%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET649^3 : 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 : n005.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 0.38s 0.58s % Output : Proof 0.38s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET649^3 : 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 % 0.18/0.34 % Computer : n005.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Tue Jun 2 16:05:48 EDT 2026 % 0.18/0.34 % CPUTime : % 0.31/0.48 %----Proving TH0 % 0.38/0.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.38/0.58 % SZS status Theorem % 0.38/0.58 % SZS output start Proof % 0.38/0.58 ( % 0.38/0.58 (declare-sort $$unsorted 0) % 0.38/0.58 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.58 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.38/0.58 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.38/0.58 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.38/0.58 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.38/0.58 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.58 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.38/0.58 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.38/0.58 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.38/0.58 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.38/0.58 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.38/0.58 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.38/0.58 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.38/0.58 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.38/0.58 (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)))))))) % 0.38/0.58 (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)))))))) % 0.38/0.58 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.38/0.58 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.38/0.58 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.38/0.58 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.58 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 0.38/0.58 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.38/0.58 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.38/0.58 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.38/0.58 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.58 (define tptp.transitive () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.38/0.58 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 0.38/0.58 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.58 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.38/0.58 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.38/0.58 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S1" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.38/0.58 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.38/0.58 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.38/0.58 (define tptp.well_founded () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "Z" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.38/0.58 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "Z" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.38/0.58 (define @t1 () (@var "Y" (-> $$unsorted Bool))) % 0.38/0.58 (define @t2 () (@var "X" (-> $$unsorted Bool))) % 0.38/0.58 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.38/0.58 (define @t4 () (_ tptp.rel_codomain @t3)) % 0.38/0.58 (define @t5 () (_ tptp.rel_domain @t3)) % 0.38/0.58 (define @t6 () (and (_ (_ tptp.subset @t5) @t2) (_ (_ tptp.subset @t4) @t1))) % 0.38/0.58 (define @t7 () (=> @t6 (_ (_ tptp.sub_rel @t3) (_ (_ tptp.cartesian_product @t2) @t1)))) % 0.38/0.58 (define @t8 () (@list @t3 @t2 @t1)) % 0.38/0.58 (define @t9 () (forall @t8 @t7)) % 0.38/0.58 (define @t10 () (not @t9)) % 0.38/0.58 (define @t11 () (@var "X" $$unsorted)) % 0.38/0.58 (define @t12 () (@var "M" (-> $$unsorted Bool))) % 0.38/0.58 (define @t13 () (lambda (@list @t11 @t12) (_ @t12 @t11))) % 0.38/0.58 (define @t14 () (@list @t11)) % 0.38/0.58 (define @t15 () (lambda @t14 false)) % 0.38/0.58 (define @t16 () (@var "Y" $$unsorted)) % 0.38/0.58 (define @t17 () (@var "U" $$unsorted)) % 0.38/0.58 (define @t18 () (= @t17 @t11)) % 0.38/0.58 (define @t19 () (lambda (@list @t11 @t16 @t17) (or @t18 (= @t17 @t16)))) % 0.38/0.58 (define @t20 () (lambda (@list @t11 @t17) @t18)) % 0.38/0.58 (define @t21 () (_ @t1 @t17)) % 0.38/0.58 (define @t22 () (_ @t2 @t17)) % 0.38/0.58 (define @t23 () (@list @t2 @t1 @t17)) % 0.38/0.58 (define @t24 () (lambda @t23 (or @t22 @t21))) % 0.38/0.58 (define @t25 () (not @t22)) % 0.38/0.58 (define @t26 () (and @t22 (not @t21))) % 0.38/0.58 (define @t27 () (lambda @t23 (or @t26 (and @t25 @t21)))) % 0.38/0.58 (define @t28 () (and @t22 @t21)) % 0.38/0.58 (define @t29 () (lambda @t23 @t28)) % 0.38/0.58 (define @t30 () (lambda @t23 @t26)) % 0.38/0.58 (define @t31 () (lambda (@list @t2 @t17) @t25)) % 0.38/0.58 (define @t32 () (@list @t2 @t1)) % 0.38/0.58 (define @t33 () (lambda @t32 (= (_ (_ tptp.intersection @t2) @t1) tptp.emptyset))) % 0.38/0.58 (define @t34 () (@list @t17)) % 0.38/0.58 (define @t35 () (forall @t34 (=> @t22 @t21))) % 0.38/0.58 (define @t36 () (lambda @t32 @t35)) % 0.38/0.58 (define @t37 () (exists @t34 @t28)) % 0.38/0.58 (define @t38 () (lambda @t32 @t37)) % 0.38/0.58 (define @t39 () (lambda @t32 (not @t37))) % 0.38/0.58 (define @t40 () (@var "V" $$unsorted)) % 0.38/0.58 (define @t41 () (and @t22 (_ @t1 @t40))) % 0.38/0.58 (define @t42 () (lambda (@list @t2 @t1 @t17 @t40) @t41)) % 0.38/0.58 (define @t43 () (lambda (@list @t11 @t16 @t17 @t40) (or @t18 (= @t40 @t16)))) % 0.38/0.58 (define @t44 () (= @t11 @t16)) % 0.38/0.58 (define @t45 () (@var "S" (-> $$unsorted Bool))) % 0.38/0.58 (define @t46 () (_ @t45 @t11)) % 0.38/0.58 (define @t47 () (lambda (@list @t45 @t11 @t16) (and @t46 @t44))) % 0.38/0.58 (define @t48 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.38/0.58 (define @t49 () (_ (_ @t48 @t11) @t16)) % 0.38/0.58 (define @t50 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.38/0.58 (define @t51 () (_ (_ @t50 @t11) @t16)) % 0.38/0.58 (define @t52 () (@list @t11 @t16)) % 0.38/0.58 (define @t53 () (forall @t52 (=> @t51 @t49))) % 0.38/0.58 (define @t54 () (@list @t50 @t48)) % 0.38/0.58 (define @t55 () (lambda @t54 @t53)) % 0.38/0.58 (define @t56 () (@var "B" (-> $$unsorted Bool))) % 0.38/0.58 (define @t57 () (@var "A" (-> $$unsorted Bool))) % 0.38/0.58 (define @t58 () (_ @t3 @t11)) % 0.38/0.58 (define @t59 () (_ @t58 @t16)) % 0.38/0.58 (define @t60 () (lambda (@list @t3 @t57 @t56) (forall @t52 (=> @t59 (and (_ @t57 @t11) (_ @t56 @t16)))))) % 0.38/0.58 (define @t61 () (@list @t3 @t45 @t11 @t16)) % 0.38/0.58 (define @t62 () (lambda @t61 (and @t46 @t59))) % 0.38/0.58 (define @t63 () (lambda @t52 @t44)) % 0.38/0.58 (define @t64 () (@var "Z" $$unsorted)) % 0.38/0.58 (define @t65 () (@list @t16)) % 0.38/0.58 (define @t66 () (lambda (@list @t50 @t48 @t11 @t64) (exists @t65 (and @t51 (_ (_ @t48 @t16) @t64))))) % 0.38/0.58 (define @t67 () (_ @t58 @t11)) % 0.38/0.58 (define @t68 () (@list @t3)) % 0.38/0.58 (define @t69 () (lambda @t68 (forall @t14 @t67))) % 0.38/0.58 (define @t70 () (lambda @t68 (forall @t14 (not @t67)))) % 0.38/0.58 (define @t71 () (_ @t3 @t16)) % 0.38/0.58 (define @t72 () (_ @t71 @t11)) % 0.38/0.58 (define @t73 () (lambda @t68 (forall @t52 (=> @t59 @t72)))) % 0.38/0.58 (define @t74 () (lambda @t68 (forall (@list @t11 @t16 @t64) (=> (and @t59 (_ @t71 @t64)) (_ @t58 @t64))))) % 0.38/0.58 (define @t75 () (lambda @t68 (and (_ tptp.reflexive @t3) (_ tptp.symmetric @t3) (_ tptp.transitive @t3)))) % 0.38/0.58 (define @t76 () (exists @t14 @t59)) % 0.38/0.58 (define @t77 () (@list @t3 @t16)) % 0.38/0.58 (define @t78 () (lambda @t77 @t76)) % 0.38/0.58 (define @t79 () (exists @t65 @t59)) % 0.38/0.58 (define @t80 () (@list @t3 @t11)) % 0.38/0.58 (define @t81 () (lambda @t80 @t79)) % 0.38/0.58 (define @t82 () (lambda (@list @t3 @t11 @t16) @t72)) % 0.38/0.58 (define @t83 () (@var "S1" (-> $$unsorted Bool))) % 0.38/0.58 (define @t84 () (lambda (@list @t3 @t83) (exists @t14 (and (_ @t83 @t11) (forall @t65 (= (_ @t83 @t16) @t59)))))) % 0.38/0.58 (define @t85 () (lambda @t61 (and (_ @t45 @t16) @t59))) % 0.38/0.58 (define @t86 () (lambda @t80 (or (_ @t5 @t11) (_ @t4 @t11)))) % 0.38/0.58 (define @t87 () (@var "W" $$unsorted)) % 0.38/0.58 (define @t88 () (not (_ @t2 @t87))) % 0.38/0.58 (define @t89 () (@list @t87)) % 0.38/0.58 (define @t90 () (_ @t2 @t16)) % 0.38/0.58 (define @t91 () (_ @t2 @t64)) % 0.38/0.58 (define @t92 () (@list @t2 @t64)) % 0.38/0.58 (define @t93 () (lambda @t68 (forall @t92 (=> @t91 (exists @t65 (and @t90 (forall @t89 (=> (_ @t71 @t87) @t88)))))))) % 0.38/0.58 (define @t94 () (lambda @t68 (forall @t92 (=> @t91 (exists @t65 (and @t90 (forall @t89 (=> (_ @t71 @t16) @t88)))))))) % 0.38/0.58 (define @t95 () (@var "BOUND_VARIABLE_8248" $$unsorted)) % 0.38/0.58 (define @t96 () (@var "BOUND_VARIABLE_8246" $$unsorted)) % 0.38/0.58 (define @t97 () (and (_ @t2 @t96) (_ @t1 @t95))) % 0.38/0.58 (define @t98 () (not (_ @t3 @t96 @t95))) % 0.38/0.58 (define @t99 () (_ @t1 @t17)) % 0.38/0.58 (define @t100 () (@var "BOUND_VARIABLE_8207" $$unsorted)) % 0.38/0.58 (define @t101 () (not (_ @t3 @t100 @t17))) % 0.38/0.58 (define @t102 () (or @t101 @t99)) % 0.38/0.58 (define @t103 () (@list @t17 @t100)) % 0.38/0.58 (define @t104 () (forall @t103 @t102)) % 0.38/0.58 (define @t105 () (not @t104)) % 0.38/0.58 (define @t106 () (_ @t2 @t17)) % 0.38/0.58 (define @t107 () (@var "BOUND_VARIABLE_8183" $$unsorted)) % 0.38/0.58 (define @t108 () (not (_ @t3 @t17 @t107))) % 0.38/0.58 (define @t109 () (@list @t17 @t107)) % 0.38/0.58 (define @t110 () (forall @t109 (or @t108 @t106))) % 0.38/0.58 (define @t111 () (not @t110)) % 0.38/0.58 (define @t112 () (or @t111 @t105 @t98 @t97)) % 0.38/0.58 (define @t113 () (or @t98 @t97)) % 0.38/0.58 (define @t114 () (or @t111 @t105 @t113)) % 0.38/0.58 (define @t115 () (@list @t3 @t2 @t1 @t96 @t95)) % 0.38/0.58 (define @t116 () (forall @t115 @t114)) % 0.38/0.58 (define @t117 () (@list @t96 @t95)) % 0.38/0.58 (define @t118 () (forall @t117 @t114)) % 0.38/0.58 (define @t119 () (forall @t117 @t113)) % 0.38/0.58 (define @t120 () (or @t111 @t105 @t119)) % 0.38/0.58 (define @t121 () (_ @t1 @t16)) % 0.38/0.58 (define @t122 () (_ @t2 @t11)) % 0.38/0.58 (define @t123 () (_ @t3 @t11 @t16)) % 0.38/0.58 (define @t124 () (not @t123)) % 0.38/0.58 (define @t125 () (forall @t52 (or @t124 (and @t122 @t121)))) % 0.38/0.58 (define @t126 () (or @t111 @t105 @t125)) % 0.38/0.58 (define @t127 () (and @t110 @t104)) % 0.38/0.58 (define @t128 () (_ @t1 @t16)) % 0.38/0.58 (define @t129 () (_ @t2 @t11)) % 0.38/0.58 (define @t130 () (and @t129 @t128)) % 0.38/0.58 (define @t131 () (or @t124 @t130)) % 0.38/0.58 (define @t132 () (lambda (@list @t17 @t40) @t41)) % 0.38/0.58 (define @t133 () (_ @t132 @t11 @t16)) % 0.38/0.58 (define @t134 () (or @t124 @t133)) % 0.38/0.58 (define @t135 () (forall @t52 @t134)) % 0.38/0.58 (define @t136 () (_ @t48 @t11 @t16)) % 0.38/0.58 (define @t137 () (lambda (@list @t48) (forall @t52 (or @t124 @t136)))) % 0.38/0.58 (define @t138 () (lambda (@list @t1 @t17 @t40) @t41)) % 0.38/0.58 (define @t139 () (_ @t42 @t2)) % 0.38/0.58 (define @t140 () (_ @t50 @t11 @t16)) % 0.38/0.58 (define @t141 () (_ (lambda @t54 (forall @t52 (or (not @t140) @t136))) @t3)) % 0.38/0.58 (define @t142 () (@list @t1)) % 0.38/0.58 (define @t143 () (@list @t100)) % 0.38/0.58 (define @t144 () (forall @t143 @t102)) % 0.38/0.58 (define @t145 () (forall @t143 @t101)) % 0.38/0.58 (define @t146 () (or @t145 @t99)) % 0.38/0.58 (define @t147 () (forall @t14 (not (_ @t3 @t11 @t17)))) % 0.38/0.58 (define @t148 () (not (forall @t14 @t124))) % 0.38/0.58 (define @t149 () (lambda @t65 @t148)) % 0.38/0.58 (define @t150 () (_ @t149 @t17)) % 0.38/0.58 (define @t151 () (not @t150)) % 0.38/0.58 (define @t152 () (or @t151 @t99)) % 0.38/0.58 (define @t153 () (forall @t34 @t152)) % 0.38/0.58 (define @t154 () (lambda @t142 @t153)) % 0.38/0.58 (define @t155 () (lambda @t32 (forall @t34 (or (not @t106) @t99)))) % 0.38/0.58 (define @t156 () (_ (lambda @t77 @t148) @t3)) % 0.38/0.58 (define @t157 () (or @t108 @t99)) % 0.38/0.58 (define @t158 () (forall @t109 @t157)) % 0.38/0.58 (define @t159 () (@list @t107)) % 0.38/0.58 (define @t160 () (forall @t159 @t157)) % 0.38/0.58 (define @t161 () (forall @t159 @t108)) % 0.38/0.58 (define @t162 () (or @t161 @t99)) % 0.38/0.58 (define @t163 () (forall @t65 (not (_ @t3 @t17 @t16)))) % 0.38/0.58 (define @t164 () (not (forall @t65 @t124))) % 0.38/0.58 (define @t165 () (lambda @t14 @t164)) % 0.38/0.58 (define @t166 () (_ @t165 @t17)) % 0.38/0.58 (define @t167 () (not @t166)) % 0.38/0.58 (define @t168 () (or @t167 @t99)) % 0.38/0.58 (define @t169 () (forall @t34 @t168)) % 0.38/0.58 (define @t170 () (lambda @t142 @t169)) % 0.38/0.58 (define @t171 () (_ (lambda @t80 @t164) @t3)) % 0.38/0.58 (define @t172 () (and (_ (_ @t155 @t171) @t2) (_ (_ @t155 @t156) @t1))) % 0.38/0.58 (define @t173 () (=> @t172 (_ @t141 (_ @t139 @t1)))) % 0.38/0.58 (define @t174 () (forall @t8 @t173)) % 0.38/0.58 (define @t175 () (not @t51)) % 0.38/0.58 (define @t176 () (or @t175 @t49)) % 0.38/0.58 (define @t177 () (not @t59)) % 0.38/0.58 (define @t178 () (forall @t14 @t177)) % 0.38/0.58 (define @t179 () (not @t178)) % 0.38/0.58 (define @t180 () (or @t25 @t21)) % 0.38/0.58 (define @t181 () (forall @t65 @t177)) % 0.38/0.58 (define @t182 () (not @t181)) % 0.38/0.58 (define @t183 () (forall @t115 @t112)) % 0.38/0.58 (define @t184 () (@quantifiers_skolemize @t183 2)) % 0.38/0.58 (define @t185 () (@quantifiers_skolemize @t183 0)) % 0.38/0.58 (define @t186 () (forall @t103 (or (not (_ @t185 @t100 @t17)) (_ @t184 @t17)))) % 0.38/0.58 (define @t187 () (@quantifiers_skolemize @t183 4)) % 0.38/0.58 (define @t188 () (_ @t184 @t187)) % 0.38/0.58 (define @t189 () (@quantifiers_skolemize @t183 3)) % 0.38/0.58 (define @t190 () (@quantifiers_skolemize @t183 1)) % 0.38/0.58 (define @t191 () (_ @t190 @t189)) % 0.38/0.58 (define @t192 () (and @t191 @t188)) % 0.38/0.58 (define @t193 () (_ @t185 @t189 @t187)) % 0.38/0.58 (define @t194 () (not @t193)) % 0.38/0.58 (define @t195 () (not @t186)) % 0.38/0.58 (define @t196 () (forall @t109 (or (not (_ @t185 @t17 @t107)) (_ @t190 @t17)))) % 0.38/0.58 (define @t197 () (not @t196)) % 0.38/0.58 (define @t198 () (or @t197 @t195 @t194 @t192)) % 0.38/0.58 (define @t199 () (@list true)) % 0.38/0.58 (define @t200 () (@list @t198)) % 0.38/0.58 (define @t201 () (or @t194 @t191)) % 0.38/0.58 (define @t202 () (@list true false)) % 0.38/0.58 (define @t203 () (or @t194 @t188)) % 0.38/0.58 (define @t204 () (not @t203)) % 0.38/0.58 (assume @p1 @t10) % 0.38/0.58 (assume @p2 true) % 0.38/0.58 (step @p3 (= tptp.in @t13) :rule refl :args (@t13)) % 0.38/0.58 (step @p4 (= tptp.is_a @t13) :rule refl :args (@t13)) % 0.38/0.58 (step @p5 (= tptp.emptyset @t15) :rule refl :args (@t15)) % 0.38/0.58 (step @p6 (= tptp.unord_pair @t19) :rule refl :args (@t19)) % 0.38/0.58 (step @p7 (= tptp.singleton @t20) :rule refl :args (@t20)) % 0.38/0.58 (step @p8 (= tptp.union @t24) :rule refl :args (@t24)) % 0.38/0.58 (step @p9 (= tptp.excl_union @t27) :rule refl :args (@t27)) % 0.38/0.58 (step @p10 (= tptp.intersection @t29) :rule refl :args (@t29)) % 0.38/0.58 (step @p11 (= tptp.setminus @t30) :rule refl :args (@t30)) % 0.38/0.58 (step @p12 (= tptp.complement @t31) :rule refl :args (@t31)) % 0.38/0.58 (step @p13 (= tptp.disjoint @t33) :rule refl :args (@t33)) % 0.38/0.58 (step @p14 (= tptp.subset @t36) :rule refl :args (@t36)) % 0.38/0.58 (step @p15 (= tptp.meets @t38) :rule refl :args (@t38)) % 0.38/0.58 (step @p16 (= tptp.misses @t39) :rule refl :args (@t39)) % 0.38/0.58 (step @p17 (= tptp.cartesian_product @t42) :rule refl :args (@t42)) % 0.38/0.58 (step @p18 (= tptp.pair_rel @t43) :rule refl :args (@t43)) % 0.38/0.58 (step @p19 (= tptp.id_rel @t47) :rule refl :args (@t47)) % 0.38/0.58 (step @p20 (= tptp.sub_rel @t55) :rule refl :args (@t55)) % 0.38/0.58 (step @p21 (= tptp.is_rel_on @t60) :rule refl :args (@t60)) % 0.38/0.58 (step @p22 (= tptp.restrict_rel_domain @t62) :rule refl :args (@t62)) % 0.38/0.58 (step @p23 (= tptp.rel_diagonal @t63) :rule refl :args (@t63)) % 0.38/0.58 (step @p24 (= tptp.rel_composition @t66) :rule refl :args (@t66)) % 0.38/0.58 (step @p25 (= tptp.reflexive @t69) :rule refl :args (@t69)) % 0.38/0.58 (step @p26 (= tptp.irreflexive @t70) :rule refl :args (@t70)) % 0.38/0.58 (step @p27 (= tptp.symmetric @t73) :rule refl :args (@t73)) % 0.38/0.58 (step @p28 (= tptp.transitive @t74) :rule refl :args (@t74)) % 0.38/0.58 (step @p29 (= tptp.equiv_rel @t75) :rule refl :args (@t75)) % 0.38/0.58 (step @p30 (= tptp.rel_codomain @t78) :rule refl :args (@t78)) % 0.38/0.58 (step @p31 (= tptp.rel_domain @t81) :rule refl :args (@t81)) % 0.38/0.58 (step @p32 (= tptp.rel_inverse @t82) :rule refl :args (@t82)) % 0.38/0.58 (step @p33 (= tptp.equiv_classes @t84) :rule refl :args (@t84)) % 0.38/0.58 (step @p34 (= tptp.restrict_rel_codomain @t85) :rule refl :args (@t85)) % 0.38/0.58 (step @p35 (= tptp.rel_field @t86) :rule refl :args (@t86)) % 0.38/0.58 (step @p36 (= tptp.well_founded @t93) :rule refl :args (@t93)) % 0.38/0.58 (step @p37 (= tptp.upwards_well_founded @t94) :rule refl :args (@t94)) % 0.38/0.58 (step @p38 :rule aci_norm :args ((= @t114 @t112))) % 0.38/0.58 (step @p39 :rule cong :premises (@p38) :args (@t116)) % 0.38/0.58 (step @p40 :rule quant-merge-prenex :args ((= (forall @t8 @t118) @t116))) % 0.38/0.58 (step @p41 :rule alpha_equiv :args (@t119 (@list @t96 @t95) (@list @t11 @t16))) % 0.38/0.58 (step @p42 :rule refl :args (@t105)) % 0.38/0.58 (step @p43 :rule refl :args (@t111)) % 0.38/0.58 (step @p44 :rule nary_cong :premises (@p43 @p42 @p41) :args (@t120)) % 0.38/0.58 (step @p45 :rule quant-miniscope-or :args ((= @t118 @t120))) % 0.38/0.58 (step @p46 :rule trans :premises (@p45 @p44)) % 0.38/0.58 (step @p47 :rule symm :premises (@p46)) % 0.38/0.58 (step @p48 :rule cong :premises (@p47) :args ((forall @t8 @t126))) % 0.38/0.58 (step @p49 :rule trans :premises (@p48 @p40)) % 0.38/0.58 (step @p50 :rule trans :premises (@p49 @p39)) % 0.38/0.58 (step @p51 :rule aci_norm :args ((= (or (or @t111 @t105) @t125) @t126))) % 0.38/0.58 (step @p52 :rule refl :args (@t125)) % 0.38/0.58 (step @p53 :rule bool-and-de-morgan :args (@t110 @t104 true)) % 0.38/0.58 (step @p54 :rule nary_cong :premises (@p53 @p52) :args ((or (not @t127) @t125))) % 0.38/0.58 (step @p55 :rule trans :premises (@p54 @p51)) % 0.38/0.58 (step @p56 :rule bool-impl-elim :args (@t127 @t125)) % 0.38/0.58 (step @p57 :rule trans :premises (@p56 @p55)) % 0.38/0.58 (step @p58 :rule cong :premises (@p57) :args ((forall @t8 (=> @t127 @t125)))) % 0.38/0.58 (step @p59 :rule trans :premises (@p58 @p50)) % 0.38/0.58 (step @p60 :rule refl :args (@t121)) % 0.38/0.58 (step @p61 :rule refl :args (@t128)) % 0.38/0.58 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t128 @t121))) % 0.38/0.58 (step @p63 :rule symm :premises (@p62)) % 0.38/0.58 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.38/0.58 (step @p65 :rule refl :args (@t122)) % 0.38/0.58 (step @p66 :rule refl :args (@t129)) % 0.38/0.58 (step @p67 :rule cong :premises (@p66 @p65) :args ((= @t129 @t122))) % 0.38/0.58 (step @p68 :rule symm :premises (@p67)) % 0.38/0.58 (step @p69 :rule eq_resolve :premises (@p66 @p68)) % 0.38/0.58 (step @p70 :rule nary_cong :premises (@p69 @p64) :args (@t130)) % 0.38/0.58 (step @p71 :rule refl :args (@t124)) % 0.38/0.58 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t131)) % 0.38/0.58 (step @p73 :rule cong :premises (@p72) :args ((forall @t52 @t131))) % 0.38/0.58 (step @p74 :rule beta-reduce :args ((= @t133 @t130))) % 0.38/0.58 (step @p75 :rule refl :args (@t124)) % 0.38/0.58 (step @p76 :rule nary_cong :premises (@p75 @p74) :args (@t134)) % 0.38/0.58 (step @p77 :rule cong :premises (@p76) :args (@t135)) % 0.38/0.58 (step @p78 :rule trans :premises (@p77 @p73)) % 0.38/0.58 (step @p79 :rule beta-reduce :args ((= (_ @t137 @t132) @t135))) % 0.38/0.58 (step @p80 :rule trans :premises (@p79 @p78)) % 0.38/0.58 (step @p81 :rule beta-reduce :args ((= (_ @t138 @t1) @t132))) % 0.38/0.58 (step @p82 :rule refl :args (@t1)) % 0.38/0.58 (step @p83 :rule beta-reduce :args ((= @t139 @t138))) % 0.38/0.58 (step @p84 :rule ho_cong :premises (@p83 @p82)) % 0.38/0.58 (step @p85 :rule trans :premises (@p84 @p81)) % 0.38/0.58 (step @p86 :rule beta-reduce :args ((= @t141 @t137))) % 0.38/0.58 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 0.38/0.58 (step @p88 :rule trans :premises (@p87 @p80)) % 0.38/0.58 (step @p89 :rule beta-reduce :args ((= (_ (lambda @t142 @t104) @t1) @t104))) % 0.38/0.58 (step @p90 :rule quant-merge-prenex :args ((= (forall @t34 @t144) @t104))) % 0.38/0.58 (step @p91 :rule refl :args (@t99)) % 0.38/0.58 (step @p92 :rule alpha_equiv :args (@t145 (@list @t100) (@list @t11))) % 0.38/0.58 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t146)) % 0.38/0.58 (step @p94 :rule quant-miniscope-or :args ((= @t144 @t146))) % 0.38/0.58 (step @p95 :rule trans :premises (@p94 @p93)) % 0.38/0.58 (step @p96 :rule symm :premises (@p95)) % 0.38/0.58 (step @p97 :rule cong :premises (@p96) :args ((forall @t34 (or @t147 @t99)))) % 0.38/0.58 (step @p98 :rule trans :premises (@p97 @p90)) % 0.38/0.58 (step @p99 :rule refl :args (@t99)) % 0.38/0.58 (step @p100 :rule bool-double-not-elim :args (@t147)) % 0.38/0.58 (step @p101 :rule beta-reduce :args ((= @t150 (not @t147)))) % 0.38/0.58 (step @p102 :rule cong :premises (@p101) :args (@t151)) % 0.38/0.58 (step @p103 :rule trans :premises (@p102 @p100)) % 0.38/0.58 (step @p104 :rule nary_cong :premises (@p103 @p99) :args (@t152)) % 0.38/0.58 (step @p105 :rule cong :premises (@p104) :args (@t153)) % 0.38/0.58 (step @p106 :rule trans :premises (@p105 @p98)) % 0.38/0.58 (step @p107 :rule cong :premises (@p106) :args (@t154)) % 0.38/0.58 (step @p108 :rule beta-reduce :args ((= (_ @t155 @t149) @t154))) % 0.38/0.58 (step @p109 :rule trans :premises (@p108 @p107)) % 0.38/0.58 (step @p110 :rule beta-reduce :args ((= @t156 @t149))) % 0.38/0.58 (step @p111 :rule refl :args (@t155)) % 0.38/0.58 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 0.38/0.58 (step @p113 :rule trans :premises (@p112 @p109)) % 0.38/0.58 (step @p114 :rule ho_cong :premises (@p113 @p82)) % 0.38/0.58 (step @p115 :rule trans :premises (@p114 @p89)) % 0.38/0.58 (step @p116 :rule beta-reduce :args ((= (_ (lambda @t142 @t158) @t2) @t110))) % 0.38/0.58 (step @p117 :rule refl :args (@t2)) % 0.38/0.58 (step @p118 :rule quant-merge-prenex :args ((= (forall @t34 @t160) @t158))) % 0.38/0.58 (step @p119 :rule alpha_equiv :args (@t161 (@list @t107) (@list @t16))) % 0.38/0.58 (step @p120 :rule nary_cong :premises (@p119 @p91) :args (@t162)) % 0.38/0.58 (step @p121 :rule quant-miniscope-or :args ((= @t160 @t162))) % 0.38/0.58 (step @p122 :rule trans :premises (@p121 @p120)) % 0.38/0.58 (step @p123 :rule symm :premises (@p122)) % 0.38/0.58 (step @p124 :rule cong :premises (@p123) :args ((forall @t34 (or @t163 @t99)))) % 0.38/0.58 (step @p125 :rule trans :premises (@p124 @p118)) % 0.38/0.58 (step @p126 :rule bool-double-not-elim :args (@t163)) % 0.38/0.58 (step @p127 :rule beta-reduce :args ((= @t166 (not @t163)))) % 0.38/0.58 (step @p128 :rule cong :premises (@p127) :args (@t167)) % 0.38/0.58 (step @p129 :rule trans :premises (@p128 @p126)) % 0.38/0.58 (step @p130 :rule nary_cong :premises (@p129 @p99) :args (@t168)) % 0.38/0.58 (step @p131 :rule cong :premises (@p130) :args (@t169)) % 0.38/0.58 (step @p132 :rule trans :premises (@p131 @p125)) % 0.38/0.58 (step @p133 :rule cong :premises (@p132) :args (@t170)) % 0.38/0.58 (step @p134 :rule beta-reduce :args ((= (_ @t155 @t165) @t170))) % 0.38/0.58 (step @p135 :rule trans :premises (@p134 @p133)) % 0.38/0.58 (step @p136 :rule beta-reduce :args ((= @t171 @t165))) % 0.38/0.58 (step @p137 :rule ho_cong :premises (@p111 @p136)) % 0.38/0.58 (step @p138 :rule trans :premises (@p137 @p135)) % 0.38/0.58 (step @p139 :rule ho_cong :premises (@p138 @p117)) % 0.38/0.58 (step @p140 :rule trans :premises (@p139 @p116)) % 0.38/0.58 (step @p141 :rule nary_cong :premises (@p140 @p115) :args (@t172)) % 0.38/0.58 (step @p142 :rule cong :premises (@p141 @p88) :args (@t173)) % 0.38/0.58 (step @p143 :rule cong :premises (@p142) :args (@t174)) % 0.38/0.58 (step @p144 :rule trans :premises (@p143 @p59)) % 0.38/0.58 (step @p145 :rule cong :premises (@p144) :args ((not @t174))) % 0.38/0.58 (step @p146 :rule ho_cong :premises (@p17 @p117)) % 0.38/0.58 (step @p147 :rule ho_cong :premises (@p146 @p82)) % 0.38/0.58 (step @p148 :rule refl :args (@t3)) % 0.38/0.58 (step @p149 :rule refl :args (@t136)) % 0.38/0.58 (step @p150 :rule refl :args (@t49)) % 0.38/0.58 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t49 @t136))) % 0.38/0.58 (step @p152 :rule symm :premises (@p151)) % 0.38/0.58 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.38/0.58 (step @p154 :rule refl :args (@t140)) % 0.38/0.58 (step @p155 :rule refl :args (@t51)) % 0.38/0.58 (step @p156 :rule cong :premises (@p155 @p154) :args ((= @t51 @t140))) % 0.38/0.58 (step @p157 :rule symm :premises (@p156)) % 0.38/0.58 (step @p158 :rule eq_resolve :premises (@p155 @p157)) % 0.38/0.58 (step @p159 :rule cong :premises (@p158) :args (@t175)) % 0.38/0.58 (step @p160 :rule nary_cong :premises (@p159 @p153) :args (@t176)) % 0.38/0.58 (step @p161 :rule cong :premises (@p160) :args ((forall @t52 @t176))) % 0.38/0.58 (step @p162 :rule bool-impl-elim :args (@t51 @t49)) % 0.38/0.58 (step @p163 :rule cong :premises (@p162) :args (@t53)) % 0.38/0.58 (step @p164 :rule trans :premises (@p163 @p161)) % 0.38/0.58 (step @p165 :rule cong :premises (@p164) :args (@t55)) % 0.38/0.58 (step @p166 :rule trans :premises (@p20 @p165)) % 0.38/0.58 (step @p167 :rule ho_cong :premises (@p166 @p148)) % 0.38/0.58 (step @p168 :rule ho_cong :premises (@p167 @p147)) % 0.38/0.58 (step @p169 :rule refl :args (@t123)) % 0.38/0.58 (step @p170 :rule refl :args (@t59)) % 0.38/0.58 (step @p171 :rule cong :premises (@p170 @p169) :args ((= @t59 @t123))) % 0.38/0.58 (step @p172 :rule symm :premises (@p171)) % 0.38/0.58 (step @p173 :rule eq_resolve :premises (@p170 @p172)) % 0.38/0.58 (step @p174 :rule cong :premises (@p173) :args (@t177)) % 0.38/0.58 (step @p175 :rule cong :premises (@p174) :args (@t178)) % 0.38/0.58 (step @p176 :rule cong :premises (@p175) :args (@t179)) % 0.38/0.58 (step @p177 :rule exists-elim :args ((= @t76 @t179))) % 0.38/0.58 (step @p178 :rule trans :premises (@p177 @p176)) % 0.38/0.58 (step @p179 :rule cong :premises (@p178) :args (@t78)) % 0.38/0.58 (step @p180 :rule trans :premises (@p30 @p179)) % 0.38/0.58 (step @p181 :rule ho_cong :premises (@p180 @p148)) % 0.38/0.58 (step @p182 :rule refl :args (@t99)) % 0.38/0.58 (step @p183 :rule refl :args (@t21)) % 0.38/0.58 (step @p184 :rule cong :premises (@p183 @p182) :args ((= @t21 @t99))) % 0.38/0.58 (step @p185 :rule symm :premises (@p184)) % 0.38/0.58 (step @p186 :rule eq_resolve :premises (@p183 @p185)) % 0.38/0.58 (step @p187 :rule refl :args (@t106)) % 0.38/0.58 (step @p188 :rule refl :args (@t22)) % 0.38/0.58 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t22 @t106))) % 0.38/0.58 (step @p190 :rule symm :premises (@p189)) % 0.38/0.58 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 0.38/0.58 (step @p192 :rule cong :premises (@p191) :args (@t25)) % 0.38/0.58 (step @p193 :rule nary_cong :premises (@p192 @p186) :args (@t180)) % 0.38/0.58 (step @p194 :rule cong :premises (@p193) :args ((forall @t34 @t180))) % 0.38/0.58 (step @p195 :rule bool-impl-elim :args (@t22 @t21)) % 0.38/0.58 (step @p196 :rule cong :premises (@p195) :args (@t35)) % 0.38/0.58 (step @p197 :rule trans :premises (@p196 @p194)) % 0.38/0.58 (step @p198 :rule cong :premises (@p197) :args (@t36)) % 0.38/0.58 (step @p199 :rule trans :premises (@p14 @p198)) % 0.38/0.58 (step @p200 :rule ho_cong :premises (@p199 @p181)) % 0.38/0.58 (step @p201 :rule ho_cong :premises (@p200 @p82)) % 0.38/0.58 (step @p202 :rule cong :premises (@p174) :args (@t181)) % 0.38/0.58 (step @p203 :rule cong :premises (@p202) :args (@t182)) % 0.38/0.58 (step @p204 :rule exists-elim :args ((= @t79 @t182))) % 0.38/0.58 (step @p205 :rule trans :premises (@p204 @p203)) % 0.38/0.58 (step @p206 :rule cong :premises (@p205) :args (@t81)) % 0.38/0.58 (step @p207 :rule trans :premises (@p31 @p206)) % 0.38/0.58 (step @p208 :rule ho_cong :premises (@p207 @p148)) % 0.38/0.58 (step @p209 :rule ho_cong :premises (@p199 @p208)) % 0.38/0.58 (step @p210 :rule ho_cong :premises (@p209 @p117)) % 0.38/0.58 (step @p211 :rule nary_cong :premises (@p210 @p201) :args (@t6)) % 0.38/0.58 (step @p212 :rule cong :premises (@p211 @p168) :args (@t7)) % 0.38/0.58 (step @p213 :rule cong :premises (@p212) :args (@t9)) % 0.38/0.58 (step @p214 :rule cong :premises (@p213) :args (@t10)) % 0.38/0.58 (step @p215 :rule trans :premises (@p214 @p145)) % 0.38/0.58 (step @p216 :rule eq_resolve :premises (@p1 @p215)) % 0.38/0.58 (step @p217 :rule skolemize :premises (@p216)) % 0.38/0.58 (step @p218 :rule bool-double-not-elim :args (@t186)) % 0.38/0.58 (step @p219 :rule refl :args (@t198)) % 0.38/0.58 (step @p220 :rule nary_cong :premises (@p219 @p218) :args ((or @t198 (not @t195)))) % 0.38/0.58 (step @p221 :rule cnf_or_neg :args (@t198 1)) % 0.38/0.58 (step @p222 :rule eq_resolve :premises (@p221 @p220)) % 0.38/0.58 (step @p223 :rule reordering :premises (@p222) :args ((or @t186 @t198))) % 0.38/0.58 (step @p224 :rule chain_m_resolution :premises (@p223 @p217) :args (@t186 @t199 @t200)) % 0.38/0.58 (step @p225 :rule bool-double-not-elim :args (@t196)) % 0.38/0.58 (step @p226 :rule nary_cong :premises (@p219 @p225) :args ((or @t198 (not @t197)))) % 0.38/0.58 (step @p227 :rule cnf_or_neg :args (@t198 0)) % 0.38/0.58 (step @p228 :rule eq_resolve :premises (@p227 @p226)) % 0.38/0.58 (step @p229 :rule reordering :premises (@p228) :args ((or @t196 @t198))) % 0.38/0.58 (step @p230 :rule chain_m_resolution :premises (@p229 @p217) :args (@t196 @t199 @t200)) % 0.38/0.58 (step @p231 :rule instantiate :premises (@p230) :args ((@list @t189 @t187))) % 0.38/0.58 (step @p232 :rule bool-double-not-elim :args (@t193)) % 0.38/0.58 (step @p233 :rule nary_cong :premises (@p219 @p232) :args ((or @t198 (not @t194)))) % 0.38/0.58 (step @p234 :rule cnf_or_neg :args (@t198 2)) % 0.38/0.58 (step @p235 :rule eq_resolve :premises (@p234 @p233)) % 0.38/0.58 (step @p236 :rule reordering :premises (@p235) :args ((or @t193 @t198))) % 0.38/0.58 (step @p237 :rule chain_m_resolution :premises (@p236 @p217) :args (@t193 @t199 @t200)) % 0.38/0.58 (step @p238 :rule cnf_or_pos :args (@t201)) % 0.38/0.58 (step @p239 :rule reordering :premises (@p238) :args ((or @t194 @t191 (not @t201)))) % 0.38/0.58 (step @p240 :rule chain_m_resolution :premises (@p239 @p237 @p231) :args (@t191 (@list false false) (@list @t193 @t201))) % 0.38/0.58 (step @p241 :rule cnf_or_neg :args (@t198 3)) % 0.38/0.58 (step @p242 :rule chain_m_resolution :premises (@p241 @p217) :args ((not @t192) @t199 @t200)) % 0.38/0.58 (step @p243 :rule cnf_and_neg :args (@t192)) % 0.38/0.58 (step @p244 :rule chain_m_resolution :premises (@p243 @p242 @p240) :args ((not @t188) @t202 (@list @t192 @t191))) % 0.38/0.58 (step @p245 :rule cnf_or_pos :args (@t203)) % 0.38/0.58 (step @p246 :rule reordering :premises (@p245) :args ((or @t194 @t188 @t204))) % 0.38/0.58 (step @p247 :rule chain_m_resolution :premises (@p246 @p237 @p244) :args (@t204 (@list false true) (@list @t193 @t188))) % 0.38/0.58 (assume-push @p254 @t186) % 0.38/0.58 (step @p249 :rule instantiate :premises (@p224) :args ((@list @t187 @t189))) % 0.38/0.58 (step-pop @p255 :rule scope :premises (@p249)) % 0.38/0.58 (step @p250 :rule process_scope :premises (@p255) :args (@t203)) % 0.38/0.58 (step @p252 :rule implies_elim :premises (@p250)) % 0.38/0.58 (step @p253 false :rule chain_m_resolution :premises (@p252 @p247 @p224) :args (false @t202 (@list @t203 @t186))) % 0.38/0.58 ) % 0.38/0.58 % SZS output end Proof % 0.38/0.58 % cvc5 exiting %------------------------------------------------------------------------------