%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL604^1 : TPTP v9.3.1. 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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:09 AM UTC 2026 % Result : Theorem 0.29s 0.59s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL604^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.05 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.13/0.38 % Computer : n008.cluster.edu % 0.13/0.38 % Model : x86_64 x86_64 % 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.38 % Memory : 8046.5625MB % 0.13/0.38 % OS : Linux 6.8.0-71-generic % 0.13/0.38 % CPULimit : 300 % 0.13/0.38 % WCLimit : 300 % 0.13/0.38 % DateTime : Sat Sep 5 01:45:53 UTC 2026 % 0.13/0.39 % CPUTime : % 0.21/0.47 %----Proving TH0 % 0.29/0.59 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.59 % SZS status Theorem % 0.29/0.59 % SZS output start Proof % 0.29/0.59 ( % 0.29/0.59 (declare-sort $$unsorted 0) % 0.29/0.59 (declare-sort tptp.individuals 0) % 0.29/0.59 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.29/0.59 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.29/0.59 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.29/0.59 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.29/0.59 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.29/0.59 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "V" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.29/0.59 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.29/0.59 (define tptp.mbox () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.29/0.59 (define tptp.mdia () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.29/0.59 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.29/0.59 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.29/0.59 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.59 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.59 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.59 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.59 (define tptp.cartesian_product () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3 _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1)))))))) % 0.29/0.59 (define tptp.pair_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "V" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1 _let_4 _let_2) (or (= _let_4 _let_3) (= _let_2 _let_1)))))))) % 0.29/0.59 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$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))))))) % 0.29/0.59 (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))))))))) % 0.29/0.59 (define tptp.is_rel_on () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "B" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_4 _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ _let_5 _let_3) _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1))))))))))) % 0.29/0.59 (define tptp.restrict_rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.59 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 0.29/0.59 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R2" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (@var "R1" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_5 _let_3 _let_4 _let_1) (exists (@list _let_2) (and (_ (_ _let_5 _let_4) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.29/0.59 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.29/0.59 