%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET672^3 : 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 : n026.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 0.37s 0.60s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET672^3 : TPTP v9.2.1. Released v3.6.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n026.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 16:07:55 EDT 2026 % 0.16/0.35 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.37/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.60 % SZS status Theorem % 0.37/0.60 % SZS output start Proof % 0.37/0.60 ( % 0.37/0.60 (declare-sort $$unsorted 0) % 0.37/0.60 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.37/0.60 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.37/0.60 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.37/0.60 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.37/0.60 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.37/0.60 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.60 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.37/0.60 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.37/0.60 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.37/0.60 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.60 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.37/0.60 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.37/0.60 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.37/0.60 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.37/0.60 (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)))))))) % 0.37/0.60 (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)))))))) % 0.37/0.60 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.37/0.60 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.37/0.60 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$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 $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.37/0.60 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.37/0.60 (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))))) % 0.37/0.60 (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 $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.37/0.60 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.60 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.37/0.60 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.60 (define tptp.transitive () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.37/0.60 (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))))) % 0.37/0.60 (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))))))) % 0.37/0.60 (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))))))) % 0.37/0.60 (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)))))) % 0.37/0.60 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.37/0.60 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.37/0.60 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.37/0.60 (define tptp.well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.37/0.60 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.37/0.60 (define @t1 () (@var "Z" (-> $$unsorted Bool))) % 0.37/0.60 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.60 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.60 (define @t4 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.60 (define @t5 () (=> (_ (_ (_ tptp.is_rel_on @t3) @t2) @t4) (_ (_ (_ tptp.is_rel_on (_ (_ tptp.restrict_rel_codomain @t3) @t1)) @t2) @t1))) % 0.37/0.60 (define @t6 () (@list @t1 @t3 @t2 @t4)) % 0.37/0.60 (define @t7 () (forall @t6 @t5)) % 0.37/0.60 (define @t8 () (not @t7)) % 0.37/0.60 (define @t9 () (@var "X" $$unsorted)) % 0.37/0.60 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.37/0.60 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.37/0.60 (define @t12 () (@list @t9)) % 0.37/0.60 (define @t13 () (lambda @t12 false)) % 0.37/0.60 (define @t14 () (@var "Y" $$unsorted)) % 0.37/0.60 (define @t15 () (@var "U" $$unsorted)) % 0.37/0.60 (define @t16 () (= @t15 @t9)) % 0.37/0.60 (define @t17 () (lambda (@list @t9 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.37/0.60 (define @t18 () (lambda (@list @t9 @t15) @t16)) % 0.37/0.60 (define @t19 () (_ @t4 @t15)) % 0.37/0.60 (define @t20 () (_ @t2 @t15)) % 0.37/0.60 (define @t21 () (@list @t2 @t4 @t15)) % 0.37/0.60 (define @t22 () (lambda @t21 (or @t20 @t19))) % 0.37/0.60 (define @t23 () (not @t20)) % 0.37/0.60 (define @t24 () (and @t20 (not @t19))) % 0.37/0.60 (define @t25 () (lambda @t21 (or @t24 (and @t23 @t19)))) % 0.37/0.60 (define @t26 () (and @t20 @t19)) % 0.37/0.60 (define @t27 () (lambda @t21 @t26)) % 0.37/0.60 (define @t28 () (lambda @t21 @t24)) % 0.37/0.60 (define @t29 () (lambda (@list @t2 @t15) @t23)) % 0.37/0.60 (define @t30 () (@list @t2 @t4)) % 0.37/0.60 (define @t31 () (lambda @t30 (= (_ (_ tptp.intersection @t2) @t4) tptp.emptyset))) % 0.37/0.60 (define @t32 () (@list @t15)) % 0.37/0.60 (define @t33 () (lambda @t30 (forall @t32 (=> @t20 @t19)))) % 0.37/0.60 (define @t34 () (exists @t32 @t26)) % 0.37/0.60 (define @t35 () (lambda @t30 @t34)) % 0.37/0.60 (define @t36 () (lambda @t30 (not @t34))) % 0.37/0.60 (define @t37 () (@var "V" $$unsorted)) % 0.37/0.60 (define @t38 () (lambda (@list @t2 @t4 @t15 @t37) (and @t20 (_ @t4 @t37)))) % 0.37/0.60 (define @t39 () (lambda (@list @t9 @t14 @t15 @t37) (or @t16 (= @t37 @t14)))) % 0.37/0.60 (define @t40 () (= @t9 @t14)) % 0.37/0.60 (define @t41 () (@var "S" (-> $$unsorted Bool))) % 0.37/0.60 (define @t42 () (_ @t41 @t9)) % 0.37/0.60 (define @t43 () (@list @t41 @t9 @t14)) % 0.37/0.60 (define @t44 () (lambda @t43 (and @t42 @t40))) % 0.37/0.60 (define @t45 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.37/0.60 (define @t46 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.37/0.60 (define @t47 () (_ (_ @t46 @t9) @t14)) % 0.37/0.60 (define @t48 () (@list @t9 @t14)) % 0.37/0.60 (define @t49 () (lambda (@list @t46 @t45) (forall @t48 (=> @t47 (_ (_ @t45 @t9) @t14))))) % 0.37/0.60 (define @t50 () (@var "B" (-> $$unsorted Bool))) % 0.37/0.60 (define @t51 () (_ @t50 @t14)) % 0.37/0.60 (define @t52 () (@var "A" (-> $$unsorted Bool))) % 