%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU457^1 : 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 0.45s 0.62s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU457^1 : 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 % 0.16/0.34 % Computer : n001.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 17:36:35 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.45/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.45/0.62 % SZS status Theorem % 0.45/0.62 % SZS output start Proof % 0.45/0.62 ( % 0.45/0.62 (declare-sort $$unsorted 0) % 0.45/0.62 (define tptp.subrel () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_3) (forall (@list _let_2 _let_1) (=> (_ (_ _let_4 _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))) % 0.45/0.62 (define tptp.inv () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))) % 0.45/0.62 (define tptp.idem () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (lambda (@list _let_2) (forall (@list _let_1) (= (_ _let_2 _let_3) _let_3))))))) % 0.45/0.62 (define tptp.infl () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ tptp.subrel _let_1) (_ _let_2 _let_1))))))) % 0.45/0.62 (define tptp.mono () (let ((_let_1 (@var "S" (-> $$unsorted $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_3 _let_1) (=> (_ (_ tptp.subrel _let_3) _let_1) (_ (_ tptp.subrel (_ _let_2 _let_3)) (_ _let_2 _let_1))))))))) % 0.45/0.62 (define tptp.refl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.45/0.62 (define tptp.irrefl () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ (_ _let_2 _let_1) _let_1))))))) % 0.45/0.62 (define tptp.rc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (= _let_2 _let_1) (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.62 (define tptp.symm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.45/0.62 (define tptp.antisymm () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (and (_ (_ _let_3 _let_2) _let_1) (_ (_ _let_3 _let_1) _let_2)) (= _let_2 _let_1)))))))) % 0.45/0.62 (define tptp.asymm () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "Y" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (not (_ (_ _let_3 _let_2) _let_1))))))))) % 0.45/0.62 (define tptp.sc () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.45/0.62 (define tptp.trans () (let ((_let_1 (@var "Z" $$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)))))))))) % 0.45/0.62 (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))))))))) % 0.45/0.62 (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)))))) % 0.45/0.62 (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)))))) % 0.45/0.62 (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))))) % 0.45/0.62 (define tptp.so () (let ((_let_1 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_1) (and (_ tptp.asymm _let_1) (_ tptp.trans _let_1))))) % 0.45/0.62 (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)))))))) % 