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cvc5---1.3.4.THM-Prf.s

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%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : SYO460^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jun  3 09:12:48 AM UTC 2026

% Result   : Theorem 0.36s 0.62s
% Output   : Proof 0.36s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SYO460^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13  % Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.16/0.35  % Computer : n011.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit : 300
% 0.16/0.35  % WCLimit  : 300
% 0.16/0.35  % DateTime : Wed Jun  3 00:10:35 EDT 2026
% 0.16/0.35  % CPUTime  : 
% 0.28/0.51  %----Proving TH0
% 0.36/0.62  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s...
% 0.36/0.62  % SZS status Theorem
% 0.36/0.62  % SZS output start Proof
% 0.36/0.62  (
% 0.36/0.62  (declare-sort $$unsorted 0)
% 0.36/0.62  (declare-sort tptp.mu 0)
% 0.36/0.62  (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool))
% 0.36/0.62  (declare-const tptp.q (-> $$unsorted Bool))
% 0.36/0.62  (declare-const tptp.r (-> $$unsorted Bool))
% 0.36/0.62  (declare-const tptp.p (-> $$unsorted Bool))
% 0.36/0.62  (declare-const tptp.mfalse (-> $$unsorted Bool))
% 0.36/0.62  (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1)))))
% 0.36/0.62  (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1)))))))
% 0.36/0.62  (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1))))))
% 0.36/0.62  (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1)))))))
% 0.36/0.62  (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1))))))
% 0.36/0.62  (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1))))))
% 0.36/0.62  (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1))))))
% 0.36/0.62  (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1))))))
% 0.36/0.62  (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1))))))
% 0.36/0.62  (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1)))))))
% 0.36/0.62  (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1)))))))
% 0.36/0.62  (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1))))))
% 0.36/0.62  (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1))))))
% 0.36/0.62  (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true))
% 0.36/0.62  (define tptp.mbox () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1)))))))))
% 0.36/0.62  (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1))))))
% 0.36/0.62  (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1))))))
% 0.36/0.62  (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1))))))))
% 0.36/0.62  (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1))))))))
% 0.36/0.62  (define tptp.mtransitive () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (_ _let_3 _let_2))) (let ((_let_5 (@var "T" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1))))))))))
% 0.36/0.62  (define tptp.meuclidean () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1))))))))))
