%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO050^2 : 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 : n003.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 0.47s 0.68s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SYO050^2 : TPTP v9.2.1. Released v4.0.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n003.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 23:52:29 EDT 2026 % 0.16/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 0.47/0.68 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.47/0.68 % SZS status Theorem % 0.47/0.68 % SZS output start Proof % 0.47/0.68 ( % 0.47/0.68 (declare-sort $$unsorted 0) % 0.47/0.68 (declare-sort tptp.mu 0) % 0.47/0.68 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.47/0.68 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.47/0.68 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.47/0.68 (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)))))) % 0.47/0.68 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.47/0.68 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.47/0.68 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.47/0.68 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.47/0.68 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.47/0.68 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.47/0.68 (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))))))) % 0.47/0.68 (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))))))) % 0.47/0.68 (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)))))) % 0.47/0.68 (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)))))) % 0.47/0.68 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.47/0.68 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.47/0.68 (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)))))) % 0.47/0.68 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.47/0.68 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.47/0.68 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.47/0.68 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.47/0.68 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.47/0.68 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.47/0.68 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.47/0.68 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.47/0.68 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.47/0.68 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.47/0.68 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.47/0.68 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.47/0.68 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.47/0.68 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.47/0.68 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.47/0.68 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.47/0.68 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.47/0.68 (define @t4 () (_ tptp.mbox @t3)) % 0.47/0.68 (define @t5 () (@list @t2 @t1)) % 0.47/0.68 (define @t6 () (lambda @t5 (_ (_ (_ tptp.mimplies (_ @t4 @t2)) @t2) @t1))) % 0.47/0.68 (define @t7 () (not (_ tptp.mvalid (_ tptp.mforall_prop @t6)))) % 0.47/0.68 (define @t8 () (@list @t3)) % 0.47/0.68 (define @t9 () (exists @t8 @t7)) % 0.47/0.68 (define @t10 () (not @t9)) % 0.47/0.68 (define @t11 () (@var "Y" tptp.mu)) % 0.47/0.68 (define @t12 () (@var "X" tptp.mu)) % 0.47/0.68 (define @t13 () (@var "W" $$unsorted)) % 0.47/0.68 (define @t14 () (lambda (@list @t12 @t11 @t13) (= @t12 @t11))) % 0.47/0.68 (define @t15 () (@var "Y" (-> $$unsorted Bool))) % 0.47/0.68 (define @t16 () (@var "X" (-> $$unsorted Bool))) % 0.47/0.68 (define @t17 () (lambda (@list @t16 @t15 @t13) (= (_ @t16 @t13) (_ @t15 @t13)))) % 0.47/0.68 (define @t18 () (@var "Phi" (-> $$unsorted Bool))) % 0.47/0.68 (define @t19 () (_ @t18 @t13)) % 0.47/0.68 (define @t20 () (not @t19)) % 0.47/0.68 (define @t21 () (@list @t18 @t13)) % 0.47/0.68 (define @t22 () (lambda @t21 @t20)) % 0.47/0.68 (define @t23 () (@var "Psi" (-> $$unsorted Bool))) % 0.47/0.68 (define @t24 () (_ @t23 @t13)) % 0.47/0.68 (define @t25 () (lambda (@list @t18 @t23 @t13) (or @t19 @t24))) % 0.47/0.68 (define @t26 () (_ tptp.mnot @t23)) % 0.47/0.68 (define @t27 () (_ tptp.mnot @t18)) % 0.47/0.68 (define @t28 () (_ tptp.mor @t27)) % 0.47/0.68 (define @t29 () (@list @t18 @t23 @t1)) % 0.47/0.68 (define @t30 () (lambda @t29 (_ (_ tptp.mnot (_ @t28 @t26)) @t1))) % 0.47/0.68 (define @t31 () (lambda @t29 (_ (_ @t28 @t23) @t1))) % 0.47/0.68 (define @t32 () (lambda @t29 (_ (_ (_ tptp.mor @t26) @t18) @t1))) % 0.47/0.68 (define @t33 () (lambda @t29 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t18) @t23)) (_ (_ tptp.mimplies @t23) @t18)) @t1))) % 0.47/0.68 (define @t34 () (lambda @t29 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t18) @t23)) @t1))) % 0.47/0.68 (define @t35 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.47/0.68 (define @t36 () (_ @t35 @t12)) % 0.47/0.68 (define @t37 () (lambda (@list @t35 @t13) (forall (@list @t12) (_ @t36 @t13)))) % 0.47/0.68 (define @t38 () (@var "P" (-> $$unsorted Bool))) % 0.47/0.68 (define @t39 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.47/0.68 (define @t40 () (_ @t39 @t38)) % 0.47/0.68 (define @t41 () (_ @t40 @t13)) % 0.47/0.68 (define @t42 () (@list @t38)) % 0.47/0.68 (define @t43 () (forall @t42 @t41)) % 0.47/0.68 (define @t44 () (@list @t39 @t13)) % 0.47/0.68 (define @t45 () (lambda @t44 @t43)) % 0.47/0.68 (define @t46 () (lambda (@list @t35 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t12 @t1) (_ (_ tptp.mnot @t36) @t1)))) @t1))) % 0.47/0.68 (define @t47 () (lambda (@list @t39 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t38 @t1) (_ (_ tptp.mnot @t40) @t1)))) @t1))) % 0.47/0.68 (define @t48 () (@list @t13)) % 0.47/0.68 (define @t49 () (lambda @t48 true)) % 0.47/0.68 (define @t50 () (@var "V" $$unsorted)) % 0.47/0.68 (define @t51 () (_ @t18 @t50)) % 0.47/0.68 (define @t52 () (_ (_ @t3 @t13) @t50)) % 0.47/0.68 (define @t53 () (not @t52)) % 0.47/0.68 (define @t54 () (or @t53 @t51)) % 0.47/0.68 (define @t55 () (@list @t50)) % 