0.45/0.62 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_2))) (let ((_let_6 (@list _let_2))) (lambda (@list _let_3) (forall (@list _let_4) (=> (exists _let_6 _let_5) (exists _let_6 (and _let_5 (forall (@list _let_1) (=> (_ _let_4 _let_1) (not (_ (_ _let_3 _let_2) _let_1)))))))))))))))) % 0.45/0.62 (define tptp.ind () (let ((_let_1 (@var "X" $$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))))))))))) % 0.45/0.62 (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)))))))) % 0.45/0.62 (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))))))) % 0.45/0.62 (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)))))))) % 0.45/0.62 (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" $$unsorted))) (lambda (@list _let_3 _let_5 _let_2) (exists (@list _let_1) (and (_ (_ _let_4 _let_5) _let_1) (_ (_ _let_4 _let_2) _let_1)))))))))) % 0.45/0.62 (define tptp.lconfl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.62 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ (_ _let_3 _let_4) _let_2) (_ (_ (_ tptp.trc _let_3) _let_4) _let_1)) (_ (_ (_ tptp.join _let_3) _let_2) _let_1))))))))) % 0.45/0.62 (define tptp.confl () (let ((_let_1 (@var "Y" $$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)))))))))) % 0.45/0.62 (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)))))))) % 0.45/0.62 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.45/0.62 (define @t2 () (@list @t1)) % 0.45/0.62 (define @t3 () (forall @t2 (_ tptp.symm (_ tptp.sc @t1)))) % 0.45/0.62 (define @t4 () (not @t3)) % 0.45/0.62 (define @t5 () (@var "Y" $$unsorted)) % 0.45/0.62 (define @t6 () (@var "X" $$unsorted)) % 0.45/0.62 (define @t7 () (@var "S" (-> $$unsorted $$unsorted Bool))) % 0.45/0.62 (define @t8 () (_ (_ @t7 @t6) @t5)) % 0.45/0.62 (define @t9 () (_ @t1 @t6)) % 0.45/0.62 (define @t10 () (_ @t9 @t5)) % 0.45/0.62 (define @t11 () (@list @t6 @t5)) % 0.45/0.62 (define @t12 () (@list @t1 @t7)) % 0.45/0.62 (define @t13 () (lambda @t12 (forall @t11 (=> @t10 @t8)))) % 0.45/0.62 (define @t14 () (_ @t1 @t5)) % 0.45/0.62 (define @t15 () (_ @t14 @t6)) % 0.45/0.62 (define @t16 () (@list @t1 @t6 @t5)) % 0.45/0.62 (define @t17 () (lambda @t16 @t15)) % 0.45/0.62 (define @t18 () (@var "F" (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool))) % 0.45/0.62 (define @t19 () (_ @t18 @t1)) % 0.45/0.62 (define @t20 () (@list @t18)) % 0.45/0.62 (define @t21 () (lambda @t20 (forall @t2 (= (_ @t18 @t19) @t19)))) % 0.45/0.62 (define @t22 () (_ tptp.subrel @t1)) % 0.45/0.62 (define @t23 () (lambda @t20 (forall @t2 (_ @t22 @t19)))) % 0.45/0.62 (define @t24 () (_ @t22 @t7)) % 0.45/0.62 (define @t25 () (lambda @t20 (forall @t12 (=> @t24 (_ (_ tptp.subrel @t19) (_ @t18 @t7)))))) % 0.45/0.62 (define @t26 () (_ @t9 @t6)) % 0.45/0.62 (define @t27 () (@list @t6)) % 0.45/0.62 (define @t28 () (lambda @t2 (forall @t27 @t26))) % 0.45/0.62 (define @t29 () (lambda @t2 (forall @t27 (not @t26)))) % 0.45/0.62 (define @t30 () (= @t6 @t5)) % 0.45/0.62 (define @t31 () (lambda @t16 (or @t30 @t10))) % 0.45/0.62 (define @t32 () (forall @t11 (=> @t10 @t15))) % 0.45/0.62 (define @t33 () (lambda @t2 @t32)) % 0.45/0.62 (define @t34 () (lambda @t2 (forall @t11 (=> (and @t10 @t15) @t30)))) % 0.45/0.62 (define @t35 () (not @t15)) % 0.45/0.62 (define @t36 () (lambda @t2 (forall @t11 (=> @t10 @t35)))) % 0.45/0.62 (define @t37 () (or @t15 @t10)) % 0.45/0.62 (define @t38 () (lambda @t16 @t37)) % 0.45/0.62 (define @t39 () (@var "Z" $$unsorted)) % 0.45/0.62 (define @t40 () (_ @t9 @t39)) % 0.45/0.62 (define @t41 () (@list @t6 @t5 @t39)) % 0.45/0.62 (define @t42 () (lambda @t2 (forall @t41 (=> (and @t10 (_ @t14 @t39)) @t40)))) % 0.45/0.62 (define @t43 () (lambda @t16 (forall (@list @t7) (=> (and (_ tptp.trans @t7) @t24) @t8)))) % 0.45/0.62 (define @t44 () (@var "__flatten_var_1" $$unsorted)) % 0.45/0.62 (define @t45 () (@var "__flatten_var_0" $$unsorted)) % 0.45/0.62 (define @t46 () (_ tptp.tc @t1)) % 0.45/0.62 (define @t47 () (_ tptp.rc @t46)) % 0.45/0.62 (define @t48 () (@list @t1 @t45 @t44)) % 0.45/0.62 (define @t49 () (lambda @t48 (_ (_ @t47 @t45) @t44))) % 0.45/0.62 (define @t50 () (lambda @t48 (_ (_ (_ tptp.sc @t47) @t45) @t44))) % 0.45/0.62 (define @t51 () (_ tptp.trans @t1)) % 0.45/0.62 (define @t52 () (lambda @t2 (and (_ tptp.refl @t1) (_ tptp.antisymm @t1) @t51))) % 0.45/0.62 (define @t53 () (lambda @t2 (and (_ tptp.asymm @t1) @t51))) % 0.45/0.62 (define @t54 () (lambda @t2 (forall @t11 (or @t30 @t10 @t15)))) % 0.45/0.62 (define @t55 () (not @t10)) % 0.45/0.62 (define @t56 () (@var "A" (-> $$unsorted Bool))) % 0.45/0.62 (define @t57 () (@list @t5)) % 0.45/0.62 (define @t58 () (_ @t56 @t6)) % 0.45/0.62 (define @t59 () (lambda @t2 (forall (@list @t56) (=> (exists @t27 @t58) (exists @t27 (and @t58 (forall @t57 (=> (_ @t56 @t5) @t55)))))))) % 0.45/0.62 (define @t60 () (@var "P" (-> $$unsorted Bool))) % 0.45/0.62 (define @t61 () (_ @t60 @t6)) % 0.45/0.62 (define @t62 () (lambda @t2 (forall (@list @t60) (=> (forall @t27 (=> (forall @t57 (=> (_ (_ @t46 @t6) @t5) (_ @t60 @t5))) @t61)) (forall @t27 @t61))))) % 0.45/0.62 (define @t63 () (lambda (@list @t1 @t6) (not (exists @t57 @t10)))) % 0.45/0.62 (define @t64 () (_ tptp.trc @t1)) % 0.45/0.62 (define @t65 () (_ @t64 @t5)) % 0.45/0.62 (define @t66 () (lambda @t16 (and (_ @t65 @t6) (_ (_ tptp.innf @t1) @t6)))) % 0.45/0.62 (define @t67 () (lambda @t2 (forall @t27 (exists @t57 (_ (_ (_ tptp.nfof @t1) @t5) @t6))))) % 0.45/0.62 (define @t68 () (_ @t64 @t6)) % 0.45/0.62 (define @t69 () (_ @t68 @t39)) % 0.45/0.62 (define @t70 () (lambda @t16 (exists (@list @t39) (and @t69 (_ @t65 @t39))))) % 0.45/0.62 (define @t71 () (_ tptp.join @t1)) % 0.45/0.62 (define @t72 () (_ (_ @t71 @t39) @t5)) % 0.45/0.62 (define @t73 () (lambda @t2 (forall @t41 (=> (and @t40 @t10) @t72)))) % 0.45/0.62 (define @t74 () (_ @t68 @t5)) % 0.45/0.62 (define @t75 () (lambda @t2 (forall @t41 (=> (and @t40 @t74) @t72)))) % 0.45/0.62 (define @t76 () (lambda @t2 (forall @t41 (=> (and @t69 @t74) @t72)))) % 0.45/0.62 (define @t77 () (lambda @t2 (forall @t11 (=> (_ (_ (_ tptp.trsc @t1) @t6) @t5) (_ (_ @t71 @t6) @t5))))) % 0.45/0.62 (define @t78 () (_ @t1 @t5 @t6)) % 0.45/0.62 (define @t79 () (_ @t1 @t6 @t5)) % 0.45/0.62 (define @t80 () (not @t79)) % 0.45/0.62 (define @t81 () (or (and (not @t78) @t80) @t79 @t78)) % 0.45/0.62 (define @t82 () (forall @t16 @t81)) % 0.45/0.62 (define @t83 () (and @t35 @t55)) % 0.45/0.62 (define @t84 () (or @t83 @t10 @t15)) % 0.45/0.62 (define @t85 () (not @t37)) % 0.45/0.62 (define @t86 () (or @t85 @t10 @t15)) % 0.45/0.62 (define @t87 () (or @t10 @t15)) % 0.45/0.62 (define @t88 () (lambda @t11 @t37)) % 0.45/0.62 (define @t89 () (_ @t88 @t5 @t6)) % 0.45/0.62 (define @t90 () (_ @t88 @t6 @t5)) % 0.45/0.62 (define @t91 () (not @t90)) % 0.45/0.62 (define @t92 () (or @t91 @t89)) % 0.45/0.62 (define @t93 () (forall @t11 @t92)) % 0.45/0.62 (define @t94 () (lambda @t2 (forall @t11 (or @t80 @t78)))) % 0.45/0.62 (define @t95 () (_ @t38 @t1)) % 0.45/0.62 (define @t96 () (forall @t2 (_ @t94 @t95))) % 0.45/0.62 (define @t97 () (or @t55 @t15)) % 0.45/0.62 (define @t98 () (@quantifiers_skolemize @t82 1)) % 0.45/0.62 (define @t99 () (@quantifiers_skolemize @t82 2)) % 0.45/0.62 (define @t100 () (@quantifiers_skolemize @t82 0)) % 0.45/0.62 (define @t101 () (_ @t100 @t99 @t98)) % 0.45/0.62 (define @t102 () (_ @t100 @t98 @t99)) % 0.45/0.62 (define @t103 () (not @t102)) % 0.45/0.62 (define @t104 () (not @t101)) % 0.45/0.62 (define @t105 () (and @t104 @t103)) % 0.45/0.62 (define @t106 () (or @t105 @t102 @t101)) % 0.45/0.62 (define @t107 () (@list true)) % 0.45/0.62 (define @t108 () (@list @t106)) % 0.45/0.62 (assume @p1 @t4) % 0.45/0.62 (assume @p2 true) % 0.45/0.62 (step @p3 (= tptp.subrel @t13) :rule refl :args (@t13)) % 0.45/0.62 (step @p4 (= tptp.inv @t17) :rule refl :args (@t17)) % 0.45/0.62 (step @p5 (= tptp.idem @t21) :rule refl :args (@t21)) % 0.45/0.62 (step @p6 (= tptp.infl @t23) :rule refl :args (@t23)) % 0.45/0.62 (step @p7 (= tptp.mono @t25) :rule refl :args (@t25)) % 0.45/0.62 (step @p8 (= tptp.refl @t28) :rule refl :args (@t28)) % 0.45/0.62 (step @p9 (= tptp.irrefl @t29) :rule refl :args (@t29)) % 0.45/0.62 (step @p10 (= tptp.rc @t31) :rule refl :args (@t31)) % 0.45/0.62 (step @p11 (= tptp.symm @t33) :rule refl :args (@t33)) % 0.45/0.62 (step @p12 (= tptp.antisymm @t34) :rule refl :args (@t34)) % 0.45/0.62 (step @p13 (= tptp.asymm @t36) :rule refl :args (@t36)) % 0.45/0.62 (step @p14 (= tptp.sc @t38) :rule refl :args (@t38)) % 0.45/0.62 (step @p15 (= tptp.trans @t42) :rule refl :args (@t42)) % 0.45/0.62 (step @p16 (= tptp.tc @t43) :rule refl :args (@t43)) % 0.45/0.62 (step @p17 (= tptp.trc @t49) :rule refl :args (@t49)) % 0.45/0.62 (step @p18 (= tptp.trsc @t50) :rule refl :args (@t50)) % 0.45/0.62 (step @p19 (= tptp.po @t52) :rule refl :args (@t52)) % 0.45/0.62 (step @p20 (= tptp.so @t53) :rule refl :args (@t53)) % 0.45/0.62 (step @p21 (= tptp.total @t54) :rule refl :args (@t54)) % 0.45/0.62 (step @p22 (= tptp.term @t59) :rule refl :args (@t59)) % 0.45/0.62 (step @p23 (= tptp.ind @t62) :rule refl :args (@t62)) % 0.45/0.62 (step @p24 (= tptp.innf @t63) :rule refl :args (@t63)) % 0.45/0.62 (step @p25 (= tptp.nfof @t66) :rule refl :args (@t66)) % 0.45/0.62 (step @p26 (= tptp.norm @t67) :rule refl :args (@t67)) % 0.45/0.62 (step @p27 (= tptp.join @t70) :rule refl :args (@t70)) % 0.45/0.62 (step @p28 (= tptp.lconfl @t73) :rule refl :args (@t73)) % 0.45/0.62 (step @p29 (= tptp.sconfl @t75) :rule refl :args (@t75)) % 0.45/0.62 (step @p30 (= tptp.confl @t76) :rule refl :args (@t76)) % 0.45/0.62 (step @p31 (= tptp.cr @t77) :rule refl :args (@t77)) % 0.45/0.62 (step @p32 :rule quant-merge-prenex :args ((= (forall @t2 (forall @t11 @t81)) @t82))) % 0.45/0.62 (step @p33 :rule refl :args (@t78)) % 0.45/0.62 (step @p34 :rule refl :args (@t15)) % 0.45/0.62 (step @p35 :rule cong :premises (@p34 @p33) :args ((= @t15 @t78))) % 0.45/0.62 (step @p36 :rule symm :premises (@p35)) % 0.45/0.62 (step @p37 :rule eq_resolve :premises (@p34 @p36)) % 0.45/0.62 (step @p38 :rule refl :args (@t79)) % 0.45/0.62 (step @p39 :rule refl :args (@t10)) % 0.45/0.62 (step @p40 :rule cong :premises (@p39 @p38) :args ((= @t10 @t79))) % 0.45/0.62 (step @p41 :rule symm :premises (@p40)) % 0.45/0.62 (step @p42 :rule eq_resolve :premises (@p39 @p41)) % 0.45/0.62 (step @p43 :rule cong :premises (@p42) :args (@t55)) % 0.45/0.62 (step @p44 :rule cong :premises (@p37) :args (@t35)) % 0.45/0.62 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t83)) % 0.45/0.62 (step @p46 :rule nary_cong :premises (@p45 @p42 @p37) :args (@t84)) % 0.45/0.63 (step @p47 :rule cong :premises (@p46) :args ((forall @t11 @t84))) % 0.45/0.63 (step @p48 :rule bool-or-de-morgan :args (@t15 @t10 false)) % 0.45/0.63 (step @p49 :rule nary_cong :premises (@p48 @p39 @p34) :args (@t86)) % 0.45/0.63 (step @p50 :rule cong :premises (@p49) :args ((forall @t11 @t86))) % 0.45/0.63 (step @p51 :rule trans :premises (@p50 @p47)) % 0.45/0.63 (step @p52 :rule aci_norm :args ((= (or @t85 @t87) @t86))) % 0.45/0.63 (step @p53 :rule beta-reduce :args ((= @t89 @t87))) % 0.45/0.63 (step @p54 :rule beta-reduce :args ((= @t90 @t37))) % 0.45/0.63 (step @p55 :rule cong :premises (@p54) :args (@t91)) % 0.45/0.63 (step @p56 :rule nary_cong :premises (@p55 @p53) :args (@t92)) % 0.45/0.63 (step @p57 :rule trans :premises (@p56 @p52)) % 0.45/0.63 (step @p58 :rule cong :premises (@p57) :args (@t93)) % 0.45/0.63 (step @p59 :rule trans :premises (@p58 @p51)) % 0.45/0.63 (step @p60 :rule beta-reduce :args ((= (_ @t94 @t88) @t93))) % 0.45/0.63 (step @p61 :rule trans :premises (@p60 @p59)) % 0.45/0.63 (step @p62 :rule beta-reduce :args ((= @t95 @t88))) % 0.45/0.63 (step @p63 :rule refl :args (@t94)) % 0.45/0.63 (step @p64 :rule ho_cong :premises (@p63 @p62)) % 0.45/0.63 (step @p65 :rule trans :premises (@p64 @p61)) % 0.45/0.63 (step @p66 :rule cong :premises (@p65) :args (@t96)) % 0.45/0.63 (step @p67 :rule trans :premises (@p66 @p32)) % 0.45/0.63 (step @p68 :rule cong :premises (@p67) :args ((not @t96))) % 0.45/0.63 (step @p69 :rule refl :args (@t1)) % 0.45/0.63 (step @p70 :rule ho_cong :premises (@p14 @p69)) % 0.45/0.63 (step @p71 :rule nary_cong :premises (@p43 @p37) :args (@t97)) % 0.45/0.63 (step @p72 :rule cong :premises (@p71) :args ((forall @t11 @t97))) % 0.45/0.63 (step @p73 :rule bool-impl-elim :args (@t10 @t15)) % 0.45/0.63 (step @p74 :rule cong :premises (@p73) :args (@t32)) % 0.45/0.63 (step @p75 :rule trans :premises (@p74 @p72)) % 0.45/0.63 (step @p76 :rule cong :premises (@p75) :args (@t33)) % 0.45/0.63 (step @p77 :rule trans :premises (@p11 @p76)) % 0.45/0.63 (step @p78 :rule ho_cong :premises (@p77 @p70)) % 0.45/0.63 (step @p79 :rule cong :premises (@p78) :args (@t3)) % 0.45/0.63 (step @p80 :rule cong :premises (@p79) :args (@t4)) % 0.45/0.63 (step @p81 :rule trans :premises (@p80 @p68)) % 0.45/0.63 (step @p82 :rule eq_resolve :premises (@p1 @p81)) % 0.45/0.63 (step @p83 :rule skolemize :premises (@p82)) % 0.45/0.63 (step @p84 :rule cnf_or_neg :args (@t106 0)) % 0.45/0.63 (step @p85 :rule chain_m_resolution :premises (@p84 @p83) :args ((not @t105) @t107 @t108)) % 0.45/0.63 (step @p86 :rule cnf_or_neg :args (@t106 1)) % 0.45/0.63 (step @p87 :rule reordering :premises (@p86) :args ((or @t103 @t106))) % 0.45/0.63 (step @p88 :rule chain_m_resolution :premises (@p87 @p83) :args (@t103 @t107 @t108)) % 0.45/0.63 (step @p89 :rule cnf_or_neg :args (@t106 2)) % 0.45/0.63 (step @p90 :rule reordering :premises (@p89) :args ((or @t104 @t106))) % 0.45/0.63 (step @p91 :rule chain_m_resolution :premises (@p90 @p83) :args (@t104 @t107 @t108)) % 0.45/0.63 (step @p92 :rule bool-double-not-elim :args (@t102)) % 0.45/0.63 (step @p93 :rule bool-double-not-elim :args (@t101)) % 0.45/0.63 (step @p94 :rule refl :args (@t105)) % 0.45/0.63 (step @p95 :rule nary_cong :premises (@p94 @p93 @p92) :args ((or @t105 (not @t104) (not @t103)))) % 0.45/0.63 (step @p96 :rule cnf_and_neg :args (@t105)) % 0.45/0.63 (step @p97 :rule eq_resolve :premises (@p96 @p95)) % 0.45/0.63 (step @p98 :rule reordering :premises (@p97) :args ((or @t101 @t102 @t105))) % 0.45/0.63 (step @p99 false :rule chain_m_resolution :premises (@p98 @p91 @p88 @p85) :args (false (@list true true true) (@list @t101 @t102 @t105))) % 0.45/0.63 ) % 0.45/0.63 % SZS output end Proof % 0.45/0.63 % cvc5 exiting %------------------------------------------------------------------------------