%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL595^1 : 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 : n001.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 11:23:08 AM UTC 2026 % Result : Theorem 0.20s 0.54s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL595^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.10/0.36 % Computer : n001.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 07:43:46 UTC 2026 % 0.10/0.36 % CPUTime : % 0.14/0.43 %----Proving TH0 % 0.20/0.54 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.20/0.54 % SZS status Theorem % 0.20/0.54 % SZS output start Proof % 0.20/0.54 ( % 0.20/0.54 (declare-sort $$unsorted 0) % 0.20/0.54 (declare-sort tptp.individuals 0) % 0.20/0.54 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.20/0.54 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.20/0.54 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.20/0.54 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.20/0.54 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.20/0.54 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.20/0.54 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.54 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.20/0.54 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.20/0.54 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.20/0.54 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.54 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.54 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.54 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.54 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.54 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.54 (define tptp.cartesian_product () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3 _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1)))))))) % 0.20/0.54 (define tptp.pair_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "V" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1 _let_4 _let_2) (or (= _let_4 _let_3) (= _let_2 _let_1)))))))) % 0.20/0.54 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$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))))))) % 0.20/0.54 (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))))))))) % 0.20/0.54 (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))))))))))) % 0.20/0.54 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.20/0.54 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 0.20/0.54 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.20/0.54 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.20/0.54 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.20/0.54 (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)))))))) % 0.20/0.54 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.20/0.54 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 0.20/0.54 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.54 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.20/0.54 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.20/0.54 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$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))))))))))) % 0.20/0.54 