%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL867^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n005.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 0.22s 0.54s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL867^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.08/0.33 % Computer : n005.cluster.edu % 0.08/0.33 % Model : x86_64 x86_64 % 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.33 % Memory : 8046.5625MB % 0.08/0.33 % OS : Linux 6.8.0-71-generic % 0.08/0.34 % CPULimit : 300 % 0.08/0.34 % WCLimit : 300 % 0.08/0.34 % DateTime : Sat Sep 5 22:00:05 UTC 2026 % 0.08/0.34 % CPUTime : % 0.12/0.42 %----Proving TH0 % 0.22/0.54 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.22/0.54 % SZS status Theorem % 0.22/0.54 % SZS output start Proof % 0.22/0.54 ( % 0.22/0.54 (declare-sort $$unsorted 0) % 0.22/0.54 (declare-sort tptp.mu 0) % 0.22/0.54 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.22/0.54 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.22/0.54 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.22/0.54 (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)))))) % 0.22/0.54 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.22/0.54 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.22/0.54 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.22/0.54 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.22/0.54 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.22/0.54 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.22/0.54 (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))))))) % 0.22/0.54 (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))))))) % 0.22/0.54 (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)))))) % 0.22/0.54 (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)))))) % 0.22/0.54 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.22/0.54 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.22/0.54 (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)))))) % 0.22/0.54 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.22/0.54 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.22/0.54 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.22/0.54 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.22/0.54 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.22/0.54 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.22/0.54 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.22/0.54 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.22/0.54 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.22/0.54 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.22/0.54 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.22/0.54 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.22/0.54 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.22/0.54 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.22/0.54 (define @t1 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.22/0.54 (define @t2 () (_ tptp.msymmetric @t1)) % 0.22/0.54 (define @t3 () (and (_ tptp.mtransitive @t1) @t2)) % 0.22/0.54 (define @t4 () (and @t2 (_ tptp.meuclidean @t1))) % 0.22/0.54 (define @t5 () (= @t4 @t3)) % 0.22/0.54 (define @t6 () (@list @t1)) % 0.22/0.54 (define @t7 () (forall @t6 @t5)) % 0.22/0.54 (define @t8 () (not @t7)) % 0.22/0.54 (define @t9 () (@var "Y" tptp.mu)) % 0.22/0.54 (define @t10 () (@var "X" tptp.mu)) % 0.22/0.54 (define @t11 () (@var "W" $$unsorted)) % 0.22/0.54 (define @t12 () (lambda (@list @t10 @t9 @t11) (= @t10 @t9))) % 0.22/0.54 (define @t13 () (@var "Y" (-> $$unsorted Bool))) % 0.22/0.54 (define @t14 () (@var "X" (-> $$unsorted Bool))) % 0.22/0.54 (define @t15 () (lambda (@list @t14 @t13 @t11) (= (_ @t14 @t11) (_ @t13 @t11)))) % 0.22/0.54 (define @t16 () (@var "Phi" (-> $$unsorted Bool))) % 0.22/0.54 (define @t17 () (_ @t16 @t11)) % 0.22/0.54 (define @t18 () (not @t17)) % 0.22/0.54 (define @t19 () (lambda (@list @t16 @t11) @t18)) % 0.22/0.54 (define @t20 () (@var "Psi" (-> $$unsorted Bool))) % 0.22/0.54 (define @t21 () (lambda (@list @t16 @t20 @t11) (or @t17 (_ @t20 @t11)))) % 0.22/0.54 (define @t22 () (@var "__flatten_var_0" $$unsorted)) % 0.22/0.54 (define @t23 () (_ tptp.mnot @t20)) % 0.22/0.54 (define @t24 () (_ tptp.mnot @t16)) % 0.22/0.54 (define @t25 () (_ tptp.mor @t24)) % 0.22/0.54 (define @t26 () (@list @t16 @t20 @t22)) % 0.22/0.54 (define @t27 () (lambda @t26 (_ (_ tptp.mnot (_ @t25 @t23)) @t22))) % 0.22/0.54 (define @t28 () (lambda @t26 (_ (_ @t25 @t20) @t22))) % 0.22/0.54 (define @t29 () (lambda @t26 (_ (_ (_ tptp.mor @t23) @t16) @t22))) % 0.22/0.54 (define @t30 () (lambda @t26 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t16) @t20)) (_ (_ tptp.mimplies @t20) @t16)) @t22))) % 0.22/0.54 (define @t31 () (lambda @t26 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t16) @t20)) @t22))) % 0.22/0.54 (define @t32 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.22/0.54 (define @t33 () (_ @t32 @t10)) % 0.22/0.54 (define @t34 () (lambda (@list @t32 @t11) (forall (@list @t10) (_ @t33 @t11)))) % 0.22/0.54 (define @t35 () (@var "P" (-> $$unsorted Bool))) % 0.22/0.54 (define @t36 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.22/0.54 (define @t37 () (_ @t36 @t35)) % 0.22/0.54 (define @t38 () (lambda (@list @t36 @t11) (forall (@list @t35) (_ @t37 @t11)))) % 0.22/0.54 (define @t39 () (lambda (@list @t32 @t22) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t10 @t22) (_ (_ tptp.mnot @t33) @t22)))) @t22))) % 0.22/0.54 (define @t40 () (lambda (@list @t36 @t22) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t35 @t22) (_ (_ tptp.mnot @t37) @t22)))) @t22))) % 0.22/0.54 (define @t41 () (@list @t11)) % 0.22/0.54 (define @t42 () (lambda @t41 true)) % 0.22/0.54 (define @t43 () (@var "V" $$unsorted)) % 0.22/0.54 (define @t44 () (@list @t43)) % 0.22/0.54 (define @t45 () (lambda (@list @t1 @t16 @t11) (forall @t44 (or (not (_ (_ @t1 @t11) @t43)) (_ @t16 @t43))))) % 0.22/0.54 (define @t46 () (lambda (@list @t1 @t16 @t22) (_ (_ tptp.mnot (_ (_ tptp.mbox @t1) @t24)) @t22))) % 0.22/0.54 (define @t47 () (@var "S" $$unsorted)) % 0.22/0.54 (define @t48 () (_ @t1 @t47)) % 0.22/0.54 (define @t49 () (@list @t47)) % 0.22/0.54 (define @t50 () (lambda @t6 (forall @t49 (_ @t48 @t47)))) % 0.22/0.54 (define @t51 () (@var "T" $$unsorted)) % 0.22/0.54 (define @t52 () (_ @t1 @t51)) % 0.22/0.54 (define @t53 () (_ @t52 @t47)) % 0.22/0.54 (define @t54 () (_ @t48 @t51)) % 0.22/0.54 (define @t55 () (@list @t47 @t51)) % 0.22/0.54 (define @t56 () (forall @t55 (=> @t54 @t53))) % 0.22/0.54 (define @t57 () (lambda @t6 @t56)) % 0.22/0.54 (define @t58 () (@list @t51)) % 0.22/0.54 (define @t59 () (lambda @t6 (forall @t49 (exists @t58 @t54)))) % 0.22/0.54 (define @t60 () (@var "U" $$unsorted)) % 0.22/0.54 (define @t61 () (_ @t48 @t60)) % 0.22/0.54 (define @t62 () (_ @t52 @t60)) % 0.22/0.54 (define @t63 () (and @t54 @t62)) % 0.22/0.54 (define @t64 () (@list @t47 @t51 @t60)) % 0.22/0.54 (define @t65 () (forall @t64 (=> @t63 @t61))) % 0.22/0.54 (define @t66 () (lambda @t6 @t65)) % 0.22/0.54 (define @t67 () (and @t54 @t61)) % 0.22/0.54 (define @t68 () (forall @t64 (=> @t67 @t62))) % 0.22/0.54 (define @t69 () (lambda @t6 @t68)) % 0.22/0.54 (define @t70 () (= @t51 @t60)) % 0.22/0.54 (define @t71 () (lambda @t6 (forall @t64 (=> @t67 @t70)))) % 0.22/0.54 (define @t72 () (@list @t60)) % 0.22/0.54 (define @t73 () (lambda @t6 (forall @t49 (exists @t58 (and @t54 (forall @t72 (=> @t61 @t70))))))) % 0.22/0.54 (define @t74 () (_ @t1 @t60)) % 0.22/0.54 (define @t75 () (_ @t74 @t51)) % 0.22/0.54 (define @t76 () (lambda @t6 (forall @t64 (=> @t54 (exists @t72 (and @t61 @t75)))))) % 0.22/0.54 (define @t77 () (lambda @t6 (forall @t64 (=> @t67 (or @t62 @t70 @t75))))) % 0.22/0.54 (define @t78 () (lambda @t6 (forall @t64 (=> @t67 (exists @t44 (and (_ @t52 @t43) (_ @t74 @t43))))))) % 0.22/0.54 (define @t79 () (@list @t16)) % 0.22/0.54 (define @t80 () (lambda @t79 (forall @t41 @t17))) % 0.22/0.54 (define @t81 () (lambda @t79 (forall @t41 @t18))) % 0.22/0.54 (define @t82 () (lambda @t79 (exists @t41 @t17))) % 0.22/0.54 (define @t83 () (lambda @t79 (exists @t41 @t18))) % 0.22/0.54 (define @t84 () (_ @t1 @t51 @t60)) % 0.22/0.54 (define @t85 () (_ @t1 @t47 @t60)) % 0.22/0.54 (define @t86 () (_ @t1 @t47 @t51)) % 0.22/0.54 (define @t87 () (not @t86)) % 0.22/0.54 (define @t88 () (forall @t64 (or @t87 (not @t85) @t84))) % 0.22/0.54 (define @t89 () (_ (lambda @t6 @t88) @t1)) % 0.22/0.54 (define @t90 () (_ @t1 @t51 @t47)) % 0.22/0.54 (define @t91 () (forall @t55 (or @t87 @t90))) % 0.22/0.54 (define @t92 () (_ (lambda @t6 @t91) @t1)) % 0.22/0.54 (define @t93 () (and @t92 @t89)) % 0.22/0.54 (define @t94 () (forall @t64 (or @t87 (not @t84) @t85))) % 0.22/0.54 (define @t95 () (_ (lambda @t6 @t94) @t1)) % 0.22/0.54 (define @t96 () (and @t95 @t92)) % 0.22/0.54 (define @t97 () (forall @t6 (= @t93 @t96))) % 0.22/0.54 (define @t98 () (not @t54)) % 0.22/0.54 (define @t99 () (or @t98 @t53)) % 0.22/0.54 (define @t100 () (not @t62)) % 0.22/0.54 (define @t101 () (or @t98 @t100 @t61)) % 0.22/0.54 (define @t102 () (not @t61)) % 0.22/0.54 (define @t103 () (or @t98 @t102 @t62)) % 0.22/0.54 (define @t104 () (@quantifiers_skolemize (forall @t6 (= (and @t94 @t91) (and @t91 @t88))) 0)) % 0.22/0.54 (define @t105 () (not (_ @t104 @t47 @t51))) % 0.22/0.54 (define @t106 () (forall @t55 (or @t105 (_ @t104 @t51 @t47)))) % 0.22/0.54 (define @t107 () (_ @t104 @t47 @t60)) % 0.22/0.54 (define @t108 () (_ @t104 @t51 @t60)) % 0.22/0.54 (define @t109 () (forall @t64 (or @t105 (not @t108) @t107))) % 0.22/0.54 (define @t110 () (and @t109 @t106)) % 0.22/0.54 (define @t111 () (not @t110)) % 0.22/0.54 (define @t112 () (forall @t64 (or @t105 (not @t107) @t108))) % 0.22/0.54 (define @t113 () (and @t106 @t112)) % 0.22/0.54 (define @t114 () (not @t113)) % 0.22/0.54 (define @t115 () (= @t110 @t113)) % 0.22/0.54 (define @t116 () (@quantifiers_skolemize @t112 2)) % 0.22/0.54 (define @t117 () (@quantifiers_skolemize @t112 0)) % 0.22/0.54 (define @t118 () (@quantifiers_skolemize @t112 1)) % 0.22/0.54 (define @t119 () (_ @t104 @t118 @t116)) % 0.22/0.54 (define @t120 () (_ @t104 @t117 @t116)) % 0.22/0.54 (define @t121 () (not @t120)) % 0.22/0.54 (define @t122 () (_ @t104 @t118 @t117)) % 0.22/0.54 (define @t123 () (not @t122)) % 0.22/0.54 (define @t124 () (or @t123 @t121 @t119)) % 0.22/0.54 (define @t125 () (_ @t104 @t117 @t118)) % 0.22/0.54 (define @t126 () (not @t125)) % 0.22/0.54 (define @t127 () (or @t126 @t122)) % 0.22/0.54 (define @t128 () (or @t126 @t121 @t119)) % 0.22/0.54 (define @t129 () (not @t128)) % 0.22/0.54 (define @t130 () (not @t112)) % 0.22/0.54 (define @t131 () (not @t109)) % 0.22/0.54 (define @t132 () (@list false)) % 0.22/0.54 (define @t133 () (@list true)) % 0.22/0.54 (define @t134 () (@list @t109)) % 0.22/0.54 (define @t135 () (@quantifiers_skolemize @t109 1)) % 0.22/0.54 (define @t136 () (@quantifiers_skolemize @t109 0)) % 0.22/0.54 (define @t137 () (@quantifiers_skolemize @t109 2)) % 0.22/0.54 (define @t138 () (_ @t104 @t136 @t137)) % 0.22/0.54 (define @t139 () (_ @t104 @t135 @t137)) % 0.22/0.54 (define @t140 () (not @t139)) % 0.22/0.54 (define @t141 () (_ @t104 @t136 @t135)) % 0.22/0.54 (define @t142 () (not @t141)) % 0.22/0.54 (define @t143 () (or @t142 @t140 @t138)) % 0.22/0.54 (define @t144 () (not @t143)) % 0.22/0.54 (define @t145 () (@list @t143)) % 0.22/0.54 (define @t146 () (_ @t104 @t135 @t136)) % 0.22/0.54 (define @t147 () (or @t142 @t146)) % 0.22/0.54 (define @t148 () (not @t146)) % 0.22/0.54 (define @t149 () (or @t148 @t140 @t138)) % 0.22/0.54 (define @t150 () (not @t149)) % 0.22/0.54 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.22/0.54 (assume @p2 @t8) % 0.22/0.54 (assume @p3 true) % 0.22/0.54 (step @p4 (= tptp.meq_ind @t12) :rule refl :args (@t12)) % 0.22/0.54 (step @p5 (= tptp.meq_prop @t15) :rule refl :args (@t15)) % 0.22/0.54 (step @p6 (= tptp.mnot @t19) :rule refl :args (@t19)) % 0.22/0.54 (step @p7 (= tptp.mor @t21) :rule refl :args (@t21)) % 0.22/0.54 (step @p8 (= tptp.mand @t27) :rule refl :args (@t27)) % 0.22/0.54 (step @p9 (= tptp.mimplies @t28) :rule refl :args (@t28)) % 0.22/0.54 (step @p10 (= tptp.mimplied @t29) :rule refl :args (@t29)) % 0.22/0.54 (step @p11 (= tptp.mequiv @t30) :rule refl :args (@t30)) % 0.22/0.54 (step @p12 (= tptp.mxor @t31) :rule refl :args (@t31)) % 0.22/0.54 (step @p13 (= tptp.mforall_ind @t34) :rule refl :args (@t34)) % 0.22/0.54 (step @p14 (= tptp.mforall_prop @t38) :rule refl :args (@t38)) % 0.22/0.54 (step @p15 (= tptp.mexists_ind @t39) :rule refl :args (@t39)) % 0.22/0.54 (step @p16 (= tptp.mexists_prop @t40) :rule refl :args (@t40)) % 0.22/0.54 (step @p17 (= tptp.mtrue @t42) :rule refl :args (@t42)) % 0.22/0.54 (step @p18 (= tptp.mbox @t45) :rule refl :args (@t45)) % 0.22/0.54 (step @p19 (= tptp.mdia @t46) :rule refl :args (@t46)) % 0.22/0.54 (step @p20 (= tptp.mreflexive @t50) :rule refl :args (@t50)) % 0.22/0.54 (step @p21 (= tptp.msymmetric @t57) :rule refl :args (@t57)) % 0.22/0.54 (step @p22 (= tptp.mserial @t59) :rule refl :args (@t59)) % 0.22/0.54 (step @p23 (= tptp.mtransitive @t66) :rule refl :args (@t66)) % 0.22/0.54 (step @p24 (= tptp.meuclidean @t69) :rule refl :args (@t69)) % 0.22/0.54 (step @p25 (= tptp.mpartially_functional @t71) :rule refl :args (@t71)) % 0.22/0.54 (step @p26 (= tptp.mfunctional @t73) :rule refl :args (@t73)) % 0.22/0.54 (step @p27 (= tptp.mweakly_dense @t76) :rule refl :args (@t76)) % 0.22/0.54 (step @p28 (= tptp.mweakly_connected @t77) :rule refl :args (@t77)) % 0.22/0.54 (step @p29 (= tptp.mweakly_directed @t78) :rule refl :args (@t78)) % 0.22/0.54 (step @p30 (= tptp.mvalid @t80) :rule refl :args (@t80)) % 0.22/0.54 (step @p31 (= tptp.minvalid @t81) :rule refl :args (@t81)) % 0.22/0.54 (step @p32 (= tptp.msatisfiable @t82) :rule refl :args (@t82)) % 0.22/0.54 (step @p33 (= tptp.mcountersatisfiable @t83) :rule refl :args (@t83)) % 0.22/0.54 (step @p34 :rule beta-reduce :args ((= @t89 @t88))) % 0.22/0.54 (step @p35 :rule beta-reduce :args ((= @t92 @t91))) % 0.22/0.54 (step @p36 :rule nary_cong :premises (@p35 @p34) :args (@t93)) % 0.22/0.54 (step @p37 :rule beta-reduce :args ((= @t95 @t94))) % 0.22/0.54 (step @p38 :rule nary_cong :premises (@p37 @p35) :args (@t96)) % 0.22/0.54 (step @p39 :rule cong :premises (@p38 @p36) :args ((= @t96 @t93))) % 0.22/0.54 (step @p40 :rule eq-symm :args (@t93 @t96)) % 0.22/0.54 (step @p41 :rule trans :premises (@p40 @p39)) % 0.22/0.54 (step @p42 :rule cong :premises (@p41) :args (@t97)) % 0.22/0.54 (step @p43 :rule cong :premises (@p42) :args ((not @t97))) % 0.22/0.54 (step @p44 :rule refl :args (@t1)) % 0.22/0.54 (step @p45 :rule refl :args (@t90)) % 0.22/0.54 (step @p46 :rule refl :args (@t53)) % 0.22/0.54 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t53 @t90))) % 0.22/0.54 (step @p48 :rule symm :premises (@p47)) % 0.22/0.54 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.22/0.54 (step @p50 :rule refl :args (@t86)) % 0.22/0.54 (step @p51 :rule refl :args (@t54)) % 0.22/0.54 (step @p52 :rule cong :premises (@p51 @p50) :args ((= @t54 @t86))) % 0.22/0.54 (step @p53 :rule symm :premises (@p52)) % 0.22/0.54 (step @p54 :rule eq_resolve :premises (@p51 @p53)) % 0.22/0.54 (step @p55 :rule cong :premises (@p54) :args (@t98)) % 0.22/0.54 (step @p56 :rule nary_cong :premises (@p55 @p49) :args (@t99)) % 0.22/0.54 (step @p57 :rule cong :premises (@p56) :args ((forall @t55 @t99))) % 0.22/0.54 (step @p58 :rule bool-impl-elim :args (@t54 @t53)) % 0.22/0.54 (step @p59 :rule cong :premises (@p58) :args (@t56)) % 0.22/0.54 (step @p60 :rule trans :premises (@p59 @p57)) % 0.22/0.54 (step @p61 :rule cong :premises (@p60) :args (@t57)) % 0.22/0.54 (step @p62 :rule trans :premises (@p21 @p61)) % 0.22/0.54 (step @p63 :rule ho_cong :premises (@p62 @p44)) % 0.22/0.54 (step @p64 :rule refl :args (@t85)) % 0.22/0.54 (step @p65 :rule refl :args (@t61)) % 0.22/0.54 (step @p66 :rule cong :premises (@p65 @p64) :args ((= @t61 @t85))) % 0.22/0.54 (step @p67 :rule symm :premises (@p66)) % 0.22/0.54 (step @p68 :rule eq_resolve :premises (@p65 @p67)) % 0.22/0.54 (step @p69 :rule refl :args (@t84)) % 0.22/0.54 (step @p70 :rule refl :args (@t62)) % 0.22/0.54 (step @p71 :rule cong :premises (@p70 @p69) :args ((= @t62 @t84))) % 0.22/0.54 (step @p72 :rule symm :premises (@p71)) % 0.22/0.54 (step @p73 :rule eq_resolve :premises (@p70 @p72)) % 