%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL880^1 : TPTP v9.3.1. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/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 11:24:05 AM UTC 2026 % Result : Theorem 0.18s 0.55s % Output : Proof 0.18s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL880^1 : TPTP v9.3.1. Released v5.2.0. % 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.08/0.35 % Computer : n005.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Fri Sep 4 22:21:36 UTC 2026 % 0.08/0.35 % CPUTime : % 0.13/0.43 %----Proving TH0 % 0.18/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.18/0.55 % SZS status Theorem % 0.18/0.55 % SZS output start Proof % 0.18/0.55 ( % 0.18/0.55 (declare-sort $$unsorted 0) % 0.18/0.55 (declare-sort tptp.mu 0) % 0.18/0.55 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.18/0.55 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.18/0.55 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.18/0.55 (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)))))) % 0.18/0.55 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.18/0.55 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.55 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.18/0.55 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.55 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.18/0.55 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.18/0.55 (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))))))) % 0.18/0.55 (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))))))) % 0.18/0.55 (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)))))) % 0.18/0.55 (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)))))) % 0.18/0.55 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.18/0.55 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.18/0.55 (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)))))) % 0.18/0.55 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.18/0.55 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.55 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.18/0.55 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.18/0.55 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.18/0.55 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.18/0.55 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.18/0.55 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.18/0.55 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.18/0.55 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.18/0.55 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.55 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.55 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.18/0.55 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.18/0.55 (define @t1 () (@var "W" $$unsorted)) % 0.18/0.55 (define @t2 () (@var "V" $$unsorted)) % 0.18/0.55 (define @t3 () (@var "I" (-> $$unsorted $$unsorted Bool))) % 0.18/0.55 (define @t4 () (_ (_ @t3 @t2) @t1)) % 0.18/0.55 (define @t5 () (@var "U" $$unsorted)) % 0.18/0.55 (define @t6 () (_ (_ @t3 @t5) @t1)) % 0.18/0.55 (define @t7 () (@var "J" (-> $$unsorted $$unsorted Bool))) % 0.18/0.55 (define @t8 () (_ (_ @t7 @t5) @t2)) % 0.18/0.55 (define @t9 () (and @t8 @t6)) % 0.18/0.55 (define @t10 () (@list @t5 @t2 @t1)) % 0.18/0.55 (define @t11 () (forall @t10 (=> @t9 @t4))) % 0.18/0.55 (define @t12 () (@var "__flatten_var_0" $$unsorted)) % 0.18/0.55 (define @t13 () (@var "Phi" (-> $$unsorted Bool))) % 0.18/0.55 (define @t14 () (_ tptp.mnot (_ (_ tptp.mbox @t3) @t13))) % 0.18/0.55 (define @t15 () (@list @t13 @t12)) % 0.18/0.55 (define @t16 () (lambda @t15 (_ (_ (_ tptp.mimplies @t14) (_ (_ tptp.mbox @t7) @t14)) @t12))) % 0.18/0.55 (define @t17 () (= (_ tptp.mvalid (_ tptp.mforall_prop @t16)) @t11)) % 0.18/0.55 (define @t18 () (@list @t3 @t7)) % 0.18/0.55 (define @t19 () (forall @t18 @t17)) % 0.18/0.55 (define @t20 () (not @t19)) % 0.18/0.55 (define @t21 () (@var "Y" tptp.mu)) % 0.18/0.55 (define @t22 () (@var "X" tptp.mu)) % 0.18/0.55 (define @t23 () (lambda (@list @t22 @t21 @t1) (= @t22 @t21))) % 0.18/0.55 (define @t24 () (@var "Y" (-> $$unsorted Bool))) % 0.18/0.55 (define @t25 () (@var "X" (-> $$unsorted Bool))) % 0.18/0.55 (define @t26 () (lambda (@list @t25 @t24 @t1) (= (_ @t25 @t1) (_ @t24 @t1)))) % 0.18/0.55 (define @t27 () (_ @t13 @t1)) % 0.18/0.55 (define @t28 () (not @t27)) % 0.18/0.55 (define @t29 () (@list @t13 @t1)) % 0.18/0.55 (define @t30 () (lambda @t29 @t28)) % 0.18/0.55 (define @t31 () (@var "Psi" (-> $$unsorted Bool))) % 0.18/0.55 (define @t32 () (_ @t31 @t1)) % 0.18/0.55 (define @t33 () (lambda (@list @t13 @t31 @t1) (or @t27 @t32))) % 0.18/0.55 (define @t34 () (_ tptp.mnot @t31)) % 0.18/0.55 (define @t35 () (_ tptp.mnot @t13)) % 0.18/0.55 (define @t36 () (_ tptp.mor @t35)) % 0.18/0.55 (define @t37 () (@list @t13 @t31 @t12)) % 0.18/0.55 (define @t38 () (lambda @t37 (_ (_ tptp.mnot (_ @t36 @t34)) @t12))) % 0.18/0.55 (define @t39 () (lambda @t37 (_ (_ @t36 @t31) @t12))) % 