%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET669^3 : 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 : n024.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 0.35s 0.60s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SET669^3 : TPTP v9.2.1. Released v3.6.0. % 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.25 % Computer : n024.cluster.edu % 0.08/0.25 % Model : x86_64 x86_64 % 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.25 % Memory : 8042.1875MB % 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.25 % CPULimit : 300 % 0.08/0.25 % WCLimit : 300 % 0.08/0.25 % DateTime : Tue Jun 2 11:06:15 EDT 2026 % 0.08/0.25 % CPUTime : % 0.16/0.33 %----Proving TH0 % 0.35/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.35/0.60 % SZS status Theorem % 0.35/0.60 % SZS output start Proof % 0.35/0.60 ( % 0.35/0.60 (declare-sort $$unsorted 0) % 0.35/0.60 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.35/0.60 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.35/0.60 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.35/0.60 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.35/0.60 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.35/0.60 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.35/0.61 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.35/0.61 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.35/0.61 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.35/0.61 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.35/0.61 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.35/0.61 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.35/0.61 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.35/0.61 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.35/0.61 (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)))))))) % 0.35/0.61 (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)))))))) % 0.35/0.61 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.35/0.61 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.35/0.61 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$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 $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.35/0.61 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.35/0.61 (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))))) % 0.35/0.61 (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 $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.35/0.61 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.35/0.61 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.35/0.61 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.35/0.61 (define tptp.transitive () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.35/0.61 (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))))) % 0.35/0.61 (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))))))) % 0.35/0.61 (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))))))) % 0.35/0.61 (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)))))) % 0.35/0.61 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.35/0.61 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.35/0.61 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.35/0.61 (define tptp.well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.35/0.61 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.35/0.61 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.35/0.61 (define @t2 () (_ tptp.rel_codomain @t1)) % 0.35/0.61 (define @t3 () (@var "X" $$unsorted)) % 0.35/0.61 (define @t4 () (@list @t3)) % 0.35/0.61 (define @t5 () (lambda @t4 true)) % 0.35/0.61 (define @t6 () (= @t5 @t2)) % 0.35/0.61 (define @t7 () (_ tptp.rel_domain @t1)) % 0.35/0.61 (define @t8 () (and (_ (_ tptp.subset @t5) @t7) @t6)) % 0.35/0.61 (define @t9 () (=> (_ (_ tptp.sub_rel (_ tptp.id_rel @t5)) @t1) @t8)) % 0.35/0.61 (define @t10 () (@list @t1)) % 0.35/0.61 (define @t11 () (forall @t10 @t9)) % 0.35/0.61 (define @t12 () (not @t11)) % 0.35/0.61 (define @t13 () (@var "M" (-> $$unsorted Bool))) % 0.35/0.61 (define @t14 () (lambda (@list @t3 @t13) (_ @t13 @t3))) % 0.35/0.61 (define @t15 () (lambda @t4 false)) % 0.35/0.61 (define @t16 () (@var "Y" $$unsorted)) % 0.35/0.61 (define @t17 () (@var "U" $$unsorted)) % 0.35/0.61 (define @t18 () (= @t17 @t3)) % 0.35/0.61 (define @t19 () (lambda (@list @t3 @t16 @t17) (or @t18 (= @t17 @t16)))) % 0.35/0.61 (define @t20 () (lambda (@list @t3 @t17) @t18)) % 0.35/0.61 (define @t21 () (@var "Y" (-> $$unsorted Bool))) % 0.35/0.61 (define @t22 () (_ @t21 @t17)) % 0.35/0.61 (define @t23 () (@var "X" (-> $$unsorted Bool))) % 0.35/0.61 (define @t24 () (_ @t23 @t17)) % 0.35/0.61 (define @t25 () (@list @t23 @t21 @t17)) % 0.35/0.61 (define @t26 () (lambda @t25 (or @t24 @t22))) % 0.35/0.61 (define @t27 () (not @t24)) % 0.35/0.61 (define @t28 () (and @t24 (not @t22))) % 0.35/0.61 (define @t29 () (lambda @t25 (or @t28 (and @t27 @t22)))) % 0.35/0.61 (define @t30 () (and @t24 @t22)) % 0.35/0.61 (define @t31 () (lambda @t25 @t30)) % 0.35/0.61 (define @t32 () (lambda @t25 @t28)) % 0.35/0.61 (define @t33 () (lambda (@list @t23 @t17) @t27)) % 0.35/0.61 (define @t34 () (@list @t23 @t21)) % 0.35/0.61 (define @t35 () (lambda @t34 (= (_ (_ tptp.intersection @t23) @t21) tptp.emptyset))) % 0.35/0.61 (define @t36 () (@list @t17)) % 0.35/0.61 (define @t37 () (forall @t36 (=> @t24 @t22))) % 0.35/0.61 (define @t38 () (lambda @t34 @t37)) % 0.35/0.61 (define @t39 () (exists @t36 @t30)) % 0.35/0.61 (define @t40 () (lambda @t34 @t39)) % 0.35/0.61 (define @t41 () (lambda @t34 (not @t39))) % 0.35/0.61 (define @t42 () (@var "V" $$unsorted)) % 0.35/0.61 (define @t43 () (lambda (@list @t23 @t21 @t17 @t42) (and @t24 (_ @t21 @t42)))) % 0.35/0.61 (define @t44 () (lambda (@list @t3 @t16 @t17 @t42) (or @t18 (= @t42 @t16)))) % 0.35/0.61 (define @t45 () (= @t3 @t16)) % 0.35/0.61 (define @t46 () (@var "S" (-> $$unsorted Bool))) % 0.35/0.61 (define @t47 () (_ @t46 @t3)) % 0.35/0.61 (define @t48 () (lambda (@list @t46 @t3 @t16) (and @t47 @t45))) % 0.35/0.61 (define @t49 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.35/0.61 (define @t50 () (_ (_ @t49 @t3) @t16)) % 0.35/0.61 (define @t51 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.35/0.61 (define @t52 () (_ (_ @t51 @t3) @t16)) % 0.35/0.61 (define @t53 () (@list @t3 @t16)) % 0.35/0.61 (define @t54 () (forall @t53 (=> @t52 @t50))) % 0.35/0.61 (define @t55 () (@list @t51 @t49)) % 0.35/0.61 (define @t56 () (lambda @t55 @t54)) % 0.35/0.61 (define @t57 () (@var "B" (-> $$unsorted Bool))) % 0.35/0.61 (define @t58 () (@var "A" (-> $$unsorted Bool))) % 0.35/0.61 (define @t59 () (_ @t1 @t3)) % 0.35/0.61 (define @t60 () (_ @t59 @t16)) % 0.35/0.61 (define @t61 () (lambda (@list @t1 @t58 @t57) (forall @t53 (=> @t60 (and (_ @t58 @t3) (_ @t57 @t16)))))) % 0.35/0.61 (define @t62 () (@list @t1 @t46 @t3 @t16)) % 0.35/0.61 (define @t63 () (lambda @t62 (and @t47 @t60))) % 0.35/0.61 (define @t64 () (lambda @t53 @t45)) % 0.35/0.61 (define @t65 () (@var "Z" $$unsorted)) % 0.35/0.61 (define @t66 () (@list @t16)) % 0.35/0.61 (define @t67 () (lambda (@list @t51 @t49 @t3 @t65) (exists @t66 (and @t52 (_ (_ @t49 @t16) @t65))))) % 0.35/0.61 (define @t68 () (_ @t59 @t3)) % 0.35/0.61 (define @t69 () (lambda @t10 (forall @t4 @t68))) % 0.35/0.61 (define @t70 () (lambda @t10 (forall @t4 (not @t68)))) % 0.35/0.61 (define @t71 () (_ @t1 @t16)) % 0.35/0.61 (define @t72 () (_ @t71 @t3)) % 0.35/0.61 (define @t73 () (lambda @t10 (forall @t53 (=> @t60 @t72)))) % 0.35/0.61 (define @t74 () (lambda @t10 (forall (@list @t3 @t16 @t65) (=> (and @t60 (_ @t71 @t65)) (_ @t59 @t65))))) % 0.35/0.61 (define @t75 () (lambda @t10 (and (_ tptp.reflexive @t1) (_ tptp.symmetric @t1) (_ tptp.transitive @t1)))) % 0.35/0.61 (define @t76 () (exists @t4 @t60)) % 0.35/0.61 (define @t77 () (@list @t1 @t16)) % 0.35/0.61 (define @t78 () (lambda @t77 @t76)) % 0.35/0.61 (define @t79 () (exists @t66 @t60)) % 0.35/0.61 (define @t80 () (@list @t1 @t3)) % 0.35/0.61 (define @t81 () (lambda @t80 @t79)) % 