0.47/0.68 (define @t56 () (forall @t55 @t54)) % 0.47/0.68 (define @t57 () (@list @t3 @t18 @t13)) % 0.47/0.68 (define @t58 () (lambda @t57 @t56)) % 0.47/0.68 (define @t59 () (lambda (@list @t3 @t18 @t1) (_ (_ tptp.mnot (_ @t4 @t27)) @t1))) % 0.47/0.68 (define @t60 () (@var "S" $$unsorted)) % 0.47/0.68 (define @t61 () (_ @t3 @t60)) % 0.47/0.68 (define @t62 () (@list @t60)) % 0.47/0.68 (define @t63 () (lambda @t8 (forall @t62 (_ @t61 @t60)))) % 0.47/0.68 (define @t64 () (@var "T" $$unsorted)) % 0.47/0.68 (define @t65 () (_ @t3 @t64)) % 0.47/0.68 (define @t66 () (_ @t61 @t64)) % 0.47/0.68 (define @t67 () (lambda @t8 (forall (@list @t60 @t64) (=> @t66 (_ @t65 @t60))))) % 0.47/0.68 (define @t68 () (@list @t64)) % 0.47/0.68 (define @t69 () (lambda @t8 (forall @t62 (exists @t68 @t66)))) % 0.47/0.68 (define @t70 () (@var "U" $$unsorted)) % 0.47/0.68 (define @t71 () (_ @t61 @t70)) % 0.47/0.68 (define @t72 () (_ @t65 @t70)) % 0.47/0.68 (define @t73 () (@list @t60 @t64 @t70)) % 0.47/0.68 (define @t74 () (lambda @t8 (forall @t73 (=> (and @t66 @t72) @t71)))) % 0.47/0.68 (define @t75 () (and @t66 @t71)) % 0.47/0.68 (define @t76 () (lambda @t8 (forall @t73 (=> @t75 @t72)))) % 0.47/0.68 (define @t77 () (= @t64 @t70)) % 0.47/0.68 (define @t78 () (lambda @t8 (forall @t73 (=> @t75 @t77)))) % 0.47/0.68 (define @t79 () (@list @t70)) % 0.47/0.68 (define @t80 () (lambda @t8 (forall @t62 (exists @t68 (and @t66 (forall @t79 (=> @t71 @t77))))))) % 0.47/0.68 (define @t81 () (_ @t3 @t70)) % 0.47/0.68 (define @t82 () (_ @t81 @t64)) % 0.47/0.68 (define @t83 () (lambda @t8 (forall @t73 (=> @t66 (exists @t79 (and @t71 @t82)))))) % 0.47/0.68 (define @t84 () (lambda @t8 (forall @t73 (=> @t75 (or @t72 @t77 @t82))))) % 0.47/0.68 (define @t85 () (lambda @t8 (forall @t73 (=> @t75 (exists @t55 (and (_ @t65 @t50) (_ @t81 @t50))))))) % 0.47/0.68 (define @t86 () (forall @t48 @t19)) % 0.47/0.68 (define @t87 () (@list @t18)) % 0.47/0.68 (define @t88 () (lambda @t87 @t86)) % 0.47/0.68 (define @t89 () (lambda @t87 (forall @t48 @t20))) % 0.47/0.68 (define @t90 () (lambda @t87 (exists @t48 @t19))) % 0.47/0.68 (define @t91 () (lambda @t87 (exists @t48 @t20))) % 0.47/0.68 (define @t92 () (_ @t38 @t13)) % 0.47/0.68 (define @t93 () (_ @t3 @t13 @t50)) % 0.47/0.68 (define @t94 () (not @t93)) % 0.47/0.68 (define @t95 () (not (forall @t55 (or @t94 (_ @t38 @t50))))) % 0.47/0.68 (define @t96 () (or @t95 @t92)) % 0.47/0.68 (define @t97 () (forall (@list @t3 @t13 @t38) @t96)) % 0.47/0.68 (define @t98 () (forall (@list @t13 @t38) @t96)) % 0.47/0.68 (define @t99 () (not @t98)) % 0.47/0.68 (define @t100 () (forall @t8 (not @t99))) % 0.47/0.68 (define @t101 () (not @t100)) % 0.47/0.68 (define @t102 () (forall @t42 @t96)) % 0.47/0.68 (define @t103 () (lambda @t48 @t102)) % 0.47/0.68 (define @t104 () (_ @t103 @t13)) % 0.47/0.68 (define @t105 () (forall @t48 @t104)) % 0.47/0.68 (define @t106 () (_ @t18 @t13)) % 0.47/0.68 (define @t107 () (lambda @t87 (forall @t48 @t106))) % 0.47/0.68 (define @t108 () (_ @t38 @t13)) % 0.47/0.68 (define @t109 () (or @t95 @t108)) % 0.47/0.68 (define @t110 () (_ @t2 @t50)) % 0.47/0.68 (define @t111 () (forall @t55 (or (not (_ @t3 @t1 @t50)) @t110))) % 0.47/0.68 (define @t112 () (not @t111)) % 0.47/0.68 (define @t113 () (or @t112 (_ @t2 @t1))) % 0.47/0.68 (define @t114 () (lambda @t5 @t113)) % 0.47/0.68 (define @t115 () (_ @t114 @t38 @t13)) % 0.47/0.68 (define @t116 () (forall @t42 @t115)) % 0.47/0.68 (define @t117 () (lambda @t48 @t116)) % 0.47/0.68 (define @t118 () (_ @t39 @t38 @t13)) % 0.47/0.68 (define @t119 () (lambda @t44 (forall @t42 @t118))) % 0.47/0.68 (define @t120 () (lambda (@list @t1) @t113)) % 0.47/0.68 (define @t121 () (_ @t23 @t1)) % 0.47/0.68 (define @t122 () (@list @t23 @t1)) % 0.47/0.68 (define @t123 () (lambda @t48 (forall @t55 (or @t94 @t110)))) % 0.47/0.68 (define @t124 () (_ @t123 @t1)) % 0.47/0.68 (define @t125 () (not @t124)) % 0.47/0.68 (define @t126 () (or @t125 @t121)) % 0.47/0.68 (define @t127 () (lambda @t122 @t126)) % 0.47/0.68 (define @t128 () (or (not (_ @t18 @t1)) @t121)) % 0.47/0.68 (define @t129 () (lambda @t29 @t128)) % 0.47/0.68 (define @t130 () (_ @t18 @t50)) % 0.47/0.68 (define @t131 () (forall @t55 (or @t94 @t130))) % 0.47/0.68 (define @t132 () (lambda @t21 @t131)) % 0.47/0.68 (define @t133 () (_ (lambda @t57 @t131) @t3)) % 0.47/0.68 (define @t134 () (lambda @t5 (_ (_ (_ @t129 (_ @t133 @t2)) @t2) @t1))) % 0.47/0.68 (define @t135 () (not (_ @t107 (_ @t119 @t134)))) % 0.47/0.68 (define @t136 () (exists @t8 @t135)) % 0.47/0.68 (define @t137 () (or @t20 @t24)) % 0.47/0.68 (define @t138 () (lambda @t48 @t137)) % 0.47/0.68 (define @t139 () (@list @t23 @t13)) % 0.47/0.68 (define @t140 () (lambda @t48 @t20)) % 0.47/0.68 (define @t141 () (_ @t140 @t13)) % 0.47/0.68 (define @t142 () (or @t141 @t24)) % 0.47/0.68 (define @t143 () (lambda @t139 @t142)) % 0.47/0.68 (define @t144 () (@purify (as @$$unsorted_0 $$unsorted))) % 0.47/0.68 (define @t145 () (lambda (@list (@var "BOUND_VARIABLE_22827" $$unsorted)) false)) % 0.47/0.68 (define @t146 () (_ @t145 @t144)) % 0.47/0.68 (define @t147 () (_ @t145 @t50)) % 0.47/0.68 (define @t148 () (lambda (@list (@var "BOUND_VARIABLE_22674" $$unsorted) (@var "BOUND_VARIABLE_22675" $$unsorted)) false)) % 0.47/0.68 (define @t149 () (_ @t148 @t144 @t50)) % 0.47/0.68 (define @t150 () (not @t149)) % 0.47/0.68 (define @t151 () (or @t150 @t147)) % 0.47/0.68 (define @t152 () (forall @t55 @t151)) % 0.47/0.68 (define @t153 () (not @t152)) % 0.47/0.68 (define @t154 () (or @t153 @t146)) % 0.47/0.68 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.47/0.68 (assume @p2 @t10) % 0.47/0.68 (assume @p3 true) % 0.47/0.68 (step @p4 (= tptp.meq_ind @t14) :rule refl :args (@t14)) % 0.47/0.68 (step @p5 (= tptp.meq_prop @t17) :rule refl :args (@t17)) % 0.47/0.68 (step @p6 (= tptp.mnot @t22) :rule refl :args (@t22)) % 0.47/0.68 (step @p7 (= tptp.mor @t25) :rule refl :args (@t25)) % 0.47/0.68 (step @p8 (= tptp.mand @t30) :rule refl :args (@t30)) % 0.47/0.68 (step @p9 (= tptp.mimplies @t31) :rule refl :args (@t31)) % 0.47/0.68 (step @p10 (= tptp.mimplied @t32) :rule refl :args (@t32)) % 0.47/0.68 (step @p11 (= tptp.mequiv @t33) :rule refl :args (@t33)) % 0.47/0.68 (step @p12 (= tptp.mxor @t34) :rule refl :args (@t34)) % 0.47/0.68 (step @p13 (= tptp.mforall_ind @t37) :rule refl :args (@t37)) % 0.47/0.68 (step @p14 (= tptp.mforall_prop @t45) :rule refl :args (@t45)) % 0.47/0.68 (step @p15 (= tptp.mexists_ind @t46) :rule refl :args (@t46)) % 0.47/0.68 (step @p16 (= tptp.mexists_prop @t47) :rule refl :args (@t47)) % 0.47/0.68 (step @p17 (= tptp.mtrue @t49) :rule refl :args (@t49)) % 0.47/0.68 (step @p18 (= tptp.mbox @t58) :rule refl :args (@t58)) % 0.47/0.68 (step @p19 (= tptp.mdia @t59) :rule refl :args (@t59)) % 0.47/0.68 (step @p20 (= tptp.mreflexive @t63) :rule refl :args (@t63)) % 0.47/0.68 (step @p21 (= tptp.msymmetric @t67) :rule refl :args (@t67)) % 0.47/0.68 (step @p22 (= tptp.mserial @t69) :rule refl :args (@t69)) % 0.47/0.68 (step @p23 (= tptp.mtransitive @t74) :rule refl :args (@t74)) % 0.47/0.68 (step @p24 (= tptp.meuclidean @t76) :rule refl :args (@t76)) % 0.47/0.68 (step @p25 (= tptp.mpartially_functional @t78) :rule refl :args (@t78)) % 0.47/0.68 (step @p26 (= tptp.mfunctional @t80) :rule refl :args (@t80)) % 0.47/0.68 (step @p27 (= tptp.mweakly_dense @t83) :rule refl :args (@t83)) % 0.47/0.68 (step @p28 (= tptp.mweakly_connected @t84) :rule refl :args (@t84)) % 0.47/0.68 (step @p29 (= tptp.mweakly_directed @t85) :rule refl :args (@t85)) % 0.47/0.68 (step @p30 (= tptp.mvalid @t88) :rule refl :args (@t88)) % 0.47/0.68 (step @p31 (= tptp.minvalid @t89) :rule refl :args (@t89)) % 0.47/0.68 (step @p32 (= tptp.msatisfiable @t90) :rule refl :args (@t90)) % 0.47/0.68 (step @p33 (= tptp.mcountersatisfiable @t91) :rule refl :args (@t91)) % 0.47/0.68 (step @p34 :rule bool-double-not-elim :args (@t97)) % 0.47/0.68 (step @p35 :rule quant-merge-prenex :args ((= (forall @t8 @t98) @t97))) % 0.47/0.68 (step @p36 :rule bool-double-not-elim :args (@t98)) % 0.47/0.68 (step @p37 :rule cong :premises (@p36) :args (@t100)) % 0.47/0.68 (step @p38 :rule trans :premises (@p37 @p35)) % 0.47/0.68 (step @p39 :rule cong :premises (@p38) :args (@t101)) % 0.47/0.68 (step @p40 :rule exists-elim :args ((= (exists @t8 @t99) @t101))) % 0.47/0.68 (step @p41 :rule trans :premises (@p40 @p39)) % 0.47/0.68 (step @p42 :rule quant-merge-prenex :args ((= (forall @t48 @t102) @t98))) % 0.47/0.68 (step @p43 :rule beta-reduce :args ((= @t104 @t102))) % 0.47/0.68 (step @p44 :rule cong :premises (@p43) :args (@t105)) % 0.47/0.68 (step @p45 :rule trans :premises (@p44 @p42)) % 0.47/0.68 (step @p46 :rule beta-reduce :args ((= (_ @t107 @t103) @t105))) % 0.47/0.68 (step @p47 :rule trans :premises (@p46 @p45)) % 0.47/0.68 (step @p48 :rule refl :args (@t92)) % 0.47/0.68 (step @p49 :rule refl :args (@t108)) % 0.47/0.68 (step @p50 :rule cong :premises (@p49 @p48) :args ((= @t108 @t92))) % 0.47/0.68 (step @p51 :rule symm :premises (@p50)) % 0.47/0.68 (step @p52 :rule eq_resolve :premises (@p49 @p51)) % 0.47/0.68 (step @p53 :rule refl :args (@t95)) % 0.47/0.68 