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.29/0.59 (define tptp.symmetric () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.59 (define tptp.transitive () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.29/0.59 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 0.29/0.59 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.29/0.59 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.29/0.59 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.29/0.59 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S1" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4) (exists (@list _let_2) (and (_ _let_4 _let_2) (forall (@list _let_1) (= (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.29/0.59 (define tptp.restrict_rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.59 (define tptp.rel_field () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (or (_ (_ tptp.rel_domain _let_2) _let_1) (_ (_ tptp.rel_codomain _let_2) _let_1)))))) % 0.29/0.59 (define tptp.well_founded () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "Z" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (not (_ _let_2 _let_1))))))))))))))) % 0.29/0.59 (define tptp.upwards_well_founded () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (@var "Z" $$unsorted))) (lambda (@list _let_4) (forall (@list _let_2 _let_5) (=> (_ _let_2 _let_5) (exists (@list _let_3) (and (_ _let_2 _let_3) (forall (@list _let_1) (=> (_ (_ _let_4 _let_3) _let_3) (not (_ _let_2 _let_1))))))))))))))) % 0.29/0.59 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.29/0.59 (define @t2 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.29/0.59 (define @t3 () (_ tptp.mbox @t2)) % 0.29/0.59 (define @t4 () (_ @t3 @t1)) % 0.29/0.59 (define @t5 () (_ tptp.mimpl @t4)) % 0.29/0.59 (define @t6 () (and (_ tptp.mvalid (_ @t5 (_ @t3 @t4))) (_ tptp.mvalid (_ @t5 @t1)))) % 0.29/0.59 (define @t7 () (@list @t1)) % 0.29/0.59 (define @t8 () (forall @t7 @t6)) % 0.29/0.59 (define @t9 () (_ tptp.transitive @t2)) % 0.29/0.59 (define @t10 () (_ tptp.reflexive @t2)) % 0.29/0.59 (define @t11 () (and @t10 @t9)) % 0.29/0.59 (define @t12 () (=> @t11 @t8)) % 0.29/0.59 (define @t13 () (@list @t2)) % 0.29/0.59 (define @t14 () (forall @t13 @t12)) % 0.29/0.59 (define @t15 () (not @t14)) % 0.29/0.59 (define @t16 () (@var "X" $$unsorted)) % 0.29/0.59 (define @t17 () (@list @t16)) % 0.29/0.59 (define @t18 () (lambda @t17 false)) % 0.29/0.59 (define @t19 () (lambda @t17 true)) % 0.29/0.59 (define @t20 () (@var "U" $$unsorted)) % 0.29/0.59 (define @t21 () (@var "X" (-> $$unsorted Bool))) % 0.29/0.59 (define @t22 () (_ @t21 @t20)) % 0.29/0.59 (define @t23 () (lambda (@list @t21 @t20) (not @t22))) % 0.29/0.59 (define @t24 () (@var "Y" (-> $$unsorted Bool))) % 0.29/0.59 (define @t25 () (_ @t24 @t20)) % 0.29/0.59 (define @t26 () (@list @t21 @t24 @t20)) % 0.29/0.59 (define @t27 () (lambda @t26 (or @t22 @t25))) % 0.29/0.59 (define @t28 () (lambda @t26 (and @t22 @t25))) % 0.29/0.59 (define @t29 () (@var "__flatten_var_0" $$unsorted)) % 0.29/0.59 (define @t30 () (@var "V" (-> $$unsorted Bool))) % 0.29/0.59 (define @t31 () (@var "U" (-> $$unsorted Bool))) % 0.29/0.59 (define @t32 () (@list @t31 @t30 @t29)) % 0.29/0.59 (define @t33 () (lambda @t32 (_ (_ (_ tptp.mor (_ tptp.mnot @t31)) @t30) @t29))) % 0.29/0.59 (define @t34 () (lambda @t32 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t31) @t30)) (_ (_ tptp.mimpl @t30) @t31)) @t29))) % 0.29/0.59 (define @t35 () (@var "Y" $$unsorted)) % 0.29/0.59 (define @t36 () (@var "P" (-> $$unsorted Bool))) % 0.29/0.59 (define @t37 () (_ @t36 @t35)) % 0.29/0.59 (define @t38 () (_ @t2 @t16)) % 0.29/0.59 (define @t39 () (_ @t38 @t35)) % 0.29/0.59 (define @t40 () (@list @t35)) % 0.29/0.59 (define @t41 () (forall @t40 (=> @t39 @t37))) % 0.29/0.59 (define @t42 () (@list @t2 @t36 @t16)) % 0.29/0.59 (define @t43 () (lambda @t42 @t41)) % 0.29/0.59 (define @t44 () (lambda @t42 (exists @t40 (and @t39 @t37)))) % 0.29/0.59 (define @t45 () (@var "W" $$unsorted)) % 0.29/0.59 (define @t46 () (@var "X" tptp.individuals)) % 0.29/0.59 (define @t47 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.29/0.59 (define @t48 () (_ (_ @t47 @t46) @t45)) % 0.29/0.59 (define @t49 () (@list @t46)) % 0.29/0.59 (define @t50 () (@list @t47 @t45)) % 0.29/0.59 (define @t51 () (lambda @t50 (forall @t49 @t48))) % 0.29/0.59 (define @t52 () (lambda @t50 (exists @t49 @t48))) % 0.29/0.59 (define @t53 () (_ @t36 @t45)) % 0.29/0.59 (define @t54 () (@list @t45)) % 0.29/0.59 (define @t55 () (forall @t54 @t53)) % 0.29/0.59 (define @t56 () (@list @t36)) % 0.29/0.59 (define @t57 () (lambda @t56 @t55)) % 0.29/0.59 (define @t58 () (lambda @t56 (exists @t54 @t53))) % 0.29/0.59 (define @t59 () (not @t53)) % 0.29/0.59 (define @t60 () (lambda @t56 (exists @t54 @t59))) % 0.29/0.59 (define @t61 () (lambda @t56 (forall @t54 @t59))) % 0.29/0.59 (define @t62 () (@var "V" $$unsorted)) % 0.29/0.59 (define @t63 () (lambda (@list @t21 @t24 @t20 @t62) (and @t22 (_ @t24 @t62)))) % 0.29/0.59 (define @t64 () (lambda (@list @t16 @t35 @t20 @t62) (or (= @t20 @t16) (= @t62 @t35)))) % 0.29/0.59 (define @t65 () (= @t16 @t35)) % 0.29/0.59 (define @t66 () (@var "S" (-> $$unsorted Bool))) % 0.29/0.59 (define @t67 () (_ @t66 @t16)) % 0.29/0.59 (define @t68 () (lambda (@list @t66 @t16 @t35) (and @t67 @t65))) % 0.29/0.59 (define @t69 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.29/0.59 (define @t70 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.29/0.59 (define @t71 () (_ (_ @t70 @t16) @t35)) % 0.29/0.59 (define @t72 () (@list @t16 @t35)) % 0.29/0.59 (define @t73 () (lambda (@list @t70 @t69) (forall @t72 (=> @t71 (_ (_ @t69 @t16) @t35))))) % 0.29/0.59 (define @t74 () (@var "B" (-> $$unsorted Bool))) % 0.29/0.59 (define @t75 () (lambda (@list @t2 @t1 @t74) (forall @t72 (=> @t39 (and (_ @t1 @t16) (_ @t74 @t35)))))) % 0.29/0.59 (define @t76 () (@list @t2 @t66 @t16 @t35)) % 0.29/0.59 (define @t77 () (lambda @t76 (and @t67 @t39))) % 0.29/0.59 (define @t78 () (lambda @t72 @t65)) % 0.29/0.59 (define @t79 () (@var "Z" $$unsorted)) % 0.29/0.59 (define @t80 () (lambda (@list @t70 @t69 @t16 @t79) (exists @t40 (and @t71 (_ (_ @t69 @t35) @t79))))) % 0.29/0.59 (define @t81 () (_ @t38 @t16)) % 0.29/0.59 (define @t82 () (forall @t17 @t81)) % 0.29/0.59 (define @t83 () (lambda @t13 @t82)) % 0.29/0.59 (define @t84 () (lambda @t13 (forall @t17 (not @t81)))) % 0.29/0.59 (define @t85 () (_ @t2 @t35)) % 0.29/0.59 (define @t86 () (_ @t85 @t16)) % 0.29/0.59 (define @t87 () (lambda @t13 (forall @t72 (=> @t39 @t86)))) % 0.29/0.59 (define @t88 () (_ @t38 @t79)) % 0.29/0.59 (define @t89 () (_ @t85 @t79)) % 0.29/0.59 (define @t90 () (and @t39 @t89)) % 0.29/0.59 (define @t91 () (@list @t16 @t35 @t79)) % 0.29/0.59 (define @t92 () (forall @t91 (=> @t90 @t88))) % 0.29/0.59 (define @t93 () (lambda @t13 @t92)) % 