%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO053^2 : TPTP v9.2.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 09:11:53 AM UTC 2026 % Result : Theorem 0.39s 0.62s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SYO053^2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n028.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % 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 23:52:50 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.39/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.39/0.62 % SZS status Theorem % 0.39/0.62 % SZS output start Proof % 0.39/0.62 ( % 0.39/0.62 (declare-sort $$unsorted 0) % 0.39/0.62 (declare-sort tptp.mu 0) % 0.39/0.62 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.39/0.62 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.39/0.62 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.39/0.62 (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)))))) % 0.39/0.62 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.39/0.62 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.62 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.39/0.62 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.62 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.39/0.62 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.39/0.62 (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))))))) % 0.39/0.62 (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))))))) % 0.39/0.62 (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)))))) % 0.39/0.62 (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)))))) % 0.39/0.62 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.39/0.62 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.39/0.62 (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)))))) % 0.39/0.62 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.39/0.62 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.62 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.39/0.62 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.39/0.62 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.39/0.62 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.39/0.62 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.39/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.39/0.62 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.39/0.62 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.62 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.62 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.39/0.62 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.39/0.62 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.39/0.62 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mdia @t1) tptp.mtrue)))) % 0.39/0.62 (define @t3 () (@list @t1)) % 0.39/0.62 (define @t4 () (exists @t3 @t2)) % 0.39/0.62 (define @t5 () (not @t4)) % 0.39/0.62 (define @t6 () (@var "Y" tptp.mu)) % 0.39/0.62 (define @t7 () (@var "X" tptp.mu)) % 0.39/0.62 (define @t8 () (@var "W" $$unsorted)) % 