0.35/0.61 (define @t82 () (lambda (@list @t1 @t3 @t16) @t72)) % 0.35/0.61 (define @t83 () (@var "S1" (-> $$unsorted Bool))) % 0.35/0.61 (define @t84 () (lambda (@list @t1 @t83) (exists @t4 (and (_ @t83 @t3) (forall @t66 (= (_ @t83 @t16) @t60)))))) % 0.35/0.61 (define @t85 () (lambda @t62 (and (_ @t46 @t16) @t60))) % 0.35/0.61 (define @t86 () (lambda @t80 (or (_ @t7 @t3) (_ @t2 @t3)))) % 0.35/0.61 (define @t87 () (@var "W" $$unsorted)) % 0.35/0.61 (define @t88 () (not (_ @t23 @t87))) % 0.35/0.61 (define @t89 () (@list @t87)) % 0.35/0.61 (define @t90 () (_ @t23 @t16)) % 0.35/0.61 (define @t91 () (_ @t23 @t65)) % 0.35/0.61 (define @t92 () (@list @t23 @t65)) % 0.35/0.61 (define @t93 () (lambda @t10 (forall @t92 (=> @t91 (exists @t66 (and @t90 (forall @t89 (=> (_ @t71 @t87) @t88)))))))) % 0.35/0.61 (define @t94 () (lambda @t10 (forall @t92 (=> @t91 (exists @t66 (and @t90 (forall @t89 (=> (_ @t71 @t16) @t88)))))))) % 0.35/0.61 (define @t95 () (@var "BOUND_VARIABLE_8172" $$unsorted)) % 0.35/0.61 (define @t96 () (lambda (@list @t95) true)) % 0.35/0.61 (define @t97 () (_ @t1 @t3 @t16)) % 0.35/0.61 (define @t98 () (not @t97)) % 0.35/0.61 (define @t99 () (not (forall @t4 @t98))) % 0.35/0.61 (define @t100 () (lambda @t66 @t99)) % 0.35/0.61 (define @t101 () (= @t100 @t96)) % 0.35/0.61 (define @t102 () (@var "BOUND_VARIABLE_8222" $$unsorted)) % 0.35/0.61 (define @t103 () (not (forall @t66 (not (_ @t1 @t102 @t16))))) % 0.35/0.61 (define @t104 () (and @t103 @t101)) % 0.35/0.61 (define @t105 () (forall @t66 (_ @t1 @t16 @t16))) % 0.35/0.61 (define @t106 () (not @t105)) % 0.35/0.61 (define @t107 () (or @t106 @t104)) % 0.35/0.61 (define @t108 () (forall (@list @t1 @t102) @t107)) % 0.35/0.61 (define @t109 () (@list @t102)) % 0.35/0.61 (define @t110 () (forall @t109 @t107)) % 0.35/0.61 (define @t111 () (forall @t109 @t101)) % 0.35/0.61 (define @t112 () (forall @t109 @t103)) % 0.35/0.61 (define @t113 () (and @t112 @t111)) % 0.35/0.61 (define @t114 () (forall @t109 @t104)) % 0.35/0.61 (define @t115 () (or @t106 @t114)) % 0.35/0.61 (define @t116 () (not (forall @t66 (not (_ @t1 @t17 @t16))))) % 0.35/0.61 (define @t117 () (and (forall @t36 @t116) @t101)) % 0.35/0.61 (define @t118 () (_ (lambda @t77 @t99) @t1)) % 0.35/0.61 (define @t119 () (= @t5 @t118)) % 0.35/0.61 (define @t120 () (not (forall @t66 @t98))) % 0.35/0.61 (define @t121 () (lambda @t4 @t120)) % 0.35/0.61 (define @t122 () (_ @t121 @t17)) % 0.35/0.61 (define @t123 () (forall @t36 @t122)) % 0.35/0.61 (define @t124 () (_ @t21 @t17)) % 0.35/0.61 (define @t125 () (@list @t21)) % 0.35/0.61 (define @t126 () (_ (lambda @t80 @t120) @t1)) % 0.35/0.61 (define @t127 () (_ @t96 @t17)) % 0.35/0.61 (define @t128 () (not @t127)) % 0.35/0.61 (define @t129 () (or @t128 @t124)) % 0.35/0.61 (define @t130 () (forall @t36 @t129)) % 0.35/0.61 (define @t131 () (lambda @t125 @t130)) % 0.35/0.61 (define @t132 () (_ @t23 @t17)) % 0.35/0.61 (define @t133 () (lambda @t34 (forall @t36 (or (not @t132) @t124)))) % 0.35/0.61 (define @t134 () (and (_ (_ @t133 @t5) @t126) @t119)) % 0.35/0.61 (define @t135 () (_ @t49 @t16 @t16)) % 0.35/0.61 (define @t136 () (@list @t49)) % 0.35/0.61 (define @t137 () (not (= @t16 @t16))) % 0.35/0.61 (define @t138 () (or @t137 @t135)) % 0.35/0.61 (define @t139 () (_ @t49 @t3 @t16)) % 0.35/0.61 (define @t140 () (not @t45)) % 0.35/0.61 (define @t141 () (or @t140 @t140 @t139)) % 0.35/0.61 (define @t142 () (or @t140 @t139)) % 0.35/0.61 (define @t143 () (forall @t4 @t142)) % 0.35/0.61 (define @t144 () (forall @t66 @t143)) % 0.35/0.61 (define @t145 () (forall (@list @t16 @t3) @t142)) % 0.35/0.61 (define @t146 () (_ @t64 @t3 @t16)) % 0.35/0.61 (define @t147 () (not @t146)) % 0.35/0.61 (define @t148 () (or @t147 @t139)) % 0.35/0.61 (define @t149 () (forall @t53 @t148)) % 0.35/0.61 (define @t150 () (lambda @t136 @t149)) % 0.35/0.61 (define @t151 () (_ @t51 @t3 @t16)) % 0.35/0.61 (define @t152 () (lambda @t55 (forall @t53 (or (not @t151) @t139)))) % 0.35/0.61 (define @t153 () (_ @t96 @t3)) % 