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.20/0.54 (define tptp.rel_field () (let ((_let_1 (@var "X" $$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)))))) % 0.20/0.54 (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))))))))))))))) % 0.20/0.54 (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))))))))))))))) % 0.20/0.54 (define @t1 () (@var "A" (-> $$unsorted Bool))) % 0.20/0.54 (define @t2 () (@list @t1)) % 0.20/0.54 (define @t3 () (forall @t2 (_ tptp.mvalid (_ (_ tptp.mimpl (_ (_ tptp.mbox tptp.r) @t1)) @t1)))) % 0.20/0.54 (define @t4 () (= @t3 (_ tptp.reflexive tptp.r))) % 0.20/0.54 (define @t5 () (not @t4)) % 0.20/0.54 (define @t6 () (@var "X" $$unsorted)) % 0.20/0.54 (define @t7 () (@list @t6)) % 0.20/0.54 (define @t8 () (lambda @t7 false)) % 0.20/0.54 (define @t9 () (lambda @t7 true)) % 0.20/0.54 (define @t10 () (@var "U" $$unsorted)) % 0.20/0.54 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.20/0.54 (define @t12 () (_ @t11 @t10)) % 0.20/0.54 (define @t13 () (lambda (@list @t11 @t10) (not @t12))) % 0.20/0.54 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.20/0.54 (define @t15 () (_ @t14 @t10)) % 0.20/0.54 (define @t16 () (@list @t11 @t14 @t10)) % 0.20/0.54 (define @t17 () (lambda @t16 (or @t12 @t15))) % 0.20/0.54 (define @t18 () (lambda @t16 (and @t12 @t15))) % 0.20/0.54 (define @t19 () (@var "__flatten_var_0" $$unsorted)) % 0.20/0.54 (define @t20 () (@var "V" (-> $$unsorted Bool))) % 0.20/0.54 (define @t21 () (@var "U" (-> $$unsorted Bool))) % 0.20/0.54 (define @t22 () (@list @t21 @t20 @t19)) % 0.20/0.54 (define @t23 () (lambda @t22 (_ (_ (_ tptp.mor (_ tptp.mnot @t21)) @t20) @t19))) % 0.20/0.54 (define @t24 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t21) @t20)) (_ (_ tptp.mimpl @t20) @t21)) @t19))) % 0.20/0.54 (define @t25 () (@var "Y" $$unsorted)) % 0.20/0.54 (define @t26 () (@var "P" (-> $$unsorted Bool))) % 0.20/0.54 (define @t27 () (_ @t26 @t25)) % 0.20/0.54 (define @t28 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.20/0.54 (define @t29 () (_ @t28 @t6)) % 0.20/0.54 (define @t30 () (_ @t29 @t25)) % 0.20/0.54 (define @t31 () (@list @t25)) % 0.20/0.54 (define @t32 () (forall @t31 (=> @t30 @t27))) % 0.20/0.54 (define @t33 () (@list @t28 @t26 @t6)) % 0.20/0.54 (define @t34 () (lambda @t33 @t32)) % 0.20/0.54 (define @t35 () (lambda @t33 (exists @t31 (and @t30 @t27)))) % 0.20/0.54 (define @t36 () (@var "W" $$unsorted)) % 0.20/0.54 (define @t37 () (@var "X" tptp.individuals)) % 0.20/0.54 (define @t38 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.20/0.54 (define @t39 () (_ (_ @t38 @t37) @t36)) % 0.20/0.54 (define @t40 () (@list @t37)) % 0.20/0.54 (define @t41 () (@list @t38 @t36)) % 0.20/0.54 (define @t42 () (lambda @t41 (forall @t40 @t39))) % 0.20/0.54 (define @t43 () (lambda @t41 (exists @t40 @t39))) % 0.20/0.54 (define @t44 () (_ @t26 @t36)) % 0.20/0.54 (define @t45 () (@list @t36)) % 0.20/0.54 (define @t46 () (forall @t45 @t44)) % 0.20/0.54 (define @t47 () (@list @t26)) % 0.20/0.54 (define @t48 () (lambda @t47 @t46)) % 0.20/0.54 (define @t49 () (lambda @t47 (exists @t45 @t44))) % 0.20/0.54 (define @t50 () (not @t44)) % 0.20/0.54 (define @t51 () (lambda @t47 (exists @t45 @t50))) % 0.20/0.54 (define @t52 () (lambda @t47 (forall @t45 @t50))) % 0.20/0.54 (define @t53 () (@var "V" $$unsorted)) % 0.20/0.54 (define @t54 () (lambda (@list @t11 @t14 @t10 @t53) (and @t12 (_ @t14 @t53)))) % 0.20/0.54 (define @t55 () (lambda (@list @t6 @t25 @t10 @t53) (or (= @t10 @t6) (= @t53 @t25)))) % 0.20/0.54 (define @t56 () (= @t6 @t25)) % 0.20/0.54 (define @t57 () (@var "S" (-> $$unsorted Bool))) % 0.20/0.54 (define @t58 () (_ @t57 @t6)) % 0.20/0.54 (define @t59 () (lambda (@list @t57 @t6 @t25) (and @t58 @t56))) % 0.20/0.54 (define @t60 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.20/0.54 (define @t61 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.20/0.54 (define @t62 () (_ (_ @t61 @t6) @t25)) % 0.20/0.54 (define @t63 () (@list @t6 @t25)) % 0.20/0.54 (define @t64 () (lambda (@list @t61 @t60) (forall @t63 (=> @t62 (_ (_ @t60 @t6) @t25))))) % 0.20/0.54 (define @t65 () (@var "B" (-> $$unsorted Bool))) % 0.20/0.54 (define @t66 () (lambda (@list @t28 @t1 @t65) (forall @t63 (=> @t30 (and (_ @t1 @t6) (_ @t65 @t25)))))) % 0.20/0.54 (define @t67 () (@list @t28 @t57 @t6 @t25)) % 0.20/0.54 (define @t68 () (lambda @t67 (and @t58 @t30))) % 0.20/0.54 (define @t69 () (lambda @t63 @t56)) % 0.20/0.54 (define @t70 () (@var "Z" $$unsorted)) % 0.20/0.54 (define @t71 () (lambda (@list @t61 @t60 @t6 @t70) (exists @t31 (and @t62 (_ (_ @t60 @t25) @t70))))) % 0.20/0.54 (define @t72 () (_ @t29 @t6)) % 0.20/0.54 (define @t73 () (forall @t7 @t72)) % 0.20/0.54 (define @t74 () (@list @t28)) % 0.20/0.54 (define @t75 () (lambda @t74 @t73)) % 0.20/0.54 (define @t76 () (lambda @t74 (forall @t7 (not @t72)))) % 0.20/0.54 (define @t77 () (_ @t28 @t25)) % 0.20/0.54 (define @t78 () (_ @t77 @t6)) % 0.20/0.54 (define @t79 () (lambda @t74 (forall @t63 (=> @t30 @t78)))) % 0.20/0.54 (define @t80 () (lambda @t74 (forall (@list @t6 @t25 @t70) (=> (and @t30 (_ @t77 @t70)) (_ @t29 @t70))))) % 0.20/0.54 (define @t81 () (lambda @t74 (and (_ tptp.reflexive @t28) (_ tptp.symmetric @t28) (_ tptp.transitive @t28)))) % 0.20/0.54 (define @t82 () (lambda (@list @t28 @t25) (exists @t7 @t30))) % 0.20/0.54 (define @t83 () (@list @t28 @t6)) % 0.20/0.54 (define @t84 () (lambda @t83 (exists @t31 @t30))) % 0.20/0.54 (define @t85 () (lambda (@list @t28 @t6 @t25) @t78)) % 0.20/0.54 (define @t86 () (@var "S1" (-> $$unsorted Bool))) % 0.20/0.54 (define @t87 () (lambda (@list @t28 @t86) (exists @t7 (and (_ @t86 @t6) (forall @t31 (= (_ @t86 @t25) @t30)))))) % 0.20/0.54 (define @t88 () (lambda @t67 (and (_ @t57 @t25) @t30))) % 0.20/0.54 (define @t89 () (lambda @t83 (or (_ (_ tptp.rel_domain @t28) @t6) (_ (_ tptp.rel_codomain @t28) @t6)))) % 0.20/0.54 (define @t90 () (not (_ @t11 @t36))) % 0.20/0.54 (define @t91 () (_ @t11 @t25)) % 0.20/0.54 (define @t92 () (_ @t11 @t70)) % 0.20/0.54 (define @t93 () (@list @t11 @t70)) % 0.20/0.54 (define @t94 () (lambda @t74 (forall @t93 (=> @t92 (exists @t31 (and @t91 (forall @t45 (=> (_ @t77 @t36) @t90)))))))) % 0.20/0.54 (define @t95 () (lambda @t74 (forall @t93 (=> @t92 (exists @t31 (and @t91 (forall @t45 (=> (_ @t77 @t25) @t90)))))))) % 0.20/0.54 (define @t96 () (_ @t1 @t36)) % 0.20/0.54 (define @t97 () (_ 