%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL708^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n006.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:40 AM UTC 2026 % Result : Theorem 0.29s 0.57s % Output : Proof 0.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL708^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.05 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.11/0.36 % Computer : n006.cluster.edu % 0.11/0.36 % Model : x86_64 x86_64 % 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.36 % Memory : 8046.5625MB % 0.11/0.36 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 20:41:46 UTC 2026 % 0.14/0.37 % CPUTime : % 0.14/0.44 %----Proving TH0 % 0.29/0.57 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.29/0.57 % SZS status Theorem % 0.29/0.57 % SZS output start Proof % 0.29/0.57 ( % 0.29/0.57 (declare-sort $$unsorted 0) % 0.29/0.57 (declare-sort tptp.mu 0) % 0.29/0.57 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.29/0.57 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.29/0.57 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.29/0.57 (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)))))) % 0.29/0.57 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.29/0.57 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.29/0.57 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.29/0.57 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.29/0.57 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.29/0.57 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.29/0.57 (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))))))) % 0.29/0.57 (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))))))) % 0.29/0.57 (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)))))) % 0.29/0.57 (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)))))) % 0.29/0.57 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.29/0.57 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.29/0.57 (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)))))) % 0.29/0.57 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.29/0.57 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.57 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.29/0.57 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.29/0.57 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.29/0.57 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.29/0.57 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.29/0.57 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.29/0.57 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.29/0.57 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.29/0.57 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.57 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.57 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.29/0.57 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.29/0.57 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.29/0.57 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.29/0.57 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.29/0.57 (define @t4 () (_ tptp.mdia @t3)) % 0.29/0.57 (define @t5 () (_ tptp.mbox @t3)) % 0.29/0.57 (define @t6 () (@list @t2 @t1)) % 0.29/0.57 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mimplies (_ @t4 (_ @t5 @t2))) (_ @t5 (_ @t4 @t2))) @t1))) % 0.29/0.57 (define @t8 () (=> (_ tptp.mweakly_directed @t3) (_ tptp.mvalid (_ tptp.mforall_prop @t7)))) % 0.29/0.57 (define @t9 () (@list @t3)) % 0.29/0.57 (define @t10 () (forall @t9 @t8)) % 0.29/0.57 (define @t11 () (not @t10)) % 0.29/0.57 (define @t12 () (@var "Y" tptp.mu)) % 0.29/0.57 (define @t13 () (@var "X" tptp.mu)) % 0.29/0.57 (define @t14 () (@var "W" $$unsorted)) % 0.29/0.57 (define @t15 () (lambda (@list @t13 @t12 @t14) (= @t13 @t12))) % 0.29/0.57 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.29/0.57 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 0.29/0.57 (define @t18 () (lambda (@list @t17 @t16 @t14) (= (_ @t17 @t14) (_ @t16 @t14)))) % 0.29/0.57 (define @t19 () (@var "Phi" (-> $$unsorted Bool))) % 0.29/0.57 (define @t20 () (_ @t19 @t14)) % 0.29/0.57 (define @t21 () (not @t20)) % 0.29/0.57 (define @t22 () (@list @t19 @t14)) % 0.29/0.57 (define @t23 () (lambda @t22 @t21)) % 0.29/0.57 (define @t24 () (@var "Psi" (-> $$unsorted Bool))) % 0.29/0.57 (define @t25 () (_ @t24 @t14)) % 0.29/0.57 (define @t26 () (lambda (@list @t19 @t24 @t14) (or @t20 @t25))) % 0.29/0.57 (define @t27 () (_ tptp.mnot @t24)) % 0.29/0.57 (define @t28 () (_ tptp.mnot @t19)) % 0.29/0.57 (define @t29 () (_ tptp.mor @t28)) % 0.29/0.57 (define @t30 () (@list @t19 @t24 @t1)) % 0.29/0.57 (define @t31 () (lambda @t30 (_ (_ tptp.mnot (_ @t29 @t27)) @t1))) % 0.29/0.57 (define @t32 () (lambda @t30 (_ (_ @t29 @t24) @t1))) % 0.29/0.57 (define @t33 () (lambda @t30 (_ (_ (_ tptp.mor @t27) @t19) @t1))) % 0.29/0.57 (define @t34 () (lambda @t30 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t19) @t24)) (_ (_ tptp.mimplies @t24) @t19)) @t1))) % 0.29/0.57 (define @t35 () (lambda @t30 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t19) @t24)) @t1))) % 0.29/0.57 (define @t36 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.29/0.57 (define @t37 () (_ @t36 @t13)) % 0.29/0.57 (define @t38 () (lambda (@list @t36 @t14) (forall (@list @t13) (_ @t37 @t14)))) % 0.29/0.57 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.29/0.57 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.29/0.57 (define @t41 () (_ @t40 @t39)) % 0.29/0.57 (define @t42 () (_ @t41 @t14)) % 0.29/0.57 (define @t43 () (@list @t39)) % 0.29/0.57 (define @t44 () (forall @t43 @t42)) % 0.29/0.57 (define @t45 () (@list @t40 @t14)) % 0.29/0.57 (define @t46 () (lambda @t45 @t44)) % 0.29/0.57 (define @t47 () (lambda (@list @t36 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t13 @t1) (_ (_ tptp.mnot @t37) @t1)))) @t1))) % 0.29/0.57 (define @t48 () (lambda (@list @t40 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t1) (_ (_ tptp.mnot @t41) @t1)))) @t1))) % 0.29/0.57 (define @t49 () (@list @t14)) % 0.29/0.57 (define @t50 () (lambda @t49 true)) % 0.29/0.57 (define @t51 () (@var "V" $$unsorted)) % 0.29/0.57 (define @t52 () (_ @t19 @t51)) % 0.29/0.57 (define @t53 () (_ (_ @t3 @t14) @t51)) % 0.29/0.57 (define @t54 () (not @t53)) % 0.29/0.57 (define @t55 () (or @t54 @t52)) % 0.29/0.57 (define @t56 () (@list @t51)) % 0.29/0.57 (define @t57 () (forall @t56 @t55)) % 0.29/0.57 (define @t58 () (@list @t3 @t19 @t14)) % 0.29/0.57 (define @t59 () (lambda @t58 @t57)) % 0.29/0.57 (define @t60 () (@list @t3 @t19 @t1)) % 0.29/0.57 (define @t61 () (lambda @t60 (_ (_ tptp.mnot (_ @t5 @t28)) @t1))) % 0.29/0.57 (define @t62 () (@var "S" $$unsorted)) % 0.29/0.57 (define @t63 () (_ @t3 @t62)) % 0.29/0.57 (define @t64 () (@list @t62)) % 0.29/0.57 (define @t65 () (lambda @t9 (forall @t64 (_ @t63 @t62)))) % 0.29/0.57 (define @t66 () (@var "T" $$unsorted)) % 0.29/0.57 (define @t67 () (_ @t3 @t66)) % 0.29/0.57 (define @t68 () (_ @t63 @t66)) % 0.29/0.57 (define @t69 () (lambda @t9 (forall (@list @t62 @t66) (=> @t68 (_ @t67 @t62))))) % 0.29/0.57 (define @t70 () (@list @t66)) % 0.29/0.57 (define @t71 () (lambda @t9 (forall @t64 (exists @t70 @t68)))) % 0.29/0.57 (define @t72 () (@var "U" $$unsorted)) % 0.29/0.58 (define @t73 () (_ @t63 @t72)) % 0.29/0.58 (define @t74 () (_ @t67 @t72)) % 0.29/0.58 (define @t75 () (@list @t62 @t66 @t72)) % 0.29/0.58 (define @t76 () (lambda @t9 (forall @t75 (=> (and @t68 @t74) @t73)))) % 0.29/0.58 (define @t77 () (and @t68 @t73)) % 0.29/0.58 (define @t78 () (lambda @t9 (forall @t75 (=> @t77 @t74)))) % 0.29/0.58 (define @t79 () (= @t66 @t72)) % 0.29/0.58 (define @t80 () (lambda @t9 (forall @t75 (=> @t77 @t79)))) % 0.29/0.58 (define @t81 () (@list @t72)) % 0.29/0.58 (define @t82 () (lambda @t9 (forall @t64 (exists @t70 (and @t68 (forall @t81 (=> @t73 @t79))))))) % 0.29/0.58 (define @t83 () (_ @t3 @t72)) % 0.29/0.58 (define @t84 () (_ @t83 @t66)) % 0.29/0.58 (define @t85 () (lambda @t9 (forall @t75 (=> @t68 (exists @t81 (and @t73 @t84)))))) % 0.29/0.58 (define @t86 () (lambda @t9 (forall @t75 (=> @t77 (or @t74 @t79 @t84))))) % 0.29/0.58 (define @t87 () (_ @t83 @t51)) % 0.29/0.58 (define @t88 () (_ @t67 @t51)) % 0.29/0.58 (define @t89 () (and @t88 @t87)) % 0.29/0.58 (define @t90 () (exists @t56 @t89)) % 0.29/0.58 (define @t91 () (=> @t77 @t90)) % 0.29/0.58 (define @t92 () (forall @t75 @t91)) % 0.29/0.58 (define @t93 () (lambda @t9 @t92)) % 0.29/0.58 (define @t94 () (forall @t49 @t20)) % 0.29/0.58 (define @t95 () (@list @t19)) % 0.29/0.58 (define @t96 () (lambda @t95 @t94)) % 0.29/0.58 (define @t97 () (lambda @t95 (forall @t49 @t21))) % 0.29/0.58 (define @t98 () (lambda @t95 (exists @t49 @t20))) % 0.29/0.58 (define @t99 () (lambda @t95 (exists @t49 @t21))) % 0.29/0.58 (define @t100 () (@var "BOUND_VARIABLE_8400" $$unsorted)) % 0.29/0.58 (define @t101 () (@var "BOUND_VARIABLE_8489" (-> $$unsorted Bool))) % 0.29/0.58 (define @t102 () (@var "BOUND_VARIABLE_8493" $$unsorted)) % 0.29/0.58 (define @t103 () (@list @t100)) % 0.29/0.58 (define @t104 () (not (forall @t103 (or (not (_ @t3 @t102 @t100)) (not (_ @t101 @t100)))))) % 0.29/0.58 (define @t105 () (@var "BOUND_VARIABLE_8487" $$unsorted)) % 0.29/0.58 (define @t106 () (not (_ @t3 @t105 @t102))) % 0.29/0.58 (define @t107 () (@var "BOUND_VARIABLE_8362" $$unsorted)) % 0.29/0.58 (define @t108 () (@var "BOUND_VARIABLE_8491" $$unsorted)) % 0.29/0.58 (define @t109 () (@list @t107)) % 0.29/0.58 (define @t110 () (not (forall @t109 (or (not (_ @t3 @t108 @t107)) (_ @t101 @t107))))) % 0.29/0.58 (define @t111 () (not (_ @t3 @t105 @t108))) % 0.29/0.58 (define @t112 () (_ @t3 @t72 @t51)) % 0.29/0.58 (define @t113 () (_ @t3 @t66 @t51)) % 0.29/0.58 (define @t114 () (not (forall @t56 (or (not @t113) (not @t112))))) % 0.29/0.58 (define @t115 () (_ @t3 @t62 @t72)) % 0.29/0.58 (define @t116 () (_ @t3 @t62 @t66)) % 0.29/0.58 (define @t117 () (forall @t75 (or (not @t116) (not @t115) @t114))) % 0.29/0.58 (define @t118 () (not @t117)) % 0.29/0.58 (define @t119 () (or @t118 @t111 @t110 @t106 @t104)) % 0.29/0.58 (define @t120 () (or @t111 @t110 @t106 @t104)) % 0.29/0.58 (define @t121 () (or @t118 @t120)) % 0.29/0.58 (define @t122 () (@list @t3 @t105 @t101 @t108 @t102)) % 0.29/0.58 (define @t123 () (forall @t122 @t121)) % 0.29/0.58 (define @t124 () (@list @t105 @t101 @t108 @t102)) % 0.29/0.58 (define @t125 () (forall @t124 @t121)) % 0.29/0.58 (define @t126 () (forall @t124 @t120)) % 0.29/0.58 (define @t127 () (@var "BOUND_VARIABLE_8460" $$unsorted)) % 0.29/0.58 (define @t128 () (@var "BOUND_VARIABLE_8450" $$unsorted)) % 0.29/0.58 (define @t129 () (or @t118 @t126)) % 0.29/0.58 (define @t130 () (not (_ @t39 @t100))) % 0.29/0.58 (define @t131 () (not (forall @t103 (or (not (_ @t3 @t127 @t100)) @t130)))) % 0.29/0.58 (define @t132 () (not (_ @t3 @t14 @t127))) % 0.29/0.58 (define @t133 () (_ @t39 @t107)) % 0.29/0.58 (define @t134 () (not (forall @t109 (or (not (_ @t3 @t128 @t107)) @t133)))) % 0.29/0.58 (define @t135 () (not (_ @t3 @t14 @t128))) % 0.29/0.58 (define @t136 () (or @t135 @t134 @t132 @t131)) % 0.29/0.58 (define @t137 () (forall (@list @t14 @t39 @t128 @t127) @t136)) % 0.29/0.58 (define @t138 () (@list @t39 @t128 @t127)) % 0.29/0.58 (define @t139 () (forall @t138 @t136)) % 0.29/0.58 (define @t140 () (lambda @t49 @t139)) % 0.29/0.58 (define @t141 () (_ @t140 @t14)) % 0.29/0.58 (define @t142 () (forall @t49 @t141)) % 0.29/0.58 (define @t143 () (_ @t19 @t14)) % 0.29/0.58 (define @t144 () (lambda @t95 (forall @t49 @t143))) % 0.29/0.58 (define @t145 () (or @t132 @t131)) % 0.29/0.58 (define @t146 () (or @t135 @t134)) % 0.29/0.58 (define @t147 () (or @t146 @t145)) % 0.29/0.58 (define @t148 () (forall @t138 @t147)) % 0.29/0.58 (define @t149 () (forall (@list @t128 @t127) @t147)) % 0.29/0.58 (define @t150 () (forall (@list @t127) @t145)) % 0.29/0.58 (define @t151 () (@list @t51)) % 0.29/0.58 (define @t152 () (forall (@list @t128) @t146)) % 0.29/0.58 (define @t153 () (or @t152 @t150)) % 0.29/0.58 (define @t154 () (not (_ @t3 @t51 @t100))) % 0.29/0.58 (define @t155 () (_ @t3 @t14 @t51)) % 0.29/0.58 (define @t156 () (not @t155)) % 0.29/0.58 (define @t157 () (not (_ @t3 @t51 @t107))) % 0.29/0.58 (define @t158 () (or (forall @t56 (or @t156 (not (forall @t109 (or @t157 @t133))))) (forall @t56 (or @t156 (not (forall @t103 (or @t154 @t130))))))) % 0.29/0.58 (define @t159 () (not (_ @t2 @t100))) % 0.29/0.58 (define @t160 () (not (forall @t103 (or @t154 @t159)))) % 0.29/0.58 (define @t161 () (not (_ @t3 @t1 @t51))) % 0.29/0.58 (define @t162 () (forall @t56 (or @t161 @t160))) % 0.29/0.58 (define @t163 () (_ @t2 @t107)) % 0.29/0.58 (define @t164 () (forall @t109 (or @t157 @t163))) % 0.29/0.58 (define @t165 () (forall @t56 (or @t161 (not @t164)))) % 0.29/0.58 (define @t166 () (or @t165 @t162)) % 0.29/0.58 (define @t167 () (lambda @t6 @t166)) % 0.29/0.58 (define @t168 () (_ @t167 @t39 @t14)) % 0.29/0.58 (define @t169 () (forall @t43 @t168)) % 0.29/0.58 (define @t170 () (lambda @t49 @t169)) % 0.29/0.58 (define @t171 () (_ @t40 @t39 @t14)) % 0.29/0.58 (define @t172 () (lambda @t45 (forall @t43 @t171))) % 0.29/0.58 (define @t173 () (@list @t1)) % 0.29/0.58 (define @t174 () (lambda @t49 (forall @t56 (or @t156 @t160)))) % 0.29/0.58 (define @t175 () (_ @t174 @t1)) % 0.29/0.58 (define @t176 () (or @t165 @t175)) % 0.29/0.58 (define @t177 () (lambda @t173 @t176)) % 0.29/0.58 (define @t178 () (_ @t24 @t1)) % 0.29/0.58 (define @t179 () (@list @t24 @t1)) % 0.29/0.58 (define @t180 () (_ @t2 @t51)) % 0.29/0.58 (define @t181 () (forall @t56 (or @t161 (not @t180)))) % 0.29/0.58 (define @t182 () (not @t181)) % 0.29/0.58 (define @t183 () (lambda @t173 @t182)) % 0.29/0.58 (define @t184 () (or @t156 (_ @t183 @t51))) % 0.29/0.58 (define @t185 () (forall @t56 @t184)) % 0.29/0.58 (define @t186 () (lambda @t49 @t185)) % 0.29/0.58 (define @t187 () (_ @t19 @t51)) % 0.29/0.58 (define @t188 () (forall @t56 (or @t156 @t187))) % 0.29/0.58 (define @t189 () (lambda @t22 @t188)) % 0.29/0.58 (define @t190 () (not @t187)) % 0.29/0.58 (define @t191 () (not (forall @t56 (or @t161 @t190)))) % 0.29/0.58 (define @t192 () (lambda (@list @t19 @t1) @t191)) % 0.29/0.58 (define @t193 () (_ (lambda @t60 @t191) @t3)) % 0.29/0.58 (define @t194 () (_ (lambda @t58 @t188) @t3)) % 0.29/0.58 (define @t195 () (not @t165)) % 0.29/0.58 (define @t196 () (lambda @t173 @t195)) % 0.29/0.58 (define @t197 () (_ @t196 @t1)) % 0.29/0.58 (define @t198 () (not @t197)) % 0.29/0.58 (define @t199 () (or @t198 @t178)) % 0.29/0.58 (define @t200 () (lambda @t179 @t199)) % 0.29/0.58 (define @t201 () (or (not (_ @t19 @t1)) @t178)) % 0.29/0.58 (define @t202 () (lambda @t30 @t201)) % 0.29/0.58 (define @t203 () (forall @t56 (or @t156 @t180))) % 0.29/0.58 (define @t204 () (lambda @t49 @t203)) % 0.29/0.58 (define @t205 () (not (_ @t204 @t51))) % 0.29/0.58 (define @t206 () (or @t161 @t205)) % 0.29/0.58 (define @t207 () (forall @t56 @t206)) % 0.29/0.58 (define @t208 () (not @t207)) % 0.29/0.58 (define @t209 () (lambda @t173 @t208)) % 0.29/0.58 (define @t210 () (lambda @t6 (_ (_ (_ @t202 (_ @t193 (_ @t194 @t2))) (_ @t194 (_ @t193 @t2))) @t1))) % 0.29/0.58 (define @t211 () (_ (lambda @t9 @t117) @t3)) % 0.29/0.58 (define @t212 () (=> @t211 (_ @t144 (_ @t172 @t210)))) % 0.29/0.58 (define @t213 () (forall @t9 @t212)) % 0.29/0.58 (define @t214 () (forall @t56 (or @t156 @t190))) % 0.29/0.58 (define @t215 () (lambda @t49 @t214)) % 0.29/0.58 (define @t216 () (_ @t215 @t14)) % 0.29/0.58 (define @t217 () (not @t216)) % 0.29/0.58 (define @t218 () (lambda @t49 @t217)) % 0.29/0.58 (define @t219 () (not @t52)) % 0.29/0.58 (define @t220 () (or @t156 @t219)) % 0.29/0.58 (define @t221 () (lambda @t49 @t21)) % 0.29/0.58 (define @t222 () (_ @t221 @t51)) % 0.29/0.58 (define @t223 () (or @t156 @t222)) % 0.29/0.58 (define @t224 () (forall @t56 @t223)) % 