%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL860^1 : 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 : n018.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 11:24:03 AM UTC 2026 % Result : Theorem 0.30s 0.62s % Output : Proof 0.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL860^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.34 % Computer : n018.cluster.edu % 0.07/0.34 % Model : x86_64 x86_64 % 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.34 % Memory : 8046.5625MB % 0.07/0.34 % OS : Linux 6.8.0-71-generic % 0.07/0.35 % CPULimit : 300 % 0.07/0.35 % WCLimit : 300 % 0.07/0.35 % DateTime : Sat Sep 5 05:13:03 UTC 2026 % 0.07/0.35 % CPUTime : % 0.13/0.42 %----Proving TH0 % 0.30/0.62 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.30/0.62 % SZS status Theorem % 0.30/0.62 % SZS output start Proof % 0.30/0.62 ( % 0.30/0.62 (declare-sort $$unsorted 0) % 0.30/0.62 (declare-sort tptp.mu 0) % 0.30/0.62 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.30/0.62 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.30/0.62 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.30/0.62 (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)))))) % 0.30/0.62 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.30/0.62 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.30/0.62 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.30/0.62 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.30/0.62 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.30/0.62 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.30/0.62 (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))))))) % 0.30/0.62 (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))))))) % 0.30/0.62 (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)))))) % 0.30/0.62 (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)))))) % 0.30/0.62 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.30/0.62 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.30/0.62 (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)))))) % 0.30/0.62 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.30/0.62 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.30/0.62 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.30/0.62 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.30/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.30/0.62 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.30/0.62 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.30/0.62 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.30/0.62 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.30/0.62 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.30/0.62 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.30/0.62 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.30/0.62 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.30/0.62 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.30/0.62 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.30/0.62 (define @t2 () (_ tptp.meuclidean @t1)) % 0.30/0.62 (define @t3 () (_ tptp.mreflexive @t1)) % 0.30/0.62 (define @t4 () (and @t3 (_ tptp.mtransitive @t1) (_ tptp.msymmetric @t1) @t2)) % 0.30/0.62 (define @t5 () (and @t3 @t2)) % 0.30/0.62 (define @t6 () (= @t5 @t4)) % 0.30/0.62 (define @t7 () (@list @t1)) % 0.30/0.62 (define @t8 () (forall @t7 @t6)) % 0.30/0.62 (define @t9 () (not @t8)) % 0.30/0.62 (define @t10 () (@var "Y" tptp.mu)) % 0.30/0.62 (define @t11 () (@var "X" tptp.mu)) % 0.30/0.62 (define @t12 () (@var "W" $$unsorted)) % 0.30/0.62 (define @t13 () (lambda (@list @t11 @t10 @t12) (= @t11 @t10))) % 0.30/0.62 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.30/0.62 (define @t15 () (@var "X" (-> $$unsorted Bool))) % 0.30/0.62 (define @t16 () (lambda (@list @t15 @t14 @t12) (= (_ @t15 @t12) (_ @t14 @t12)))) % 0.30/0.62 (define @t17 () (@var "Phi" (-> $$unsorted Bool))) % 0.30/0.62 (define @t18 () (_ @t17 @t12)) % 0.30/0.62 (define @t19 () (not @t18)) % 0.30/0.62 (define @t20 () (lambda (@list @t17 @t12) @t19)) % 0.30/0.62 (define @t21 () (@var "Psi" (-> $$unsorted Bool))) % 0.30/0.62 (define @t22 () (lambda (@list @t17 @t21 @t12) (or @t18 (_ @t21 @t12)))) % 0.30/0.62 (define @t23 () (@var "__flatten_var_0" $$unsorted)) % 0.30/0.62 (define @t24 () (_ tptp.mnot @t21)) % 0.30/0.62 (define @t25 () (_ tptp.mnot @t17)) % 0.30/0.62 (define @t26 () (_ tptp.mor @t25)) % 0.30/0.62 (define @t27 () (@list @t17 @t21 @t23)) % 0.30/0.62 (define @t28 () (lambda @t27 (_ (_ tptp.mnot (_ @t26 @t24)) @t23))) % 0.30/0.62 (define @t29 () (lambda @t27 (_ (_ @t26 @t21) @t23))) % 0.30/0.62 (define @t30 () (lambda @t27 (_ (_ (_ tptp.mor @t24) @t17) @t23))) % 0.30/0.62 (define @t31 () (lambda @t27 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t17) @t21)) (_ (_ tptp.mimplies @t21) @t17)) @t23))) % 0.30/0.62 (define @t32 () (lambda @t27 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t17) @t21)) @t23))) % 0.30/0.62 (define @t33 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.30/0.62 (define @t34 () (_ @t33 @t11)) % 0.30/0.62 (define @t35 () (lambda (@list @t33 @t12) (forall (@list @t11) (_ @t34 @t12)))) % 0.30/0.62 (define @t36 () (@var "P" (-> $$unsorted Bool))) % 0.30/0.62 (define @t37 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.30/0.62 (define @t38 () (_ @t37 @t36)) % 0.30/0.62 (define @t39 () (lambda (@list @t37 @t12) (forall (@list @t36) (_ @t38 @t12)))) % 0.30/0.62 (define @t40 () (lambda (@list @t33 @t23) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t11 @t23) (_ (_ tptp.mnot @t34) @t23)))) @t23))) % 0.30/0.62 (define @t41 () (lambda (@list @t37 @t23) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t36 @t23) (_ (_ tptp.mnot @t38) @t23)))) @t23))) % 0.30/0.62 (define @t42 () (@list @t12)) % 0.30/0.62 (define @t43 () (lambda @t42 true)) % 0.30/0.62 (define @t44 () (@var "V" $$unsorted)) % 0.30/0.62 (define @t45 () (@list @t44)) % 0.30/0.62 (define @t46 () (lambda (@list @t1 @t17 @t12) (forall @t45 (or (not (_ (_ @t1 @t12) @t44)) (_ @t17 @t44))))) % 0.30/0.62 (define @t47 () (lambda (@list @t1 @t17 @t23) (_ (_ tptp.mnot (_ (_ tptp.mbox @t1) @t25)) @t23))) % 0.30/0.62 (define @t48 () (@var "S" $$unsorted)) % 0.30/0.62 (define @t49 () (_ @t1 @t48)) % 0.30/0.62 (define @t50 () (_ @t49 @t48)) % 0.30/0.62 (define @t51 () (@list @t48)) % 0.30/0.62 (define @t52 () (forall @t51 @t50)) % 0.30/0.62 (define @t53 () (lambda @t7 @t52)) % 0.30/0.62 (define @t54 () (@var "T" $$unsorted)) % 0.30/0.62 (define @t55 () (_ @t1 @t54)) % 0.30/0.62 (define @t56 () (_ @t55 @t48)) % 0.30/0.62 (define @t57 () (_ @t49 @t54)) % 0.30/0.62 (define @t58 () (@list @t48 @t54)) % 0.30/0.62 (define @t59 () (forall @t58 (=> @t57 @t56))) % 0.30/0.62 (define @t60 () (lambda @t7 @t59)) % 0.30/0.62 (define @t61 () (@list @t54)) % 0.30/0.62 (define @t62 () (lambda @t7 (forall @t51 (exists @t61 @t57)))) % 0.30/0.62 (define @t63 () (@var "U" $$unsorted)) % 0.30/0.62 (define @t64 () (_ @t49 @t63)) % 0.30/0.62 (define @t65 () (_ @t55 @t63)) % 0.30/0.62 (define @t66 () (and @t57 @t65)) % 0.30/0.62 (define @t67 () (@list @t48 @t54 @t63)) % 0.30/0.62 (define @t68 () (forall @t67 (=> @t66 @t64))) % 0.30/0.62 (define @t69 () (lambda @t7 @t68)) % 0.30/0.62 (define @t70 () (and @t57 @t64)) % 0.30/0.62 (define @t71 () (forall @t67 (=> @t70 @t65))) % 0.30/0.62 (define @t72 () (lambda @t7 @t71)) % 0.30/0.62 (define @t73 () (= @t54 @t63)) % 0.30/0.62 (define @t74 () (lambda @t7 (forall @t67 (=> @t70 @t73)))) % 0.30/0.62 (define @t75 () (@list @t63)) % 0.30/0.62 (define @t76 () (lambda @t7 (forall @t51 (exists @t61 (and @t57 (forall @t75 (=> @t64 @t73))))))) % 0.30/0.62 (define @t77 () (_ @t1 @t63)) % 0.30/0.62 (define @t78 () (_ @t77 @t54)) % 0.30/0.62 (define @t79 () (lambda @t7 (forall @t67 (=> @t57 (exists @t75 (and @t64 @t78)))))) % 0.30/0.62 (define @t80 () (lambda @t7 (forall @t67 (=> @t70 (or @t65 @t73 @t78))))) % 0.30/0.62 (define @t81 () (lambda @t7 (forall @t67 (=> @t70 (exists @t45 (and (_ @t55 @t44) (_ @t77 @t44))))))) % 0.30/0.62 (define @t82 () (@list @t17)) % 0.30/0.62 (define @t83 () (lambda @t82 (forall @t42 @t18))) % 0.30/0.62 (define @t84 () (lambda @t82 (forall @t42 @t19))) % 0.30/0.62 (define @t85 () (lambda @t82 (exists @t42 @t18))) % 0.30/0.62 (define @t86 () (lambda @t82 (exists @t42 @t19))) % 0.30/0.62 (define @t87 () (_ @t1 @t54 @t63)) % 0.30/0.62 (define @t88 () (_ @t1 @t48 @t63)) % 0.30/0.62 (define @t89 () (_ @t1 @t48 @t54)) % 0.30/0.62 (define @t90 () (not @t89)) % 0.30/0.62 (define @t91 () (forall @t67 (or @t90 (not @t88) @t87))) % 0.30/0.63 (define @t92 () (_ (lambda @t7 @t91) @t1)) % 0.30/0.63 (define @t93 () (_ @t1 @t48 @t48)) % 0.30/0.63 (define @t94 () (forall @t51 @t93)) % 0.30/0.63 (define @t95 () (_ (lambda @t7 @t94) @t1)) % 0.30/0.63 (define @t96 () (and @t95 @t92)) % 0.30/0.63 (define @t97 () (_ @t1 @t54 @t48)) % 0.30/0.63 (define @t98 () (forall @t58 (or @t90 @t97))) % 0.30/0.63 (define @t99 () (_ (lambda @t7 @t98) @t1)) % 0.30/0.63 (define @t100 () (forall @t67 (or @t90 (not @t87) @t88))) % 0.30/0.63 (define @t101 () (_ (lambda @t7 @t100) @t1)) % 0.30/0.63 (define @t102 () (and @t95 @t101 @t99 @t92)) % 0.30/0.63 (define @t103 () (forall @t7 (= @t96 @t102))) % 0.30/0.63 (define @t104 () (not @t64)) % 0.30/0.63 (define @t105 () (not @t57)) % 0.30/0.63 (define @t106 () (or @t105 @t104 @t65)) % 0.30/0.63 (define @t107 () (or @t105 @t56)) % 0.30/0.63 (define @t108 () (not @t65)) % 0.30/0.63 (define @t109 () (or @t105 @t108 @t64)) % 0.30/0.63 (define @t110 () (@quantifiers_skolemize (forall @t7 (= (and @t94 @t100 @t98 @t91) (and @t94 @t91))) 0)) % 0.30/0.63 (define @t111 () (forall @t51 (_ @t110 @t48 @t48))) % 0.30/0.63 (define @t112 () (not (_ @t110 @t48 @t54))) % 0.30/0.63 (define @t113 () (forall @t58 (or @t112 (_ @t110 @t54 @t48)))) % 0.30/0.63 (define @t114 () (@quantifiers_skolemize @t113 0)) % 0.30/0.63 (define @t115 () (_ @t110 @t114 @t114)) % 0.30/0.63 (define @t116 () (@quantifiers_skolemize @t113 1)) % 0.30/0.63 (define @t117 () (_ @t110 @t114 @t116)) % 0.30/0.63 (define @t118 () (_ @t110 @t116 @t114)) % 0.30/0.63 (define @t119 () (not @t117)) % 0.30/0.63 (define @t120 () (or @t119 @t118)) % 0.30/0.63 (define @t121 () (_ @t110 @t54 @t63)) % 0.30/0.63 (define @t122 () (_ @t110 @t48 @t63)) % 0.30/0.63 (define @t123 () (forall @t67 (or @t112 (not @t122) @t121))) % 0.30/0.63 (define @t124 () (forall @t67 (or @t112 (not @t121) @t122))) % 0.30/0.63 (define @t125 () (and @t111 @t124 @t113 @t123)) % 0.30/0.63 (define @t126 () (not @t125)) % 0.30/0.63 (define @t127 () (and @t111 @t123)) % 0.30/0.63 (define @t128 () (not @t127)) % 0.30/0.63 (define @t129 () (= @t125 @t127)) % 0.30/0.63 (define @t130 () (@list true true true)) % 0.30/0.63 (define @t131 () (not @t115)) % 0.30/0.63 (define @t132 () (or @t119 @t131 @t118)) % 0.30/0.63 (define @t133 () (not @t120)) % 0.30/0.63 (define @t134 () (not @t113)) % 0.30/0.63 (define @t135 () (not @t124)) % 0.30/0.63 (define @t136 () (not @t111)) % 0.30/0.63 (define @t137 () (@quantifiers_skolemize @t124 1)) % 0.30/0.63 (define @t138 () (@quantifiers_skolemize @t124 0)) % 0.30/0.63 (define @t139 () (_ @t110 @t137 @t138)) % 0.30/0.63 (define @t140 () (_ @t110 @t138 @t137)) % 0.30/0.63 (define @t141 () (not @t140)) % 0.30/0.63 (define @t142 () (or @t141 @t139)) % 0.30/0.63 (define @t143 () (@quantifiers_skolemize @t124 2)) % 0.30/0.63 (define @t144 () (_ @t110 @t138 @t143)) % 0.30/0.63 (define @t145 () (_ @t110 @t137 @t143)) % 0.30/0.63 (define @t146 () (not @t145)) % 0.30/0.63 (define @t147 () (or @t141 @t146 @t144)) % 0.30/0.63 (define @t148 () (not @t147)) % 0.30/0.63 (define @t149 () (not @t139)) % 0.30/0.63 (define @t150 () (or @t149 @t146 @t144)) % 0.30/0.63 (define @t151 () (@list true)) % 0.30/0.63 (define @t152 () (@list @t111)) % 0.30/0.63 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.30/0.63 (assume @p2 @t9) % 0.30/0.63 (assume @p3 true) % 0.30/0.63 (step @p4 (= tptp.meq_ind @t13) :rule refl :args (@t13)) % 0.30/0.63 (step @p5 (= tptp.meq_prop @t16) :rule refl :args (@t16)) % 0.30/0.63 (step @p6 (= tptp.mnot @t20) :rule refl :args (@t20)) % 0.30/0.63 (step @p7 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.30/0.63 (step @p8 (= tptp.mand @t28) :rule refl :args (@t28)) % 0.30/0.63 (step @p9 (= tptp.mimplies @t29) :rule refl :args (@t29)) % 0.30/0.63 (step @p10 (= tptp.mimplied @t30) :rule refl :args (@t30)) % 0.30/0.63 (step @p11 (= tptp.mequiv @t31) :rule refl :args (@t31)) % 0.30/0.63 (step @p12 (= tptp.mxor @t32) :rule refl :args (@t32)) % 0.30/0.63 (step @p13 (= tptp.mforall_ind @t35) :rule refl :args (@t35)) % 0.30/0.63 (step @p14 (= tptp.mforall_prop @t39) :rule refl :args (@t39)) % 0.30/0.63 (step @p15 (= tptp.mexists_ind @t40) :rule refl :args (@t40)) % 0.30/0.63 (step @p16 (= tptp.mexists_prop @t41) :rule refl :args (@t41)) % 