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0.20/0.54 (define @t116 () (or @t115 @t110)) % 0.20/0.54 (define @t117 () (lambda @t111 @t116)) % 0.20/0.54 (define @t118 () (or (not (_ @t21 @t19)) @t110)) % 0.20/0.54 (define @t119 () (lambda @t22 @t118)) % 0.20/0.54 (define @t120 () (_ @t26 @t25)) % 0.20/0.54 (define @t121 () (lambda (@list @t26 @t6) (forall @t31 (or @t112 @t120)))) % 0.20/0.54 (define @t122 () (_ @t28 @t6 @t25)) % 0.20/0.54 (define @t123 () (_ (lambda @t33 (forall @t31 (or (not @t122) @t120))) tptp.r)) % 0.20/0.54 (define @t124 () (forall @t2 (_ @t109 (_ (_ @t119 (_ @t123 @t1)) @t1)))) % 0.20/0.54 (define @t125 () (forall @t7 (tptp.r @t6 @t6))) % 0.20/0.54 (define @t126 () (_ @t28 @t6 @t6)) % 0.20/0.54 (define @t127 () (_ (lambda @t74 (forall @t7 @t126)) tptp.r)) % 0.20/0.54 (define @t128 () (not @t30)) % 0.20/0.54 (define @t129 () (or @t128 @t27)) % 0.20/0.54 (define @t130 () (not (_ @t21 @t10))) % 0.20/0.54 (define @t131 () (@list @t10)) % 0.20/0.54 (define @t132 () (lambda @t131 (or @t130 (_ @t20 @t10)))) % 0.20/0.54 (define @t133 () (@list @t14 @t10)) % 0.20/0.54 (define @t134 () (lambda @t131 @t130)) % 0.20/0.54 (define @t135 () (_ @t134 @t10)) % 0.20/0.54 (define @t136 () (or @t135 @t15)) % 0.20/0.54 (define @t137 () (lambda @t133 @t136)) % 0.20/0.54 (define @t138 () (@quantifiers_skolemize @t100 1)) % 0.20/0.54 (define @t139 () (@quantifiers_skolemize @t100 0)) % 0.20/0.54 (define @t140 () (_ @t139 @t138)) % 0.20/0.54 (define @t141 () (forall @t31 (or (not (tptp.r @t138 @t25)) (_ @t139 @t25)))) % 0.20/0.54 (define @t142 () (not @t141)) % 0.20/0.54 (define @t143 () (or @t142 @t140)) % 0.20/0.54 (define @t144 () (not @t143)) % 0.20/0.54 (define @t145 () (not @t100)) % 0.20/0.54 (define @t146 () (@list @t138)) % 0.20/0.54 (define @t147 () (tptp.r @t138 @t138)) % 0.20/0.54 (define @t148 () (not @t147)) % 0.20/0.54 (define @t149 () (or @t148 @t140)) % 0.20/0.54 (define @t150 () (not @t125)) % 0.20/0.54 (define @t151 () (@list true)) % 0.20/0.54 (define @t152 () (@list @t125)) % 0.20/0.54 (define @t153 () (@quantifiers_skolemize @t125 0)) % 0.20/0.54 (define @t154 () (tptp.r @t153 @t153)) % 0.20/0.54 (define @t155 () (not @t154)) % 0.20/0.54 (define @t156 () (_ tptp.r @t153)) % 0.20/0.54 (define @t157 () (_ @t156 @t153)) % 0.20/0.54 (define @t158 () (_ @t156 @t153)) % 0.20/0.54 (define @t159 () (tptp.r @t153 @t25)) % 0.20/0.54 (define @t160 () (not @t159)) % 0.20/0.54 (define @t161 () (_ @t156 @t25)) % 0.20/0.54 (define @t162 () (or @t160 @t161)) % 0.20/0.54 (define @t163 () (_ @t156 @t25)) % 0.20/0.54 (define @t164 () (or @t160 @t163)) % 0.20/0.54 (define @t165 () (forall @t31 @t164)) % 0.20/0.54 (define @t166 () (not @t165)) % 0.20/0.54 (define @t167 () (or @t166 @t158)) % 0.20/0.54 (assume @p1 @t5) % 0.20/0.54 (assume @p2 true) % 0.20/0.54 (step @p3 (= tptp.mfalse @t8) :rule refl :args (@t8)) % 0.20/0.54 (step @p4 (= tptp.mtrue @t9) :rule refl :args (@t9)) % 0.20/0.54 (step @p5 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.20/0.54 (step @p6 (= tptp.mor @t17) :rule 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:premises (@p140 @p142)) % 0.20/0.54 (step @p144 :rule cong :premises (@p143) :args (@t46)) % 