%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL601^1 : 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 : n015.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 150.25s 151.58s % Output : Proof 150.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL601^1 : 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 % 0.11/0.36 % Computer : n015.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.36 % CPULimit : 300 % 0.11/0.36 % WCLimit : 300 % 0.11/0.36 % DateTime : Sat Sep 5 15:44:43 UTC 2026 % 0.15/0.37 % CPUTime : % 0.15/0.44 %----Proving TH0 % 150.25/151.58 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 150.25/151.58 --- 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... % 150.25/151.58 --- 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... % 150.25/151.58 --- Run --ho-elim --full-saturate-quant at 18s... % 150.25/151.58 % SZS status Theorem % 150.25/151.58 % SZS output start Proof % 150.25/151.58 ( % 150.25/151.58 (declare-sort $$unsorted 0) % 150.25/151.58 (declare-sort tptp.individuals 0) % 150.25/151.58 (define tptp.mfalse () (lambda (@list (@var "X" $$unsorted)) false)) % 150.25/151.58 (define tptp.mtrue () (lambda (@list (@var "X" $$unsorted)) true)) % 150.25/151.58 (define tptp.mnot () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 150.25/151.58 (define tptp.mor () (let ((_let_1 (@var "U" $$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))))))) % 150.25/151.58 (define tptp.mand () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 150.25/151.58 (define tptp.mimpl () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 150.25/151.58 (define tptp.miff () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "U" (-> $$unsorted Bool)))) (let ((_let_3 (@var "V" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimpl _let_2) _let_3)) (_ (_ tptp.mimpl _let_3) _let_2)) _let_1)))))) % 150.25/151.58 (define tptp.mbox () (let ((_let_1 (@var "Y" $$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))))))))) % 150.25/151.58 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 150.25/151.58 (define tptp.mall () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 150.25/151.58 (define tptp.mexists () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.individuals))) (let ((_let_3 (@var "P" (-> tptp.individuals $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 150.25/151.58 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 150.25/151.58 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 150.25/151.58 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 150.25/151.58 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 150.25/151.58 (define tptp.cartesian_product () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "U" $$unsorted))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3 _let_1) (and (_ _let_4 _let_3) (_ _let_2 _let_1)))))))) % 150.25/151.58 (define tptp.pair_rel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "V" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "U" $$unsorted))) (lambda (@list _let_3 _let_1 _let_4 _let_2) (or (= _let_4 _let_3) (= _let_2 _let_1)))))))) % 150.25/151.58 (define tptp.id_rel () (let ((_let_1 (@var "Y" $$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))))))) % 150.25/151.58 (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))))))))) % 150.25/151.58 (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))))))))))) % 150.25/151.58 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 150.25/151.58 (define tptp.rel_diagonal () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_2 _let_1) (= _let_2 _let_1))))) % 150.25/151.58 (define tptp.rel_composition () (let ((_let_1 (@var "Z" $$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)))))))))) % 150.25/151.58 (define tptp.reflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 150.25/151.58 (define tptp.irreflexive () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 150.25/151.58 (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)))))))) % 150.25/151.58 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 150.25/151.58 (define tptp.equiv_rel () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.reflexive _let_1) (_ tptp.symmetric _let_1) (_ tptp.transitive _let_1))))) % 150.25/151.58 (define tptp.rel_codomain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 150.25/151.58 (define tptp.rel_domain () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 150.25/151.58 (define tptp.rel_inverse () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 150.25/151.58 (define tptp.equiv_classes () (let ((_let_1 (@var "Y" $$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))))))))))) % 150.25/151.58 (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" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_4 _let_2 _let_1) (and (_ _let_4 _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 150.25/151.58 (define tptp.rel_field () (let ((_let_1 (@var "X" $$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)))))) % 150.25/151.58 (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))))))))))))))) % 150.25/151.58 (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))))))))))))))) % 150.25/151.58 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 150.25/151.58 (define @t2 () (_ tptp.transitive @t1)) % 150.25/151.58 (define @t3 () (@list @t1)) % 150.25/151.58 (define @t4 () (forall @t3 @t2)) % 150.25/151.58 (define @t5 () (@var "A" (-> $$unsorted Bool))) % 150.25/151.58 (define @t6 () (_ tptp.mbox @t1)) % 150.25/151.58 (define @t7 () (_ @t6 @t5)) % 150.25/151.58 (define @t8 () (@list @t1 @t5)) % 150.25/151.58 (define @t9 () (forall @t8 (_ tptp.mvalid (_ (_ tptp.mimpl @t7) (_ @t6 @t7))))) % 150.25/151.58 (define @t10 () (= @t9 @t4)) % 150.25/151.58 (define @t11 () (not @t10)) % 150.25/151.58 (define @t12 () (@var "X" $$unsorted)) % 150.25/151.58 (define @t13 () (@list @t12)) % 150.25/151.58 (define @t14 () (lambda @t13 false)) % 150.25/151.58 (define @t15 () (lambda @t13 true)) % 150.25/151.58 (define @t16 () (@var "U" $$unsorted)) % 150.25/151.58 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 150.25/151.58 (define @t18 () (_ @t17 @t16)) % 150.25/151.58 (define @t19 () (lambda (@list @t17 @t16) (not @t18))) % 150.25/151.58 (define @t20 () (@var "Y" (-> $$unsorted Bool))) % 150.25/151.58 (define @t21 () (_ @t20 @t16)) % 150.25/151.58 (define @t22 () (@list @t17 @t20 @t16)) % 150.25/151.58 (define @t23 () (lambda @t22 (or @t18 @t21))) % 150.25/151.58 (define @t24 () (lambda @t22 (and @t18 @t21))) % 150.25/151.58 (define @t25 () (@var "__flatten_var_0" $$unsorted)) % 150.25/151.58 (define @t26 () (@var "V" (-> $$unsorted Bool))) % 150.25/151.58 (define @t27 () (@var "U" (-> $$unsorted Bool))) % 150.25/151.58 (define @t28 () (@list @t27 @t26 @t25)) % 150.25/151.58 (define @t29 () (lambda @t28 (_ (_ (_ tptp.mor (_ tptp.mnot @t27)) @t26) @t25))) % 150.25/151.58 (define @t30 () (lambda @t28 (_ (_ (_ tptp.mand (_ (_ tptp.mimpl @t27) @t26)) (_ (_ tptp.mimpl @t26) @t27)) @t25))) % 150.25/151.58 (define @t31 () (@var "Y" $$unsorted)) % 150.25/151.58 (define @t32 () (@var "P" (-> $$unsorted Bool))) % 150.25/151.58 (define @t33 () (_ @t32 @t31)) % 150.25/151.58 (define @t34 () (_ @t1 @t12)) % 150.25/151.58 (define @t35 () (_ @t34 @t31)) % 150.25/151.58 (define @t36 () (@list @t31)) % 150.25/151.58 (define @t37 () (forall @t36 (=> @t35 @t33))) % 150.25/151.58 (define @t38 () (@list @t1 @t32 @t12)) % 150.25/151.58 (define @t39 () (lambda @t38 @t37)) % 150.25/151.58 (define @t40 () (lambda @t38 (exists @t36 (and @t35 @t33)))) % 150.25/151.58 (define @t41 () (@var "W" $$unsorted)) % 150.25/151.58 (define @t42 () (@var "X" tptp.individuals)) % 150.25/151.58 (define @t43 () (@var "P" (-> tptp.individuals $$unsorted Bool))) % 150.25/151.58 (define @t44 () (_ (_ @t43 @t42) @t41)) % 150.25/151.58 (define @t45 () (@list @t42)) % 150.25/151.58 (define @t46 () (@list @t43 @t41)) % 150.25/151.58 (define @t47 () (lambda @t46 (forall @t45 @t44))) % 150.25/151.58 (define @t48 () (lambda @t46 (exists @t45 @t44))) % 150.25/151.58 (define @t49 () (_ @t32 @t41)) % 150.25/151.58 (define @t50 () (@list @t41)) % 150.25/151.58 (define @t51 () (forall @t50 @t49)) % 150.25/151.58 (define @t52 () (@list @t32)) % 150.25/151.58 (define @t53 () (lambda @t52 @t51)) % 150.25/151.58 (define @t54 () (lambda @t52 (exists @t50 @t49))) % 150.25/151.58 (define @t55 () (not @t49)) % 150.25/151.58 (define @t56 () (lambda @t52 (exists @t50 @t55))) % 150.25/151.58 (define @t57 () (lambda @t52 (forall @t50 @t55))) % 150.25/151.58 (define @t58 () (@var "V" $$unsorted)) % 150.25/151.58 (define @t59 () (lambda (@list @t17 @t20 @t16 @t58) (and @t18 (_ @t20 @t58)))) % 150.25/151.58 (define @t60 () (lambda (@list @t12 @t31 @t16 @t58) (or (= @t16 @t12) (= @t58 @t31)))) % 150.25/151.58 (define @t61 () (= @t12 @t31)) % 150.25/151.58 (define @t62 () (@var "S" (-> $$unsorted Bool))) % 150.25/151.58 (define @t63 () (_ @t62 @t12)) % 150.25/151.58 (define @t64 () (lambda (@list @t62 @t12 @t31) (and @t63 @t61))) % 150.25/151.58 (define @t65 () (@var "R2" (-> $$unsorted $$unsorted Bool))) % 150.25/151.58 (define @t66 () (@var "R1" (-> $$unsorted $$unsorted Bool))) % 150.25/151.58 (define @t67 () (_ (_ @t66 @t12) @t31)) % 150.25/151.58 (define @t68 () (@list @t12 @t31)) % 150.25/151.58 (define @t69 () (lambda (@list @t66 @t65) (forall @t68 (=> @t67 (_ (_ @t65 @t12) @t31))))) % 150.25/151.58 (define @t70 () (@var "B" (-> $$unsorted Bool))) % 150.25/151.58 (define @t71 () (lambda (@list @t1 @t5 @t70) (forall @t68 (=> @t35 (and (_ @t5 @t12) (_ @t70 @t31)))))) % 150.25/151.58 (define @t72 () (@list @t1 @t62 @t12 @t31)) % 150.25/151.58 (define @t73 () (lambda @t72 (and @t63 @t35))) % 150.25/151.58 (define @t74 () (lambda @t68 @t61)) % 150.25/151.58 (define @t75 () (@var "Z" $$unsorted)) % 150.25/151.58 (define @t76 () (lambda (@list @t66 @t65 @t12 @t75) (exists @t36 (and @t67 (_ (_ @t65 @t31) @t75))))) % 150.25/151.58 (define @t77 () (_ @t34 @t12)) % 150.25/151.58 (define @t78 () (lambda @t3 (forall @t13 @t77))) % 150.25/151.58 (define @t79 () (lambda @t3 (forall @t13 (not @t77)))) % 150.25/151.58 (define @t80 () (_ @t1 @t31)) % 150.25/151.58 (define @t81 () (_ @t80 @t12)) % 150.25/151.58 (define @t82 () (lambda @t3 (forall @t68 (=> @t35 @t81)))) % 150.25/151.58 (define @t83 () (_ @t34 @t75)) % 150.25/151.58 (define @t84 () (_ @t80 @t75)) % 150.25/151.58 (define @t85 () (and @t35 @t84)) % 150.25/151.58 (define @t86 () (@list @t12 @t31 @t75)) % 150.25/151.58 (define @t87 () (forall @t86 (=> @t85 @t83))) % 150.25/151.58 (define @t88 () (lambda @t3 @t87)) % 150.25/151.58 (define @t89 () (lambda @t3 (and (_ tptp.reflexive @t1) (_ tptp.symmetric @t1) @t2))) % 150.25/151.58 (define @t90 () (lambda (@list @t1 @t31) (exists @t13 @t35))) % 150.25/151.58 (define @t91 () (@list @t1 @t12)) % 150.25/151.58 (define @t92 () (lambda @t91 (exists @t36 @t35))) % 150.25/151.58 (define @t93 () (lambda (@list @t1 @t12 @t31) @t81)) % 150.25/151.58 (define @t94 () (@var "S1" (-> $$unsorted Bool))) % 150.25/151.58 (define @t95 () (lambda (@list @t1 @t94) (exists @t13 (and (_ @t94 @t12) (forall @t36 (= (_ @t94 @t31) @t35)))))) % 150.25/151.58 (define @t96 () (lambda @t72 (and (_ @t62 @t31) @t35))) % 150.25/151.58 (define @t97 () (lambda @t91 (or (_ (_ tptp.rel_domain @t1) @t12) (_ (_ tptp.rel_codomain @t1) @t12)))) % 150.25/151.58 (define @t98 () (not (_ @t17 @t41))) % 150.25/151.58 (define @t99 () (_ @t17 @t31)) % 150.25/151.58 (define @t100 () (_ @t17 @t75)) % 150.25/151.58 (define @t101 () (@list @t17 @t75)) % 150.25/151.58 (define @t102 () (lambda @t3 (forall @t101 (=> @t100 (exists @t36 (and @t99 (forall @t50 (=> (_ @t80 @t41) @t98)))))))) % 150.25/151.58 (define @t103 () (lambda @t3 (forall @t101 (=> @t100 (exists @t36 (and @t99 (forall @t50 (=> (_ @t80 @t31) @t98)))))))) % 150.25/151.58 (define @t104 () (@var "BOUND_VARIABLE_8405" (@ho-elim-sort (-> $$unsorted $$unsorted Bool)))) % 150.25/151.58 (define @t105 () (@const 0 (-> (@ho-elim-sort (-> $$unsorted $$unsorted Bool)) $$unsorted (@ho-elim-sort (-> $$unsorted Bool))))) % 150.25/151.58 (define @t106 () (_ @t105 @t104 @t12)) % 150.25/151.58 (define @t107 () (@const 1 (-> (@ho-elim-sort (-> $$unsorted Bool)) $$unsorted Bool))) % 150.25/151.58 (define @t108 () (forall (@list @t104 @t12 @t31 @t75) (or (not (_ @t107 @t106 @t31)) (not (_ @t107 (_ @t105 @t104 @t31) @t75)) (_ @t107 @t106 @t75)))) % 150.25/151.58 (define @t109 () (@var "BOUND_VARIABLE_8378" $$unsorted)) % 150.25/151.58 (define @t110 () (@var "BOUND_VARIABLE_8398" (@ho-elim-sort (-> $$unsorted Bool)))) % 150.25/151.58 (define @t111 () (@var "BOUND_VARIABLE_8376" $$unsorted)) % 150.25/151.58 (define @t112 () (_ @t105 @t104 @t41)) % 150.25/151.58 (define @t113 () (forall (@list @t104 @t110 @t41 @t111 @t109) (or (not (forall @t36 (or (not (_ @t107 @t112 @t31)) (_ @t107 @t110 @t31)))) (not (_ @t107 @t112 @t111)) (not (_ @t107 (_ @t105 @t104 @t111) @t109)) (_ @t107 @t110 @t109)))) % 150.25/151.58 (define @t114 () (not (= @t108 @t113))) % 150.25/151.58 (define @t115 () (_ @t5 @t109)) % 150.25/151.58 (define @t116 () (not (_ @t1 @t111 @t109))) % 150.25/151.58 (define @t117 () (not (_ @t1 @t41 @t111))) % 150.25/151.58 (define @t118 () (_ @t5 @t31)) % 150.25/151.58 (define @t119 () (not (_ @t1 @t41 @t31))) % 150.25/151.58 (define @t120 () (not (forall @t36 (or @t119 @t118)))) % 150.25/151.58 (define @t121 () (or @t120 @t117 @t116 @t115)) % 150.25/151.58 (define @t122 () (forall (@list @t1 @t5 @t41 @t111 @t109) @t121)) % 150.25/151.58 (define @t123 () (_ @t1 @t12 @t75)) % 150.25/151.58 (define @t124 () (_ @t1 @t31 @t75)) % 150.25/151.58 (define @t125 () (_ @t1 @t12 @t31)) % 150.25/151.58 (define @t126 () (not @t125)) % 150.25/151.58 (define @t127 () (or @t126 (not @t124) @t123)) % 150.25/151.58 (define @t128 () (forall (@list @t1 @t12 @t31 @t75) @t127)) % 150.25/151.58 (define @t129 () (@list @t41 @t111 @t109)) % 150.25/151.58 (define @t130 () (or @t117 @t116 @t115)) % 150.25/151.58 (define @t131 () (or @t120 @t130)) % 150.25/151.58 (define @t132 () (forall @t129 @t131)) % 150.25/151.58 (define @t133 () (@list @t111 @t109)) % 150.25/151.58 (define @t134 () (forall @t133 @t131)) % 150.25/151.58 (define @t135 () (forall @t133 @t130)) % 150.25/151.58 (define @t136 () (@var "BOUND_VARIABLE_8343" $$unsorted)) % 150.25/151.58 (define @t137 () (or @t120 @t135)) % 150.25/151.58 (define @t138 () (_ @t5 @t136)) % 150.25/151.58 (define @t139 () (not (_ @t1 @t31 @t136))) % 150.25/151.58 (define @t140 () (@list @t31 @t136)) % 150.25/151.58 (define @t141 () (or @t120 (forall @t140 (or @t119 @t139 @t138)))) % 150.25/151.58 (define @t142 () (not (_ @t1 @t25 @t31))) % 150.25/151.58 (define @t143 () (forall @t140 (or @t142 @t139 @t138))) % 150.25/151.58 (define @t144 () (forall @t36 (or @t142 @t118))) % 150.25/151.58 (define @t145 () (not @t144)) % 150.25/151.58 (define @t146 () (@list @t25)) % 150.25/151.58 (define @t147 () (lambda @t146 (or @t145 @t143))) % 150.25/151.58 (define @t148 () (_ @t147 @t41)) % 150.25/151.58 (define @t149 () (forall @t50 @t148)) % 150.25/151.58 (define @t150 () (_ @t32 @t41)) % 150.25/151.58 (define @t151 () (lambda @t52 (forall @t50 @t150))) % 150.25/151.58 (define @t152 () (or @t126 @t139 @t138)) % 150.25/151.58 (define @t153 () (lambda @t13 (forall @t140 @t152))) % 150.25/151.58 (define @t154 () (_ @t153 @t25)) % 150.25/151.58 (define @t155 () (or @t145 @t154)) % 150.25/151.58 (define @t156 () (lambda @t146 @t155)) % 150.25/151.58 (define @t157 () (_ @t26 @t25)) % 150.25/151.58 (define @t158 () (@list @t26 @t25)) % 150.25/151.58 (define @t159 () (or @t139 @t138)) % 150.25/151.58 (define @t160 () (or @t126 @t159)) % 150.25/151.58 (define @t161 () (forall @t140 @t160)) % 150.25/151.58 (define @t162 () (@list @t136)) % 150.25/151.58 (define @t163 () (forall @t162 @t160)) % 150.25/151.58 (define @t164 () (forall @t162 @t159)) % 150.25/151.58 (define @t165 () (@var "BOUND_VARIABLE_8327" $$unsorted)) % 150.25/151.58 (define @t166 () (@list @t165)) % 150.25/151.58 (define @t167 () (or @t126 @t164)) % 150.25/151.58 (define @t168 () (_ @t5 @t165)) % 150.25/151.58 (define @t169 () (@list @t165)) % 150.25/151.58 (define @t170 () (forall @t169 (or (not (_ @t1 @t31 @t165)) @t168))) % 150.25/151.58 (define @t171 () (forall @t36 (or @t126 @t118))) % 150.25/151.58 (define @t172 () (lambda @t13 @t171)) % 150.25/151.58 (define @t173 () (or @t126 (_ @t172 @t31))) % 150.25/151.58 (define @t174 () (forall @t36 @t173)) % 150.25/151.58 (define @t175 () (lambda @t13 @t174)) % 150.25/151.58 (define @t176 () (_ @t32 @t31)) % 150.25/151.58 (define @t177 () (forall @t36 (or @t126 @t176))) % 150.25/151.58 (define @t178 () (lambda (@list @t32 @t12) @t177)) % 150.25/151.58 (define @t179 () (_ (lambda @t38 @t177) @t1)) % 150.25/151.58 (define @t180 () (_ @t172 @t25)) % 150.25/151.58 (define @t181 () (not @t180)) % 150.25/151.58 (define @t182 () (or @t181 @t157)) % 150.25/151.58 (define @t183 () (lambda @t158 @t182)) % 150.25/151.58 (define @t184 () (or (not (_ @t27 @t25)) @t157)) % 150.25/151.58 (define @t185 () (lambda @t28 @t184)) % 150.25/151.58 (define @t186 () (_ @t179 @t5)) % 150.25/151.58 (define @t187 () (forall @t8 (_ @t151 (_ (_ @t185 @t186) (_ @t179 @t186))))) % 150.25/151.58 (define @t188 () (forall @t86 @t127)) % 150.25/151.58 (define @t189 () (_ (lambda @t3 @t188) @t1)) % 150.25/151.58 (define @t190 () (forall @t3 @t189)) % 150.25/151.58 (define @t191 () (not @t84)) % 150.25/151.58 (define @t192 () (not @t35)) % 150.25/151.58 (define @t193 () (or @t192 @t191 @t83)) % 150.25/151.58 (define @t194 () (or @t192 @t33)) % 150.25/151.58 (define @t195 () (not (_ @t27 @t16))) % 150.25/151.58 (define @t196 () (@list @t16)) % 150.25/151.58 (define @t197 () (lambda @t196 (or @t195 (_ @t26 @t16)))) % 150.25/151.58 (define @t198 () (@list @t20 @t16)) % 150.25/151.58 (define @t199 () (lambda @t196 @t195)) % 150.25/151.58 (define @t200 () (_ @t199 @t16)) % 150.25/151.58 (define @t201 () (or @t200 @t21)) % 150.25/151.58 (define @t202 () (lambda @t198 @t201)) % 150.25/151.58 (define @t203 () (@quantifiers_skolemize @t108 3)) % 150.25/151.58 (define @t204 () (@quantifiers_skolemize @t108 1)) % 150.25/151.58 (define @t205 () (@quantifiers_skolemize @t108 0)) % 150.25/151.58 (define @t206 () (_ @t105 @t205 @t204)) % 150.25/151.58 (define @t207 () (_ @t107 @t206 @t203)) % 150.25/151.58 (define @t208 () (@quantifiers_skolemize @t108 2)) % 150.25/151.58 (define @t209 () (not (_ @t107 (_ @t105 @t205 @t208) @t203))) % 150.25/151.58 (define @t210 () (not (_ @t107 @t206 @t208))) % 150.25/151.58 (define @t211 () (or @t210 @t209 @t207)) % 150.25/151.58 (define @t212 () (not @t211)) % 150.25/151.58 (define @t213 () (not @t108)) % 150.25/151.58 (define @t214 () (_ @t107 @t206 @t31)) % 150.25/151.58 (define @t215 () (forall @t36 (or (not @t214) @t214))) % 150.25/151.58 (define @t216 () (not @t215)) % 150.25/151.58 (define @t217 () (or @t216 @t210 @t209 @t207)) % 150.25/151.58 (define @t218 () (not @t113)) % 150.25/151.58 (define @t219 () (@quantifiers_skolemize @t113 4)) % 150.25/151.58 (define @t220 () (@quantifiers_skolemize @t113 1)) % 150.25/151.58 (define @t221 () (_ @t107 @t220 @t219)) % 150.25/151.58 (define @t222 () (@quantifiers_skolemize @t113 3)) % 150.25/151.58 (define @t223 () (@quantifiers_skolemize @t113 0)) % 150.25/151.58 (define @t224 () (_ @t107 (_ @t105 @t223 @t222) @t219)) % 150.25/151.58 (define @t225 () (not @t224)) % 150.25/151.58 (define @t226 () (@quantifiers_skolemize @t113 2)) % 150.25/151.58 (define @t227 () (_ @t105 @t223 @t226)) % 150.25/151.58 (define @t228 () (_ @t107 @t227 @t222)) % 150.25/151.58 (define @t229 () (not @t228)) % 150.25/151.58 (define @t230 () (forall @t36 (or (not (_ @t107 @t227 @t31)) (_ @t107 @t220 @t31)))) % 150.25/151.58 (define @t231 () (not @t230)) % 150.25/151.58 (define @t232 () (or @t231 @t229 @t225 @t221)) % 150.25/151.58 (define @t233 () (not @t232)) % 150.25/151.58 (define @t234 () (@list true)) % 150.25/151.58 (define @t235 () (@list @t113)) % 150.25/151.58 (define @t236 () (@list @t232)) % 150.25/151.58 (define @t237 () (_ @t107 @t227 @t219)) % 150.25/151.58 (define @t238 () (not @t237)) % 150.25/151.58 (define @t239 () (or @t238 @t221)) % 150.25/151.58 (define @t240 () (@list false)) % 150.25/151.58 (define @t241 () (or @t229 @t225 @t237)) % 150.25/151.58 (assume @p1 @t11) % 150.25/151.58 (assume @p2 true) % 150.25/151.58 (step @p3 (= tptp.mfalse @t14) :rule refl :args (@t14)) % 150.25/151.58 (step @p4 (= tptp.mtrue @t15) :rule refl :args (@t15)) % 150.25/151.58 (step @p5 (= tptp.mnot @t19) :rule refl :args (@t19)) % 150.25/151.58 (step @p6 (= tptp.mor @t23) :rule refl :args (@t23)) % 150.25/151.58 (step @p7 (= tptp.mand @t24) :rule refl :args (@t24)) % 150.25/151.58 (step @p8 (= tptp.mimpl @t29) :rule refl :args (@t29)) % 150.25/151.58 (step @p9 (= tptp.miff @t30) :rule refl :args (@t30)) % 150.25/151.58 (step @p10 (= tptp.mbox @t39) :rule refl :args (@t39)) % 150.25/151.58 (step @p11 (= tptp.mdia @t40) :rule refl :args (@t40)) % 150.25/151.58 (step @p12 (= tptp.mall @t47) :rule refl :args (@t47)) % 150.25/151.58 (step @p13 (= tptp.mexists @t48) :rule refl :args (@t48)) % 150.25/151.58 (step @p14 (= tptp.mvalid @t53) :rule refl :args (@t53)) % 150.25/151.58 (step @p15 (= tptp.msatisfiable @t54) :rule refl :args (@t54)) % 150.25/151.58 (step @p16 (= tptp.mcountersatisfiable @t56) :rule refl :args (@t56)) % 150.25/151.58 (step @p17 (= tptp.minvalid @t57) :rule refl :args (@t57)) % 150.25/151.58 (step @p18 (= tptp.cartesian_product @t59) :rule refl :args (@t59)) % 150.25/151.58 (step @p19 (= tptp.pair_rel @t60) :rule refl :args (@t60)) % 150.25/151.58 (step @p20 (= tptp.id_rel @t64) :rule refl :args (@t64)) % 150.25/151.58 (step @p21 (= tptp.sub_rel @t69) :rule refl :args (@t69)) % 150.25/151.58 (step @p22 (= tptp.is_rel_on @t71) :rule refl :args (@t71)) % 150.25/151.58 (step @p23 (= tptp.restrict_rel_domain @t73) :rule refl :args (@t73)) % 150.25/151.58 (step @p24 (= tptp.rel_diagonal @t74) :rule refl :args (@t74)) % 150.25/151.58 (step @p25 (= tptp.rel_composition @t76) :rule refl :args (@t76)) % 150.25/151.58 (step @p26 (= tptp.reflexive @t78) :rule refl :args (@t78)) % 150.25/151.58 (step @p27 (= tptp.irreflexive @t79) :rule refl :args (@t79)) % 150.25/151.58 (step @p28 (= tptp.symmetric @t82) :rule refl :args (@t82)) % 150.25/151.58 (step @p29 (= tptp.transitive @t88) :rule refl :args (@t88)) % 150.25/151.58 (step @p30 (= tptp.equiv_rel @t89) :rule refl :args (@t89)) % 150.25/151.58 (step @p31 (= tptp.rel_codomain @t90) :rule refl :args (@t90)) % 150.25/151.58 (step @p32 (= tptp.rel_domain @t92) :rule refl :args (@t92)) % 150.25/151.58 (step @p33 (= tptp.rel_inverse @t93) :rule refl :args (@t93)) % 150.25/151.58 (step @p34 (= tptp.equiv_classes @t95) :rule refl :args (@t95)) % 150.25/151.58 (step @p35 (= tptp.restrict_rel_codomain @t96) :rule refl :args (@t96)) % 150.25/151.58 (step @p36 (= tptp.rel_field @t97) :rule refl :args (@t97)) % 150.25/151.58 (step @p37 (= tptp.well_founded @t102) :rule refl :args (@t102)) % 150.25/151.58 (step @p38 (= tptp.upwards_well_founded @t103) :rule refl :args (@t103)) % 150.25/151.58 (step @p39 :rule eq-symm :args (@t108 @t113)) % 150.25/151.58 (step @p40 :rule cong :premises (@p39) :args (@t114)) % 150.25/151.58 ; WARNING: add trust step for TRUST % 150.25/151.58 ; trust TRUST PREPROCESS_HO_ELIM % 150.25/151.58 (step @p41 :rule trust :premises () :args ((= (not (= @t128 @t122)) @t114))) % 150.25/151.58 (step @p42 :rule quant-merge-prenex :args ((= (forall @t8 (forall @t129 @t121)) @t122))) % 150.25/151.58 (step @p43 :rule aci_norm :args ((= @t131 @t121))) % 150.25/151.58 (step @p44 :rule cong :premises (@p43) :args (@t132)) % 150.25/151.58 (step @p45 :rule quant-merge-prenex :args ((= (forall @t50 @t134) @t132))) % 150.25/151.58 (step @p46 :rule alpha_equiv :args (@t135 (@list @t111 @t109) (@list @t31 @t136))) % 150.25/151.58 (step @p47 :rule refl :args (@t120)) % 150.25/151.58 (step @p48 :rule nary_cong :premises (@p47 @p46) :args (@t137)) % 150.25/151.58 (step @p49 :rule quant-miniscope-or :args ((= @t134 @t137))) % 150.25/151.58 (step @p50 :rule trans :premises (@p49 @p48)) % 150.25/151.58 (step @p51 :rule symm :premises (@p50)) % 150.25/151.58 (step @p52 :rule cong :premises (@p51) :args ((forall @t50 @t141))) % 150.25/151.58 (step @p53 :rule trans :premises (@p52 @p45)) % 150.25/151.58 (step @p54 :rule trans :premises (@p53 @p44)) % 150.25/151.58 (step @p55 :rule beta-reduce :args ((= @t148 @t141))) % 150.25/151.58 (step @p56 :rule cong :premises (@p55) :args (@t149)) % 150.25/151.58 (step @p57 :rule trans :premises (@p56 @p54)) % 150.25/151.58 (step @p58 :rule beta-reduce :args ((= (_ @t151 @t147) @t149))) % 150.25/151.58 (step @p59 :rule trans :premises (@p58 @p57)) % 150.25/151.58 (step @p60 :rule beta-reduce :args ((= @t154 @t143))) % 150.25/151.58 (step @p61 :rule refl :args (@t145)) % 150.25/151.58 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t155)) % 150.25/151.58 (step @p63 :rule cong :premises (@p62) :args (@t156)) % 150.25/151.58 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t158 (or @t145 @t157)) @t153) @t156))) % 150.25/151.58 (step @p65 :rule trans :premises (@p64 @p63)) % 150.25/151.58 (step @p66 :rule aci_norm :args ((= @t160 @t152))) % 150.25/151.58 (step @p67 :rule cong :premises (@p66) :args (@t161)) % 150.25/151.58 (step @p68 :rule quant-merge-prenex :args ((= (forall @t36 @t163) @t161))) % 150.25/151.58 (step @p69 :rule alpha_equiv :args (@t164 (@list @t136) @t166)) % 150.25/151.58 (step @p70 :rule refl :args (@t126)) % 150.25/151.58 (step @p71 :rule nary_cong :premises (@p70 @p69) :args (@t167)) % 150.25/151.58 (step @p72 :rule quant-miniscope-or :args ((= @t163 @t167))) % 150.25/151.58 (step @p73 :rule trans :premises (@p72 @p71)) % 150.25/151.58 (step @p74 :rule symm :premises (@p73)) % 150.25/151.58 (step @p75 :rule cong :premises (@p74) :args ((forall @t36 (or @t126 @t170)))) % 150.25/151.58 (step @p76 :rule trans :premises (@p75 @p68)) % 150.25/151.58 (step @p77 :rule trans :premises (@p76 @p67)) % 150.25/151.58 (step @p78 :rule beta-reduce :args ((= (_ (lambda @t13 (forall @t169 (or (not (_ @t1 @t12 @t165)) @t168))) @t31) @t170))) % 150.25/151.58 (step @p79 :rule refl :args (@t31)) % 150.25/151.58 (step @p80 :rule alpha_equiv :args (@t171 (@list @t31) @t166)) % 150.25/151.58 (step @p81 :rule cong :premises (@p80) :args (@t172)) % 150.25/151.58 (step @p82 :rule ho_cong :premises (@p81 @p79)) % 150.25/151.58 (step @p83 :rule trans :premises (@p82 @p78)) % 150.25/151.58 (step @p84 :rule refl :args (@t126)) % 150.25/151.58 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t173)) % 150.25/151.58 (step @p86 :rule cong :premises (@p85) :args (@t174)) % 150.25/151.58 (step @p87 :rule trans :premises (@p86 @p77)) % 150.25/151.58 (step @p88 :rule cong :premises (@p87) :args (@t175)) % 150.25/151.58 (step @p89 :rule beta-reduce :args ((= (_ @t178 @t172) @t175))) % 150.25/151.58 (step @p90 :rule trans :premises (@p89 @p88)) % 150.25/151.58 (step @p91 :rule beta-reduce :args ((= (_ @t178 @t5) @t172))) % 150.25/151.58 (step @p92 :rule refl :args (@t5)) % 150.25/151.58 (step @p93 :rule beta-reduce :args ((= @t179 @t178))) % 150.25/151.58 (step @p94 :rule ho_cong :premises (@p93 @p92)) % 150.25/151.58 (step @p95 :rule trans :premises (@p94 @p91)) % 150.25/151.58 (step @p96 :rule ho_cong :premises (@p93 @p95)) % 150.25/151.58 (step @p97 :rule trans :premises (@p96 @p90)) % 150.25/151.58 (step @p98 :rule refl :args (@t157)) % 150.25/151.58 (step @p99 :rule beta-reduce :args ((= @t180 @t144))) % 150.25/151.58 (step @p100 :rule cong :premises (@p99) :args (@t181)) % 150.25/151.58 (step @p101 :rule nary_cong :premises (@p100 @p98) :args (@t182)) % 150.25/151.58 (step @p102 :rule cong :premises (@p101) :args (@t183)) % 150.25/151.58 (step @p103 :rule beta-reduce :args ((= (_ @t185 @t172) @t183))) % 150.25/151.58 (step @p104 :rule trans :premises (@p103 @p102)) % 150.25/151.58 (step @p105 :rule refl :args (@t185)) % 150.25/151.58 (step @p106 :rule ho_cong :premises (@p105 @p95)) % 150.25/151.58 (step @p107 :rule trans :premises (@p106 @p104)) % 150.25/151.58 (step @p108 :rule ho_cong :premises (@p107 @p97)) % 150.25/151.58 (step @p109 :rule trans :premises (@p108 @p65)) % 150.25/151.58 (step @p110 :rule refl :args (@t151)) % 150.25/151.58 (step @p111 :rule ho_cong :premises (@p110 @p109)) % 150.25/151.58 (step @p112 :rule trans :premises (@p111 @p59)) % 150.25/151.58 (step @p113 :rule cong :premises (@p112) :args (@t187)) % 150.25/151.58 (step @p114 :rule trans :premises (@p113 @p42)) % 150.25/151.58 (step @p115 :rule quant-merge-prenex :args ((= (forall @t3 @t188) @t128))) % 150.25/151.58 (step @p116 :rule beta-reduce :args ((= @t189 @t188))) % 150.25/151.58 (step @p117 :rule cong :premises (@p116) :args (@t190)) % 150.25/151.58 (step @p118 :rule trans :premises (@p117 @p115)) % 150.25/151.58 (step @p119 :rule cong :premises (@p118 @p114) :args ((= @t190 @t187))) % 150.25/151.58 (step @p120 :rule eq-symm :args (@t187 @t190)) % 150.25/151.58 (step @p121 :rule trans :premises (@p120 @p119)) % 150.25/151.58 (step @p122 :rule cong :premises (@p121) :args ((not (= @t187 @t190)))) % 150.25/151.58 (step @p123 :rule refl :args (@t1)) % 150.25/151.58 (step @p124 :rule refl :args (@t123)) % 150.25/151.58 (step @p125 :rule refl :args (@t83)) % 150.25/151.58 (step @p126 :rule cong :premises (@p125 @p124) :args ((= @t83 @t123))) % 150.25/151.58 (step @p127 :rule symm :premises (@p126)) % 150.25/151.58 (step @p128 :rule eq_resolve :premises (@p125 @p127)) % 150.25/151.58 (step @p129 :rule refl :args (@t124)) % 150.25/151.58 (step @p130 :rule refl :args (@t84)) % 150.25/151.58 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t84 @t124))) % 150.25/151.58 (step @p132 :rule symm :premises (@p131)) % 150.25/151.58 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 150.25/151.58 (step @p134 :rule cong :premises (@p133) :args (@t191)) % 150.25/151.58 (step @p135 :rule refl :args (@t125)) % 150.25/151.58 (step @p136 :rule refl :args (@t35)) % 150.25/151.58 (step @p137 :rule cong :premises (@p136 @p135) :args ((= @t35 @t125))) % 150.25/151.58 (step @p138 :rule symm :premises (@p137)) % 150.25/151.58 (step @p139 :rule eq_resolve :premises (@p136 @p138)) % 150.25/151.58 (step @p140 :rule cong :premises (@p139) :args (@t192)) % 150.25/151.58 (step @p141 :rule nary_cong :premises (@p140 @p134 @p128) :args (@t193)) % 150.25/151.58 (step @p142 :rule cong :premises (@p141) :args ((forall @t86 @t193))) % 150.25/151.58 (step @p143 :rule aci_norm :args ((= (or (or @t192 @t191) @t83) @t193))) % 150.25/151.58 (step @p144 :rule bool-and-de-morgan :args (@t35 @t84 true)) % 150.25/151.58 (step @p145 :rule nary_cong :premises (@p144 @p125) :args ((or (not @t85) @t83))) % 150.25/151.58 (step @p146 :rule trans :premises (@p145 @p143)) % 150.25/151.58 (step @p147 :rule bool-impl-elim :args (@t85 @t83)) % 150.25/151.58 (step @p148 :rule trans :premises (@p147 @p146)) % 150.25/151.58 (step @p149 :rule cong :premises (@p148) :args (@t87)) % 150.25/151.58 (step @p150 :rule trans :premises (@p149 @p142)) % 150.25/151.58 (step @p151 :rule cong :premises (@p150) :args (@t88)) % 150.25/151.58 (step @p152 :rule trans :premises (@p29 @p151)) % 150.25/151.58 (step @p153 :rule ho_cong :premises (@p152 @p123)) % 150.25/151.58 (step @p154 :rule cong :premises (@p153) :args (@t4)) % 150.25/151.58 (step @p155 :rule refl :args (@t176)) % 150.25/151.58 (step @p156 :rule refl :args (@t33)) % 150.25/151.58 (step @p157 :rule cong :premises (@p156 @p155) :args ((= @t33 @t176))) % 150.25/151.58 (step @p158 :rule symm :premises (@p157)) % 150.25/151.58 (step @p159 :rule eq_resolve :premises (@p156 @p158)) % 150.25/151.58 (step @p160 :rule nary_cong :premises (@p140 @p159) :args (@t194)) % 150.25/151.58 (step @p161 :rule cong :premises (@p160) :args ((forall @t36 @t194))) % 150.25/151.58 (step @p162 :rule bool-impl-elim :args (@t35 @t33)) % 150.25/151.58 (step @p163 :rule cong :premises (@p162) :args (@t37)) % 150.25/151.58 (step @p164 :rule trans :premises (@p163 @p161)) % 150.25/151.58 (step @p165 :rule cong :premises (@p164) :args (@t39)) % 150.25/151.58 (step @p166 :rule trans :premises (@p10 @p165)) % 150.25/151.58 (step @p167 :rule ho_cong :premises (@p166 @p123)) % 150.25/151.59 (step @p168 :rule ho_cong :premises (@p167 @p92)) % 150.25/151.59 (step @p169 :rule ho_cong :premises (@p167 @p168)) % 150.25/151.59 (step @p170 :rule beta-reduce :args ((= (_ @t197 @t25) @t184))) % 150.25/151.59 (step @p171 :rule refl :args (@t25)) % 150.25/151.59 (step @p172 :rule beta-reduce :args ((= (_ (lambda @t198 (or @t195 @t21)) @t26) @t197))) % 150.25/151.59 (step @p173 :rule refl :args (@t26)) % 150.25/151.59 (step @p174 :rule refl :args (@t21)) % 150.25/151.59 (step @p175 :rule beta-reduce :args ((= @t200 @t195))) % 150.25/151.59 (step @p176 :rule nary_cong :premises (@p175 @p174) :args (@t201)) % 150.25/151.59 (step @p177 :rule cong :premises (@p176) :args (@t202)) % 150.25/151.59 (step @p178 :rule beta-reduce :args ((= (_ @t23 @t199) @t202))) % 150.25/151.59 (step @p179 :rule trans :premises (@p178 @p177)) % 150.25/151.59 (step @p180 :rule beta-reduce :args ((= (_ @t19 @t27) @t199))) % 150.25/151.59 (step @p181 :rule refl :args (@t23)) % 150.25/151.59 (step @p182 :rule ho_cong :premises (@p181 @p180)) % 150.25/151.59 (step @p183 :rule trans :premises (@p182 @p179)) % 150.25/151.59 (step @p184 :rule ho_cong :premises (@p183 @p173)) % 150.25/151.59 (step @p185 :rule trans :premises (@p184 @p172)) % 150.25/151.59 (step @p186 :rule ho_cong :premises (@p185 @p171)) % 150.25/151.59 (step @p187 :rule trans :premises (@p186 @p170)) % 150.25/151.59 (step @p188 :rule refl :args (@t27)) % 150.25/151.59 (step @p189 :rule ho_cong :premises (@p5 @p188)) % 150.25/151.59 (step @p190 :rule ho_cong :premises (@p6 @p189)) % 150.25/151.59 (step @p191 :rule ho_cong :premises (@p190 @p173)) % 150.25/151.59 (step @p192 :rule ho_cong :premises (@p191 @p171)) % 150.25/151.59 (step @p193 :rule trans :premises (@p192 @p187)) % 150.25/151.59 (step @p194 :rule cong :premises (@p193) :args (@t29)) % 150.25/151.59 (step @p195 :rule trans :premises (@p8 @p194)) % 150.25/151.59 (step @p196 :rule ho_cong :premises (@p195 @p168)) % 150.25/151.59 (step @p197 :rule ho_cong :premises (@p196 @p169)) % 150.25/151.59 (step @p198 :rule refl :args (@t150)) % 150.25/151.59 (step @p199 :rule refl :args (@t49)) % 150.25/151.59 (step @p200 :rule cong :premises (@p199 @p198) :args ((= @t49 @t150))) % 150.25/151.59 (step @p201 :rule symm :premises (@p200)) % 150.25/151.59 (step @p202 :rule eq_resolve :premises (@p199 @p201)) % 150.25/151.59 (step @p203 :rule cong :premises (@p202) :args (@t51)) % 150.25/151.59 (step @p204 :rule cong :premises (@p203) :args (@t53)) % 150.25/151.59 (step @p205 :rule trans :premises (@p14 @p204)) % 150.25/151.59 (step @p206 :rule ho_cong :premises (@p205 @p197)) % 150.25/151.59 (step @p207 :rule cong :premises (@p206) :args (@t9)) % 150.25/151.59 (step @p208 :rule cong :premises (@p207 @p154) :args (@t10)) % 150.25/151.59 (step @p209 :rule cong :premises (@p208) :args (@t11)) % 150.25/151.59 (step @p210 :rule trans :premises (@p209 @p122)) % 150.25/151.59 (step @p211 :rule trans :premises (@p210 @p41 @p40)) % 150.25/151.59 (step @p212 :rule eq_resolve :premises (@p1 @p211)) % 150.25/151.59 (step @p213 :rule not_equiv_elim2 :premises (@p212)) % 150.25/151.59 (step @p214 :rule refl :args (@t212)) % 150.25/151.59 (step @p215 :rule bool-double-not-elim :args (@t108)) % 150.25/151.59 (step @p216 :rule nary_cong :premises (@p215 @p214) :args ((or (not @t213) @t212))) % 150.25/151.59 (assume-push @p296 @t213) % 150.25/151.59 (step @p218 :rule skolemize :premises (@p296)) % 150.25/151.59 (step-pop @p297 :rule scope :premises (@p218)) % 150.25/151.59 (step @p219 :rule process_scope :premises (@p297) :args (@t212)) % 150.25/151.59 (step @p221 :rule implies_elim :premises (@p219)) % 150.25/151.59 (step @p222 :rule eq_resolve :premises (@p221 @p216)) % 150.25/151.59 (step @p223 :rule aci_norm :args ((= (or false @t210 @t209 @t207) @t211))) % 150.25/151.59 (step @p224 :rule refl :args (@t207)) % 150.25/151.59 (step @p225 :rule refl :args (@t209)) % 150.25/151.59 (step @p226 :rule refl :args (@t210)) % 150.25/151.59 (step @p227 :rule evaluate :args ((not true))) % 150.25/151.59 (step @p228 :rule quant-unused-vars :args ((= (forall @t36 true) true))) % 150.25/151.59 (step @p229 :rule bool-or-taut2 :args (false @t214 false false)) % 150.25/151.59 (step @p230 :rule cong :premises (@p229) :args (@t215)) % 150.25/151.59 (step @p231 :rule trans :premises (@p230 @p228)) % 150.25/151.59 (step @p232 :rule cong :premises (@p231) :args (@t216)) % 150.25/151.59 (step @p233 :rule trans :premises (@p232 @p227)) % 150.25/151.59 (step @p234 :rule nary_cong :premises (@p233 @p226 @p225 @p224) :args (@t217)) % 150.25/151.59 (step @p235 :rule trans :premises (@p234 @p223)) % 150.25/151.59 (step @p236 :rule refl :args (@t113)) % 150.25/151.59 (step @p237 :rule cong :premises (@p236 @p235) :args ((=> @t113 @t217))) % 150.25/151.59 (assume-push @p298 @t113) % 150.25/151.59 (step @p239 :rule instantiate :premises (@p298) :args ((@list @t205 @t206 @t204 @t208 @t203))) % 150.25/151.59 (step-pop @p299 :rule scope :premises (@p239)) % 150.25/151.59 (step @p240 :rule process_scope :premises (@p299) :args (@t217)) % 150.25/151.59 (step @p242 :rule eq_resolve :premises (@p240 @p237)) % 150.25/151.59 (step @p243 :rule implies_elim :premises (@p242)) % 150.25/151.59 (step @p244 :rule chain_m_resolution :premises (@p243 @p222 @p213) :args (@t218 (@list true true) (@list @t211 @t108))) % 150.25/151.59 (step @p245 :rule refl :args (@t233)) % 150.25/151.59 (step @p246 :rule bool-double-not-elim :args (@t113)) % 150.25/151.59 (step @p247 :rule nary_cong :premises (@p246 @p245) :args ((or (not @t218) @t233))) % 150.25/151.59 (assume-push @p300 @t218) % 150.25/151.59 (step @p249 :rule skolemize :premises (@p300)) % 150.25/151.59 (step-pop @p301 :rule scope :premises (@p249)) % 150.25/151.59 (step @p250 :rule process_scope :premises (@p301) :args (@t233)) % 150.25/151.59 (step @p252 :rule implies_elim :premises (@p250)) % 150.25/151.59 (step @p253 :rule eq_resolve :premises (@p252 @p247)) % 150.25/151.59 (step @p254 :rule chain_m_resolution :premises (@p253 @p244) :args (@t233 @t234 @t235)) % 150.25/151.59 (step @p255 :rule cnf_or_neg :args (@t232 3)) % 150.25/151.59 (step @p256 :rule chain_m_resolution :premises (@p255 @p254) :args ((not @t221) @t234 @t236)) % 150.25/151.59 (step @p257 :rule bool-double-not-elim :args (@t230)) % 150.25/151.59 (step @p258 :rule refl :args (@t232)) % 150.25/151.59 (step @p259 :rule nary_cong :premises (@p258 @p257) :args ((or @t232 (not @t231)))) % 150.25/151.59 (step @p260 :rule cnf_or_neg :args (@t232 0)) % 150.25/151.59 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 150.25/151.59 (step @p262 :rule reordering :premises (@p261) :args ((or @t230 @t232))) % 150.25/151.59 (step @p263 :rule chain_m_resolution :premises (@p262 @p254) :args (@t230 @t234 @t236)) % 150.25/151.59 (assume-push @p302 @t230) % 150.25/151.59 (step @p265 :rule instantiate :premises (@p302) :args ((@list @t219))) % 150.25/151.59 (step-pop @p303 :rule scope :premises (@p265)) % 150.25/151.59 (step @p266 :rule process_scope :premises (@p303) :args (@t239)) % 150.25/151.59 (step @p268 :rule implies_elim :premises (@p266)) % 150.25/151.59 (step @p269 :rule chain_m_resolution :premises (@p268 @p263) :args (@t239 @t240 (@list @t230))) % 150.25/151.59 (step @p270 :rule not_equiv_elim1 :premises (@p212)) % 150.25/151.59 (step @p271 :rule chain_m_resolution :premises (@p270 @p244) :args (@t108 @t234 @t235)) % 150.25/151.59 (assume-push @p304 @t108) % 150.25/151.59 (step @p273 :rule instantiate :premises (@p304) :args ((@list @t223 @t226 @t222 @t219))) % 150.25/151.59 (step-pop @p305 :rule scope :premises (@p273)) % 150.25/151.59 (step @p274 :rule process_scope :premises (@p305) :args (@t241)) % 150.25/151.59 (step @p276 :rule implies_elim :premises (@p274)) % 150.25/151.59 (step @p277 :rule chain_m_resolution :premises (@p276 @p271) :args (@t241 @t240 (@list @t108))) % 150.25/151.59 (step @p278 :rule bool-double-not-elim :args (@t224)) % 150.25/151.59 (step @p279 :rule nary_cong :premises (@p258 @p278) :args ((or @t232 (not @t225)))) % 150.25/151.59 (step @p280 :rule cnf_or_neg :args (@t232 2)) % 150.25/151.59 (step @p281 :rule eq_resolve :premises (@p280 @p279)) % 150.25/151.59 (step @p282 :rule reordering :premises (@p281) :args ((or @t224 @t232))) % 150.25/151.59 (step @p283 :rule chain_m_resolution :premises (@p282 @p254) :args (@t224 @t234 @t236)) % 150.25/151.59 (step @p284 :rule bool-double-not-elim :args (@t228)) % 150.25/151.59 (step @p285 :rule nary_cong :premises (@p258 @p284) :args ((or @t232 (not @t229)))) % 150.25/151.59 (step @p286 :rule cnf_or_neg :args (@t232 1)) % 150.25/151.59 (step @p287 :rule eq_resolve :premises (@p286 @p285)) % 150.25/151.59 (step @p288 :rule reordering :premises (@p287) :args ((or @t228 @t232))) % 150.25/151.59 (step @p289 :rule chain_m_resolution :premises (@p288 @p254) :args (@t228 @t234 @t236)) % 150.25/151.59 (step @p290 :rule cnf_or_pos :args (@t241)) % 150.25/151.59 (step @p291 :rule reordering :premises (@p290) :args ((or @t229 @t225 @t237 (not @t241)))) % 150.25/151.59 (step @p292 :rule chain_m_resolution :premises (@p291 @p289 @p283 @p277) :args (@t237 (@list false false false) (@list @t228 @t224 @t241))) % 150.25/151.59 (step @p293 :rule cnf_or_pos :args (@t239)) % 150.25/151.59 (step @p294 :rule reordering :premises (@p293) :args ((or @t221 @t238 (not @t239)))) % 150.25/151.59 (step @p295 false :rule chain_m_resolution :premises (@p294 @p292 @p269 @p256) :args (false (@list false false true) (@list @t237 @t239 @t221))) % 150.25/151.59 ) % 150.25/151.59 % SZS output end Proof % 150.25/151.59 % cvc5 exiting %------------------------------------------------------------------------------