0.18/0.55 (define @t40 () (lambda @t37 (_ (_ (_ tptp.mor @t34) @t13) @t12))) % 0.18/0.55 (define @t41 () (lambda @t37 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t13) @t31)) (_ (_ tptp.mimplies @t31) @t13)) @t12))) % 0.18/0.55 (define @t42 () (lambda @t37 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t13) @t31)) @t12))) % 0.18/0.55 (define @t43 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.18/0.55 (define @t44 () (_ @t43 @t22)) % 0.18/0.55 (define @t45 () (lambda (@list @t43 @t1) (forall (@list @t22) (_ @t44 @t1)))) % 0.18/0.55 (define @t46 () (@var "P" (-> $$unsorted Bool))) % 0.18/0.55 (define @t47 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.18/0.55 (define @t48 () (_ @t47 @t46)) % 0.18/0.55 (define @t49 () (_ @t48 @t1)) % 0.18/0.55 (define @t50 () (@list @t46)) % 0.18/0.55 (define @t51 () (forall @t50 @t49)) % 0.18/0.55 (define @t52 () (@list @t47 @t1)) % 0.18/0.55 (define @t53 () (lambda @t52 @t51)) % 0.18/0.55 (define @t54 () (lambda (@list @t43 @t12) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t22 @t12) (_ (_ tptp.mnot @t44) @t12)))) @t12))) % 0.18/0.55 (define @t55 () (lambda (@list @t47 @t12) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t46 @t12) (_ (_ tptp.mnot @t48) @t12)))) @t12))) % 0.18/0.55 (define @t56 () (@list @t1)) % 0.18/0.55 (define @t57 () (lambda @t56 true)) % 0.18/0.55 (define @t58 () (_ @t13 @t2)) % 0.18/0.55 (define @t59 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.18/0.55 (define @t60 () (_ (_ @t59 @t1) @t2)) % 0.18/0.55 (define @t61 () (not @t60)) % 0.18/0.55 (define @t62 () (or @t61 @t58)) % 0.18/0.55 (define @t63 () (@list @t2)) % 0.18/0.55 (define @t64 () (forall @t63 @t62)) % 0.18/0.55 (define @t65 () (@list @t59 @t13 @t1)) % 0.18/0.55 (define @t66 () (lambda @t65 @t64)) % 0.18/0.55 (define @t67 () (lambda (@list @t59 @t13 @t12) (_ (_ tptp.mnot (_ (_ tptp.mbox @t59) @t35)) @t12))) % 0.18/0.55 (define @t68 () (@var "S" $$unsorted)) % 0.18/0.55 (define @t69 () (_ @t59 @t68)) % 0.18/0.55 (define @t70 () (@list @t68)) % 0.18/0.55 (define @t71 () (@list @t59)) % 0.18/0.55 (define @t72 () (lambda @t71 (forall @t70 (_ @t69 @t68)))) % 0.18/0.55 (define @t73 () (@var "T" $$unsorted)) % 0.18/0.55 (define @t74 () (_ @t59 @t73)) % 0.18/0.55 (define @t75 () (_ @t69 @t73)) % 0.18/0.55 (define @t76 () (lambda @t71 (forall (@list @t68 @t73) (=> @t75 (_ @t74 @t68))))) % 0.18/0.55 (define @t77 () (@list @t73)) % 0.18/0.55 (define @t78 () (lambda @t71 (forall @t70 (exists @t77 @t75)))) % 0.18/0.55 (define @t79 () (_ @t69 @t5)) % 0.18/0.55 (define @t80 () (_ @t74 @t5)) % 0.18/0.55 (define @t81 () (@list @t68 @t73 @t5)) % 0.18/0.55 (define @t82 () (lambda @t71 (forall @t81 (=> (and @t75 @t80) @t79)))) % 0.18/0.55 (define @t83 () (and @t75 @t79)) % 0.18/0.55 (define @t84 () (lambda @t71 (forall @t81 (=> @t83 @t80)))) % 0.18/0.55 (define @t85 () (= @t73 @t5)) % 0.18/0.55 (define @t86 () (lambda @t71 (forall @t81 (=> @t83 @t85)))) % 0.18/0.55 (define @t87 () (@list @t5)) % 0.18/0.55 (define @t88 () (lambda @t71 (forall @t70 (exists @t77 (and @t75 (forall @t87 (=> @t79 @t85))))))) % 0.18/0.55 (define @t89 () (_ @t59 @t5)) % 0.18/0.55 (define @t90 () (_ @t89 @t73)) % 0.18/0.55 (define @t91 () (lambda @t71 (forall @t81 (=> @t75 (exists @t87 (and @t79 @t90)))))) % 0.18/0.55 (define @t92 () (lambda @t71 (forall @t81 (=> @t83 (or @t80 @t85 @t90))))) % 0.18/0.55 (define @t93 () (lambda @t71 (forall @t81 (=> @t83 (exists @t63 (and (_ @t74 @t2) (_ @t89 @t2))))))) % 0.18/0.55 (define @t94 () (forall @t56 @t27)) % 0.18/0.55 (define @t95 () (@list @t13)) % 0.18/0.55 (define @t96 () (lambda @t95 @t94)) % 0.18/0.55 (define @t97 () (lambda @t95 (forall @t56 @t28))) % 0.18/0.55 (define @t98 () (lambda @t95 (exists @t56 @t27))) % 0.18/0.55 (define @t99 () (lambda @t95 (exists @t56 @t28))) % 0.18/0.55 (define @t100 () (@var "BOUND_VARIABLE_8408" $$unsorted)) % 0.18/0.55 (define @t101 () (_ @t46 @t100)) % 0.18/0.55 (define @t102 () (@var "BOUND_VARIABLE_8461" $$unsorted)) % 0.18/0.55 (define @t103 () (@list @t100)) % 0.18/0.55 (define @t104 () (not (forall @t103 (or (not (_ @t3 @t102 @t100)) @t101)))) % 0.18/0.55 (define @t105 () (not (_ @t7 @t1 @t102))) % 0.18/0.55 (define @t106 () (@var "BOUND_VARIABLE_8455" $$unsorted)) % 0.18/0.55 (define @t107 () (_ @t46 @t106)) % 0.18/0.55 (define @t108 () (not (_ @t3 @t1 @t106))) % 0.18/0.55 (define @t109 () (or @t108 @t107 @t105 @t104)) % 0.18/0.55 (define @t110 () (@list @t1 @t46 @t106 @t102)) % 0.18/0.55 (define @t111 () (forall @t110 @t109)) % 0.18/0.55 (define @t112 () (@list @t46 @t106 @t102)) % 0.18/0.55 (define @t113 () (forall @t112 @t109)) % 0.18/0.55 (define @t114 () (lambda @t56 @t113)) % 0.18/0.55 (define @t115 () (_ @t114 @t1)) % 0.18/0.55 (define @t116 () (forall @t56 @t115)) % 0.18/0.55 (define @t117 () (_ @t13 @t1)) % 0.18/0.55 (define @t118 () (lambda @t95 (forall @t56 @t117))) % 0.18/0.55 (define @t119 () (or @t105 @t104)) % 0.18/0.55 (define @t120 () (or @t108 @t107)) % 