%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL703^1 : 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 : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:40 AM UTC 2026 % Result : Theorem 0.20s 0.55s % Output : Proof 0.20s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL703^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.09/0.35 % Computer : n008.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 22:03:23 UTC 2026 % 0.09/0.35 % CPUTime : % 0.14/0.43 %----Proving TH0 % 0.20/0.55 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.20/0.55 % SZS status Theorem % 0.20/0.55 % SZS output start Proof % 0.20/0.55 ( % 0.20/0.55 (declare-sort $$unsorted 0) % 0.20/0.55 (declare-sort tptp.mu 0) % 0.20/0.55 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.20/0.55 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.20/0.55 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.20/0.55 (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)))))) % 0.20/0.55 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.20/0.55 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.55 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.20/0.55 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.55 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.20/0.55 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.20/0.55 (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))))))) % 0.20/0.55 (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))))))) % 0.20/0.55 (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)))))) % 0.20/0.55 (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)))))) % 0.20/0.55 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.20/0.55 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.20/0.55 (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)))))) % 0.20/0.55 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.20/0.55 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.20/0.55 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.20/0.55 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.20/0.55 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.20/0.55 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.20/0.55 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.20/0.55 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.20/0.55 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.20/0.55 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.20/0.55 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.55 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.55 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.20/0.55 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.20/0.55 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.20/0.55 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.20/0.55 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.20/0.55 (define @t4 () (_ (_ tptp.mdia @t3) @t2)) % 0.20/0.55 (define @t5 () (_ tptp.mbox @t3)) % 0.20/0.55 (define @t6 () (@list @t2 @t1)) % 0.20/0.55 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mimplies @t4) (_ @t5 @t4)) @t1))) % 0.20/0.55 (define @t8 () (=> (_ tptp.meuclidean @t3) (_ tptp.mvalid (_ tptp.mforall_prop @t7)))) % 0.20/0.55 (define @t9 () (@list @t3)) % 0.20/0.55 (define @t10 () (forall @t9 @t8)) % 0.20/0.55 (define @t11 () (not @t10)) % 0.20/0.55 (define @t12 () (@var "Y" tptp.mu)) % 0.20/0.55 (define @t13 () (@var "X" tptp.mu)) % 0.20/0.55 (define @t14 () (@var "W" $$unsorted)) % 0.20/0.55 (define @t15 () (lambda (@list @t13 @t12 @t14) (= @t13 @t12))) % 0.20/0.55 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.20/0.55 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 0.20/0.55 (define @t18 () (lambda (@list @t17 @t16 @t14) (= (_ @t17 @t14) (_ @t16 @t14)))) % 0.20/0.55 (define @t19 () (@var "Phi" (-> $$unsorted Bool))) % 0.20/0.55 (define @t20 () (_ @t19 @t14)) % 0.20/0.55 (define @t21 () (not @t20)) % 0.20/0.55 (define @t22 () (@list @t19 @t14)) % 0.20/0.55 (define @t23 () (lambda @t22 @t21)) % 0.20/0.55 (define @t24 () (@var "Psi" (-> $$unsorted Bool))) % 0.20/0.55 (define @t25 () (_ @t24 @t14)) % 0.20/0.55 (define @t26 () (lambda (@list @t19 @t24 @t14) (or @t20 @t25))) % 0.20/0.55 (define @t27 () (_ tptp.mnot @t24)) % 0.20/0.55 (define @t28 () (_ tptp.mnot @t19)) % 0.20/0.55 (define @t29 () (_ tptp.mor @t28)) % 0.20/0.55 (define @t30 () (@list @t19 @t24 @t1)) % 0.20/0.55 (define @t31 () (lambda @t30 (_ (_ tptp.mnot (_ @t29 @t27)) @t1))) % 0.20/0.55 (define @t32 () (lambda @t30 (_ (_ @t29 @t24) @t1))) % 0.20/0.55 (define @t33 () (lambda @t30 (_ (_ (_ tptp.mor @t27) @t19) @t1))) % 0.20/0.55 (define @t34 () (lambda @t30 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t19) @t24)) (_ (_ tptp.mimplies @t24) @t19)) @t1))) % 0.20/0.55 (define @t35 () (lambda @t30 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t19) @t24)) @t1))) % 0.20/0.55 (define @t36 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.20/0.55 (define @t37 () (_ @t36 @t13)) % 0.20/0.55 (define @t38 () (lambda (@list @t36 @t14) (forall (@list @t13) (_ @t37 @t14)))) % 0.20/0.55 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.20/0.55 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.20/0.55 (define @t41 () (_ @t40 @t39)) % 0.20/0.55 (define @t42 () (_ @t41 @t14)) % 0.20/0.55 (define @t43 () (@list @t39)) % 0.20/0.55 (define @t44 () (forall @t43 @t42)) % 0.20/0.55 (define @t45 () (@list @t40 @t14)) % 0.20/0.55 (define @t46 () (lambda @t45 @t44)) % 0.20/0.55 (define @t47 () (lambda (@list @t36 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t13 @t1) (_ (_ tptp.mnot @t37) @t1)))) @t1))) % 0.20/0.55 (define @t48 () (lambda (@list @t40 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t1) (_ (_ tptp.mnot @t41) @t1)))) @t1))) % 0.20/0.55 (define @t49 () (@list @t14)) % 0.20/0.55 (define @t50 () (lambda @t49 true)) % 0.20/0.55 (define @t51 () (@var "V" $$unsorted)) % 0.20/0.55 (define @t52 () (_ @t19 @t51)) % 0.20/0.55 (define @t53 () (_ (_ @t3 @t14) @t51)) % 0.20/0.55 (define @t54 () (not @t53)) % 0.20/0.55 (define @t55 () (or @t54 @t52)) % 0.20/0.55 (define @t56 () (@list @t51)) % 0.20/0.55 (define @t57 () (forall @t56 @t55)) % 0.20/0.55 (define @t58 () (@list @t3 @t19 @t14)) % 0.20/0.55 (define @t59 () (lambda @t58 @t57)) % 0.20/0.55 (define @t60 () (@list @t3 @t19 @t1)) % 0.20/0.55 (define @t61 () (lambda @t60 (_ (_ tptp.mnot (_ @t5 @t28)) @t1))) % 0.20/0.55 (define @t62 () (@var "S" $$unsorted)) % 0.20/0.55 (define @t63 () (_ @t3 @t62)) % 0.20/0.55 (define @t64 () (@list @t62)) % 0.20/0.55 (define @t65 () (lambda @t9 (forall @t64 (_ @t63 @t62)))) % 0.20/0.55 (define @t66 () (@var "T" $$unsorted)) % 0.20/0.55 (define @t67 () (_ @t3 @t66)) % 0.20/0.55 (define @t68 () (_ @t63 @t66)) % 0.20/0.55 (define @t69 () (lambda @t9 (forall (@list @t62 @t66) (=> @t68 (_ @t67 @t62))))) % 0.20/0.55 (define @t70 () (@list @t66)) % 0.20/0.55 (define @t71 () (lambda @t9 (forall @t64 (exists @t70 @t68)))) % 0.20/0.55 (define @t72 () (@var "U" $$unsorted)) % 0.20/0.55 (define @t73 () (_ @t63 @t72)) % 0.20/0.55 (define @t74 () (_ @t67 @t72)) % 0.20/0.55 (define @t75 () (@list @t62 @t66 @t72)) % 0.20/0.55 (define @t76 () (lambda @t9 (forall @t75 (=> (and @t68 @t74) @t73)))) % 0.20/0.55 (define @t77 () (and @t68 @t73)) % 0.20/0.55 (define @t78 () (forall @t75 (=> @t77 @t74))) % 0.20/0.55 (define @t79 () (lambda @t9 @t78)) % 0.20/0.55 (define @t80 () (= @t66 @t72)) % 0.20/0.55 (define @t81 () (lambda @t9 (forall @t75 (=> @t77 @t80)))) % 0.20/0.55 (define @t82 () (@list @t72)) % 0.20/0.55 (define @t83 () (lambda @t9 (forall @t64 (exists @t70 (and @t68 (forall @t82 (=> @t73 @t80))))))) % 0.20/0.55 (define @t84 () (_ @t3 @t72)) % 0.20/0.55 (define @t85 () (_ @t84 @t66)) % 0.20/0.55 (define @t86 () (lambda @t9 (forall @t75 (=> @t68 (exists @t82 (and @t73 @t85)))))) % 0.20/0.55 (define @t87 () (lambda @t9 (forall @t75 (=> @t77 (or @t74 @t80 @t85))))) % 0.20/0.55 (define @t88 () (lambda @t9 (forall @t75 (=> @t77 (exists @t56 (and (_ @t67 @t51) (_ @t84 @t51))))))) % 0.20/0.55 (define @t89 () (forall @t49 @t20)) % 0.20/0.55 (define @t90 () (@list @t19)) % 0.20/0.55 (define @t91 () (lambda @t90 @t89)) % 0.20/0.55 (define @t92 () (lambda @t90 (forall @t49 @t21))) % 0.20/0.55 (define @t93 () (lambda @t90 (exists @t49 @t20))) % 0.20/0.55 (define @t94 () (lambda @t90 (exists @t49 @t21))) % 0.20/0.55 (define @t95 () (@var "BOUND_VARIABLE_8366" $$unsorted)) % 0.20/0.55 (define @t96 () (@var "BOUND_VARIABLE_8450" (-> $$unsorted Bool))) % 0.20/0.55 (define @t97 () (@var "BOUND_VARIABLE_8454" $$unsorted)) % 0.20/0.55 (define @t98 () (@list @t95)) % 0.20/0.55 (define @t99 () (not (forall @t98 (or (not (_ @t3 @t97 @t95)) (not (_ @t96 @t95)))))) % 0.20/0.55 (define @t100 () (@var "BOUND_VARIABLE_8448" $$unsorted)) % 0.20/0.55 (define @t101 () (not (_ @t3 @t100 @t97))) % 0.20/0.55 (define @t102 () (@var "BOUND_VARIABLE_8452" $$unsorted)) % 0.20/0.55 (define @t103 () (not (_ @t96 @t102))) % 0.20/0.55 (define @t104 () (not (_ @t3 @t100 @t102))) % 0.20/0.55 (define @t105 () (_ @t3 @t66 @t72)) % 0.20/0.55 (define @t106 () (_ @t3 @t62 @t72)) % 0.20/0.55 (define @t107 () (_ @t3 @t62 @t66)) % 0.20/0.55 (define @t108 () (forall @t75 (or (not @t107) (not @t106) @t105))) % 0.20/0.55 (define @t109 () (not @t108)) % 0.20/0.55 (define @t110 () (or @t109 @t104 @t103 @t101 @t99)) % 0.20/0.55 (define @t111 () (or @t104 @t103 @t101 @t99)) % 0.20/0.55 (define @t112 () (or @t109 @t111)) % 0.20/0.55 (define @t113 () (@list @t3 @t100 @t96 @t102 @t97)) % 0.20/0.55 (define @t114 () (forall @t113 @t112)) % 0.20/0.55 (define @t115 () (@list @t100 @t96 @t102 @t97)) % 0.20/0.55 (define @t116 () (forall @t115 @t112)) % 0.20/0.55 (define @t117 () (forall @t115 @t111)) % 0.20/0.55 (define @t118 () (@var "BOUND_VARIABLE_8421" $$unsorted)) % 0.20/0.55 (define @t119 () (@var "BOUND_VARIABLE_8414" $$unsorted)) % 0.20/0.55 (define @t120 () (or @t109 @t117)) % 0.20/0.55 (define @t121 () (not (_ @t39 @t95))) % 0.20/0.55 (define @t122 () (not (forall @t98 (or (not (_ @t3 @t118 @t95)) @t121)))) % 0.20/0.55 (define @t123 () (not (_ @t3 @t14 @t118))) % 0.20/0.55 (define @t124 () (not (_ @t39 @t119))) % 0.20/0.55 (define @t125 () (not (_ @t3 @t14 @t119))) % 0.20/0.55 (define @t126 () (or @t125 @t124 @t123 @t122)) % 0.20/0.55 (define @t127 () (forall (@list @t14 @t39 @t119 @t118) @t126)) % 0.20/0.55 (define @t128 () (@list @t39 @t119 @t118)) % 0.20/0.55 (define @t129 () (forall @t128 @t126)) % 0.20/0.55 (define @t130 () (lambda @t49 @t129)) % 0.20/0.55 (define @t131 () (_ @t130 @t14)) % 0.20/0.55 (define @t132 () (forall @t49 @t131)) % 0.20/0.55 (define @t133 () (_ @t19 @t14)) % 0.20/0.55 (define @t134 () (lambda @t90 (forall @t49 @t133))) % 0.20/0.55 (define @t135 () (or @t123 @t122)) % 0.20/0.55 (define @t136 () (or @t125 @t124)) % 0.20/0.55 (define @t137 () (or @t136 @t135)) % 0.20/0.55 (define @t138 () (forall @t128 @t137)) % 0.20/0.55 (define @t139 () (forall (@list @t119 @t118) @t137)) % 0.20/0.55 (define @t140 () (forall (@list @t118) @t135)) % 0.20/0.55 (define @t141 () (@list @t51)) % 0.20/0.55 (define @t142 () (forall (@list @t119) @t136)) % 0.20/0.55 (define @t143 () (or @t142 @t140)) % 0.20/0.55 (define @t144 () (not (_ @t3 @t51 @t95))) % 0.20/0.55 (define @t145 () (_ @t3 @t14 @t51)) % 0.20/0.55 (define @t146 () (not @t145)) % 0.20/0.55 (define @t147 () (or (forall @t56 (or @t146 (not (_ @t39 @t51)))) (forall @t56 (or @t146 (not (forall @t98 (or @t144 @t121))))))) % 0.20/0.55 (define @t148 () (not (_ @t2 @t95))) % 0.20/0.55 (define @t149 () (not (forall @t98 (or @t144 @t148)))) % 0.20/0.55 (define @t150 () (not (_ @t3 @t1 @t51))) % 0.20/0.55 (define @t151 () (forall @t56 (or @t150 @t149))) % 0.20/0.55 (define @t152 () (forall @t56 (or @t150 (not (_ @t2 @t51))))) % 0.20/0.55 (define @t153 () (or @t152 @t151)) % 0.20/0.55 (define @t154 () (lambda @t6 @t153)) % 0.20/0.55 (define @t155 () (_ @t154 @t39 @t14)) % 0.20/0.55 (define @t156 () (forall @t43 @t155)) % 0.20/0.55 (define @t157 () (lambda @t49 @t156)) % 0.20/0.55 (define @t158 () (_ @t40 @t39 @t14)) % 0.20/0.55 (define @t159 () (lambda @t45 (forall @t43 @t158))) % 0.20/0.55 (define @t160 () (@list @t1)) % 0.20/0.55 (define @t161 () (lambda @t49 (forall @t56 (or @t146 @t149)))) % 0.20/0.55 (define @t162 () (_ @t161 @t1)) % 0.20/0.55 (define @t163 () (or @t152 @t162)) % 0.20/0.55 (define @t164 () (lambda @t160 @t163)) % 0.20/0.55 (define @t165 () (_ @t24 @t1)) % 0.20/0.55 (define @t166 () (@list @t24 @t1)) % 0.20/0.55 (define @t167 () (not @t152)) % 0.20/0.55 (define @t168 () (lambda @t160 @t167)) % 0.20/0.55 (define @t169 () (or @t146 (_ @t168 @t51))) % 0.20/0.55 (define @t170 () (forall @t56 @t169)) % 0.20/0.55 (define @t171 () (lambda @t49 @t170)) % 0.20/0.55 (define @t172 () (_ @t19 @t51)) % 0.20/0.55 (define @t173 () (forall @t56 (or @t146 @t172))) % 0.20/0.55 (define @t174 () (lambda @t22 @t173)) % 0.20/0.55 (define @t175 () (not @t172)) % 0.20/0.55 (define @t176 () (not (forall @t56 (or @t150 @t175)))) % 0.20/0.55 (define @t177 () (lambda (@list @t19 @t1) @t176)) % 0.20/0.55 (define @t178 () (_ (lambda @t60 @t176) @t3)) % 0.20/0.55 (define @t179 () (_ (lambda @t58 @t173) @t3)) % 0.20/0.55 (define @t180 () (_ @t168 @t1)) % 0.20/0.55 (define @t181 () (not @t180)) % 0.20/0.55 (define @t182 () (or @t181 @t165)) % 0.20/0.55 (define @t183 () (lambda @t166 @t182)) % 0.20/0.55 (define @t184 () (or (not (_ @t19 @t1)) @t165)) % 0.20/0.55 (define @t185 () (lambda @t30 @t184)) % 0.20/0.55 (define @t186 () (_ @t178 @t2)) % 0.20/0.55 (define @t187 () (lambda @t6 (_ (_ (_ @t185 @t186) (_ @t179 @t186)) @t1))) % 0.20/0.55 (define @t188 () (_ (lambda @t9 @t108) @t3)) % 0.20/0.55 (define @t189 () (=> @t188 (_ @t134 (_ @t159 @t187)))) % 0.20/0.55 (define @t190 () (forall @t9 @t189)) % 0.20/0.55 (define @t191 () (forall @t56 (or @t146 @t175))) % 0.20/0.55 (define @t192 () (lambda @t49 @t191)) % 0.20/0.55 (define @t193 () (_ @t192 @t14)) % 0.20/0.55 (define @t194 () (not @t193)) % 0.20/0.55 (define @t195 () (lambda @t49 @t194)) % 0.20/0.55 (define @t196 () (not @t52)) % 0.20/0.55 (define @t197 () (or @t146 @t196)) % 0.20/0.55 (define @t198 () (lambda @t49 @t21)) % 0.20/0.55 (define @t199 () (_ @t198 @t51)) % 0.20/0.55 (define @t200 () (or @t146 @t199)) % 0.20/0.55 (define @t201 () (forall @t56 @t200)) % 0.20/0.55 (define @t202 () (lambda @t49 @t201)) % 0.20/0.55 (define @t203 () (or @t21 @t25)) % 0.20/0.55 (define @t204 () (lambda @t49 @t203)) % 0.20/0.55 (define @t205 () (@list @t24 @t14)) % 0.20/0.55 (define @t206 () (_ @t198 @t14)) % 0.20/0.55 (define @t207 () (or @t206 @t25)) % 0.20/0.55 (define @t208 () (lambda @t205 @t207)) % 0.20/0.55 (define @t209 () (not @t73)) % 0.20/0.55 (define @t210 () (not @t68)) % 0.20/0.55 (define @t211 () (or @t210 @t209 @t74)) % 0.20/0.55 (define @t212 () (forall @t113 @t110)) % 0.20/0.55 (define @t213 () (@quantifiers_skolemize @t212 0)) % 0.20/0.55 (define @t214 () (forall @t75 (or (not (_ @t213 @t62 @t66)) (not (_ @t213 @t62 @t72)) (_ @t213 @t66 @t72)))) % 0.20/0.55 (define @t215 () (@quantifiers_skolemize @t212 2)) % 0.20/0.55 (define @t216 () (@quantifiers_skolemize @t212 4)) % 0.20/0.55 (define @t217 () (forall @t98 (or (not (_ @t213 @t216 @t95)) (not (_ @t215 @t95))))) % 0.20/0.55 (define @t218 () (not @t217)) % 0.20/0.55 (define @t219 () (@quantifiers_skolemize @t212 1)) % 0.20/0.55 (define @t220 () (_ @t213 @t219 @t216)) % 0.20/0.55 (define @t221 () (not @t220)) % 0.20/0.55 (define @t222 () (@quantifiers_skolemize @t212 3)) % 0.20/0.55 (define @t223 () (_ @t215 @t222)) % 0.20/0.55 (define @t224 () (not @t223)) % 0.20/0.55 (define @t225 () (_ @t213 @t219 @t222)) % 0.20/0.55 (define @t226 () (not @t225)) % 0.20/0.55 (define @t227 () (not @t214)) % 0.20/0.55 (define @t228 () (or @t227 @t226 @t224 @t221 @t218)) % 0.20/0.55 (define @t229 () (@list true)) % 0.20/0.55 (define @t230 () (@list @t228)) % 0.20/0.55 (define @t231 () (_ @t213 @t216 @t222)) % 0.20/0.55 (define @t232 () (not @t231)) % 0.20/0.55 (define @t233 () (or @t232 @t224)) % 0.20/0.55 (define @t234 () (or @t221 @t226 @t231)) % 0.20/0.55 (define @t235 () (not @t234)) % 0.20/0.55 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.20/0.55 (assume @p2 @t11) % 0.20/0.55 (assume @p3 true) % 0.20/0.55 (step @p4 (= tptp.meq_ind @t15) :rule refl :args (@t15)) % 0.20/0.55 (step @p5 (= tptp.meq_prop @t18) :rule refl :args (@t18)) % 0.20/0.55 (step @p6 (= tptp.mnot @t23) :rule refl :args (@t23)) % 0.20/0.55 (step @p7 (= tptp.mor @t26) :rule refl :args (@t26)) % 0.20/0.55 (step @p8 (= tptp.mand @t31) :rule refl :args (@t31)) % 0.20/0.55 (step @p9 (= tptp.mimplies @t32) :rule refl :args (@t32)) % 0.20/0.55 (step @p10 (= tptp.mimplied @t33) :rule refl :args (@t33)) % 0.20/0.55 (step @p11 (= tptp.mequiv @t34) :rule refl :args (@t34)) % 0.20/0.55 (step @p12 (= tptp.mxor @t35) :rule refl :args (@t35)) % 0.20/0.55 (step @p13 (= tptp.mforall_ind @t38) :rule refl :args (@t38)) % 0.20/0.55 (step @p14 (= tptp.mforall_prop @t46) :rule refl :args (@t46)) % 0.20/0.55 (step @p15 (= tptp.mexists_ind @t47) :rule refl :args (@t47)) % 0.20/0.55 (step @p16 (= tptp.mexists_prop @t48) :rule refl :args (@t48)) % 0.20/0.55 (step @p17 (= tptp.mtrue @t50) :rule refl :args (@t50)) % 0.20/0.55 (step @p18 (= tptp.mbox @t59) :rule refl :args (@t59)) % 0.20/0.55 (step @p19 (= tptp.mdia @t61) :rule refl :args (@t61)) % 0.20/0.55 (step @p20 (= tptp.mreflexive @t65) :rule refl :args (@t65)) % 0.20/0.55 (step @p21 (= tptp.msymmetric @t69) :rule refl :args (@t69)) % 0.20/0.55 (step @p22 (= tptp.mserial @t71) :rule refl :args (@t71)) % 0.20/0.55 (step @p23 (= tptp.mtransitive @t76) :rule refl :args (@t76)) % 0.20/0.55 (step @p24 (= tptp.meuclidean @t79) :rule refl :args (@t79)) % 0.20/0.55 (step @p25 (= tptp.mpartially_functional @t81) :rule refl :args (@t81)) % 0.20/0.55 (step @p26 (= tptp.mfunctional @t83) :rule refl :args (@t83)) % 0.20/0.55 (step @p27 (= tptp.mweakly_dense @t86) :rule refl :args (@t86)) % 0.20/0.55 (step @p28 (= tptp.mweakly_connected @t87) :rule refl :args (@t87)) % 0.20/0.55 (step @p29 (= tptp.mweakly_directed @t88) :rule refl :args (@t88)) % 0.20/0.55 (step @p30 (= tptp.mvalid @t91) :rule refl :args (@t91)) % 0.20/0.55 (step @p31 (= tptp.minvalid @t92) :rule refl :args (@t92)) % 0.20/0.55 (step @p32 (= tptp.msatisfiable @t93) :rule refl :args (@t93)) % 0.20/0.55 (step @p33 (= tptp.mcountersatisfiable @t94) :rule refl :args (@t94)) % 0.20/0.55 (step @p34 :rule aci_norm :args ((= @t112 @t110))) % 0.20/0.55 (step @p35 :rule cong :premises (@p34) :args (@t114)) % 0.20/0.55 (step @p36 :rule quant-merge-prenex :args ((= (forall @t9 @t116) @t114))) % 0.20/0.55 (step @p37 :rule alpha_equiv :args (@t117 (@list @t100 @t96 @t102 @t97) (@list @t14 @t39 @t119 @t118))) % 0.20/0.55 (step @p38 :rule refl :args (@t109)) % 0.20/0.55 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t120)) % 0.20/0.55 (step @p40 :rule quant-miniscope-or :args ((= @t116 @t120))) % 0.20/0.55 (step @p41 :rule trans :premises (@p40 @p39)) % 0.20/0.55 (step @p42 :rule symm :premises (@p41)) % 0.20/0.55 (step @p43 :rule cong :premises (@p42) :args ((forall @t9 (or @t109 @t127)))) % 0.20/0.55 (step @p44 :rule trans :premises (@p43 @p36)) % 0.20/0.55 (step @p45 :rule trans :premises (@p44 @p35)) % 0.20/0.55 (step @p46 :rule bool-impl-elim :args (@t108 @t127)) % 0.20/0.55 (step @p47 :rule cong :premises (@p46) :args ((forall @t9 (=> @t108 @t127)))) % 0.20/0.55 (step @p48 :rule trans :premises (@p47 @p45)) % 0.20/0.55 (step @p49 :rule quant-merge-prenex :args ((= (forall @t49 @t129) @t127))) % 0.20/0.55 (step @p50 :rule beta-reduce :args ((= @t131 @t129))) % 0.20/0.55 (step @p51 :rule cong :premises (@p50) :args (@t132)) % 0.20/0.55 (step @p52 :rule trans :premises (@p51 @p49)) % 0.20/0.55 (step @p53 :rule beta-reduce :args ((= (_ @t134 @t130) @t132))) % 0.20/0.55 (step @p54 :rule trans :premises (@p53 @p52)) % 0.20/0.55 (step @p55 :rule aci_norm :args ((= @t137 @t126))) % 0.20/0.55 (step @p56 :rule cong :premises (@p55) :args (@t138)) % 0.20/0.55 (step @p57 :rule quant-merge-prenex :args ((= (forall @t43 @t139) @t138))) % 0.20/0.55 (step @p58 :rule alpha_equiv :args (@t140 (@list @t118) @t141)) % 0.20/0.55 (step @p59 :rule alpha_equiv :args (@t142 (@list @t119) @t141)) % 0.20/0.55 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t143)) % 0.20/0.55 (step @p61 :rule quant-miniscope-or :args ((= @t139 @t143))) % 0.20/0.55 (step @p62 :rule trans :premises (@p61 @p60)) % 0.20/0.55 (step @p63 :rule symm :premises (@p62)) % 0.20/0.55 (step @p64 :rule cong :premises (@p63) :args ((forall @t43 @t147))) % 0.20/0.55 (step @p65 :rule trans :premises (@p64 @p57)) % 0.20/0.55 (step @p66 :rule trans :premises (@p65 @p56)) % 0.20/0.55 (step @p67 :rule beta-reduce :args ((= @t155 @t147))) % 0.20/0.55 (step @p68 :rule cong :premises (@p67) :args (@t156)) % 0.20/0.55 (step @p69 :rule trans :premises (@p68 @p66)) % 0.20/0.55 (step @p70 :rule cong :premises (@p69) :args (@t157)) % 0.20/0.55 (step @p71 :rule beta-reduce :args ((= (_ @t159 @t154) @t157))) % 0.20/0.55 (step @p72 :rule trans :premises (@p71 @p70)) % 0.20/0.55 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t160 @t153) @t1) @t153))) % 0.20/0.55 (step @p74 :rule refl :args (@t1)) % 0.20/0.55 (step @p75 :rule beta-reduce :args ((= @t162 @t151))) % 0.20/0.55 (step @p76 :rule refl :args (@t152)) % 0.20/0.55 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t163)) % 0.20/0.55 (step @p78 :rule cong :premises (@p77) :args (@t164)) % 0.20/0.55 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t166 (or @t152 @t165)) @t161) @t164))) % 0.20/0.55 (step @p80 :rule trans :premises (@p79 @p78)) % 0.20/0.55 (step @p81 :rule beta-reduce :args ((= (_ (lambda @t160 (not (forall @t98 (or (not (_ @t3 @t1 @t95)) @t148)))) @t51) @t149))) % 0.20/0.55 (step @p82 :rule refl :args (@t51)) % 0.20/0.55 (step @p83 :rule alpha_equiv :args (@t152 @t141 (@list @t95))) % 0.20/0.55 (step @p84 :rule cong :premises (@p83) :args (@t167)) % 0.20/0.55 (step @p85 :rule cong :premises (@p84) :args (@t168)) % 0.20/0.55 (step @p86 :rule ho_cong :premises (@p85 @p82)) % 0.20/0.55 (step @p87 :rule trans :premises (@p86 @p81)) % 0.20/0.55 (step @p88 :rule refl :args (@t146)) % 0.20/0.55 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t169)) % 0.20/0.55 (step @p90 :rule cong :premises (@p89) :args (@t170)) % 0.20/0.55 (step @p91 :rule cong :premises (@p90) :args (@t171)) % 0.20/0.55 (step @p92 :rule beta-reduce :args ((= (_ @t174 @t168) @t171))) % 0.20/0.55 (step @p93 :rule trans :premises (@p92 @p91)) % 0.20/0.55 (step @p94 :rule beta-reduce :args ((= (_ @t177 @t2) @t168))) % 0.20/0.55 (step @p95 :rule refl :args (@t2)) % 0.20/0.55 (step @p96 :rule beta-reduce :args ((= @t178 @t177))) % 0.20/0.55 (step @p97 :rule ho_cong :premises (@p96 @p95)) % 0.20/0.55 (step @p98 :rule trans :premises (@p97 @p94)) % 0.20/0.55 (step @p99 :rule beta-reduce :args ((= @t179 @t174))) % 0.20/0.55 (step @p100 :rule ho_cong :premises (@p99 @p98)) % 0.20/0.55 (step @p101 :rule trans :premises (@p100 @p93)) % 0.20/0.55 (step @p102 :rule refl :args (@t165)) % 0.20/0.55 (step @p103 :rule bool-double-not-elim :args (@t152)) % 0.20/0.55 (step @p104 :rule beta-reduce :args ((= @t180 @t167))) % 0.20/0.55 (step @p105 :rule cong :premises (@p104) :args (@t181)) % 0.20/0.55 (step @p106 :rule trans :premises (@p105 @p103)) % 0.20/0.55 (step @p107 :rule nary_cong :premises (@p106 @p102) :args (@t182)) % 0.20/0.55 (step @p108 :rule cong :premises (@p107) :args (@t183)) % 0.20/0.55 (step @p109 :rule beta-reduce :args ((= (_ @t185 @t168) @t183))) % 0.20/0.55 (step @p110 :rule trans :premises (@p109 @p108)) % 0.20/0.55 (step @p111 :rule refl :args (@t185)) % 0.20/0.55 (step @p112 :rule ho_cong :premises (@p111 @p98)) % 0.20/0.55 (step @p113 :rule trans :premises (@p112 @p110)) % 0.20/0.55 (step @p114 :rule ho_cong :premises (@p113 @p101)) % 0.20/0.55 (step @p115 :rule trans :premises (@p114 @p80)) % 0.20/0.55 (step @p116 :rule ho_cong :premises (@p115 @p74)) % 0.20/0.55 (step @p117 :rule trans :premises (@p116 @p73)) % 0.20/0.55 (step @p118 :rule cong :premises (@p117) :args (@t187)) % 0.20/0.55 (step @p119 :rule refl :args (@t159)) % 0.20/0.55 (step @p120 :rule ho_cong :premises (@p119 @p118)) % 0.20/0.55 (step @p121 :rule trans :premises (@p120 @p72)) % 0.20/0.55 (step @p122 :rule refl :args (@t134)) % 0.20/0.55 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 0.20/0.55 (step @p124 :rule trans :premises (@p123 @p54)) % 0.20/0.55 (step @p125 :rule beta-reduce :args ((= @t188 @t108))) % 0.20/0.55 (step @p126 :rule cong :premises (@p125 @p124) :args (@t189)) % 0.20/0.55 (step @p127 :rule cong :premises (@p126) :args (@t190)) % 0.20/0.55 (step @p128 :rule trans :premises (@p127 @p48)) % 0.20/0.55 (step @p129 :rule cong :premises (@p128) :args ((not @t190))) % 0.20/0.55 (step @p130 :rule refl :args (@t3)) % 0.20/0.55 (step @p131 :rule beta-reduce :args ((= (_ (lambda @t49 (not @t191)) @t1) @t176))) % 0.20/0.55 (step @p132 :rule beta-reduce :args ((= @t193 @t191))) % 0.20/0.55 (step @p133 :rule cong :premises (@p132) :args (@t194)) % 0.20/0.55 (step @p134 :rule cong :premises (@p133) :args (@t195)) % 0.20/0.55 (step @p135 :rule beta-reduce :args ((= (_ @t23 @t192) @t195))) % 0.20/0.55 (step @p136 :rule trans :premises (@p135 @p134)) % 0.20/0.55 (step @p137 :rule refl :args (@t172)) % 0.20/0.55 (step @p138 :rule refl :args (@t52)) % 0.20/0.55 (step @p139 :rule cong :premises (@p138 @p137) :args ((= @t52 @t172))) % 0.20/0.55 (step @p140 :rule symm :premises (@p139)) % 0.20/0.55 (step @p141 :rule eq_resolve :premises (@p138 @p140)) % 0.20/0.55 (step @p142 :rule cong :premises (@p141) :args (@t196)) % 0.20/0.55 (step @p143 :rule refl :args (@t146)) % 0.20/0.55 (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t197)) % 0.20/0.55 (step @p145 :rule cong :premises (@p144) :args ((forall @t56 @t197))) % 0.20/0.55 (step @p146 :rule beta-reduce :args ((= @t199 @t196))) % 0.20/0.55 (step @p147 :rule nary_cong :premises (@p88 @p146) :args (@t200)) % 0.20/0.55 (step @p148 :rule cong :premises (@p147) :args (@t201)) % 0.20/0.55 (step @p149 :rule trans :premises (@p148 @p145)) % 0.20/0.55 (step @p150 :rule cong :premises (@p149) :args (@t202)) % 0.20/0.55 (step @p151 :rule beta-reduce :args ((= (_ @t174 @t198) @t202))) % 0.20/0.55 (step @p152 :rule trans :premises (@p151 @p150)) % 0.20/0.55 (step @p153 :rule beta-reduce :args ((= (_ @t23 @t19) @t198))) % 0.20/0.55 (step @p154 :rule ho_cong :premises (@p99 @p153)) % 0.20/0.55 (step @p155 :rule trans :premises (@p154 @p152)) % 0.20/0.55 (step @p156 :rule refl :args (@t23)) % 0.20/0.55 (step @p157 :rule ho_cong :premises (@p156 @p155)) % 0.20/0.55 (step @p158 :rule trans :premises (@p157 @p136)) % 0.20/0.55 (step @p159 :rule ho_cong :premises (@p158 @p74)) % 0.20/0.55 (step @p160 :rule trans :premises (@p159 @p131)) % 0.20/0.55 (step 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:premises (@p223) :args (@t91)) % 0.20/0.55 (step @p225 :rule trans :premises (@p30 @p224)) % 0.20/0.55 (step @p226 :rule ho_cong :premises (@p225 @p217)) % 0.20/0.55 (step @p227 :rule refl :args (@t105)) % 0.20/0.55 (step @p228 :rule refl :args (@t74)) % 0.20/0.55 (step @p229 :rule cong :premises (@p228 @p227) :args ((= @t74 @t105))) % 0.20/0.55 (step @p230 :rule symm :premises (@p229)) % 0.20/0.55 (step @p231 :rule eq_resolve :premises (@p228 @p230)) % 0.20/0.55 (step @p232 :rule refl :args (@t106)) % 0.20/0.55 (step @p233 :rule refl :args (@t73)) % 0.20/0.55 (step @p234 :rule cong :premises (@p233 @p232) :args ((= @t73 @t106))) % 0.20/0.55 (step @p235 :rule symm :premises (@p234)) % 0.20/0.55 (step @p236 :rule eq_resolve :premises (@p233 @p235)) % 0.20/0.55 (step @p237 :rule cong :premises (@p236) :args (@t209)) % 0.20/0.55 (step @p238 :rule refl :args (@t107)) % 0.20/0.55 (step @p239 :rule refl :args (@t68)) % 0.20/0.55 (step @p240 :rule cong :premises (@p239 @p238) :args ((= @t68 @t107))) % 0.20/0.55 (step @p241 :rule symm :premises (@p240)) % 0.20/0.55 (step @p242 :rule eq_resolve :premises (@p239 @p241)) % 0.20/0.55 (step @p243 :rule cong :premises (@p242) :args (@t210)) % 0.20/0.55 (step @p244 :rule nary_cong :premises (@p243 @p237 @p231) :args (@t211)) % 0.20/0.55 (step @p245 :rule cong :premises (@p244) :args ((forall @t75 @t211))) % 0.20/0.55 (step @p246 :rule aci_norm :args ((= (or (or @t210 @t209) @t74) @t211))) % 0.20/0.55 (step @p247 :rule bool-and-de-morgan :args (@t68 @t73 true)) % 0.20/0.55 (step @p248 :rule nary_cong :premises (@p247 @p228) :args ((or (not @t77) @t74))) % 0.20/0.55 (step @p249 :rule trans :premises (@p248 @p246)) % 0.20/0.55 (step @p250 :rule bool-impl-elim :args (@t77 @t74)) % 0.20/0.55 (step @p251 :rule trans :premises (@p250 @p249)) % 0.20/0.55 (step @p252 :rule cong :premises (@p251) :args (@t78)) % 0.20/0.55 (step @p253 :rule trans :premises (@p252 @p245)) % 0.20/0.55 (step @p254 :rule cong :premises (@p253) :args (@t79)) % 0.20/0.55 (step @p255 :rule trans :premises (@p24 @p254)) % 0.20/0.55 (step @p256 :rule ho_cong :premises (@p255 @p130)) % 0.20/0.55 (step @p257 :rule cong :premises (@p256 @p226) :args (@t8)) % 0.20/0.55 (step @p258 :rule cong :premises (@p257) :args (@t10)) % 0.20/0.55 (step @p259 :rule cong :premises (@p258) :args (@t11)) % 0.20/0.55 (step @p260 :rule trans :premises (@p259 @p129)) % 0.20/0.55 (step @p261 :rule eq_resolve :premises (@p2 @p260)) % 0.20/0.55 (step @p262 :rule skolemize :premises (@p261)) % 0.20/0.55 (step @p263 :rule bool-double-not-elim :args (@t214)) % 0.20/0.55 (step @p264 :rule refl :args (@t228)) % 0.20/0.55 (step @p265 :rule nary_cong :premises (@p264 @p263) :args ((or @t228 (not @t227)))) % 0.20/0.55 (step @p266 :rule cnf_or_neg :args (@t228 0)) % 0.20/0.55 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 0.20/0.55 (step @p268 :rule reordering :premises (@p267) :args ((or @t214 @t228))) % 0.20/0.55 (step @p269 :rule chain_m_resolution :premises (@p268 @p262) :args (@t214 @t229 @t230)) % 0.20/0.55 (step @p270 :rule bool-double-not-elim :args (@t217)) % 0.20/0.55 (step @p271 :rule nary_cong :premises (@p264 @p270) :args ((or @t228 (not @t218)))) % 0.20/0.55 (step @p272 :rule cnf_or_neg :args (@t228 4)) % 0.20/0.55 (step @p273 :rule eq_resolve :premises (@p272 @p271)) % 0.20/0.55 (step @p274 :rule reordering :premises (@p273) :args ((or @t217 @t228))) % 0.20/0.55 (step @p275 :rule chain_m_resolution :premises (@p274 @p262) :args (@t217 @t229 @t230)) % 0.20/0.55 (step @p276 :rule instantiate :premises (@p275) :args ((@list @t222))) % 0.20/0.55 (step @p277 :rule bool-double-not-elim :args (@t223)) % 0.20/0.55 (step @p278 :rule nary_cong :premises (@p264 @p277) :args ((or @t228 (not @t224)))) % 0.20/0.55 (step @p279 :rule cnf_or_neg :args (@t228 2)) % 0.20/0.55 (step @p280 :rule eq_resolve :premises (@p279 @p278)) % 0.20/0.55 (step @p281 :rule reordering :premises (@p280) :args ((or @t223 @t228))) % 0.20/0.55 (step @p282 :rule chain_m_resolution :premises (@p281 @p262) :args (@t223 @t229 @t230)) % 0.20/0.55 (step @p283 :rule cnf_or_pos :args (@t233)) % 0.20/0.55 (step @p284 :rule reordering :premises (@p283) :args ((or @t224 @t232 (not @t233)))) % 0.20/0.55 (step @p285 :rule chain_m_resolution :premises (@p284 @p282 @p276) :args (@t232 (@list false false) (@list @t223 @t233))) % 0.20/0.55 (step @p286 :rule bool-double-not-elim :args (@t220)) % 0.20/0.55 (step @p287 :rule nary_cong :premises (@p264 @p286) :args ((or @t228 (not @t221)))) % 0.20/0.55 (step @p288 :rule cnf_or_neg :args (@t228 3)) % 0.20/0.55 (step @p289 :rule eq_resolve :premises (@p288 @p287)) % 0.20/0.55 (step @p290 :rule reordering :premises (@p289) :args ((or @t220 @t228))) % 0.20/0.55 (step @p291 :rule chain_m_resolution :premises (@p290 @p262) :args (@t220 @t229 @t230)) % 0.20/0.55 (step @p292 :rule bool-double-not-elim :args (@t225)) % 0.20/0.55 (step @p293 :rule nary_cong :premises (@p264 @p292) :args ((or @t228 (not @t226)))) % 0.20/0.55 (step @p294 :rule cnf_or_neg :args (@t228 1)) % 0.20/0.55 (step @p295 :rule eq_resolve :premises (@p294 @p293)) % 0.20/0.55 (step @p296 :rule reordering :premises (@p295) :args ((or @t225 @t228))) % 0.20/0.55 (step @p297 :rule chain_m_resolution :premises (@p296 @p262) :args (@t225 @t229 @t230)) % 0.20/0.55 (step @p298 :rule cnf_or_pos :args (@t234)) % 0.20/0.55 (step @p299 :rule reordering :premises (@p298) :args ((or @t226 @t221 @t231 @t235))) % 0.20/0.55 (step @p300 :rule chain_m_resolution :premises (@p299 @p297 @p291 @p285) :args (@t235 (@list false false true) (@list @t225 @t220 @t231))) % 0.20/0.55 (assume-push @p307 @t214) % 0.20/0.55 (step @p302 :rule instantiate :premises (@p269) :args ((@list @t219 @t216 @t222))) % 0.20/0.55 (step-pop @p308 :rule scope :premises (@p302)) % 0.20/0.55 (step @p303 :rule process_scope :premises (@p308) :args (@t234)) % 0.20/0.55 (step @p305 :rule implies_elim :premises (@p303)) % 0.20/0.55 (step @p306 false :rule chain_m_resolution :premises (@p305 @p300 @p269) :args (false (@list true false) (@list @t234 @t214))) % 0.20/0.55 ) % 0.20/0.55 % SZS output end Proof % 0.20/0.55 % cvc5 exiting %------------------------------------------------------------------------------