0.30/0.63 (step @p17 (= tptp.mtrue @t43) :rule refl :args (@t43)) % 0.30/0.63 (step @p18 (= tptp.mbox @t46) :rule refl :args (@t46)) % 0.30/0.63 (step @p19 (= tptp.mdia @t47) :rule refl :args (@t47)) % 0.30/0.63 (step @p20 (= tptp.mreflexive @t53) :rule refl :args (@t53)) % 0.30/0.63 (step @p21 (= tptp.msymmetric @t60) :rule refl :args (@t60)) % 0.30/0.63 (step @p22 (= tptp.mserial @t62) :rule refl :args (@t62)) % 0.30/0.63 (step @p23 (= tptp.mtransitive @t69) :rule refl :args (@t69)) % 0.30/0.63 (step @p24 (= tptp.meuclidean @t72) :rule refl :args (@t72)) % 0.30/0.63 (step @p25 (= tptp.mpartially_functional @t74) :rule refl :args (@t74)) % 0.30/0.63 (step @p26 (= tptp.mfunctional @t76) :rule refl :args (@t76)) % 0.30/0.63 (step @p27 (= tptp.mweakly_dense @t79) :rule refl :args (@t79)) % 0.30/0.63 (step @p28 (= tptp.mweakly_connected @t80) :rule refl :args (@t80)) % 0.30/0.63 (step @p29 (= tptp.mweakly_directed @t81) :rule refl :args (@t81)) % 0.30/0.63 (step @p30 (= tptp.mvalid @t83) :rule refl :args (@t83)) % 0.30/0.63 (step @p31 (= tptp.minvalid @t84) :rule refl :args (@t84)) % 0.30/0.63 (step @p32 (= tptp.msatisfiable @t85) :rule refl :args (@t85)) % 0.30/0.63 (step @p33 (= tptp.mcountersatisfiable @t86) :rule refl :args (@t86)) % 0.30/0.63 (step @p34 :rule beta-reduce :args ((= @t92 @t91))) % 0.30/0.63 (step @p35 :rule beta-reduce :args ((= @t95 @t94))) % 0.30/0.63 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t96)) % 0.30/0.63 (step @p37 :rule beta-reduce :args ((= @t99 @t98))) % 0.30/0.63 (step @p38 :rule beta-reduce :args ((= @t101 @t100))) % 0.30/0.63 (step @p39 :rule nary_cong :premises (@p35 @p38 @p37 @p34) :args (@t102)) % 0.30/0.63 (step @p40 :rule cong :premises (@p39 @p36) :args ((= @t102 @t96))) % 0.30/0.63 (step @p41 :rule eq-symm :args (@t96 @t102)) % 0.30/0.63 (step @p42 :rule trans :premises (@p41 @p40)) % 0.30/0.63 (step @p43 :rule cong :premises (@p42) :args (@t103)) % 0.30/0.63 (step @p44 :rule cong :premises (@p43) :args ((not @t103))) % 0.30/0.63 (step @p45 :rule refl :args (@t1)) % 0.30/0.63 (step @p46 :rule refl :args (@t87)) % 0.30/0.63 (step @p47 :rule refl :args (@t65)) % 0.30/0.63 (step @p48 :rule cong :premises (@p47 @p46) :args ((= @t65 @t87))) % 0.30/0.63 (step @p49 :rule symm :premises (@p48)) % 0.30/0.63 (step @p50 :rule eq_resolve :premises (@p47 @p49)) % 0.30/0.63 (step @p51 :rule refl :args (@t88)) % 0.30/0.63 (step @p52 :rule refl :args (@t64)) % 0.30/0.63 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t64 @t88))) % 0.30/0.63 (step @p54 :rule symm :premises (@p53)) % 0.30/0.63 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.30/0.63 (step @p56 :rule cong :premises (@p55) :args (@t104)) % 0.30/0.63 (step @p57 :rule refl :args (@t89)) % 0.30/0.63 (step @p58 :rule refl :args (@t57)) % 0.30/0.63 (step @p59 :rule cong :premises (@p58 @p57) :args ((= @t57 @t89))) % 0.30/0.63 (step @p60 :rule symm :premises (@p59)) % 0.30/0.63 (step @p61 :rule eq_resolve :premises (@p58 @p60)) % 0.30/0.63 (step @p62 :rule cong :premises (@p61) :args (@t105)) % 0.30/0.63 (step @p63 :rule nary_cong :premises (@p62 @p56 @p50) :args (@t106)) % 0.30/0.63 (step @p64 :rule cong :premises (@p63) :args ((forall @t67 @t106))) % 0.30/0.63 (step @p65 :rule aci_norm :args ((= (or (or @t105 @t104) @t65) @t106))) % 0.30/0.63 (step @p66 :rule bool-and-de-morgan :args (@t57 @t64 true)) % 0.30/0.63 (step @p67 :rule nary_cong :premises (@p66 @p47) :args ((or (not @t70) @t65))) % 0.30/0.63 (step @p68 :rule trans :premises (@p67 @p65)) % 0.30/0.63 (step @p69 :rule bool-impl-elim :args (@t70 @t65)) % 0.30/0.63 (step @p70 :rule trans :premises (@p69 @p68)) % 0.30/0.63 (step @p71 :rule cong :premises (@p70) :args (@t71)) % 0.30/0.63 (step @p72 :rule trans :premises (@p71 @p64)) % 0.30/0.63 (step @p73 :rule cong :premises (@p72) :args (@t72)) % 0.30/0.63 (step @p74 :rule trans :premises (@p24 @p73)) % 0.30/0.63 (step @p75 :rule ho_cong :premises (@p74 @p45)) % 0.30/0.63 (step @p76 :rule refl :args (@t97)) % 0.30/0.63 (step @p77 :rule refl :args (@t56)) % 0.30/0.63 (step @p78 :rule cong :premises (@p77 @p76) :args ((= @t56 @t97))) % 0.30/0.63 (step @p79 :rule symm :premises (@p78)) % 0.30/0.63 (step @p80 :rule eq_resolve :premises (@p77 @p79)) % 0.30/0.63 (step @p81 :rule nary_cong :premises (@p62 @p80) :args (@t107)) % 0.30/0.63 (step @p82 :rule cong :premises (@p81) :args ((forall @t58 @t107))) % 0.30/0.63 (step @p83 :rule bool-impl-elim :args (@t57 @t56)) % 0.30/0.63 (step @p84 :rule cong :premises (@p83) :args (@t59)) % 0.30/0.63 (step @p85 :rule trans :premises (@p84 @p82)) % 0.30/0.63 (step @p86 :rule cong :premises (@p85) :args (@t60)) % 0.30/0.63 (step @p87 :rule trans :premises (@p21 @p86)) % 0.30/0.63 (step @p88 :rule ho_cong :premises (@p87 @p45)) % 0.30/0.63 (step @p89 :rule cong :premises (@p50) :args (@t108)) % 0.30/0.63 (step @p90 :rule nary_cong :premises (@p62 @p89 @p55) :args (@t109)) % 0.30/0.63 (step @p91 :rule cong :premises (@p90) :args ((forall @t67 @t109))) % 0.30/0.63 (step @p92 :rule aci_norm :args ((= (or (or @t105 @t108) @t64) @t109))) % 0.30/0.63 (step @p93 :rule bool-and-de-morgan :args (@t57 @t65 true)) % 0.30/0.63 (step @p94 :rule nary_cong :premises (@p93 @p52) :args ((or (not @t66) @t64))) % 0.30/0.63 (step @p95 :rule trans :premises (@p94 @p92)) % 0.30/0.63 (step @p96 :rule bool-impl-elim :args (@t66 @t64)) % 0.30/0.63 (step @p97 :rule trans :premises (@p96 @p95)) % 0.30/0.63 (step @p98 :rule cong :premises (@p97) :args (@t68)) % 0.30/0.63 (step @p99 :rule trans :premises (@p98 @p91)) % 0.30/0.63 (step @p100 :rule cong :premises (@p99) :args (@t69)) % 0.30/0.63 (step @p101 :rule trans :premises (@p23 @p100)) % 0.30/0.63 (step @p102 :rule ho_cong :premises (@p101 @p45)) % 0.30/0.63 (step @p103 :rule refl :args (@t93)) % 0.30/0.63 (step @p104 :rule refl :args (@t50)) % 0.30/0.63 (step @p105 :rule cong :premises (@p104 @p103) :args ((= @t50 @t93))) % 0.30/0.63 (step @p106 :rule symm :premises (@p105)) % 0.30/0.63 (step @p107 :rule eq_resolve :premises (@p104 @p106)) % 0.30/0.63 (step @p108 :rule cong :premises (@p107) :args (@t52)) % 0.30/0.63 (step @p109 :rule cong :premises (@p108) :args (@t53)) % 0.30/0.63 (step @p110 :rule trans :premises (@p20 @p109)) % 0.30/0.63 (step @p111 :rule ho_cong :premises (@p110 @p45)) % 0.30/0.63 (step @p112 :rule nary_cong :premises (@p111 @p102 @p88 @p75) :args (@t4)) % 0.30/0.63 (step @p113 :rule nary_cong :premises (@p111 @p75) :args (@t5)) % 0.30/0.63 (step @p114 :rule cong :premises (@p113 @p112) :args (@t6)) % 0.30/0.63 (step @p115 :rule cong :premises (@p114) :args (@t8)) % 0.30/0.63 (step @p116 :rule cong :premises (@p115) :args (@t9)) % 0.30/0.63 (step @p117 :rule trans :premises (@p116 @p44)) % 0.30/0.63 (step @p118 :rule eq_resolve :premises (@p2 @p117)) % 0.30/0.63 (step @p119 :rule skolemize :premises (@p118)) % 0.30/0.63 (assume-push @p195 @t111) % 0.30/0.63 (step @p121 :rule instantiate :premises (@p195) :args ((@list @t114))) % 0.30/0.63 (step-pop @p196 :rule scope :premises (@p121)) % 0.30/0.63 (step @p122 :rule process_scope :premises (@p196) :args (@t115)) % 0.30/0.63 (step @p124 :rule implies_elim :premises (@p122)) % 0.30/0.63 (step @p125 :rule bool-double-not-elim :args (@t117)) % 0.30/0.63 (step @p126 :rule refl :args (@t120)) % 0.30/0.63 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((or @t120 (not @t119)))) % 0.30/0.63 (step @p128 :rule cnf_or_neg :args (@t120 0)) % 0.30/0.63 (step @p129 :rule eq_resolve :premises (@p128 @p127)) % 0.30/0.63 (step @p130 :rule reordering :premises (@p129) :args ((or @t117 @t120))) % 0.30/0.63 (step @p131 :rule cnf_or_neg :args (@t120 1)) % 0.30/0.63 (step @p132 :rule cnf_and_pos :args (@t125 3)) % 0.30/0.63 (step @p133 :rule reordering :premises (@p132) :args ((or @t123 @t126))) % 0.30/0.63 (step @p134 :rule cnf_and_pos :args (@t127 1)) % 0.30/0.63 (step @p135 :rule reordering :premises (@p134) :args ((or @t123 @t128))) % 0.30/0.63 (step @p136 :rule cnf_equiv_neg1 :args (@t129)) % 0.30/0.63 (step @p137 :rule reordering :premises (@p136) :args ((or @t125 @t127 @t129))) % 0.30/0.63 (step @p138 :rule chain_m_resolution :premises (@p137 @p119 @p135 @p133) :args (@t123 @t130 (@list @t129 @t127 @t125))) % 0.30/0.63 (step @p139 :rule instantiate :premises (@p138) :args ((@list @t114 @t116 @t114))) % 0.30/0.63 (step @p140 :rule cnf_or_pos :args (@t132)) % 0.30/0.63 (step @p141 :rule reordering :premises (@p140) :args ((or @t119 @t118 @t131 (not @t132)))) % 0.30/0.63 (step @p142 :rule chain_m_resolution :premises (@p141 @p139 @p131 @p130) :args ((or @t120 @t131) (@list false true false) (@list @t132 @t118 @t117))) % 0.30/0.63 (step @p143 :rule refl :args (@t133)) % 0.30/0.63 (step @p144 :rule bool-double-not-elim :args (@t113)) % 0.30/0.63 (step @p145 :rule nary_cong :premises (@p144 @p143) :args ((or (not @t134) @t133))) % 0.30/0.63 (assume-push @p197 @t134) % 0.30/0.63 (step @p147 :rule skolemize :premises (@p197)) % 0.30/0.63 (step-pop @p198 :rule scope :premises (@p147)) % 0.30/0.63 (step @p148 :rule process_scope :premises (@p198) :args (@t133)) % 0.30/0.63 (step @p150 :rule implies_elim :premises (@p148)) % 0.30/0.63 (step @p151 :rule eq_resolve :premises (@p150 @p145)) % 0.30/0.63 (step @p152 :rule cnf_and_neg :args (@t127)) % 0.30/0.63 (step @p153 :rule cnf_and_neg :args (@t125)) % 0.30/0.63 (step @p154 :rule cnf_equiv_neg2 :args (@t129)) % 0.30/0.63 (step @p155 :rule chain_m_resolution :premises (@p154 @p119 @p153 @p152) :args ((or @t136 @t135 @t134 (not @t123)) (@list true false false) (@list @t129 @t125 @t127))) % 0.30/0.63 (assume-push @p199 @t113) % 0.30/0.63 (step @p157 :rule instantiate :premises (@p199) :args ((@list @t138 @t137))) % 0.30/0.63 (step-pop @p200 :rule scope :premises (@p157)) % 0.30/0.63 (step @p158 :rule process_scope :premises (@p200) :args (@t142)) % 0.30/0.63 (step @p160 :rule implies_elim :premises (@p158)) % 0.30/0.63 (step @p161 :rule refl :args (@t148)) % 0.30/0.63 (step @p162 :rule bool-double-not-elim :args (@t124)) % 0.30/0.63 (step @p163 :rule nary_cong :premises (@p162 @p161) :args ((or (not @t135) @t148))) % 0.30/0.63 (assume-push @p201 @t135) % 0.30/0.63 (step @p165 :rule skolemize :premises (@p201)) % 0.30/0.63 (step-pop @p202 :rule scope :premises (@p165)) % 0.30/0.63 (step @p166 :rule process_scope :premises (@p202) :args (@t148)) % 0.30/0.63 (step @p168 :rule implies_elim :premises (@p166)) % 0.30/0.63 (step @p169 :rule eq_resolve :premises (@p168 @p163)) % 0.30/0.63 (step @p170 :rule bool-double-not-elim :args (@t140)) % 0.30/0.63 (step @p171 :rule refl :args (@t147)) % 0.30/0.63 (step @p172 :rule nary_cong :premises (@p171 @p170) :args ((or @t147 (not @t141)))) % 0.30/0.63 (step @p173 :rule cnf_or_neg :args (@t147 0)) % 0.30/0.63 (step @p174 :rule eq_resolve :premises (@p173 @p172)) % 0.30/0.63 (step @p175 :rule reordering :premises (@p174) :args ((or @t140 @t147))) % 0.30/0.63 (step @p176 :rule bool-double-not-elim :args (@t145)) % 0.30/0.63 (step @p177 :rule nary_cong :premises (@p171 @p176) :args ((or @t147 (not @t146)))) % 0.30/0.63 (step @p178 :rule cnf_or_neg :args (@t147 1)) % 0.30/0.63 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.30/0.63 (step @p180 :rule reordering :premises (@p179) :args ((or @t145 @t147))) % 0.30/0.63 (step @p181 :rule cnf_or_neg :args (@t147 2)) % 0.30/0.63 (step @p182 :rule cnf_or_pos :args (@t142)) % 0.30/0.63 (step @p183 :rule reordering :premises (@p182) :args ((or @t141 @t139 (not @t142)))) % 0.30/0.63 (step @p184 :rule instantiate :premises (@p138) :args ((@list @t137 @t138 @t143))) % 0.30/0.63 (step @p185 :rule cnf_or_pos :args (@t150)) % 0.30/0.63 (step @p186 :rule reordering :premises (@p185) :args ((or @t146 @t144 @t149 (not @t150)))) % 0.30/0.63 (step @p187 :rule chain_m_resolution :premises (@p186 @p184 @p183 @p181 @p180 @p175 @p169 @p160 @p155 @p138 @p151 @p142 @p124) :args (@t136 (@list false false true false false true false true false false false false) (@list @t150 @t139 @t144 @t145 @t140 @t147 @t142 @t124 @t123 @t113 @t120 @t115))) % 0.30/0.63 (step @p188 :rule cnf_and_pos :args (@t125 0)) % 0.30/0.63 (step @p189 :rule reordering :premises (@p188) :args ((or @t111 @t126))) % 0.30/0.63 (step @p190 :rule chain_m_resolution :premises (@p189 @p187) :args (@t126 @t151 @t152)) % 0.30/0.63 (step @p191 :rule cnf_and_pos :args (@t127 0)) % 0.30/0.63 (step @p192 :rule reordering :premises (@p191) :args ((or @t111 @t128))) % 0.30/0.63 (step @p193 :rule chain_m_resolution :premises (@p192 @p187) :args (@t128 @t151 @t152)) % 0.30/0.63 (step @p194 false :rule chain_m_resolution :premises (@p137 @p193 @p190 @p119) :args (false @t130 (@list @t127 @t125 @t129))) % 0.30/0.63 ) % 0.30/0.63 % SZS output end Proof % 0.41/0.63 % cvc5 exiting %------------------------------------------------------------------------------