%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n010.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 150.29s 151.44s % Output : Proof 150.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL600^1 : TPTP v9.3.1. Released v3.6.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.09/0.36 % Computer : n010.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 04:55:24 UTC 2026 % 0.09/0.36 % CPUTime : % 0.09/0.44 %----Proving TH0 % 150.29/151.44 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.29/151.44 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 150.29/151.44 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 150.29/151.44 --- Run --ho-elim --full-saturate-quant at 18s... % 150.29/151.44 % SZS status Theorem % 150.29/151.44 % SZS output start Proof % 150.29/151.44 ( % 150.29/151.44 (declare-sort $$unsorted 0) % 150.29/151.44 (declare-sort tptp.individuals 0) % 150.29/151.44 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 150.29/151.44 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 150.29/151.44 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 150.29/151.44 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 150.29/151.44 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 150.29/151.44 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 150.29/151.44 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 150.29/151.44 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 150.29/151.44 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 150.29/151.44 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 150.29/151.44 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 150.29/151.44 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 150.29/151.44 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 150.29/151.44 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 150.29/151.44 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 150.29/151.44 (define tptp.cartesian_product () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3 _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1)))))))) % 150.29/151.44 (define tptp.pair_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "V" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1 _let_4 _let_2) (or (= _let_4 _let_3) (= _let_2 _let_1)))))))) % 150.29/151.44 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$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))))))) % 150.29/151.44 (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))))))))) % 150.29/151.44 (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))))))))))) % 150.29/151.44 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 150.29/151.44 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 150.29/151.44 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$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)))))))))) % 150.29/151.44 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 150.29/151.44 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 150.29/151.44 (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)))))))) % 150.29/151.44 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 150.29/151.44 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 150.29/151.44 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 150.29/151.44 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 150.29/151.44 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 150.29/151.44 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$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))))))))))) % 150.29/151.44 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 150.29/151.44 (define tptp.rel_field () (let ((_let_1 (@var "X" $$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)))))) % 150.29/151.44 (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))))))))))))))) % 150.29/151.44 (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))))))))))))))) % 150.29/151.44 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 150.29/151.44 (define @t2 () (_ tptp.transitive @t1)) % 150.29/151.44 (define @t3 () (@var "A" (-> $$unsorted Bool))) % 150.29/151.44 (define @t4 () (_ tptp.mbox @t1)) % 150.29/151.44 (define @t5 () (_ @t4 @t3)) % 150.29/151.44 (define @t6 () (@list @t3)) % 150.29/151.44 (define @t7 () (forall @t6 (_ tptp.mvalid (_ (_ tptp.mimpl @t5) (_ @t4 @t5))))) % 150.29/151.44 (define @t8 () (= @t7 @t2)) % 150.29/151.44 (define @t9 () (@list @t1)) % 150.29/151.44 (define @t10 () (forall @t9 @t8)) % 150.29/151.44 (define @t11 () (not @t10)) % 150.29/151.44 (define @t12 () (@var "X" $$unsorted)) % 150.29/151.44 (define @t13 () (@list @t12)) % 150.29/151.44 (define @t14 () (lambda @t13 false)) % 150.29/151.44 (define @t15 () (lambda @t13 true)) % 150.29/151.44 (define @t16 () (@var "U" $$unsorted)) % 150.29/151.44 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 150.29/151.44 (define @t18 () (_ @t17 @t16)) % 150.29/151.44 (define @t19 () (lambda (@list @t17 @t16) (not @t18))) % 150.29/151.44 (define @t20 () (@var "Y" (-> $$unsorted Bool))) % 150.29/151.44 (define @t21 () (_ @t20 @t16)) % 150.29/151.44 (define @t22 () (@list @t17 @t20 @t16)) % 150.29/151.44 (define @t23 () (lambda @t22 (or @t18 @t21))) % 150.29/151.44 (define @t24 () (lambda @t22 (and @t18 @t21))) % 150.29/151.44 (define @t25 () (@var "__flatten_var_0" $$unsorted)) % 150.29/151.44 (define @t26 () (@var "V" (-> $$unsorted Bool))) % 150.29/151.44 (define @t27 () (@var "U" (-> $$unsorted Bool))) % 150.29/151.44 (define @t28 () (@list @t27 @t26 @t25)) % 150.29/151.44 (define @t29 () (lambda @t28 (_ (_ (_ tptp.mor (_ tptp.mnot @t27)) @t26) @t25))) % 150.29/151.44 (define @t30 () (lambda @t28 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t27) @t26)) (_ (_ tptp.mimpl @t26) @t27)) @t25))) % 150.29/151.44 (define @t31 () (@var "Y" $$unsorted)) % 150.29/151.44 (define @t32 () (@var "P" (-> $$unsorted Bool))) % 150.29/151.44 (define @t33 () (_ @t32 @t31)) % 150.29/151.44 (define @t34 () (_ @t1 @t12)) % 150.29/151.44 (define @t35 () (_ @t34 @t31)) % 150.29/151.44 (define @t36 () (@list @t31)) % 150.29/151.44 (define @t37 () (forall @t36 (=> @t35 @t33))) % 150.29/151.44 (define @t38 () (@list @t1 @t32 @t12)) % 150.29/151.44 (define @t39 () (lambda @t38 @t37)) % 150.29/151.44 (define @t40 () (lambda @t38 (exists @t36 (and @t35 @t33)))) % 150.29/151.44 (define @t41 () (@var "W" $$unsorted)) % 150.29/151.44 (define @t42 () (@var "X" tptp.individuals)) % 150.29/151.44 (define @t43 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 150.29/151.44 (define @t44 () (_ (_ @t43 @t42) @t41)) % 150.29/151.44 (define @t45 () (@list @t42)) % 150.29/151.44 (define @t46 () (@list @t43 @t41)) % 150.29/151.44 (define @t47 () (lambda @t46 (forall @t45 @t44))) % 150.29/151.44 (define @t48 () (lambda @t46 (exists @t45 @t44))) % 150.29/151.44 (define @t49 () (_ @t32 @t41)) % 150.29/151.44 (define @t50 () (@list @t41)) % 150.29/151.44 (define @t51 () (forall @t50 @t49)) % 150.29/151.44 (define @t52 () (@list @t32)) % 150.29/151.44 (define @t53 () (lambda @t52 @t51)) % 150.29/151.44 (define @t54 () (lambda @t52 (exists @t50 @t49))) % 150.29/151.44 (define @t55 () (not @t49)) % 150.29/151.44 (define @t56 () (lambda @t52 (exists @t50 @t55))) % 150.29/151.44 (define @t57 () (lambda @t52 (forall @t50 @t55))) % 150.29/151.44 (define @t58 () (@var "V" $$unsorted)) % 150.29/151.44 (define @t59 () (lambda (@list @t17 @t20 @t16 @t58) (and @t18 (_ @t20 @t58)))) % 150.29/151.44 (define @t60 () (lambda (@list @t12 @t31 @t16 @t58) (or (= @t16 @t12) (= @t58 @t31)))) % 150.29/151.44 (define @t61 () (= @t12 @t31)) % 150.29/151.44 (define @t62 () (@var "S" (-> $$unsorted Bool))) % 150.29/151.44 (define @t63 () (_ @t62 @t12)) % 150.29/151.44 (define @t64 () (lambda (@list @t62 @t12 @t31) (and @t63 @t61))) % 150.29/151.44 (define @t65 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 150.29/151.44 (define @t66 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 150.29/151.44 (define @t67 () (_ (_ @t66 @t12) @t31)) % 150.29/151.44 (define @t68 () (@list @t12 @t31)) % 150.29/151.44 (define @t69 () (lambda (@list @t66 @t65) (forall @t68 (=> @t67 (_ (_ @t65 @t12) @t31))))) % 150.29/151.44 (define @t70 () (@var "B" (-> $$unsorted Bool))) % 150.29/151.44 (define @t71 () (lambda (@list @t1 @t3 @t70) (forall @t68 (=> @t35 (and (_ @t3 @t12) (_ @t70 @t31)))))) % 150.29/151.44 (define @t72 () (@list @t1 @t62 @t12 @t31)) % 150.29/151.44 (define @t73 () (lambda @t72 (and @t63 @t35))) % 150.29/151.44 (define @t74 () (lambda @t68 @t61)) % 150.29/151.44 (define @t75 () (@var "Z" $$unsorted)) % 150.29/151.44 (define @t76 () (lambda (@list @t66 @t65 @t12 @t75) (exists @t36 (and @t67 (_ (_ @t65 @t31) @t75))))) % 150.29/151.44 (define @t77 () (_ @t34 @t12)) % 150.29/151.44 (define @t78 () (lambda @t9 (forall @t13 @t77))) % 150.29/151.44 (define @t79 () (lambda @t9 (forall @t13 (not @t77)))) % 150.29/151.44 (define @t80 () (_ @t1 @t31)) % 150.29/151.44 (define @t81 () (_ @t80 @t12)) % 150.29/151.44 (define @t82 () (lambda @t9 (forall @t68 (=> @t35 @t81)))) % 150.29/151.44 (define @t83 () (_ @t34 @t75)) % 150.29/151.44 (define @t84 () (_ @t80 @t75)) % 150.29/151.44 (define @t85 () (and @t35 @t84)) % 150.29/151.44 (define @t86 () (@list @t12 @t31 @t75)) % 150.29/151.44 (define @t87 () (forall @t86 (=> @t85 @t83))) % 150.29/151.44 (define @t88 () (lambda @t9 @t87)) % 150.29/151.44 (define @t89 () (lambda @t9 (and (_ tptp.reflexive @t1) (_ tptp.symmetric @t1) @t2))) % 150.29/151.44 (define @t90 () (lambda (@list @t1 @t31) (exists @t13 @t35))) % 150.29/151.45 (define @t91 () (@list @t1 @t12)) % 150.29/151.45 (define @t92 () (lambda @t91 (exists @t36 @t35))) % 150.29/151.45 (define @t93 () (lambda (@list @t1 @t12 @t31) @t81)) % 150.29/151.45 (define @t94 () (@var "S1" (-> $$unsorted Bool))) % 150.29/151.45 (define @t95 () (lambda (@list @t1 @t94) (exists @t13 (and (_ @t94 @t12) (forall @t36 (= (_ @t94 @t31) @t35)))))) % 150.29/151.45 (define @t96 () (lambda @t72 (and (_ @t62 @t31) @t35))) % 150.29/151.45 (define @t97 () (lambda @t91 (or (_ (_ tptp.rel_domain @t1) @t12) (_ (_ tptp.rel_codomain @t1) @t12)))) % 150.29/151.45 (define @t98 () (not (_ @t17 @t41))) % 150.29/151.45 (define @t99 () (_ @t17 @t31)) % 150.29/151.45 (define @t100 () (_ @t17 @t75)) % 150.29/151.45 (define @t101 () (@list @t17 @t75)) % 