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t109)) % 0.47/0.68 (step @p55 :rule cong :premises (@p54) :args ((forall @t42 @t109))) % 0.47/0.68 (step @p56 :rule beta-reduce :args ((= @t115 @t109))) % 0.47/0.68 (step @p57 :rule cong :premises (@p56) :args (@t116)) % 0.47/0.68 (step @p58 :rule trans :premises (@p57 @p55)) % 0.47/0.68 (step @p59 :rule cong :premises (@p58) :args (@t117)) % 0.47/0.68 (step @p60 :rule beta-reduce :args ((= (_ @t119 @t114) @t117))) % 0.47/0.68 (step @p61 :rule trans :premises (@p60 @p59)) % 0.47/0.68 (step @p62 :rule beta-reduce :args ((= (_ @t120 @t1) @t113))) % 0.47/0.68 (step @p63 :rule refl :args (@t1)) % 0.47/0.68 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t122 (or @t112 @t121)) @t2) @t120))) % 0.47/0.68 (step @p65 :rule refl :args (@t2)) % 0.47/0.68 (step @p66 :rule refl :args (@t121)) % 0.47/0.68 (step @p67 :rule beta-reduce :args ((= @t124 @t111))) % 0.47/0.68 (step @p68 :rule cong :premises (@p67) :args (@t125)) % 0.47/0.68 (step @p69 :rule nary_cong :premises (@p68 @p66) :args (@t126)) % 0.47/0.68 (step @p70 :rule cong :premises (@p69) :args (@t127)) % 0.47/0.68 (step @p71 :rule beta-reduce :args ((= (_ @t129 @t123) @t127))) % 0.47/0.68 (step @p72 :rule trans :premises (@p71 @p70)) % 0.47/0.68 (step @p73 :rule beta-reduce :args ((= (_ @t132 @t2) @t123))) % 0.47/0.68 (step @p74 :rule beta-reduce :args ((= @t133 @t132))) % 0.47/0.68 (step @p75 :rule ho_cong :premises (@p74 @p65)) % 0.47/0.68 (step @p76 :rule trans :premises (@p75 @p73)) % 0.47/0.68 (step @p77 :rule refl :args (@t129)) % 0.47/0.68 (step @p78 :rule ho_cong :premises (@p77 @p76)) % 0.47/0.68 (step @p79 :rule trans :premises (@p78 @p72)) % 0.47/0.68 (step @p80 :rule ho_cong :premises (@p79 @p65)) % 0.47/0.68 (step @p81 :rule trans :premises (@p80 @p64)) % 0.47/0.68 (step @p82 :rule ho_cong :premises (@p81 @p63)) % 0.47/0.68 (step @p83 :rule trans :premises (@p82 @p62)) % 0.47/0.68 (step @p84 :rule cong :premises (@p83) :args (@t134)) % 0.47/0.68 (step @p85 :rule refl :args (@t119)) % 0.47/0.68 (step @p86 :rule ho_cong :premises (@p85 @p84)) % 0.47/0.68 (step @p87 :rule trans :premises (@p86 @p61)) % 0.47/0.68 (step @p88 :rule refl :args (@t107)) % 0.47/0.68 (step @p89 :rule ho_cong :premises (@p88 @p87)) % 0.47/0.68 (step @p90 :rule trans :premises (@p89 @p47)) % 0.47/0.68 (step @p91 :rule cong :premises (@p90) :args (@t135)) % 0.47/0.68 (step @p92 :rule cong :premises (@p91) :args (@t136)) % 0.47/0.68 (step @p93 :rule trans :premises (@p92 @p41)) % 0.47/0.68 (step @p94 :rule cong :premises (@p93) :args ((not @t136))) % 0.47/0.68 (step @p95 :rule trans :premises (@p94 @p34)) % 0.47/0.68 (step @p96 :rule refl :args (@t3)) % 0.47/0.68 (step @p97 :rule refl :args (@t130)) % 0.47/0.68 (step @p98 :rule refl :args (@t51)) % 0.47/0.68 (step @p99 :rule cong :premises (@p98 @p97) :args ((= @t51 @t130))) % 0.47/0.68 (step @p100 :rule symm :premises (@p99)) % 0.47/0.68 (step @p101 :rule eq_resolve :premises (@p98 @p100)) % 0.47/0.68 (step @p102 :rule refl :args (@t93)) % 