%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n012.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 11:23:11 AM UTC 2026 % Result : Theorem 0.06s 0.40s % Output : Proof 0.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.01 % Problem : LCL626^1 : TPTP v9.3.1. Bugfixed v7.3.0. % 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.03/0.30 % Computer : n012.cluster.edu % 0.03/0.30 % Model : x86_64 x86_64 % 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.03/0.30 % Memory : 8046.5625MB % 0.03/0.30 % OS : Linux 6.8.0-71-generic % 0.03/0.30 % CPULimit : 300 % 0.03/0.30 % WCLimit : 300 % 0.03/0.30 % DateTime : Fri Sep 4 23:03:42 UTC 2026 % 0.03/0.30 % CPUTime : % 0.06/0.35 %----Proving TH0 % 0.06/0.40 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.06/0.40 % SZS status Theorem % 0.06/0.40 % SZS output start Proof % 0.06/0.40 ( % 0.06/0.40 (declare-sort $$unsorted 0) % 0.06/0.40 (declare-sort tptp.individuals 0) % 0.06/0.40 (declare-const tptp.r (-> $$unsorted $$unsorted Bool)) % 0.06/0.40 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 0.06/0.40 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 0.06/0.40 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.06/0.40 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 0.06/0.40 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.06/0.40 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.06/0.40 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 0.06/0.40 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 0.06/0.40 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.06/0.40 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.06/0.40 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.06/0.40 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.06/0.40 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.06/0.40 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.06/0.40 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.06/0.40 (define tptp.cartesian_product () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3 _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1)))))))) % 0.06/0.40 (define tptp.pair_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "V" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1 _let_4 _let_2) (or (= _let_4 _let_3) (= _let_2 _let_1)))))))) % 0.06/0.40 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$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))))))) % 0.06/0.40 (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))))))))) % 0.06/0.40 (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))))))))))) % 0.06/0.40 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.06/0.40 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 0.06/0.40 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.06/0.40 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.06/0.40 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.06/0.40 (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)))))))) % 0.06/0.40 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.06/0.40 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 0.06/0.40 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.06/0.40 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.06/0.40 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.06/0.40 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$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))))))))))) % 0.06/0.40 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.06/0.40 (define tptp.rel_field () (let ((_let_1 (@var "X" $$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)))))) % 0.06/0.40 (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))))))))))))))) % 0.06/0.40 (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))))))))))))))) % 0.06/0.40 (define @t1 () (@var "X" (-> $$unsorted Bool))) % 0.06/0.40 (define @t2 () (_ tptp.mbox tptp.r)) % 0.06/0.40 (define @t3 () (_ @t2 @t1)) % 0.06/0.40 (define @t4 () (@list @t1)) % 0.06/0.40 (define @t5 () (forall @t4 (_ tptp.mvalid (_ (_ tptp.mimpl @t3) (_ @t2 (_ @t2 @t3)))))) % 0.06/0.40 (define @t6 () (not @t5)) % 0.06/0.40 (define @t7 () (@var "X" $$unsorted)) % 0.06/0.40 (define @t8 () (@list @t7)) % 0.06/0.40 (define @t9 () (lambda @t8 false)) % 0.06/0.40 (define @t10 () (lambda @t8 true)) % 0.06/0.40 (define @t11 () (@var "U" $$unsorted)) % 0.06/0.40 (define @t12 () (_ @t1 @t11)) % 0.06/0.40 (define @t13 () (lambda (@list @t1 @t11) (not @t12))) % 0.06/0.40 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.06/0.40 (define @t15 () (_ @t14 @t11)) % 0.06/0.40 (define @t16 () (@list @t1 @t14 @t11)) % 0.06/0.40 (define @t17 () (lambda @t16 (or @t12 @t15))) % 0.06/0.40 (define @t18 () (lambda @t16 (and @t12 @t15))) % 0.06/0.40 (define @t19 () (@var "__flatten_var_0" $$unsorted)) % 0.06/0.40 (define @t20 () (@var "V" (-> $$unsorted Bool))) % 0.06/0.40 (define @t21 () (@var "U" (-> $$unsorted Bool))) % 0.06/0.40 (define @t22 () (@list @t21 @t20 @t19)) % 0.06/0.40 (define @t23 () (lambda @t22 (_ (_ (_ tptp.mor (_ tptp.mnot @t21)) @t20) @t19))) % 0.06/0.40 (define @t24 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t21) @t20)) (_ (_ tptp.mimpl @t20) @t21)) @t19))) % 0.06/0.40 (define @t25 () (@var "Y" $$unsorted)) % 0.06/0.40 (define @t26 () (@var "P" (-> $$unsorted Bool))) % 0.06/0.40 (define @t27 () (_ @t26 @t25)) % 0.06/0.40 (define @t28 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.06/0.40 (define @t29 () (_ @t28 @t7)) % 0.06/0.40 (define @t30 () (_ @t29 @t25)) % 0.06/0.40 (define @t31 () (@list @t25)) % 0.06/0.40 (define @t32 () (forall @t31 (=> @t30 @t27))) % 0.06/0.40 (define @t33 () (@list @t28 @t26 @t7)) % 0.06/0.40 (define @t34 () (lambda @t33 @t32)) % 0.06/0.40 (define @t35 () (lambda @t33 (exists @t31 (and @t30 @t27)))) % 0.06/0.40 (define @t36 () (@var "W" $$unsorted)) % 0.06/0.40 (define @t37 () (@var "X" tptp.individuals)) % 0.06/0.40 (define @t38 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 0.06/0.40 (define @t39 () (_ (_ @t38 @t37) @t36)) % 0.06/0.40 (define @t40 () (@list @t37)) % 0.06/0.40 (define @t41 () (@list @t38 @t36)) % 0.06/0.40 (define @t42 () (lambda @t41 (forall @t40 @t39))) % 0.06/0.40 (define @t43 () (lambda @t41 (exists @t40 @t39))) % 0.06/0.40 (define @t44 () (_ @t26 @t36)) % 0.06/0.40 (define @t45 () (@list @t36)) % 0.06/0.40 (define @t46 () (forall @t45 @t44)) % 0.06/0.40 (define @t47 () (@list @t26)) % 0.06/0.40 (define @t48 () (lambda @t47 @t46)) % 0.06/0.40 (define @t49 () (lambda @t47 (exists @t45 @t44))) % 0.06/0.40 (define @t50 () (not @t44)) % 0.06/0.40 (define @t51 () (lambda @t47 (exists @t45 @t50))) % 0.06/0.40 (define @t52 () (lambda @t47 (forall @t45 @t50))) % 0.06/0.40 (define @t53 () (@var "V" $$unsorted)) % 0.06/0.40 (define @t54 () (lambda (@list @t1 @t14 @t11 @t53) (and @t12 (_ @t14 @t53)))) % 0.06/0.40 (define @t55 () (lambda (@list @t7 @t25 @t11 @t53) (or (= @t11 @t7) (= @t53 @t25)))) % 0.06/0.40 (define @t56 () (= @t7 @t25)) % 0.06/0.40 (define @t57 () (@var "S" (-> $$unsorted Bool))) % 0.06/0.40 (define @t58 () (_ @t57 @t7)) % 0.06/0.40 (define @t59 () (lambda (@list @t57 @t7 @t25) (and @t58 @t56))) % 0.06/0.40 (define @t60 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 0.06/0.40 (define @t61 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 0.06/0.40 (define @t62 () (_ (_ @t61 @t7) @t25)) % 0.06/0.40 (define @t63 () (@list @t7 @t25)) % 0.06/0.40 (define @t64 () (lambda (@list @t61 @t60) (forall @t63 (=> @t62 (_ (_ @t60 @t7) @t25))))) % 0.06/0.40 (define @t65 () (@var "B" (-> $$unsorted Bool))) % 0.06/0.40 (define @t66 () (@var "A" (-> $$unsorted Bool))) % 0.06/0.40 (define @t67 () (lambda (@list @t28 @t66 @t65) (forall @t63 (=> @t30 (and (_ @t66 @t7) (_ @t65 @t25)))))) % 0.06/0.40 (define @t68 () (@list @t28 @t57 @t7 @t25)) % 0.06/0.40 (define @t69 () (lambda @t68 (and @t58 @t30))) % 0.06/0.40 (define @t70 () (lambda @t63 @t56)) % 0.06/0.40 (define @t71 () (@var "Z" $$unsorted)) % 0.06/0.40 (define @t72 () (lambda (@list @t61 @t60 @t7 @t71) (exists @t31 (and @t62 (_ (_ @t60 @t25) @t71))))) % 0.06/0.40 (define @t73 () (_ @t29 @t7)) % 0.06/0.40 (define @t74 () (@list @t28)) % 0.06/0.40 (define @t75 () (lambda @t74 (forall @t8 @t73))) % 0.06/0.40 (define @t76 () (lambda @t74 (forall @t8 (not @t73)))) % 0.06/0.40 (define @t77 () (_ @t28 @t25)) % 0.06/0.40 (define @t78 () (_ @t77 @t7)) % 0.06/0.40 (define @t79 () (lambda @t74 (forall @t63 (=> @t30 @t78)))) % 0.06/0.40 (define @t80 () (_ @t29 @t71)) % 0.06/0.40 (define @t81 () (_ @t77 @t71)) % 0.06/0.40 (define @t82 () (and @t30 @t81)) % 0.06/0.40 (define @t83 () (@list @t7 @t25 @t71)) % 0.06/0.40 (define @t84 () (forall @t83 (=> @t82 @t80))) % 0.06/0.40 (define @t85 () (lambda @t74 @t84)) % 0.06/0.40 (define @t86 () (lambda @t74 (and (_ tptp.reflexive @t28) (_ tptp.symmetric @t28) (_ tptp.transitive @t28)))) % 0.06/0.40 (define @t87 () (lambda (@list @t28 @t25) (exists @t8 @t30))) % 0.06/0.40 (define @t88 () (@list @t28 @t7)) % 0.06/0.40 (define @t89 () (lambda @t88 (exists @t31 @t30))) % 0.06/0.40 (define @t90 () (lambda (@list @t28 @t7 @t25) @t78)) % 0.06/0.40 (define @t91 () (@var "S1" (-> $$unsorted Bool))) % 0.06/0.40 (define @t92 () (lambda (@list @t28 @t91) (exists @t8 (and (_ @t91 @t7) (forall @t31 (= (_ @t91 @t25) @t30)))))) % 0.06/0.40 (define @t93 () (lambda @t68 (and (_ @t57 @t25) @t30))) % 0.06/0.40 (define @t94 () (lambda @t88 (or (_ (_ tptp.rel_domain @t28) @t7) (_ (_ tptp.rel_codomain @t28) @t7)))) % 0.06/0.40 (define @t95 () (not (_ @t1 @t36))) % 0.06/0.40 (define @t96 () (_ @t1 @t25)) % 0.06/0.40 (define @t97 () (_ @t1 @t71)) % 0.06/0.40 (define @t98 () (@list @t1 @t71)) % 0.06/0.40 (define @t99 () (lambda @t74 (forall @t98 (=> @t97 (exists @t31 (and @t96 (forall @t45 (=> (_ @t77 @t36) @t95)))))))) % 0.06/0.40 (define @t100 () (lambda @t74 (forall @t98 (=> @t97 (exists @t31 (and @t96 (forall @t45 (=> (_ @t77 @t25) @t95)))))))) % 0.06/0.40 (define @t101 () (not (tptp.r @t7 @t25))) % 0.06/0.40 (define @t102 () (forall @t83 (or @t101 (not (tptp.r @t25 @t71)) (tptp.r @t7 @t71)))) % 0.06/0.40 (define @t103 () (_ @t28 @t7 @t71)) % 0.06/0.40 (define @t104 () (_ @t28 @t25 @t71)) % 0.06/0.40 (define @t105 () (_ @t28 @t7 @t25)) % 0.06/0.40 (define @t106 () (not @t105)) % 0.06/0.40 (define @t107 () (not @t81)) % 0.06/0.40 (define @t108 () (not @t30)) % 0.06/0.40 (define @t109 () (or @t108 @t107 @t80)) % 0.06/0.40 (define @t110 () (@var "BOUND_VARIABLE_8436" $$unsorted)) % 0.06/0.40 (define @t111 () (_ @t1 @t110)) % 0.06/0.40 (define @t112 () (@var "BOUND_VARIABLE_8434" $$unsorted)) % 0.06/0.40 (define @t113 () (not (tptp.r @t112 @t110))) % 0.06/0.40 (define @t114 () (@var "BOUND_VARIABLE_8432" $$unsorted)) % 0.06/0.40 (define @t115 () (not (tptp.r @t114 @t112))) % 0.06/0.40 (define @t116 () (not (tptp.r @t36 @t114))) % 0.06/0.40 (define @t117 () (_ @t1 @t25)) % 0.06/0.40 (define @t118 () (not (tptp.r @t36 @t25))) % 0.06/0.40 (define @t119 () (not (forall @t31 (or @t118 @t117)))) % 0.06/0.40 (define @t120 () (or @t119 @t116 @t115 @t113 @t111)) % 0.06/0.40 (define @t121 () (forall (@list @t1 @t36 @t114 @t112 @t110) @t120)) % 0.06/0.40 (define @t122 () (@quantifiers_skolemize @t121 4)) % 0.06/0.40 (define @t123 () (@quantifiers_skolemize @t121 3)) % 0.06/0.40 (define @t124 () (@quantifiers_skolemize @t121 2)) % 0.06/0.40 (define @t125 () (@list @t36 @t114 @t112 @t110)) % 0.06/0.40 (define @t126 () (or @t116 @t115 @t113 @t111)) % 0.06/0.40 (define @t127 () (or @t119 @t126)) % 0.06/0.40 (define @t128 () (forall @t125 @t127)) % 0.06/0.40 (define @t129 () (@list @t114 @t112 @t110)) % 0.06/0.40 (define @t130 () (forall @t129 @t127)) % 0.06/0.40 (define @t131 () (forall @t129 @t126)) % 0.06/0.40 (define @t132 () (@var "BOUND_VARIABLE_8397" $$unsorted)) % 0.06/0.40 (define @t133 () (@var "BOUND_VARIABLE_8395" $$unsorted)) % 0.06/0.40 (define @t134 () (or @t119 @t131)) % 0.06/0.40 (define @t135 () (_ @t1 @t132)) % 0.06/0.40 (define @t136 () (not (tptp.r @t133 @t132))) % 0.06/0.40 (define @t137 () (not (tptp.r @t25 @t133))) % 0.06/0.40 (define @t138 () (@list @t25 @t133 @t132)) % 0.06/0.40 (define @t139 () (or @t119 (forall @t138 (or @t118 @t137 @t136 @t135)))) % 0.06/0.40 (define @t140 () (not (tptp.r @t19 @t25))) % 0.06/0.40 (define @t141 () (forall @t138 (or @t140 @t137 @t136 @t135))) % 0.06/0.40 (define @t142 () (forall @t31 (or @t140 @t117))) % 0.06/0.40 (define @t143 () (not @t142)) % 0.06/0.40 (define @t144 () (@list @t19)) % 0.06/0.40 (define @t145 () (lambda @t144 (or @t143 @t141))) % 0.06/0.40 (define @t146 () (_ @t145 @t36)) % 0.06/0.40 (define @t147 () (forall @t45 @t146)) % 0.06/0.40 (define @t148 () (_ @t26 @t36)) % 0.06/0.40 (define @t149 () (lambda @t47 (forall @t45 @t148))) % 0.06/0.40 (define @t150 () (or @t101 @t137 @t136 @t135)) % 0.06/0.40 (define @t151 () (lambda @t8 (forall @t138 @t150))) % 0.06/0.40 (define @t152 () (_ @t151 @t19)) % 0.06/0.40 (define @t153 () (or @t143 @t152)) % 0.06/0.40 (define @t154 () (lambda @t144 @t153)) % 0.06/0.40 (define @t155 () (_ @t20 @t19)) % 0.06/0.40 (define @t156 () (@list @t20 @t19)) % 0.06/0.40 (define @t157 () (or @t137 @t136 @t135)) % 0.06/0.40 (define @t158 () (or @t101 @t157)) % 0.06/0.40 (define @t159 () (forall @t138 @t158)) % 0.06/0.40 (define @t160 () (@list @t133 @t132)) % 0.06/0.40 (define @t161 () (forall @t160 @t158)) % 0.06/0.40 (define @t162 () (forall @t160 @t157)) % 0.06/0.40 (define @t163 () (@var "BOUND_VARIABLE_8361" $$unsorted)) % 0.06/0.40 (define @t164 () (@var "BOUND_VARIABLE_8378" $$unsorted)) % 0.06/0.40 (define @t165 () (or @t101 @t162)) % 0.06/0.40 (define @t166 () (_ @t1 @t163)) % 0.06/0.40 (define @t167 () (not (tptp.r @t164 @t163))) % 0.06/0.40 (define @t168 () (@list @t164 @t163)) % 0.06/0.40 (define @t169 () (forall @t168 (or (not (tptp.r @t25 @t164)) @t167 @t166))) % 0.06/0.40 (define @t170 () (not (tptp.r @t25 @t163))) % 0.06/0.40 (define @t171 () (or @t101 @t170 @t166)) % 0.06/0.40 (define @t172 () (@list @t25 @t163)) % 0.06/0.40 (define @t173 () (forall @t172 @t171)) % 0.06/0.40 (define @t174 () (@list @t25)) % 0.06/0.40 (define @t175 () (lambda @t8 @t173)) % 0.06/0.40 (define @t176 () (or @t101 (_ @t175 @t25))) % 0.06/0.40 (define @t177 () (forall @t31 @t176)) % 0.06/0.40 (define @t178 () (lambda @t8 @t177)) % 0.06/0.40 (define @t179 () (_ @t26 @t25)) % 0.06/0.40 (define @t180 () (lambda (@list @t26 @t7) (forall @t31 (or @t101 @t179)))) % 0.06/0.40 (define @t181 () (or @t170 @t166)) % 0.06/0.40 (define @t182 () (or @t101 @t181)) % 0.06/0.40 (define @t183 () (forall @t172 @t182)) % 0.06/0.40 (define @t184 () (@list @t163)) % 0.06/0.40 (define @t185 () (forall @t184 @t182)) % 0.06/0.40 (define @t186 () (forall @t184 @t181)) % 0.06/0.40 (define @t187 () (@var "BOUND_VARIABLE_8345" $$unsorted)) % 0.06/0.40 (define @t188 () (@list @t187)) % 0.06/0.40 (define @t189 () (or @t101 @t186)) % 0.06/0.40 (define @t190 () (_ @t1 @t187)) % 0.06/0.40 (define @t191 () (@list @t187)) % 0.06/0.40 (define @t192 () (forall @t191 (or (not (tptp.r @t25 @t187)) @t190))) % 0.06/0.40 (define @t193 () (forall @t31 (or @t101 @t117))) % 0.06/0.40 (define @t194 () (lambda @t8 @t193)) % 0.06/0.40 (define @t195 () (or @t101 (_ @t194 @t25))) % 0.06/0.40 (define @t196 () (forall @t31 @t195)) % 0.06/0.40 (define @t197 () (lambda @t8 @t196)) % 0.06/0.40 (define @t198 () (_ (lambda @t33 (forall @t31 (or @t106 @t179))) tptp.r)) % 0.06/0.40 (define @t199 () (_ @t194 @t19)) % 0.06/0.40 (define @t200 () (not @t199)) % 0.06/0.40 (define @t201 () (or @t200 @t155)) % 0.06/0.40 (define @t202 () (lambda @t156 @t201)) % 0.06/0.40 (define @t203 () (or (not (_ @t21 @t19)) @t155)) % 0.06/0.40 (define @t204 () (lambda @t22 @t203)) % 0.06/0.40 (define @t205 () (_ @t198 @t1)) % 0.06/0.40 (define @t206 () (forall @t4 (_ @t149 (_ (_ @t204 @t205) (_ @t198 (_ @t198 @t205)))))) % 0.06/0.40 (define @t207 () (or @t108 @t27)) % 0.06/0.40 (define @t208 () (not (_ @t21 @t11))) % 0.06/0.40 (define @t209 () (@list @t11)) % 0.06/0.40 (define @t210 () (lambda @t209 (or @t208 (_ @t20 @t11)))) % 0.06/0.40 (define @t211 () (@list @t14 @t11)) % 0.06/0.40 (define @t212 () (lambda @t209 @t208)) % 0.06/0.40 (define @t213 () (_ @t212 @t11)) % 0.06/0.40 (define @t214 () (or @t213 @t15)) % 0.06/0.40 (define @t215 () (lambda @t211 @t214)) % 0.06/0.40 (define @t216 () (tptp.r @t123 @t122)) % 0.06/0.40 (define @t217 () (@quantifiers_skolemize @t121 0)) % 0.06/0.40 (define @t218 () (_ @t217 @t122)) % 0.06/0.40 (define @t219 () (not @t216)) % 0.06/0.40 (define @t220 () (tptp.r @t124 @t123)) % 0.06/0.40 (define @t221 () (not @t220)) % 0.06/0.40 (define @t222 () (@quantifiers_skolemize @t121 1)) % 0.06/0.40 (define @t223 () (tptp.r @t222 @t124)) % 0.06/0.40 (define @t224 () (not @t223)) % 0.06/0.40 (define @t225 () (forall @t31 (or (not (tptp.r @t222 @t25)) (_ @t217 @t25)))) % 0.06/0.40 (define @t226 () (not @t225)) % 0.06/0.40 (define @t227 () (or @t226 @t224 @t221 @t219 @t218)) % 0.06/0.40 (define @t228 () (@list true)) % 0.06/0.40 (define @t229 () (@list @t227)) % 0.06/0.40 (define @t230 () (tptp.r @t124 @t122)) % 0.06/0.40 (define @t231 () (or @t221 @t219 @t230)) % 0.06/0.40 (define @t232 () (tptp.r @t222 @t122)) % 0.06/0.40 (define @t233 () (not @t232)) % 0.06/0.40 (define @t234 () (or @t233 @t218)) % 0.06/0.40 (define @t235 () (@list true false)) % 0.06/0.40 (define @t236 () (not @t230)) % 0.06/0.40 (define @t237 () (or @t224 @t236 @t232)) % 0.06/0.40 (define @t238 () (not @t237)) % 0.06/0.40 (assume @p1 (and (_ tptp.transitive tptp.r) (_ tptp.upwards_well_founded tptp.r))) % 0.06/0.40 (assume @p2 @t6) % 0.06/0.40 (assume @p3 true) % 0.06/0.40 (step @p4 (= tptp.mfalse @t9) :rule refl :args (@t9)) % 0.06/0.40 (step @p5 (= tptp.mtrue @t10) :rule refl :args (@t10)) % 0.06/0.40 (step @p6 (= tptp.mnot @t13) :rule refl :args (@t13)) % 0.06/0.40 (step @p7 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.06/0.40 (step @p8 (= tptp.mand @t18) :rule refl :args (@t18)) % 0.06/0.40 (step @p9 (= tptp.mimpl @t23) :rule refl :args (@t23)) % 0.06/0.40 (step @p10 (= tptp.miff @t24) :rule refl :args (@t24)) % 0.06/0.40 (step @p11 (= tptp.mbox @t34) :rule refl :args (@t34)) % 0.06/0.40 (step @p12 (= tptp.mdia @t35) :rule refl :args (@t35)) % 0.06/0.40 (step @p13 (= tptp.mall @t42) :rule refl :args (@t42)) % 0.06/0.40 (step @p14 (= tptp.mexists @t43) :rule refl :args (@t43)) % 0.06/0.40 (step @p15 (= tptp.mvalid @t48) :rule refl :args (@t48)) % 0.06/0.40 (step @p16 (= tptp.msatisfiable @t49) :rule refl :args (@t49)) % 0.06/0.40 (step @p17 (= tptp.mcountersatisfiable @t51) :rule refl :args (@t51)) % 0.06/0.40 (step @p18 (= tptp.minvalid @t52) :rule refl :args (@t52)) % 0.06/0.40 (step @p19 (= tptp.cartesian_product @t54) :rule refl :args (@t54)) % 0.06/0.40 (step @p20 (= tptp.pair_rel @t55) :rule refl :args (@t55)) % 0.06/0.40 (step @p21 (= tptp.id_rel @t59) :rule refl :args (@t59)) % 0.06/0.40 (step @p22 (= tptp.sub_rel @t64) :rule refl :args (@t64)) % 0.06/0.40 (step @p23 (= tptp.is_rel_on @t67) :rule refl :args (@t67)) % 0.06/0.40 (step @p24 (= tptp.restrict_rel_domain @t69) :rule refl :args (@t69)) % 0.06/0.40 (step @p25 (= tptp.rel_diagonal @t70) :rule refl :args (@t70)) % 0.06/0.40 (step @p26 (= tptp.rel_composition @t72) :rule refl :args (@t72)) % 0.06/0.40 (step @p27 (= tptp.reflexive @t75) :rule refl :args (@t75)) % 0.06/0.40 (step @p28 (= tptp.irreflexive @t76) :rule refl :args (@t76)) % 0.06/0.40 (step @p29 (= tptp.symmetric @t79) :rule refl :args (@t79)) % 0.06/0.40 (step @p30 (= tptp.transitive @t85) :rule refl :args (@t85)) % 0.06/0.40 (step @p31 (= tptp.equiv_rel @t86) :rule refl :args (@t86)) % 0.06/0.40 (step @p32 (= tptp.rel_codomain @t87) :rule refl :args (@t87)) % 0.06/0.40 (step @p33 (= tptp.rel_domain @t89) :rule refl :args (@t89)) % 0.06/0.40 (step @p34 (= tptp.rel_inverse @t90) :rule refl :args (@t90)) % 0.06/0.40 (step @p35 (= tptp.equiv_classes @t92) :rule refl :args (@t92)) % 0.06/0.40 (step @p36 (= tptp.restrict_rel_codomain @t93) :rule refl :args (@t93)) % 0.06/0.40 (step @p37 (= tptp.rel_field @t94) :rule refl :args (@t94)) % 0.06/0.40 (step @p38 (= tptp.well_founded @t99) :rule refl :args (@t99)) % 0.06/0.40 (step @p39 (= tptp.upwards_well_founded @t100) :rule refl :args (@t100)) % 0.06/0.40 (step @p40 :rule beta-reduce :args ((= (_ (lambda @t74 (forall @t83 (or @t106 (not @t104) @t103))) tptp.r) @t102))) % 0.06/0.40 (step @p41 :rule refl :args (tptp.r)) % 0.06/0.40 (step @p42 :rule refl :args (@t103)) % 0.06/0.40 (step @p43 :rule refl :args (@t80)) % 0.06/0.40 (step @p44 :rule cong :premises (@p43 @p42) :args ((= @t80 @t103))) % 0.06/0.40 (step @p45 :rule symm :premises (@p44)) % 0.06/0.40 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.06/0.40 (step @p47 :rule refl :args (@t104)) % 0.06/0.40 (step @p48 :rule refl :args (@t81)) % 0.06/0.40 (step @p49 :rule cong :premises (@p48 @p47) :args ((= @t81 @t104))) % 0.06/0.40 (step @p50 :rule symm :premises (@p49)) % 0.06/0.40 (step @p51 :rule eq_resolve :premises (@p48 @p50)) % 0.06/0.40 (step @p52 :rule cong :premises (@p51) :args (@t107)) % 0.06/0.40 (step @p53 :rule refl :args (@t105)) % 0.06/0.40 (step @p54 :rule refl :args (@t30)) % 0.06/0.40 (step @p55 :rule cong :premises (@p54 @p53) :args ((= @t30 @t105))) % 0.06/0.40 (step @p56 :rule symm :premises (@p55)) % 0.06/0.40 (step @p57 :rule eq_resolve :premises (@p54 @p56)) % 0.06/0.40 (step @p58 :rule cong :premises (@p57) :args (@t108)) % 0.06/0.40 (step @p59 :rule nary_cong :premises (@p58 @p52 @p46) :args (@t109)) % 0.06/0.40 (step @p60 :rule cong :premises (@p59) :args ((forall @t83 @t109))) % 0.06/0.40 (step @p61 :rule aci_norm :args ((= (or (or @t108 @t107) @t80) @t109))) % 0.06/0.40 (step @p62 :rule bool-and-de-morgan :args (@t30 @t81 true)) % 0.06/0.40 (step @p63 :rule nary_cong :premises (@p62 @p43) :args ((or (not @t82) @t80))) % 0.06/0.40 (step @p64 :rule trans :premises (@p63 @p61)) % 0.06/0.40 (step @p65 :rule bool-impl-elim :args (@t82 @t80)) % 0.06/0.40 (step @p66 :rule trans :premises (@p65 @p64)) % 0.06/0.40 (step @p67 :rule cong :premises (@p66) :args (@t84)) % 0.06/0.40 (step @p68 :rule trans :premises (@p67 @p60)) % 0.06/0.40 (step @p69 :rule cong :premises (@p68) :args (@t85)) % 0.06/0.40 (step @p70 :rule trans :premises (@p30 @p69)) % 0.06/0.40 (step @p71 :rule ho_cong :premises (@p70 @p41)) % 0.06/0.40 (step @p72 :rule trans :premises (@p71 @p40)) % 0.06/0.40 (step @p73 :rule and_elim :premises (@p1) :args (0)) % 0.06/0.40 (step @p74 :rule eq_resolve :premises (@p73 @p72)) % 0.06/0.40 (step @p75 :rule instantiate :premises (@p74) :args ((@list @t124 @t123 @t122))) % 0.06/0.40 (step @p76 :rule quant-merge-prenex :args ((= (forall @t4 (forall @t125 @t120)) @t121))) % 0.06/0.40 (step @p77 :rule aci_norm :args ((= @t127 @t120))) % 0.06/0.40 (step @p78 :rule cong :premises (@p77) :args (@t128)) % 0.06/0.40 (step @p79 :rule quant-merge-prenex :args ((= (forall @t45 @t130) @t128))) % 0.06/0.40 (step @p80 :rule alpha_equiv :args (@t131 (@list @t114 @t112 @t110) (@list @t25 @t133 @t132))) % 0.06/0.40 (step @p81 :rule refl :args (@t119)) % 0.06/0.40 (step @p82 :rule nary_cong :premises (@p81 @p80) :args (@t134)) % 0.06/0.40 (step @p83 :rule quant-miniscope-or :args ((= @t130 @t134))) % 0.06/0.40 (step @p84 :rule trans :premises (@p83 @p82)) % 0.06/0.40 (step @p85 :rule symm :premises (@p84)) % 0.06/0.40 (step @p86 :rule cong :premises (@p85) :args ((forall @t45 @t139))) % 0.06/0.40 (step @p87 :rule trans :premises (@p86 @p79)) % 0.06/0.40 (step @p88 :rule trans :premises (@p87 @p78)) % 0.06/0.40 (step @p89 :rule beta-reduce :args ((= @t146 @t139))) % 0.06/0.40 (step @p90 :rule cong :premises (@p89) :args (@t147)) % 0.06/0.40 (step @p91 :rule trans :premises (@p90 @p88)) % 0.06/0.40 (step @p92 :rule beta-reduce :args ((= (_ @t149 @t145) @t147))) % 0.06/0.40 (step @p93 :rule trans :premises (@p92 @p91)) % 0.06/0.40 (step @p94 :rule beta-reduce :args ((= @t152 @t141))) % 0.06/0.40 (step @p95 :rule refl :args (@t143)) % 0.06/0.40 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t153)) % 0.06/0.40 (step @p97 :rule cong :premises (@p96) :args (@t154)) % 0.06/0.40 (step @p98 :rule beta-reduce :args ((= (_ (lambda @t156 (or @t143 @t155)) @t151) @t154))) % 0.06/0.40 (step @p99 :rule trans :premises (@p98 @p97)) % 0.06/0.40 (step @p100 :rule aci_norm :args ((= @t158 @t150))) % 0.06/0.40 (step @p101 :rule cong :premises (@p100) :args (@t159)) % 0.06/0.40 (step @p102 :rule quant-merge-prenex :args ((= (forall @t31 @t161) @t159))) % 0.06/0.40 (step @p103 :rule alpha_equiv :args (@t162 (@list @t133 @t132) (@list @t164 @t163))) % 0.06/0.40 (step @p104 :rule refl :args (@t101)) % 0.06/0.40 (step @p105 :rule nary_cong :premises (@p104 @p103) :args (@t165)) % 0.06/0.40 (step @p106 :rule quant-miniscope-or :args ((= @t161 @t165))) % 0.06/0.40 (step @p107 :rule trans :premises (@p106 @p105)) % 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beta-reduce :args ((= (_ (lambda @t8 (forall @t191 (or (not (tptp.r @t7 @t187)) @t190))) @t25) @t192))) % 0.06/0.40 (step @p137 :rule alpha_equiv :args (@t193 @t174 @t188)) % 0.06/0.40 (step @p138 :rule cong :premises (@p137) :args (@t194)) % 0.06/0.40 (step @p139 :rule ho_cong :premises (@p138 @p113)) % 0.06/0.40 (step @p140 :rule trans :premises (@p139 @p136)) % 0.06/0.40 (step @p141 :rule nary_cong :premises (@p118 @p140) :args (@t195)) % 0.06/0.40 (step @p142 :rule