refl :args (@t151)) % 0.36/0.59 (step @p176 :rule refl :args (@t152)) % 0.36/0.59 (step @p177 :rule ho_cong :premises (@p147 @p176 @p175)) % 0.36/0.59 (step @p178 :rule cong :premises (@p177 @p171) :args ((= @t157 @t155))) % 0.36/0.59 (step @p179 :rule trans :premises (@p178 @p174)) % 0.36/0.59 (step @p180 :rule true_elim :premises (@p179)) % 0.36/0.59 (step @p181 :rule refl :args (@t153)) % 0.36/0.59 (step @p182 :rule cong :premises (@p181 @p180) :args (@t158)) % 0.36/0.59 (step @p183 :rule cong :premises (@p182) :args (@t159)) % 0.36/0.59 (step @p184 :rule refl :args (@t136)) % 0.36/0.59 (step @p185 :rule nary_cong :premises (@p184 @p183) :args (@t160)) % 0.36/0.59 ; WARNING: add trust step for TRUST % 0.36/0.59 ; trust TRUST THEORY_LEMMA % 0.36/0.59 (step @p186 :rule trust :premises () :args (@t160)) % 0.36/0.59 (step @p187 :rule eq_resolve :premises (@p186 @p185)) % 0.36/0.59 (step @p188 :rule chain_m_resolution :premises (@p187 @p169) :args ((not @t161) @t149 (@list @t136))) % 0.36/0.59 (step @p189 :rule cnf_equiv_neg2 :args (@t161)) % 0.36/0.59 (step @p190 :rule bool-double-not-elim :args (@t141)) % 0.36/0.59 (step @p191 :rule refl :args (@t143)) % 0.36/0.59 (step @p192 :rule nary_cong :premises (@p191 @p190) :args ((or @t143 (not @t142)))) % 0.36/0.59 (step @p193 :rule cnf_or_neg :args (@t143 0)) % 0.36/0.59 (step @p194 :rule eq_resolve :premises (@p193 @p192)) % 0.36/0.59 (step @p195 :rule reordering :premises (@p194) :args ((or @t141 @t143))) % 0.36/0.59 (step @p196 :rule chain_m_resolution :premises (@p195 @p167) :args (@t141 @t149 @t150)) % 0.36/0.59 (step @p197 :rule instantiate :premises (@p196) :args ((@list @t152 @t151))) % 0.36/0.59 (step @p198 :rule cnf_or_pos :args (@t165)) % 0.36/0.59 (step @p199 :rule reordering :premises (@p198) :args ((or @t164 @t163 (not @t165)))) % 0.36/0.59 (step @p200 :rule cnf_and_neg :args (@t155)) % 0.36/0.59 (step @p201 :rule reordering :premises (@p200) :args ((or @t155 @t164 (not @t154)))) % 0.36/0.59 (step @p202 :rule cnf_and_pos :args (@t163 0)) % 0.36/0.59 (step @p203 :rule reordering :premises (@p202) :args ((or @t162 (not @t163)))) % 0.36/0.59 (step @p204 :rule bool-double-not-elim :args (@t138)) % 0.36/0.59 (step @p205 :rule nary_cong :premises (@p191 @p204) :args ((or @t143 (not @t139)))) % 0.36/0.59 (step @p206 :rule cnf_or_neg :args (@t143 1)) % 0.36/0.59 (step @p207 :rule eq_resolve :premises (@p206 @p205)) % 0.36/0.59 (step @p208 :rule reordering :premises (@p207) :args ((or @t138 @t143))) % 0.36/0.59 (step @p209 :rule chain_m_resolution :premises (@p208 @p167) :args (@t138 @t149 @t150)) % 0.36/0.59 (step @p210 :rule instantiate :premises (@p209) :args ((@list @t152))) % 0.36/0.59 (step @p211 :rule cnf_or_pos :args (@t167)) % 0.36/0.59 (step @p212 :rule reordering :premises (@p211) :args ((or @t154 @t166 (not @t167)))) % 0.36/0.59 (step @p213 :rule chain_m_resolution :premises (@p212 @p210 @p203 @p201 @p199 @p197 @p189 @p188) :args (@t164 (@list false false true false false true true) (@list @t167 @t162 @t154 @t163 @t165 @t155 @t161))) % 0.36/0.59 (step @p214 :rule cnf_and_pos :args (@t155 1)) % 0.36/0.59 (step @p215 :rule reordering :premises (@p214) :args ((or @t153 @t168))) % 0.36/0.59 (step @p216 :rule chain_m_resolution :premises (@p215 @p213) :args (@t168 @t149 (@list @t153))) % 0.36/0.59 (step @p217 :rule cnf_equiv_neg1 :args (@t161)) % 0.36/0.59 (step @p218 :rule reordering :premises (@p217) :args ((or @t153 @t155 @t161))) % 0.36/0.59 (step @p219 false :rule chain_m_resolution :premises (@p218 @p216 @p213 @p188) :args (false (@list true true true) (@list @t155 @t153 @t161))) % 0.36/0.59 ) % 0.36/0.59 % SZS output end Proof % 0.36/0.59 % cvc5 exiting %------------------------------------------------------------------------------