0.20/0.54 (step @p145 :rule cong :premises (@p144) :args (@t48)) % 0.20/0.54 (step @p146 :rule trans :premises (@p14 @p145)) % 0.20/0.54 (step @p147 :rule ho_cong :premises (@p146 @p138)) % 0.20/0.54 (step @p148 :rule cong :premises (@p147) :args (@t3)) % 0.20/0.54 (step @p149 :rule cong :premises (@p148 @p90) :args (@t4)) % 0.20/0.54 (step @p150 :rule cong :premises (@p149) :args (@t5)) % 0.20/0.54 (step @p151 :rule trans :premises (@p150 @p80)) % 0.20/0.54 (step @p152 :rule eq_resolve :premises (@p1 @p151)) % 0.20/0.54 (step @p153 :rule not_equiv_elim2 :premises (@p152)) % 0.20/0.54 (step @p154 :rule refl :args (@t144)) % 0.20/0.54 (step @p155 :rule bool-double-not-elim :args (@t100)) % 0.20/0.54 (step @p156 :rule nary_cong :premises (@p155 @p154) :args ((or (not @t145) @t144))) % 0.20/0.54 (assume-push @p236 @t145) % 0.20/0.54 (step @p158 :rule skolemize :premises (@p236)) % 0.20/0.54 (step-pop @p237 :rule scope :premises (@p158)) % 0.20/0.54 (step @p159 :rule process_scope :premises (@p237) :args (@t144)) % 0.20/0.54 (step @p161 :rule implies_elim :premises (@p159)) % 0.20/0.54 (step @p162 :rule eq_resolve :premises (@p161 @p156)) % 0.20/0.54 (step @p163 :rule bool-double-not-elim :args (@t141)) % 0.20/0.54 (step @p164 :rule refl :args (@t143)) % 0.20/0.54 (step @p165 :rule nary_cong :premises (@p164 @p163) :args ((or @t143 (not @t142)))) % 0.20/0.54 (step @p166 :rule cnf_or_neg :args (@t143 0)) % 0.20/0.54 (step @p167 :rule eq_resolve :premises (@p166 @p165)) % 0.20/0.54 (step @p168 :rule reordering :premises (@p167) :args ((or @t141 @t143))) % 0.20/0.54 (step @p169 :rule cnf_or_neg :args (@t143 1)) % 0.20/0.54 (assume-push @p238 @t141) % 0.20/0.54 (step @p171 :rule instantiate :premises (@p238) :args (@t146)) % 0.20/0.54 (step-pop @p239 :rule scope :premises (@p171)) % 0.20/0.54 (step @p172 :rule process_scope :premises (@p239) :args (@t149)) % 0.20/0.54 (step @p174 :rule implies_elim :premises (@p172)) % 0.20/0.54 (step @p175 :rule cnf_or_pos :args (@t149)) % 0.20/0.54 (step @p176 :rule reordering :premises (@p175) :args ((or @t140 @t148 (not @t149)))) % 0.20/0.54 (assume-push @p240 @t125) % 0.20/0.54 (step @p178 :rule instantiate :premises (@p240) :args (@t146)) % 0.20/0.54 (step-pop @p241 :rule scope :premises (@p178)) % 0.20/0.54 (step @p179 :rule process_scope :premises (@p241) :args (@t147)) % 0.20/0.54 (step @p181 :rule implies_elim :premises (@p179)) % 0.20/0.54 (step @p182 :rule chain_m_resolution :premises (@p181 @p176 @p174 @p169 @p168 @p162 @p153) :args (@t150 (@list true false true false true true) (@list @t147 @t149 @t140 @t141 @t143 @t100))) % 0.20/0.54 (step @p183 :rule not_equiv_elim1 :premises (@p152)) % 0.20/0.54 (step @p184 :rule chain_m_resolution :premises (@p183 @p182) :args (@t100 @t151 @t152)) % 0.20/0.54 (step @p185 :rule refl :args (@t155)) % 0.20/0.54 (step @p186 :rule bool-double-not-elim :args (@t125)) % 0.20/0.54 (step @p187 :rule nary_cong :premises (@p186 @p185) :args ((or (not @t150) @t155))) % 0.20/0.54 (assume-push @p242 @t150) % 0.20/0.54 (step @p189 :rule skolemize :premises (@p242)) % 0.20/0.54 (step-pop @p243 :rule scope :premises (@p189)) % 0.20/0.54 (step @p190 :rule process_scope :premises (@p243) :args (@t155)) % 0.20/0.54 (step @p192 :rule implies_elim :premises (@p190)) % 0.20/0.54 (step @p193 :rule eq_resolve :premises (@p192 @p187)) % 0.20/0.54 (step @p194 :rule chain_m_resolution :premises (@p193 @p182) :args (@t155 @t151 @t152)) % 0.20/0.54 (step @p195 :rule refl :args (@t154)) % 0.20/0.54 (step @p196 :rule refl :args (@t157)) % 0.20/0.54 (step @p197 :rule cong :premises (@p196 @p195) :args ((= @t157 @t154))) % 0.20/0.54 (step @p198 :rule symm :premises (@p197)) % 0.20/0.54 (step @p199 :rule eq_resolve :premises (@p196 @p198)) % 0.20/0.54 (step @p200 :rule refl :args (@t100)) % 0.20/0.54 (step @p201 :rule cong :premises (@p200 @p199) :args ((=> @t100 @t157))) % 0.20/0.54 (step @p202 :rule aci_norm :args ((= (or false @t157) @t157))) % 0.20/0.54 (step @p203 :rule refl :args (@t158)) % 0.20/0.54 (step @p204 :rule evaluate :args ((not true))) % 0.20/0.54 (step @p205 :rule quant-unused-vars :args ((= (forall @t31 true) true))) % 0.20/0.54 (step @p206 :rule bool-or-taut2 :args (false @t159 false false)) % 0.20/0.54 (step @p207 :rule cong :premises (@p206) :args ((forall @t31 (or @t160 @t159)))) % 0.20/0.54 (step @p208 :rule trans :premises (@p207 @p205)) % 0.20/0.54 (step @p209 :rule refl :args (@t159)) % 0.20/0.54 (step @p210 :rule refl :args (@t161)) % 0.20/0.54 (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t161 @t159))) % 0.20/0.54 (step @p212 :rule symm :premises (@p211)) % 0.20/0.54 (step @p213 :rule eq_resolve :premises (@p210 @p212)) % 0.20/0.54 (step @p214 :rule refl :args (@t160)) % 0.20/0.54 (step @p215 :rule nary_cong :premises (@p214 @p213) :args (@t162)) % 0.20/0.54 (step @p216 :rule cong :premises (@p215) :args ((forall @t31 @t162))) % 0.20/0.54 (step @p217 :rule trans :premises (@p216 @p208)) % 0.20/0.54 (step @p218 :rule refl :args (@t163)) % 0.20/0.54 (step @p219 :rule refl :args (@t160)) % 0.20/0.54 (step @p220 :rule nary_cong :premises (@p219 @p218) :args (@t164)) % 0.20/0.54 (step @p221 :rule cong :premises (@p220) :args (@t165)) % 0.20/0.54 (step @p222 :rule trans :premises (@p221 @p217)) % 0.20/0.54 (step @p223 :rule cong :premises (@p222) :args (@t166)) % 0.20/0.54 (step @p224 :rule trans :premises (@p223 @p204)) % 0.20/0.54 (step @p225 :rule nary_cong :premises (@p224 @p203) :args (@t167)) % 0.20/0.54 (step @p226 :rule trans :premises (@p225 @p202)) % 0.20/0.54 (step @p227 :rule cong :premises (@p200 @p226) :args ((=> @t100 @t167))) % 0.20/0.54 (assume-push @p244 @t100) % 0.20/0.54 (step @p229 :rule instantiate :premises (@p244) :args ((@list @t156 @t153))) % 0.20/0.54 (step-pop @p245 :rule scope :premises (@p229)) % 0.20/0.54 (step @p230 :rule process_scope :premises (@p245) :args (@t167)) % 0.20/0.54 (step @p232 :rule eq_resolve :premises (@p230 @p227)) % 0.20/0.54 (step @p233 :rule eq_resolve :premises (@p232 @p201)) % 0.20/0.54 (step @p234 :rule implies_elim :premises (@p233)) % 0.20/0.54 (step @p235 false :rule chain_m_resolution :premises (@p234 @p194 @p184) :args (false (@list true false) (@list @t154 @t100))) % 0.20/0.54 ) % 0.20/0.54 % SZS output end Proof % 0.20/0.54 % cvc5 exiting %------------------------------------------------------------------------------