150.29/151.45 (define @t102 () (lambda @t9 (forall @t101 (=> @t100 (exists @t36 (and @t99 (forall @t50 (=> (_ @t80 @t41) @t98)))))))) % 150.29/151.45 (define @t103 () (lambda @t9 (forall @t101 (=> @t100 (exists @t36 (and @t99 (forall @t50 (=> (_ @t80 @t31) @t98)))))))) % 150.29/151.45 (define @t104 () (@var "BOUND_VARIABLE_8403" (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 150.29/151.45 (define @t105 () (@const 0 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 150.29/151.45 (define @t106 () (_ @t105 @t104 @t12)) % 150.29/151.45 (define @t107 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 150.29/151.45 (define @t108 () (forall @t86 (or (not (_ @t107 @t106 @t31)) (not (_ @t107 (_ @t105 @t104 @t31) @t75)) (_ @t107 @t106 @t75)))) % 150.29/151.45 (define @t109 () (@var "BOUND_VARIABLE_8375" $$unsorted)) % 150.29/151.45 (define @t110 () (@var "BOUND_VARIABLE_8396" (@ho-elim-sort (-> $$unsorted Bool)))) % 150.29/151.45 (define @t111 () (_ @t107 @t110 @t109)) % 150.29/151.45 (define @t112 () (@var "BOUND_VARIABLE_8373" $$unsorted)) % 150.29/151.45 (define @t113 () (_ @t105 @t104 @t41)) % 150.29/151.45 (define @t114 () (_ @t107 @t110 @t31)) % 150.29/151.45 (define @t115 () (@list @t110 @t41 @t112 @t109)) % 150.29/151.45 (define @t116 () (forall @t115 (or (not (forall @t36 (or (not (_ @t107 @t113 @t31)) @t114))) (not (_ @t107 @t113 @t112)) (not (_ @t107 (_ @t105 @t104 @t112) @t109)) @t111))) % 150.29/151.45 (define @t117 () (@list @t104)) % 150.29/151.45 (define @t118 () (forall @t117 (= @t108 @t116))) % 150.29/151.45 (define @t119 () (not @t118)) % 150.29/151.45 (define @t120 () (_ @t3 @t109)) % 150.29/151.45 (define @t121 () (not (_ @t1 @t112 @t109))) % 150.29/151.45 (define @t122 () (not (_ @t1 @t41 @t112))) % 150.29/151.45 (define @t123 () (_ @t3 @t31)) % 150.29/151.45 (define @t124 () (not (_ @t1 @t41 @t31))) % 150.29/151.45 (define @t125 () (not (forall @t36 (or @t124 @t123)))) % 150.29/151.45 (define @t126 () (or @t125 @t122 @t121 @t120)) % 150.29/151.45 (define @t127 () (forall (@list @t3 @t41 @t112 @t109) @t126)) % 150.29/151.45 (define @t128 () (_ @t1 @t12 @t75)) % 150.29/151.45 (define @t129 () (_ @t1 @t31 @t75)) % 150.29/151.45 (define @t130 () (_ @t1 @t12 @t31)) % 150.29/151.45 (define @t131 () (not @t130)) % 150.29/151.45 (define @t132 () (forall @t86 (or @t131 (not @t129) @t128))) % 150.29/151.45 (define @t133 () (@list @t41 @t112 @t109)) % 150.29/151.45 (define @t134 () (or @t122 @t121 @t120)) % 150.29/151.45 (define @t135 () (or @t125 @t134)) % 150.29/151.45 (define @t136 () (forall @t133 @t135)) % 150.29/151.45 (define @t137 () (@list @t112 @t109)) % 150.29/151.45 (define @t138 () (forall @t137 @t135)) % 150.29/151.45 (define @t139 () (forall @t137 @t134)) % 150.29/151.45 (define @t140 () (@var "BOUND_VARIABLE_8340" $$unsorted)) % 150.29/151.45 (define @t141 () (or @t125 @t139)) % 150.29/151.45 (define @t142 () (_ @t3 @t140)) % 150.29/151.45 (define @t143 () (not (_ @t1 @t31 @t140))) % 150.29/151.45 (define @t144 () (@list @t31 @t140)) % 150.29/151.45 (define @t145 () (or @t125 (forall @t144 (or @t124 @t143 @t142)))) % 150.29/151.45 (define @t146 () (not (_ @t1 @t25 @t31))) % 150.29/151.45 (define @t147 () (forall @t144 (or @t146 @t143 @t142))) % 150.29/151.45 (define @t148 () (forall @t36 (or @t146 @t123))) % 150.29/151.45 (define @t149 () (not @t148)) % 150.29/151.45 (define @t150 () (@list @t25)) % 150.29/151.45 (define @t151 () (lambda @t150 (or @t149 @t147))) % 150.29/151.45 (define @t152 () (_ @t151 @t41)) % 150.29/151.45 (define @t153 () (forall @t50 @t152)) % 150.29/151.45 (define @t154 () (_ @t32 @t41)) % 150.29/151.45 (define @t155 () (lambda @t52 (forall @t50 @t154))) % 150.29/151.45 (define @t156 () (or @t131 @t143 @t142)) % 150.29/151.45 (define @t157 () (lambda @t13 (forall @t144 @t156))) % 150.29/151.45 (define @t158 () (_ @t157 @t25)) % 150.29/151.45 (define @t159 () (or @t149 @t158)) % 150.29/151.45 (define @t160 () (lambda @t150 @t159)) % 150.29/151.45 (define @t161 () (_ @t26 @t25)) % 150.29/151.45 (define @t162 () (@list @t26 @t25)) % 150.29/151.45 (define @t163 () (or @t143 @t142)) % 150.29/151.45 (define @t164 () (or @t131 @t163)) % 150.29/151.45 (define @t165 () (forall @t144 @t164)) % 150.29/151.45 (define @t166 () (@list @t140)) % 150.29/151.45 (define @t167 () (forall @t166 @t164)) % 150.29/151.45 (define @t168 () (forall @t166 @t163)) % 150.29/151.45 (define @t169 () (@var "BOUND_VARIABLE_8324" $$unsorted)) % 150.29/151.45 (define @t170 () (@list @t169)) % 150.29/151.45 (define @t171 () (or @t131 @t168)) % 150.29/151.45 (define @t172 () (_ @t3 @t169)) % 150.29/151.45 (define @t173 () (@list @t169)) % 150.29/151.45 (define @t174 () (forall @t173 (or (not (_ @t1 @t31 @t169)) @t172))) % 150.29/151.45 (define @t175 () (forall @t36 (or @t131 @t123))) % 150.29/151.45 (define @t176 () (lambda @t13 @t175)) % 150.29/151.45 (define @t177 () (or @t131 (_ @t176 @t31))) % 150.29/151.45 (define @t178 () (forall @t36 @t177)) % 150.29/151.45 (define @t179 () (lambda @t13 @t178)) % 150.29/151.45 (define @t180 () (_ @t32 @t31)) % 150.29/151.45 (define @t181 () (forall @t36 (or @t131 @t180))) % 150.29/151.45 (define @t182 () (lambda (@list @t32 @t12) @t181)) % 150.29/151.45 (define @t183 () (_ (lambda @t38 @t181) @t1)) % 150.29/151.45 (define @t184 () (_ @t176 @t25)) % 150.29/151.45 (define @t185 () (not @t184)) % 150.29/151.45 (define @t186 () (or @t185 @t161)) % 150.29/151.45 (define @t187 () (lambda @t162 @t186)) % 150.29/151.45 (define @t188 () (or (not (_ @t27 @t25)) @t161)) % 150.29/151.45 (define @t189 () (lambda @t28 @t188)) % 150.29/151.45 (define @t190 () (_ @t183 @t3)) % 150.29/151.45 (define @t191 () (forall @t6 (_ @t155 (_ (_ @t189 @t190) (_ @t183 @t190))))) % 150.29/151.45 (define @t192 () (_ (lambda @t9 @t132) @t1)) % 150.29/151.45 (define @t193 () (forall @t9 (= @t191 @t192))) % 150.29/151.45 (define @t194 () (not @t84)) % 150.29/151.45 (define @t195 () (not @t35)) % 150.29/151.45 (define @t196 () (or @t195 @t194 @t83)) % 150.29/151.45 (define @t197 () (or @t195 @t33)) % 150.29/151.45 (define @t198 () (not (_ @t27 @t16))) % 150.29/151.45 (define @t199 () (@list @t16)) % 150.29/151.45 (define @t200 () (lambda @t199 (or @t198 (_ @t26 @t16)))) % 150.29/151.45 (define @t201 () (@list @t20 @t16)) % 150.29/151.45 (define @t202 () (lambda @t199 @t198)) % 150.29/151.45 (define @t203 () (_ @t202 @t16)) % 150.29/151.45 (define @t204 () (or @t203 @t21)) % 150.29/151.45 (define @t205 () (lambda @t201 @t204)) % 150.29/151.45 (define @t206 () (@quantifiers_skolemize (forall @t117 (= @t116 @t108)) 0)) % 150.29/151.45 (define @t207 () (_ @t105 @t206 @t12)) % 150.29/151.45 (define @t208 () (forall @t86 (or (not (_ @t107 @t207 @t31)) (not (_ @t107 (_ @t105 @t206 @t31) @t75)) (_ @t107 @t207 @t75)))) % 150.29/151.45 (define @t209 () (_ @t105 @t206 @t41)) % 150.29/151.45 (define @t210 () (forall @t115 (or (not (forall @t36 (or (not (_ @t107 @t209 @t31)) @t114))) (not (_ @t107 @t209 @t112)) (not (_ @t107 (_ @t105 @t206 @t112) @t109)) @t111))) % 150.29/151.45 (define @t211 () (= @t210 @t208)) % 150.29/151.45 (define @t212 () (@quantifiers_skolemize @t208 2)) % 150.29/151.45 (define @t213 () (@quantifiers_skolemize @t208 0)) % 150.29/151.45 (define @t214 () (_ @t105 @t206 @t213)) % 150.29/151.45 (define @t215 () (_ @t107 @t214 @t212)) % 150.29/151.45 (define @t216 () (@quantifiers_skolemize @t208 1)) % 150.29/151.45 (define @t217 () (not (_ @t107 (_ @t105 @t206 @t216) @t212))) % 150.29/151.45 (define @t218 () (not (_ @t107 @t214 @t216))) % 150.29/151.45 (define @t219 () (or @t218 @t217 @t215)) % 150.29/151.45 (define @t220 () (not @t219)) % 150.29/151.45 (define @t221 () (not @t208)) % 150.29/151.45 (define @t222 () (_ @t107 @t214 @t31)) % 150.29/151.45 (define @t223 () (forall @t36 (or (not @t222) @t222))) % 150.29/151.45 (define @t224 () (not @t223)) % 150.29/151.45 (define @t225 () (or @t224 @t218 @t217 @t215)) % 150.29/151.45 (define @t226 () (not @t210)) % 150.29/151.45 (define @t227 () (@quantifiers_skolemize @t210 3)) % 150.29/151.45 (define @t228 () (@quantifiers_skolemize @t210 0)) % 150.29/151.45 (define @t229 () (_ @t107 @t228 @t227)) % 150.29/151.45 (define @t230 () (@quantifiers_skolemize @t210 2)) % 150.29/151.45 (define @t231 () (_ @t107 (_ @t105 @t206 @t230) @t227)) % 150.29/151.45 (define @t232 () (not @t231)) % 150.29/151.45 (define @t233 () (@quantifiers_skolemize @t210 1)) % 150.29/151.45 (define @t234 () (_ @t105 @t206 @t233)) % 150.29/151.45 (define @t235 () (_ @t107 @t234 @t230)) % 150.29/151.45 (define @t236 () (not @t235)) % 150.29/151.45 (define @t237 () (forall @t36 (or (not (_ @t107 @t234 @t31)) (_ @t107 @t228 @t31)))) % 150.29/151.45 (define @t238 () (not @t237)) % 150.29/151.45 (define @t239 () (or @t238 @t236 @t232 @t229)) % 150.29/151.45 (define @t240 () (not @t239)) % 150.29/151.45 (define @t241 () (@list true)) % 150.29/151.45 (define @t242 () (@list @t239)) % 150.29/151.45 (define @t243 () (_ @t107 @t234 @t227)) % 150.29/151.45 (define @t244 () (not @t243)) % 150.29/151.45 (define @t245 () (or @t244 @t229)) % 150.29/151.45 (define @t246 () (@list false)) % 150.29/151.45 (define @t247 () (or @t236 @t232 @t243)) % 150.29/151.45 (assume @p1 @t11) % 150.29/151.45 (assume @p2 true) % 150.29/151.45 (step @p3 (= tptp.mfalse @t14) :rule refl :args (@t14)) % 150.29/151.45 (step @p4 (= tptp.mtrue @t15) :rule refl :args (@t15)) % 150.29/151.45 (step @p5 (= tptp.mnot @t19) :rule refl :args (@t19)) % 150.29/151.45 (step @p6 (= tptp.mor @t23) :rule refl :args (@t23)) % 150.29/151.45 (step @p7 (= tptp.mand @t24) :rule refl :args (@t24)) % 150.29/151.45 (step @p8 (= tptp.mimpl @t29) :rule refl :args (@t29)) % 150.29/151.45 (step @p9 (= tptp.miff @t30) :rule refl :args (@t30)) % 150.29/151.45 (step @p10 (= tptp.mbox @t39) :rule refl :args (@t39)) % 150.29/151.45 (step @p11 (= tptp.mdia @t40) :rule refl :args (@t40)) % 150.29/151.45 (step @p12 (= tptp.mall @t47) :rule refl :args (@t47)) % 150.29/151.45 (step @p13 (= tptp.mexists @t48) :rule refl :args (@t48)) % 150.29/151.45 (step @p14 (= tptp.mvalid @t53) :rule refl :args (@t53)) % 150.29/151.45 (step @p15 (= tptp.msatisfiable @t54) :rule refl :args (@t54)) % 150.29/151.45 (step @p16 (= tptp.mcountersatisfiable @t56) :rule refl :args (@t56)) % 150.29/151.45 (step @p17 (= tptp.minvalid @t57) :rule refl :args (@t57)) % 150.29/151.45 (step @p18 (= tptp.cartesian_product @t59) :rule refl :args (@t59)) % 150.29/151.45 (step @p19 (= tptp.pair_rel @t60) :rule refl :args (@t60)) % 150.29/151.45 (step @p20 (= tptp.id_rel @t64) :rule refl :args (@t64)) % 150.29/151.45 (step @p21 (= tptp.sub_rel @t69) :rule refl :args (@t69)) % 150.29/151.45 (step @p22 (= tptp.is_rel_on @t71) :rule refl :args (@t71)) % 150.29/151.45 (step @p23 (= tptp.restrict_rel_domain @t73) :rule refl :args (@t73)) % 150.29/151.45 (step @p24 (= tptp.rel_diagonal @t74) :rule refl :args (@t74)) % 150.29/151.45 (step @p25 (= tptp.rel_composition @t76) :rule refl :args (@t76)) % 150.29/151.45 (step @p26 (= tptp.reflexive @t78) :rule refl :args (@t78)) % 150.29/151.45 (step @p27 (= tptp.irreflexive @t79) :rule refl :args (@t79)) % 150.29/151.45 (step @p28 (= tptp.symmetric @t82) :rule refl :args (@t82)) % 150.29/151.45 (step @p29 (= tptp.transitive @t88) :rule refl :args (@t88)) % 150.29/151.45 (step @p30 (= tptp.equiv_rel @t89) :rule refl :args (@t89)) % 150.29/151.45 (step @p31 (= tptp.rel_codomain @t90) :rule refl :args (@t90)) % 150.29/151.45 (step @p32 (= tptp.rel_domain @t92) :rule refl :args (@t92)) % 150.29/151.45 (step @p33 (= tptp.rel_inverse @t93) :rule refl :args (@t93)) % 150.29/151.45 (step @p34 (= tptp.equiv_classes @t95) :rule refl :args (@t95)) % 150.29/151.45 (step @p35 (= tptp.restrict_rel_codomain @t96) :rule refl :args (@t96)) % 150.29/151.45 (step @p36 (= tptp.rel_field @t97) :rule refl :args (@t97)) % 150.29/151.45 (step @p37 (= tptp.well_founded @t102) :rule refl :args (@t102)) % 150.29/151.45 (step @p38 (= tptp.upwards_well_founded @t103) :rule refl :args (@t103)) % 150.29/151.45 (step @p39 :rule eq-symm :args (@t108 @t116)) % 150.29/151.45 (step @p40 :rule cong :premises (@p39) :args (@t118)) % 150.29/151.45 (step @p41 :rule cong :premises (@p40) :args (@t119)) % 150.29/151.45 ; WARNING: add trust step for TRUST % 150.29/151.45 ; trust TRUST PREPROCESS_HO_ELIM % 150.29/151.45 (step @p42 :rule trust :premises () :args ((= (not (forall @t9 (= @t132 @t127))) @t119))) % 150.29/151.45 (step @p43 :rule quant-merge-prenex :args ((= (forall @t6 (forall @t133 @t126)) @t127))) % 150.29/151.45 (step @p44 :rule aci_norm :args ((= @t135 @t126))) % 150.29/151.45 (step @p45 :rule cong :premises (@p44) :args (@t136)) % 150.29/151.45 (step @p46 :rule quant-merge-prenex :args ((= (forall @t50 @t138) @t136))) % 150.29/151.45 (step @p47 :rule alpha_equiv :args (@t139 (@list @t112 @t109) (@list @t31 @t140))) % 150.29/151.45 (step @p48 :rule refl :args (@t125)) % 150.29/151.45 (step @p49 :rule nary_cong :premises (@p48 @p47) :args (@t141)) % 150.29/151.45 (step @p50 :rule quant-miniscope-or :args ((= @t138 @t141))) % 150.29/151.45 (step @p51 :rule trans :premises (@p50 @p49)) % 150.29/151.45 (step @p52 :rule symm :premises (@p51)) % 150.29/151.45 (step @p53 :rule cong :premises (@p52) :args ((forall @t50 @t145))) % 150.29/151.45 (step @p54 :rule trans :premises (@p53 @p46)) % 150.29/151.45 (step @p55 :rule trans :premises (@p54 @p45)) % 150.29/151.45 (step @p56 :rule beta-reduce :args ((= @t152 @t145))) % 150.29/151.45 (step @p57 :rule cong :premises (@p56) :args (@t153)) % 150.29/151.45 (step @p58 :rule trans :premises (@p57 @p55)) % 150.29/151.45 (step @p59 :rule beta-reduce :args ((= (_ @t155 @t151) @t153))) % 150.29/151.45 (step @p60 :rule trans :premises (@p59 @p58)) % 150.29/151.45 (step @p61 :rule beta-reduce :args ((= @t158 @t147))) % 150.29/151.45 (step @p62 :rule refl :args (@t149)) % 150.29/151.45 (step @p63 :rule nary_cong :premises (@p62 @p61) :args (@t159)) % 150.29/151.45 (step @p64 :rule cong :premises (@p63) :args (@t160)) % 150.29/151.45 (step @p65 :rule beta-reduce :args ((= (_ (lambda @t162 (or @t149 @t161)) @t157) @t160))) % 150.29/151.45 (step @p66 :rule trans :premises (@p65 @p64)) % 150.29/151.45 (step @p67 :rule aci_norm :args ((= @t164 @t156))) % 150.29/151.45 (step @p68 :rule cong :premises (@p67) :args (@t165)) % 150.29/151.45 (step @p69 :rule quant-merge-prenex :args ((= (forall @t36 @t167) @t165))) % 150.29/151.45 (step @p70 :rule alpha_equiv :args (@t168 (@list @t140) @t170)) % 150.29/151.45 (step @p71 :rule refl :args (@t131)) % 150.29/151.45 (step @p72 :rule nary_cong :premises (@p71 @p70) :args (@t171)) % 150.29/151.45 (step @p73 :rule quant-miniscope-or :args ((= @t167 @t171))) % 150.29/151.45 (step @p74 :rule trans :premises (@p73 @p72)) % 150.29/151.45 (step @p75 :rule symm :premises (@p74)) % 150.29/151.45 (step @p76 :rule cong :premises (@p75) :args ((forall @t36 (or @t131 @t174)))) % 150.29/151.45 (step @p77 :rule trans :premises (@p76 @p69)) % 150.29/151.45 (step @p78 :rule trans :premises (@p77 @p68)) % 150.29/151.45 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t13 (forall @t173 (or (not (_ @t1 @t12 @t169)) @t172))) @t31) @t174))) % 150.29/151.45 (step @p80 :rule refl :args (@t31)) % 150.29/151.45 (step @p81 :rule alpha_equiv :args (@t175 (@list @t31) @t170)) % 150.29/151.45 (step @p82 :rule cong :premises (@p81) :args (@t176)) % 150.29/151.45 (step @p83 :rule ho_cong :premises (@p82 @p80)) % 150.29/151.45 (step @p84 :rule trans :premises (@p83 @p79)) % 