0.22/0.54 (step @p74 :rule cong :premises (@p73) :args (@t100)) % 0.22/0.54 (step @p75 :rule nary_cong :premises (@p55 @p74 @p68) :args (@t101)) % 0.22/0.54 (step @p76 :rule cong :premises (@p75) :args ((forall @t64 @t101))) % 0.22/0.54 (step @p77 :rule aci_norm :args ((= (or (or @t98 @t100) @t61) @t101))) % 0.22/0.54 (step @p78 :rule bool-and-de-morgan :args (@t54 @t62 true)) % 0.22/0.54 (step @p79 :rule nary_cong :premises (@p78 @p65) :args ((or (not @t63) @t61))) % 0.22/0.54 (step @p80 :rule trans :premises (@p79 @p77)) % 0.22/0.54 (step @p81 :rule bool-impl-elim :args (@t63 @t61)) % 0.22/0.54 (step @p82 :rule trans :premises (@p81 @p80)) % 0.22/0.54 (step @p83 :rule cong :premises (@p82) :args (@t65)) % 0.22/0.54 (step @p84 :rule trans :premises (@p83 @p76)) % 0.22/0.54 (step @p85 :rule cong :premises (@p84) :args (@t66)) % 0.22/0.54 (step @p86 :rule trans :premises (@p23 @p85)) % 0.22/0.54 (step @p87 :rule ho_cong :premises (@p86 @p44)) % 0.22/0.54 (step @p88 :rule nary_cong :premises (@p87 @p63) :args (@t3)) % 0.22/0.54 (step @p89 :rule cong :premises (@p68) :args (@t102)) % 0.22/0.54 (step @p90 :rule nary_cong :premises (@p55 @p89 @p73) :args (@t103)) % 0.22/0.54 (step @p91 :rule cong :premises (@p90) :args ((forall @t64 @t103))) % 0.22/0.54 (step @p92 :rule aci_norm :args ((= (or (or @t98 @t102) @t62) @t103))) % 0.22/0.54 (step @p93 :rule bool-and-de-morgan :args (@t54 @t61 true)) % 0.22/0.54 (step @p94 :rule nary_cong :premises (@p93 @p70) :args ((or (not @t67) @t62))) % 0.22/0.54 (step @p95 :rule trans :premises (@p94 @p92)) % 0.22/0.54 (step @p96 :rule bool-impl-elim :args (@t67 @t62)) % 0.22/0.54 (step @p97 :rule trans :premises (@p96 @p95)) % 0.22/0.54 (step @p98 :rule cong :premises (@p97) :args (@t68)) % 0.22/0.54 (step @p99 :rule trans :premises (@p98 @p91)) % 0.22/0.54 (step @p100 :rule cong :premises (@p99) :args (@t69)) % 0.22/0.54 (step @p101 :rule trans :premises (@p24 @p100)) % 0.22/0.54 (step @p102 :rule ho_cong :premises (@p101 @p44)) % 0.22/0.54 (step @p103 :rule nary_cong :premises (@p63 @p102) :args (@t4)) % 0.22/0.54 (step @p104 :rule cong :premises (@p103 @p88) :args (@t5)) % 0.22/0.54 (step @p105 :rule cong :premises (@p104) :args (@t7)) % 0.22/0.54 (step @p106 :rule cong :premises (@p105) :args (@t8)) % 0.22/0.54 (step @p107 :rule trans :premises (@p106 @p43)) % 0.22/0.54 (step @p108 :rule eq_resolve :premises (@p2 @p107)) % 0.22/0.54 (step @p109 :rule skolemize :premises (@p108)) % 0.22/0.54 (step @p110 :rule cnf_and_pos :args (@t110 1)) % 0.22/0.54 (step @p111 :rule reordering :premises (@p110) :args ((or @t106 @t111))) % 0.22/0.54 (step @p112 :rule cnf_and_pos :args (@t113 0)) % 0.22/0.54 (step @p113 :rule reordering :premises (@p112) :args ((or @t106 @t114))) % 0.22/0.54 (step @p114 :rule cnf_equiv_neg1 :args (@t115)) % 0.22/0.54 (step @p115 :rule reordering :premises (@p114) :args ((or @t110 @t113 @t115))) % 0.22/0.54 (step @p116 :rule chain_m_resolution :premises (@p115 @p109 @p113 @p111) :args (@t106 (@list true true true) (@list @t115 @t113 @t110))) % 0.22/0.54 (assume-push @p202 @t109) % 0.22/0.54 (step @p118 :rule instantiate :premises (@p202) :args ((@list @t118 @t117 @t116))) % 0.22/0.54 (step-pop @p203 :rule scope :premises (@p118)) % 0.22/0.54 (step @p119 :rule process_scope :premises (@p203) :args (@t124)) % 0.22/0.54 (step @p121 :rule implies_elim :premises (@p119)) % 0.22/0.54 (step @p122 :rule cnf_and_neg :args (@t110)) % 0.22/0.54 (assume-push @p204 @t106) % 0.22/0.54 (step @p124 :rule instantiate :premises (@p116) :args ((@list @t117 @t118))) % 0.22/0.54 (step-pop @p205 :rule scope :premises (@p124)) % 0.22/0.54 (step @p125 :rule process_scope :premises (@p205) :args (@t127)) % 0.22/0.54 (step @p127 :rule implies_elim :premises (@p125)) % 0.22/0.54 (step @p128 :rule cnf_equiv_neg2 :args (@t115)) % 0.22/0.54 (step @p129 :rule cnf_and_neg :args (@t113)) % 0.22/0.54 (step @p130 :rule refl :args (@t129)) % 0.22/0.54 (step @p131 :rule bool-double-not-elim :args (@t112)) % 0.22/0.54 (step @p132 :rule nary_cong :premises (@p131 @p130) :args ((or (not @t130) @t129))) % 0.22/0.54 (assume-push @p206 @t130) % 0.22/0.54 (step @p134 :rule skolemize :premises (@p206)) % 0.22/0.54 (step-pop @p207 :rule scope :premises (@p134)) % 0.22/0.54 (step @p135 :rule process_scope :premises (@p207) :args (@t129)) % 0.22/0.54 (step @p137 :rule implies_elim :premises (@p135)) % 0.22/0.54 (step @p138 :rule eq_resolve :premises (@p137 @p132)) % 0.22/0.54 (step @p139 :rule bool-double-not-elim :args (@t125)) % 0.22/0.54 (step @p140 :rule refl :args (@t128)) % 0.22/0.54 (step @p141 :rule nary_cong :premises (@p140 @p139) :args ((or @t128 (not @t126)))) % 0.22/0.54 (step @p142 :rule cnf_or_neg :args (@t128 0)) % 0.22/0.54 (step @p143 :rule eq_resolve :premises (@p142 @p141)) % 0.22/0.54 (step @p144 :rule reordering :premises (@p143) :args ((or @t125 @t128))) % 0.22/0.54 (step @p145 :rule bool-double-not-elim :args (@t120)) % 0.22/0.54 (step @p146 :rule nary_cong :premises (@p140 @p145) :args ((or @t128 (not @t121)))) % 0.22/0.54 (step @p147 :rule cnf_or_neg :args (@t128 1)) % 0.22/0.54 (step @p148 :rule eq_resolve :premises (@p147 @p146)) % 0.22/0.54 (step @p149 :rule reordering :premises (@p148) :args ((or @t120 @t128))) % 0.22/0.54 (step @p150 :rule cnf_or_neg :args (@t128 2)) % 0.22/0.54 (step @p151 :rule cnf_or_pos :args (@t127)) % 0.22/0.54 (step @p152 :rule reordering :premises (@p151) :args ((or @t126 @t122 (not @t127)))) % 0.22/0.54 (step @p153 :rule cnf_or_pos :args (@t124)) % 0.22/0.54 (step @p154 :rule reordering :premises (@p153) :args ((or @t121 @t119 @t123 (not @t124)))) % 0.22/0.54 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p150 @p149 @p144 @p138 @p129 @p128 @p109 @p127 @p122 @p121) :args ((or @t131 (not @t106)) (@list false true false false true true true true false false false) (@list @t122 @t119 @t120 @t125 @t128 @t112 @t113 @t115 @t127 @t110 @t124))) % 0.22/0.54 (step @p156 :rule chain_m_resolution :premises (@p155 @p116) :args (@t131 @t132 (@list @t106))) % 0.22/0.54 (step @p157 :rule cnf_and_pos :args (@t110 0)) % 0.22/0.54 (step @p158 :rule reordering :premises (@p157) :args ((or @t109 @t111))) % 0.22/0.54 (step @p159 :rule chain_m_resolution :premises (@p158 @p156) :args (@t111 @t133 @t134)) % 0.22/0.54 (step @p160 :rule chain_m_resolution :premises (@p115 @p159 @p109) :args (@t113 (@list true true) (@list @t110 @t115))) % 0.22/0.54 (step @p161 :rule cnf_and_pos :args (@t113 1)) % 0.22/0.54 (step @p162 :rule reordering :premises (@p161) :args ((or @t112 @t114))) % 0.22/0.54 (step @p163 :rule chain_m_resolution :premises (@p162 @p160) :args (@t112 @t132 (@list @t113))) % 0.22/0.54 (step @p164 :rule instantiate :premises (@p116) :args ((@list @t136 @t135))) % 0.22/0.54 (step @p165 :rule refl :args (@t144)) % 0.22/0.54 (step @p166 :rule bool-double-not-elim :args (@t109)) % 0.22/0.54 (step @p167 :rule nary_cong :premises (@p166 @p165) :args ((or (not @t131) @t144))) % 0.22/0.54 (assume-push @p208 @t131) % 0.22/0.54 (step @p169 :rule skolemize :premises (@p208)) % 0.22/0.54 (step-pop @p209 :rule scope :premises (@p169)) % 0.22/0.54 (step @p170 :rule process_scope :premises (@p209) :args (@t144)) % 0.22/0.54 (step @p172 :rule implies_elim :premises (@p170)) % 0.22/0.55 (step @p173 :rule eq_resolve :premises (@p172 @p167)) % 0.22/0.55 (step @p174 :rule chain_m_resolution :premises (@p173 @p156) :args (@t144 @t133 @t134)) % 0.22/0.55 (step @p175 :rule bool-double-not-elim :args (@t141)) % 0.22/0.55 (step @p176 :rule refl :args (@t143)) % 0.22/0.55 (step @p177 :rule nary_cong :premises (@p176 @p175) :args ((or @t143 (not @t142)))) % 0.22/0.55 (step @p178 :rule cnf_or_neg :args (@t143 0)) % 0.22/0.55 (step @p179 :rule eq_resolve :premises (@p178 @p177)) % 0.22/0.55 (step @p180 :rule reordering :premises (@p179) :args ((or @t141 @t143))) % 0.22/0.55 (step @p181 :rule chain_m_resolution :premises (@p180 @p174) :args (@t141 @t133 @t145)) % 0.22/0.55 (step @p182 :rule cnf_or_pos :args (@t147)) % 0.22/0.55 (step @p183 :rule reordering :premises (@p182) :args ((or @t142 @t146 (not @t147)))) % 0.22/0.55 (step @p184 :rule chain_m_resolution :premises (@p183 @p181 @p164) :args (@t146 (@list false false) (@list @t141 @t147))) % 0.22/0.55 (step @p185 :rule cnf_or_neg :args (@t143 2)) % 0.22/0.55 (step @p186 :rule chain_m_resolution :premises (@p185 @p174) :args ((not @t138) @t133 @t145)) % 0.22/0.55 (step @p187 :rule bool-double-not-elim :args (@t139)) % 0.22/0.55 (step @p188 :rule nary_cong :premises (@p176 @p187) :args ((or @t143 (not @t140)))) % 0.22/0.55 (step @p189 :rule cnf_or_neg :args (@t143 1)) % 0.22/0.55 (step @p190 :rule eq_resolve :premises (@p189 @p188)) % 0.22/0.55 (step @p191 :rule reordering :premises (@p190) :args ((or @t139 @t143))) % 0.22/0.55 (step @p192 :rule chain_m_resolution :premises (@p191 @p174) :args (@t139 @t133 @t145)) % 0.22/0.55 (step @p193 :rule cnf_or_pos :args (@t149)) % 0.22/0.55 (step @p194 :rule reordering :premises (@p193) :args ((or @t140 @t138 @t148 @t150))) % 0.22/0.55 (step @p195 :rule chain_m_resolution :premises (@p194 @p192 @p186 @p184) :args (@t150 (@list false true false) (@list @t139 @t138 @t146))) % 0.22/0.55 (assume-push @p210 @t112) % 0.22/0.55 (step @p197 :rule instantiate :premises (@p210) :args ((@list @t135 @t136 @t137))) % 0.22/0.55 (step-pop @p211 :rule scope :premises (@p197)) % 0.22/0.55 (step @p198 :rule process_scope :premises (@p211) :args (@t149)) % 0.22/0.55 (step @p200 :rule implies_elim :premises (@p198)) % 0.22/0.55 (step @p201 false :rule chain_m_resolution :premises (@p200 @p195 @p163) :args (false (@list true false) (@list @t149 @t112))) % 0.22/0.55 ) % 0.22/0.55 % SZS output end Proof % 0.22/0.55 % cvc5 exiting %------------------------------------------------------------------------------