0.37/0.60 (define @t53 () (_ @t52 @t9)) % 0.37/0.60 (define @t54 () (and @t53 @t51)) % 0.37/0.60 (define @t55 () (_ @t3 @t9)) % 0.37/0.60 (define @t56 () (_ @t55 @t14)) % 0.37/0.60 (define @t57 () (forall @t48 (=> @t56 @t54))) % 0.37/0.60 (define @t58 () (@list @t3 @t52 @t50)) % 0.37/0.60 (define @t59 () (lambda @t58 @t57)) % 0.37/0.60 (define @t60 () (@list @t3 @t41 @t9 @t14)) % 0.37/0.60 (define @t61 () (lambda @t60 (and @t42 @t56))) % 0.37/0.60 (define @t62 () (lambda @t48 @t40)) % 0.37/0.60 (define @t63 () (@var "Z" $$unsorted)) % 0.37/0.60 (define @t64 () (@list @t14)) % 0.37/0.60 (define @t65 () (lambda (@list @t46 @t45 @t9 @t63) (exists @t64 (and @t47 (_ (_ @t45 @t14) @t63))))) % 0.37/0.60 (define @t66 () (_ @t55 @t9)) % 0.37/0.60 (define @t67 () (@list @t3)) % 0.37/0.60 (define @t68 () (lambda @t67 (forall @t12 @t66))) % 0.37/0.60 (define @t69 () (lambda @t67 (forall @t12 (not @t66)))) % 0.37/0.60 (define @t70 () (_ @t3 @t14)) % 0.37/0.60 (define @t71 () (_ @t70 @t9)) % 0.37/0.60 (define @t72 () (lambda @t67 (forall @t48 (=> @t56 @t71)))) % 0.37/0.60 (define @t73 () (lambda @t67 (forall (@list @t9 @t14 @t63) (=> (and @t56 (_ @t70 @t63)) (_ @t55 @t63))))) % 0.37/0.60 (define @t74 () (lambda @t67 (and (_ tptp.reflexive @t3) (_ tptp.symmetric @t3) (_ tptp.transitive @t3)))) % 0.37/0.60 (define @t75 () (lambda (@list @t3 @t14) (exists @t12 @t56))) % 0.37/0.60 (define @t76 () (@list @t3 @t9)) % 0.37/0.60 (define @t77 () (lambda @t76 (exists @t64 @t56))) % 0.37/0.60 (define @t78 () (lambda (@list @t3 @t9 @t14) @t71)) % 0.37/0.60 (define @t79 () (@var "S1" (-> $$unsorted Bool))) % 0.37/0.60 (define @t80 () (lambda (@list @t3 @t79) (exists @t12 (and (_ @t79 @t9) (forall @t64 (= (_ @t79 @t14) @t56)))))) % 0.37/0.60 (define @t81 () (and (_ @t41 @t14) @t56)) % 0.37/0.60 (define @t82 () (lambda @t60 @t81)) % 0.37/0.60 (define @t83 () (lambda @t76 (or (_ (_ tptp.rel_domain @t3) @t9) (_ (_ tptp.rel_codomain @t3) @t9)))) % 0.37/0.60 (define @t84 () (@var "W" $$unsorted)) % 0.37/0.60 (define @t85 () (not (_ @t2 @t84))) % 0.37/0.60 (define @t86 () (@list @t84)) % 0.37/0.60 (define @t87 () (_ @t2 @t14)) % 0.37/0.60 (define @t88 () (_ @t2 @t63)) % 0.37/0.60 (define @t89 () (@list @t2 @t63)) % 0.37/0.60 (define @t90 () (lambda @t67 (forall @t89 (=> @t88 (exists @t64 (and @t87 (forall @t86 (=> (_ @t70 @t84) @t85)))))))) % 0.37/0.60 (define @t91 () (lambda @t67 (forall @t89 (=> @t88 (exists @t64 (and @t87 (forall @t86 (=> (_ @t70 @t14) @t85)))))))) % 0.37/0.60 (define @t92 () (@var "BOUND_VARIABLE_8220" $$unsorted)) % 0.37/0.60 (define @t93 () (_ @t1 @t92)) % 0.37/0.60 (define @t94 () (@var "BOUND_VARIABLE_8218" $$unsorted)) % 0.37/0.60 (define @t95 () (and (_ @t2 @t94) @t93)) % 0.37/0.60 (define @t96 () (not (_ @t3 @t94 @t92))) % 0.37/0.60 (define @t97 () (not @t93)) % 0.37/0.60 (define @t98 () (_ @t2 @t9)) % 0.37/0.60 (define @t99 () (_ @t3 @t9 @t14)) % 0.37/0.60 (define @t100 () (not @t99)) % 0.37/0.60 (define @t101 () (forall @t48 (or @t100 (and @t98 (_ @t4 @t14))))) % 0.37/0.60 (define @t102 () (not @t101)) % 0.37/0.60 (define @t103 () (or @t102 @t97 @t96 @t95)) % 0.37/0.60 (define @t104 () (or @t97 @t96 @t95)) % 0.37/0.60 (define @t105 () (or @t102 @t104)) % 0.37/0.60 (define @t106 () (@list @t1 @t3 @t2 @t4 @t94 @t92)) % 0.37/0.60 (define @t107 () (forall @t106 @t105)) % 0.37/0.60 (define @t108 () (@list @t94 @t92)) % 0.37/0.60 (define @t109 () (forall @t108 @t105)) % 0.37/0.60 (define @t110 () (forall @t108 @t104)) % 0.37/0.60 (define @t111 () (or @t102 @t110)) % 0.37/0.60 (define @t112 () (_ @t1 @t14)) % 0.37/0.60 (define @t113 () (not @t112)) % 0.37/0.60 (define @t114 () (forall @t48 (or @t113 @t100 (and @t98 @t112)))) % 0.37/0.60 (define @t115 () (_ @t50 @t14)) % 0.37/0.60 (define @t116 () (and @t98 @t115)) % 0.37/0.60 (define @t117 () (@list @t50)) % 0.37/0.60 (define @t118 () (lambda @t117 (forall @t48 (or @t113 @t100 @t116)))) % 0.37/0.60 (define @t119 () (_ @t52 @t9)) % 0.37/0.60 (define @t120 () (and @t119 @t115)) % 0.37/0.60 (define @t121 () (@list @t52 @t50)) % 0.37/0.60 (define @t122 () (not @t56)) % 0.37/0.60 (define @t123 () (_ @t1 @t14)) % 0.37/0.60 (define @t124 () (not @t123)) % 0.37/0.60 (define @t125 () (or @t124 @t122 @t120)) % 0.37/0.60 (define @t126 () (and @t123 @t56)) % 0.37/0.60 (define @t127 () (or (not @t126) @t120)) % 0.37/0.60 (define @t128 () (lambda @t48 @t126)) % 0.37/0.60 (define @t129 () (_ @t128 @t9 @t14)) % 0.37/0.60 (define @t130 () (not @t129)) % 0.37/0.60 (define @t131 () (or @t130 @t120)) % 0.37/0.60 (define @t132 () (forall @t48 @t131)) % 0.37/0.60 (define @t133 () (lambda @t121 @t132)) % 0.37/0.60 (define @t134 () (forall @t48 (or @t100 @t120))) % 0.37/0.60 (define @t135 () (lambda @t58 @t134)) % 0.37/0.60 (define @t136 () (lambda @t43 @t81)) % 0.37/0.60 (define @t137 () (_ @t82 @t3)) % 0.37/0.60 (define @t138 () (lambda @t117 (forall @t48 (or @t100 @t116)))) % 0.37/0.60 (define @t139 () (lambda @t121 @t134)) % 0.37/0.60 (define @t140 () (_ @t135 @t3)) % 0.37/0.60 (define @t141 () (=> (_ (_ @t140 @t2) @t4) (_ (_ (_ @t135 (_ @t137 @t1)) @t2) @t1))) % 0.37/0.60 (define @t142 () (forall @t6 @t141)) % 0.37/0.60 (define @t143 () (or @t122 @t54)) % 0.37/0.60 (define @t144 () (forall @t106 @t103)) % 0.37/0.60 (define @t145 () (@quantifiers_skolemize @t144 5)) % 0.37/0.60 (define @t146 () (@quantifiers_skolemize @t144 4)) % 0.37/0.60 (define @t147 () (@quantifiers_skolemize @t144 1)) % 0.37/0.60 (define @t148 () (_ @t147 @t146 @t145)) % 0.37/0.60 (define @t149 () (_ (@quantifiers_skolemize @t144 0) @t145)) % 0.37/0.60 (define @t150 () (@quantifiers_skolemize @t144 2)) % 0.37/0.60 (define @t151 () (_ @t150 @t146)) % 0.37/0.60 (define @t152 () (and @t151 @t149)) % 0.37/0.60 (define @t153 () (not @t148)) % 0.37/0.60 (define @t154 () (not @t149)) % 0.37/0.60 (define @t155 () (@quantifiers_skolemize @t144 3)) % 0.37/0.60 (define @t156 () (forall @t48 (or (not (_ @t147 @t9 @t14)) (and (_ @t150 @t9) (_ @t155 @t14))))) % 0.37/0.60 (define @t157 () (not @t156)) % 0.37/0.60 (define @t158 () (or @t157 @t154 @t153 @t152)) % 0.37/0.60 (define @t159 () (@list true)) % 0.37/0.60 (define @t160 () (@list @t158)) % 