0.35/0.61 (define @t154 () (and @t153 @t45)) % 0.35/0.61 (define @t155 () (lambda @t53 @t154)) % 0.35/0.61 (define @t156 () (=> (_ (_ @t152 (_ @t48 @t5)) @t1) @t134)) % 0.35/0.61 (define @t157 () (forall @t10 @t156)) % 0.35/0.61 (define @t158 () (not @t60)) % 0.35/0.61 (define @t159 () (forall @t4 @t158)) % 0.35/0.61 (define @t160 () (not @t159)) % 0.35/0.61 (define @t161 () (forall @t66 @t158)) % 0.35/0.61 (define @t162 () (not @t161)) % 0.35/0.61 (define @t163 () (or @t27 @t22)) % 0.35/0.61 (define @t164 () (not @t52)) % 0.35/0.61 (define @t165 () (or @t164 @t50)) % 0.35/0.61 (define @t166 () (@purify @t96)) % 0.35/0.61 (define @t167 () (@quantifiers_skolemize @t108 0)) % 0.35/0.61 (define @t168 () (lambda @t66 (not (forall @t4 (not (_ @t167 @t3 @t16)))))) % 0.35/0.61 (define @t169 () (@purify @t168)) % 0.35/0.61 (define @t170 () (= @t169 @t166)) % 0.35/0.61 (define @t171 () (@quantifiers_skolemize @t108 1)) % 0.35/0.61 (define @t172 () (forall @t66 (not (_ @t167 @t171 @t16)))) % 0.35/0.61 (define @t173 () (not @t172)) % 0.35/0.61 (define @t174 () (and @t173 @t170)) % 0.35/0.61 (define @t175 () (forall @t66 (_ @t167 @t16 @t16))) % 0.35/0.61 (define @t176 () (not @t175)) % 0.35/0.61 (define @t177 () (or @t176 @t174)) % 0.35/0.61 (define @t178 () (not @t177)) % 0.35/0.61 (define @t179 () (not @t108)) % 0.35/0.61 (define @t180 () (= @t96 @t168)) % 0.35/0.61 (define @t181 () (and @t173 @t180)) % 0.35/0.61 (define @t182 () (or @t176 @t181)) % 0.35/0.61 (define @t183 () (not @t182)) % 0.35/0.61 (define @t184 () (and @t173 (= @t168 @t96))) % 0.35/0.61 (define @t185 () (or @t176 @t184)) % 0.35/0.61 (define @t186 () (not @t185)) % 0.35/0.61 (define @t187 () (@list true)) % 0.35/0.61 (define @t188 () (@list @t177)) % 0.35/0.61 (define @t189 () (@list @t171)) % 0.35/0.61 (define @t190 () (_ @t167 @t171 @t171)) % 0.35/0.61 (define @t191 () (not @t170)) % 0.35/0.61 (define @t192 () (@const 0 $$unsorted)) % 0.35/0.61 (define @t193 () (forall @t4 (not (_ @t167 @t3 @t192)))) % 0.35/0.61 (define @t194 () (not @t193)) % 0.35/0.61 (define @t195 () (_ @t166 @t192)) % 0.35/0.61 (define @t196 () (_ @t168 @t192)) % 0.35/0.61 (define @t197 () (_ @t169 @t192)) % 0.35/0.61 (define @t198 () (= @t197 @t195)) % 0.35/0.61 (define @t199 () (not @t198)) % 0.35/0.61 (define @t200 () (or @t170 @t199)) % 0.35/0.61 (define @t201 () (@list @t192)) % 0.35/0.61 (define @t202 () (_ @t167 @t192 @t192)) % 0.35/0.61 (assume @p1 @t12) % 0.35/0.61 (assume @p2 true) % 0.35/0.61 (step @p3 (= tptp.in @t14) :rule refl :args (@t14)) % 0.35/0.61 (step @p4 (= tptp.is_a @t14) :rule refl :args (@t14)) % 0.35/0.61 (step @p5 (= tptp.emptyset @t15) :rule refl :args (@t15)) % 0.35/0.61 (step @p6 (= tptp.unord_pair @t19) :rule refl :args (@t19)) % 0.35/0.61 (step @p7 (= tptp.singleton @t20) :rule refl :args (@t20)) % 0.35/0.61 (step @p8 (= tptp.union @t26) :rule refl :args (@t26)) % 0.35/0.61 (step @p9 (= tptp.excl_union @t29) :rule refl :args (@t29)) % 0.35/0.61 (step @p10 (= tptp.intersection @t31) :rule refl :args (@t31)) % 0.35/0.61 (step @p11 (= tptp.setminus @t32) :rule refl :args (@t32)) % 0.35/0.61 (step @p12 (= tptp.complement @t33) :rule refl :args (@t33)) % 0.35/0.61 (step @p13 (= tptp.disjoint @t35) :rule refl :args (@t35)) % 0.35/0.61 (step @p14 (= tptp.subset @t38) :rule refl :args (@t38)) % 0.35/0.61 (step @p15 (= tptp.meets @t40) :rule refl :args (@t40)) % 0.35/0.61 (step @p16 (= tptp.misses @t41) :rule refl :args (@t41)) % 0.35/0.61 (step @p17 (= tptp.cartesian_product @t43) :rule refl :args (@t43)) % 0.35/0.61 (step @p18 (= tptp.pair_rel @t44) :rule refl :args (@t44)) % 0.35/0.61 (step @p19 (= tptp.id_rel @t48) :rule refl :args (@t48)) % 0.35/0.61 (step @p20 (= tptp.sub_rel @t56) :rule refl :args (@t56)) % 0.35/0.61 (step @p21 (= tptp.is_rel_on @t61) :rule refl :args (@t61)) % 0.35/0.61 (step @p22 (= tptp.restrict_rel_domain @t63) :rule refl :args (@t63)) % 0.35/0.61 (step @p23 (= tptp.rel_diagonal @t64) :rule refl :args (@t64)) % 0.35/0.61 (step @p24 (= tptp.rel_composition @t67) :rule refl :args (@t67)) % 0.35/0.61 (step @p25 (= tptp.reflexive @t69) :rule refl :args (@t69)) % 0.35/0.61 (step @p26 (= tptp.irreflexive @t70) :rule refl :args (@t70)) % 0.35/0.61 (step @p27 (= tptp.symmetric @t73) :rule refl :args (@t73)) % 0.35/0.61 (step @p28 (= tptp.transitive @t74) :rule refl :args (@t74)) % 0.35/0.61 (step @p29 (= tptp.equiv_rel @t75) :rule refl :args (@t75)) % 0.35/0.61 (step @p30 (= tptp.rel_codomain @t78) :rule refl :args (@t78)) % 0.35/0.61 (step @p31 (= tptp.rel_domain @t81) :rule refl :args (@t81)) % 0.35/0.61 (step @p32 (= tptp.rel_inverse @t82) :rule refl :args (@t82)) % 0.35/0.61 (step @p33 (= tptp.equiv_classes @t84) :rule refl :args (@t84)) % 0.35/0.61 (step @p34 (= tptp.restrict_rel_codomain @t85) :rule refl :args (@t85)) % 0.35/0.61 (step @p35 (= tptp.rel_field @t86) :rule refl :args (@t86)) % 0.35/0.61 (step @p36 (= tptp.well_founded @t93) :rule refl :args (@t93)) % 0.35/0.61 (step @p37 (= tptp.upwards_well_founded @t94) :rule refl :args (@t94)) % 0.35/0.61 (step @p38 :rule quant-merge-prenex :args ((= (forall @t10 @t110) @t108))) % 0.35/0.61 (step @p39 :rule quant-unused-vars :args ((= @t111 @t101))) % 0.35/0.61 (step @p40 :rule alpha_equiv :args (@t112 (@list @t102) (@list @t17))) % 0.35/0.61 (step @p41 :rule nary_cong :premises (@p40 @p39) :args (@t113)) % 0.35/0.61 (step @p42 :rule quant-miniscope-and :args ((= @t114 @t113))) % 0.35/0.61 (step @p43 :rule trans :premises (@p42 @p41)) % 0.35/0.61 (step @p44 :rule refl :args (@t106)) % 0.35/0.61 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t115)) % 0.35/0.61 (step @p46 :rule quant-miniscope-or :args ((= @t110 @t115))) % 0.35/0.61 (step @p47 :rule trans :premises (@p46 @p45)) % 0.35/0.61 (step @p48 :rule symm :premises (@p47)) % 0.35/0.61 (step @p49 :rule cong :premises (@p48) :args ((forall @t10 (or @t106 @t117)))) % 0.35/0.61 (step @p50 :rule trans :premises (@p49 @p38)) % 0.35/0.61 (step @p51 :rule bool-impl-elim :args (@t105 @t117)) % 0.35/0.61 (step @p52 :rule cong :premises (@p51) :args ((forall @t10 (=> @t105 @t117)))) % 0.35/0.61 (step @p53 :rule trans :premises (@p52 @p50)) % 0.35/0.61 (step @p54 :rule eq-symm :args (@t96 @t100)) % 0.35/0.61 (step @p55 :rule beta-reduce :args ((= @t118 @t100))) % 0.35/0.61 (step @p56 :rule refl :args (@t96)) % 0.35/0.61 (step @p57 :rule symm :premises (@p56)) % 0.35/0.61 (step @p58 :rule alpha_equiv :args (@t5 (@list @t3) (@list @t95))) % 0.35/0.61 (step @p59 :rule trans :premises (@p58 @p57)) % 0.35/0.61 (step @p60 :rule cong :premises (@p59 @p55) :args (@t119)) % 0.35/0.61 (step @p61 :rule trans :premises (@p60 @p54)) % 0.35/0.61 (step @p62 :rule beta-reduce :args ((= @t122 @t116))) % 0.35/0.61 (step @p63 :rule cong :premises (@p62) :args (@t123)) % 0.35/0.61 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t125 (forall @t36 @t124)) @t121) @t123))) % 0.35/0.61 (step @p65 :rule trans :premises (@p64 @p63)) % 0.35/0.61 (step @p66 :rule beta-reduce :args ((= @t126 @t121))) % 0.35/0.61 (step @p67 :rule aci_norm :args ((= (or false @t124) @t124))) % 0.35/0.61 (step @p68 :rule refl :args (@t124)) % 0.35/0.61 (step @p69 :rule evaluate :args ((not true))) % 0.35/0.61 (step @p70 :rule beta-reduce :args ((= @t127 true))) % 0.35/0.61 (step @p71 :rule cong :premises (@p70) :args (@t128)) % 0.35/0.61 (step @p72 :rule trans :premises (@p71 @p69)) % 0.35/0.61 (step @p73 :rule nary_cong :premises (@p72 @p68) :args (@t129)) % 0.35/0.61 (step @p74 :rule trans :premises (@p73 @p67)) % 0.35/0.61 (step @p75 :rule cong :premises (@p74) :args (@t130)) % 0.35/0.61 (step @p76 :rule cong :premises (@p75) :args (@t131)) % 0.35/0.61 (step @p77 :rule beta-reduce :args ((= (_ @t133 @t96) @t131))) % 0.35/0.61 (step @p78 :rule trans :premises (@p77 @p76)) % 0.35/0.61 (step @p79 :rule refl :args (@t133)) % 0.35/0.61 (step @p80 :rule ho_cong :premises (@p79 @p59)) % 0.35/0.61 (step @p81 :rule trans :premises (@p80 @p78)) % 0.35/0.61 (step @p82 :rule ho_cong :premises (@p81 @p66)) % 0.35/0.61 (step @p83 :rule trans :premises (@p82 @p65)) % 0.35/0.61 (step @p84 :rule nary_cong :premises (@p83 @p61) :args (@t134)) % 0.35/0.61 (step @p85 :rule beta-reduce :args ((= (_ (lambda @t136 (forall @t66 @t135)) @t1) @t105))) % 0.35/0.61 (step @p86 :rule refl :args (@t1)) % 0.35/0.61 (step @p87 :rule aci_norm :args ((= (or false @t135) @t135))) % 0.35/0.61 (step @p88 :rule refl :args (@t135)) % 0.35/0.61 (step @p89 :rule eq-refl :args (@t16)) % 0.35/0.61 (step @p90 :rule cong :premises (@p89) :args (@t137)) % 0.35/0.61 (step @p91 :rule trans :premises (@p90 @p69)) % 0.35/0.61 (step @p92 :rule nary_cong :premises (@p91 @p88) :args (@t138)) % 0.35/0.61 (step @p93 :rule trans :premises (@p92 @p87)) % 0.35/0.61 (step @p94 :rule cong :premises (@p93) :args 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@p121)) % 0.35/0.61 (step @p125 :rule refl :args (@t152)) % 0.35/0.61 (step @p126 :rule ho_cong :premises (@p125 @p124)) % 0.35/0.61 (step @p127 :rule trans :premises (@p126 @p113)) % 0.35/0.61 (step @p128 :rule ho_cong :premises (@p127 @p86)) % 0.35/0.61 (step @p129 :rule trans :premises (@p128 @p85)) % 0.35/0.61 (step @p130 :rule cong :premises (@p129 @p84) :args (@t156)) % 0.35/0.61 (step @p131 :rule cong :premises (@p130) :args (@t157)) % 0.35/0.61 (step @p132 :rule trans :premises (@p131 @p53)) % 0.35/0.61 (step @p133 :rule cong :premises (@p132) :args ((not @t157))) % 0.35/0.61 (step @p134 :rule refl :args (@t97)) % 0.35/0.61 (step @p135 :rule refl :args (@t60)) % 0.35/0.61 (step @p136 :rule cong :premises (@p135 @p134) :args ((= @t60 @t97))) % 0.35/0.61 (step @p137 :rule symm :premises (@p136)) % 0.35/0.61 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 0.35/0.61 (step @p139 :rule cong :premises (@p138) :args (@t158)) % 0.35/0.61 (step @p140 :rule cong :premises (@p139) :args (@t159)) % 0.35/0.61 (step @p141 :rule cong :premises (@p140) :args (@t160)) % 0.35/0.61 (step @p142 :rule exists-elim :args ((= @t76 @t160))) % 0.35/0.61 (step @p143 :rule trans :premises (@p142 @p141)) % 0.35/0.61 (step @p144 :rule cong :premises (@p143) :args (@t78)) % 0.35/0.61 (step @p145 :rule trans :premises (@p30 @p144)) % 0.35/0.61 (step @p146 :rule ho_cong :premises (@p145 @p86)) % 0.35/0.61 (step @p147 :rule refl :args (@t5)) % 0.35/0.61 (step @p148 :rule cong :premises (@p147 @p146) :args (@t6)) % 0.35/0.61 (step @p149 :rule cong :premises (@p139) :args (@t161)) % 0.35/0.61 (step @p150 :rule cong :premises (@p149) :args (@t162)) % 0.35/0.61 (step @p151 :rule exists-elim :args ((= @t79 @t162))) % 0.35/0.61 (step @p152 :rule trans :premises (@p151 @p150)) % 0.35/0.61 (step @p153 :rule cong :premises (@p152) :args (@t81)) % 0.35/0.61 (step @p154 :rule trans :premises (@p31 @p153)) % 0.35/0.61 (step @p155 :rule ho_cong :premises (@p154 @p86)) % 0.35/0.61 (step @p156 :rule 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0.35/0.61 (step @p172 :rule cong :premises (@p171) :args (@t38)) % 0.35/0.61 (step @p173 :rule trans :premises (@p14 @p172)) % 0.35/0.61 (step @p174 :rule ho_cong :premises (@p173 @p147)) % 0.35/0.61 (step @p175 :rule ho_cong :premises (@p174 @p155)) % 0.35/0.61 (step @p176 :rule nary_cong :premises (@p175 @p148) :args (@t8)) % 0.35/0.61 (step @p177 :rule ho_cong :premises (@p19 @p147)) % 0.35/0.61 (step @p178 :rule refl :args (@t139)) % 0.35/0.61 (step @p179 :rule refl :args (@t50)) % 0.35/0.61 (step @p180 :rule cong :premises (@p179 @p178) :args ((= @t50 @t139))) % 0.35/0.61 (step @p181 :rule symm :premises (@p180)) % 0.35/0.61 (step @p182 :rule eq_resolve :premises (@p179 @p181)) % 0.35/0.61 (step @p183 :rule refl :args (@t151)) % 0.35/0.61 (step @p184 :rule refl :args (@t52)) % 0.35/0.61 (step @p185 :rule cong :premises (@p184 @p183) :args ((= @t52 @t151))) % 0.35/0.61 (step @p186 :rule symm :premises (@p185)) % 0.35/0.61 (step @p187 :rule eq_resolve :premises (@p184 @p186)) % 0.35/0.61 (step @p188 :rule cong :premises (@p187) :args (@t164)) % 0.35/0.61 (step @p189 :rule nary_cong :premises (@p188 @p182) :args (@t165)) % 0.35/0.61 (step @p190 :rule cong :premises (@p189) :args ((forall @t53 @t165))) % 0.35/0.61 (step @p191 :rule bool-impl-elim :args (@t52 @t50)) % 0.35/0.61 (step @p192 :rule cong :premises (@p191) :args (@t54)) % 0.35/0.61 (step @p193 :rule trans :premises (@p192 @p190)) % 0.35/0.61 (step @p194 :rule cong :premises (@p193) :args (@t56)) % 0.35/0.61 (step @p195 :rule trans :premises (@p20 @p194)) % 0.35/0.61 (step @p196 :rule ho_cong :premises (@p195 @p177)) % 0.35/0.61 (step @p197 :rule ho_cong :premises (@p196 @p86)) % 0.35/0.61 (step @p198 :rule cong :premises (@p197 @p176) :args (@t9)) % 0.35/0.61 (step @p199 :rule cong :premises (@p198) :args (@t11)) % 0.35/0.61 (step @p200 :rule cong :premises (@p199) :args (@t12)) % 0.35/0.61 (step @p201 :rule trans :premises (@p200 @p133)) % 0.35/0.61 (step @p202 :rule eq_resolve :premises (@p1 @p201)) % 0.35/0.61 (step @p203 :rule refl :args (@t178)) % 0.35/0.61 (step @p204 :rule bool-double-not-elim :args (@t108)) % 0.35/0.61 (step @p205 :rule nary_cong :premises (@p204 @p203) :args ((or (not @t179) @t178))) % 0.35/0.61 (step @p206 :rule eq-symm :args (@t166 @t169)) % 0.35/0.61 (step @p207 :rule eq-refl :args (@t168)) % 0.35/0.61 (step @p208 :rule skolem_intro :args (@t169)) % 0.35/0.61 (step @p209 :rule refl :args (@t168)) % 0.35/0.61 (step @p210 :rule cong :premises (@p209 @p208) :args ((= @t168 @t169))) % 0.35/0.61 (step @p211 :rule trans :premises (@p210 @p207)) % 0.35/0.61 (step @p212 :rule true_elim :premises (@p211)) % 0.35/0.61 (step @p213 :rule eq-refl :args (@t96)) % 0.35/0.61 (step @p214 :rule refl :args (@t96)) % 0.35/0.61 (step @p215 :rule cong :premises (@p214 @p57) :args ((= @t96 @t96))) % 0.35/0.61 (step @p216 :rule trans :premises (@p215 @p213)) % 0.35/0.61 (step @p217 :rule skolem_intro :args (@t166)) % 0.35/0.61 (step @p218 :rule cong :premises (@p214 @p217) :args ((= @t96 @t166))) % 0.35/0.61 (step @p219 :rule trans :premises (@p218 @p216)) % 0.35/0.61 (step @p220 :rule true_elim :premises (@p219)) % 0.35/0.61 (step @p221 :rule cong :premises (@p220 @p212) :args (@t180)) % 0.35/0.61 (step @p222 :rule trans :premises (@p221 @p206)) % 0.35/0.61 (step @p223 :rule refl :args (@t173)) % 0.35/0.61 (step @p224 :rule nary_cong :premises (@p223 @p222) :args (@t181)) % 0.35/0.61 (step @p225 :rule refl :args (@t176)) % 0.35/0.61 (step @p226 :rule nary_cong :premises (@p225 @p224) :args (@t182)) % 0.35/0.61 (step @p227 :rule cong :premises (@p226) :args (@t183)) % 0.35/0.61 (step @p228 :rule refl :args (@t179)) % 0.35/0.61 (step @p229 :rule cong :premises (@p228 @p227) :args ((=> @t179 @t183))) % 0.35/0.61 (step @p230 :rule eq-symm :args (@t168 @t96)) % 0.35/0.61 (step @p231 :rule nary_cong :premises (@p223 @p230) :args (@t184)) % 0.35/0.61 (step @p232 :rule nary_cong :premises (@p225 @p231) :args (@t185)) % 0.35/0.61 (step @p233 :rule cong :premises (@p232) :args (@t186)) % 0.35/0.61 (step @p234 :rule cong :premises (@p228 @p233) :args ((=> @t179 @t186))) % 0.35/0.61 (step @p235 :rule trans :premises (@p234 @p229)) % 0.35/0.61 (assume-push @p303 @t179) % 0.35/0.61 (step @p237 :rule skolemize :premises (@p202)) % 0.35/0.61 (step-pop @p304 :rule scope :premises (@p237)) % 0.35/0.61 (step @p238 :rule process_scope :premises (@p304) :args (@t186)) % 0.35/0.61 (step @p240 :rule eq_resolve :premises (@p238 @p235)) % 0.35/0.61 (step @p241 :rule implies_elim :premises (@p240)) % 0.35/0.61 (step @p242 :rule eq_resolve :premises (@p241 @p205)) % 0.35/0.61 (step @p243 :rule chain_m_resolution :premises (@p242 @p202) :args (@t178 @t187 (@list @t108))) % 0.35/0.61 (step @p244 :rule cnf_or_neg :args (@t177 1)) % 0.35/0.61 (step @p245 :rule chain_m_resolution :premises (@p244 @p243) :args ((not @t174) @t187 @t188)) % 0.35/0.61 (step @p246 :rule bool-double-not-elim :args (@t175)) % 0.35/0.61 (step @p247 :rule refl :args (@t177)) % 0.35/0.61 (step @p248 :rule nary_cong :premises (@p247 @p246) :args ((or @t177 (not @t176)))) % 0.35/0.61 (step @p249 :rule cnf_or_neg :args (@t177 0)) % 0.35/0.61 (step @p250 :rule eq_resolve :premises (@p249 @p248)) % 0.35/0.61 (step @p251 :rule reordering :premises (@p250) :args ((or @t175 @t177))) % 0.35/0.61 (step @p252 :rule chain_m_resolution :premises (@p251 @p243) :args (@t175 @t187 @t188)) % 0.35/0.61 (step @p253 :rule instantiate :premises (@p252) :args (@t189)) % 0.35/0.61 (assume-push @p305 @t172) % 0.35/0.61 (step @p255 :rule instantiate :premises (@p305) :args (@t189)) % 0.35/0.61 (step-pop @p306 :rule scope :premises (@p255)) % 0.35/0.61 (step @p256 :rule process_scope :premises (@p306) :args ((not @t190))) % 0.35/0.61 (step @p258 :rule implies_elim :premises (@p256)) % 0.35/0.61 (step @p259 :rule chain_m_resolution :premises (@p258 @p253) :args (@t173 (@list false) (@list @t190))) % 0.35/0.61 (step @p260 :rule refl :args (@t191)) % 0.35/0.61 (step @p261 :rule bool-double-not-elim :args (@t172)) % 0.35/0.61 (step @p262 :rule refl :args (@t174)) % 0.35/0.61 (step @p263 :rule nary_cong :premises (@p262 @p261 @p260) :args ((or @t174 (not @t173) @t191))) % 0.35/0.61 (step @p264 :rule cnf_and_neg :args (@t174)) % 0.35/0.61 (step @p265 :rule eq_resolve :premises (@p264 @p263)) % 0.35/0.61 (step @p266 :rule reordering :premises (@p265) :args ((or @t172 @t174 @t191))) % 0.35/0.61 (step @p267 :rule chain_m_resolution :premises (@p266 @p259 @p245) :args (@t191 (@list true true) (@list @t172 @t174))) % 0.35/0.61 (step @p268 :rule bool-double-not-elim :args (@t193)) % 0.35/0.61 (step @p269 :rule bool-eq-true :args (@t194)) % 0.35/0.61 (step @p270 :rule beta-reduce :args ((= (_ @t96 @t192) true))) % 0.35/0.61 (step @p271 :rule refl :args (@t192)) % 0.35/0.61 (step @p272 :rule ho_cong :premises (@p217 @p271)) % 0.35/0.61 (step @p273 :rule bool-eq-true :args (@t195)) % 0.35/0.61 (step @p274 :rule trans :premises (@p273 @p272 @p270)) % 0.35/0.61 (step @p275 :rule true_elim :premises (@p274)) % 0.35/0.61 (step @p276 :rule eq-refl :args (@t194)) % 0.35/0.61 (step @p277 :rule beta-reduce :args ((= @t196 @t194))) % 0.35/0.61 (step @p278 :rule refl :args (@t194)) % 0.35/0.61 (step @p279 :rule cong :premises (@p278 @p277) :args ((= @t194 @t196))) % 0.35/0.61 (step @p280 :rule trans :premises (@p279 @p276)) % 0.35/0.61 (step @p281 :rule eq-symm :args (@t196 @t194)) % 0.35/0.61 (step @p282 :rule trans :premises (@p281 @p280)) % 0.35/0.61 (step @p283 :rule ho_cong :premises (@p208 @p271)) % 0.35/0.61 (step @p284 :rule cong :premises (@p283 @p278) :args ((= @t197 @t194))) % 0.35/0.61 (step @p285 :rule trans :premises (@p284 @p282)) % 0.35/0.61 (step @p286 :rule true_elim :premises (@p285)) % 0.35/0.61 (step @p287 :rule cong :premises (@p286 @p275) :args (@t198)) % 0.35/0.61 (step @p288 :rule trans :premises (@p287 @p269)) % 0.35/0.61 (step @p289 :rule cong :premises (@p288) :args (@t199)) % 0.35/0.61 (step @p290 :rule trans :premises (@p289 @p268)) % 0.35/0.61 (step @p291 :rule refl :args (@t170)) % 0.35/0.61 (step @p292 :rule nary_cong :premises (@p291 @p290) :args (@t200)) % 0.35/0.61 ; WARNING: add trust step for TRUST % 0.35/0.61 ; trust TRUST THEORY_LEMMA % 0.35/0.61 (step @p293 :rule trust :premises () :args (@t200)) % 0.35/0.61 (step @p294 :rule eq_resolve :premises (@p293 @p292)) % 0.35/0.61 (step @p295 :rule chain_m_resolution :premises (@p294 @p267) :args (@t193 @t187 (@list @t170))) % 0.35/0.61 (step @p296 :rule instantiate :premises (@p252) :args (@t201)) % 0.35/0.61 (assume-push @p307 @t193) % 0.35/0.61 (step @p298 :rule instantiate :premises (@p307) :args (@t201)) % 0.35/0.61 (step-pop @p308 :rule scope :premises (@p298)) % 0.35/0.61 (step @p299 :rule process_scope :premises (@p308) :args ((not @t202))) % 0.35/0.61 (step @p301 :rule implies_elim :premises (@p299)) % 0.35/0.61 (step @p302 false :rule chain_m_resolution :premises (@p301 @p296 @p295) :args (false (@list false false) (@list @t202 @t193))) % 0.35/0.61 ) % 0.35/0.61 % SZS output end Proof % 0.35/0.61 % cvc5 exiting %------------------------------------------------------------------------------