0.47/0.68 (step @p103 :rule refl :args (@t52)) % 0.47/0.68 (step @p104 :rule cong :premises (@p103 @p102) :args ((= @t52 @t93))) % 0.47/0.68 (step @p105 :rule symm :premises (@p104)) % 0.47/0.68 (step @p106 :rule eq_resolve :premises (@p103 @p105)) % 0.47/0.68 (step @p107 :rule cong :premises (@p106) :args (@t53)) % 0.47/0.68 (step @p108 :rule nary_cong :premises (@p107 @p101) :args (@t54)) % 0.47/0.68 (step @p109 :rule cong :premises (@p108) :args (@t56)) % 0.47/0.68 (step @p110 :rule cong :premises (@p109) :args (@t58)) % 0.47/0.68 (step @p111 :rule trans :premises (@p18 @p110)) % 0.47/0.68 (step @p112 :rule ho_cong :premises (@p111 @p96)) % 0.47/0.68 (step @p113 :rule ho_cong :premises (@p112 @p65)) % 0.47/0.68 (step @p114 :rule beta-reduce :args ((= (_ @t138 @t1) @t128))) % 0.47/0.68 (step @p115 :rule beta-reduce :args ((= (_ (lambda @t139 @t137) @t23) @t138))) % 0.47/0.68 (step @p116 :rule refl :args (@t23)) % 0.47/0.68 (step @p117 :rule refl :args (@t24)) % 0.47/0.68 (step @p118 :rule beta-reduce :args ((= @t141 @t20))) % 0.47/0.68 (step @p119 :rule nary_cong :premises (@p118 @p117) :args (@t142)) % 0.47/0.68 (step @p120 :rule cong :premises (@p119) :args (@t143)) % 0.47/0.68 (step @p121 :rule beta-reduce :args ((= (_ @t25 @t140) @t143))) % 0.47/0.68 (step @p122 :rule trans :premises (@p121 @p120)) % 0.47/0.68 (step @p123 :rule beta-reduce :args ((= (_ @t22 @t18) @t140))) % 0.47/0.68 (step @p124 :rule refl :args (@t25)) % 0.47/0.68 (step @p125 :rule ho_cong :premises (@p124 @p123)) % 0.47/0.68 (step @p126 :rule trans :premises (@p125 @p122)) % 0.47/0.68 (step @p127 :rule ho_cong :premises (@p126 @p116)) % 0.47/0.68 (step @p128 :rule trans :premises (@p127 @p115)) % 0.47/0.68 (step @p129 :rule ho_cong :premises (@p128 @p63)) % 0.47/0.68 (step @p130 :rule trans :premises (@p129 @p114)) % 0.47/0.68 (step @p131 :rule refl :args (@t18)) % 0.47/0.68 (step @p132 :rule ho_cong :premises (@p6 @p131)) % 0.47/0.68 (step @p133 :rule ho_cong :premises (@p7 @p132)) % 0.47/0.68 (step @p134 :rule ho_cong :premises (@p133 @p116)) % 0.47/0.68 (step @p135 :rule ho_cong :premises (@p134 @p63)) % 0.47/0.68 (step @p136 :rule trans :premises (@p135 @p130)) % 0.47/0.68 (step @p137 :rule cong :premises (@p136) :args (@t31)) % 0.47/0.68 (step @p138 :rule trans :premises (@p9 @p137)) % 0.47/0.68 (step @p139 :rule ho_cong :premises (@p138 @p113)) % 0.47/0.68 (step @p140 :rule ho_cong :premises (@p139 @p65)) % 0.47/0.68 (step @p141 :rule ho_cong :premises (@p140 @p63)) % 0.47/0.68 (step @p142 :rule cong :premises (@p141) :args (@t6)) % 0.47/0.68 (step @p143 :rule refl :args (@t118)) % 0.47/0.68 (step @p144 :rule refl :args (@t41)) % 0.47/0.68 (step @p145 :rule cong :premises (@p144 @p143) :args ((= @t41 @t118))) % 0.47/0.68 (step @p146 :rule symm :premises (@p145)) % 0.47/0.68 (step @p147 :rule eq_resolve :premises (@p144 @p146)) % 0.47/0.68 (step @p148 :rule cong :premises (@p147) :args (@t43)) % 0.47/0.68 (step @p149 :rule cong :premises (@p148) :args (@t45)) % 0.47/0.68 (step @p150 :rule trans :premises (@p14 @p149)) % 0.47/0.68 (step @p151 :rule ho_cong :premises (@p150 @p142)) % 0.47/0.68 (step @p152 :rule refl :args (@t106)) % 0.47/0.68 (step @p153 :rule refl :args (@t19)) % 0.47/0.68 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t19 @t106))) % 0.47/0.68 (step @p155 :rule symm :premises (@p154)) % 0.47/0.68 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 0.47/0.68 (step @p157 :rule cong :premises (@p156) :args (@t86)) % 0.47/0.68 (step @p158 :rule cong :premises (@p157) :args (@t88)) % 0.47/0.68 (step @p159 :rule trans :premises (@p30 @p158)) % 0.47/0.68 (step @p160 :rule ho_cong :premises (@p159 @p151)) % 0.47/0.68 (step @p161 :rule cong :premises (@p160) :args (@t7)) % 0.47/0.68 (step @p162 :rule cong :premises (@p161) :args (@t9)) % 0.47/0.68 (step @p163 :rule cong :premises (@p162) :args (@t10)) % 0.47/0.68 (step @p164 :rule trans :premises (@p163 @p95)) % 0.47/0.68 (step @p165 :rule eq_resolve :premises (@p2 @p164)) % 0.47/0.68 (step @p166 :rule bool-impl-false1 :args (@t97)) % 0.47/0.68 (step @p167 :rule evaluate :args ((or false false))) % 0.47/0.68 (step @p168 :rule beta-reduce :args ((= @t146 false))) % 0.47/0.68 (step @p169 :rule evaluate :args ((not true))) % 0.47/0.68 (step @p170 :rule quant-unused-vars :args ((= (forall @t55 true) true))) % 0.47/0.68 (step @p171 :rule evaluate :args ((or true false))) % 0.47/0.68 (step @p172 :rule beta-reduce :args ((= @t147 false))) % 0.47/0.68 (step @p173 :rule evaluate :args ((not false))) % 0.47/0.68 (step @p174 :rule beta-reduce :args ((= @t149 false))) % 0.47/0.68 (step @p175 :rule cong :premises (@p174) :args (@t150)) % 0.47/0.68 (step @p176 :rule trans :premises (@p175 @p173)) % 0.47/0.68 (step @p177 :rule nary_cong :premises (@p176 @p172) :args (@t151)) % 0.47/0.68 (step @p178 :rule trans :premises (@p177 @p171)) % 0.47/0.68 (step @p179 :rule cong :premises (@p178) :args (@t152)) % 0.47/0.68 (step @p180 :rule trans :premises (@p179 @p170)) % 0.47/0.68 (step @p181 :rule cong :premises (@p180) :args (@t153)) % 0.47/0.68 (step @p182 :rule trans :premises (@p181 @p169)) % 0.47/0.68 (step @p183 :rule nary_cong :premises (@p182 @p168) :args (@t154)) % 0.47/0.68 (step @p184 :rule trans :premises (@p183 @p167)) % 0.47/0.68 (step @p185 :rule refl :args (@t97)) % 0.47/0.68 (step @p186 :rule cong :premises (@p185 @p184) :args ((=> @t97 @t154))) % 0.47/0.68 (step @p187 :rule trans :premises (@p186 @p166)) % 0.47/0.68 (assume-push @p194 @t97) % 0.47/0.68 (step @p189 :rule instantiate :premises (@p165) :args ((@list @t148 @t144 @t145))) % 0.47/0.68 (step-pop @p195 :rule scope :premises (@p189)) % 0.47/0.68 (step @p190 :rule process_scope :premises (@p195) :args (@t154)) % 0.47/0.68 (step @p192 :rule eq_resolve :premises (@p190 @p187)) % 0.47/0.68 (step @p193 false :rule chain_m_resolution :premises (@p192 @p165) :args (false (@list false) (@list @t97))) % 0.47/0.68 ) % 0.47/0.68 % SZS output end Proof % 0.47/0.68 % cvc5 exiting %------------------------------------------------------------------------------