0.29/0.59 (define @t94 () (lambda @t13 (and @t10 (_ tptp.symmetric @t2) @t9))) % 0.29/0.59 (define @t95 () (lambda (@list @t2 @t35) (exists @t17 @t39))) % 0.29/0.59 (define @t96 () (@list @t2 @t16)) % 0.29/0.59 (define @t97 () (lambda @t96 (exists @t40 @t39))) % 0.29/0.59 (define @t98 () (lambda (@list @t2 @t16 @t35) @t86)) % 0.29/0.59 (define @t99 () (@var "S1" (-> $$unsorted Bool))) % 0.29/0.59 (define @t100 () (lambda (@list @t2 @t99) (exists @t17 (and (_ @t99 @t16) (forall @t40 (= (_ @t99 @t35) @t39)))))) % 0.29/0.59 (define @t101 () (lambda @t76 (and (_ @t66 @t35) @t39))) % 0.29/0.59 (define @t102 () (lambda @t96 (or (_ (_ tptp.rel_domain @t2) @t16) (_ (_ tptp.rel_codomain @t2) @t16)))) % 0.29/0.59 (define @t103 () (not (_ @t21 @t45))) % 0.29/0.59 (define @t104 () (_ @t21 @t35)) % 0.29/0.59 (define @t105 () (_ @t21 @t79)) % 0.29/0.59 (define @t106 () (@list @t21 @t79)) % 0.29/0.59 (define @t107 () (lambda @t13 (forall @t106 (=> @t105 (exists @t40 (and @t104 (forall @t54 (=> (_ @t85 @t45) @t103)))))))) % 0.29/0.59 (define @t108 () (lambda @t13 (forall @t106 (=> @t105 (exists @t40 (and @t104 (forall @t54 (=> (_ @t85 @t35) @t103)))))))) % 0.29/0.59 (define @t109 () (@var "BOUND_VARIABLE_8468" $$unsorted)) % 0.29/0.59 (define @t110 () (@var "BOUND_VARIABLE_8466" (-> $$unsorted Bool))) % 0.29/0.59 (define @t111 () (or (not (forall @t40 (or (not (_ @t2 @t109 @t35)) (_ @t110 @t35)))) (_ @t110 @t109))) % 0.29/0.59 (define @t112 () (@var "BOUND_VARIABLE_8452" $$unsorted)) % 0.29/0.59 (define @t113 () (@var "BOUND_VARIABLE_8446" (-> $$unsorted Bool))) % 0.29/0.59 (define @t114 () (@var "BOUND_VARIABLE_8450" $$unsorted)) % 0.29/0.59 (define @t115 () (@var "BOUND_VARIABLE_8448" $$unsorted)) % 0.29/0.59 (define @t116 () (or (not (forall @t40 (or (not (_ @t2 @t115 @t35)) (_ @t113 @t35)))) (not (_ @t2 @t115 @t114)) (not (_ @t2 @t114 @t112)) (_ @t113 @t112))) % 0.29/0.59 (define @t117 () (and @t116 @t111)) % 0.29/0.59 (define @t118 () (_ @t2 @t16 @t79)) % 0.29/0.59 (define @t119 () (_ @t2 @t35 @t79)) % 0.29/0.59 (define @t120 () (_ @t2 @t16 @t35)) % 0.29/0.59 (define @t121 () (not @t120)) % 0.29/0.59 (define @t122 () (forall @t91 (or @t121 (not @t119) @t118))) % 0.29/0.59 (define @t123 () (not @t122)) % 0.29/0.59 (define @t124 () (_ @t2 @t16 @t16)) % 0.29/0.59 (define @t125 () (forall @t17 @t124)) % 0.29/0.59 (define @t126 () (not @t125)) % 0.29/0.59 (define @t127 () (or @t126 @t123 @t117)) % 0.29/0.59 (define @t128 () (forall (@list @t2 @t113 @t115 @t114 @t112 @t110 @t109) @t127)) % 0.29/0.59 (define @t129 () (@quantifiers_skolemize @t128 5)) % 0.29/0.59 (define @t130 () (@quantifiers_skolemize @t128 6)) % 0.29/0.59 (define @t131 () (@quantifiers_skolemize @t128 0)) % 0.29/0.59 (define @t132 () (forall @t40 (or (not (_ @t131 @t130 @t35)) (_ @t129 @t35)))) % 0.29/0.59 (define @t133 () (_ @t129 @t130)) % 0.29/0.59 (define @t134 () (not @t132)) % 0.29/0.59 (define @t135 () (or @t134 @t133)) % 0.29/0.59 (define @t136 () (@list @t130)) % 0.29/0.59 (define @t137 () (_ @t131 @t130 @t130)) % 0.29/0.59 (define @t138 () (not @t137)) % 0.29/0.59 (define @t139 () (or @t138 @t133)) % 0.29/0.59 (define @t140 () (@list @t113 @t115 @t114 @t112 @t110 @t109)) % 0.29/0.59 (define @t141 () (forall @t140 @t127)) % 0.29/0.59 (define @t142 () (forall (@list @t110 @t109) @t111)) % 0.29/0.59 (define @t143 () (@var "BOUND_VARIABLE_8421" (-> $$unsorted Bool))) % 0.29/0.59 (define @t144 () (forall @t140 @t111)) % 0.29/0.59 (define @t145 () (forall (@list @t113 @t115 @t114 @t112) @t116)) % 0.29/0.59 (define @t146 () (@var "BOUND_VARIABLE_8382" $$unsorted)) % 0.29/0.59 (define @t147 () (@var "BOUND_VARIABLE_8380" $$unsorted)) % 0.29/0.59 (define @t148 () (@var "BOUND_VARIABLE_8410" (-> $$unsorted Bool))) % 0.29/0.59 (define @t149 () (forall @t140 @t116)) % 0.29/0.59 (define @t150 () (and @t149 @t144)) % 0.29/0.59 (define @t151 () (forall @t140 @t117)) % 0.29/0.59 (define @t152 () (or @t126 @t123 @t151)) % 0.29/0.59 (define @t153 () (not (_ @t2 @t45 @t35))) % 0.29/0.59 (define @t154 () (or (not (forall @t40 (or @t153 (_ @t143 @t35)))) (_ @t143 @t45))) % 0.29/0.59 (define @t155 () (forall (@list @t143 @t45) @t154)) % 0.29/0.59 (define @t156 () (not (_ @t2 @t147 @t146))) % 0.29/0.59 (define @t157 () (not (_ @t2 @t45 @t147))) % 0.29/0.59 (define @t158 () (or (not (forall @t40 (or @t153 (_ @t148 @t35)))) @t157 @t156 (_ @t148 @t146))) % 0.29/0.59 (define @t159 () (forall (@list @t148 @t45 @t147 @t146) @t158)) % 0.29/0.59 (define @t160 () (and @t159 @t155)) % 0.29/0.59 (define @t161 () (or @t126 @t123 @t160)) % 0.29/0.59 (define @t162 () (and @t125 @t122)) % 0.29/0.59 (define @t163 () (forall (@list @t143) (forall @t54 @t154))) % 0.29/0.59 (define @t164 () (@list @t45 @t147 @t146)) % 0.29/0.59 (define @t165 () (forall (@list @t148) (forall @t164 @t158))) % 0.29/0.59 (define @t166 () (_ @t1 @t45)) % 0.29/0.59 (define @t167 () (_ @t1 @t35)) % 0.29/0.59 (define @t168 () (not (forall @t40 (or @t153 @t167)))) % 0.29/0.59 (define @t169 () (forall @t54 (or @t168 @t166))) % 0.29/0.59 (define @t170 () (forall @t7 @t169)) % 0.29/0.59 (define @t171 () (@list @t1)) % 0.29/0.59 (define @t172 () (_ @t1 @t146)) % 0.29/0.59 (define @t173 () (or @t168 @t157 @t156 @t172)) % 0.29/0.59 (define @t174 () (forall @t164 @t173)) % 0.29/0.59 (define @t175 () (forall @t7 @t174)) % 0.29/0.59 (define @t176 () (and @t175 @t170)) % 0.29/0.59 (define @t177 () (_ @t1 @t45)) % 0.29/0.59 (define @t178 () (or @t168 @t177)) % 0.29/0.59 (define @t179 () (not (_ @t2 @t29 @t35))) % 0.29/0.59 (define @t180 () (forall @t40 (or @t179 @t167))) % 0.29/0.59 (define @t181 () (not @t180)) % 0.29/0.59 (define @t182 () (@list @t29)) % 0.29/0.59 (define @t183 () (lambda @t182 (or @t181 (_ @t1 @t29)))) % 0.29/0.59 (define @t184 () (_ @t183 @t45)) % 0.29/0.59 (define @t185 () (forall @t54 @t184)) % 0.29/0.59 (define @t186 () (_ @t36 @t45)) % 0.29/0.59 (define @t187 () (lambda @t56 (forall @t54 @t186))) % 0.29/0.59 (define @t188 () (_ @t30 @t29)) % 0.29/0.59 (define @t189 () (@list @t30 @t29)) % 0.29/0.59 (define @t190 () (lambda @t189 (or @t181 @t188))) % 0.29/0.59 (define @t191 () (forall @t40 (or @t121 @t167))) % 0.29/0.59 (define @t192 () (lambda @t17 @t191)) % 0.29/0.59 (define @t193 () (_ @t192 @t29)) % 0.29/0.59 (define @t194 () (not @t193)) % 0.29/0.59 (define @t195 () (or @t194 @t188)) % 0.29/0.59 (define @t196 () (lambda @t189 @t195)) % 0.29/0.59 (define @t197 () (or (not (_ @t31 @t29)) @t188)) % 0.29/0.59 (define @t198 () (lambda @t32 @t197)) % 0.29/0.59 (define @t199 () (_ @t36 @t35)) % 0.29/0.59 (define @t200 () (forall @t40 (or @t121 @t199))) % 0.29/0.59 (define @t201 () (lambda (@list @t36 @t16) @t200)) % 0.29/0.59 (define @t202 () (_ (lambda @t42 @t200) @t2)) % 0.29/0.59 (define @t203 () (or @t157 @t156 @t172)) % 0.29/0.59 (define @t204 () (or @t168 @t203)) % 0.29/0.59 (define @t205 () (forall @t164 @t204)) % 0.29/0.59 (define @t206 () (@list @t147 @t146)) % 0.29/0.59 (define @t207 () (forall @t206 @t204)) % 0.29/0.59 (define @t208 () (forall @t206 @t203)) % 0.29/0.59 (define @t209 () (@var "BOUND_VARIABLE_8347" $$unsorted)) % 0.29/0.59 (define @t210 () (or @t168 @t208)) % 0.29/0.59 (define @t211 () (_ @t1 @t209)) % 0.29/0.59 (define @t212 () (not (_ @t2 @t35 @t209))) % 0.29/0.59 (define @t213 () (@list @t35 @t209)) % 0.29/0.59 (define @t214 () (or @t168 (forall @t213 (or @t153 @t212 @t211)))) % 0.29/0.59 (define @t215 () (forall @t213 (or @t179 @t212 @t211))) % 0.29/0.59 (define @t216 () (lambda @t182 (or @t181 @t215))) % 0.29/0.59 (define @t217 () (_ @t216 @t45)) % 0.29/0.59 (define @t218 () (forall @t54 @t217)) % 0.29/0.59 (define @t219 () (or @t121 @t212 @t211)) % 0.29/0.59 (define @t220 () (lambda @t17 (forall @t213 @t219))) % 0.29/0.59 (define @t221 () (_ @t220 @t29)) % 0.29/0.59 (define @t222 () (or @t181 @t221)) % 0.29/0.59 (define @t223 () (lambda @t182 @t222)) % 0.29/0.59 (define @t224 () (or @t212 @t211)) % 0.29/0.59 (define @t225 () (or @t121 @t224)) % 0.29/0.59 (define @t226 () (forall @t213 @t225)) % 0.29/0.59 (define @t227 () (@list @t209)) % 0.29/0.59 (define @t228 () (forall @t227 @t225)) % 0.29/0.59 (define @t229 () (forall @t227 @t224)) % 0.29/0.59 (define @t230 () (@var "BOUND_VARIABLE_8331" $$unsorted)) % 0.29/0.59 (define @t231 () (@list @t230)) % 0.29/0.59 (define @t232 () (or @t121 @t229)) % 0.29/0.59 (define @t233 () (_ @t1 @t230)) % 0.29/0.59 (define @t234 () (@list @t230)) % 0.29/0.59 (define @t235 () (forall @t234 (or (not (_ @t2 @t35 @t230)) @t233))) % 0.29/0.59 (define @t236 () (or @t121 (_ @t192 @t35))) % 0.29/0.59 (define @t237 () (forall @t40 @t236)) % 0.29/0.59 (define @t238 () (lambda @t17 @t237)) % 0.29/0.59 (define @t239 () (_ @t202 @t1)) % 0.29/0.59 (define @t240 () (_ @t198 @t239)) % 0.29/0.59 (define @t241 () (and (_ @t187 (_ @t240 (_ @t202 @t239))) (_ @t187 (_ @t240 @t1)))) % 0.29/0.59 (define @t242 () (forall @t7 @t241)) % 0.29/0.59 (define @t243 () (_ (lambda @t13 @t122) @t2)) % 0.29/0.59 (define @t244 () (_ (lambda @t13 @t125) @t2)) % 0.29/0.59 (define @t245 () (and @t244 @t243)) % 0.29/0.59 (define @t246 () (=> @t245 @t242)) % 0.29/0.59 (define @t247 () (forall @t13 @t246)) % 0.29/0.59 (define @t248 () (not @t39)) % 0.29/0.59 (define @t249 () (or @t248 @t37)) % 0.29/0.59 (define @t250 () (not (_ @t31 @t20))) % 0.29/0.59 (define @t251 () (@list @t20)) % 0.29/0.59 (define @t252 () (lambda @t251 (or @t250 (_ @t30 @t20)))) % 0.29/0.59 (define @t253 () (@list @t24 @t20)) % 0.29/0.59 (define @t254 () (lambda @t251 @t250)) % 0.29/0.59 (define @t255 () (_ @t254 @t20)) % 0.29/0.59 (define @t256 () (or @t255 @t25)) % 0.29/0.59 (define @t257 () (lambda @t253 @t256)) % 0.29/0.59 (define @t258 () (not @t89)) % 0.29/0.59 (define @t259 () (or @t248 @t258 @t88)) % 0.29/0.59 (define @t260 () (forall @t17 (_ @t131 @t16 @t16))) % 0.29/0.59 (define @t261 () (@quantifiers_skolemize @t128 4)) % 0.29/0.59 (define @t262 () (@quantifiers_skolemize @t128 1)) % 0.29/0.59 (define @t263 () (_ @t262 @t261)) % 0.29/0.59 (define @t264 () (@quantifiers_skolemize @t128 3)) % 0.29/0.59 (define @t265 () (_ @t131 @t264 @t261)) % 0.29/0.59 (define @t266 () (not @t265)) % 0.29/0.59 (define @t267 () (@quantifiers_skolemize @t128 2)) % 0.29/0.59 (define @t268 () (_ @t131 @t267 @t264)) % 0.29/0.59 (define @t269 () (not @t268)) % 0.29/0.59 (define @t270 () (forall @t40 (or (not (_ @t131 @t267 @t35)) (_ @t262 @t35)))) % 0.29/0.59 (define @t271 () (not @t270)) % 0.29/0.59 (define @t272 () (or @t271 @t269 @t266 @t263)) % 0.29/0.59 (define @t273 () (and @t272 @t135)) % 0.29/0.59 (define @t274 () (forall @t91 (or (not (_ @t131 @t16 @t35)) (not (_ @t131 @t35 @t79)) (_ @t131 @t16 @t79)))) % 0.29/0.59 (define @t275 () (not @t274)) % 0.29/0.59 (define @t276 () (not @t260)) % 0.29/0.59 (define @t277 () (or @t276 @t275 @t273)) % 0.29/0.59 (define @t278 () (@list true)) % 0.29/0.59 (define @t279 () (@list @t277)) % 0.29/0.59 (define @t280 () (@list @t272)) % 0.29/0.59 (define @t281 () (_ @t131 @t267 @t261)) % 0.29/0.59 (define @t282 () (not @t281)) % 0.29/0.59 (define @t283 () (or @t282 @t263)) % 0.29/0.59 (define @t284 () (or @t269 @t266 @t281)) % 0.29/0.59 (assume @p1 @t15) % 0.29/0.59 (assume @p2 true) % 0.29/0.59 (step @p3 (= tptp.mfalse @t18) :rule refl :args (@t18)) % 0.29/0.59 (step @p4 (= tptp.mtrue @t19) :rule refl :args (@t19)) % 0.29/0.59 (step @p5 (= tptp.mnot @t23) :rule refl :args (@t23)) % 0.29/0.59 (step @p6 (= tptp.mor @t27) :rule refl :args (@t27)) % 0.29/0.59 (step @p7 (= tptp.mand @t28) :rule refl :args (@t28)) % 0.29/0.59 (step @p8 (= tptp.mimpl @t33) :rule refl :args (@t33)) % 0.29/0.59 (step @p9 (= tptp.miff @t34) :rule refl :args (@t34)) % 0.29/0.59 (step @p10 (= tptp.mbox @t43) :rule refl :args (@t43)) % 0.29/0.59 (step @p11 (= tptp.mdia @t44) :rule refl :args (@t44)) % 0.29/0.59 (step @p12 (= tptp.mall @t51) :rule refl :args (@t51)) % 0.29/0.59 (step @p13 (= tptp.mexists @t52) :rule refl :args (@t52)) % 0.29/0.59 (step @p14 (= tptp.mvalid @t57) :rule refl :args (@t57)) % 0.29/0.59 (step @p15 (= tptp.msatisfiable @t58) :rule refl :args (@t58)) % 0.29/0.59 (step @p16 (= tptp.mcountersatisfiable @t60) :rule refl :args (@t60)) % 0.29/0.59 (step @p17 (= tptp.minvalid @t61) :rule refl :args (@t61)) % 0.29/0.59 (step @p18 (= tptp.cartesian_product @t63) :rule refl :args (@t63)) % 0.29/0.59 (step @p19 (= tptp.pair_rel @t64) :rule refl :args (@t64)) % 0.29/0.59 (step @p20 (= tptp.id_rel @t68) :rule refl :args (@t68)) % 0.29/0.59 (step @p21 (= tptp.sub_rel @t73) :rule refl :args (@t73)) % 0.29/0.59 (step @p22 (= tptp.is_rel_on @t75) :rule refl :args (@t75)) % 0.29/0.59 (step @p23 (= tptp.restrict_rel_domain @t77) :rule refl :args (@t77)) % 0.29/0.59 (step @p24 (= tptp.rel_diagonal @t78) :rule refl :args (@t78)) % 0.29/0.59 (step @p25 (= tptp.rel_composition @t80) :rule refl :args (@t80)) % 0.29/0.59 (step @p26 (= tptp.reflexive @t83) :rule refl :args (@t83)) % 0.29/0.59 (step @p27 (= tptp.irreflexive @t84) :rule refl :args (@t84)) % 0.29/0.59 (step @p28 (= tptp.symmetric @t87) :rule refl :args (@t87)) % 0.29/0.59 (step @p29 (= tptp.transitive @t93) :rule refl :args (@t93)) % 0.29/0.59 (step @p30 (= tptp.equiv_rel @t94) :rule refl :args (@t94)) % 0.29/0.59 (step @p31 (= tptp.rel_codomain @t95) :rule refl :args (@t95)) % 0.29/0.59 (step @p32 (= tptp.rel_domain @t97) :rule refl :args (@t97)) % 0.29/0.59 (step @p33 (= tptp.rel_inverse @t98) :rule refl :args (@t98)) % 0.29/0.59 (step @p34 (= tptp.equiv_classes @t100) :rule refl :args (@t100)) % 0.29/0.59 (step @p35 (= tptp.restrict_rel_codomain @t101) :rule refl :args (@t101)) % 0.29/0.59 (step @p36 (= tptp.rel_field @t102) :rule refl :args (@t102)) % 0.29/0.59 (step @p37 (= tptp.well_founded @t107) :rule refl :args (@t107)) % 0.29/0.59 (step @p38 (= tptp.upwards_well_founded @t108) :rule refl :args (@t108)) % 0.29/0.59 (step @p39 :rule 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cnf_or_neg :args (@t272 0)) % 0.29/0.59 (step @p306 :rule eq_resolve :premises (@p305 @p304)) % 0.29/0.59 (step @p307 :rule reordering :premises (@p306) :args ((or @t270 @t272))) % 0.29/0.59 (step @p308 :rule chain_m_resolution :premises (@p307 @p301) :args (@t270 @t278 @t280)) % 0.29/0.59 (assume-push @p344 @t270) % 0.29/0.59 (step @p310 :rule instantiate :premises (@p344) :args ((@list @t261))) % 0.29/0.59 (step-pop @p345 :rule scope :premises (@p310)) % 0.29/0.59 (step @p311 :rule process_scope :premises (@p345) :args (@t283)) % 0.29/0.59 (step @p313 :rule implies_elim :premises (@p311)) % 0.29/0.59 (step @p314 :rule chain_m_resolution :premises (@p313 @p308) :args (@t283 (@list false) (@list @t270))) % 0.29/0.59 (step @p315 :rule cnf_or_neg :args (@t272 3)) % 0.29/0.59 (step @p316 :rule chain_m_resolution :premises (@p315 @p301) :args ((not @t263) @t278 @t280)) % 0.29/0.59 (step @p317 :rule bool-double-not-elim :args (@t274)) % 0.29/0.59 (step @p318 :rule nary_cong :premises (@p288 @p317) :args ((or @t277 (not @t275)))) % 0.29/0.59 (step @p319 :rule cnf_or_neg :args (@t277 1)) % 0.29/0.59 (step @p320 :rule eq_resolve :premises (@p319 @p318)) % 0.29/0.59 (step @p321 :rule reordering :premises (@p320) :args ((or @t274 @t277))) % 0.29/0.59 (step @p322 :rule chain_m_resolution :premises (@p321 @p286) :args (@t274 @t278 @t279)) % 0.29/0.59 (step @p323 :rule instantiate :premises (@p322) :args ((@list @t267 @t264 @t261))) % 0.29/0.60 (step @p324 :rule bool-double-not-elim :args (@t265)) % 0.29/0.60 (step @p325 :rule nary_cong :premises (@p303 @p324) :args ((or @t272 (not @t266)))) % 0.29/0.60 (step @p326 :rule cnf_or_neg :args (@t272 2)) % 0.29/0.60 (step @p327 :rule eq_resolve :premises (@p326 @p325)) % 0.29/0.60 (step @p328 :rule reordering :premises (@p327) :args ((or @t265 @t272))) % 0.29/0.60 (step @p329 :rule chain_m_resolution :premises (@p328 @p301) :args (@t265 @t278 @t280)) % 0.29/0.60 (step @p330 :rule bool-double-not-elim :args (@t268)) % 0.29/0.60 (step @p331 :rule nary_cong :premises (@p303 @p330) :args ((or @t272 (not @t269)))) % 0.29/0.60 (step @p332 :rule cnf_or_neg :args (@t272 1)) % 0.29/0.60 (step @p333 :rule eq_resolve :premises (@p332 @p331)) % 0.29/0.60 (step @p334 :rule reordering :premises (@p333) :args ((or @t268 @t272))) % 0.29/0.60 (step @p335 :rule chain_m_resolution :premises (@p334 @p301) :args (@t268 @t278 @t280)) % 0.29/0.60 (step @p336 :rule cnf_or_pos :args (@t284)) % 0.29/0.60 (step @p337 :rule reordering :premises (@p336) :args ((or @t269 @t266 @t281 (not @t284)))) % 0.29/0.60 (step @p338 :rule chain_m_resolution :premises (@p337 @p335 @p329 @p323) :args (@t281 (@list false false false) (@list @t268 @t265 @t284))) % 0.29/0.60 (step @p339 :rule cnf_or_pos :args (@t283)) % 0.29/0.60 (step @p340 :rule reordering :premises (@p339) :args ((or @t263 @t282 (not @t283)))) % 0.29/0.60 (step @p341 false :rule chain_m_resolution :premises (@p340 @p338 @p316 @p314) :args (false (@list false true false) (@list @t281 @t263 @t283))) % 0.29/0.60 ) % 0.29/0.60 % SZS output end Proof % 0.29/0.60 % cvc5 exiting %------------------------------------------------------------------------------