0.29/0.58 (define @t225 () (lambda @t49 @t224)) % 0.29/0.58 (define @t226 () (or @t21 @t25)) % 0.29/0.58 (define @t227 () (lambda @t49 @t226)) % 0.29/0.58 (define @t228 () (@list @t24 @t14)) % 0.29/0.58 (define @t229 () (_ @t221 @t14)) % 0.29/0.58 (define @t230 () (or @t229 @t25)) % 0.29/0.58 (define @t231 () (lambda @t228 @t230)) % 0.29/0.58 (define @t232 () (not @t73)) % 0.29/0.58 (define @t233 () (not @t68)) % 0.29/0.58 (define @t234 () (or @t233 @t232 @t114)) % 0.29/0.58 (define @t235 () (not @t87)) % 0.29/0.58 (define @t236 () (not @t88)) % 0.29/0.58 (define @t237 () (or @t236 @t235)) % 0.29/0.58 (define @t238 () (forall @t56 (not @t89))) % 0.29/0.58 (define @t239 () (not @t238)) % 0.29/0.58 (define @t240 () (forall @t122 @t119)) % 0.29/0.58 (define @t241 () (@quantifiers_skolemize @t240 0)) % 0.29/0.58 (define @t242 () (forall @t75 (or (not (_ @t241 @t62 @t66)) (not (_ @t241 @t62 @t72)) (not (forall @t56 (or (not (_ @t241 @t66 @t51)) (not (_ @t241 @t72 @t51)))))))) % 0.29/0.58 (define @t243 () (@quantifiers_skolemize @t240 2)) % 0.29/0.58 (define @t244 () (@quantifiers_skolemize @t240 4)) % 0.29/0.58 (define @t245 () (forall @t103 (or (not (_ @t241 @t244 @t100)) (not (_ @t243 @t100))))) % 0.29/0.58 (define @t246 () (not @t245)) % 0.29/0.58 (define @t247 () (@quantifiers_skolemize @t240 1)) % 0.29/0.58 (define @t248 () (_ @t241 @t247 @t244)) % 0.29/0.58 (define @t249 () (not @t248)) % 0.29/0.58 (define @t250 () (@quantifiers_skolemize @t240 3)) % 0.29/0.58 (define @t251 () (forall @t109 (or (not (_ @t241 @t250 @t107)) (_ @t243 @t107)))) % 0.29/0.58 (define @t252 () (not @t251)) % 0.29/0.58 (define @t253 () (_ @t241 @t247 @t250)) % 0.29/0.58 (define @t254 () (not @t253)) % 0.29/0.58 (define @t255 () (not @t242)) % 0.29/0.58 (define @t256 () (or @t255 @t254 @t252 @t249 @t246)) % 0.29/0.58 (define @t257 () (@list true)) % 0.29/0.58 (define @t258 () (@list @t256)) % 0.29/0.58 (define @t259 () (forall @t56 (or (not (_ @t241 @t250 @t51)) (not (_ @t241 @t244 @t51))))) % 0.29/0.58 (define @t260 () (not @t259)) % 0.29/0.58 (define @t261 () (or @t254 @t249 @t260)) % 0.29/0.58 (define @t262 () (@list false false false)) % 0.29/0.58 (define @t263 () (@quantifiers_skolemize @t259 0)) % 0.29/0.58 (define @t264 () (_ @t241 @t244 @t263)) % 0.29/0.58 (define @t265 () (not @t264)) % 0.29/0.58 (define @t266 () (_ @t241 @t250 @t263)) % 0.29/0.58 (define @t267 () (not @t266)) % 0.29/0.58 (define @t268 () (or @t267 @t265)) % 0.29/0.58 (define @t269 () (@list @t268)) % 0.29/0.58 (define @t270 () (@list @t263)) % 0.29/0.58 (define @t271 () (_ @t243 @t263)) % 0.29/0.58 (define @t272 () (or @t267 @t271)) % 0.29/0.58 (define @t273 () (not @t271)) % 0.29/0.58 (define @t274 () (or @t265 @t273)) % 0.29/0.58 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.29/0.58 (assume @p2 @t11) % 0.29/0.58 (assume @p3 true) % 0.29/0.58 (step @p4 (= tptp.meq_ind @t15) :rule refl :args (@t15)) % 0.29/0.58 (step @p5 (= tptp.meq_prop @t18) :rule refl :args (@t18)) % 0.29/0.58 (step @p6 (= tptp.mnot @t23) :rule refl :args (@t23)) % 0.29/0.58 (step @p7 (= tptp.mor @t26) :rule refl :args (@t26)) % 0.29/0.58 (step @p8 (= tptp.mand @t31) :rule