cong :premises (@p141) :args (@t196)) % 0.06/0.40 (step @p143 :rule trans :premises (@p142 @p135)) % 0.06/0.40 (step @p144 :rule cong :premises (@p143) :args (@t197)) % 0.06/0.40 (step @p145 :rule beta-reduce :args ((= (_ @t180 @t194) @t197))) % 0.06/0.40 (step @p146 :rule trans :premises (@p145 @p144)) % 0.06/0.40 (step @p147 :rule beta-reduce :args ((= (_ @t180 @t1) @t194))) % 0.06/0.40 (step @p148 :rule refl :args (@t1)) % 0.06/0.40 (step @p149 :rule beta-reduce :args ((= @t198 @t180))) % 0.06/0.40 (step @p150 :rule 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(step @p166 :rule ho_cong :premises (@p165 @p155)) % 0.06/0.40 (step @p167 :rule trans :premises (@p166 @p99)) % 0.06/0.40 (step @p168 :rule refl :args (@t149)) % 0.06/0.40 (step @p169 :rule ho_cong :premises (@p168 @p167)) % 0.06/0.40 (step @p170 :rule trans :premises (@p169 @p93)) % 0.06/0.40 (step @p171 :rule cong :premises (@p170) :args (@t206)) % 0.06/0.40 (step @p172 :rule trans :premises (@p171 @p76)) % 0.06/0.40 (step @p173 :rule cong :premises (@p172) :args ((not @t206))) % 0.06/0.40 (step @p174 :rule refl :args (@t179)) % 0.06/0.40 (step @p175 :rule refl :args (@t27)) % 0.06/0.40 (step @p176 :rule cong :premises (@p175 @p174) :args ((= @t27 @t179))) % 0.06/0.40 (step @p177 :rule symm :premises (@p176)) % 0.06/0.40 (step @p178 :rule eq_resolve :premises (@p175 @p177)) % 0.06/0.40 (step @p179 :rule nary_cong :premises (@p58 @p178) :args (@t207)) % 0.06/0.40 (step @p180 :rule cong :premises (@p179) :args ((forall @t31 @t207))) % 0.06/0.40 (step @p181 :rule bool-impl-elim :args (@t30 @t27)) % 0.06/0.40 (step @p182 :rule cong :premises (@p181) :args (@t32)) % 0.06/0.40 (step @p183 :rule trans :premises (@p182 @p180)) % 0.06/0.40 (step @p184 :rule cong :premises (@p183) :args (@t34)) % 0.06/0.40 (step @p185 :rule trans :premises (@p11 @p184)) % 0.06/0.40 (step @p186 :rule ho_cong :premises (@p185 @p41)) % 0.06/0.40 (step @p187 :rule ho_cong :premises (@p186 @p148)) % 0.06/0.40 (step @p188 :rule ho_cong :premises (@p186 @p187)) % 0.06/0.40 (step @p189 :rule ho_cong :premises (@p186 @p188)) % 0.06/0.40 (step @p190 :rule beta-reduce :args ((= (_ @t210 @t19) @t203))) % 0.06/0.40 (step @p191 :rule refl :args (@t19)) % 0.06/0.40 (step @p192 :rule beta-reduce :args ((= (_ (lambda @t211 (or @t208 @t15)) @t20) @t210))) % 0.06/0.40 (step @p193 :rule refl :args (@t20)) % 0.06/0.40 (step @p194 :rule refl :args (@t15)) % 0.06/0.40 (step @p195 :rule beta-reduce :args ((= @t213 @t208))) % 0.06/0.40 (step @p196 :rule nary_cong :premises (@p195 @p194) :args (@t214)) % 0.06/0.40 (step @p197 :rule cong :premises (@p196) :args (@t215)) % 0.06/0.40 (step @p198 :rule beta-reduce :args ((= (_ @t17 @t212) @t215))) % 0.06/0.40 (step @p199 :rule trans :premises (@p198 @p197)) % 0.06/0.40 (step @p200 :rule beta-reduce :args ((= (_ @t13 @t21) @t212))) % 0.06/0.40 (step @p201 :rule refl :args (@t17)) % 0.06/0.40 (step @p202 :rule ho_cong :premises (@p201 @p200)) % 0.06/0.40 (step @p203 :rule trans :premises (@p202 @p199)) % 0.06/0.40 (step @p204 :rule ho_cong :premises (@p203 @p193)) % 0.06/0.40 (step @p205 :rule trans :premises (@p204 @p192)) % 0.06/0.40 (step @p206 :rule ho_cong :premises (@p205 @p191)) % 0.06/0.40 (step @p207 :rule trans :premises (@p206 @p190)) % 0.06/0.40 (step @p208 :rule refl :args (@t21)) % 0.06/0.40 (step @p209 :rule ho_cong :premises (@p6 @p208)) % 0.06/0.40 (step @p210 :rule ho_cong :premises (@p7 @p209)) % 0.06/0.40 (step @p211 :rule ho_cong :premises (@p210 @p193)) % 0.06/0.40 (step @p212 :rule ho_cong :premises (@p211 @p191)) % 0.06/0.40 (step @p213 :rule trans :premises (@p212 @p207)) % 0.06/0.40 (step @p214 :rule cong :premises (@p213) :args (@t23)) % 0.06/0.40 (step @p215 :rule trans :premises (@p9 @p214)) % 0.06/0.40 (step @p216 :rule ho_cong :premises (@p215 @p187)) % 0.06/0.40 (step @p217 :rule ho_cong :premises (@p216 @p189)) % 0.06/0.40 (step @p218 :rule refl :args (@t148)) % 0.06/0.40 (step @p219 :rule refl :args (@t44)) % 0.06/0.40 (step @p220 :rule cong :premises (@p219 @p218) :args ((= @t44 @t148))) % 0.06/0.40 (step @p221 :rule symm :premises (@p220)) % 0.06/0.40 (step @p222 :rule eq_resolve :premises (@p219 @p221)) % 0.06/0.40 (step @p223 :rule cong :premises (@p222) :args (@t46)) % 0.06/0.40 (step @p224 :rule cong :premises (@p223) :args (@t48)) % 0.06/0.40 (step @p225 :rule trans :premises (@p15 @p224)) % 0.06/0.40 (step @p226 :rule ho_cong :premises (@p225 @p217)) % 0.06/0.40 (step @p227 :rule cong :premises (@p226) :args (@t5)) % 0.06/0.40 (step @p228 :rule cong :premises (@p227) :args (@t6)) % 0.06/0.40 (step @p229 :rule trans :premises (@p228 @p173)) % 0.06/0.40 (step @p230 :rule eq_resolve :premises (@p2 @p229)) % 0.06/0.40 (step @p231 :rule skolemize :premises (@p230)) % 0.06/0.40 (step @p232 :rule bool-double-not-elim :args (@t216)) % 0.06/0.40 (step @p233 :rule refl :args (@t227)) % 0.06/0.40 (step @p234 :rule nary_cong :premises (@p233 @p232) :args ((or @t227 (not @t219)))) % 0.06/0.40 (step @p235 :rule cnf_or_neg :args (@t227 3)) % 0.06/0.40 (step @p236 :rule eq_resolve :premises (@p235 @p234)) % 0.06/0.40 (step @p237 :rule reordering :premises (@p236) :args ((or @t216 @t227))) % 0.06/0.40 (step @p238 :rule chain_m_resolution :premises (@p237 @p231) :args (@t216 @t228 @t229)) % 0.06/0.40 (step @p239 :rule bool-double-not-elim :args (@t220)) % 0.06/0.40 (step @p240 :rule nary_cong :premises (@p233 @p239) :args ((or @t227 (not @t221)))) % 0.06/0.40 (step @p241 :rule cnf_or_neg :args (@t227 2)) % 0.06/0.40 (step @p242 :rule eq_resolve :premises (@p241 @p240)) % 0.06/0.40 (step @p243 :rule reordering :premises (@p242) :args ((or @t220 @t227))) % 0.06/0.40 (step @p244 :rule chain_m_resolution :premises (@p243 @p231) :args (@t220 @t228 @t229)) % 0.06/0.40 (step @p245 :rule cnf_or_pos :args (@t231)) % 0.06/0.40 (step @p246 :rule reordering :premises (@p245) :args ((or @t221 @t219 @t230 (not @t231)))) % 0.06/0.40 (step @p247 :rule chain_m_resolution :premises (@p246 @p244 @p238 @p75) :args (@t230 (@list false false false) (@list @t220 @t216 @t231))) % 0.06/0.40 (step @p248 :rule bool-double-not-elim :args (@t225)) % 0.06/0.40 (step @p249 :rule nary_cong :premises (@p233 @p248) :args ((or @t227 (not @t226)))) % 0.06/0.40 (step @p250 :rule cnf_or_neg :args (@t227 0)) % 0.06/0.40 (step @p251 :rule eq_resolve :premises (@p250 @p249)) % 0.06/0.40 (step @p252 :rule reordering :premises (@p251) :args ((or @t225 @t227))) % 0.06/0.40 (step @p253 :rule chain_m_resolution :premises (@p252 @p231) :args (@t225 @t228 @t229)) % 0.06/0.40 (step @p254 :rule instantiate :premises (@p253) :args ((@list @t122))) % 0.06/0.40 (step @p255 :rule cnf_or_neg :args (@t227 4)) % 0.06/0.40 (step @p256 :rule chain_m_resolution :premises (@p255 @p231) :args ((not @t218) @t228 @t229)) % 0.06/0.40 (step @p257 :rule cnf_or_pos :args (@t234)) % 0.06/0.40 (step @p258 :rule reordering :premises (@p257) :args ((or @t218 @t233 (not @t234)))) % 0.06/0.40 (step @p259 :rule chain_m_resolution :premises (@p258 @p256 @p254) :args (@t233 @t235 (@list @t218 @t234))) % 0.06/0.40 (step @p260 :rule bool-double-not-elim :args (@t223)) % 0.06/0.40 (step @p261 :rule nary_cong :premises (@p233 @p260) :args ((or @t227 (not @t224)))) % 0.06/0.40 (step @p262 :rule cnf_or_neg :args (@t227 1)) % 0.06/0.40 (step @p263 :rule eq_resolve :premises (@p262 @p261)) % 0.06/0.40 (step @p264 :rule reordering :premises (@p263) :args ((or @t223 @t227))) % 0.06/0.40 (step @p265 :rule chain_m_resolution :premises (@p264 @p231) :args (@t223 @t228 @t229)) % 0.06/0.40 (step @p266 :rule cnf_or_pos :args (@t237)) % 0.06/0.40 (step @p267 :rule reordering :premises (@p266) :args ((or @t224 @t232 @t236 @t238))) % 0.06/0.40 (step @p268 :rule chain_m_resolution :premises (@p267 @p265 @p259 @p247) :args (@t238 (@list false true false) (@list @t223 @t232 @t230))) % 0.06/0.40 (assume-push @p275 @t102) % 0.06/0.40 (step @p270 :rule instantiate :premises (@p74) :args ((@list @t222 @t124 @t122))) % 0.06/0.40 (step-pop @p276 :rule scope :premises (@p270)) % 0.06/0.40 (step @p271 :rule process_scope :premises (@p276) :args (@t237)) % 0.06/0.40 (step @p273 :rule implies_elim :premises (@p271)) % 0.06/0.40 (step @p274 false :rule chain_m_resolution :premises (@p273 @p268 @p74) :args (false @t235 (@list @t237 @t102))) % 0.06/0.40 ) % 0.06/0.40 % SZS output end Proof % 0.06/0.40 % cvc5 exiting %------------------------------------------------------------------------------