%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL866^1 : 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 11:24:04 AM UTC 2026 % Result : Theorem 0.18s 0.51s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL866^1 : 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 % 0.09/0.35 % Computer : n006.cluster.edu % 0.09/0.35 % Model : x86_64 x86_64 % 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.35 % Memory : 8046.5625MB % 0.09/0.35 % OS : Linux 6.8.0-71-generic % 0.09/0.35 % CPULimit : 300 % 0.09/0.35 % WCLimit : 300 % 0.09/0.35 % DateTime : Sat Sep 5 19:59:16 UTC 2026 % 0.09/0.35 % CPUTime : % 0.12/0.42 %----Proving TH0 % 0.18/0.51 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.18/0.51 % SZS status Theorem % 0.18/0.51 % SZS output start Proof % 0.18/0.51 ( % 0.18/0.51 (declare-sort $$unsorted 0) % 0.18/0.51 (declare-sort tptp.mu 0) % 0.18/0.51 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.18/0.51 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.18/0.51 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.18/0.51 (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)))))) % 0.18/0.51 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.51 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.51 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.18/0.51 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.51 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.18/0.51 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.51 (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))))))) % 0.18/0.51 (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))))))) % 0.18/0.51 (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)))))) % 0.18/0.51 (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)))))) % 0.18/0.51 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.18/0.51 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.18/0.51 (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)))))) % 0.18/0.51 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.18/0.51 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.51 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.51 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.18/0.51 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.18/0.51 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.18/0.51 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.18/0.51 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.18/0.51 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.18/0.51 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.18/0.51 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.51 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.51 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.51 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.51 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.18/0.51 (define @t2 () (_ tptp.meuclidean @t1)) % 0.18/0.51 (define @t3 () (_ tptp.msymmetric @t1)) % 0.18/0.51 (define @t4 () (and (_ tptp.mtransitive @t1) @t3 @t2)) % 0.18/0.51 (define @t5 () (and @t3 @t2)) % 0.18/0.51 (define @t6 () (= @t5 @t4)) % 0.18/0.51 (define @t7 () (@list @t1)) % 0.18/0.51 (define @t8 () (forall @t7 @t6)) % 0.18/0.51 (define @t9 () (not @t8)) % 0.18/0.51 (define @t10 () (@var "Y" tptp.mu)) % 0.18/0.51 (define @t11 () (@var "X" tptp.mu)) % 0.18/0.51 (define @t12 () (@var "W" $$unsorted)) % 0.18/0.51 (define @t13 () (lambda (@list @t11 @t10 @t12) (= @t11 @t10))) % 0.18/0.51 (define @t14 () (@var "Y" (-> $$unsorted Bool))) % 0.18/0.51 (define @t15 () (@var "X" (-> $$unsorted Bool))) % 0.18/0.51 (define @t16 () (lambda (@list @t15 @t14 @t12) (= (_ @t15 @t12) (_ @t14 @t12)))) % 0.18/0.51 (define @t17 () (@var "Phi" (-> $$unsorted Bool))) % 0.18/0.51 (define @t18 () (_ @t17 @t12)) % 0.18/0.51 (define @t19 () (not @t18)) % 0.18/0.51 (define @t20 () (lambda (@list @t17 @t12) @t19)) % 0.18/0.51 (define @t21 () (@var "Psi" (-> $$unsorted Bool))) % 0.18/0.51 (define @t22 () (lambda (@list @t17 @t21 @t12) (or @t18 (_ @t21 @t12)))) % 0.18/0.51 (define @t23 () (@var "__flatten_var_0" $$unsorted)) % 0.18/0.51 (define @t24 () (_ tptp.mnot @t21)) % 0.18/0.51 (define @t25 () (_ tptp.mnot @t17)) % 0.18/0.51 (define @t26 () (_ tptp.mor @t25)) % 0.18/0.51 (define @t27 () (@list @t17 @t21 @t23)) % 0.18/0.51 (define @t28 () (lambda @t27 (_ (_ tptp.mnot (_ @t26 @t24)) @t23))) % 0.18/0.51 (define @t29 () (lambda @t27 (_ (_ @t26 @t21) @t23))) % 0.18/0.51 (define @t30 () (lambda @t27 (_ (_ (_ tptp.mor @t24) @t17) @t23))) % 0.18/0.51 (define @t31 () (lambda @t27 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t17) @t21)) (_ (_ tptp.mimplies @t21) @t17)) @t23))) % 0.18/0.51 (define @t32 () (lambda @t27 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t17) @t21)) @t23))) % 0.18/0.51 (define @t33 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.18/0.51 (define @t34 () (_ @t33 @t11)) % 0.18/0.51 (define @t35 () (lambda (@list @t33 @t12) (forall (@list @t11) (_ @t34 @t12)))) % 0.18/0.51 (define @t36 () (@var "P" (-> $$unsorted Bool))) % 0.18/0.51 (define @t37 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.18/0.51 (define @t38 () (_ @t37 @t36)) % 0.18/0.51 (define @t39 () (lambda (@list @t37 @t12) (forall (@list @t36) (_ @t38 @t12)))) % 0.18/0.51 (define @t40 () (lambda (@list @t33 @t23) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t11 @t23) (_ (_ tptp.mnot @t34) @t23)))) @t23))) % 0.18/0.51 (define @t41 () (lambda (@list @t37 @t23) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t36 @t23) (_ (_ tptp.mnot @t38) @t23)))) @t23))) % 0.18/0.51 (define @t42 () (@list @t12)) % 0.18/0.51 (define @t43 () (lambda @t42 true)) % 0.18/0.51 (define @t44 () (@var "V" $$unsorted)) % 0.18/0.51 (define @t45 () (@list @t44)) % 0.18/0.51 (define @t46 () (lambda (@list @t1 @t17 @t12) (forall @t45 (or (not (_ (_ @t1 @t12) @t44)) (_ @t17 @t44))))) % 0.18/0.51 (define @t47 () (lambda (@list @t1 @t17 @t23) (_ (_ tptp.mnot (_ (_ tptp.mbox @t1) @t25)) @t23))) % 0.18/0.51 (define @t48 () (@var "S" $$unsorted)) % 0.18/0.51 (define @t49 () (_ @t1 @t48)) % 0.18/0.51 (define @t50 () (@list @t48)) % 0.18/0.51 (define @t51 () (lambda @t7 (forall @t50 (_ @t49 @t48)))) % 0.18/0.51 (define @t52 () (@var "T" $$unsorted)) % 0.18/0.51 (define @t53 () (_ @t1 @t52)) % 0.18/0.51 (define @t54 () (_ @t53 @t48)) % 0.18/0.51 (define @t55 () (_ @t49 @t52)) % 0.18/0.51 (define @t56 () (@list @t48 @t52)) % 0.18/0.51 (define @t57 () (forall @t56 (=> @t55 @t54))) % 0.18/0.51 (define @t58 () (lambda @t7 @t57)) % 0.18/0.51 (define @t59 () (@list @t52)) % 0.18/0.51 (define @t60 () (lambda @t7 (forall @t50 (exists @t59 @t55)))) % 0.18/0.51 (define @t61 () (@var "U" $$unsorted)) % 0.18/0.51 (define @t62 () (_ @t49 @t61)) % 0.18/0.51 (define @t63 () (_ @t53 @t61)) % 0.18/0.51 (define @t64 () (and @t55 @t63)) % 0.18/0.51 (define @t65 () (@list @t48 @t52 @t61)) % 0.18/0.51 (define @t66 () (forall @t65 (=> @t64 @t62))) % 0.18/0.51 (define @t67 () (lambda @t7 @t66)) % 0.18/0.51 (define @t68 () (and @t55 @t62)) % 0.18/0.51 (define @t69 () (forall @t65 (=> @t68 @t63))) % 0.18/0.51 (define @t70 () (lambda @t7 @t69)) % 0.18/0.51 (define @t71 () (= @t52 @t61)) % 0.18/0.51 (define @t72 () (lambda @t7 (forall @t65 (=> @t68 @t71)))) % 0.18/0.51 (define @t73 () (@list @t61)) % 0.18/0.51 (define @t74 () (lambda @t7 (forall @t50 (exists @t59 (and @t55 (forall @t73 (=> @t62 @t71))))))) % 0.18/0.51 (define @t75 () (_ @t1 @t61)) % 0.18/0.51 (define @t76 () (_ @t75 @t52)) % 0.18/0.51 (define @t77 () (lambda @t7 (forall @t65 (=> @t55 (exists @t73 (and @t62 @t76)))))) % 0.18/0.51 (define @t78 () (lambda @t7 (forall @t65 (=> @t68 (or @t63 @t71 @t76))))) % 0.18/0.51 (define @t79 () (lambda @t7 (forall @t65 (=> @t68 (exists @t45 (and (_ @t53 @t44) (_ @t75 @t44))))))) % 0.18/0.51 (define @t80 () (@list @t17)) % 0.18/0.51 (define @t81 () (lambda @t80 (forall @t42 @t18))) % 0.18/0.51 (define @t82 () (lambda @t80 (forall @t42 @t19))) % 0.18/0.51 (define @t83 () (lambda @t80 (exists @t42 @t18))) % 0.18/0.51 (define @t84 () (lambda @t80 (exists @t42 @t19))) % 0.18/0.51 (define @t85 () (_ @t1 @t52 @t61)) % 0.18/0.51 (define @t86 () (_ @t1 @t48 @t61)) % 0.18/0.51 (define @t87 () (_ @t1 @t48 @t52)) % 0.18/0.51 (define @t88 () (not @t87)) % 0.18/0.51 (define @t89 () (forall @t65 (or @t88 (not @t86) @t85))) % 0.18/0.51 (define @t90 () (_ @t1 @t52 @t48)) % 0.18/0.51 (define @t91 () (forall @t56 (or @t88 @t90))) % 0.18/0.51 (define @t92 () (forall @t65 (or @t88 (not @t85) @t86))) % 0.18/0.51 (define @t93 () (@quantifiers_skolemize (forall @t7 (= (and @t92 @t91 @t89) (and @t91 @t89))) 0)) % 0.18/0.51 (define @t94 () (_ @t93 @t52 @t61)) % 0.18/0.51 (define @t95 () (_ @t93 @t48 @t61)) % 0.18/0.51 (define @t96 () (not (_ @t93 @t48 @t52))) % 0.18/0.51 (define @t97 () (forall @t65 (or @t96 (not @t95) @t94))) % 0.18/0.51 (define @t98 () (forall @t56 (or @t96 (_ @t93 @t52 @t48)))) % 0.18/0.51 (define @t99 () (forall @t65 (or @t96 (not @t94) @t95))) % 0.18/0.51 (define @t100 () (and @t99 @t98 @t97)) % 0.18/0.51 (define @t101 () (not @t100)) % 0.18/0.51 (define @t102 () (and @t98 @t97)) % 0.18/0.51 (define @t103 () (not @t102)) % 0.18/0.51 (define @t104 () (_ (lambda @t7 @t89) @t1)) % 0.18/0.51 (define @t105 () (_ (lambda @t7 @t91) @t1)) % 0.18/0.51 (define @t106 () (and @t105 @t104)) % 0.18/0.51 (define @t107 () (_ (lambda @t7 @t92) @t1)) % 0.18/0.51 (define @t108 () (and @t107 @t105 @t104)) % 0.18/0.51 (define @t109 () (forall @t7 (= @t106 @t108))) % 0.18/0.51 (define @t110 () (not @t62)) % 0.18/0.51 (define @t111 () (not @t55)) % 0.18/0.51 (define @t112 () (or @t111 @t110 @t63)) % 0.18/0.51 (define @t113 () (or @t111 @t54)) % 0.18/0.51 (define @t114 () (not @t63)) % 0.18/0.51 (define @t115 () (or @t111 @t114 @t62)) % 0.18/0.51 (define @t116 () (= @t100 @t102)) % 0.18/0.51 (define @t117 () (@list true true true)) % 0.18/0.51 (define @t118 () (@list @t116 @t102 @t100)) % 0.18/0.51 (define @t119 () (@quantifiers_skolemize @t99 1)) % 0.18/0.51 (define @t120 () (@quantifiers_skolemize @t99 0)) % 0.18/0.51 (define @t121 () (not @t99)) % 0.18/0.51 (define @t122 () (@list false false)) % 0.18/0.51 (define @t123 () (_ @t93 @t120 @t119)) % 0.18/0.51 (define @t124 () (@quantifiers_skolemize @t99 2)) % 0.18/0.51 (define @t125 () (_ @t93 @t120 @t124)) % 0.18/0.51 (define @t126 () (_ @t93 @t119 @t124)) % 0.18/0.51 (define @t127 () (not @t126)) % 0.18/0.51 (define @t128 () (not @t123)) % 0.18/0.51 (define @t129 () (or @t128 @t127 @t125)) % 0.18/0.51 (define @t130 () (@list true)) % 0.18/0.51 (define @t131 () (@list @t129)) % 0.18/0.51 (define @t132 () (_ @t93 @t119 @t120)) % 0.18/0.51 (define @t133 () (or @t128 @t132)) % 0.18/0.51 (define @t134 () (not @t132)) % 0.18/0.51 (define @t135 () (or @t134 @t127 @t125)) % 0.18/0.51 (define @t136 () (not @t135)) % 0.18/0.51 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.18/0.51 (assume @p2 @t9) % 0.18/0.51 (assume @p3 true) % 0.18/0.51 (step @p4 (= tptp.meq_ind @t13) :rule refl :args (@t13)) % 0.18/0.51 (step @p5 (= tptp.meq_prop @t16) :rule refl :args (@t16)) % 0.18/0.51 (step @p6 (= tptp.mnot @t20) :rule refl :args (@t20)) % 0.18/0.51 (step @p7 (= tptp.mor @t22) :rule refl :args (@t22)) % 0.18/0.51 (step @p8 (= tptp.mand @t28) :rule refl :args (@t28)) % 0.18/0.51 (step @p9 (= tptp.mimplies @t29) :rule refl :args (@t29)) % 0.18/0.51 (step @p10 (= tptp.mimplied @t30) :rule refl :args (@t30)) % 0.18/0.51 (step @p11 (= tptp.mequiv @t31) :rule refl :args (@t31)) % 0.18/0.51 (step @p12 (= tptp.mxor @t32) :rule refl :args (@t32)) % 0.18/0.51 (step @p13 (= tptp.mforall_ind @t35) :rule refl :args (@t35)) % 0.18/0.51 (step @p14 (= tptp.mforall_prop @t39) :rule refl :args (@t39)) % 0.18/0.51 (step @p15 (= tptp.mexists_ind @t40) :rule refl :args (@t40)) % 0.18/0.51 (step @p16 (= tptp.mexists_prop @t41) :rule refl :args (@t41)) % 0.18/0.51 (step @p17 (= tptp.mtrue @t43) :rule refl :args (@t43)) % 0.18/0.51 (step @p18 (= tptp.mbox @t46) :rule refl :args (@t46)) % 0.18/0.51 (step @p19 (= tptp.mdia @t47) :rule refl :args (@t47)) % 0.18/0.51 (step @p20 (= tptp.mreflexive @t51) :rule refl :args (@t51)) % 0.18/0.51 (step @p21 (= tptp.msymmetric @t58) :rule refl :args (@t58)) % 0.18/0.51 (step @p22 (= tptp.mserial @t60) :rule refl :args (@t60)) % 0.18/0.51 (step @p23 (= tptp.mtransitive @t67) :rule refl :args (@t67)) % 0.18/0.51 (step @p24 (= tptp.meuclidean @t70) :rule refl :args (@t70)) % 0.18/0.51 (step @p25 (= tptp.mpartially_functional @t72) :rule refl :args (@t72)) % 0.18/0.51 (step @p26 (= tptp.mfunctional @t74) :rule refl :args (@t74)) % 0.18/0.51 (step @p27 (= tptp.mweakly_dense @t77) :rule refl :args (@t77)) % 0.18/0.51 (step @p28 (= tptp.mweakly_connected @t78) :rule refl :args (@t78)) % 0.18/0.51 (step @p29 (= tptp.mweakly_directed @t79) :rule refl :args (@t79)) % 0.18/0.51 (step @p30 (= tptp.mvalid @t81) :rule refl :args (@t81)) % 0.18/0.51 (step @p31 (= tptp.minvalid @t82) :rule refl :args (@t82)) % 0.18/0.51 (step @p32 (= tptp.msatisfiable @t83) :rule refl :args (@t83)) % 0.18/0.51 (step @p33 (= tptp.mcountersatisfiable @t84) :rule refl :args (@t84)) % 0.18/0.51 (step @p34 :rule cnf_and_pos :args (@t100 2)) % 0.18/0.51 (step @p35 :rule reordering :premises (@p34) :args ((or @t97 @t101))) % 0.18/0.51 (step @p36 :rule cnf_and_pos :args (@t102 1)) % 0.18/0.51 (step @p37 :rule reordering :premises (@p36) :args ((or @t97 @t103))) % 0.18/0.51 (step @p38 :rule beta-reduce :args ((= @t104 @t89))) % 0.18/0.51 (step @p39 :rule beta-reduce :args ((= @t105 @t91))) % 0.18/0.51 (step @p40 :rule nary_cong :premises (@p39 @p38) :args (@t106)) % 0.18/0.51 (step @p41 :rule beta-reduce :args ((= @t107 @t92))) % 0.18/0.51 (step @p42 :rule nary_cong :premises (@p41 @p39 @p38) :args (@t108)) % 0.18/0.51 (step @p43 :rule cong :premises (@p42 @p40) :args ((= @t108 @t106))) % 0.18/0.51 (step @p44 :rule eq-symm :args (@t106 @t108)) % 0.18/0.51 (step @p45 :rule trans :premises (@p44 @p43)) % 0.18/0.51 (step @p46 :rule cong :premises (@p45) :args (@t109)) % 0.18/0.51 (step @p47 :rule cong :premises (@p46) :args ((not @t109))) % 0.18/0.51 (step @p48 :rule refl :args (@t1)) % 0.18/0.51 (step @p49 :rule refl :args (@t85)) % 0.18/0.51 (step @p50 :rule refl :args (@t63)) % 0.18/0.51 (step @p51 :rule cong :premises (@p50 @p49) :args ((= @t63 @t85))) % 0.18/0.51 (step @p52 :rule symm :premises (@p51)) % 0.18/0.51 (step @p53 :rule eq_resolve :premises (@p50 @p52)) % 0.18/0.51 (step @p54 :rule refl :args (@t86)) % 0.18/0.51 (step @p55 :rule refl :args (@t62)) % 0.18/0.51 (step @p56 :rule cong :premises (@p55 @p54) :args ((= @t62 @t86))) % 0.18/0.51 (step @p57 :rule symm :premises (@p56)) % 0.18/0.51 (step @p58 :rule eq_resolve :premises (@p55 @p57)) % 0.18/0.51 (step @p59 :rule cong :premises (@p58) :args (@t110)) % 0.18/0.51 (step @p60 :rule refl :args (@t87)) % 0.18/0.51 (step @p61 :rule refl :args (@t55)) % 0.18/0.51 (step @p62 :rule cong :premises (@p61 @p60) :args ((= @t55 @t87))) % 0.18/0.51 (step @p63 :rule symm :premises (@p62)) % 0.18/0.51 (step @p64 :rule eq_resolve :premises (@p61 @p63)) % 0.18/0.51 (step @p65 :rule cong :premises (@p64) :args (@t111)) % 0.18/0.51 (step @p66 :rule nary_cong :premises (@p65 @p59 @p53) :args (@t112)) % 0.18/0.51 (step @p67 :rule cong :premises (@p66) :args ((forall @t65 @t112))) % 0.18/0.51 (step @p68 :rule aci_norm :args ((= (or (or @t111 @t110) @t63) @t112))) % 0.18/0.51 (step @p69 :rule bool-and-de-morgan :args (@t55 @t62 true)) % 0.18/0.51 (step @p70 :rule nary_cong :premises (@p69 @p50) :args ((or (not @t68) @t63))) % 0.18/0.51 (step @p71 :rule trans :premises (@p70 @p68)) % 0.18/0.51 (step @p72 :rule bool-impl-elim :args (@t68 @t63)) % 0.18/0.51 (step @p73 :rule trans :premises (@p72 @p71)) % 0.18/0.51 (step @p74 :rule cong :premises (@p73) :args (@t69)) % 0.18/0.51 (step @p75 :rule trans :premises (@p74 @p67)) % 0.18/0.51 (step @p76 :rule cong :premises (@p75) :args (@t70)) % 0.18/0.51 (step @p77 :rule trans :premises (@p24 @p76)) % 0.18/0.51 (step @p78 :rule ho_cong :premises (@p77 @p48)) % 0.18/0.51 (step @p79 :rule refl :args (@t90)) % 0.18/0.51 (step @p80 :rule refl :args (@t54)) % 0.18/0.51 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t54 @t90))) % 0.18/0.51 (step @p82 :rule symm :premises (@p81)) % 0.18/0.51 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.18/0.51 (step @p84 :rule nary_cong :premises (@p65 @p83) :args (@t113)) % 0.18/0.51 (step @p85 :rule cong :premises (@p84) :args ((forall @t56 @t113))) % 0.18/0.51 (step @p86 :rule bool-impl-elim :args (@t55 @t54)) % 0.18/0.51 (step @p87 :rule cong :premises (@p86) :args (@t57)) % 0.18/0.51 (step @p88 :rule trans :premises (@p87 @p85)) % 0.18/0.51 (step @p89 :rule cong :premises (@p88) :args (@t58)) % 0.18/0.51 (step @p90 :rule trans :premises (@p21 @p89)) % 0.18/0.51 (step @p91 :rule ho_cong :premises (@p90 @p48)) % 0.18/0.51 (step @p92 :rule cong :premises (@p53) :args (@t114)) % 0.18/0.51 (step @p93 :rule nary_cong :premises (@p65 @p92 @p58) :args (@t115)) % 0.18/0.51 (step @p94 :rule cong :premises (@p93) :args ((forall @t65 @t115))) % 0.18/0.51 (step @p95 :rule aci_norm :args ((= (or (or @t111 @t114) @t62) @t115))) % 0.18/0.51 (step @p96 :rule bool-and-de-morgan :args (@t55 @t63 true)) % 0.18/0.51 (step @p97 :rule nary_cong :premises (@p96 @p55) :args ((or (not @t64) @t62))) % 0.18/0.52 (step @p98 :rule trans :premises (@p97 @p95)) % 0.18/0.52 (step @p99 :rule bool-impl-elim :args (@t64 @t62)) % 0.18/0.52 (step @p100 :rule trans :premises (@p99 @p98)) % 0.18/0.52 (step @p101 :rule cong :premises (@p100) :args (@t66)) % 0.18/0.52 (step @p102 :rule trans :premises (@p101 @p94)) % 0.18/0.52 (step @p103 :rule cong :premises (@p102) :args (@t67)) % 0.18/0.52 (step @p104 :rule trans :premises (@p23 @p103)) % 0.18/0.52 (step @p105 :rule ho_cong :premises (@p104 @p48)) % 0.18/0.52 (step @p106 :rule nary_cong :premises (@p105 @p91 @p78) :args (@t4)) % 0.18/0.52 (step @p107 :rule nary_cong :premises (@p91 @p78) :args (@t5)) % 0.18/0.52 (step @p108 :rule cong :premises (@p107 @p106) :args (@t6)) % 0.18/0.52 (step @p109 :rule cong :premises (@p108) :args (@t8)) % 0.18/0.52 (step @p110 :rule cong :premises (@p109) :args (@t9)) % 0.18/0.52 (step @p111 :rule trans :premises (@p110 @p47)) % 0.18/0.52 (step @p112 :rule eq_resolve :premises (@p2 @p111)) % 0.18/0.52 (step @p113 :rule skolemize :premises (@p112)) % 0.18/0.52 (step @p114 :rule cnf_equiv_neg1 :args (@t116)) % 0.18/0.52 (step @p115 :rule reordering :premises (@p114) :args ((or @t100 @t102 @t116))) % 0.18/0.52 (step @p116 :rule chain_m_resolution :premises (@p115 @p113 @p37 @p35) :args (@t97 @t117 @t118)) % 0.18/0.52 (step @p117 :rule cnf_and_pos :args (@t100 1)) % 0.18/0.52 (step @p118 :rule reordering :premises (@p117) :args ((or @t98 @t101))) % 0.18/0.52 (step @p119 :rule cnf_and_pos :args (@t102 0)) % 0.18/0.52 (step @p120 :rule