% 0.36/0.62  (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1))))))))))
% 0.36/0.62  (define tptp.mfunctional () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "S" $$unsorted))) (let ((_let_4 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1)))))))))))))
% 0.36/0.62  (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))))
% 0.36/0.62  (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "S" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))
% 0.36/0.62  (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (let ((_let_4 (@var "T" $$unsorted))) (let ((_let_5 (@var "S" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))))))))
% 0.36/0.62  (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1))))))
% 0.36/0.62  (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1)))))))
% 0.36/0.62  (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1))))))
% 0.36/0.62  (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1)))))))
% 0.36/0.62  (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1))))))))
% 0.36/0.62  (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1)))))
% 0.36/0.62  (define @t1 () (_ tptp.mand tptp.p))
% 0.36/0.62  (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimplies (_ (_ tptp.mor (_ tptp.mdia_s4 (_ @t1 tptp.q))) (_ tptp.mdia_s4 (_ @t1 tptp.r)))) (_ tptp.mdia_s4 tptp.p)))))
% 0.36/0.62  (define @t3 () (@var "Y" tptp.mu))
% 0.36/0.62  (define @t4 () (@var "X" tptp.mu))
% 0.36/0.62  (define @t5 () (@var "W" $$unsorted))
% 0.36/0.62  (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3)))
% 0.36/0.62  (define @t7 () (@var "Y" (-> $$unsorted Bool)))
% 0.36/0.62  (define @t8 () (@var "X" (-> $$unsorted Bool)))
% 0.36/0.62  (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5))))
% 0.36/0.62  (define @t10 () (@var "Phi" (-> $$unsorted Bool)))
% 0.36/0.62  (define @t11 () (_ @t10 @t5))
% 0.36/0.62  (define @t12 () (not @t11))
% 0.36/0.62  (define @t13 () (@list @t10 @t5))
% 0.36/0.62  (define @t14 () (lambda @t13 @t12))
% 0.36/0.62  (define @t15 () (@var "Psi" (-> $$unsorted Bool)))
% 0.36/0.62  (define @t16 () (_ @t15 @t5))
% 0.36/0.62  (define @t17 () (lambda (@list @t10 @t15 @t5) (or @t11 @t16)))
% 0.36/0.62  (define @t18 () (@var "__flatten_var_0" $$unsorted))
% 0.36/0.62  (define @t19 () (_ tptp.mnot @t15))
% 0.36/0.62  (define @t20 () (_ tptp.mnot @t10))
% 0.36/0.62  (define @t21 () (_ tptp.mor @t20))
% 0.36/0.62  (define @t22 () (@list @t10 @t15 @t18))
% 0.36/0.62  (define @t23 () (lambda @t22 (_ (_ tptp.mnot (_ @t21 @t19)) @t18)))
% 0.36/0.62  (define @t24 () (lambda @t22 (_ (_ @t21 @t15) @t18)))
% 0.36/0.62  (define @t25 () (lambda @t22 (_ (_ (_ tptp.mor @t19) @t10) @t18)))
% 0.36/0.62  (define @t26 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t18)))
% 0.36/0.62  (define @t27 () (lambda @t22 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t18)))
% 0.36/0.62  (define @t28 () (@var "Phi" (-> tptp.mu $$unsorted Bool)))
% 0.36/0.62  (define @t29 () (_ @t28 @t4))
% 0.36/0.62  (define @t30 () (lambda (@list @t28 @t5) (forall (@list @t4) (_ @t29 @t5))))