0.39/0.62 (define @t9 () (lambda (@list @t7 @t6 @t8) (= @t7 @t6))) % 0.39/0.62 (define @t10 () (@var "Y" (-> $$unsorted Bool))) % 0.39/0.62 (define @t11 () (@var "X" (-> $$unsorted Bool))) % 0.39/0.62 (define @t12 () (lambda (@list @t11 @t10 @t8) (= (_ @t11 @t8) (_ @t10 @t8)))) % 0.39/0.62 (define @t13 () (@var "Phi" (-> $$unsorted Bool))) % 0.39/0.62 (define @t14 () (_ @t13 @t8)) % 0.39/0.62 (define @t15 () (not @t14)) % 0.39/0.62 (define @t16 () (@list @t13 @t8)) % 0.39/0.62 (define @t17 () (lambda @t16 @t15)) % 0.39/0.62 (define @t18 () (@var "Psi" (-> $$unsorted Bool))) % 0.39/0.62 (define @t19 () (lambda (@list @t13 @t18 @t8) (or @t14 (_ @t18 @t8)))) % 0.39/0.62 (define @t20 () (@var "__flatten_var_0" $$unsorted)) % 0.39/0.62 (define @t21 () (_ tptp.mnot @t18)) % 0.39/0.62 (define @t22 () (_ tptp.mnot @t13)) % 0.39/0.62 (define @t23 () (_ tptp.mor @t22)) % 0.39/0.62 (define @t24 () (@list @t13 @t18 @t20)) % 0.39/0.62 (define @t25 () (lambda @t24 (_ (_ tptp.mnot (_ @t23 @t21)) @t20))) % 0.39/0.62 (define @t26 () (lambda @t24 (_ (_ @t23 @t18) @t20))) % 0.39/0.62 (define @t27 () (lambda @t24 (_ (_ (_ tptp.mor @t21) @t13) @t20))) % 0.39/0.62 (define @t28 () (lambda @t24 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t13) @t18)) (_ (_ tptp.mimplies @t18) @t13)) @t20))) % 0.39/0.62 (define @t29 () (lambda @t24 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t13) @t18)) @t20))) % 0.39/0.62 (define @t30 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.39/0.62 (define @t31 () (_ @t30 @t7)) % 0.39/0.62 (define @t32 () (lambda (@list @t30 @t8) (forall (@list @t7) (_ @t31 @t8)))) % 0.39/0.62 (define @t33 () (@var "P" (-> $$unsorted Bool))) % 0.39/0.62 (define @t34 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.39/0.62 (define @t35 () (_ @t34 @t33)) % 0.39/0.62 (define @t36 () (lambda (@list @t34 @t8) (forall (@list @t33) (_ @t35 @t8)))) % 0.39/0.62 (define @t37 () (lambda (@list @t30 @t20) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t7 @t20) (_ (_ tptp.mnot @t31) @t20)))) @t20))) % 0.39/0.62 (define @t38 () (lambda (@list @t34 @t20) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t33 @t20) (_ (_ tptp.mnot @t35) @t20)))) @t20))) % 0.39/0.62 (define @t39 () (@list @t8)) % 0.39/0.62 (define @t40 () (lambda @t39 true)) % 0.39/0.62 (define @t41 () (@var "V" $$unsorted)) % 0.39/0.62 (define @t42 () (_ @t13 @t41)) % 0.39/0.62 (define @t43 () (_ (_ @t1 @t8) @t41)) % 0.39/0.62 (define @t44 () (not @t43)) % 0.39/0.62 (define @t45 () (or @t44 @t42)) % 0.39/0.62 (define @t46 () (@list @t41)) % 0.39/0.62 (define @t47 () (forall @t46 @t45)) % 0.39/0.62 (define @t48 () (@list @t1 @t13 @t8)) % 0.39/0.62 (define @t49 () (lambda @t48 @t47)) % 0.39/0.62 (define @t50 () (@list @t1 @t13 @t20)) % 0.39/0.62 (define @t51 () (lambda @t50 (_ (_ tptp.mnot (_ (_ tptp.mbox @t1) @t22)) @t20))) % 0.39/0.62 (define @t52 () (@var "S" $$unsorted)) % 0.39/0.62 (define @t53 () (_ @t1 @t52)) % 0.39/0.62 (define @t54 () (@list @t52)) % 0.39/0.62 (define @t55 () (lambda @t3 (forall @t54 (_ @t53 @t52)))) % 0.39/0.62 (define @t56 () (@var "T" $$unsorted)) % 0.39/0.62 (define @t57 () (_ @t1 @t56)) % 0.39/0.62 (define @t58 () (_ @t53 @t56)) % 0.39/0.62 (define @t59 () (lambda @t3 (forall (@list @t52 @t56) (=> @t58 (_ @t57 @t52))))) % 0.39/0.62 (define @t60 () (@list @t56)) % 0.39/0.62 (define @t61 () (lambda @t3 (forall @t54 (exists @t60 @t58)))) % 0.39/0.62 (define @t62 () (@var "U" $$unsorted)) % 0.39/0.62 (define @t63 () (_ @t53 @t62)) % 0.39/0.62 (define @t64 () (_ @t57 @t62)) % 0.39/0.62 (define @t65 () (@list @t52 @t56 @t62)) % 0.39/0.62 (define @t66 () (lambda @t3 (forall @t65 (=> (and @t58 @t64) @t63)))) % 0.39/0.62 (define @t67 () (and @t58 @t63)) % 0.39/0.62 (define @t68 () (lambda @t3 (forall @t65 (=> @t67 @t64)))) % 0.39/0.62 (define @t69 () (= @t56 @t62)) % 0.39/0.62 (define @t70 () (lambda @t3 (forall @t65 (=> @t67 @t69)))) % 0.39/0.62 (define @t71 () (@list @t62)) % 0.39/0.62 (define @t72 () (lambda @t3 (forall @t54 (exists @t60 (and @t58 (forall @t71 (=> @t63 @t69))))))) % 0.39/0.62 (define @t73 () (_ @t1 @t62)) % 0.39/0.62 (define @t74 () (_ @t73 @t56)) % 0.39/0.62 (define @t75 () (lambda @t3 (forall @t65 (=> @t58 (exists @t71 (and @t63 @t74)))))) % 0.39/0.62 (define @t76 () (lambda @t3 (forall @t65 (=> @t67 (or @t64 @t69 @t74))))) % 0.39/0.62 (define @t77 () (lambda @t3 (forall @t65 (=> @t67 (exists @t46 (and (_ @t57 @t41) (_ @t73 @t41))))))) % 0.39/0.62 (define @t78 () (forall @t39 @t14)) % 0.39/0.62 (define @t79 () (@list @t13)) % 0.39/0.62 (define @t80 () (lambda @t79 @t78)) % 0.39/0.62 (define @t81 () (lambda @t79 (forall @t39 @t15))) % 0.39/0.62 (define @t82 () (lambda @t79 (exists @t39 @t14))) % 0.39/0.62 (define @t83 () (lambda @t79 (exists @t39 @t15))) % 0.39/0.62 (define @t84 () (_ @t1 @t8 @t41)) % 0.39/0.62 (define @t85 () (not @t84)) % 0.39/0.62 (define @t86 () (not (forall @t46 @t85))) % 0.39/0.62 (define @t87 () (forall (@list @t1 @t8) @t86)) % 0.39/0.62 (define @t88 () (forall @t39 @t86)) % 0.39/0.62 (define @t89 () (not @t88)) % 0.39/0.62 (define @t90 () (forall @t3 (not @t89))) % 0.39/0.62 (define @t91 () (not @t90)) % 0.39/0.62 (define @t92 () (not (_ @t1 @t20 @t41))) % 0.39/0.62 (define @t93 () (@list @t20)) % 0.39/0.62 (define @t94 () (lambda @t93 (not (forall @t46 @t92)))) % 0.39/0.62 (define @t95 () (_ @t94 @t8)) % 0.39/0.62 (define @t96 () (forall @t39 @t95)) % 0.39/0.62 (define @t97 () (_ @t13 @t8)) % 0.39/0.62 (define @t98 () (lambda @t79 (forall @t39 @t97))) % 0.39/0.62 (define @t99 () (@var "BOUND_VARIABLE_8278" $$unsorted)) % 0.39/0.62 (define @t100 () (lambda (@list @t99) true)) % 0.39/0.62 (define @t101 () (_ @t100 @t41)) % 0.39/0.62 (define @t102 () (not @t101)) % 0.39/0.62 (define @t103 () (or @t92 @t102)) % 0.39/0.62 (define @t104 () (forall @t46 @t103)) % 0.39/0.62 (define @t105 () (not @t104)) % 0.39/0.62 (define @t106 () (lambda @t93 @t105)) % 0.39/0.62 (define @t107 () (_ @t13 @t41)) % 0.39/0.62 (define @t108 () (not @t107)) % 0.39/0.62 (define @t109 () (not (forall @t46 (or @t92 @t108)))) % 0.39/0.62 (define @t110 () (lambda (@list @t13 @t20) @t109)) % 0.39/0.62 (define @t111 () (_ (lambda @t50 @t109) @t1)) % 0.39/0.62 (define @t112 () (not (_ @t98 (_ @t111 @t40)))) % 0.39/0.62 (define @t113 () (exists @t3 @t112)) % 0.39/0.62 (define @t114 () (forall @t46 (or @t85 @t108))) % 0.39/0.62 (define @t115 () (lambda @t39 @t114)) % 0.39/0.62 (define @t116 () (_ @t115 @t8)) % 0.39/0.62 (define @t117 () (not @t116)) % 0.39/0.62 (define @t118 () (lambda @t39 @t117)) % 0.39/0.62 (define @t119 () (not @t42)) % 0.39/0.62 (define @t120 () (or @t85 @t119)) % 0.39/0.62 (define @t121 () (lambda @t39 @t15)) % 0.39/0.62 (define @t122 () (_ @t121 @t41)) % 0.39/0.62 (define @t123 () (or @t85 @t122)) % 0.39/0.62 (define @t124 () (forall @t46 @t123)) % 0.39/0.62 (define @t125 () (lambda @t39 @t124)) % 0.39/0.62 (define @t126 () (forall @t46 (or @t85 @t107))) % 0.39/0.62 (define @t127 () (lambda @t16 @t126)) % 0.39/0.62 (define @t128 () (@purify (as @$$unsorted_0 $$unsorted))) % 0.39/0.62 (define @t129 () (lambda (@list (@var "BOUND_VARIABLE_15398" $$unsorted) (@var "BOUND_VARIABLE_15399" $$unsorted)) false)) % 0.39/0.62 (define @t130 () (_ @t129 @t128 @t41)) % 0.39/0.62 (define @t131 () (not @t130)) % 0.39/0.62 (define @t132 () (forall @t46 @t131)) % 0.39/0.62 (define @t133 () (not @t132)) % 0.39/0.62 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.39/0.62 (assume @p2 @t5) % 0.39/0.62 (assume @p3 true) % 0.39/0.62 (step @p4 (= tptp.meq_ind @t9) :rule refl :args (@t9)) % 0.39/0.62 (step @p5 (= tptp.meq_prop @t12) :rule refl :args (@t12)) % 0.39/0.62 (step @p6 (= tptp.mnot @t17) :rule refl :args (@t17)) % 0.39/0.62 (step @p7 (= tptp.mor @t19) :rule refl :args (@t19)) % 0.39/0.62 (step @p8 (= tptp.mand @t25) :rule refl :args (@t25)) % 0.39/0.62 (step @p9 (= tptp.mimplies @t26) :rule refl :args (@t26)) % 0.39/0.62 (step @p10 (= tptp.mimplied @t27) :rule refl :args (@t27)) % 0.39/0.62 (step @p11 (= tptp.mequiv @t28) :rule refl :args (@t28)) % 0.39/0.62 (step @p12 (= tptp.mxor @t29) :rule refl :args (@t29)) % 0.39/0.62 (step @p13 (= tptp.mforall_ind @t32) :rule refl :args (@t32)) % 0.39/0.62 (step @p14 (= tptp.mforall_prop @t36) :rule refl :args (@t36)) % 0.39/0.62 (step @p15 (= tptp.mexists_ind @t37) :rule refl :args (@t37)) % 0.39/0.62 (step @p16 (= tptp.mexists_prop @t38) :rule refl :args (@t38)) % 0.39/0.62 (step @p17 (= tptp.mtrue @t40) :rule refl :args (@t40)) % 0.39/0.62 (step @p18 (= tptp.mbox @t49) :rule refl :args (@t49)) % 0.39/0.62 (step @p19 (= tptp.mdia @t51) :rule refl :args (@t51)) % 0.39/0.62 (step @p20 (= tptp.mreflexive @t55) :rule refl :args (@t55)) % 0.39/0.62 (step @p21 (= tptp.msymmetric @t59) :rule refl :args (@t59)) % 0.39/0.62 (step @p22 (= tptp.mserial @t61) :rule refl :args (@t61)) % 0.39/0.62 (step @p23 (= tptp.mtransitive @t66) :rule refl :args (@t66)) % 0.39/0.62 (step @p24 (= tptp.meuclidean @t68) :rule refl :args (@t68)) % 0.39/0.62 (step @p25 (= tptp.mpartially_functional @t70) :rule refl :args (@t70)) % 0.39/0.62 (step @p26 (= tptp.mfunctional @t72) :rule refl :args (@t72)) % 0.39/0.62 (step @p27 (= tptp.mweakly_dense @t75) :rule refl :args (@t75)) % 0.39/0.62 (step @p28 (= tptp.mweakly_connected @t76) :rule refl :args (@t76)) % 0.39/0.62 (step @p29 (= tptp.mweakly_directed @t77) :rule refl :args (@t77)) % 0.39/0.62 (step @p30 (= tptp.mvalid @t80) :rule refl :args (@t80)) % 0.39/0.62 (step @p31 (= tptp.minvalid @t81) :rule refl :args (@t81)) % 0.39/0.62 (step @p32 (= tptp.msatisfiable @t82) :rule refl :args (@t82)) % 0.39/0.62 (step @p33 (= tptp.mcountersatisfiable @t83) :rule refl :args (@t83)) % 0.39/0.62 (step @p34 :rule bool-double-not-elim :args (@t87)) % 0.39/0.62 (step @p35 :rule quant-merge-prenex :args ((= (forall @t3 @t88) @t87))) % 0.39/0.62 (step @p36 :rule bool-double-not-elim :args (@t88)) % 0.39/0.62 (step @p37 :rule cong :premises (@p36) :args (@t90)) % 0.39/0.62 (step @p38 :rule trans :premises (@p37 @p35)) % 0.39/0.62 (step @p39 :rule cong :premises (@p38) :args (@t91)) % 0.39/0.62 (step @p40 :rule exists-elim :args ((= (exists @t3 @t89) @t91))) % 0.39/0.62 (step @p41 :rule trans :premises (@p40 @p39)) % 0.39/0.62 (step @p42 :rule beta-reduce :args ((= @t95 @t86))) % 0.39/0.62 (step @p43 :rule cong :premises (@p42) :args (@t96)) % 0.39/0.62 (step @p44 :rule beta-reduce :args ((= (_ @t98 @t94) @t96))) % 0.39/0.62 (step @p45 :rule trans :premises (@p44 @p43)) % 0.39/0.62 (step @p46 :rule aci_norm :args ((= (or @t92 false) @t92))) % 0.39/0.62 (step @p47 :rule evaluate :args ((not true))) % 0.39/0.62 (step @p48 :rule beta-reduce :args ((= @t101 true))) % 0.39/0.62 (step @p49 :rule cong :premises (@p48) :args (@t102)) % 0.39/0.62 (step @p50 :rule trans :premises (@p49 @p47)) % 0.39/0.62 (step @p51 :rule refl :args (@t92)) % 0.39/0.62 (step @p52 :rule nary_cong :premises (@p51 @p50) :args (@t103)) % 0.39/0.62 (step @p53 :rule trans :premises (@p52 @p46)) % 0.39/0.62 (step @p54 :rule cong :premises (@p53) :args (@t104)) % 0.39/0.62 (step @p55 :rule cong :premises (@p54) :args (@t105)) % 0.39/0.62 (step @p56 :rule cong :premises (@p55) :args (@t106)) % 0.39/0.62 (step @p57 :rule beta-reduce :args ((= (_ @t110 @t100) @t106))) % 0.39/0.62 (step @p58 :rule trans :premises (@p57 @p56)) % 0.39/0.62 (step @p59 :rule refl :args (@t100)) % 0.39/0.62 (step @p60 :rule symm :premises (@p59)) % 0.39/0.62 (step @p61 :rule alpha_equiv :args (@t40 (@list @t8) (@list @t99))) % 0.39/0.62 (step @p62 :rule trans :premises (@p61 @p60)) % 0.39/0.62 (step @p63 :rule beta-reduce :args ((= @t111 @t110))) % 0.39/0.62 (step @p64 :rule ho_cong :premises (@p63 @p62)) % 0.39/0.62 (step @p65 :rule trans :premises (@p64 @p58)) % 0.39/0.62 (step @p66 :rule refl :args (@t98)) % 0.39/0.62 (step @p67 :rule ho_cong :premises (@p66 @p65)) % 0.39/0.62 (step @p68 :rule trans :premises (@p67 @p45)) % 0.39/0.62 (step @p69 :rule cong :premises (@p68) :args (@t112)) % 0.39/0.62 (step @p70 :rule cong :premises (@p69) :args (@t113)) % 