0.18/0.55 (define @t121 () (or @t120 @t119)) % 0.18/0.55 (define @t122 () (forall @t112 @t121)) % 0.18/0.55 (define @t123 () (forall (@list @t106 @t102) @t121)) % 0.18/0.55 (define @t124 () (forall (@list @t102) @t119)) % 0.18/0.55 (define @t125 () (@list @t2)) % 0.18/0.55 (define @t126 () (forall (@list @t106) @t120)) % 0.18/0.55 (define @t127 () (or @t126 @t124)) % 0.18/0.55 (define @t128 () (not (_ @t3 @t2 @t100))) % 0.18/0.55 (define @t129 () (not (_ @t7 @t1 @t2))) % 0.18/0.55 (define @t130 () (not (_ @t3 @t1 @t2))) % 0.18/0.55 (define @t131 () (or (forall @t63 (or @t130 (_ @t46 @t2))) (forall @t63 (or @t129 (not (forall @t103 (or @t128 @t101))))))) % 0.18/0.55 (define @t132 () (_ @t13 @t100)) % 0.18/0.55 (define @t133 () (not (forall @t103 (or @t128 @t132)))) % 0.18/0.55 (define @t134 () (forall @t63 (or (not (_ @t7 @t12 @t2)) @t133))) % 0.18/0.55 (define @t135 () (_ @t13 @t2)) % 0.18/0.55 (define @t136 () (forall @t63 (or (not (_ @t3 @t12 @t2)) @t135))) % 0.18/0.55 (define @t137 () (or @t136 @t134)) % 0.18/0.55 (define @t138 () (lambda @t15 @t137)) % 0.18/0.55 (define @t139 () (_ @t138 @t46 @t1)) % 0.18/0.55 (define @t140 () (forall @t50 @t139)) % 0.18/0.55 (define @t141 () (lambda @t56 @t140)) % 0.18/0.55 (define @t142 () (_ @t47 @t46 @t1)) % 0.18/0.55 (define @t143 () (lambda @t52 (forall @t50 @t142))) % 0.18/0.55 (define @t144 () (@list @t12)) % 0.18/0.55 (define @t145 () (lambda @t56 (forall @t63 (or @t129 @t133)))) % 0.18/0.55 (define @t146 () (_ @t145 @t12)) % 0.18/0.55 (define @t147 () (or @t136 @t146)) % 0.18/0.55 (define @t148 () (lambda @t144 @t147)) % 0.18/0.55 (define @t149 () (_ @t31 @t12)) % 0.18/0.55 (define @t150 () (@list @t31 @t12)) % 0.18/0.55 (define @t151 () (forall @t63 (or @t130 @t135))) % 0.18/0.55 (define @t152 () (not @t151)) % 0.18/0.55 (define @t153 () (lambda @t56 @t152)) % 0.18/0.55 (define @t154 () (or @t129 (_ @t153 @t2))) % 0.18/0.55 (define @t155 () (forall @t63 @t154)) % 0.18/0.55 (define @t156 () (lambda @t56 @t155)) % 0.18/0.55 (define @t157 () (lambda @t29 (forall @t63 (or @t129 @t135)))) % 0.18/0.55 (define @t158 () (lambda @t56 @t151)) % 0.18/0.55 (define @t159 () (_ @t158 @t1)) % 0.18/0.55 (define @t160 () (not @t159)) % 0.18/0.55 (define @t161 () (lambda @t56 @t160)) % 0.18/0.55 (define @t162 () (lambda @t29 @t151)) % 0.18/0.55 (define @t163 () (_ @t59 @t1 @t2)) % 0.18/0.55 (define @t164 () (lambda @t65 (forall @t63 (or (not @t163) @t135)))) % 0.18/0.55 (define @t165 () (_ @t164 @t3)) % 0.18/0.55 (define @t166 () (_ @t164 @t7)) % 0.18/0.55 (define @t167 () (_ @t153 @t12)) % 0.18/0.55 (define @t168 () (not @t167)) % 0.18/0.55 (define @t169 () (or @t168 @t149)) % 0.18/0.55 (define @t170 () (lambda @t150 @t169)) % 0.18/0.55 (define @t171 () (or (not (_ @t13 @t12)) @t149)) % 0.18/0.55 (define @t172 () (lambda @t37 @t171)) % 0.18/0.55 (define @t173 () (_ @t30 (_ @t165 @t13))) % 0.18/0.55 (define @t174 () (lambda @t15 (_ (_ (_ @t172 @t173) (_ @t166 @t173)) @t12))) % 0.18/0.55 (define @t175 () (_ @t3 @t2 @t1)) % 0.18/0.55 (define @t176 () (_ @t3 @t5 @t1)) % 0.18/0.55 (define @t177 () (not @t6)) % 0.18/0.55 (define @t178 () (_ @t7 @t5 @t2)) % 0.18/0.55 (define @t179 () (not @t8)) % 0.18/0.55 (define @t180 () (or @t179 @t177 @t4)) % 0.18/0.55 (define @t181 () (_ @t118 (_ @t143 @t174))) % 0.18/0.55 (define @t182 () (forall @t18 (= @t181 @t11))) % 0.18/0.55 (define @t183 () (or @t28 @t32)) % 0.18/0.55 (define @t184 () (lambda @t56 @t183)) % 0.18/0.55 (define @t185 () (@list @t31 @t1)) % 0.18/0.55 (define @t186 () (lambda @t56 @t28)) % 0.18/0.55 (define @t187 () (_ @t186 @t1)) % 0.18/0.55 (define @t188 () (or @t187 @t32)) % 0.18/0.55 (define @t189 () (lambda @t185 @t188)) % 0.18/0.55 (define @t190 () (forall @t18 (= (forall @t10 (or (not @t178) (not @t176) @t175)) @t111))) % 0.18/0.55 (define @t191 () (@quantifiers_skolemize @t190 0)) % 0.18/0.55 (define @t192 () (@quantifiers_skolemize @t190 1)) % 0.18/0.55 (define @t193 () (forall @t110 (or (not (_ @t191 @t1 @t106)) @t107 (not (_ @t192 @t1 @t102)) (not (forall @t103 (or (not (_ @t191 @t102 @t100)) @t101)))))) % 0.18/0.55 (define @t194 () (forall @t10 (or (not (_ @t192 @t5 @t2)) (not (_ @t191 @t5 @t1)) (_ @t191 @t2 @t1)))) % 0.18/0.55 (define @t195 () (= @t194 @t193)) % 0.18/0.55 (define @t196 () (@quantifiers_skolemize @t193 1)) % 0.18/0.55 (define @t197 () (@quantifiers_skolemize @t193 3)) % 0.18/0.55 (define @t198 () (forall @t103 (or (not (_ @t191 @t197 @t100)) (_ @t196 @t100)))) % 0.18/0.55 (define @t199 () (not @t198)) % 0.18/0.55 (define @t200 () (@quantifiers_skolemize @t193 0)) % 0.18/0.55 (define @t201 () (_ @t192 @t200 @t197)) % 0.18/0.55 (define @t202 () (not @t201)) % 0.18/0.55 (define @t203 () (@quantifiers_skolemize @t193 2)) % 0.18/0.55 (define @t204 () (_ @t196 @t203)) % 0.18/0.55 (define @t205 () (_ @t191 @t200 @t203)) % 0.18/0.55 (define @t206 () (not @t205)) % 0.18/0.55 (define @t207 () (or @t206 @t204 @t202 @t199)) % 0.18/0.55 (define @t208 () (not @t207)) % 0.18/0.55 (define @t209 () (not @t193)) % 0.18/0.55 (define @t210 () (_ @t191 @t197 @t203)) % 0.18/0.55 (define @t211 () (or @t202 @t206 @t210)) % 0.18/0.55 (define @t212 () (not @t210)) % 0.18/0.55 (define @t213 () (or @t212 @t204)) % 0.18/0.55 (define @t214 () (not @t194)) % 0.18/0.55 (define @t215 () (@quantifiers_skolemize @t194 2)) % 0.18/0.55 (define @t216 () (@quantifiers_skolemize @t194 1)) % 0.18/0.55 (define @t217 () (_ @t191 @t216 @t215)) % 0.18/0.55 (define @t218 () (@quantifiers_skolemize @t194 0)) % 0.18/0.55 (define @t219 () (_ @t191 @t218 @t215)) % 0.18/0.55 (define @t220 () (not @t219)) % 0.18/0.55 (define @t221 () (_ @t192 @t218 @t216)) % 0.18/0.55 (define @t222 () (not @t221)) % 0.18/0.55 (define @t223 () (or @t222 @t220 @t217)) % 0.18/0.55 (define @t224 () (not @t223)) % 0.18/0.55 (define @t225 () (@list true)) % 0.18/0.55 (define @t226 () (@list @t223)) % 0.18/0.55 (define @t227 () (or @t220 @t217 @t222)) % 0.18/0.55 (define @t228 () (not @t227)) % 0.18/0.55 (define @t229 () (_ @t191 @t216)) % 0.18/0.55 (define @t230 () (_ @t229 @t215)) % 0.18/0.55 (define @t231 () (or @t220 @t230 @t222)) % 0.18/0.55 (define @t232 () (_ @t191 @t216 @t100)) % 0.18/0.55 (define @t233 () (not @t232)) % 0.18/0.55 (define @t234 () (_ @t229 @t100)) % 0.18/0.55 (define @t235 () (or @t233 @t234)) % 0.18/0.55 (define @t236 () (_ @t229 @t100)) % 0.18/0.55 (define @t237 () (or @t233 @t236)) % 0.18/0.55 (define @t238 () (forall @t103 @t237)) % 0.18/0.55 (define @t239 () (not @t238)) % 0.18/0.55 (define @t240 () (_ @t229 @t215)) % 0.18/0.55 (define @t241 () (or @t220 @t240 @t222 @t239)) % 0.18/0.55 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.18/0.55 (assume @p2 @t20) % 0.18/0.55 (assume @p3 true) % 0.18/0.55 (step @p4 (= tptp.meq_ind @t23) :rule refl :args (@t23)) % 0.18/0.55 (step @p5 (= tptp.meq_prop @t26) :rule refl :args (@t26)) % 0.18/0.55 (step @p6 (= tptp.mnot @t30) :rule refl :args (@t30)) % 0.18/0.55 (step @p7 (= tptp.mor @t33) :rule refl :args (@t33)) % 0.18/0.55 (step @p8 (= tptp.mand @t38) :rule refl :args (@t38)) % 0.18/0.55 (step @p9 (= tptp.mimplies @t39) :rule refl :args (@t39)) % 0.18/0.55 (step @p10 (= tptp.mimplied @t40) :rule refl :args (@t40)) % 0.18/0.55 (step @p11 (= tptp.mequiv @t41) :rule refl :args (@t41)) % 0.18/0.55 (step @p12 (= tptp.mxor @t42) :rule refl :args (@t42)) % 0.18/0.55 (step @p13 (= tptp.mforall_ind @t45) :rule refl :args (@t45)) % 0.18/0.55 (step @p14 (= tptp.mforall_prop @t53) :rule refl :args (@t53)) % 0.18/0.55 (step @p15 (= tptp.mexists_ind @t54) :rule refl :args (@t54)) % 0.18/0.55 (step @p16 (= tptp.mexists_prop @t55) :rule refl :args (@t55)) % 0.18/0.55 (step @p17 (= tptp.mtrue @t57) :rule refl :args (@t57)) % 0.18/0.55 (step @p18 (= tptp.mbox @t66) :rule refl :args (@t66)) % 0.18/0.55 (step @p19 (= tptp.mdia @t67) :rule refl :args (@t67)) % 0.18/0.55 (step @p20 (= tptp.mreflexive @t72) :rule refl :args (@t72)) % 0.18/0.55 (step @p21 (= tptp.msymmetric @t76) :rule refl :args (@t76)) % 0.18/0.55 (step @p22 (= tptp.mserial @t78) :rule refl :args (@t78)) % 0.18/0.55 (step @p23 (= tptp.mtransitive @t82) :rule refl :args (@t82)) % 0.18/0.55 (step @p24 (= tptp.meuclidean @t84) :rule refl :args (@t84)) % 0.18/0.55 (step @p25 (= tptp.mpartially_functional @t86) :rule refl :args (@t86)) % 0.18/0.55 (step @p26 (= tptp.mfunctional @t88) :rule refl :args (@t88)) % 0.18/0.55 (step @p27 (= tptp.mweakly_dense @t91) :rule refl :args (@t91)) % 0.18/0.55 (step @p28 (= tptp.mweakly_connected @t92) :rule refl :args (@t92)) % 0.18/0.55 (step @p29 (= tptp.mweakly_directed @t93) :rule refl :args (@t93)) % 0.18/0.55 (step @p30 (= tptp.mvalid @t96) :rule refl :args (@t96)) % 0.18/0.55 (step @p31 (= tptp.minvalid @t97) :rule refl :args (@t97)) % 0.18/0.55 (step @p32 (= tptp.msatisfiable @t98) :rule refl :args (@t98)) % 0.18/0.55 (step @p33 (= tptp.mcountersatisfiable @t99) :rule refl :args (@t99)) % 0.18/0.55 (step @p34 :rule quant-merge-prenex :args ((= (forall @t56 @t113) @t111))) % 0.18/0.55 (step @p35 :rule beta-reduce :args ((= @t115 @t113))) % 0.18/0.55 (step @p36 :rule cong :premises (@p35) :args (@t116)) % 0.18/0.55 (step @p37 :rule trans :premises (@p36 @p34)) % 0.18/0.55 (step @p38 :rule beta-reduce :args ((= (_ @t118 @t114) @t116))) % 0.18/0.55 (step @p39 :rule trans :premises (@p38 @p37)) % 0.18/0.55 (step @p40 :rule aci_norm :args ((= @t121 @t109))) % 0.18/0.55 (step @p41 :rule cong :premises (@p40) :args (@t122)) % 0.18/0.55 (step @p42 :rule quant-merge-prenex :args ((= (forall @t50 @t123) @t122))) % 0.18/0.55 (step @p43 :rule alpha_equiv :args (@t124 (@list @t102) @t125)) % 0.18/0.55 (step @p44 :rule alpha_equiv :args (@t126 (@list @t106) @t125)) % 0.18/0.55 (step @p45 :rule nary_cong :premises (@p44 @p43) :args (@t127)) % 0.18/0.55 (step @p46 :rule quant-miniscope-or :args ((= @t123 @t127))) % 0.18/0.55 (step @p47 :rule trans :premises (@p46 @p45)) % 0.18/0.55 (step @p48 :rule symm :premises (@p47)) % 0.18/0.55 (step @p49 :rule cong :premises (@p48) :args ((forall @t50 @t131))) % 0.18/0.55 (step @p50 :rule trans :premises (@p49 @p42)) % 0.18/0.55 (step @p51 :rule trans :premises (@p50 @p41)) % 0.18/0.55 (step @p52 :rule beta-reduce :args ((= @t139 @t131))) % 0.18/0.55 (step @p53 :rule cong :premises (@p52) :args (@t140)) % 0.18/0.55 (step @p54 :rule trans :premises (@p53 @p51)) % 0.18/0.55 (step @p55 :rule cong :premises (@p54) :args (@t141)) % 0.18/0.55 (step @p56 :rule beta-reduce :args ((= (_ @t143 @t138) @t141))) % 0.18/0.55 (step @p57 :rule trans :premises (@p56 @p55)) % 0.18/0.55 (step @p58 :rule beta-reduce :args ((= (_ (lambda @t144 @t137) @t12) @t137))) % 0.18/0.55 (step @p59 :rule refl :args (@t12)) % 0.18/0.55 (step @p60 :rule beta-reduce :args ((= @t146 @t134))) % 0.18/0.55 (step @p61 :rule refl :args (@t136)) % 0.18/0.55 (step @p62 :rule nary_cong :premises (@p61 @p60) :args (@t147)) % 0.18/0.55 (step @p63 :rule cong :premises (@p62) :args (@t148)) % 0.18/0.55 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t150 (or @t136 @t149)) @t145) @t148))) % 0.18/0.55 (step @p65 :rule trans :premises (@p64 @p63)) % 0.18/0.55 (step @p66 :rule beta-reduce :args ((= (_ (lambda @t56 (not (forall @t103 (or (not (_ @t3 @t1 @t100)) @t132)))) @t2) @t133))) % 0.18/0.55 (step @p67 :rule refl :args (@t2)) % 0.18/0.55 (step @p68 :rule alpha_equiv :args (@t151 @t125 (@list @t100))) % 0.18/0.55 (step @p69 :rule cong :premises (@p68) :args (@t152)) % 0.18/0.55 (step @p70 :rule cong :premises (@p69) :args (@t153)) % 0.18/0.55 (step @p71 :rule ho_cong :premises (@p70 @p67)) % 0.18/0.55 (step @p72 :rule trans :premises (@p71 @p66)) % 0.18/0.55 (step @p73 :rule refl :args (@t129)) % 0.18/0.55 (step @p74 :rule nary_cong :premises (@p73 @p72) :args (@t154)) % 0.18/0.55 (step @p75 :rule cong :premises (@p74) :args (@t155)) % 0.18/0.55 (step @p76 :rule cong :premises (@p75) :args (@t156)) % 0.18/0.55 (step @p77 :rule beta-reduce :args ((= (_ @t157 @t153) @t156))) % 0.18/0.55 (step @p78 :rule trans :premises (@p77 @p76)) % 0.18/0.55 (step @p79 :rule beta-reduce :args ((= @t159 @t151))) % 0.18/0.55 (step @p80 :rule cong :premises (@p79) :args (@t160)) % 0.18/0.55 (step @p81 :rule cong :premises (@p80) :args (@t161)) % 0.18/0.55 (step @p82 :rule beta-reduce :args ((= (_ @t30 @t158) @t161))) % 0.18/0.55 (step @p83 :rule trans :premises (@p82 @p81)) % 0.18/0.55 (step @p84 :rule beta-reduce :args ((= (_ @t162 @t13) @t158))) % 0.18/0.55 (step @p85 :rule refl :args (@t13)) % 0.18/0.55 (step @p86 :rule beta-reduce :args ((= @t165 @t162))) % 0.18/0.55 (step @p87 :rule ho_cong :premises (@p86 @p85)) % 0.18/0.55 (step @p88 :rule trans :premises (@p87 @p84)) % 0.18/0.55 (step @p89 :rule refl :args (@t30)) % 0.18/0.55 (step @p90 :rule ho_cong :premises (@p89 @p88)) % 0.18/0.55 (step @p91 :rule trans :premises (@p90 @p83)) % 0.18/0.55 (step @p92 :rule beta-reduce :args ((= @t166 @t157))) % 0.18/0.55 (step @p93 :rule ho_cong :premises (@p92 @p91)) % 0.18/0.55 (step @p94 :rule trans :premises (@p93 @p78)) % 0.18/0.55 (step @p95 :rule refl :args (@t149)) % 0.18/0.55 (step @p96 :rule bool-double-not-elim :args (@t136)) % 0.18/0.55 (step @p97 :rule beta-reduce :args ((= @t167 (not @t136)))) % 0.18/0.55 (step @p98 :rule cong :premises (@p97) :args (@t168)) % 0.18/0.55 (step @p99 :rule trans :premises (@p98 @p96)) % 0.18/0.55 (step @p100 :rule nary_cong :premises (@p99 @p95) :args (@t169)) % 0.18/0.55 (step @p101 :rule cong :premises (@p100) :args (@t170)) % 0.18/0.55 (step @p102 :rule beta-reduce :args ((= (_ @t172 @t153) @t170))) % 0.18/0.55 (step @p103 :rule trans :premises (@p102 @p101)) % 0.18/0.55 (step @p104 :rule refl :args (@t172)) % 0.18/0.55 (step @p105 :rule ho_cong :premises (@p104 @p91)) % 0.18/0.55 (step @p106 :rule trans :premises (@p105 @p103)) % 0.18/0.55 (step @p107 :rule ho_cong :premises (@p106 @p94)) % 0.18/0.55 (step @p108 :rule trans :premises (@p107 @p65)) % 0.18/0.55 (step @p109 :rule ho_cong :premises (@p108 @p59)) % 0.18/0.55 (step @p110 :rule trans :premises (@p109 @p58)) % 0.18/0.55 (step @p111 :rule cong :premises (@p110) :args (@t174)) % 0.18/0.55 (step @p112 :rule refl :args (@t143)) % 0.18/0.55 (step @p113 :rule ho_cong :premises (@p112 @p111)) % 0.18/0.55 (step @p114 :rule trans :premises (@p113 @p57)) % 0.18/0.55 (step @p115 :rule refl :args (@t118)) % 0.18/0.55 (step @p116 :rule ho_cong :premises (@p115 @p114)) % 0.18/0.55 (step @p117 :rule trans :premises (@p116 @p39)) % 0.18/0.55 (step @p118 :rule refl :args (@t175)) % 0.18/0.55 (step @p119 :rule refl :args (@t4)) % 0.18/0.55 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t4 @t175))) % 0.18/0.55 (step @p121 :rule symm :premises (@p120)) % 0.18/0.55 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 0.18/0.55 (step @p123 :rule refl :args (@t176)) % 0.18/0.55 (step @p124 :rule refl :args (@t6)) % 0.18/0.55 (step @p125 :rule cong :premises (@p124 @p123) :args ((= @t6 @t176))) % 0.18/0.55 (step @p126 :rule symm :premises (@p125)) % 0.18/0.55 (step @p127 :rule