% 0.36/0.62  (define @t31 () (@var "P" (-> $$unsorted Bool)))
% 0.36/0.62  (define @t32 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))
% 0.36/0.62  (define @t33 () (_ @t32 @t31))
% 0.36/0.62  (define @t34 () (lambda (@list @t32 @t5) (forall (@list @t31) (_ @t33 @t5))))
% 0.36/0.62  (define @t35 () (lambda (@list @t28 @t18) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t18) (_ (_ tptp.mnot @t29) @t18)))) @t18)))
% 0.36/0.62  (define @t36 () (lambda (@list @t32 @t18) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t31 @t18) (_ (_ tptp.mnot @t33) @t18)))) @t18)))
% 0.36/0.62  (define @t37 () (@list @t5))
% 0.36/0.62  (define @t38 () (lambda @t37 true))
% 0.36/0.62  (define @t39 () (@var "V" $$unsorted))
% 0.36/0.62  (define @t40 () (_ @t10 @t39))
% 0.36/0.62  (define @t41 () (@var "R" (-> $$unsorted $$unsorted Bool)))
% 0.36/0.62  (define @t42 () (@list @t39))
% 0.36/0.62  (define @t43 () (lambda (@list @t41 @t10 @t5) (forall @t42 (or (not (_ (_ @t41 @t5) @t39)) @t40))))
% 0.36/0.62  (define @t44 () (lambda (@list @t41 @t10 @t18) (_ (_ tptp.mnot (_ (_ tptp.mbox @t41) @t20)) @t18)))
% 0.36/0.62  (define @t45 () (@var "S" $$unsorted))
% 0.36/0.62  (define @t46 () (_ @t41 @t45))
% 0.36/0.62  (define @t47 () (@list @t45))
% 0.36/0.62  (define @t48 () (@list @t41))
% 0.36/0.62  (define @t49 () (lambda @t48 (forall @t47 (_ @t46 @t45))))
% 0.36/0.62  (define @t50 () (@var "T" $$unsorted))
% 0.36/0.62  (define @t51 () (_ @t41 @t50))
% 0.36/0.62  (define @t52 () (_ @t46 @t50))
% 0.36/0.62  (define @t53 () (lambda @t48 (forall (@list @t45 @t50) (=> @t52 (_ @t51 @t45)))))
% 0.36/0.62  (define @t54 () (@list @t50))
% 0.36/0.62  (define @t55 () (lambda @t48 (forall @t47 (exists @t54 @t52))))
% 0.36/0.62  (define @t56 () (@var "U" $$unsorted))
% 0.36/0.62  (define @t57 () (_ @t46 @t56))
% 0.36/0.62  (define @t58 () (_ @t51 @t56))
% 0.36/0.62  (define @t59 () (@list @t45 @t50 @t56))
% 0.36/0.62  (define @t60 () (lambda @t48 (forall @t59 (=> (and @t52 @t58) @t57))))
% 0.36/0.62  (define @t61 () (and @t52 @t57))
% 0.36/0.62  (define @t62 () (lambda @t48 (forall @t59 (=> @t61 @t58))))
% 0.36/0.62  (define @t63 () (= @t50 @t56))
% 0.36/0.62  (define @t64 () (lambda @t48 (forall @t59 (=> @t61 @t63))))
% 0.36/0.62  (define @t65 () (@list @t56))
% 0.36/0.62  (define @t66 () (lambda @t48 (forall @t47 (exists @t54 (and @t52 (forall @t65 (=> @t57 @t63)))))))
% 0.36/0.62  (define @t67 () (_ @t41 @t56))
% 0.36/0.62  (define @t68 () (_ @t67 @t50))
% 0.36/0.62  (define @t69 () (lambda @t48 (forall @t59 (=> @t52 (exists @t65 (and @t57 @t68))))))
% 0.36/0.62  (define @t70 () (lambda @t48 (forall @t59 (=> @t61 (or @t58 @t63 @t68)))))
% 0.36/0.62  (define @t71 () (lambda @t48 (forall @t59 (=> @t61 (exists @t42 (and (_ @t51 @t39) (_ @t67 @t39)))))))
% 0.36/0.62  (define @t72 () (forall @t37 @t11))
% 0.36/0.62  (define @t73 () (@list @t10))
% 0.36/0.62  (define @t74 () (lambda @t73 @t72))
% 0.36/0.62  (define @t75 () (lambda @t73 (forall @t37 @t12)))
% 0.36/0.62  (define @t76 () (lambda @t73 (exists @t37 @t11)))
