%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET648^3 : 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 08:48:21 AM UTC 2026 % Result : Theorem 0.36s 0.61s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET648^3 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n026.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 16:06:10 EDT 2026 % 0.18/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.36/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.36/0.61 % SZS status Theorem % 0.36/0.61 % SZS output start Proof % 0.36/0.61 ( % 0.36/0.61 (declare-sort $$unsorted 0) % 0.36/0.61 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.61 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.36/0.61 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.36/0.61 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.36/0.61 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.36/0.61 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.36/0.61 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.36/0.61 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.36/0.61 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.36/0.61 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.36/0.61 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.36/0.61 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.36/0.61 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.36/0.61 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.36/0.61 (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)))))))) % 0.36/0.61 (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)))))))) % 0.36/0.61 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_2) (= _let_2 _let_1))))))) % 0.36/0.61 (define tptp.sub_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.36/0.61 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$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 $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.36/0.61 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.36/0.61 (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))))) % 0.36/0.61 (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 $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.36/0.61 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.36/0.61 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.36/0.61 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.36/0.61 (define tptp.transitive () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.36/0.61 (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))))) % 0.36/0.61 (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))))))) % 0.36/0.61 (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))))))) % 0.36/0.61 (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)))))) % 0.36/0.61 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.36/0.61 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$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)))))))) % 0.36/0.61 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.36/0.61 (define tptp.well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.36/0.61 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$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" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.36/0.61 (define @t1 () (@var "Y" (-> $$unsorted Bool))) % 0.36/0.61 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t3 () (_ tptp.rel_domain @t2)) % 0.36/0.61 (define @t4 () (_ tptp.rel_codomain @t2)) % 0.36/0.61 (define @t5 () (=> (_ (_ tptp.subset @t4) @t1) (_ (_ tptp.sub_rel @t2) (_ (_ tptp.cartesian_product @t3) @t1)))) % 0.36/0.61 (define @t6 () (@list @t2 @t1)) % 0.36/0.61 (define @t7 () (forall @t6 @t5)) % 0.36/0.61 (define @t8 () (not @t7)) % 0.36/0.61 (define @t9 () (@var "X" $$unsorted)) % 0.36/0.61 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.36/0.61 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.36/0.61 (define @t12 () (@list @t9)) % 0.36/0.61 (define @t13 () (lambda @t12 false)) % 0.36/0.61 (define @t14 () (@var "Y" $$unsorted)) % 0.36/0.61 (define @t15 () (@var "U" $$unsorted)) % 0.36/0.61 (define @t16 () (= @t15 @t9)) % 0.36/0.61 (define @t17 () (lambda (@list @t9 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.36/0.61 (define @t18 () (lambda (@list @t9 @t15) @t16)) % 0.36/0.61 (define @t19 () (_ @t1 @t15)) % 0.36/0.61 (define @t20 () (@var "X" (-> $$unsorted Bool))) % 0.36/0.61 (define @t21 () (_ @t20 @t15)) % 0.36/0.61 (define @t22 () (@list @t20 @t1 @t15)) % 0.36/0.61 (define @t23 () (lambda @t22 (or @t21 @t19))) % 0.36/0.61 (define @t24 () (not @t21)) % 0.36/0.61 (define @t25 () (and @t21 (not @t19))) % 0.36/0.61 (define @t26 () (lambda @t22 (or @t25 (and @t24 @t19)))) % 0.36/0.61 (define @t27 () (and @t21 @t19)) % 0.36/0.61 (define @t28 () (lambda @t22 @t27)) % 0.36/0.61 (define @t29 () (lambda @t22 @t25)) % 0.36/0.61 (define @t30 () (lambda (@list @t20 @t15) @t24)) % 0.36/0.61 (define @t31 () (@list @t20 @t1)) % 0.36/0.61 (define @t32 () (lambda @t31 (= (_ (_ tptp.intersection @t20) @t1) tptp.emptyset))) % 0.36/0.61 (define @t33 () (@list @t15)) % 0.36/0.61 (define @t34 () (forall @t33 (=> @t21 @t19))) % 0.36/0.61 (define @t35 () (lambda @t31 @t34)) % 0.36/0.61 (define @t36 () (exists @t33 @t27)) % 0.36/0.61 (define @t37 () (lambda @t31 @t36)) % 0.36/0.61 (define @t38 () (lambda @t31 (not @t36))) % 0.36/0.61 (define @t39 () (@var "V" $$unsorted)) % 0.36/0.61 (define @t40 () (_ @t1 @t39)) % 0.36/0.61 (define @t41 () (lambda (@list @t20 @t1 @t15 @t39) (and @t21 @t40))) % 0.36/0.61 (define @t42 () (lambda (@list @t9 @t14 @t15 @t39) (or @t16 (= @t39 @t14)))) % 0.36/0.61 (define @t43 () (= @t9 @t14)) % 0.36/0.61 (define @t44 () (@var "S" (-> $$unsorted Bool))) % 0.36/0.61 (define @t45 () (_ @t44 @t9)) % 0.36/0.61 (define @t46 () (lambda (@list @t44 @t9 @t14) (and @t45 @t43))) % 0.36/0.61 (define @t47 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t48 () (_ (_ @t47 @t9) @t14)) % 0.36/0.61 (define @t49 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.36/0.61 (define @t50 () (_ (_ @t49 @t9) @t14)) % 0.36/0.61 (define @t51 () (@list @t9 @t14)) % 0.36/0.61 (define @t52 () (forall @t51 (=> @t50 @t48))) % 0.36/0.61 (define @t53 () (@list @t49 @t47)) % 0.36/0.61 (define @t54 () (lambda @t53 @t52)) % 0.36/0.61 (define @t55 () (@var "B" (-> $$unsorted Bool))) % 0.36/0.61 (define @t56 () (@var "A" (-> $$unsorted Bool))) % 0.36/0.61 (define @t57 () (_ @t2 @t9)) % 0.36/0.61 (define @t58 () (_ @t57 @t14)) % 0.36/0.61 (define @t59 () (lambda (@list @t2 @t56 @t55) (forall @t51 (=> @t58 (and (_ @t56 @t9) (_ @t55 @t14)))))) % 0.36/0.61 (define @t60 () (@list @t2 @t44 @t9 @t14)) % 0.36/0.61 (define @t61 () (lambda @t60 (and @t45 @t58))) % 0.36/0.61 (define @t62 () (lambda @t51 @t43)) % 0.36/0.61 (define @t63 () (@var "Z" $$unsorted)) % 0.36/0.61 (define @t64 () (@list @t14)) % 0.36/0.61 (define @t65 () (lambda (@list @t49 @t47 @t9 @t63) (exists @t64 (and @t50 (_ (_ @t47 @t14) @t63))))) % 0.36/0.61 (define @t66 () (_ @t57 @t9)) % 0.36/0.61 (define @t67 () (@list @t2)) % 0.36/0.61 (define @t68 () (lambda @t67 (forall @t12 @t66))) % 0.36/0.61 (define @t69 () (lambda @t67 (forall @t12 (not @t66)))) % 0.36/0.61 (define @t70 () (_ @t2 @t14)) % 0.36/0.61 (define @t71 () (_ @t70 @t9)) % 0.36/0.61 (define @t72 () (lambda @t67 (forall @t51 (=> @t58 @t71)))) % 0.36/0.61 (define @t73 () (lambda @t67 (forall (@list @t9 @t14 @t63) (=> (and @t58 (_ @t70 @t63)) (_ @t57 @t63))))) % 0.36/0.61 (define @t74 () (lambda @t67 (and (_ tptp.reflexive @t2) (_ tptp.symmetric @t2) (_ tptp.transitive @t2)))) % 0.36/0.61 (define @t75 () (exists @t12 @t58)) % 0.36/0.61 (define @t76 () (@list @t2 @t14)) % 0.36/0.61 (define @t77 () (lambda @t76 @t75)) % 0.36/0.61 (define @t78 () (exists @t64 @t58)) % 0.36/0.61 (define @t79 () (@list @t2 @t9)) % 0.36/0.61 (define @t80 () (lambda @t79 @t78)) % 0.36/0.61 (define @t81 () (lambda (@list @t2 @t9 @t14) @t71)) % 0.36/0.61 (define @t82 () (@var "S1" (-> $$unsorted Bool))) % 0.36/0.61 (define @t83 () (lambda (@list @t2 @t82) (exists @t12 (and (_ @t82 @t9) (forall @t64 (= (_ @t82 @t14) @t58)))))) % 0.36/0.61 (define @t84 () (lambda @t60 (and (_ @t44 @t14) @t58))) % 0.36/0.61 (define @t85 () (lambda @t79 (or (_ @t3 @t9) (_ @t4 @t9)))) % 0.36/0.61 (define @t86 () (@var "W" $$unsorted)) % 0.36/0.61 (define @t87 () (not (_ @t20 @t86))) % 0.36/0.61 (define @t88 () (@list @t86)) % 0.36/0.61 (define @t89 () (_ @t20 @t14)) % 0.36/0.61 (define @t90 () (_ @t20 @t63)) % 0.36/0.61 (define @t91 () (@list @t20 @t63)) % 0.36/0.61 (define @t92 () (lambda @t67 (forall @t91 (=> @t90 (exists @t64 (and @t89 (forall @t88 (=> (_ @t70 @t86) @t87)))))))) % 0.36/0.61 (define @t93 () (lambda @t67 (forall @t91 (=> @t90 (exists @t64 (and @t89 (forall @t88 (=> (_ @t70 @t14) @t87)))))))) % 0.36/0.61 (define @t94 () (@var "BOUND_VARIABLE_8236" $$unsorted)) % 0.36/0.61 (define @t95 () (@var "BOUND_VARIABLE_8207" $$unsorted)) % 0.36/0.61 (define @t96 () (@var "BOUND_VARIABLE_8234" $$unsorted)) % 0.36/0.61 (define @t97 () (@list @t95)) % 0.36/0.61 (define @t98 () (and (not (forall @t97 (not (_ @t2 @t96 @t95)))) (_ @t1 @t94))) % 0.36/0.61 (define @t99 () (not (_ @t2 @t96 @t94))) % 0.36/0.61 (define @t100 () (_ @t1 @t15)) % 0.36/0.61 (define @t101 () (@var "BOUND_VARIABLE_8177" $$unsorted)) % 0.36/0.61 (define @t102 () (not (_ @t2 @t101 @t15))) % 0.36/0.61 (define @t103 () (or @t102 @t100)) % 0.36/0.61 (define @t104 () (@list @t15 @t101)) % 0.36/0.61 (define @t105 () (forall @t104 @t103)) % 0.36/0.61 (define @t106 () (not @t105)) % 0.36/0.61 (define @t107 () (or @t106 @t99 @t98)) % 0.36/0.61 (define @t108 () (or @t99 @t98)) % 0.36/0.61 (define @t109 () (or @t106 @t108)) % 0.36/0.61 (define @t110 () (@list @t2 @t1 @t96 @t94)) % 0.36/0.61 (define @t111 () (forall @t110 @t109)) % 0.36/0.61 (define @t112 () (@list @t96 @t94)) % 0.36/0.61 (define @t113 () (forall @t112 @t109)) % 0.36/0.61 (define @t114 () (forall @t112 @t108)) % 0.36/0.61 (define @t115 () (or @t106 @t114)) % 0.36/0.61 (define @t116 () (_ @t1 @t14)) % 0.36/0.61 (define @t117 () (not (forall @t97 (not (_ @t2 @t9 @t95))))) % 0.36/0.61 (define @t118 () (_ @t2 @t9 @t14)) % 0.36/0.61 (define @t119 () (not @t118)) % 0.36/0.61 (define @t120 () (forall @t51 (or @t119 (and @t117 @t116)))) % 0.36/0.61 (define @t121 () (_ @t1 @t14)) % 0.36/0.61 (define @t122 () (and @t117 @t121)) % 0.36/0.61 (define @t123 () (or @t119 @t122)) % 0.36/0.61 (define @t124 () (@list @t15 @t39)) % 0.36/0.61 (define @t125 () (forall @t64 (not (_ @t2 @t15 @t14)))) % 0.36/0.61 (define @t126 () (not @t125)) % 0.36/0.61 (define @t127 () (and @t126 @t40)) % 0.36/0.61 (define @t128 () (lambda @t124 @t127)) % 0.36/0.61 (define @t129 () (or @t119 (_ @t128 @t9 @t14))) % 0.36/0.61 (define @t130 () (forall @t51 @t129)) % 0.36/0.61 (define @t131 () (_ @t47 @t9 @t14)) % 0.36/0.61 (define @t132 () (lambda (@list @t47) (forall @t51 (or @t119 @t131)))) % 0.36/0.61 (define @t133 () (@list @t1 @t15 @t39)) % 0.36/0.61 (define @t134 () (not (forall @t64 @t119))) % 0.36/0.61 (define @t135 () (lambda @t12 @t134)) % 0.36/0.61 (define @t136 () (_ @t135 @t15)) % 0.36/0.61 (define @t137 () (and @t136 @t40)) % 0.36/0.61 (define @t138 () (lambda @t133 @t137)) % 0.36/0.61 (define @t139 () (_ (lambda @t79 @t134) @t2)) % 0.36/0.61 (define @t140 () (_ @t49 @t9 @t14)) % 0.36/0.61 (define @t141 () (_ (lambda @t53 (forall @t51 (or (not @t140) @t131))) @t2)) % 0.36/0.61 (define @t142 () (@list @t1)) % 0.36/0.61 (define @t143 () (@list @t101)) % 0.36/0.61 (define @t144 () (forall @t143 @t103)) % 0.36/0.61 (define @t145 () (forall @t143 @t102)) % 0.36/0.61 (define @t146 () (or @t145 @t100)) % 0.36/0.61 (define @t147 () (forall @t12 (not (_ @t2 @t9 @t15)))) % 0.36/0.61 (define @t148 () (not (forall @t12 @t119))) % 0.36/0.61 (define @t149 () (lambda @t64 @t148)) % 0.36/0.61 (define @t150 () (_ @t149 @t15)) % 0.36/0.61 (define @t151 () (not @t150)) % 0.36/0.61 (define @t152 () (or @t151 @t100)) % 0.36/0.61 (define @t153 () (forall @t33 @t152)) % 0.36/0.61 (define @t154 () (lambda @t142 @t153)) % 0.36/0.61 (define @t155 () (_ @t20 @t15)) % 0.36/0.61 (define @t156 () (lambda @t31 (forall @t33 (or (not @t155) @t100)))) % 0.36/0.61 (define @t157 () (_ (lambda @t76 @t148) @t2)) % 0.36/0.61 (define @t158 () (=> (_ (_ @t156 @t157) @t1) (_ @t141 (_ (_ @t41 @t139) @t1)))) % 0.36/0.61 (define @t159 () (forall @t6 @t158)) % 0.36/0.61 (define @t160 () (not @t58)) % 0.36/0.61 (define @t161 () (forall @t64 @t160)) % 0.36/0.61 (define @t162 () (not @t161)) % 0.36/0.61 (define @t163 () (not @t50)) % 0.36/0.61 (define @t164 () (or @t163 @t48)) % 0.36/0.61 (define @t165 () (forall @t12 @t160)) % 0.36/0.61 (define @t166 () (not @t165)) % 0.36/0.61 (define @t167 () (or @t24 @t19)) % 0.36/0.61 (define @t168 () (forall @t110 @t107)) % 0.36/0.61 (define @t169 () (@quantifiers_skolemize @t168 1)) % 0.36/0.61 (define @t170 () (@quantifiers_skolemize @t168 0)) % 0.36/0.61 (define @t171 () (forall @t104 (or (not (_ @t170 @t101 @t15)) (_ @t169 @t15)))) % 0.36/0.61 (define @t172 () (@quantifiers_skolemize @t168 3)) % 0.36/0.61 (define @t173 () (_ @t169 @t172)) % 0.36/0.61 (define @t174 () (@quantifiers_skolemize @t168 2)) % 0.36/0.61 (define @t175 () (forall @t97 (not (_ @t170 @t174 @t95)))) % 0.36/0.61 (define @t176 () (not @t175)) % 0.36/0.61 (define @t177 () (and @t176 @t173)) % 0.36/0.61 (define @t178 () (_ @t170 @t174 @t172)) % 0.36/0.61 (define @t179 () (not @t178)) % 0.36/0.61 (define @t180 () (not @t171)) % 0.36/0.61 (define @t181 () (or @t180 @t179 @t177)) % 0.36/0.61 (define @t182 () (@list true)) % 0.36/0.61 (define @t183 () (@list @t181)) % 0.36/0.61 (define @t184 () (not @t173)) % 0.36/0.61 (define @t185 () (or @t179 @t173)) % 0.36/0.61 (define @t186 () (not @t185)) % 0.36/0.61 (assume @p1 @t8) % 0.36/0.61 (assume @p2 true) % 0.36/0.61 (step @p3 (= tptp.in @t11) :rule refl :args (@t11)) % 0.36/0.61 (step @p4 (= tptp.is_a @t11) :rule refl :args (@t11)) % 0.36/0.61 (step @p5 (= tptp.emptyset @t13) :rule refl :args (@t13)) % 0.36/0.61 (step @p6 (= tptp.unord_pair @t17) :rule refl :args (@t17)) % 0.36/0.61 (step @p7 (= tptp.singleton @t18) :rule refl :args (@t18)) % 0.36/0.61 (step @p8 (= tptp.union @t23) :rule refl :args (@t23)) % 0.36/0.61 (step @p9 (= tptp.excl_union @t26) :rule refl :args (@t26)) % 0.36/0.61 (step @p10 (= tptp.intersection @t28) :rule refl :args (@t28)) % 0.36/0.61 (step @p11 (= tptp.setminus @t29) :rule refl :args (@t29)) % 0.36/0.61 (step @p12 (= tptp.complement @t30) :rule refl :args (@t30)) % 0.36/0.61 (step @p13 (= tptp.disjoint @t32) :rule refl :args (@t32)) % 0.36/0.61 (step @p14 (= tptp.subset @t35) :rule refl :args (@t35)) % 0.36/0.61 (step @p15 (= tptp.meets @t37) :rule refl :args (@t37)) % 0.36/0.61 (step @p16 (= tptp.misses @t38) :rule refl :args (@t38)) % 0.36/0.61 (step @p17 (= tptp.cartesian_product @t41) :rule refl :args (@t41)) % 0.36/0.61 (step @p18 (= tptp.pair_rel @t42) :rule refl :args (@t42)) % 0.36/0.61 (step @p19 (= tptp.id_rel @t46) :rule refl :args (@t46)) % 0.36/0.61 (step @p20 (= tptp.sub_rel @t54) :rule refl :args (@t54)) % 0.36/0.61 (step @p21 (= tptp.is_rel_on @t59) :rule refl :args (@t59)) % 0.36/0.61 (step @p22 (= tptp.restrict_rel_domain @t61) :rule refl :args (@t61)) % 0.36/0.61 (step @p23 (= tptp.rel_diagonal @t62) :rule refl :args (@t62)) % 0.36/0.61 (step @p24 (= tptp.rel_composition @t65) :rule refl :args (@t65)) % 0.36/0.61 (step @p25 (= tptp.reflexive @t68) :rule refl :args (@t68)) % 0.36/0.61 (step @p26 (= tptp.irreflexive @t69) :rule refl :args (@t69)) % 0.36/0.61 (step @p27 (= tptp.symmetric @t72) :rule refl :args (@t72)) % 0.36/0.61 (step @p28 (= tptp.transitive @t73) :rule refl :args (@t73)) % 0.36/0.61 (step @p29 (= tptp.equiv_rel @t74) :rule refl :args (@t74)) % 0.36/0.61 (step @p30 (= tptp.rel_codomain @t77) :rule refl :args (@t77)) % 0.36/0.61 (step @p31 (= tptp.rel_domain @t80) :rule refl :args (@t80)) % 0.36/0.61 (step @p32 (= tptp.rel_inverse @t81) :rule refl :args (@t81)) % 0.36/0.61 (step @p33 (= tptp.equiv_classes @t83) :rule refl :args (@t83)) % 0.36/0.61 (step @p34 (= tptp.restrict_rel_codomain @t84) :rule refl :args (@t84)) % 0.36/0.61 (step @p35 (= tptp.rel_field @t85) :rule refl :args (@t85)) % 0.36/0.61 (step @p36 (= tptp.well_founded @t92) :rule refl :args (@t92)) % 0.36/0.61 (step @p37 (= tptp.upwards_well_founded @t93) :rule refl :args (@t93)) % 0.36/0.61 (step @p38 :rule aci_norm :args ((= @t109 @t107))) % 0.36/0.61 (step @p39 :rule cong :premises (@p38) :args (@t111)) % 0.36/0.61 (step @p40 :rule quant-merge-prenex :args ((= (forall @t6 @t113) @t111))) % 0.36/0.61 (step @p41 :rule alpha_equiv :args (@t114 (@list @t96 @t94) (@list @t9 @t14))) % 0.36/0.61 (step @p42 :rule refl :args (@t106)) % 0.36/0.61 (step @p43 :rule nary_cong :premises (@p42 @p41) :args (@t115)) % 0.36/0.61 (step @p44 :rule quant-miniscope-or :args ((= @t113 @t115))) % 0.36/0.61 (step @p45 :rule trans :premises (@p44 @p43)) % 0.36/0.61 (step @p46 :rule symm :premises (@p45)) % 0.36/0.61 (step @p47 :rule cong :premises (@p46) :args ((forall @t6 (or @t106 @t120)))) % 0.36/0.61 (step @p48 :rule trans :premises (@p47 @p40)) % 0.36/0.61 (step @p49 :rule trans :premises (@p48 @p39)) % 0.36/0.61 (step @p50 :rule bool-impl-elim :args (@t105 @t120)) % 0.36/0.61 (step @p51 :rule cong :premises (@p50) :args ((forall @t6 (=> @t105 @t120)))) % 0.36/0.61 (step @p52 :rule trans :premises (@p51 @p49)) % 0.36/0.61 (step @p53 :rule refl :args (@t116)) % 0.36/0.61 (step @p54 :rule refl :args (@t121)) % 0.36/0.61 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t121 @t116))) % 0.36/0.61 (step @p56 :rule symm :premises (@p55)) % 0.36/0.61 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.36/0.61 (step @p58 :rule refl :args (@t117)) % 0.36/0.61 (step @p59 :rule nary_cong :premises (@p58 @p57) :args (@t122)) % 0.36/0.61 (step @p60 :rule refl :args (@t119)) % 0.36/0.61 (step @p61 :rule nary_cong :premises (@p60 @p59) :args (@t123)) % 0.36/0.61 (step @p62 :rule cong :premises (@p61) :args ((forall @t51 @t123))) % 0.36/0.61 (step @p63 :rule beta-reduce :args ((= (_ (lambda @t124 (and (not (forall @t97 (not (_ @t2 @t15 @t95)))) @t40)) @t9 @t14) @t122))) % 0.36/0.61 (step @p64 :rule refl :args (@t14)) % 0.36/0.61 (step @p65 :rule refl :args (@t9)) % 0.36/0.61 (step @p66 :rule refl :args (@t40)) % 0.36/0.61 (step @p67 :rule alpha_equiv :args (@t125 (@list @t14) (@list @t95))) % 0.36/0.61 (step @p68 :rule cong :premises (@p67) :args (@t126)) % 0.36/0.61 (step @p69 :rule nary_cong :premises (@p68 @p66) :args (@t127)) % 0.36/0.61 (step @p70 :rule cong :premises (@p69) :args (@t128)) % 0.36/0.61 (step @p71 :rule ho_cong :premises (@p70 @p65 @p64)) % 0.36/0.61 (step @p72 :rule trans :premises (@p71 @p63)) % 0.36/0.61 (step @p73 :rule refl :args (@t119)) % 0.36/0.61 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t129)) % 0.36/0.61 (step @p75 :rule cong :premises (@p74) :args (@t130)) % 0.36/0.61 (step @p76 :rule trans :premises (@p75 @p62)) % 0.36/0.61 (step @p77 :rule beta-reduce :args ((= (_ @t132 @t128) @t130))) % 0.36/0.61 (step @p78 :rule trans :premises (@p77 @p76)) % 0.36/0.61 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t133 @t127) @t1) @t128))) % 0.36/0.61 (step @p80 :rule refl :args (@t1)) % 0.36/0.61 (step @p81 :rule refl :args (@t40)) % 0.36/0.61 (step @p82 :rule beta-reduce :args ((= @t136 @t126))) % 0.36/0.61 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t137)) % 0.36/0.61 (step @p84 :rule cong :premises (@p83) :args (@t138)) % 0.36/0.61 (step @p85 :rule beta-reduce :args ((= (_ @t41 @t135) @t138))) % 0.36/0.61 (step @p86 :rule trans :premises (@p85 @p84)) % 0.36/0.61 (step @p87 :rule beta-reduce :args ((= @t139 @t135))) % 0.36/0.61 (step @p88 :rule refl :args (@t41)) % 0.36/0.61 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.36/0.61 (step @p90 :rule trans :premises (@p89 @p86)) % 0.36/0.61 (step @p91 :rule ho_cong :premises (@p90 @p80)) % 0.36/0.61 (step @p92 :rule trans :premises (@p91 @p79)) % 0.36/0.61 (step @p93 :rule beta-reduce :args ((= @t141 @t132))) % 0.36/0.61 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 0.36/0.61 (step @p95 :rule trans :premises (@p94 @p78)) % 0.36/0.61 (step @p96 :rule beta-reduce :args ((= (_ (lambda @t142 @t105) @t1) @t105))) % 0.36/0.61 (step @p97 :rule quant-merge-prenex :args ((= (forall @t33 @t144) @t105))) % 0.36/0.61 (step @p98 :rule refl :args (@t100)) % 0.36/0.61 (step @p99 :rule alpha_equiv :args (@t145 (@list @t101) (@list @t9))) % 0.36/0.61 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t146)) % 0.36/0.61 (step @p101 :rule quant-miniscope-or :args ((= @t144 @t146))) % 0.36/0.61 (step @p102 :rule trans :premises (@p101 @p100)) % 0.36/0.61 (step @p103 :rule symm :premises (@p102)) % 0.36/0.61 (step @p104 :rule cong :premises (@p103) :args ((forall @t33 (or @t147 @t100)))) % 0.36/0.61 (step @p105 :rule trans :premises (@p104 @p97)) % 0.36/0.61 (step @p106 :rule refl :args (@t100)) % 0.36/0.61 (step @p107 :rule bool-double-not-elim :args (@t147)) % 0.36/0.61 (step @p108 :rule beta-reduce :args ((= @t150 (not @t147)))) % 0.36/0.61 (step @p109 :rule cong :premises (@p108) :args (@t151)) % 0.36/0.61 (step @p110 :rule trans :premises (@p109 @p107)) % 0.36/0.61 (step @p111 :rule nary_cong :premises (@p110 @p106) :args (@t152)) % 0.36/0.61 (step @p112 :rule cong :premises (@p111) :args (@t153)) % 0.36/0.61 (step @p113 :rule trans :premises (@p112 @p105)) % 0.36/0.61 (step @p114 :rule cong :premises (@p113) :args (@t154)) % 0.36/0.61 (step @p115 :rule beta-reduce :args ((= (_ @t156 @t149) @t154))) % 0.36/0.61 (step @p116 :rule trans :premises (@p115 @p114)) % 0.36/0.61 (step @p117 :rule beta-reduce :args ((= @t157 @t149))) % 0.36/0.61 (step @p118 :rule refl :args (@t156)) % 0.36/0.61 (step @p119 :rule ho_cong :premises (@p118 @p117)) % 0.36/0.61 (step @p120 :rule trans :premises (@p119 @p116)) % 0.36/0.61 (step @p121 :rule ho_cong :premises (@p120 @p80)) % 0.36/0.61 (step @p122 :rule trans :premises (@p121 @p96)) % 0.36/0.61 (step @p123 :rule cong :premises (@p122 @p95) :args (@t158)) % 0.36/0.61 (step @p124 :rule cong :premises (@p123) :args (@t159)) % 0.36/0.61 (step @p125 :rule trans :premises (@p124 @p52)) % 0.36/0.61 (step @p126 :rule cong :premises (@p125) :args ((not @t159))) % 0.36/0.61 (step @p127 :rule refl :args (@t2)) % 0.36/0.61 (step @p128 :rule refl :args (@t118)) % 0.36/0.61 (step @p129 :rule refl :args (@t58)) % 0.36/0.61 (step @p130 :rule cong :premises (@p129 @p128) :args ((= @t58 @t118))) % 0.36/0.61 (step @p131 :rule symm :premises (@p130)) % 0.36/0.61 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 0.36/0.61 (step @p133 :rule cong :premises (@p132) :args (@t160)) % 0.36/0.61 (step @p134 :rule cong :premises (@p133) :args (@t161)) % 0.36/0.61 (step @p135 :rule cong :premises (@p134) :args (@t162)) % 0.36/0.61 (step @p136 :rule exists-elim :args ((= @t78 @t162))) % 0.36/0.61 (step @p137 :rule trans :premises (@p136 @p135)) % 0.36/0.61 (step @p138 :rule cong :premises (@p137) :args (@t80)) % 0.36/0.61 (step @p139 :rule trans :premises (@p31 @p138)) % 0.36/0.61 (step @p140 :rule ho_cong :premises (@p139 @p127)) % 0.36/0.61 (step @p141 :rule ho_cong :premises (@p17 @p140)) % 0.36/0.61 (step @p142 :rule ho_cong :premises (@p141 @p80)) % 0.36/0.61 (step @p143 :rule refl :args (@t131)) % 0.36/0.61 (step @p144 :rule refl :args (@t48)) % 0.36/0.61 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t48 @t131))) % 0.36/0.61 (step @p146 :rule symm :premises (@p145)) % 0.36/0.61 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.36/0.61 (step @p148 :rule refl :args (@t140)) % 0.36/0.61 (step @p149 :rule refl :args (@t50)) % 0.36/0.61 (step @p150 :rule cong :premises (@p149 @p148) :args ((= @t50 @t140))) % 0.36/0.61 (step @p151 :rule symm :premises (@p150)) % 0.36/0.61 (step @p152 :rule eq_resolve :premises (@p149 @p151)) % 0.36/0.61 (step @p153 :rule cong :premises (@p152) :args (@t163)) % 0.36/0.61 (step @p154 :rule nary_cong :premises (@p153 @p147) :args (@t164)) % 0.36/0.61 (step @p155 :rule cong :premises (@p154) :args ((forall @t51 @t164))) % 0.36/0.61 (step @p156 :rule bool-impl-elim :args (@t50 @t48)) % 0.36/0.61 (step @p157 :rule cong :premises (@p156) :args (@t52)) % 0.36/0.61 (step @p158 :rule trans :premises (@p157 @p155)) % 0.36/0.61 (step @p159 :rule cong :premises (@p158) :args (@t54)) % 0.36/0.61 (step @p160 :rule trans :premises (@p20 @p159)) % 0.36/0.61 (step @p161 :rule ho_cong :premises (@p160 @p127)) % 0.36/0.61 (step @p162 :rule ho_cong :premises (@p161 @p142)) % 0.36/0.61 (step @p163 :rule cong :premises (@p133) :args (@t165)) % 0.36/0.61 (step @p164 :rule cong :premises (@p163) :args (@t166)) % 0.36/0.61 (step @p165 :rule exists-elim :args ((= @t75 @t166))) % 0.36/0.61 (step @p166 :rule trans :premises (@p165 @p164)) % 0.36/0.61 (step @p167 :rule cong :premises (@p166) :args (@t77)) % 0.36/0.61 (step @p168 :rule trans :premises (@p30 @p167)) % 0.36/0.61 (step @p169 :rule ho_cong :premises (@p168 @p127)) % 0.36/0.61 (step @p170 :rule refl :args (@t100)) % 0.36/0.61 (step @p171 :rule refl :args (@t19)) % 0.36/0.61 (step @p172 :rule cong :premises (@p171 @p170) :args ((= @t19 @t100))) % 0.36/0.61 (step @p173 :rule symm :premises (@p172)) % 0.36/0.61 (step @p174 :rule eq_resolve :premises (@p171 @p173)) % 0.36/0.61 (step @p175 :rule refl :args (@t155)) % 0.36/0.61 (step @p176 :rule refl :args (@t21)) % 0.36/0.61 (step @p177 :rule cong :premises (@p176 @p175) :args ((= @t21 @t155))) % 0.36/0.61 (step @p178 :rule symm :premises (@p177)) % 0.36/0.61 (step @p179 :rule eq_resolve :premises (@p176 @p178)) % 0.36/0.61 (step @p180 :rule cong :premises (@p179) :args (@t24)) % 0.36/0.61 (step @p181 :rule nary_cong :premises (@p180 @p174) :args (@t167)) % 0.36/0.61 (step @p182 :rule cong :premises (@p181) :args ((forall @t33 @t167))) % 0.36/0.61 (step @p183 :rule bool-impl-elim :args (@t21 @t19)) % 0.36/0.61 (step @p184 :rule cong :premises (@p183) :args (@t34)) % 0.36/0.61 (step @p185 :rule trans :premises (@p184 @p182)) % 0.36/0.61 (step @p186 :rule cong :premises (@p185) :args (@t35)) % 0.36/0.61 (step @p187 :rule trans :premises (@p14 @p186)) % 0.36/0.61 (step @p188 :rule ho_cong :premises (@p187 @p169)) % 0.36/0.61 (step @p189 :rule ho_cong :premises (@p188 @p80)) % 0.36/0.61 (step @p190 :rule cong :premises (@p189 @p162) :args (@t5)) % 0.36/0.61 (step @p191 :rule cong :premises (@p190) :args (@t7)) % 0.36/0.61 (step @p192 :rule cong :premises (@p191) :args (@t8)) % 0.36/0.61 (step @p193 :rule trans :premises (@p192 @p126)) % 0.36/0.61 (step @p194 :rule eq_resolve :premises (@p1 @p193)) % 0.36/0.61 (step @p195 :rule skolemize :premises (@p194)) % 0.36/0.61 (step @p196 :rule bool-double-not-elim :args (@t171)) % 0.36/0.61 (step @p197 :rule refl :args (@t181)) % 0.36/0.61 (step @p198 :rule nary_cong :premises (@p197 @p196) :args ((or @t181 (not @t180)))) % 0.36/0.61 (step @p199 :rule cnf_or_neg :args (@t181 0)) % 0.36/0.61 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.36/0.61 (step @p201 :rule reordering :premises (@p200) :args ((or @t171 @t181))) % 0.36/0.61 (step @p202 :rule chain_m_resolution :premises (@p201 @p195) :args (@t171 @t182 @t183)) % 0.36/0.61 (step @p203 :rule cnf_or_neg :args (@t181 2)) % 0.36/0.61 (step @p204 :rule chain_m_resolution :premises (@p203 @p195) :args ((not @t177) @t182 @t183)) % 0.36/0.61 (step @p205 :rule bool-double-not-elim :args (@t178)) % 0.36/0.61 (step @p206 :rule nary_cong :premises (@p197 @p205) :args ((or @t181 (not @t179)))) % 0.36/0.61 (step @p207 :rule cnf_or_neg :args (@t181 1)) % 0.36/0.61 (step @p208 :rule eq_resolve :premises (@p207 @p206)) % 0.36/0.61 (step @p209 :rule reordering :premises (@p208) :args ((or @t178 @t181))) % 0.36/0.61 (step @p210 :rule chain_m_resolution :premises (@p209 @p195) :args (@t178 @t182 @t183)) % 0.36/0.61 (assume-push @p235 @t175) % 0.36/0.61 (step @p212 :rule instantiate :premises (@p235) :args ((@list @t172))) % 0.36/0.61 (step-pop @p236 :rule scope :premises (@p212)) % 0.36/0.61 (step @p213 :rule process_scope :premises (@p236) :args (@t179)) % 0.36/0.61 (step @p215 :rule implies_elim :premises (@p213)) % 0.36/0.61 (step @p216 :rule reordering :premises (@p215) :args ((or @t179 @t176))) % 0.36/0.61 (step @p217 :rule chain_m_resolution :premises (@p216 @p210) :args (@t176 (@list false) (@list @t178))) % 0.36/0.61 (step @p218 :rule refl :args (@t184)) % 0.36/0.61 (step @p219 :rule bool-double-not-elim :args (@t175)) % 0.36/0.61 (step @p220 :rule refl :args (@t177)) % 0.36/0.61 (step @p221 :rule nary_cong :premises (@p220 @p219 @p218) :args ((or @t177 (not @t176) @t184))) % 0.36/0.61 (step @p222 :rule cnf_and_neg :args (@t177)) % 0.36/0.61 (step @p223 :rule eq_resolve :premises (@p222 @p221)) % 0.36/0.61 (step @p224 :rule reordering :premises (@p223) :args ((or @t175 @t177 @t184))) % 0.36/0.61 (step @p225 :rule chain_m_resolution :premises (@p224 @p217 @p204) :args (@t184 (@list true true) (@list @t175 @t177))) % 0.36/0.61 (step @p226 :rule cnf_or_pos :args (@t185)) % 0.36/0.61 (step @p227 :rule reordering :premises (@p226) :args ((or @t179 @t173 @t186))) % 0.36/0.61 (step @p228 :rule chain_m_resolution :premises (@p227 @p210 @p225) :args (@t186 (@list false true) (@list @t178 @t173))) % 0.36/0.61 (assume-push @p237 @t171) % 0.36/0.61 (step @p230 :rule instantiate :premises (@p202) :args ((@list @t172 @t174))) % 0.36/0.61 (step-pop @p238 :rule scope :premises (@p230)) % 0.36/0.61 (step @p231 :rule process_scope :premises (@p238) :args (@t185)) % 0.36/0.61 (step @p233 :rule implies_elim :premises (@p231)) % 0.36/0.61 (step @p234 false :rule chain_m_resolution :premises (@p233 @p228 @p202) :args (false (@list true false) (@list @t185 @t171))) % 0.36/0.61 ) % 0.36/0.61 % SZS output end Proof % 0.36/0.61 % cvc5 exiting %------------------------------------------------------------------------------