eq_resolve :premises (@p124 @p126)) % 0.18/0.55 (step @p128 :rule cong :premises (@p127) :args (@t177)) % 0.18/0.55 (step @p129 :rule refl :args (@t178)) % 0.18/0.55 (step @p130 :rule refl :args (@t8)) % 0.18/0.55 (step @p131 :rule cong :premises (@p130 @p129) :args ((= @t8 @t178))) % 0.18/0.55 (step @p132 :rule symm :premises (@p131)) % 0.18/0.55 (step @p133 :rule eq_resolve :premises (@p130 @p132)) % 0.18/0.55 (step @p134 :rule cong :premises (@p133) :args (@t179)) % 0.18/0.55 (step @p135 :rule nary_cong :premises (@p134 @p128 @p122) :args (@t180)) % 0.18/0.55 (step @p136 :rule cong :premises (@p135) :args ((forall @t10 @t180))) % 0.18/0.55 (step @p137 :rule aci_norm :args ((= (or (or @t179 @t177) @t4) @t180))) % 0.18/0.55 (step @p138 :rule bool-and-de-morgan :args (@t8 @t6 true)) % 0.18/0.55 (step @p139 :rule nary_cong :premises (@p138 @p119) :args ((or (not @t9) @t4))) % 0.18/0.55 (step @p140 :rule trans :premises (@p139 @p137)) % 0.18/0.55 (step @p141 :rule bool-impl-elim :args (@t9 @t4)) % 0.18/0.55 (step @p142 :rule trans :premises (@p141 @p140)) % 0.18/0.55 (step @p143 :rule cong :premises (@p142) :args (@t11)) % 0.18/0.55 (step @p144 :rule trans :premises (@p143 @p136)) % 0.18/0.55 (step @p145 :rule cong :premises (@p144 @p117) :args ((= @t11 @t181))) % 0.18/0.55 (step @p146 :rule eq-symm :args (@t181 @t11)) % 0.18/0.55 (step @p147 :rule trans :premises (@p146 @p145)) % 0.18/0.55 (step @p148 :rule cong :premises (@p147) :args (@t182)) % 0.18/0.55 (step @p149 :rule cong :premises (@p148) :args ((not @t182))) % 0.18/0.55 (step @p150 :rule refl :args (@t11)) % 0.18/0.55 (step @p151 :rule refl :args (@t3)) % 0.18/0.55 (step @p152 :rule refl :args (@t135)) % 0.18/0.55 (step @p153 :rule refl :args (@t58)) % 0.18/0.55 (step @p154 :rule cong :premises (@p153 @p152) :args ((= @t58 @t135))) % 0.18/0.55 (step @p155 :rule symm :premises (@p154)) % 0.18/0.55 (step @p156 :rule eq_resolve :premises (@p153 @p155)) % 0.18/0.55 (step @p157 :rule refl :args (@t163)) % 0.18/0.55 (step @p158 :rule refl :args (@t60)) % 0.18/0.55 (step @p159 :rule cong :premises (@p158 @p157) :args ((= @t60 @t163))) % 0.18/0.55 (step @p160 :rule symm :premises (@p159)) % 0.18/0.55 (step @p161 :rule eq_resolve :premises (@p158 @p160)) % 0.18/0.55 (step @p162 :rule cong :premises (@p161) :args (@t61)) % 0.18/0.55 (step @p163 :rule nary_cong :premises (@p162 @p156) :args (@t62)) % 0.18/0.55 (step @p164 :rule cong :premises (@p163) :args (@t64)) % 0.18/0.55 (step @p165 :rule cong :premises (@p164) :args (@t66)) % 0.18/0.55 (step @p166 :rule trans :premises (@p18 @p165)) % 0.18/0.55 (step @p167 :rule ho_cong :premises (@p166 @p151)) % 0.18/0.55 (step @p168 :rule ho_cong :premises (@p167 @p85)) % 0.18/0.55 (step @p169 :rule ho_cong :premises (@p6 @p168)) % 0.18/0.55 (step @p170 :rule refl :args (@t7)) % 0.18/0.55 (step @p171 :rule ho_cong :premises (@p166 @p170)) % 0.18/0.55 (step @p172 :rule ho_cong :premises (@p171 @p169)) % 0.18/0.55 (step @p173 :rule beta-reduce :args ((= (_ @t184 @t12) @t171))) % 0.18/0.55 (step @p174 :rule beta-reduce :args ((= (_ (lambda @t185 @t183) @t31) @t184))) % 0.18/0.55 (step @p175 :rule refl :args (@t31)) % 0.18/0.55 (step @p176 :rule refl :args (@t32)) % 0.18/0.55 (step @p177 :rule beta-reduce :args ((= @t187 @t28))) % 0.18/0.55 (step @p178 :rule nary_cong :premises (@p177 @p176) :args (@t188)) % 0.18/0.55 (step @p179 :rule cong :premises (@p178) :args (@t189)) % 0.18/0.55 (step @p180 :rule beta-reduce :args ((= (_ @t33 @t186) @t189))) % 0.18/0.55 (step @p181 :rule trans :premises (@p180 @p179)) % 0.18/0.55 (step @p182 :rule beta-reduce :args ((= (_ @t30 @t13) @t186))) % 0.18/0.55 (step @p183 :rule refl :args (@t33)) % 0.18/0.55 (step @p184 :rule ho_cong :premises (@p183 @p182)) % 0.18/0.55 (step @p185 :rule trans :premises (@p184 @p181)) % 0.18/0.55 (step @p186 :rule ho_cong :premises (@p185 @p175)) % 0.18/0.55 (step @p187 :rule trans :premises (@p186 @p174)) % 0.18/0.55 (step @p188 :rule ho_cong :premises (@p187 @p59)) % 0.18/0.55 (step @p189 :rule trans :premises (@p188 @p173)) % 0.18/0.55 (step @p190 :rule ho_cong :premises (@p6 @p85)) % 0.18/0.55 (step @p191 :rule ho_cong :premises (@p7 @p190)) % 0.18/0.55 (step @p192 :rule ho_cong :premises (@p191 @p175)) % 0.18/0.55 (step @p193 :rule ho_cong :premises (@p192 @p59)) % 0.18/0.55 (step @p194 :rule trans :premises (@p193 @p189)) % 0.18/0.55 (step @p195 :rule cong :premises (@p194) :args (@t39)) % 0.18/0.55 (step @p196 :rule trans :premises (@p9 @p195)) % 0.18/0.55 (step @p197 :rule ho_cong :premises (@p196 @p169)) % 0.18/0.55 (step @p198 :rule ho_cong :premises (@p197 @p172)) % 0.18/0.55 (step @p199 :rule ho_cong :premises (@p198 @p59)) % 0.18/0.55 (step @p200 :rule cong :premises (@p199) :args (@t16)) % 0.18/0.55 (step @p201 :rule refl :args (@t142)) % 0.18/0.55 (step @p202 :rule refl :args (@t49)) % 0.18/0.55 (step @p203 :rule cong :premises (@p202 @p201) :args ((= @t49 @t142))) % 0.18/0.55 (step @p204 :rule symm :premises (@p203)) % 