0.39/0.62 (step @p71 :rule trans :premises (@p70 @p41)) % 0.39/0.62 (step @p72 :rule cong :premises (@p71) :args ((not @t113))) % 0.39/0.62 (step @p73 :rule trans :premises (@p72 @p34)) % 0.39/0.62 (step @p74 :rule refl :args (@t1)) % 0.39/0.62 (step @p75 :rule beta-reduce :args ((= (_ (lambda @t39 (not @t114)) @t20) @t109))) % 0.39/0.62 (step @p76 :rule refl :args (@t20)) % 0.39/0.62 (step @p77 :rule beta-reduce :args ((= @t116 @t114))) % 0.39/0.62 (step @p78 :rule cong :premises (@p77) :args (@t117)) % 0.39/0.62 (step @p79 :rule cong :premises (@p78) :args (@t118)) % 0.39/0.62 (step @p80 :rule beta-reduce :args ((= (_ @t17 @t115) @t118))) % 0.39/0.62 (step @p81 :rule trans :premises (@p80 @p79)) % 0.39/0.62 (step @p82 :rule refl :args (@t107)) % 0.39/0.62 (step @p83 :rule refl :args (@t42)) % 0.39/0.62 (step @p84 :rule cong :premises (@p83 @p82) :args ((= @t42 @t107))) % 0.39/0.62 (step @p85 :rule symm :premises (@p84)) % 0.39/0.62 (step @p86 :rule eq_resolve :premises (@p83 @p85)) % 0.39/0.62 (step @p87 :rule cong :premises (@p86) :args (@t119)) % 0.39/0.62 (step @p88 :rule refl :args (@t85)) % 0.39/0.62 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t120)) % 0.39/0.62 (step @p90 :rule cong :premises (@p89) :args ((forall @t46 @t120))) % 0.39/0.62 (step @p91 :rule beta-reduce :args ((= @t122 @t119))) % 0.39/0.62 (step @p92 :rule refl :args (@t85)) % 0.39/0.62 (step @p93 :rule nary_cong :premises (@p92 @p91) :args (@t123)) % 0.39/0.62 (step @p94 :rule cong :premises (@p93) :args (@t124)) % 0.39/0.62 (step @p95 :rule trans :premises (@p94 @p90)) % 0.39/0.62 (step @p96 :rule cong :premises (@p95) :args (@t125)) % 0.39/0.62 (step @p97 :rule beta-reduce :args ((= (_ @t127 @t121) @t125))) % 0.39/0.62 (step @p98 :rule trans :premises (@p97 @p96)) % 0.39/0.62 (step @p99 :rule beta-reduce :args ((= (_ @t17 @t13) @t121))) % 0.39/0.62 (step @p100 :rule beta-reduce :args ((= (_ (lambda @t48 @t126) @t1) @t127))) % 0.39/0.62 (step @p101 :rule ho_cong :premises (@p100 @p99)) % 0.39/0.62 (step @p102 :rule trans :premises (@p101 @p98)) % 0.39/0.62 (step @p103 :rule refl :args (@t17)) % 0.39/0.62 (step @p104 :rule ho_cong :premises (@p103 @p102)) % 0.39/0.62 (step @p105 :rule trans :premises (@p104 @p81)) % 0.39/0.62 (step @p106 :rule ho_cong :premises (@p105 @p76)) % 0.39/0.62 (step @p107 :rule trans :premises (@p106 @p75)) % 0.39/0.62 (step @p108 :rule refl :args (@t13)) % 0.39/0.62 (step @p109 :rule ho_cong :premises (@p6 @p108)) % 0.39/0.62 (step @p110 :rule refl :args (@t84)) % 0.39/0.62 (step @p111 :rule refl :args (@t43)) % 0.39/0.62 (step @p112 :rule cong :premises (@p111 @p110) :args ((= @t43 @t84))) % 0.39/0.62 (step @p113 :rule symm :premises (@p112)) % 0.39/0.62 (step @p114 :rule eq_resolve :premises (@p111 @p113)) % 0.39/0.62 (step @p115 :rule cong :premises (@p114) :args (@t44)) % 0.39/0.62 (step @p116 :rule nary_cong :premises (@p115 @p86) :args (@t45)) % 0.39/0.62 (step @p117 :rule cong :premises (@p116) :args (@t47)) % 0.39/0.62 (step @p118 :rule cong :premises (@p117) :args (@t49)) % 0.39/0.62 (step @p119 :rule trans :premises (@p18 @p118)) % 0.39/0.62 (step @p120 :rule ho_cong :premises (@p119 @p74)) % 0.39/0.62 (step @p121 :rule ho_cong :premises (@p120 @p109)) % 0.39/0.62 (step @p122 :rule ho_cong :premises (@p6 @p121)) % 0.39/0.62 (step @p123 :rule ho_cong :premises (@p122 @p76)) % 0.39/0.62 (step @p124 :rule trans :premises (@p123 @p107)) % 0.39/0.62 (step @p125 :rule cong :premises (@p124) :args (@t51)) % 0.39/0.62 (step @p126 :rule trans :premises (@p19 @p125)) % 0.39/0.62 (step @p127 :rule ho_cong :premises (@p126 @p74)) % 0.39/0.62 (step @p128 :rule ho_cong :premises (@p127 @p17)) % 0.39/0.62 (step @p129 :rule refl :args (@t97)) % 0.39/0.62 (step @p130 :rule refl :args (@t14)) % 0.39/0.62 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t14 @t97))) % 0.39/0.62 (step @p132 :rule symm :premises (@p131)) % 0.39/0.62 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.39/0.62 (step @p134 :rule cong :premises (@p133) :args (@t78)) % 0.39/0.62 (step @p135 :rule cong :premises (@p134) :args (@t80)) % 0.39/0.62 (step @p136 :rule trans :premises (@p30 @p135)) % 0.39/0.62 (step @p137 :rule ho_cong :premises (@p136 @p128)) % 0.39/0.62 (step @p138 :rule cong :premises (@p137) :args (@t2)) % 0.39/0.62 (step @p139 :rule cong :premises (@p138) :args (@t4)) % 0.39/0.62 (step @p140 :rule cong :premises (@p139) :args (@t5)) % 0.39/0.62 (step @p141 :rule trans :premises (@p140 @p73)) % 0.39/0.62 (step @p142 :rule eq_resolve :premises (@p2 @p141)) % 0.39/0.62 (step @p143 :rule bool-impl-false1 :args (@t87)) % 0.39/0.62 (step @p144 :rule quant-unused-vars :args ((= (forall @t46 true) true))) % 0.39/0.62 (step @p145 :rule evaluate :args ((not false))) % 0.39/0.62 (step @p146 :rule beta-reduce :args ((= @t130 false))) % 0.39/0.62 (step @p147 :rule cong :premises (@p146) :args (@t131)) % 0.39/0.62 (step @p148 :rule trans :premises (@p147 @p145)) % 0.39/0.62 (step @p149 :rule cong :premises (@p148) :args (@t132)) % 0.39/0.62 (step @p150 :rule trans :premises (@p149 @p144)) % 0.39/0.62 (step @p151 :rule cong :premises (@p150) :args (@t133)) % 0.39/0.62 (step @p152 :rule trans :premises (@p151 @p47)) % 0.39/0.62 (step @p153 :rule refl :args (@t87)) % 0.39/0.62 (step @p154 :rule cong :premises (@p153 @p152) :args ((=> @t87 @t133))) % 0.39/0.62 (step @p155 :rule trans :premises (@p154 @p143)) % 0.39/0.62 (assume-push @p162 @t87) % 0.39/0.62 (step @p157 :rule instantiate :premises (@p142) :args ((@list @t129 @t128))) % 0.39/0.62 (step-pop @p163 :rule scope :premises (@p157)) % 0.39/0.62 (step @p158 :rule process_scope :premises (@p163) :args (@t133)) % 0.39/0.62 (step @p160 :rule eq_resolve :premises (@p158 @p155)) % 0.39/0.62 (step @p161 false :rule chain_m_resolution :premises (@p160 @p142) :args (false (@list false) (@list @t87))) % 0.39/0.62 ) % 0.39/0.62 % SZS output end Proof % 0.39/0.62 % cvc5 exiting %------------------------------------------------------------------------------