refl :args (@t31)) % 0.29/0.58 (step @p9 (= tptp.mimplies @t32) :rule refl :args (@t32)) % 0.29/0.58 (step @p10 (= tptp.mimplied @t33) :rule refl :args (@t33)) % 0.29/0.58 (step @p11 (= tptp.mequiv @t34) :rule refl :args (@t34)) % 0.29/0.58 (step @p12 (= tptp.mxor @t35) :rule refl :args (@t35)) % 0.29/0.58 (step @p13 (= tptp.mforall_ind @t38) :rule refl :args (@t38)) % 0.29/0.58 (step @p14 (= tptp.mforall_prop @t46) :rule refl :args (@t46)) % 0.29/0.58 (step @p15 (= tptp.mexists_ind @t47) :rule refl :args (@t47)) % 0.29/0.58 (step @p16 (= tptp.mexists_prop @t48) :rule refl :args (@t48)) % 0.29/0.58 (step @p17 (= tptp.mtrue @t50) :rule refl :args (@t50)) % 0.29/0.58 (step @p18 (= tptp.mbox @t59) :rule refl :args (@t59)) % 0.29/0.58 (step @p19 (= tptp.mdia @t61) :rule refl :args (@t61)) % 0.29/0.58 (step @p20 (= tptp.mreflexive @t65) :rule refl :args (@t65)) % 0.29/0.58 (step @p21 (= tptp.msymmetric @t69) :rule refl :args (@t69)) % 0.29/0.58 (step @p22 (= tptp.mserial @t71) :rule refl :args (@t71)) % 0.29/0.58 (step @p23 (= tptp.mtransitive @t76) :rule refl :args (@t76)) % 0.29/0.58 (step @p24 (= tptp.meuclidean @t78) :rule refl :args (@t78)) % 0.29/0.58 (step @p25 (= tptp.mpartially_functional @t80) :rule refl :args (@t80)) % 0.29/0.58 (step @p26 (= tptp.mfunctional @t82) :rule refl :args (@t82)) % 0.29/0.58 (step @p27 (= tptp.mweakly_dense @t85) :rule refl :args (@t85)) % 0.29/0.58 (step @p28 (= tptp.mweakly_connected @t86) :rule refl :args (@t86)) % 0.29/0.58 (step @p29 (= tptp.mweakly_directed @t93) :rule refl :args (@t93)) % 0.29/0.58 (step @p30 (= tptp.mvalid @t96) :rule refl :args (@t96)) % 0.29/0.58 (step @p31 (= tptp.minvalid @t97) :rule refl :args (@t97)) % 0.29/0.58 (step @p32 (= tptp.msatisfiable @t98) :rule refl :args (@t98)) % 0.29/0.58 (step @p33 (= tptp.mcountersatisfiable @t99) :rule refl :args (@t99)) % 0.29/0.58 (step @p34 :rule aci_norm :args ((= @t121 @t119))) % 0.29/0.58 (step @p35 :rule cong :premises (@p34) :args (@t123)) % 0.29/0.58 (step @p36 :rule quant-merge-prenex :args ((= (forall @t9 @t125) @t123))) % 0.29/0.58 (step @p37 :rule alpha_equiv :args (@t126 (@list @t105 @t101 @t108 @t102) (@list @t14 @t39 @t128 @t127))) % 0.29/0.58 (step @p38 :rule refl :args (@t118)) % 0.29/0.58 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t129)) % 0.29/0.58 (step @p40 :rule quant-miniscope-or :args ((= @t125 @t129))) % 0.29/0.58 (step @p41 :rule trans :premises (@p40 @p39)) % 0.29/0.58 (step @p42 :rule symm :premises (@p41)) % 0.29/0.58 (step @p43 :rule cong :premises (@p42) :args ((forall @t9 (or @t118 @t137)))) % 0.29/0.58 (step @p44 :rule trans :premises (@p43 @p36)) % 0.29/0.58 (step @p45 :rule trans :premises (@p44 @p35)) % 0.29/0.58 (step @p46 :rule bool-impl-elim :args (@t117 @t137)) % 0.29/0.58 (step @p47 :rule cong :premises (@p46) :args ((forall @t9 (=> @t117 @t137)))) % 0.29/0.58 (step @p48 :rule trans :premises (@p47 @p45)) % 0.29/0.58 (step @p49 :rule quant-merge-prenex :args ((= (forall @t49 @t139) @t137))) % 0.29/0.58 (step @p50 :rule beta-reduce :args ((= @t141 @t139))) % 0.29/0.58 (step @p51 :rule cong :premises (@p50) :args (@t142)) % 0.29/0.58 (step @p52 :rule