150.29/151.45 (step @p85 :rule refl :args (@t131)) % 150.29/151.45 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t177)) % 150.29/151.45 (step @p87 :rule cong :premises (@p86) :args (@t178)) % 150.29/151.45 (step @p88 :rule trans :premises (@p87 @p78)) % 150.29/151.45 (step @p89 :rule cong :premises (@p88) :args (@t179)) % 150.29/151.45 (step @p90 :rule beta-reduce :args ((= (_ @t182 @t176) @t179))) % 150.29/151.45 (step @p91 :rule trans :premises (@p90 @p89)) % 150.29/151.45 (step @p92 :rule beta-reduce :args ((= (_ @t182 @t3) @t176))) % 150.29/151.45 (step @p93 :rule refl :args (@t3)) % 150.29/151.45 (step @p94 :rule beta-reduce :args ((= @t183 @t182))) % 150.29/151.45 (step @p95 :rule ho_cong :premises (@p94 @p93)) % 150.29/151.45 (step @p96 :rule trans :premises (@p95 @p92)) % 150.29/151.45 (step @p97 :rule ho_cong :premises (@p94 @p96)) % 150.29/151.45 (step @p98 :rule trans :premises (@p97 @p91)) % 150.29/151.45 (step @p99 :rule refl :args (@t161)) % 150.29/151.45 (step @p100 :rule beta-reduce :args ((= @t184 @t148))) % 150.29/151.45 (step @p101 :rule cong :premises (@p100) :args (@t185)) % 150.29/151.45 (step @p102 :rule nary_cong :premises (@p101 @p99) :args (@t186)) % 150.29/151.45 (step @p103 :rule cong :premises (@p102) :args (@t187)) % 150.29/151.45 (step @p104 :rule beta-reduce :args ((= (_ @t189 @t176) @t187))) % 150.29/151.45 (step @p105 :rule trans :premises (@p104 @p103)) % 150.29/151.45 (step @p106 :rule refl :args (@t189)) % 150.29/151.45 (step @p107 :rule ho_cong :premises (@p106 @p96)) % 150.29/151.45 (step @p108 :rule trans :premises (@p107 @p105)) % 150.29/151.45 (step @p109 :rule ho_cong :premises (@p108 @p98)) % 150.29/151.45 (step @p110 :rule trans :premises (@p109 @p66)) % 150.29/151.45 (step @p111 :rule refl :args (@t155)) % 150.29/151.45 (step @p112 :rule ho_cong :premises (@p111 @p110)) % 150.29/151.45 (step @p113 :rule trans :premises (@p112 @p60)) % 150.29/151.45 (step @p114 :rule cong :premises (@p113) :args (@t191)) % 150.29/151.45 (step @p115 :rule trans :premises (@p114 @p43)) % 150.29/151.45 (step @p116 :rule beta-reduce :args ((= @t192 @t132))) % 150.29/151.45 (step @p117 :rule cong :premises (@p116 @p115) :args ((= @t192 @t191))) % 150.29/151.45 (step @p118 :rule eq-symm :args (@t191 @t192)) % 150.29/151.45 (step @p119 :rule trans :premises (@p118 @p117)) % 150.29/151.45 (step @p120 :rule cong :premises (@p119) :args (@t193)) % 150.29/151.45 (step @p121 :rule cong :premises (@p120) :args ((not @t193))) % 150.29/151.45 (step @p122 :rule refl :args (@t1)) % 150.29/151.45 (step @p123 :rule refl :args (@t128)) % 150.29/151.45 (step @p124 :rule refl :args (@t83)) % 150.29/151.45 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t83 @t128))) % 150.29/151.45 (step @p126 :rule symm :premises (@p125)) % 150.29/151.45 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 150.29/151.45 (step @p128 :rule refl :args (@t129)) % 150.29/151.45 (step @p129 :rule refl :args (@t84)) % 150.29/151.45 (step @p130 :rule cong :premises (@p129 @p128) :args ((= @t84 @t129))) % 150.29/151.45 (step @p131 :rule symm :premises (@p130)) % 150.29/151.45 (step @p132 :rule eq_resolve :premises (@p129 @p131)) % 150.29/151.45 (step @p133 :rule cong :premises (@p132) :args (@t194)) % 150.29/151.45 (step @p134 :rule refl :args (@t130)) % 150.29/151.45 (step @p135 :rule refl :args (@t35)) % 150.29/151.45 (step @p136 :rule cong :premises (@p135 @p134) :args ((= @t35 @t130))) % 150.29/151.45 (step @p137 :rule symm :premises (@p136)) % 150.29/151.45 (step @p138 :rule eq_resolve :premises (@p135 @p137)) % 150.29/151.45 (step @p139 :rule cong :premises (@p138) :args (@t195)) % 150.29/151.45 (step @p140 :rule nary_cong :premises (@p139 @p133 @p127) :args (@t196)) % 150.29/151.45 (step @p141 :rule cong :premises (@p140) :args ((forall @t86 @t196))) % 150.29/151.45 (step @p142 :rule aci_norm :args ((= (or (or @t195 @t194) @t83) @t196))) % 150.29/151.45 (step @p143 :rule bool-and-de-morgan :args (@t35 @t84 true)) % 150.29/151.45 (step @p144 :rule nary_cong :premises (@p143 @p124) :args ((or (not @t85) @t83))) % 150.29/151.45 (step @p145 :rule trans :premises (@p144 @p142)) % 150.29/151.45 (step @p146 :rule bool-impl-elim :args (@t85 @t83)) % 150.29/151.45 (step @p147 :rule trans :premises (@p146 @p145)) % 150.29/151.45 (step @p148 :rule cong :premises (@p147) :args (@t87)) % 150.29/151.45 (step @p149 :rule trans :premises (@p148 @p141)) % 150.29/151.45 (step @p150 :rule cong :premises (@p149) :args (@t88)) % 150.29/151.45 (step @p151 :rule trans :premises (@p29 @p150)) % 150.29/151.45 (step @p152 :rule ho_cong :premises (@p151 @p122)) % 150.29/151.45 (step @p153 :rule refl :args (@t180)) % 150.29/151.45 (step @p154 :rule refl :args (@t33)) % 150.29/151.45 (step @p155 :rule cong :premises (@p154 @p153) :args ((= @t33 @t180))) % 150.29/151.45 (step @p156 :rule symm :premises (@p155)) % 150.29/151.45 (step @p157 :rule eq_resolve :premises (@p154 @p156)) % 150.29/151.45 (step @p158 :rule nary_cong :premises (@p139 @p157) :args (@t197)) % 150.29/151.45 (step @p159 :rule cong :premises (@p158) :args ((forall @t36 @t197))) % 150.29/151.45 (step @p160 :rule