0.37/0.60 (define @t161 () (not @t151)) % 0.37/0.60 (define @t162 () (and @t151 (_ @t155 @t145))) % 0.37/0.60 (define @t163 () (not @t162)) % 0.37/0.60 (define @t164 () (or @t153 @t162)) % 0.37/0.60 (assume @p1 @t8) % 0.37/0.60 (assume @p2 true) % 0.37/0.60 (step @p3 (= tptp.in @t11) :rule refl :args (@t11)) % 0.37/0.60 (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11)) % 0.37/0.60 (step @p5 (= tptp.emptyset @t13) :rule refl :args (@t13)) % 0.37/0.60 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.37/0.60 (step @p7 (= tptp.singleton @t18) :rule refl :args (@t18)) % 0.37/0.60 (step @p8 (= tptp.union @t22) :rule refl :args (@t22)) % 0.37/0.60 (step @p9 (= tptp.excl_union @t25) :rule refl :args (@t25)) % 0.37/0.60 (step @p10 (= tptp.intersection @t27) :rule refl :args (@t27)) % 0.37/0.60 (step @p11 (= tptp.setminus @t28) :rule refl :args (@t28)) % 0.37/0.60 (step @p12 (= tptp.complement @t29) :rule refl :args (@t29)) % 0.37/0.60 (step @p13 (= tptp.disjoint @t31) :rule refl :args (@t31)) % 0.37/0.60 (step @p14 (= tptp.subset @t33) :rule refl :args (@t33)) % 0.37/0.60 (step @p15 (= tptp.meets @t35) :rule refl :args (@t35)) % 0.37/0.60 (step @p16 (= tptp.misses @t36) :rule refl :args (@t36)) % 0.37/0.60 (step @p17 (= tptp.cartesian_product @t38) :rule refl :args (@t38)) % 0.37/0.60 (step @p18 (= tptp.pair_rel @t39) :rule refl :args (@t39)) % 0.37/0.60 (step @p19 (= tptp.id_rel @t44) :rule refl :args (@t44)) % 0.37/0.60 (step @p20 (= tptp.sub_rel @t49) :rule refl :args (@t49)) % 0.37/0.60 (step @p21 (= tptp.is_rel_on @t59) :rule refl :args (@t59)) % 0.37/0.60 (step @p22 (= tptp.restrict_rel_domain @t61) :rule refl :args (@t61)) % 0.37/0.60 (step @p23 (= tptp.rel_diagonal @t62) :rule refl :args (@t62)) % 0.37/0.60 (step @p24 (= tptp.rel_composition @t65) :rule refl :args (@t65)) % 0.37/0.60 (step @p25 (= tptp.reflexive @t68) :rule refl :args (@t68)) % 0.37/0.60 (step @p26 (= tptp.irreflexive @t69) :rule refl :args (@t69)) % 0.37/0.60 (step @p27 (= tptp.symmetric @t72) :rule refl :args (@t72)) % 0.37/0.60 (step @p28 (= tptp.transitive @t73) :rule refl :args (@t73)) % 0.37/0.60 (step @p29 (= tptp.equiv_rel @t74) :rule refl :args (@t74)) % 0.37/0.60 (step @p30 (= tptp.rel_codomain @t75) :rule refl :args (@t75)) % 0.37/0.60 (step @p31 (= tptp.rel_domain @t77) :rule refl :args (@t77)) % 0.37/0.60 (step @p32 (= tptp.rel_inverse @t78) :rule refl :args (@t78)) % 0.37/0.60 (step @p33 (= tptp.equiv_classes @t80) :rule refl :args (@t80)) % 0.37/0.60 (step @p34 (= tptp.restrict_rel_codomain @t82) :rule refl :args (@t82)) % 0.37/0.60 (step @p35 (= tptp.rel_field @t83) :rule refl :args (@t83)) % 0.37/0.60 (step @p36 (= tptp.well_founded @t90) :rule refl :args (@t90)) % 0.37/0.60 (step @p37 (= tptp.upwards_well_founded @t91) :rule refl :args (@t91)) % 0.37/0.60 (step @p38 :rule aci_norm :args ((= @t105 @t103))) % 0.37/0.60 (step @p39 :rule cong :premises (@p38) :args (@t107)) % 0.37/0.60 (step @p40 :rule quant-merge-prenex :args ((= (forall @t6 @t109) @t107))) % 0.37/0.60 (step @p41 :rule alpha_equiv :args (@t110 (@list @t94 @t92) (@list @t9 @t14))) % 0.37/0.60 (step @p42 :rule refl :args (@t102)) % 0.37/0.60 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t111)) % 0.37/0.60 (step @p44 :rule quant-miniscope-or :args ((= @t109 @t111))) % 0.37/0.60 (step @p45 :rule trans :premises (@p44 @p43)) % 0.37/0.60 (step @p46 :rule symm :premises (@p45)) % 0.37/0.60 (step @p47 :rule cong :premises (@p46) :args ((forall @t6 (or @t102 @t114)))) % 0.37/0.60 (step @p48 :rule trans :premises (@p47 @p40)) % 0.37/0.60 (step @p49 :rule trans :premises (@p48 @p39)) % 0.37/0.60 (step @p50 :rule bool-impl-elim :args (@t101 @t114)) % 0.37/0.60 (step @p51 :rule cong :premises (@p50) :args ((forall @t6 (=> @t101 @t114)))) % 0.37/0.60 (step @p52 :rule trans :premises (@p51 @p49)) % 0.37/0.60 (step @p53 :rule beta-reduce :args ((= (_ @t118 @t1) @t114))) % 0.37/0.60 (step @p54 :rule refl :args (@t1)) % 0.37/0.60 (step @p55 :rule beta-reduce :args ((= (_ (lambda @t121 (forall @t48 (or @t113 @t100 @t120))) @t2) @t118))) % 0.37/0.60 (step @p56 :rule refl :args (@t2)) % 0.37/0.60 (step @p57 :rule refl :args (@t120)) % 0.37/0.60 (step @p58 :rule refl :args (@t99)) % 0.37/0.60 (step @p59 :rule refl :args (@t56)) % 0.37/0.60 (step @p60 :rule cong :premises (@p59 @p58) :args ((= @t56 @t99))) % 0.37/0.60 (step @p61 :rule symm :premises (@p60)) % 0.37/0.60 (step @p62 :rule eq_resolve :premises (@p59 @p61)) % 0.37/0.60 (step @p63 :rule cong :premises (@p62) :args (@t122)) % 0.37/0.60 (step @p64 :rule refl :args (@t112)) % 0.37/0.60 (step @p65 :rule refl :args (@t123)) % 0.37/0.60 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t123 @t112))) % 0.37/0.60 (step @p67 :rule symm :premises (@p66)) % 0.37/0.60 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.37/0.60 (step @p69 :rule cong :premises (@p68) :args (@t124)) % 0.37/0.60 (step @p70 :rule nary_cong :premises (@p69 @p63 @p57) :args (@t125)) % 0.37/0.60 (step @p71 :rule cong :premises (@p70) :args ((forall @t48 @t125))) % 0.37/0.60 (step @p72 :rule aci_norm :args ((= (or (or @t124 @t122) @t120) @t125))) % 0.37/0.60 (step @p73 :rule bool-and-de-morgan :args (@t123 @t56 true)) % 0.37/0.60 (step @p74 :rule nary_cong :premises (@p73 @p57) :args (@t127)) % 0.37/0.60 (step @p75 :rule trans :premises (@p74 @p72)) % 0.37/0.60 (step @p76 :rule cong :premises (@p75) :args ((forall @t48 @t127))) % 0.37/0.60 (step @p77 :rule trans :premises (@p76 @p71)) % 0.37/0.60 (step @p78 :rule refl :args (@t120)) % 0.37/0.60 (step @p79 :rule beta-reduce :args ((= @t129 @t126))) % 0.37/0.60 (step @p80 :rule cong :premises (@p79) :args (@t130)) % 0.37/0.60 (step @p81 :rule nary_cong :premises (@p80 @p78) :args (@t131)) % 0.37/0.60 (step @p82 :rule cong :premises (@p81) :args (@t132)) % 0.37/0.60 (step @p83 :rule trans :premises (@p82 @p77)) % 0.37/0.60 (step @p84 :rule cong :premises (@p83) :args (@t133)) % 0.37/0.60 (step @p85 :rule beta-reduce :args ((= (_ @t135 @t128) @t133))) % 0.37/0.60 (step @p86 :rule trans :premises (@p85 @p84)) % 0.37/0.60 (step @p87 :rule beta-reduce :args ((= (_ @t136 @t1) @t128))) % 0.37/0.60 (step @p88 :rule beta-reduce :args ((= @t137 @t136))) % 0.37/0.60 (step @p89 :rule ho_cong :premises (@p88 @p54)) % 0.37/0.60 (step @p90 :rule trans :premises (@p89 @p87)) % 0.37/0.60 (step @p91 :rule refl :args (@t135)) % 0.37/0.60 (step @p92 :rule ho_cong :premises (@p91 @p90)) % 0.37/0.60 (step @p93 :rule trans :premises (@p92 @p86)) % 0.37/0.60 (step @p94 :rule ho_cong :premises (@p93 @p56)) % 0.37/0.60 (step @p95 :rule trans :premises (@p94 @p55)) % 0.37/0.60 (step @p96 :rule ho_cong :premises (@p95 @p54)) % 0.37/0.60 (step @p97 :rule trans :premises (@p96 @p53)) % 0.37/0.60 (step @p98 :rule beta-reduce :args ((= (_ @t138 @t4) @t101))) % 0.37/0.60 (step @p99 :rule refl :args (@t4)) % 0.37/0.60 (step @p100 :rule beta-reduce :args ((= (_ @t139 @t2) @t138))) % 0.37/0.60 (step @p101 :rule beta-reduce :args ((= @t140 @t139))) % 0.37/0.60 (step @p102 :rule ho_cong :premises (@p101 @p56)) % 0.37/0.60 (step @p103 :rule trans :premises (@p102 @p100)) % 0.37/0.60 (step @p104 :rule ho_cong :premises (@p103 @p99)) % 0.37/0.60 (step @p105 :rule trans :premises (@p104 @p98)) % 0.37/0.60 (step @p106 :rule cong :premises (@p105 @p97) :args (@t141)) % 0.37/0.60 (step @p107 :rule cong :premises (@p106) :args (@t142)) % 0.37/0.60 (step @p108 :rule trans :premises (@p107 @p52)) % 0.37/0.60 (step @p109 :rule cong :premises (@p108) :args ((not @t142))) % 0.37/0.60 (step @p110 :rule refl :args (@t3)) % 0.37/0.60 (step @p111 :rule ho_cong :premises (@p34 @p110)) % 0.37/0.60 (step @p112 :rule ho_cong :premises (@p111 @p54)) % 0.37/0.60 (step @p113 :rule refl :args (@t115)) % 0.37/0.60 (step @p114 :rule refl :args (@t51)) % 0.37/0.60 (step @p115 :rule cong :premises (@p114 @p113) :args ((= @t51 @t115))) % 0.37/0.60 (step @p116 :rule symm :premises (@p115)) % 0.37/0.60 (step @p117 :rule eq_resolve :premises (@p114 @p116)) % 0.37/0.60 (step @p118 :rule refl :args (@t119)) % 0.37/0.60 (step @p119 :rule refl :args (@t53)) % 0.37/0.60 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t53 @t119))) % 0.37/0.60 (step @p121 :rule symm :premises (@p120)) % 0.37/0.60 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.37/0.60 (step @p123 :rule nary_cong :premises (@p122 @p117) :args (@t54)) % 0.37/0.60 (step @p124 :rule nary_cong :premises (@p63 @p123) :args (@t143)) % 0.37/0.60 (step @p125 :rule cong :premises (@p124) :args ((forall @t48 @t143))) % 0.37/0.60 (step @p126 :rule bool-impl-elim :args (@t56 @t54)) % 0.37/0.60 (step @p127 :rule cong :premises (@p126) :args (@t57)) % 0.37/0.60 (step @p128 :rule trans :premises (@p127 @p125)) % 0.37/0.60 (step @p129 :rule cong :premises (@p128) :args (@t59)) % 0.37/0.60 (step @p130 :rule trans :premises (@p21 @p129)) % 0.37/0.60 (step @p131 :rule ho_cong :premises (@p130 @p112)) % 0.37/0.60 (step @p132 :rule ho_cong :premises (@p131 @p56)) % 0.37/0.60 (step @p133 :rule ho_cong :premises (@p132 @p54)) % 0.37/0.60 (step @p134 :rule ho_cong :premises (@p130 @p110)) % 0.37/0.60 (step @p135 :rule ho_cong :premises (@p134 @p56)) % 0.37/0.60 (step @p136 :rule ho_cong :premises (@p135 @p99)) % 0.37/0.60 (step @p137 :rule cong :premises (@p136 @p133) :args (@t5)) % 0.37/0.60 (step @p138 :rule cong :premises (@p137) :args (@t7)) % 0.37/0.60 (step @p139 :rule cong :premises (@p138) :args (@t8)) % 0.37/0.60 (step @p140 :rule trans :premises (@p139 @p109)) % 0.37/0.60 (step @p141 :rule eq_resolve :premises (@p1 @p140)) % 0.37/0.60 (step @p142 :rule skolemize :premises (@p141)) % 0.37/0.60 (step @p143 :rule bool-double-not-elim :args (@t148)) % 0.37/0.60 (step @p144 :rule refl :args (@t158)) % 0.37/0.60 (step @p145 :rule nary_cong :premises (@p144 @p143) :args ((or @t158 (not @t153)))) % 0.37/0.60 (step @p146 :rule cnf_or_neg :args (@t158 2)) % 0.37/0.60 (step @p147 :rule eq_resolve :premises (@p146 @p145)) % 0.37/0.60 (step @p148 :rule reordering :premises (@p147) :args ((or @t148 @t158))) % 0.37/0.60 (step @p149 :rule chain_m_resolution :premises (@p148 @p142) :args (@t148 @t159 @t160)) % 0.37/0.60 (step @p150 :rule cnf_or_neg :args (@t158 3)) % 0.37/0.60 (step @p151 :rule chain_m_resolution :premises (@p150 @p142) :args ((not @t152) @t159 @t160)) % 0.37/0.60 (step @p152 :rule bool-double-not-elim :args (@t149)) % 0.37/0.60 (step @p153 :rule nary_cong :premises (@p144 @p152) :args ((or @t158 (not @t154)))) % 0.37/0.60 (step @p154 :rule cnf_or_neg :args (@t158 1)) % 0.37/0.60 (step @p155 :rule eq_resolve :premises (@p154 @p153)) % 0.37/0.60 (step @p156 :rule reordering :premises (@p155) :args ((or @t149 @t158))) % 0.37/0.60 (step @p157 :rule chain_m_resolution :premises (@p156 @p142) :args (@t149 @t159 @t160)) % 0.37/0.60 (step @p158 :rule cnf_and_neg :args (@t152)) % 0.37/0.60 (step @p159 :rule reordering :premises (@p158) :args ((or @t154 @t152 @t161))) % 0.37/0.60 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p151) :args (@t161 (@list false true) (@list @t149 @t152))) % 0.37/0.60 (step @p161 :rule cnf_and_pos :args (@t162 0)) % 0.37/0.60 (step @p162 :rule reordering :premises (@p161) :args ((or @t151 @t163))) % 0.37/0.60 (step @p163 :rule chain_m_resolution :premises (@p162 @p160) :args (@t163 @t159 (@list @t151))) % 0.37/0.60 (step @p164 :rule bool-double-not-elim :args (@t156)) % 0.37/0.60 (step @p165 :rule nary_cong :premises (@p144 @p164) :args ((or @t158 (not @t157)))) % 0.37/0.60 (step @p166 :rule cnf_or_neg :args (@t158 0)) % 0.37/0.60 (step @p167 :rule eq_resolve :premises (@p166 @p165)) % 0.37/0.60 (step @p168 :rule reordering :premises (@p167) :args ((or @t156 @t158))) % 0.37/0.60 (step @p169 :rule chain_m_resolution :premises (@p168 @p142) :args (@t156 @t159 @t160)) % 0.37/0.60 (step @p170 :rule instantiate :premises (@p169) :args ((@list @t146 @t145))) % 0.37/0.60 (step @p171 :rule cnf_or_pos :args (@t164)) % 0.37/0.60 (step @p172 :rule reordering :premises (@p171) :args ((or @t153 @t162 (not @t164)))) % 0.37/0.60 (step @p173 false :rule chain_m_resolution :premises (@p172 @p170 @p163 @p149) :args (false (@list false true false) (@list @t164 @t162 @t148))) % 0.37/0.60 ) % 0.37/0.60 % SZS output end Proof % 0.37/0.60 % cvc5 exiting %------------------------------------------------------------------------------