% 0.36/0.62  (define @t77 () (lambda @t73 (exists @t37 @t12)))
% 0.36/0.62  (define @t78 () (_ (_ tptp.rel_s4 @t5) @t39))
% 0.36/0.62  (define @t79 () (not @t78))
% 0.36/0.62  (define @t80 () (or @t79 @t40))
% 0.36/0.62  (define @t81 () (forall @t42 @t80))
% 0.36/0.62  (define @t82 () (lambda @t13 @t81))
% 0.36/0.62  (define @t83 () (@list @t10 @t18))
% 0.36/0.62  (define @t84 () (lambda @t83 (_ (_ tptp.mnot (_ tptp.mbox_s4 @t20)) @t18)))
% 0.36/0.62  (define @t85 () (tptp.p @t39))
% 0.36/0.62  (define @t86 () (not @t85))
% 0.36/0.62  (define @t87 () (tptp.rel_s4 @t5 @t39))
% 0.36/0.62  (define @t88 () (not @t87))
% 0.36/0.62  (define @t89 () (not (forall @t42 (or @t88 @t86))))
% 0.36/0.62  (define @t90 () (@var "BOUND_VARIABLE_8549" $$unsorted))
% 0.36/0.62  (define @t91 () (or (not (tptp.rel_s4 @t5 @t90)) (not (tptp.p @t90)) (not (tptp.r @t90))))
% 0.36/0.62  (define @t92 () (@var "BOUND_VARIABLE_8540" $$unsorted))
% 0.36/0.62  (define @t93 () (or (not (tptp.rel_s4 @t5 @t92)) (not (tptp.p @t92)) (not (tptp.q @t92))))
% 0.36/0.62  (define @t94 () (and @t93 @t91))
% 0.36/0.62  (define @t95 () (or @t94 @t89))
% 0.36/0.62  (define @t96 () (forall (@list @t5 @t92 @t90) @t95))
% 0.36/0.62  (define @t97 () (@list @t92 @t90))
% 0.36/0.62  (define @t98 () (forall @t97 @t95))
% 0.36/0.62  (define @t99 () (forall (@list @t90) @t91))
% 0.36/0.62  (define @t100 () (@list @t39))
% 0.36/0.62  (define @t101 () (forall @t97 @t91))
% 0.36/0.62  (define @t102 () (forall (@list @t92) @t93))
% 0.36/0.62  (define @t103 () (forall @t97 @t93))
% 0.36/0.62  (define @t104 () (and @t103 @t101))
% 0.36/0.62  (define @t105 () (forall @t97 @t94))
% 0.36/0.62  (define @t106 () (or @t105 @t89))
% 0.36/0.62  (define @t107 () (tptp.r @t39))
% 0.36/0.62  (define @t108 () (not @t107))
% 0.36/0.62  (define @t109 () (forall @t42 (or @t88 @t86 @t108)))
% 0.36/0.62  (define @t110 () (tptp.q @t39))
% 0.36/0.62  (define @t111 () (not @t110))
% 0.36/0.62  (define @t112 () (forall @t42 (or @t88 @t86 @t111)))
% 0.36/0.62  (define @t113 () (not @t109))
% 0.36/0.62  (define @t114 () (not @t112))
% 0.36/0.62  (define @t115 () (or @t114 @t113))
% 0.36/0.62  (define @t116 () (or (not @t115) @t89))
% 0.36/0.62  (define @t117 () (not (tptp.rel_s4 @t18 @t39)))
% 0.36/0.62  (define @t118 () (not (forall @t42 (or @t117 @t86))))
% 0.36/0.62  (define @t119 () (not (forall @t42 (or @t117 @t86 @t108))))
% 0.36/0.62  (define @t120 () (not (forall @t42 (or @t117 @t86 @t111))))
% 0.36/0.62  (define @t121 () (or @t120 @t119))
% 0.36/0.62  (define @t122 () (not @t121))
% 0.36/0.62  (define @t123 () (@list @t18))
% 0.36/0.62  (define @t124 () (lambda @t123 (or @t122 @t118)))
% 0.36/0.62  (define @t125 () (_ @t124 @t5))
% 0.36/0.62  (define @t126 () (forall @t37 @t125))
% 0.36/0.62  (define @t127 () (_ @t10 @t5))
% 0.36/0.62  (define @t128 () (lambda @t73 (forall @t37 @t127)))
% 0.36/0.62  (define @t129 () (lambda @t123 @t118))
% 0.36/0.62  (define @t130 () (_ @t129 @t18))
% 0.36/0.62  (define @t131 () (or @t122 @t130))
% 0.36/0.62  (define @t132 () (lambda @t123 @t131))