bool-impl-elim :args (@t35 @t33)) % 150.29/151.45 (step @p161 :rule cong :premises (@p160) :args (@t37)) % 150.29/151.45 (step @p162 :rule trans :premises (@p161 @p159)) % 150.29/151.45 (step @p163 :rule cong :premises (@p162) :args (@t39)) % 150.29/151.45 (step @p164 :rule trans :premises (@p10 @p163)) % 150.29/151.45 (step @p165 :rule ho_cong :premises (@p164 @p122)) % 150.29/151.45 (step @p166 :rule ho_cong :premises (@p165 @p93)) % 150.29/151.45 (step @p167 :rule ho_cong :premises (@p165 @p166)) % 150.29/151.45 (step @p168 :rule beta-reduce :args ((= (_ @t200 @t25) @t188))) % 150.29/151.45 (step @p169 :rule refl :args (@t25)) % 150.29/151.45 (step @p170 :rule beta-reduce :args ((= (_ (lambda @t201 (or @t198 @t21)) @t26) @t200))) % 150.29/151.45 (step @p171 :rule refl :args (@t26)) % 150.29/151.45 (step @p172 :rule refl :args (@t21)) % 150.29/151.45 (step @p173 :rule beta-reduce :args ((= @t203 @t198))) % 150.29/151.45 (step @p174 :rule nary_cong :premises (@p173 @p172) :args (@t204)) % 150.29/151.45 (step @p175 :rule cong :premises (@p174) :args (@t205)) % 150.29/151.45 (step @p176 :rule beta-reduce :args ((= (_ @t23 @t202) @t205))) % 150.29/151.45 (step @p177 :rule trans :premises (@p176 @p175)) % 150.29/151.45 (step @p178 :rule beta-reduce :args ((= (_ @t19 @t27) @t202))) % 150.29/151.45 (step @p179 :rule refl :args (@t23)) % 150.29/151.45 (step @p180 :rule ho_cong :premises (@p179 @p178)) % 150.29/151.45 (step @p181 :rule trans :premises (@p180 @p177)) % 150.29/151.45 (step @p182 :rule ho_cong :premises (@p181 @p171)) % 150.29/151.45 (step @p183 :rule trans :premises (@p182 @p170)) % 150.29/151.45 (step @p184 :rule ho_cong :premises (@p183 @p169)) % 150.29/151.45 (step @p185 :rule trans :premises (@p184 @p168)) % 150.29/151.45 (step @p186 :rule refl :args (@t27)) % 150.29/151.45 (step @p187 :rule ho_cong :premises (@p5 @p186)) % 150.29/151.45 (step @p188 :rule ho_cong :premises (@p6 @p187)) % 150.29/151.45 (step @p189 :rule ho_cong :premises (@p188 @p171)) % 150.29/151.45 (step @p190 :rule ho_cong :premises (@p189 @p169)) % 150.29/151.45 (step @p191 :rule trans :premises (@p190 @p185)) % 150.29/151.45 (step @p192 :rule cong :premises (@p191) :args (@t29)) % 150.29/151.45 (step @p193 :rule trans :premises (@p8 @p192)) % 150.29/151.45 (step @p194 :rule ho_cong :premises (@p193 @p166)) % 150.29/151.45 (step @p195 :rule ho_cong :premises (@p194 @p167)) % 150.29/151.45 (step @p196 :rule refl :args (@t154)) % 150.29/151.45 (step @p197 :rule refl :args (@t49)) % 150.29/151.45 (step @p198 :rule cong :premises (@p197 @p196) :args ((= @t49 @t154))) % 150.29/151.45 (step @p199 :rule symm :premises (@p198)) % 150.29/151.45 (step @p200 :rule eq_resolve :premises (@p197 @p199)) % 150.29/151.45 (step @p201 :rule cong :premises (@p200) :args (@t51)) % 150.29/151.45 (step @p202 :rule cong :premises (@p201) :args (@t53)) % 150.29/151.45 (step @p203 :rule trans :premises (@p14 @p202)) % 150.29/151.45 (step @p204 :rule ho_cong :premises (@p203 @p195)) % 150.29/151.45 (step @p205 :rule cong :premises (@p204) :args (@t7)) % 150.29/151.45 (step @p206 :rule cong :premises (@p205 @p152) :args (@t8)) % 150.29/151.45 (step @p207 :rule cong :premises (@p206) :args (@t10)) % 150.29/151.45 (step @p208 :rule cong :premises (@p207) :args (@t11)) % 150.29/151.45 (step @p209 :rule trans :premises (@p208 @p121)) % 150.29/151.45 (step @p210 :rule trans :premises (@p209 @p42 @p41)) % 150.29/151.45 (step @p211 :rule eq_resolve :premises (@p1 @p210)) % 150.29/151.45 (step @p212 :rule skolemize :premises (@p211)) % 150.29/151.45 (step @p213 :rule cnf_equiv_neg2 :args (@t211)) % 150.29/151.45 (step @p214 :rule refl :args (@t220)) % 150.29/151.45 (step @p215 :rule bool-double-not-elim :args (@t208)) % 150.29/151.45 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or (not @t221) @t220))) % 150.29/151.45 (assume-push @p297 @t221) % 150.29/151.45 (step @p218 :rule skolemize :premises (@p297)) % 150.29/151.45 (step-pop @p298 :rule scope :premises (@p218)) % 150.29/151.45 (step @p219 :rule process_scope :premises (@p298) :args (@t220)) % 150.29/151.45 (step @p221 :rule implies_elim :premises (@p219)) % 150.29/151.45 (step @p222 :rule eq_resolve :premises (@p221 @p216)) % 150.29/151.45 (step @p223 :rule aci_norm :args ((= (or false @t218 @t217 @t215) @t219))) % 150.29/151.45 (step @p224 :rule refl :args (@t215)) % 150.29/151.45 (step @p225 :rule refl :args (@t217)) % 150.29/151.45 (step @p226 :rule refl :args (@t218)) % 150.29/151.45 (step @p227 :rule evaluate :args ((not true))) % 150.29/151.45 (step @p228 :rule quant-unused-vars :args ((= (forall @t36 true) true))) % 150.29/151.45 (step @p229 :rule bool-or-taut2 :args (false @t222 false false)) % 150.29/151.45 (step @p230 :rule cong :premises (@p229) :args (@t223)) % 150.29/151.45 (step @p231 :rule trans :premises (@p230 @p228)) % 150.29/151.45 (step @p232 :rule cong :premises (@p231) :args (@t224)) % 150.29/151.45 (step @p233 :rule trans :premises (@p232 @p227)) % 150.29/151.45 (step @p234 :rule nary_cong :premises (@p233 @p226 @p225 @p224) :args (@t225)) % 150.29/151.45 (step @p235 :rule trans :premises (@p234 @p223)) % 150.29/151.45 (step @p236 :rule refl :args (@t210)) % 150.29/151.45 (step @p237 :rule cong :premises (@p236 @p235) :args ((=> @t210 @t225))) % 150.29/151.45 (assume-push @p299 @t210) % 150.29/151.45 (step @p239 :rule instantiate :premises (@p299) :args ((@list @t214 @t213 @t216 @t212))) % 150.29/151.45 (step-pop @p300 :rule scope :premises (@p239)) % 150.29/151.45 (step @p240 :rule process_scope :premises (@p300) :args (@t225)) % 150.29/151.45 (step @p242 :rule eq_resolve :premises (@p240 @p237)) % 150.29/151.45 (step @p243 :rule implies_elim :premises (@p242)) % 150.29/151.45 (step @p244 :rule chain_m_resolution :premises (@p243 @p222 @p213 @p212) :args (@t226 (@list true true true) (@list @t219 @t208 @t211))) % 150.29/151.45 (step @p245 :rule refl :args (@t240)) % 150.29/151.45 (step @p246 :rule bool-double-not-elim :args (@t210)) % 150.29/151.45 (step @p247 :rule nary_cong :premises (@p246 @p245) :args ((or (not @t226) @t240))) % 150.29/151.45 (assume-push @p301 @t226) % 150.29/151.45 (step @p249 :rule skolemize :premises (@p301)) % 150.29/151.45 (step-pop @p302 :rule scope :premises (@p249)) % 150.29/151.45 (step @p250 :rule process_scope :premises (@p302) :args (@t240)) % 150.29/151.45 (step @p252 :rule implies_elim :premises (@p250)) % 150.29/151.45 (step @p253 :rule eq_resolve :premises (@p252 @p247)) % 150.29/151.45 (step @p254 :rule chain_m_resolution :premises (@p253 @p244) :args (@t240 @t241 (@list @t210))) % 150.29/151.45 (step @p255 :rule cnf_or_neg :args (@t239 3)) % 150.29/151.45 (step @p256 :rule chain_m_resolution :premises (@p255 @p254) :args ((not @t229) @t241 @t242)) % 150.29/151.45 (step @p257 :rule bool-double-not-elim :args (@t237)) % 150.29/151.45 (step @p258 :rule refl :args (@t239)) % 150.29/151.45 (step @p259 :rule nary_cong :premises (@p258 @p257) :args ((or @t239 (not @t238)))) % 150.29/151.45 (step @p260 :rule cnf_or_neg :args (@t239 0)) % 150.29/151.45 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 150.29/151.45 (step @p262 :rule reordering :premises (@p261) :args ((or @t237 @t239))) % 150.29/151.45 (step @p263 :rule chain_m_resolution :premises (@p262 @p254) :args (@t237 @t241 @t242)) % 150.29/151.45 (assume-push @p303 @t237) % 150.29/151.45 (step @p265 :rule instantiate :premises (@p303) :args ((@list @t227))) % 150.29/151.45 (step-pop @p304 :rule scope :premises (@p265)) % 150.29/151.45 (step @p266 :rule process_scope :premises (@p304) :args (@t245)) % 150.29/151.45 (step @p268 :rule implies_elim :premises (@p266)) % 150.29/151.45 (step @p269 :rule chain_m_resolution :premises (@p268 @p263) :args (@t245 @t246 (@list @t237))) % 150.29/151.45 (step @p270 :rule cnf_equiv_neg1 :args (@t211)) % 150.29/151.45 (step @p271 :rule reordering :premises (@p270) :args ((or @t210 @t208 @t211))) % 150.29/151.45 (step @p272 :rule chain_m_resolution :premises (@p271 @p244 @p212) :args (@t208 (@list true true) (@list @t210 @t211))) % 150.29/151.45 (assume-push @p305 @t208) % 150.29/151.45 (step @p274 :rule instantiate :premises (@p305) :args ((@list @t233 @t230 @t227))) % 150.29/151.45 (step-pop @p306 :rule scope :premises (@p274)) % 150.29/151.45 (step @p275 :rule process_scope :premises (@p306) :args (@t247)) % 150.29/151.45 (step @p277 :rule implies_elim :premises (@p275)) % 150.29/151.45 (step @p278 :rule chain_m_resolution :premises (@p277 @p272) :args (@t247 @t246 (@list @t208))) % 150.29/151.45 (step @p279 :rule bool-double-not-elim :args (@t231)) % 150.29/151.45 (step @p280 :rule nary_cong :premises (@p258 @p279) :args ((or @t239 (not @t232)))) % 150.29/151.45 (step @p281 :rule cnf_or_neg :args (@t239 2)) % 150.29/151.45 (step @p282 :rule eq_resolve :premises (@p281 @p280)) % 150.29/151.45 (step @p283 :rule reordering :premises (@p282) :args ((or @t231 @t239))) % 150.29/151.45 (step @p284 :rule chain_m_resolution :premises (@p283 @p254) :args (@t231 @t241 @t242)) % 150.29/151.45 (step @p285 :rule bool-double-not-elim :args (@t235)) % 150.29/151.45 (step @p286 :rule nary_cong :premises (@p258 @p285) :args ((or @t239 (not @t236)))) % 150.29/151.45 (step @p287 :rule cnf_or_neg :args (@t239 1)) % 150.29/151.45 (step @p288 :rule eq_resolve :premises (@p287 @p286)) % 150.29/151.45 (step @p289 :rule reordering :premises (@p288) :args ((or @t235 @t239))) % 150.29/151.45 (step @p290 :rule chain_m_resolution :premises (@p289 @p254) :args (@t235 @t241 @t242)) % 150.29/151.45 (step @p291 :rule cnf_or_pos :args (@t247)) % 150.29/151.45 (step @p292 :rule reordering :premises (@p291) :args ((or @t236 @t232 @t243 (not @t247)))) % 150.29/151.45 (step @p293 :rule chain_m_resolution :premises (@p292 @p290 @p284 @p278) :args (@t243 (@list false false false) (@list @t235 @t231 @t247))) % 150.29/151.45 (step @p294 :rule cnf_or_pos :args (@t245)) % 150.29/151.45 (step @p295 :rule reordering :premises (@p294) :args ((or @t229 @t244 (not @t245)))) % 150.29/151.45 (step @p296 false :rule chain_m_resolution :premises (@p295 @p293 @p269 @p256) :args (false (@list false false true) (@list @t243 @t245 @t229))) % 150.29/151.45 ) % 150.29/151.45 % SZS output end Proof % 150.29/151.45 % cvc5 exiting %------------------------------------------------------------------------------