reordering :premises (@p119) :args ((or @t98 @t103))) % 0.18/0.52 (step @p121 :rule chain_m_resolution :premises (@p115 @p113 @p120 @p118) :args (@t98 @t117 @t118)) % 0.18/0.52 (step @p122 :rule instantiate :premises (@p121) :args ((@list @t120 @t119))) % 0.18/0.52 (step @p123 :rule cnf_and_neg :args (@t102)) % 0.18/0.52 (step @p124 :rule cnf_and_neg :args (@t100)) % 0.18/0.52 (step @p125 :rule cnf_equiv_neg2 :args (@t116)) % 0.18/0.52 (step @p126 :rule chain_m_resolution :premises (@p125 @p113 @p124 @p123) :args ((or @t121 (not @t98) (not @t97)) (@list true false false) (@list @t116 @t100 @t102))) % 0.18/0.52 (step @p127 :rule chain_m_resolution :premises (@p126 @p121 @p116) :args (@t121 @t122 (@list @t98 @t97))) % 0.18/0.52 (step @p128 :rule skolemize :premises (@p127)) % 0.18/0.52 (step @p129 :rule bool-double-not-elim :args (@t123)) % 0.18/0.52 (step @p130 :rule refl :args (@t129)) % 0.18/0.52 (step @p131 :rule nary_cong :premises (@p130 @p129) :args ((or @t129 (not @t128)))) % 0.18/0.52 (step @p132 :rule cnf_or_neg :args (@t129 0)) % 0.18/0.52 (step @p133 :rule eq_resolve :premises (@p132 @p131)) % 0.18/0.52 (step @p134 :rule reordering :premises (@p133) :args ((or @t123 @t129))) % 0.18/0.52 (step @p135 :rule chain_m_resolution :premises (@p134 @p128) :args (@t123 @t130 @t131)) % 0.18/0.52 (step @p136 :rule cnf_or_pos :args (@t133)) % 0.18/0.52 (step @p137 :rule reordering :premises (@p136) :args ((or @t128 @t132 (not @t133)))) % 0.18/0.52 (step @p138 :rule chain_m_resolution :premises (@p137 @p135 @p122) :args (@t132 @t122 (@list @t123 @t133))) % 0.18/0.52 (step @p139 :rule cnf_or_neg :args (@t129 2)) % 0.18/0.52 (step @p140 :rule chain_m_resolution :premises (@p139 @p128) :args ((not @t125) @t130 @t131)) % 0.18/0.52 (step @p141 :rule bool-double-not-elim :args (@t126)) % 0.18/0.52 (step @p142 :rule nary_cong :premises (@p130 @p141) :args ((or @t129 (not @t127)))) % 0.18/0.52 (step @p143 :rule cnf_or_neg :args (@t129 1)) % 0.18/0.52 (step @p144 :rule eq_resolve :premises (@p143 @p142)) % 0.18/0.52 (step @p145 :rule reordering :premises (@p144) :args ((or @t126 @t129))) % 0.18/0.52 (step @p146 :rule chain_m_resolution :premises (@p145 @p128) :args (@t126 @t130 @t131)) % 0.18/0.52 (step @p147 :rule cnf_or_pos :args (@t135)) % 0.18/0.52 (step @p148 :rule reordering :premises (@p147) :args ((or @t127 @t125 @t134 @t136))) % 0.18/0.52 (step @p149 :rule chain_m_resolution :premises (@p148 @p146 @p140 @p138) :args (@t136 (@list false true false) (@list @t126 @t125 @t132))) % 0.18/0.52 (assume-push @p156 @t97) % 0.18/0.52 (step @p151 :rule instantiate :premises (@p116) :args ((@list @t119 @t120 @t124))) % 0.18/0.52 (step-pop @p157 :rule scope :premises (@p151)) % 0.18/0.52 (step @p152 :rule process_scope :premises (@p157) :args (@t135)) % 0.18/0.52 (step @p154 :rule implies_elim :premises (@p152)) % 0.18/0.52 (step @p155 false :rule chain_m_resolution :premises (@p154 @p149 @p116) :args (false (@list true false) (@list @t135 @t97))) % 0.18/0.52 ) % 0.18/0.52 % SZS output end Proof % 0.18/0.52 % cvc5 exiting %------------------------------------------------------------------------------