% 0.36/0.62  (define @t133 () (_ @t15 @t18))
% 0.36/0.62  (define @t134 () (@list @t15 @t18))
% 0.36/0.62  (define @t135 () (_ @t10 @t39))
% 0.36/0.62  (define @t136 () (not @t135))
% 0.36/0.62  (define @t137 () (not (forall @t42 (or @t117 @t136))))
% 0.36/0.62  (define @t138 () (lambda @t83 @t137))
% 0.36/0.62  (define @t139 () (_ @t138 tptp.p))
% 0.36/0.62  (define @t140 () (lambda @t37 @t115))
% 0.36/0.62  (define @t141 () (_ @t140 @t18))
% 0.36/0.62  (define @t142 () (not @t141))
% 0.36/0.62  (define @t143 () (or @t142 @t133))
% 0.36/0.62  (define @t144 () (lambda @t134 @t143))
% 0.36/0.62  (define @t145 () (not (_ @t10 @t18)))
% 0.36/0.62  (define @t146 () (or @t145 @t133))
% 0.36/0.62  (define @t147 () (lambda @t22 @t146))
% 0.36/0.62  (define @t148 () (lambda @t123 @t119))
% 0.36/0.62  (define @t149 () (_ @t148 @t5))
% 0.36/0.62  (define @t150 () (or @t114 @t149))
% 0.36/0.62  (define @t151 () (lambda @t37 @t150))
% 0.36/0.62  (define @t152 () (@list @t15 @t5))
% 0.36/0.62  (define @t153 () (_ tptp.r @t39))
% 0.36/0.62  (define @t154 () (not @t153))
% 0.36/0.62  (define @t155 () (_ tptp.p @t39))
% 0.36/0.62  (define @t156 () (not @t155))
% 0.36/0.62  (define @t157 () (or @t117 @t156 @t154))
% 0.36/0.62  (define @t158 () (or @t156 @t154))
% 0.36/0.62  (define @t159 () (not (_ tptp.p @t18)))
% 0.36/0.62  (define @t160 () (lambda @t123 (not (or @t159 (not (_ tptp.r @t18))))))
% 0.36/0.62  (define @t161 () (_ @t160 @t39))
% 0.36/0.62  (define @t162 () (not @t161))
% 0.36/0.62  (define @t163 () (or @t117 @t162))
% 0.36/0.62  (define @t164 () (forall @t42 @t163))
% 0.36/0.62  (define @t165 () (not @t164))
% 0.36/0.62  (define @t166 () (lambda @t123 @t165))
% 0.36/0.62  (define @t167 () (not @t133))
% 0.36/0.62  (define @t168 () (lambda @t134 (not (or @t159 @t167))))
% 0.36/0.62  (define @t169 () (not (or @t145 @t167)))
% 0.36/0.62  (define @t170 () (_ (lambda @t22 @t169) tptp.p))
% 0.36/0.62  (define @t171 () (lambda @t123 @t120))
% 0.36/0.62  (define @t172 () (_ @t171 @t5))
% 0.36/0.62  (define @t173 () (or @t172 @t16))
% 0.36/0.62  (define @t174 () (lambda @t152 @t173))
% 0.36/0.62  (define @t175 () (_ tptp.q @t39))
% 0.36/0.62  (define @t176 () (not @t175))
% 0.36/0.62  (define @t177 () (or @t117 @t156 @t176))
% 0.36/0.62  (define @t178 () (or @t156 @t176))
% 0.36/0.62  (define @t179 () (lambda @t123 (not (or @t159 (not (_ tptp.q @t18))))))
% 0.36/0.62  (define @t180 () (_ @t179 @t39))
% 0.36/0.62  (define @t181 () (not @t180))
% 0.36/0.62  (define @t182 () (or @t117 @t181))
% 0.36/0.62  (define @t183 () (forall @t42 @t182))
% 0.36/0.62  (define @t184 () (not @t183))
% 0.36/0.62  (define @t185 () (lambda @t123 @t184))
% 0.36/0.62  (define @t186 () (forall @t42 (or @t88 @t136)))
% 0.36/0.62  (define @t187 () (lambda @t37 @t186))
% 0.36/0.62  (define @t188 () (_ @t187 @t5))
% 0.36/0.62  (define @t189 () (not @t188))
% 0.36/0.62  (define @t190 () (lambda @t37 @t189))
% 0.36/0.62  (define @t191 () (not @t40))
% 0.36/0.62  (define @t192 () (or @t88 @t191))
% 0.36/0.62  (define @t193 () (lambda @t37 @t12))