trans :premises (@p51 @p49)) % 0.29/0.58 (step @p53 :rule beta-reduce :args ((= (_ @t144 @t140) @t142))) % 0.29/0.58 (step @p54 :rule trans :premises (@p53 @p52)) % 0.29/0.58 (step @p55 :rule aci_norm :args ((= @t147 @t136))) % 0.29/0.58 (step @p56 :rule cong :premises (@p55) :args (@t148)) % 0.29/0.58 (step @p57 :rule quant-merge-prenex :args ((= (forall @t43 @t149) @t148))) % 0.29/0.58 (step @p58 :rule alpha_equiv :args (@t150 (@list @t127) @t151)) % 0.29/0.58 (step @p59 :rule alpha_equiv :args (@t152 (@list @t128) @t151)) % 0.29/0.58 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t153)) % 0.29/0.58 (step @p61 :rule quant-miniscope-or :args ((= @t149 @t153))) % 0.29/0.58 (step @p62 :rule trans :premises (@p61 @p60)) % 0.29/0.58 (step @p63 :rule symm :premises (@p62)) % 0.29/0.58 (step @p64 :rule cong :premises (@p63) :args ((forall @t43 @t158))) % 0.29/0.58 (step @p65 :rule trans :premises (@p64 @p57)) % 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(@p304 @p334) :args ((or @t256 (not @t246)))) % 0.29/0.58 (step @p336 :rule cnf_or_neg :args (@t256 4)) % 0.29/0.58 (step @p337 :rule eq_resolve :premises (@p336 @p335)) % 0.29/0.58 (step @p338 :rule reordering :premises (@p337) :args ((or @t245 @t256))) % 0.29/0.58 (step @p339 :rule chain_m_resolution :premises (@p338 @p302) :args (@t245 @t257 @t258)) % 0.29/0.58 (step @p340 :rule instantiate :premises (@p339) :args (@t270)) % 0.29/0.58 (step @p341 :rule bool-double-not-elim :args (@t251)) % 0.29/0.58 (step @p342 :rule nary_cong :premises (@p304 @p341) :args ((or @t256 (not @t252)))) % 0.29/0.58 (step @p343 :rule cnf_or_neg :args (@t256 2)) % 0.29/0.58 (step @p344 :rule eq_resolve :premises (@p343 @p342)) % 0.29/0.58 (step @p345 :rule reordering :premises (@p344) :args ((or @t251 @t256))) % 0.29/0.58 (step @p346 :rule chain_m_resolution :premises (@p345 @p302) :args (@t251 @t257 @t258)) % 0.29/0.58 (step @p347 :rule instantiate :premises (@p346) :args (@t270)) % 0.29/0.58 (step @p348 :rule bool-double-not-elim :args (@t266)) % 0.29/0.58 (step @p349 :rule nary_cong :premises (@p328 @p348) :args ((or @t268 (not @t267)))) % 0.29/0.58 (step @p350 :rule cnf_or_neg :args (@t268 0)) % 0.29/0.58 (step @p351 :rule eq_resolve :premises (@p350 @p349)) % 0.29/0.58 (step @p352 :rule reordering :premises (@p351) :args ((or @t266 @t268))) % 0.29/0.58 (step @p353 :rule chain_m_resolution :premises (@p352 @p326) :args (@t266 @t257 @t269)) % 0.29/0.58 (step @p354 :rule cnf_or_pos :args (@t272)) % 0.29/0.58 (step @p355 :rule reordering :premises (@p354) :args ((or @t267 @t271 (not @t272)))) % 0.29/0.58 (step @p356 :rule chain_m_resolution :premises (@p355 @p353 @p347) :args (@t271 (@list false false) (@list @t266 @t272))) % 0.29/0.58 (step @p357 :rule cnf_or_pos :args (@t274)) % 0.29/0.58 (step @p358 :rule reordering :premises (@p357) :args ((or @t265 @t273 (not @t274)))) % 0.29/0.58 (step @p359 false :rule chain_m_resolution :premises (@p358 @p356 @p340 @p333) :args (false @t262 (@list @t271 @t274 @t264))) % 0.29/0.58 ) % 0.29/0.58 % SZS output end Proof % 0.29/0.58 % cvc5 exiting %------------------------------------------------------------------------------