0.18/0.55 (step @p205 :rule eq_resolve :premises (@p202 @p204)) % 0.18/0.55 (step @p206 :rule cong :premises (@p205) :args (@t51)) % 0.18/0.55 (step @p207 :rule cong :premises (@p206) :args (@t53)) % 0.18/0.55 (step @p208 :rule trans :premises (@p14 @p207)) % 0.18/0.55 (step @p209 :rule ho_cong :premises (@p208 @p200)) % 0.18/0.55 (step @p210 :rule refl :args (@t117)) % 0.18/0.55 (step @p211 :rule refl :args (@t27)) % 0.18/0.55 (step @p212 :rule cong :premises (@p211 @p210) :args ((= @t27 @t117))) % 0.18/0.55 (step @p213 :rule symm :premises (@p212)) % 0.18/0.55 (step @p214 :rule eq_resolve :premises (@p211 @p213)) % 0.18/0.55 (step @p215 :rule cong :premises (@p214) :args (@t94)) % 0.18/0.55 (step @p216 :rule cong :premises (@p215) :args (@t96)) % 0.18/0.55 (step @p217 :rule trans :premises (@p30 @p216)) % 0.18/0.55 (step @p218 :rule ho_cong :premises (@p217 @p209)) % 0.18/0.55 (step @p219 :rule cong :premises (@p218 @p150) :args (@t17)) % 0.18/0.55 (step @p220 :rule cong :premises (@p219) :args (@t19)) % 0.18/0.55 (step @p221 :rule cong :premises (@p220) :args (@t20)) % 0.18/0.55 (step @p222 :rule trans :premises (@p221 @p149)) % 0.18/0.55 (step @p223 :rule eq_resolve :premises (@p2 @p222)) % 0.18/0.55 (step @p224 :rule skolemize :premises (@p223)) % 0.18/0.55 (step @p225 :rule cnf_equiv_neg2 :args (@t195)) % 0.18/0.55 (step @p226 :rule refl :args (@t208)) % 0.18/0.55 (step @p227 :rule bool-double-not-elim :args (@t193)) % 0.18/0.55 (step @p228 :rule nary_cong :premises (@p227 @p226) :args ((or (not @t209) @t208))) % 0.18/0.55 (assume-push @p342 @t209) % 0.18/0.55 (step @p230 :rule skolemize :premises (@p342)) % 0.18/0.55 (step-pop @p343 :rule scope :premises (@p230)) % 0.18/0.55 (step @p231 :rule process_scope :premises (@p343) :args (@t208)) % 0.18/0.55 (step @p233 :rule implies_elim :premises (@p231)) % 0.18/0.55 (step @p234 :rule eq_resolve :premises (@p233 @p228)) % 0.18/0.55 (step @p235 :rule bool-double-not-elim :args (@t205)) % 0.18/0.55 (step @p236 :rule refl :args (@t207)) % 0.18/0.55 (step @p237 :rule nary_cong :premises (@p236 @p235) :args ((or @t207 (not @t206)))) % 0.18/0.55 (step @p238 :rule cnf_or_neg :args (@t207 0)) % 0.18/0.55 (step @p239 :rule eq_resolve :premises (@p238 @p237)) % 0.18/0.55 (step @p240 :rule reordering :premises (@p239) :args ((or @t205 @t207))) % 0.18/0.55 (step @p241 :rule cnf_or_neg :args (@t207 1)) % 0.18/0.55 (step @p242 :rule bool-double-not-elim :args (@t201)) % 0.18/0.55 (step @p243 :rule nary_cong :premises (@p236 @p242) :args ((or @t207 (not @t202)))) % 0.18/0.55 (step @p244 :rule cnf_or_neg :args (@t207 2)) % 0.18/0.55 (step @p245 :rule eq_resolve :premises (@p244 @p243)) % 0.18/0.55 (step @p246 :rule reordering :premises (@p245) :args ((or @t201 @t207))) % 0.18/0.55 (step @p247 :rule bool-double-not-elim :args (@t198)) % 0.18/0.55 (step @p248 :rule nary_cong :premises (@p236 @p247) :args ((or @t207 (not @t199)))) % 0.18/0.55 (step @p249 :rule cnf_or_neg :args (@t207 3)) % 0.18/0.55 (step @p250 :rule eq_resolve :premises (@p249 @p248)) % 0.18/0.55 (step @p251 :rule reordering :premises (@p250) :args ((or @t198 @t207))) % 0.18/0.55 (assume-push @p344 @t194) % 0.18/0.55 (step @p253 :rule instantiate :premises (@p344) :args ((@list @t200 @t197 @t203))) % 0.18/0.55 (step-pop @p345 :rule scope :premises (@p253)) % 0.18/0.55 (step @p254 :rule process_scope :premises (@p345) :args (@t211)) % 0.18/0.55 (step @p256 :rule implies_elim :premises (@p254)) % 0.18/0.55 (assume-push @p346 @t198) % 0.18/0.55 (step @p258 :rule instantiate :premises (@p346) :args ((@list @t203))) % 0.18/0.55 (step-pop @p347 :rule scope :premises (@p258)) % 0.18/0.55 (step @p259 :rule process_scope :premises (@p347) :args (@t213)) % 0.18/0.55 (step @p261 :rule implies_elim :premises (@p259)) % 0.18/0.55 (step @p262 :rule cnf_or_pos :args (@t211)) % 0.18/0.55 (step @p263 :rule reordering :premises (@p262) :args ((or @t206 @t202 @t210 (not @t211)))) % 0.18/0.55 (step @p264 :rule cnf_or_pos :args (@t213)) % 0.18/0.55 (step @p265 :rule reordering :premises (@p264) :args ((or @t204 @t212 (not @t213)))) % 0.18/0.55 (step @p266 :rule chain_m_resolution :premises (@p265 @p263 @p261 @p256 @p251 @p246 @p241 @p240 @p234 @p225 @p224) :args (@t214 (@list false false false false false true false true true true) (@list @t210 @t213 @t211 @t198 @t201 @t204 @t205 @t207 @t193 @t195))) % 0.18/0.55 (step @p267 :rule cnf_equiv_neg1 :args (@t195)) % 0.18/0.55 (step @p268 :rule reordering :premises (@p267) :args ((or @t194 @t193 @t195))) % 0.18/0.55 (step @p269 :rule chain_m_resolution :premises (@p268 @p266 @p224) :args (@t193 (@list true true) (@list @t194 @t195))) % 0.18/0.55 (step @p270 :rule refl :args (@t224)) % 0.18/0.55 (step @p271 :rule bool-double-not-elim :args (@t194)) % 0.18/0.55 (step @p272 :rule nary_cong :premises (@p271 @p270) :args ((or (not @t214) @t224))) % 0.18/0.55 (assume-push @p348 @t214) % 0.18/0.55 (step @p274 :rule skolemize :premises (@p348)) % 0.18/0.55 (step-pop @p349 :rule scope :premises (@p274)) % 0.18/0.55 (step @p275 :rule process_scope :premises (@p349) :args (@t224)) % 0.18/0.55 (step @p277 :rule implies_elim :premises (@p275)) % 0.18/0.55 (step @p278 :rule eq_resolve :premises (@p277 @p272)) % 0.18/0.55 (step @p279 :rule chain_m_resolution :premises (@p278 @p266) :args (@t224 @t225 (@list @t194))) % 0.18/0.55 (step @p280 :rule cnf_or_neg :args (@t223 2)) % 0.18/0.55 (step @p281 :rule chain_m_resolution :premises (@p280 @p279) :args ((not @t217) @t225 @t226)) % 0.18/0.55 (step @p282 :rule bool-double-not-elim :args (@t219)) % 0.18/0.55 (step @p283 :rule refl :args (@t223)) % 0.18/0.55 (step @p284 :rule nary_cong :premises (@p283 @p282) :args ((or @t223 (not @t220)))) % 0.18/0.55 (step @p285 :rule cnf_or_neg :args (@t223 1)) % 0.18/0.55 (step @p286 :rule eq_resolve :premises (@p285 @p284)) % 0.18/0.55 (step @p287 :rule reordering :premises (@p286) :args ((or @t219 @t223))) % 0.18/0.55 (step @p288 :rule chain_m_resolution :premises (@p287 @p279) :args (@t219 @t225 @t226)) % 0.18/0.55 (step @p289 :rule bool-double-not-elim :args (@t221)) % 0.18/0.55 (step @p290 :rule nary_cong :premises (@p283 @p289) :args ((or @t223 (not @t222)))) % 0.18/0.55 (step @p291 :rule cnf_or_neg :args (@t223 0)) % 0.18/0.55 (step @p292 :rule eq_resolve :premises (@p291 @p290)) % 0.18/0.55 (step @p293 :rule reordering :premises (@p292) :args ((or @t221 @t223))) % 0.18/0.55 (step @p294 :rule chain_m_resolution :premises (@p293 @p279) :args (@t221 @t225 @t226)) % 0.18/0.55 (step @p295 :rule cnf_or_pos :args (@t227)) % 0.18/0.55 (step @p296 :rule reordering :premises (@p295) :args ((or @t222 @t220 @t217 @t228))) % 0.18/0.55 (step @p297 :rule chain_m_resolution :premises (@p296 @p294 @p288 @p281) :args (@t228 (@list false false true) (@list @t221 @t219 @t217))) % 0.18/0.55 (step @p298 :rule refl :args (@t222)) % 0.18/0.55 (step @p299 :rule refl :args (@t217)) % 0.18/0.55 (step @p300 :rule refl :args (@t230)) % 0.18/0.55 (step @p301 :rule cong :premises (@p300 @p299) :args ((= @t230 @t217))) % 0.18/0.55 (step @p302 :rule symm :premises (@p301)) % 0.18/0.55 (step @p303 :rule eq_resolve :premises (@p300 @p302)) % 0.18/0.55 (step @p304 :rule refl :args (@t220)) % 0.18/0.55 (step @p305 :rule nary_cong :premises (@p304 @p303 @p298) :args (@t231)) % 0.18/0.55 (step @p306 :rule refl :args (@t193)) % 0.18/0.55 (step @p307 :rule cong :premises (@p306 @p305) :args ((=> @t193 @t231))) % 0.18/0.55 (step @p308 :rule aci_norm :args ((= (or @t220 @t230 @t222 false) @t231))) % 0.18/0.55 (step @p309 :rule evaluate :args ((not true))) % 0.18/0.55 (step @p310 :rule quant-unused-vars :args ((= (forall @t103 true) true))) % 0.18/0.55 (step @p311 :rule bool-or-taut2 :args (false @t232 false false)) % 0.18/0.55 (step @p312 :rule cong :premises (@p311) :args ((forall @t103 (or @t233 @t232)))) % 0.18/0.55 (step @p313 :rule trans :premises (@p312 @p310)) % 0.18/0.55 (step @p314 :rule refl :args (@t232)) % 0.18/0.55 (step @p315 :rule refl :args (@t234)) % 0.18/0.55 (step @p316 :rule cong :premises (@p315 @p314) :args ((= @t234 @t232))) % 0.18/0.55 (step @p317 :rule symm :premises (@p316)) % 0.18/0.55 (step @p318 :rule eq_resolve :premises (@p315 @p317)) % 0.18/0.55 (step @p319 :rule refl :args (@t233)) % 0.18/0.55 (step @p320 :rule nary_cong :premises (@p319 @p318) :args (@t235)) % 0.18/0.55 (step @p321 :rule cong :premises (@p320) :args ((forall @t103 @t235))) % 0.18/0.55 (step @p322 :rule trans :premises (@p321 @p313)) % 0.18/0.55 (step @p323 :rule refl :args (@t236)) % 0.18/0.55 (step @p324 :rule refl :args (@t233)) % 0.18/0.55 (step @p325 :rule nary_cong :premises (@p324 @p323) :args (@t237)) % 0.18/0.55 (step @p326 :rule cong :premises (@p325) :args (@t238)) % 0.18/0.55 (step @p327 :rule trans :premises (@p326 @p322)) % 0.18/0.55 (step @p328 :rule cong :premises (@p327) :args (@t239)) % 0.18/0.55 (step @p329 :rule trans :premises (@p328 @p309)) % 0.18/0.55 (step @p330 :rule refl :args (@t240)) % 0.18/0.55 (step @p331 :rule nary_cong :premises (@p304 @p330 @p298 @p329) :args (@t241)) % 0.18/0.55 (step @p332 :rule trans :premises (@p331 @p308)) % 0.18/0.55 (step @p333 :rule cong :premises (@p306 @p332) :args ((=> @t193 @t241))) % 0.18/0.55 (assume-push @p350 @t193) % 0.18/0.55 (step @p335 :rule instantiate :premises (@p350) :args ((@list @t218 @t229 @t215 @t216))) % 0.18/0.55 (step-pop @p351 :rule scope :premises (@p335)) % 0.18/0.55 (step @p336 :rule process_scope :premises (@p351) :args (@t241)) % 0.18/0.55 (step @p338 :rule eq_resolve :premises (@p336 @p333)) % 0.18/0.55 (step @p339 :rule eq_resolve :premises (@p338 @p307)) % 0.18/0.55 (step @p340 :rule implies_elim :premises (@p339)) % 0.18/0.55 (step @p341 false :rule chain_m_resolution :premises (@p340 @p297 @p269) :args (false (@list true false) (@list @t227 @t193))) % 0.18/0.55 ) % 0.18/0.55 % SZS output end Proof % 0.18/0.55 % cvc5 exiting %------------------------------------------------------------------------------