%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO047^1 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n020.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 09:11:52 AM UTC 2026 % Result : Theorem 0.39s 0.60s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO047^1 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n020.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 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 23:52:55 EDT 2026 % 0.16/0.34 % CPUTime : % 0.30/0.50 %----Proving TH0 % 0.39/0.60 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.60 % SZS status Theorem % 0.39/0.60 % SZS output start Proof % 0.39/0.60 ( % 0.39/0.60 (declare-sort $$unsorted 0) % 0.39/0.60 (declare-sort tptp.mu 0) % 0.39/0.60 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.39/0.60 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.39/0.60 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.39/0.60 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.60 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.39/0.60 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.39/0.60 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.39/0.60 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.39/0.60 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.39/0.60 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.39/0.60 (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.39/0.60 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.39/0.60 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.39/0.60 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.60 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.60 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$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)))))))))) % 0.39/0.60 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.39/0.60 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.39/0.60 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.39/0.60 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.39/0.60 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.39/0.60 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.39/0.60 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.60 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.60 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.60 (define @t2 () (@var "B" (-> $$unsorted Bool))) % 0.39/0.60 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.60 (define @t4 () (_ tptp.mdia @t3)) % 0.39/0.60 (define @t5 () (@var "A" (-> $$unsorted Bool))) % 0.39/0.60 (define @t6 () (_ tptp.mbox @t3)) % 0.39/0.60 (define @t7 () (@list @t2 @t1)) % 0.39/0.60 (define @t8 () (lambda @t7 (_ (_ (_ tptp.mimplies (_ @t6 (_ (_ tptp.mimplies @t5) @t2))) (_ (_ tptp.mimplies (_ @t4 @t5)) (_ @t4 @t2))) @t1))) % 0.39/0.60 (define @t9 () (@list @t5 @t1)) % 0.39/0.60 (define @t10 () (lambda @t9 (_ (_ tptp.mforall_prop @t8) @t1))) % 0.39/0.60 (define @t11 () (@list @t3)) % 0.39/0.60 (define @t12 () (forall @t11 (_ tptp.mvalid (_ tptp.mforall_prop @t10)))) % 0.39/0.60 (define @t13 () (not @t12)) % 0.39/0.60 (define @t14 () (@var "Y" tptp.mu)) % 0.39/0.60 (define @t15 () (@var "X" tptp.mu)) % 0.39/0.60 (define @t16 () (@var "W" $$unsorted)) % 0.39/0.60 (define @t17 () (lambda (@list @t15 @t14 @t16) (= @t15 @t14))) % 0.39/0.60 (define @t18 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.60 (define @t19 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.60 (define @t20 () (lambda (@list @t19 @t18 @t16) (= (_ @t19 @t16) (_ @t18 @t16)))) % 0.39/0.60 (define @t21 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t22 () (_ @t21 @t16)) % 0.39/0.60 (define @t23 () (not @t22)) % 0.39/0.60 (define @t24 () (@list @t21 @t16)) % 0.39/0.60 (define @t25 () (lambda @t24 @t23)) % 0.39/0.60 (define @t26 () (@var "Psi" (-> $$unsorted Bool))) % 0.39/0.60 (define @t27 () (_ @t26 @t16)) % 0.39/0.60 (define @t28 () (lambda (@list @t21 @t26 @t16) (or @t22 @t27))) % 0.39/0.60 (define @t29 () (_ tptp.mnot @t26)) % 0.39/0.60 (define @t30 () (_ tptp.mnot @t21)) % 0.39/0.60 (define @t31 () (_ tptp.mor @t30)) % 0.39/0.60 (define @t32 () (@list @t21 @t26 @t1)) % 0.39/0.60 (define @t33 () (lambda @t32 (_ (_ tptp.mnot (_ @t31 @t29)) @t1))) % 0.39/0.60 (define @t34 () (lambda @t32 (_ (_ @t31 @t26) @t1))) % 0.39/0.60 (define @t35 () (lambda @t32 (_ (_ (_ tptp.mor @t29) @t21) @t1))) % 0.39/0.60 (define @t36 () (lambda @t32 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t21) @t26)) (_ (_ tptp.mimplies @t26) @t21)) @t1))) % 0.39/0.60 (define @t37 () (lambda @t32 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t21) @t26)) @t1))) % 0.39/0.60 (define @t38 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.39/0.60 (define @t39 () (_ @t38 @t15)) % 0.39/0.60 (define @t40 () (lambda (@list @t38 @t16) (forall (@list @t15) (_ @t39 @t16)))) % 0.39/0.60 (define @t41 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.60 (define @t42 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.39/0.60 (define @t43 () (_ @t42 @t41)) % 0.39/0.60 (define @t44 () (_ @t43 @t16)) % 0.39/0.60 (define @t45 () (@list @t41)) % 0.39/0.60 (define @t46 () (forall @t45 @t44)) % 0.39/0.60 (define @t47 () (@list @t42 @t16)) % 0.39/0.60 (define @t48 () (lambda @t47 @t46)) % 0.39/0.60 (define @t49 () (lambda (@list @t38 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t15 @t1) (_ (_ tptp.mnot @t39) @t1)))) @t1))) % 0.39/0.60 (define @t50 () (lambda (@list @t42 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t41 @t1) (_ (_ tptp.mnot @t43) @t1)))) @t1))) % 0.39/0.60 (define @t51 () (@list @t16)) % 0.39/0.60 (define @t52 () (lambda @t51 true)) % 0.39/0.60 (define @t53 () (@var "V" $$unsorted)) % 0.39/0.60 (define @t54 () (_ @t21 @t53)) % 0.39/0.60 (define @t55 () (_ (_ @t3 @t16) @t53)) % 0.39/0.60 (define @t56 () (not @t55)) % 0.39/0.60 (define @t57 () (or @t56 @t54)) % 0.39/0.60 (define @t58 () (@list @t53)) % 0.39/0.60 (define @t59 () (forall @t58 @t57)) % 0.39/0.60 (define @t60 () (@list @t3 @t21 @t16)) % 0.39/0.60 (define @t61 () (lambda @t60 @t59)) % 0.39/0.60 (define @t62 () (@list @t3 @t21 @t1)) % 0.39/0.60 (define @t63 () (lambda @t62 (_ (_ tptp.mnot (_ @t6 @t30)) @t1))) % 0.39/0.60 (define @t64 () (@var "S" $$unsorted)) % 0.39/0.60 (define @t65 () (_ @t3 @t64)) % 0.39/0.60 (define @t66 () (@list @t64)) % 0.39/0.60 (define @t67 () (lambda @t11 (forall @t66 (_ @t65 @t64)))) % 0.39/0.60 (define @t68 () (@var "T" $$unsorted)) % 0.39/0.60 (define @t69 () (_ @t3 @t68)) % 0.39/0.60 (define @t70 () (_ @t65 @t68)) % 0.39/0.60 (define @t71 () (lambda @t11 (forall (@list @t64 @t68) (=> @t70 (_ @t69 @t64))))) % 0.39/0.60 (define @t72 () (@list @t68)) % 0.39/0.60 (define @t73 () (lambda @t11 (forall @t66 (exists @t72 @t70)))) % 0.39/0.60 (define @t74 () (@var "U" $$unsorted)) % 0.39/0.60 (define @t75 () (_ @t65 @t74)) % 0.39/0.60 (define @t76 () (_ @t69 @t74)) % 0.39/0.60 (define @t77 () (@list @t64 @t68 @t74)) % 0.39/0.60 (define @t78 () (lambda @t11 (forall @t77 (=> (and @t70 @t76) @t75)))) % 0.39/0.60 (define @t79 () (and @t70 @t75)) % 0.39/0.60 (define @t80 () (lambda @t11 (forall @t77 (=> @t79 @t76)))) % 0.39/0.60 (define @t81 () (= @t68 @t74)) % 0.39/0.60 (define @t82 () (lambda @t11 (forall @t77 (=> @t79 @t81)))) % 0.39/0.60 (define @t83 () (@list @t74)) % 0.39/0.60 (define @t84 () (lambda @t11 (forall @t66 (exists @t72 (and @t70 (forall @t83 (=> @t75 @t81))))))) % 0.39/0.60 (define @t85 () (_ @t3 @t74)) % 0.39/0.60 (define @t86 () (_ @t85 @t68)) % 0.39/0.60 (define @t87 () (lambda @t11 (forall @t77 (=> @t70 (exists @t83 (and @t75 @t86)))))) % 0.39/0.60 (define @t88 () (lambda @t11 (forall @t77 (=> @t79 (or @t76 @t81 @t86))))) % 0.39/0.60 (define @t89 () (lambda @t11 (forall @t77 (=> @t79 (exists @t58 (and (_ @t69 @t53) (_ @t85 @t53))))))) % 0.39/0.60 (define @t90 () (forall @t51 @t22)) % 0.39/0.60 (define @t91 () (@list @t21)) % 0.39/0.60 (define @t92 () (lambda @t91 @t90)) % 0.39/0.60 (define @t93 () (lambda @t91 (forall @t51 @t23))) % 0.39/0.60 (define @t94 () (lambda @t91 (exists @t51 @t22))) % 0.39/0.60 (define @t95 () (lambda @t91 (exists @t51 @t23))) % 0.39/0.60 (define @t96 () (@var "BOUND_VARIABLE_8501" (-> $$unsorted Bool))) % 0.39/0.60 (define @t97 () (_ @t96 @t53)) % 0.39/0.60 (define @t98 () (_ @t3 @t16 @t53)) % 0.39/0.60 (define @t99 () (not @t98)) % 0.39/0.60 (define @t100 () (not (forall @t58 (or @t99 (not @t97))))) % 0.39/0.60 (define @t101 () (_ @t41 @t53)) % 0.39/0.60 (define @t102 () (not @t101)) % 0.39/0.60 (define @t103 () (not (forall @t58 (or @t99 @t102 @t97)))) % 0.39/0.60 (define @t104 () (@var "BOUND_VARIABLE_8494" $$unsorted)) % 0.39/0.60 (define @t105 () (not (_ @t41 @t104))) % 0.39/0.60 (define @t106 () (not (_ @t3 @t16 @t104))) % 0.39/0.60 (define @t107 () (or @t106 @t105 @t103 @t100)) % 0.39/0.60 (define @t108 () (forall (@list @t3 @t16 @t41 @t104 @t96) @t107)) % 0.39/0.60 (define @t109 () (forall (@list @t16 @t41 @t104 @t96) @t107)) % 0.39/0.60 (define @t110 () (@list @t41 @t104 @t96)) % 0.39/0.60 (define @t111 () (forall @t110 @t107)) % 0.39/0.60 (define @t112 () (lambda @t51 @t111)) % 0.39/0.60 (define @t113 () (_ @t112 @t16)) % 0.39/0.60 (define @t114 () (forall @t51 @t113)) % 0.39/0.60 (define @t115 () (_ @t21 @t16)) % 0.39/0.60 (define @t116 () (lambda @t91 (forall @t51 @t115))) % 0.39/0.60 (define @t117 () (or @t103 @t100)) % 0.39/0.60 (define @t118 () (or @t106 @t105)) % 0.39/0.60 (define @t119 () (or @t118 @t117)) % 0.39/0.60 (define @t120 () (forall @t110 @t119)) % 0.39/0.60 (define @t121 () (forall (@list @t104 @t96) @t119)) % 0.39/0.60 (define @t122 () (forall (@list @t96) @t117)) % 0.39/0.60 (define @t123 () (@var "BOUND_VARIABLE_8468" (-> $$unsorted Bool))) % 0.39/0.60 (define @t124 () (@list @t123)) % 0.39/0.60 (define @t125 () (forall (@list @t104) @t118)) % 0.39/0.60 (define @t126 () (or @t125 @t122)) % 0.39/0.60 (define @t127 () (_ @t123 @t53)) % 0.39/0.60 (define @t128 () (not @t127)) % 0.39/0.60 (define @t129 () (@list @t123)) % 0.39/0.60 (define @t130 () (forall @t58 (or @t99 @t102))) % 0.39/0.60 (define @t131 () (or @t130 (forall @t129 (or (not (forall @t58 (or @t99 @t102 @t127))) (not (forall @t58 (or @t99 @t128))))))) % 0.39/0.60 (define @t132 () (not (_ @t3 @t1 @t53))) % 0.39/0.60 (define @t133 () (_ @t5 @t53)) % 0.39/0.60 (define @t134 () (not @t133)) % 0.39/0.60 (define @t135 () (forall @t58 (or @t132 @t134))) % 0.39/0.60 (define @t136 () (forall @t45 (or (not (forall @t58 (or @t132 @t134 @t101))) (not (forall @t58 (or @t132 @t102)))))) % 0.39/0.60 (define @t137 () (or @t135 @t136)) % 0.39/0.60 (define @t138 () (lambda @t9 @t137)) % 0.39/0.60 (define @t139 () (forall @t45 (_ @t138 @t41 @t16))) % 0.39/0.60 (define @t140 () (lambda @t51 @t139)) % 0.39/0.60 (define @t141 () (_ @t42 @t41 @t16)) % 0.39/0.60 (define @t142 () (lambda @t47 (forall @t45 @t141))) % 0.39/0.60 (define @t143 () (not @t130)) % 0.39/0.60 (define @t144 () (not (forall @t58 (or @t99 @t134 @t101)))) % 0.39/0.60 (define @t145 () (or @t144 @t143)) % 0.39/0.60 (define @t146 () (forall @t58 (or @t99 @t134))) % 0.39/0.60 (define @t147 () (or @t146 (forall @t45 @t145))) % 0.39/0.60 (define @t148 () (or @t146 @t145)) % 0.39/0.60 (define @t149 () (or @t144 @t146 @t143)) % 0.39/0.60 (define @t150 () (_ @t2 @t53)) % 0.39/0.60 (define @t151 () (not (forall @t58 (or @t132 (not @t150))))) % 0.39/0.60 (define @t152 () (forall @t58 (or @t132 @t134 @t150))) % 0.39/0.60 (define @t153 () (not @t152)) % 0.39/0.60 (define @t154 () (or @t153 @t135 @t151)) % 0.39/0.60 (define @t155 () (lambda @t7 @t154)) % 0.39/0.60 (define @t156 () (_ @t155 @t41 @t16)) % 0.39/0.60 (define @t157 () (forall @t45 @t156)) % 0.39/0.60 (define @t158 () (lambda @t51 @t157)) % 0.39/0.60 (define @t159 () (@list @t1)) % 0.39/0.60 (define @t160 () (or @t135 @t151)) % 0.39/0.60 (define @t161 () (lambda @t159 @t160)) % 0.39/0.60 (define @t162 () (_ @t161 @t1)) % 0.39/0.60 (define @t163 () (or @t153 @t162)) % 0.39/0.60 (define @t164 () (lambda @t159 @t163)) % 0.39/0.60 (define @t165 () (_ @t26 @t1)) % 0.39/0.60 (define @t166 () (@list @t26 @t1)) % 0.39/0.60 (define @t167 () (lambda @t159 @t151)) % 0.39/0.60 (define @t168 () (_ @t167 @t1)) % 0.39/0.60 (define @t169 () (or @t135 @t168)) % 0.39/0.60 (define @t170 () (lambda @t159 @t169)) % 0.39/0.60 (define @t171 () (_ @t21 @t53)) % 0.39/0.60 (define @t172 () (not @t171)) % 0.39/0.60 (define @t173 () (not (forall @t58 (or @t132 @t172)))) % 0.39/0.60 (define @t174 () (lambda (@list @t21 @t1) @t173)) % 0.39/0.60 (define @t175 () (_ (lambda @t62 @t173) @t3)) % 0.39/0.60 (define @t176 () (not @t135)) % 0.39/0.60 (define @t177 () (lambda @t159 @t176)) % 0.39/0.60 (define @t178 () (_ @t177 @t1)) % 0.39/0.60 (define @t179 () (not @t178)) % 0.39/0.60 (define @t180 () (or @t179 @t165)) % 0.39/0.60 (define @t181 () (lambda @t166 @t180)) % 0.39/0.60 (define @t182 () (or (not (_ @t21 @t1)) @t165)) % 0.39/0.60 (define @t183 () (lambda @t32 @t182)) % 0.39/0.60 (define @t184 () (lambda @t51 (forall @t58 (or @t99 @t134 @t150)))) % 0.39/0.60 (define @t185 () (_ @t184 @t1)) % 0.39/0.60 (define @t186 () (not @t185)) % 0.39/0.60 (define @t187 () (or @t186 @t165)) % 0.39/0.60 (define @t188 () (lambda @t166 @t187)) % 0.39/0.60 (define @t189 () (_ @t2 @t53)) % 0.39/0.60 (define @t190 () (_ @t5 @t53)) % 0.39/0.60 (define @t191 () (not @t190)) % 0.39/0.60 (define @t192 () (or @t99 @t191 @t189)) % 0.39/0.60 (define @t193 () (or @t191 @t189)) % 0.39/0.60 (define @t194 () (not (_ @t5 @t1))) % 0.39/0.60 (define @t195 () (lambda @t159 (or @t194 (_ @t2 @t1)))) % 0.39/0.60 (define @t196 () (_ @t195 @t53)) % 0.39/0.60 (define @t197 () (or @t99 @t196)) % 0.39/0.60 (define @t198 () (forall @t58 @t197)) % 0.39/0.60 (define @t199 () (lambda @t51 @t198)) % 0.39/0.60 (define @t200 () (forall @t58 (or @t99 @t171))) % 0.39/0.60 (define @t201 () (lambda @t24 @t200)) % 0.39/0.60 (define @t202 () (lambda @t166 (or @t194 @t165))) % 0.39/0.60 (define @t203 () (_ @t183 @t5)) % 0.39/0.60 (define @t204 () (_ (lambda @t60 @t200) @t3)) % 0.39/0.60 (define @t205 () (lambda @t7 (_ (_ (_ @t183 (_ @t204 (_ @t203 @t2))) (_ (_ @t183 (_ @t175 @t5)) (_ @t175 @t2))) @t1))) % 0.39/0.60 (define @t206 () (lambda @t9 (_ (_ @t142 @t205) @t1))) % 0.39/0.60 (define @t207 () (forall @t11 (_ @t116 (_ @t142 @t206)))) % 0.39/0.60 (define @t208 () (forall @t58 (or @t99 @t172))) % 0.39/0.60 (define @t209 () (lambda @t51 @t208)) % 0.39/0.60 (define @t210 () (_ @t209 @t16)) % 0.39/0.60 (define @t211 () (not @t210)) % 0.39/0.60 (define @t212 () (lambda @t51 @t211)) % 0.39/0.60 (define @t213 () (not @t54)) % 0.39/0.60 (define @t214 () (or @t99 @t213)) % 0.39/0.60 (define @t215 () (lambda @t51 @t23)) % 0.39/0.60 (define @t216 () (_ @t215 @t53)) % 0.39/0.60 (define @t217 () (or @t99 @t216)) % 0.39/0.60 (define @t218 () (forall @t58 @t217)) % 0.39/0.60 (define @t219 () (lambda @t51 @t218)) % 0.39/0.60 (define @t220 () (or @t23 @t27)) % 0.39/0.60 (define @t221 () (lambda @t51 @t220)) % 0.39/0.60 (define @t222 () (@list @t26 @t16)) % 0.39/0.60 (define @t223 () (_ @t215 @t16)) % 0.39/0.60 (define @t224 () (or @t223 @t27)) % 0.39/0.60 (define @t225 () (lambda @t222 @t224)) % 0.39/0.60 (define @t226 () (@quantifiers_skolemize @t108 3)) % 0.39/0.60 (define @t227 () (@quantifiers_skolemize @t108 1)) % 0.39/0.60 (define @t228 () (@quantifiers_skolemize @t108 0)) % 0.39/0.60 (define @t229 () (_ @t228 @t227 @t226)) % 0.39/0.60 (define @t230 () (@quantifiers_skolemize @t108 4)) % 0.39/0.60 (define @t231 () (_ @t230 @t53)) % 0.39/0.60 (define @t232 () (not (_ @t228 @t227 @t53))) % 0.39/0.60 (define @t233 () (forall @t58 (or @t232 (not @t231)))) % 0.39/0.60 (define @t234 () (not @t233)) % 0.39/0.60 (define @t235 () (@quantifiers_skolemize @t108 2)) % 0.39/0.60 (define @t236 () (forall @t58 (or @t232 (not (_ @t235 @t53)) @t231))) % 0.39/0.60 (define @t237 () (not @t236)) % 0.39/0.60 (define @t238 () (_ @t235 @t226)) % 0.39/0.60 (define @t239 () (not @t238)) % 0.39/0.60 (define @t240 () (not @t229)) % 0.39/0.60 (define @t241 () (or @t240 @t239 @t237 @t234)) % 0.39/0.60 (define @t242 () (@list true)) % 0.39/0.60 (define @t243 () (@list @t241)) % 0.39/0.60 (define @t244 () (@list @t226)) % 0.39/0.60 (define @t245 () (_ @t230 @t226)) % 0.39/0.60 (define @t246 () (or @t240 @t239 @t245)) % 0.39/0.60 (define @t247 () (@list false false false)) % 0.39/0.60 (define @t248 () (not @t245)) % 0.39/0.60 (define @t249 () (or @t240 @t248)) % 0.39/0.60 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.39/0.60 (assume @p2 @t13) % 0.39/0.60 (assume @p3 true) % 0.39/0.60 (step @p4 (= tptp.meq_ind @t17) :rule refl :args (@t17)) % 0.39/0.60 (step @p5 (= tptp.meq_prop @t20) :rule refl :args (@t20)) % 0.39/0.60 (step @p6 (= tptp.mnot @t25) :rule refl :args (@t25)) % 0.39/0.60 (step @p7 (= tptp.mor @t28) :rule refl :args (@t28)) % 0.39/0.60 (step @p8 (= tptp.mand @t33) :rule refl :args (@t33)) % 0.39/0.60 (step @p9 (= tptp.mimplies @t34) :rule refl :args (@t34)) % 0.39/0.60 (step @p10 (= tptp.mimplied @t35) :rule refl :args (@t35)) % 0.39/0.60 (step @p11 (= tptp.mequiv @t36) :rule refl :args (@t36)) % 0.39/0.60 (step @p12 (= tptp.mxor @t37) :rule refl :args (@t37)) % 0.39/0.60 (step @p13 (= tptp.mforall_ind @t40) :rule refl :args (@t40)) % 0.39/0.60 (step @p14 (= tptp.mforall_prop @t48) :rule refl :args (@t48)) % 0.39/0.60 (step @p15 (= tptp.mexists_ind @t49) :rule refl :args (@t49)) % 0.39/0.60 (step @p16 (= tptp.mexists_prop @t50) :rule refl :args (@t50)) % 0.39/0.60 (step @p17 (= tptp.mtrue @t52) :rule refl :args (@t52)) % 0.39/0.60 (step @p18 (= tptp.mbox @t61) :rule refl :args (@t61)) % 0.39/0.60 (step @p19 (= tptp.mdia @t63) :rule refl :args (@t63)) % 0.39/0.60 (step @p20 (= tptp.mreflexive @t67) :rule refl :args (@t67)) % 0.39/0.60 (step @p21 (= tptp.msymmetric @t71) :rule refl :args (@t71)) % 0.39/0.60 (step @p22 (= tptp.mserial @t73) :rule refl :args (@t73)) % 0.39/0.60 (step @p23 (= tptp.mtransitive @t78) :rule refl :args (@t78)) % 0.39/0.60 (step @p24 (= tptp.meuclidean @t80) :rule refl :args (@t80)) % 0.39/0.60 (step @p25 (= tptp.mpartially_functional @t82) :rule refl :args (@t82)) % 0.39/0.60 (step @p26 (= tptp.mfunctional @t84) :rule refl :args (@t84)) % 0.39/0.60 (step @p27 (= tptp.mweakly_dense @t87) :rule refl :args (@t87)) % 0.39/0.60 (step @p28 (= tptp.mweakly_connected @t88) :rule refl :args (@t88)) % 0.39/0.60 (step @p29 (= tptp.mweakly_directed @t89) :rule refl :args (@t89)) % 0.39/0.60 (step @p30 (= tptp.mvalid @t92) :rule refl :args (@t92)) % 0.39/0.60 (step @p31 (= tptp.minvalid @t93) :rule refl :args (@t93)) % 0.39/0.60 (step @p32 (= tptp.msatisfiable @t94) :rule refl :args (@t94)) % 0.39/0.60 (step @p33 (= tptp.mcountersatisfiable @t95) :rule refl :args (@t95)) % 0.39/0.60 (step @p34 :rule quant-merge-prenex :args ((= (forall @t11 @t109) @t108))) % 0.39/0.60 (step @p35 :rule quant-merge-prenex :args ((= (forall @t51 @t111) @t109))) % 0.39/0.60 (step @p36 :rule beta-reduce :args ((= @t113 @t111))) % 0.39/0.60 (step @p37 :rule cong :premises (@p36) :args (@t114)) % 0.39/0.60 (step @p38 :rule trans :premises (@p37 @p35)) % 0.39/0.60 (step @p39 :rule beta-reduce :args ((= (_ @t116 @t112) @t114))) % 0.39/0.60 (step @p40 :rule trans :premises (@p39 @p38)) % 0.39/0.60 (step @p41 :rule aci_norm :args ((= @t119 @t107))) % 0.39/0.60 (step @p42 :rule cong :premises (@p41) :args (@t120)) % 0.39/0.60 (step @p43 :rule quant-merge-prenex :args ((= (forall @t45 @t121) @t120))) % 0.39/0.60 (step @p44 :rule alpha_equiv :args (@t122 (@list @t96) @t124)) % 0.39/0.60 (step @p45 :rule alpha_equiv :args (@t125 (@list @t104) (@list @t53))) % 0.39/0.60 (step @p46 :rule nary_cong :premises (@p45 @p44) :args (@t126)) % 0.39/0.60 (step @p47 :rule quant-miniscope-or :args ((= @t121 @t126))) % 0.39/0.60 (step @p48 :rule trans :premises (@p47 @p46)) % 0.39/0.60 (step @p49 :rule symm :premises (@p48)) % 0.39/0.60 (step @p50 :rule cong :premises (@p49) :args ((forall @t45 @t131))) % 0.39/0.60 (step @p51 :rule trans :premises (@p50 @p43)) % 0.39/0.60 (step @p52 :rule trans :premises (@p51 @p42)) % 0.39/0.60 (step @p53 :rule beta-reduce :args ((= (_ (lambda @t9 (or @t135 (forall @t129 (or (not (forall @t58 (or @t132 @t134 @t127))) (not (forall @t58 (or @t132 @t128))))))) @t41 @t16) @t131))) % 0.39/0.60 (step @p54 :rule refl :args (@t16)) % 0.39/0.60 (step @p55 :rule refl :args (@t41)) % 0.39/0.60 (step @p56 :rule alpha_equiv :args (@t136 (@list @t41) @t124)) % 0.39/0.60 (step @p57 :rule refl :args (@t135)) % 0.39/0.60 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t137)) % 0.39/0.60 (step @p59 :rule cong :premises (@p58) :args (@t138)) % 0.39/0.60 (step @p60 :rule ho_cong :premises (@p59 @p55 @p54)) % 0.39/0.60 (step @p61 :rule trans :premises (@p60 @p53)) % 0.39/0.60 (step @p62 :rule cong :premises (@p61) :args (@t139)) % 0.39/0.60 (step @p63 :rule trans :premises (@p62 @p52)) % 0.39/0.60 (step @p64 :rule cong :premises (@p63) :args (@t140)) % 0.39/0.60 (step @p65 :rule beta-reduce :args ((= (_ @t142 @t138) @t140))) % 0.39/0.60 (step @p66 :rule trans :premises (@p65 @p64)) % 0.39/0.60 (step @p67 :rule beta-reduce :args ((= (_ (lambda @t51 @t147) @t1) @t137))) % 0.39/0.60 (step @p68 :rule refl :args (@t1)) % 0.39/0.60 (step @p69 :rule quant-miniscope-or :args ((= (forall @t45 @t148) @t147))) % 0.39/0.60 (step @p70 :rule aci_norm :args ((= @t149 @t148))) % 0.39/0.60 (step @p71 :rule cong :premises (@p70) :args ((forall @t45 @t149))) % 0.39/0.60 (step @p72 :rule trans :premises (@p71 @p69)) % 0.39/0.60 (step @p73 :rule beta-reduce :args ((= @t156 @t149))) % 0.39/0.60 (step @p74 :rule cong :premises (@p73) :args (@t157)) % 0.39/0.60 (step @p75 :rule trans :premises (@p74 @p72)) % 0.39/0.60 (step @p76 :rule cong :premises (@p75) :args (@t158)) % 0.39/0.60 (step @p77 :rule beta-reduce :args ((= (_ @t142 @t155) @t158))) % 0.39/0.60 (step @p78 :rule trans :premises (@p77 @p76)) % 0.39/0.60 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t159 @t154) @t1) @t154))) % 0.39/0.60 (step @p80 :rule aci_norm :args ((= (or @t153 @t160) @t154))) % 0.39/0.60 (step @p81 :rule beta-reduce :args ((= @t162 @t160))) % 0.39/0.60 (step @p82 :rule refl :args (@t153)) % 0.39/0.60 (step @p83 :rule nary_cong :premises (@p82 @p81) :args (@t163)) % 0.39/0.60 (step @p84 :rule trans :premises (@p83 @p80)) % 0.39/0.60 (step @p85 :rule cong :premises (@p84) :args (@t164)) % 0.39/0.60 (step @p86 :rule beta-reduce :args ((= (_ (lambda @t166 (or @t153 @t165)) @t161) @t164))) % 0.39/0.60 (step @p87 :rule trans :premises (@p86 @p85)) % 0.39/0.60 (step @p88 :rule beta-reduce :args ((= @t168 @t151))) % 0.39/0.60 (step @p89 :rule refl :args (@t135)) % 0.39/0.60 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t169)) % 0.39/0.60 (step @p91 :rule cong :premises (@p90) :args (@t170)) % 0.39/0.60 (step @p92 :rule beta-reduce :args ((= (_ (lambda @t166 (or @t135 @t165)) @t167) @t170))) % 0.39/0.60 (step @p93 :rule trans :premises (@p92 @p91)) % 0.39/0.60 (step @p94 :rule beta-reduce :args ((= (_ @t174 @t2) @t167))) % 0.39/0.60 (step @p95 :rule refl :args (@t2)) % 0.39/0.60 (step @p96 :rule beta-reduce :args ((= @t175 @t174))) % 0.39/0.60 (step @p97 :rule ho_cong :premises (@p96 @p95)) % 0.39/0.60 (step @p98 :rule trans :premises (@p97 @p94)) % 0.39/0.60 (step @p99 :rule refl :args (@t165)) % 0.39/0.60 (step @p100 :rule bool-double-not-elim :args (@t135)) % 0.39/0.60 (step @p101 :rule beta-reduce :args ((= @t178 @t176))) % 0.39/0.60 (step @p102 :rule cong :premises (@p101) :args (@t179)) % 0.39/0.60 (step @p103 :rule trans :premises (@p102 @p100)) % 0.39/0.60 (step @p104 :rule nary_cong :premises (@p103 @p99) :args (@t180)) % 0.39/0.60 (step @p105 :rule cong :premises (@p104) :args (@t181)) % 0.39/0.60 (step @p106 :rule beta-reduce :args ((= (_ @t183 @t177) @t181))) % 0.39/0.60 (step @p107 :rule trans :premises (@p106 @p105)) % 0.39/0.60 (step @p108 :rule beta-reduce :args ((= (_ @t174 @t5) @t177))) % 0.39/0.60 (step @p109 :rule refl :args (@t5)) % 0.39/0.60 (step @p110 :rule ho_cong :premises (@p96 @p109)) % 0.39/0.60 (step @p111 :rule trans :premises (@p110 @p108)) % 0.39/0.60 (step @p112 :rule refl :args (@t183)) % 0.39/0.60 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.39/0.60 (step @p114 :rule trans :premises (@p113 @p107)) % 0.39/0.60 (step @p115 :rule ho_cong :premises (@p114 @p98)) % 0.39/0.60 (step @p116 :rule trans :premises (@p115 @p93)) % 0.39/0.60 (step @p117 :rule beta-reduce :args ((= @t185 @t152))) % 0.39/0.60 (step @p118 :rule cong :premises 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@p314 :rule cnf_or_pos :args (@t249)) % 0.39/0.61 (step @p315 :rule reordering :premises (@p314) :args ((or @t240 @t248 (not @t249)))) % 0.39/0.61 (step @p316 false :rule chain_m_resolution :premises (@p315 @p313 @p297 @p290) :args (false @t247 (@list @t245 @t249 @t229))) % 0.39/0.61 ) % 0.39/0.61 % SZS output end Proof % 0.39/0.61 % cvc5 exiting %------------------------------------------------------------------------------