% 0.36/0.62  (define @t194 () (_ @t193 @t39))
% 0.36/0.62  (define @t195 () (or @t88 @t194))
% 0.36/0.62  (define @t196 () (forall @t42 @t195))
% 0.36/0.62  (define @t197 () (lambda @t37 @t196))
% 0.36/0.62  (define @t198 () (lambda @t13 (forall @t42 (or @t88 @t135))))
% 0.36/0.62  (define @t199 () (not @t16))
% 0.36/0.62  (define @t200 () (or @t12 @t199))
% 0.36/0.62  (define @t201 () (lambda @t37 @t200))
% 0.36/0.62  (define @t202 () (_ @t201 @t5))
% 0.36/0.62  (define @t203 () (not @t202))
% 0.36/0.62  (define @t204 () (lambda @t37 @t203))
% 0.36/0.62  (define @t205 () (lambda @t37 @t199))
% 0.36/0.62  (define @t206 () (_ @t205 @t5))
% 0.36/0.62  (define @t207 () (or @t12 @t206))
% 0.36/0.62  (define @t208 () (lambda @t37 @t207))
% 0.36/0.62  (define @t209 () (or @t12 @t16))
% 0.36/0.62  (define @t210 () (lambda @t152 @t209))
% 0.36/0.62  (define @t211 () (_ @t193 @t5))
% 0.36/0.62  (define @t212 () (or @t211 @t16))
% 0.36/0.62  (define @t213 () (lambda @t152 @t212))
% 0.36/0.62  (define @t214 () (lambda @t37 @t209))
% 0.36/0.62  (define @t215 () (@quantifiers_skolemize @t96 0))
% 0.36/0.62  (define @t216 () (forall @t42 (or (not (tptp.rel_s4 @t215 @t39)) @t86)))
% 0.36/0.62  (define @t217 () (not @t216))
% 0.36/0.62  (define @t218 () (@quantifiers_skolemize @t96 2))
% 0.36/0.62  (define @t219 () (tptp.p @t218))
% 0.36/0.62  (define @t220 () (not @t219))
% 0.36/0.62  (define @t221 () (tptp.rel_s4 @t215 @t218))
% 0.36/0.62  (define @t222 () (not @t221))
% 0.36/0.62  (define @t223 () (or @t222 @t220 (not (tptp.r @t218))))
% 0.36/0.62  (define @t224 () (@quantifiers_skolemize @t96 1))
% 0.36/0.62  (define @t225 () (tptp.p @t224))
% 0.36/0.62  (define @t226 () (not @t225))
% 0.36/0.62  (define @t227 () (tptp.rel_s4 @t215 @t224))
% 0.36/0.62  (define @t228 () (not @t227))
% 0.36/0.62  (define @t229 () (or @t228 @t226 (not (tptp.q @t224))))
% 0.36/0.62  (define @t230 () (and @t229 @t223))
% 0.36/0.62  (define @t231 () (or @t230 @t217))
% 0.36/0.62  (define @t232 () (@list true))
% 0.36/0.62  (define @t233 () (@list @t231))
% 0.36/0.62  (define @t234 () (or @t222 @t220))
% 0.36/0.62  (define @t235 () (@list false false false))
% 0.36/0.62  (define @t236 () (@list @t229))
% 0.36/0.62  (define @t237 () (or @t228 @t226))
% 0.36/0.62  (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue)))
% 0.36/0.62  (assume @p2 (_ tptp.mreflexive tptp.rel_s4))
% 0.36/0.62  (assume @p3 (_ tptp.mtransitive tptp.rel_s4))
% 0.36/0.62  (assume @p4 @t2)
% 0.36/0.62  (assume @p5 true)
% 0.36/0.62  (step @p6 (= tptp.meq_ind @t6) :rule refl :args (@t6))
% 0.36/0.62  (step @p7 (= tptp.meq_prop @t9) :rule refl :args (@t9))
% 0.36/0.62  (step @p8 (= tptp.mnot @t14) :rule refl :args (@t14))
% 0.36/0.62  (step @p9 (= tptp.mor @t17) :rule refl :args (@t17))
% 0.36/0.62  (step @p10 (= tptp.mand @t23) :rule refl :args (@t23))
% 0.36/0.62  (step @p11 (= tptp.mimplies @t24) :rule refl :args (@t24))
% 0.36/0.62  (step @p12 (= tptp.mimplied @t25) :rule refl :args (@t25))
% 0.36/0.62  (step @p13 (= tptp.mequiv @t26) :rule refl :args (@t26))
