%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU464^1 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n001.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:51:53 AM UTC 2026 % Result : Theorem 0.46s 0.64s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU464^1 : TPTP v9.2.1. Released v3.6.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n001.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 17:37:05 EDT 2026 % 0.17/0.35 % CPUTime : % 0.31/0.50 %----Proving TH0 % 0.46/0.64 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.64 % SZS status Theorem % 0.46/0.64 % SZS output start Proof % 0.46/0.64 ( % 0.46/0.64 (declare-sort $$unsorted 0) % 0.46/0.64 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.46/0.64 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.46/0.64 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.46/0.64 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.46/0.64 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.46/0.64 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.46/0.64 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.46/0.64 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.64 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.46/0.64 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.46/0.64 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.46/0.64 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.64 (define tptp.trans () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "Y" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.46/0.64 (define tptp.tc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_1) (forall (@list _let_3) (=> (and (_ tptp.trans _let_3) (_ (_ tptp.subrel _let_4) _let_3)) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.46/0.64 (define tptp.trc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.rc (_ tptp.tc _let_3)) _let_2) _let_1)))))) % 0.46/0.64 (define tptp.trsc () (let ((_let_1 (@var "__flatten_var_1" $$unsorted))) (let ((_let_2 (@var "__flatten_var_0" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.sc (_ tptp.rc (_ tptp.tc _let_3))) _let_2) _let_1)))))) % 0.46/0.64 (define tptp.po () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.refl _let_1) (_ tptp.antisymm _let_1) (_ tptp.trans _let_1))))) % 0.46/0.64 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.46/0.64 (define tptp.total () (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) (or (= _let_1 _let_2) (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.46/0.64 (define tptp.term () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.46/0.64 (define tptp.ind () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@list _let_1))) (let ((_let_5 (@var "Y" $$unsorted))) (let ((_let_6 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_6) (forall (@list _let_2) (=> (forall _let_4 (=> (forall (@list _let_5) (=> (_ (_ (_ tptp.tc _let_6) _let_1) _let_5) (_ _let_2 _let_5))) _let_3)) (forall _let_4 _let_3))))))))))) % 0.46/0.64 (define tptp.innf () (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) (not (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.46/0.64 (define tptp.nfof () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (and (_ (_ (_ tptp.trc _let_2) _let_3) _let_1) (_ (_ tptp.innf _let_2) _let_1))))))) % 0.46/0.64 (define tptp.norm () (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) (exists (@list _let_2) (_ (_ (_ tptp.nfof _let_3) _let_2) _let_1)))))))) % 0.46/0.64 (define tptp.join () (let ((_let_1 (@var "Z" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ tptp.trc _let_3))) (let ((_let_5 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.46/0.64 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.46/0.64 (define tptp.sconfl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.46/0.64 (define tptp.confl () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Z" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (_ (_ tptp.trc _let_3) _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))))) % 0.46/0.64 (define tptp.cr () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ (_ tptp.trsc _let_3) _let_2) _let_1) (_ (_ (_ tptp.join _let_3) _let_2) _let_1)))))))) % 0.46/0.64 (define @t1 () (@var "Y" $$unsorted)) % 0.46/0.64 (define @t2 () (@var "X" $$unsorted)) % 0.46/0.64 (define @t3 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.46/0.64 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.46/0.64 (define @t5 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.46/0.64 (define @t6 () (_ tptp.subrel @t5)) % 0.46/0.64 (define @t7 () (_ @t6 @t3)) % 0.46/0.64 (define @t8 () (_ tptp.trans @t3)) % 0.46/0.64 (define @t9 () (and @t8 @t7)) % 0.46/0.64 (define @t10 () (=> @t9 @t4)) % 0.46/0.64 (define @t11 () (@list @t3)) % 0.46/0.64 (define @t12 () (forall @t11 @t10)) % 0.46/0.64 (define @t13 () (and @t8 @t7 @t12)) % 0.46/0.64 (define @t14 () (=> @t13 @t4)) % 0.46/0.64 (define @t15 () (@list @t5 @t2 @t1 @t3)) % 0.46/0.64 (define @t16 () (forall @t15 @t14)) % 0.46/0.64 (define @t17 () (not @t16)) % 0.46/0.64 (define @t18 () (_ @t5 @t2)) % 0.46/0.64 (define @t19 () (_ @t18 @t1)) % 0.46/0.64 (define @t20 () (@list @t2 @t1)) % 0.46/0.64 (define @t21 () (forall @t20 (=> @t19 @t4))) % 0.46/0.64 (define @t22 () (@list @t5 @t3)) % 0.46/0.64 (define @t23 () (lambda @t22 @t21)) % 0.46/0.64 (define @t24 () (_ @t5 @t1)) % 0.46/0.64 (define @t25 () (_ @t24 @t2)) % 0.46/0.64 (define @t26 () (@list @t5 @t2 @t1)) % 0.46/0.64 (define @t27 () (lambda @t26 @t25)) % 0.46/0.64 (define @t28 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.46/0.64 (define @t29 () (_ @t28 @t5)) % 0.46/0.64 (define @t30 () (@list @t5)) % 0.46/0.64 (define @t31 () (@list @t28)) % 0.46/0.64 (define @t32 () (lambda @t31 (forall @t30 (= (_ @t28 @t29) @t29)))) % 0.46/0.64 (define @t33 () (lambda @t31 (forall @t30 (_ @t6 @t29)))) % 0.46/0.64 (define @t34 () (lambda @t31 (forall @t22 (=> @t7 (_ (_ tptp.subrel @t29) (_ @t28 @t3)))))) % 0.46/0.64 (define @t35 () (_ @t18 @t2)) % 0.46/0.64 (define @t36 () (@list @t2)) % 0.46/0.64 (define @t37 () (lambda @t30 (forall @t36 @t35))) % 0.46/0.64 (define @t38 () (lambda @t30 (forall @t36 (not @t35)))) % 0.46/0.64 (define @t39 () (= @t2 @t1)) % 0.46/0.64 (define @t40 () (lambda @t26 (or @t39 @t19))) % 0.46/0.64 (define @t41 () (lambda @t30 (forall @t20 (=> @t19 @t25)))) % 0.46/0.64 (define @t42 () (lambda @t30 (forall @t20 (=> (and @t19 @t25) @t39)))) % 0.46/0.64 (define @t43 () (lambda @t30 (forall @t20 (=> @t19 (not @t25))))) % 0.46/0.64 (define @t44 () (lambda @t26 (or @t25 @t19))) % 0.46/0.64 (define @t45 () (@var "Z" $$unsorted)) % 0.46/0.64 (define @t46 () (_ @t18 @t45)) % 0.46/0.64 (define @t47 () (_ @t24 @t45)) % 0.46/0.64 (define @t48 () (and @t19 @t47)) % 0.46/0.64 (define @t49 () (@list @t2 @t1 @t45)) % 0.46/0.64 (define @t50 () (forall @t49 (=> @t48 @t46))) % 0.46/0.64 (define @t51 () (lambda @t30 @t50)) % 0.46/0.64 (define @t52 () (lambda @t26 @t12)) % 0.46/0.64 (define @t53 () (@var "__flatten_var_1" $$unsorted)) % 0.46/0.64 (define @t54 () (@var "__flatten_var_0" $$unsorted)) % 0.46/0.64 (define @t55 () (_ tptp.tc @t5)) % 0.46/0.64 (define @t56 () (_ tptp.rc @t55)) % 0.46/0.64 (define @t57 () (@list @t5 @t54 @t53)) % 0.46/0.64 (define @t58 () (lambda @t57 (_ (_ @t56 @t54) @t53))) % 0.46/0.64 (define @t59 () (lambda @t57 (_ (_ (_ tptp.sc @t56) @t54) @t53))) % 0.46/0.64 (define @t60 () (_ tptp.trans @t5)) % 0.46/0.64 (define @t61 () (lambda @t30 (and (_ tptp.refl @t5) (_ tptp.antisymm @t5) @t60))) % 0.46/0.64 (define @t62 () (lambda @t30 (and (_ tptp.asymm @t5) @t60))) % 0.46/0.64 (define @t63 () (lambda @t30 (forall @t20 (or @t39 @t19 @t25)))) % 0.46/0.64 (define @t64 () (not @t19)) % 0.46/0.64 (define @t65 () (@var "A" (-> $$unsorted Bool))) % 0.46/0.64 (define @t66 () (@list @t1)) % 0.46/0.64 (define @t67 () (_ @t65 @t2)) % 0.46/0.64 (define @t68 () (lambda @t30 (forall (@list @t65) (=> (exists @t36 @t67) (exists @t36 (and @t67 (forall @t66 (=> (_ @t65 @t1) @t64)))))))) % 0.46/0.64 (define @t69 () (@var "P" (-> $$unsorted Bool))) % 0.46/0.64 (define @t70 () (_ @t69 @t2)) % 0.46/0.64 (define @t71 () (lambda @t30 (forall (@list @t69) (=> (forall @t36 (=> (forall @t66 (=> (_ (_ @t55 @t2) @t1) (_ @t69 @t1))) @t70)) (forall @t36 @t70))))) % 0.46/0.64 (define @t72 () (lambda (@list @t5 @t2) (not (exists @t66 @t19)))) % 0.46/0.64 (define @t73 () (_ tptp.trc @t5)) % 0.46/0.64 (define @t74 () (_ @t73 @t1)) % 0.46/0.64 (define @t75 () (lambda @t26 (and (_ @t74 @t2) (_ (_ tptp.innf @t5) @t2)))) % 0.46/0.64 (define @t76 () (lambda @t30 (forall @t36 (exists @t66 (_ (_ (_ tptp.nfof @t5) @t1) @t2))))) % 0.46/0.64 (define @t77 () (_ @t73 @t2)) % 0.46/0.64 (define @t78 () (_ @t77 @t45)) % 0.46/0.64 (define @t79 () (lambda @t26 (exists (@list @t45) (and @t78 (_ @t74 @t45))))) % 0.46/0.64 (define @t80 () (_ tptp.join @t5)) % 0.46/0.64 (define @t81 () (_ (_ @t80 @t45) @t1)) % 0.46/0.64 (define @t82 () (lambda @t30 (forall @t49 (=> (and @t46 @t19) @t81)))) % 0.46/0.64 (define @t83 () (_ @t77 @t1)) % 0.46/0.64 (define @t84 () (lambda @t30 (forall @t49 (=> (and @t46 @t83) @t81)))) % 0.46/0.64 (define @t85 () (lambda @t30 (forall @t49 (=> (and @t78 @t83) @t81)))) % 0.46/0.64 (define @t86 () (lambda @t30 (forall @t20 (=> (_ (_ (_ tptp.trsc @t5) @t2) @t1) (_ (_ @t80 @t2) @t1))))) % 0.46/0.64 (define @t87 () (_ @t3 @t2 @t1)) % 0.46/0.64 (define @t88 () (@var "BOUND_VARIABLE_8861" (-> $$unsorted $$unsorted Bool))) % 0.46/0.64 (define @t89 () (@var "BOUND_VARIABLE_8837" $$unsorted)) % 0.46/0.64 (define @t90 () (@var "BOUND_VARIABLE_8835" $$unsorted)) % 0.46/0.64 (define @t91 () (_ @t88 @t90 @t89)) % 0.46/0.64 (define @t92 () (not (_ @t5 @t90 @t89))) % 0.46/0.64 (define @t93 () (@list @t90 @t89)) % 0.46/0.64 (define @t94 () (@var "BOUND_VARIABLE_8846" $$unsorted)) % 0.46/0.64 (define @t95 () (@var "BOUND_VARIABLE_8848" $$unsorted)) % 0.46/0.64 (define @t96 () (@list @t94 @t95 @t45)) % 0.46/0.64 (define @t97 () (not (forall @t96 (or (not (_ @t88 @t94 @t95)) (not (_ @t88 @t95 @t45)) (_ @t88 @t94 @t45))))) % 0.46/0.64 (define @t98 () (@list @t88)) % 0.46/0.64 (define @t99 () (forall @t98 (or @t97 (not (forall @t93 (or @t92 @t91))) (_ @t88 @t2 @t1)))) % 0.46/0.64 (define @t100 () (not @t99)) % 0.46/0.64 (define @t101 () (forall @t93 (or @t92 (_ @t3 @t90 @t89)))) % 0.46/0.64 (define @t102 () (not @t101)) % 0.46/0.64 (define @t103 () (forall @t96 (or (not (_ @t3 @t94 @t95)) (not (_ @t3 @t95 @t45)) (_ @t3 @t94 @t45)))) % 0.46/0.64 (define @t104 () (not @t103)) % 0.46/0.64 (define @t105 () (or @t104 @t102 @t100 @t4)) % 0.46/0.64 (define @t106 () (or @t104 @t102 @t100)) % 0.46/0.64 (define @t107 () (and @t103 @t101 @t99)) % 0.46/0.64 (define @t108 () (_ @t5 @t2 @t1)) % 0.46/0.64 (define @t109 () (not @t108)) % 0.46/0.64 (define @t110 () (forall @t20 (or @t109 @t87))) % 0.46/0.64 (define @t111 () (not @t110)) % 0.46/0.64 (define @t112 () (forall @t49 (or (not @t87) (not (_ @t3 @t1 @t45)) (_ @t3 @t2 @t45)))) % 0.46/0.64 (define @t113 () (not @t112)) % 0.46/0.64 (define @t114 () (forall @t11 (or @t113 @t111 @t87))) % 0.46/0.64 (define @t115 () (@list @t2 @t1)) % 0.46/0.64 (define @t116 () (and @t112 @t110 @t114)) % 0.46/0.64 (define @t117 () (=> @t116 @t4)) % 0.46/0.64 (define @t118 () (or @t113 @t111 @t4)) % 0.46/0.64 (define @t119 () (and @t112 @t110)) % 0.46/0.64 (define @t120 () (lambda @t11 @t110)) % 0.46/0.64 (define @t121 () (_ (lambda @t22 @t110) @t5)) % 0.46/0.64 (define @t122 () (_ @t5 @t2 @t45)) % 0.46/0.64 (define @t123 () (_ @t5 @t1 @t45)) % 0.46/0.64 (define @t124 () (_ (lambda @t30 (forall @t49 (or @t109 (not @t123) @t122))) @t3)) % 0.46/0.64 (define @t125 () (_ @t121 @t3)) % 0.46/0.64 (define @t126 () (and @t124 @t125)) % 0.46/0.64 (define @t127 () (=> @t126 @t4)) % 0.46/0.64 (define @t128 () (forall @t11 @t127)) % 0.46/0.64 (define @t129 () (and @t124 @t125 @t128)) % 0.46/0.64 (define @t130 () (=> @t129 @t4)) % 0.46/0.64 (define @t131 () (forall @t15 @t130)) % 0.46/0.64 (define @t132 () (or @t64 @t4)) % 0.46/0.64 (define @t133 () (not @t47)) % 0.46/0.64 (define @t134 () (or @t64 @t133 @t46)) % 0.46/0.64 (define @t135 () (forall @t15 (or @t104 @t102 @t100 @t87))) % 0.46/0.64 (define @t136 () (@quantifiers_skolemize @t135 2)) % 0.46/0.64 (define @t137 () (@quantifiers_skolemize @t135 1)) % 0.46/0.64 (define @t138 () (not (_ (@quantifiers_skolemize @t135 0) @t90 @t89))) % 0.46/0.64 (define @t139 () (forall @t98 (or @t97 (not (forall @t93 (or @t138 @t91))) (_ @t88 @t137 @t136)))) % 0.46/0.64 (define @t140 () (@quantifiers_skolemize @t135 3)) % 0.46/0.64 (define @t141 () (_ @t140 @t137 @t136)) % 0.46/0.64 (define @t142 () (not @t139)) % 0.46/0.64 (define @t143 () (forall @t93 (or @t138 (_ @t140 @t90 @t89)))) % 0.46/0.64 (define @t144 () (not @t143)) % 0.46/0.64 (define @t145 () (forall @t96 (or (not (_ @t140 @t94 @t95)) (not (_ @t140 @t95 @t45)) (_ @t140 @t94 @t45)))) % 0.46/0.64 (define @t146 () (not @t145)) % 0.46/0.64 (define @t147 () (or @t146 @t144 @t142 @t141)) % 0.46/0.64 (define @t148 () (@list true)) % 0.46/0.64 (define @t149 () (@list @t147)) % 0.46/0.64 (define @t150 () (or @t146 @t144 @t141)) % 0.46/0.64 (define @t151 () (not @t150)) % 0.46/0.64 (assume @p1 @t17) % 0.46/0.64 (assume @p2 true) % 0.46/0.64 (step @p3 (= tptp.subrel @t23) :rule refl :args (@t23)) % 0.46/0.64 (step @p4 (= tptp.inv @t27) :rule refl :args (@t27)) % 0.46/0.64 (step @p5 (= tptp.idem @t32) :rule refl :args (@t32)) % 0.46/0.64 (step @p6 (= tptp.infl @t33) :rule refl :args (@t33)) % 0.46/0.64 (step @p7 (= tptp.mono @t34) :rule refl :args (@t34)) % 0.46/0.64 (step @p8 (= tptp.refl @t37) :rule refl :args (@t37)) % 0.46/0.64 (step @p9 (= tptp.irrefl @t38) :rule refl :args (@t38)) % 0.46/0.64 (step @p10 (= tptp.rc @t40) :rule refl :args (@t40)) % 0.46/0.64 (step @p11 (= tptp.symm @t41) :rule refl :args (@t41)) % 0.46/0.64 (step @p12 (= tptp.antisymm @t42) :rule refl :args (@t42)) % 0.46/0.64 (step @p13 (= tptp.asymm @t43) :rule refl :args (@t43)) % 0.46/0.64 (step @p14 (= tptp.sc @t44) :rule refl :args (@t44)) % 0.46/0.64 (step @p15 (= tptp.trans @t51) :rule refl :args (@t51)) % 0.46/0.64 (step @p16 (= tptp.tc @t52) :rule refl :args (@t52)) % 0.46/0.64 (step @p17 (= tptp.trc @t58) :rule refl :args (@t58)) % 0.46/0.64 (step @p18 (= tptp.trsc @t59) :rule refl :args (@t59)) % 0.46/0.64 (step @p19 (= tptp.po @t61) :rule refl :args (@t61)) % 0.46/0.64 (step @p20 (= tptp.so @t62) :rule refl :args (@t62)) % 0.46/0.64 (step @p21 (= tptp.total @t63) :rule refl :args (@t63)) % 0.46/0.64 (step @p22 (= tptp.term @t68) :rule refl :args (@t68)) % 0.46/0.64 (step @p23 (= tptp.ind @t71) :rule refl :args (@t71)) % 0.46/0.64 (step @p24 (= tptp.innf @t72) :rule refl :args (@t72)) % 0.46/0.64 (step @p25 (= tptp.nfof @t75) :rule refl :args (@t75)) % 0.46/0.64 (step @p26 (= tptp.norm @t76) :rule refl :args (@t76)) % 0.46/0.64 (step @p27 (= tptp.join @t79) :rule refl :args (@t79)) % 0.46/0.64 (step @p28 (= tptp.lconfl @t82) :rule refl :args (@t82)) % 0.46/0.64 (step @p29 (= tptp.sconfl @t84) :rule refl :args (@t84)) % 0.46/0.64 (step @p30 (= tptp.confl @t85) :rule refl :args (@t85)) % 0.46/0.64 (step @p31 (= tptp.cr @t86) :rule refl :args (@t86)) % 0.46/0.64 (step @p32 :rule refl :args (@t87)) % 0.46/0.64 (step @p33 :rule refl :args (@t4)) % 0.46/0.64 (step @p34 :rule cong :premises (@p33 @p32) :args ((= @t4 @t87))) % 0.46/0.64 (step @p35 :rule symm :premises (@p34)) % 0.46/0.64 (step @p36 :rule eq_resolve :premises (@p33 @p35)) % 0.46/0.64 (step @p37 :rule refl :args (@t100)) % 0.46/0.64 (step @p38 :rule refl :args (@t102)) % 0.46/0.64 (step @p39 :rule refl :args (@t104)) % 0.46/0.64 (step @p40 :rule nary_cong :premises (@p39 @p38 @p37 @p36) :args (@t105)) % 0.46/0.64 (step @p41 :rule cong :premises (@p40) :args ((forall @t15 @t105))) % 0.46/0.64 (step @p42 :rule aci_norm :args ((= (or @t106 @t4) @t105))) % 0.46/0.64 (step @p43 :rule aci_norm :args ((= (or @t104 (or @t102 @t100)) @t106))) % 0.46/0.64 (step @p44 :rule bool-and-de-morgan :args (@t101 @t99 true)) % 0.46/0.64 (step @p45 :rule nary_cong :premises (@p39 @p44) :args ((or @t104 (not (and @t101 @t99))))) % 0.46/0.64 (step @p46 :rule bool-and-de-morgan :args (@t103 @t101 (and @t99))) % 0.46/0.64 (step @p47 :rule trans :premises (@p46 @p45)) % 0.46/0.64 (step @p48 :rule trans :premises (@p47 @p43)) % 0.46/0.64 (step @p49 :rule nary_cong :premises (@p48 @p33) :args ((or (not @t107) @t4))) % 0.46/0.64 (step @p50 :rule trans :premises (@p49 @p42)) % 0.46/0.64 (step @p51 :rule bool-impl-elim :args (@t107 @t4)) % 0.46/0.64 (step @p52 :rule trans :premises (@p51 @p50)) % 0.46/0.64 (step @p53 :rule cong :premises (@p52) :args ((forall @t15 (=> @t107 @t4)))) % 0.46/0.64 (step @p54 :rule trans :premises (@p53 @p41)) % 0.46/0.64 ; WARNING: add trust step for TRUST % 0.46/0.64 ; trust TRUST MACRO_THEORY_REWRITE_RCONS_SIMPLE % 0.46/0.64 (step @p55 :rule trust :premises () :args ((= @t114 @t99))) % 0.46/0.64 (step @p56 :rule alpha_equiv :args (@t110 @t115 (@list @t90 @t89))) % 0.46/0.64 (step @p57 :rule alpha_equiv :args (@t112 @t115 (@list @t94 @t95))) % 0.46/0.64 (step @p58 :rule nary_cong :premises (@p57 @p56 @p55) :args (@t116)) % 0.46/0.64 (step @p59 :rule cong :premises (@p58 @p33) :args (@t117)) % 0.46/0.64 (step @p60 :rule cong :premises (@p59) :args ((forall @t15 @t117))) % 0.46/0.64 (step @p61 :rule trans :premises (@p60 @p54)) % 0.46/0.64 (step @p62 :rule refl :args (@t4)) % 0.46/0.64 (step @p63 :rule refl :args (@t111)) % 0.46/0.64 (step @p64 :rule refl :args (@t113)) % 0.46/0.64 (step @p65 :rule nary_cong :premises (@p64 @p63 @p36) :args (@t118)) % 0.46/0.64 (step @p66 :rule cong :premises (@p65) :args ((forall @t11 @t118))) % 0.46/0.64 (step @p67 :rule aci_norm :args ((= (or (or @t113 @t111) @t4) @t118))) % 0.46/0.64 (step @p68 :rule bool-and-de-morgan :args (@t112 @t110 true)) % 0.46/0.64 (step @p69 :rule nary_cong :premises (@p68 @p33) :args ((or (not @t119) @t4))) % 0.46/0.64 (step @p70 :rule trans :premises (@p69 @p67)) % 0.46/0.64 (step @p71 :rule bool-impl-elim :args (@t119 @t4)) % 0.46/0.64 (step @p72 :rule trans :premises (@p71 @p70)) % 0.46/0.64 (step @p73 :rule cong :premises (@p72) :args ((forall @t11 (=> @t119 @t4)))) % 0.46/0.64 (step @p74 :rule trans :premises (@p73 @p66)) % 0.46/0.64 (step @p75 :rule beta-reduce :args ((= (_ @t120 @t3) @t110))) % 0.46/0.64 (step @p76 :rule refl :args (@t3)) % 0.46/0.64 (step @p77 :rule beta-reduce :args ((= @t121 @t120))) % 0.46/0.64 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 0.46/0.64 (step @p79 :rule trans :premises (@p78 @p75)) % 0.46/0.64 (step @p80 :rule beta-reduce :args ((= @t124 @t112))) % 0.46/0.64 (step @p81 :rule nary_cong :premises (@p80 @p79) :args (@t126)) % 0.46/0.64 (step @p82 :rule cong :premises (@p81 @p62) :args (@t127)) % 0.46/0.64 (step @p83 :rule cong :premises (@p82) :args (@t128)) % 0.46/0.64 (step @p84 :rule trans :premises (@p83 @p74)) % 0.46/0.64 (step @p85 :rule nary_cong :premises (@p80 @p79 @p84) :args (@t129)) % 0.46/0.64 (step @p86 :rule cong :premises (@p85 @p62) :args (@t130)) % 0.46/0.64 (step @p87 :rule cong :premises (@p86) :args (@t131)) % 0.46/0.64 (step @p88 :rule trans :premises (@p87 @p61)) % 0.46/0.64 (step @p89 :rule cong :premises (@p88) :args ((not @t131))) % 0.46/0.64 (step @p90 :rule refl :args (@t5)) % 0.46/0.64 (step @p91 :rule refl :args (@t108)) % 0.46/0.64 (step @p92 :rule refl :args (@t19)) % 0.46/0.64 (step @p93 :rule cong :premises (@p92 @p91) :args ((= @t19 @t108))) % 0.46/0.64 (step @p94 :rule symm :premises (@p93)) % 0.46/0.64 (step @p95 :rule eq_resolve :premises (@p92 @p94)) % 0.46/0.64 (step @p96 :rule cong :premises (@p95) :args (@t64)) % 0.46/0.64 (step @p97 :rule nary_cong :premises (@p96 @p36) :args (@t132)) % 0.46/0.64 (step @p98 :rule cong :premises (@p97) :args ((forall @t20 @t132))) % 0.46/0.64 (step @p99 :rule bool-impl-elim :args (@t19 @t4)) % 0.46/0.64 (step @p100 :rule cong :premises (@p99) :args (@t21)) % 0.46/0.64 (step @p101 :rule trans :premises (@p100 @p98)) % 0.46/0.64 (step @p102 :rule cong :premises (@p101) :args (@t23)) % 0.46/0.64 (step @p103 :rule trans :premises (@p3 @p102)) % 0.46/0.64 (step @p104 :rule ho_cong :premises (@p103 @p90)) % 0.46/0.64 (step @p105 :rule ho_cong :premises (@p104 @p76)) % 0.46/0.64 (step @p106 :rule refl :args (@t122)) % 0.46/0.64 (step @p107 :rule refl :args (@t46)) % 0.46/0.64 (step @p108 :rule cong :premises (@p107 @p106) :args ((= @t46 @t122))) % 0.46/0.64 (step @p109 :rule symm :premises (@p108)) % 0.46/0.64 (step @p110 :rule eq_resolve :premises (@p107 @p109)) % 0.46/0.64 (step @p111 :rule refl :args (@t123)) % 0.46/0.64 (step @p112 :rule refl :args (@t47)) % 0.46/0.64 (step @p113 :rule cong :premises (@p112 @p111) :args ((= @t47 @t123))) % 0.46/0.64 (step @p114 :rule symm :premises (@p113)) % 0.46/0.64 (step @p115 :rule eq_resolve :premises (@p112 @p114)) % 0.46/0.64 (step @p116 :rule cong :premises (@p115) :args (@t133)) % 0.46/0.64 (step @p117 :rule nary_cong :premises (@p96 @p116 @p110) :args (@t134)) % 0.46/0.64 (step @p118 :rule cong :premises (@p117) :args ((forall @t49 @t134))) % 0.46/0.64 (step @p119 :rule aci_norm :args ((= (or (or @t64 @t133) @t46) @t134))) % 0.46/0.64 (step @p120 :rule bool-and-de-morgan :args (@t19 @t47 true)) % 0.46/0.64 (step @p121 :rule nary_cong :premises (@p120 @p107) :args ((or (not @t48) @t46))) % 0.46/0.64 (step @p122 :rule trans :premises (@p121 @p119)) % 0.46/0.64 (step @p123 :rule bool-impl-elim :args (@t48 @t46)) % 0.46/0.64 (step @p124 :rule trans :premises (@p123 @p122)) % 0.46/0.64 (step @p125 :rule cong :premises (@p124) :args (@t50)) % 0.46/0.64 (step @p126 :rule trans :premises (@p125 @p118)) % 0.46/0.64 (step @p127 :rule cong :premises (@p126) :args (@t51)) % 0.46/0.64 (step @p128 :rule trans :premises (@p15 @p127)) % 0.46/0.64 (step @p129 :rule ho_cong :premises (@p128 @p76)) % 0.46/0.64 (step @p130 :rule nary_cong :premises (@p129 @p105) :args (@t9)) % 0.46/0.64 (step @p131 :rule cong :premises (@p130 @p62) :args (@t10)) % 0.46/0.64 (step @p132 :rule cong :premises (@p131) :args (@t12)) % 0.46/0.64 (step @p133 :rule nary_cong :premises (@p129 @p105 @p132) :args (@t13)) % 0.46/0.64 (step @p134 :rule cong :premises (@p133 @p62) :args (@t14)) % 0.46/0.64 (step @p135 :rule cong :premises (@p134) :args (@t16)) % 0.46/0.64 (step @p136 :rule cong :premises (@p135) :args (@t17)) % 0.46/0.64 (step @p137 :rule trans :premises (@p136 @p89)) % 0.46/0.64 (step @p138 :rule eq_resolve :premises (@p1 @p137)) % 0.46/0.64 (step @p139 :rule skolemize :premises (@p138)) % 0.46/0.64 (step @p140 :rule bool-double-not-elim :args (@t139)) % 0.46/0.64 (step @p141 :rule refl :args (@t147)) % 0.46/0.64 (step @p142 :rule nary_cong :premises (@p141 @p140) :args ((or @t147 (not @t142)))) % 0.46/0.64 (step @p143 :rule cnf_or_neg :args (@t147 2)) % 0.46/0.64 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.46/0.64 (step @p145 :rule reordering :premises (@p144) :args ((or @t139 @t147))) % 0.46/0.64 (step @p146 :rule chain_m_resolution :premises (@p145 @p139) :args (@t139 @t148 @t149)) % 0.46/0.64 (step @p147 :rule cnf_or_neg :args (@t147 3)) % 0.46/0.64 (step @p148 :rule chain_m_resolution :premises (@p147 @p139) :args ((not @t141) @t148 @t149)) % 0.46/0.64 (step @p149 :rule bool-double-not-elim :args (@t143)) % 0.46/0.64 (step @p150 :rule nary_cong :premises (@p141 @p149) :args ((or @t147 (not @t144)))) % 0.46/0.64 (step @p151 :rule cnf_or_neg :args (@t147 1)) % 0.46/0.64 (step @p152 :rule eq_resolve :premises (@p151 @p150)) % 0.46/0.64 (step @p153 :rule reordering :premises (@p152) :args ((or @t143 @t147))) % 0.46/0.64 (step @p154 :rule chain_m_resolution :premises (@p153 @p139) :args (@t143 @t148 @t149)) % 0.46/0.64 (step @p155 :rule bool-double-not-elim :args (@t145)) % 0.46/0.64 (step @p156 :rule nary_cong :premises (@p141 @p155) :args ((or @t147 (not @t146)))) % 0.46/0.64 (step @p157 :rule cnf_or_neg :args (@t147 0)) % 0.46/0.64 (step @p158 :rule eq_resolve :premises (@p157 @p156)) % 0.46/0.64 (step @p159 :rule reordering :premises (@p158) :args ((or @t145 @t147))) % 0.46/0.64 (step @p160 :rule chain_m_resolution :premises (@p159 @p139) :args (@t145 @t148 @t149)) % 0.46/0.64 (step @p161 :rule cnf_or_pos :args (@t150)) % 0.46/0.64 (step @p162 :rule reordering :premises (@p161) :args ((or @t146 @t144 @t141 @t151))) % 0.46/0.64 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p154 @p148) :args (@t151 (@list false false true) (@list @t145 @t143 @t141))) % 0.46/0.64 (assume-push @p170 @t139) % 0.46/0.64 (step @p165 :rule instantiate :premises (@p146) :args ((@list @t140))) % 0.46/0.64 (step-pop @p171 :rule scope :premises (@p165)) % 0.46/0.64 (step @p166 :rule process_scope :premises (@p171) :args (@t150)) % 0.46/0.64 (step @p168 :rule implies_elim :premises (@p166)) % 0.46/0.64 (step @p169 false :rule chain_m_resolution :premises (@p168 @p163 @p146) :args (false (@list true false) (@list @t150 @t139))) % 0.46/0.64 ) % 0.46/0.64 % SZS output end Proof % 0.46/0.64 % cvc5 exiting %------------------------------------------------------------------------------