% 0.36/0.62  (step @p14 (= tptp.mxor @t27) :rule refl :args (@t27))
% 0.36/0.62  (step @p15 (= tptp.mforall_ind @t30) :rule refl :args (@t30))
% 0.36/0.62  (step @p16 (= tptp.mforall_prop @t34) :rule refl :args (@t34))
% 0.36/0.62  (step @p17 (= tptp.mexists_ind @t35) :rule refl :args (@t35))
% 0.36/0.62  (step @p18 (= tptp.mexists_prop @t36) :rule refl :args (@t36))
% 0.36/0.62  (step @p19 (= tptp.mtrue @t38) :rule refl :args (@t38))
% 0.36/0.62  (step @p20 (= tptp.mbox @t43) :rule refl :args (@t43))
% 0.36/0.62  (step @p21 (= tptp.mdia @t44) :rule refl :args (@t44))
% 0.36/0.62  (step @p22 (= tptp.mreflexive @t49) :rule refl :args (@t49))
% 0.36/0.62  (step @p23 (= tptp.msymmetric @t53) :rule refl :args (@t53))
% 0.36/0.62  (step @p24 (= tptp.mserial @t55) :rule refl :args (@t55))
% 0.36/0.62  (step @p25 (= tptp.mtransitive @t60) :rule refl :args (@t60))
% 0.36/0.62  (step @p26 (= tptp.meuclidean @t62) :rule refl :args (@t62))
% 0.36/0.62  (step @p27 (= tptp.mpartially_functional @t64) :rule refl :args (@t64))
% 0.36/0.62  (step @p28 (= tptp.mfunctional @t66) :rule refl :args (@t66))
% 0.36/0.62  (step @p29 (= tptp.mweakly_dense @t69) :rule refl :args (@t69))
% 0.36/0.62  (step @p30 (= tptp.mweakly_connected @t70) :rule refl :args (@t70))
% 0.36/0.62  (step @p31 (= tptp.mweakly_directed @t71) :rule refl :args (@t71))
% 0.36/0.62  (step @p32 (= tptp.mvalid @t74) :rule refl :args (@t74))
% 0.36/0.62  (step @p33 (= tptp.minvalid @t75) :rule refl :args (@t75))
% 0.36/0.62  (step @p34 (= tptp.msatisfiable @t76) :rule refl :args (@t76))
% 0.36/0.62  (step @p35 (= tptp.mcountersatisfiable @t77) :rule refl :args (@t77))
% 0.36/0.62  (step @p36 (= tptp.mbox_s4 @t82) :rule refl :args (@t82))
% 0.36/0.62  (step @p37 (= tptp.mdia_s4 @t84) :rule refl :args (@t84))
% 0.36/0.62  (step @p38 :rule quant-merge-prenex :args ((= (forall @t37 @t98) @t96)))
% 0.36/0.62  (step @p39 :rule refl :args (@t89))
% 0.36/0.62  (step @p40 :rule alpha_equiv :args (@t99 (@list @t90) @t100))
% 0.36/0.62  (step @p41 :rule quant-unused-vars :args ((= @t101 @t99)))
% 0.36/0.62  (step @p42 :rule trans :premises (@p41 @p40))
% 0.36/0.62  (step @p43 :rule alpha_equiv :args (@t102 (@list @t92) @t100))
% 0.36/0.62  (step @p44 :rule quant-unused-vars :args ((= @t103 @t102)))
% 0.36/0.62  (step @p45 :rule trans :premises (@p44 @p43))
% 0.36/0.62  (step @p46 :rule nary_cong :premises (@p45 @p42) :args (@t104))
% 0.36/0.62  (step @p47 :rule quant-miniscope-and :args ((= @t105 @t104)))
% 0.36/0.62  (step @p48 :rule trans :premises (@p47 @p46))
% 0.36/0.62  (step @p49 :rule nary_cong :premises (@p48 @p39) :args (@t106))
% 0.36/0.62  (step @p50 :rule quant-miniscope-or :args ((= @t98 @t106)))
% 0.36/0.62  (step @p51 :rule trans :premises (@p50 @p49))
% 0.36/0.62  (step @p52 :rule symm :premises (@p51))
% 0.36/0.62  (step @p53 :rule cong :premises (@p52) :args ((forall @t37 (or (and @t112 @t109) @t89))))
% 0.36/0.62  (step @p54 :rule trans :premises (@p53 @p38))
% 0.36/0.62  (step @p55 :rule bool-double-not-elim :args (@t109))
% 0.36/0.62  (step @p56 :rule bool-double-not-elim :args (@t112))
% 0.36/0.62  (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((and (not @t114) (not @t113))))
% 0.36/0.62  (step @p58 :rule bool-or-de-morgan :args (@t114 @t113 false))
% 0.36/0.62  (step @p59 :rule trans :premises (@p58 @p57))
% 0.36/0.62  (step @p60 :rule nary_cong :premises (@p59 @p39) :args (@t116))
% 0.36/0.62  (step @p61 :rule cong :premises (@p60) :args ((forall @t37 @t116)))
% 0.36/0.62  (step @p62 :rule trans :premises (@p61 @p54))
% 0.36/0.62  (step @p63 :rule beta-reduce :args ((= @t125 @t116)))
% 0.36/0.62  (step @p64 :rule cong :premises (@p63) :args (@t126))
% 0.36/0.62  (step @p65 :rule trans :premises (@p64 @p62))
% 0.36/0.62  (step @p66 :rule beta-reduce :args ((= (_ @t128 @t124) @t126)))
% 0.36/0.62  (step @p67 :rule trans :premises (@p66 @p65))
% 0.36/0.62  (step @p68 :rule beta-reduce :args ((= @t130 @t118)))
% 0.36/0.62  (step @p69 :rule refl :args (@t122))
% 0.36/0.62  (step @p70 :rule nary_cong :premises (@p69 @p68) :args (@t131))
% 0.36/0.62  (step @p71 :rule cong :premises (@p70) :args (@t132))
% 0.36/0.62  (step @p72 :rule beta-reduce :args ((= (_ (lambda @t134 (or @t122 @t133)) @t129) @t132)))
% 0.36/0.62  (step @p73 :rule trans :premises (@p72 @p71))
% 0.36/0.62  (step @p74 :rule beta-reduce :args ((= @t139 @t129)))
% 0.36/0.62  (step @p75 :rule refl :args (@t133))
% 0.36/0.62  (step @p76 :rule beta-reduce :args ((= @t141 @t121)))
% 0.36/0.62  (step @p77 :rule cong :premises (@p76) :args (@t142))
% 0.36/0.62  (step @p78 :rule nary_cong :premises (@p77 @p75) :args (@t143))
% 0.36/0.62  (step @p79 :rule cong :premises (@p78) :args (@t144))
% 0.36/0.62  (step @p80 :rule beta-reduce :args ((= (_ @t147 @t140) @t144)))
% 0.36/0.62  (step @p81 :rule trans :premises (@p80 @p79))
% 0.36/0.62  (step @p82 :rule beta-reduce :args ((= @t149 @t113)))
% 0.36/0.62  (step @p83 :rule refl :args (@t114))
% 0.36/0.62  (step @p84 :rule nary_cong :premises (@p83 @p82) :args (@t150))
% 0.36/0.62  (step @p85 :rule cong :premises (@p84) :args (@t151))
% 0.36/0.62  (step @p86 :rule beta-reduce :args ((= (_ (lambda @t152 (or @t114 @t16)) @t148) @t151)))
% 0.36/0.62  (step @p87 :rule trans :premises (@p86 @p85))
% 0.36/0.62  (step @p88 :rule refl :args (@t107))
% 0.36/0.62  (step @p89 :rule refl :args (@t153))
% 0.36/0.62  (step @p90 :rule cong :premises (@p89 @p88) :args ((= @t153 @t107)))
% 0.36/0.62  (step @p91 :rule symm :premises (@p90))
% 0.36/0.62  (step @p92 :rule eq_resolve :premises (@p89 @p91))
% 0.36/0.62  (step @p93 :rule cong :premises (@p92) :args (@t154))
% 0.36/0.62  (step @p94 :rule refl :args (@t85))
% 0.36/0.62  (step @p95 :rule refl :args (@t155))
% 0.36/0.62  (step @p96 :rule cong :premises (@p95 @p94) :args ((= @t155 @t85)))
% 0.36/0.62  (step @p97 :rule symm :premises (@p96))
% 0.36/0.62  (step @p98 :rule eq_resolve :premises (@p95 @p97))
% 0.36/0.62  (step @p99 :rule cong :premises (@p98) :args (@t156))
% 0.36/0.62  (step @p100 :rule refl :args (@t117))
% 0.36/0.62  (step @p101 :rule nary_cong :premises (@p100 @p99 @p93) :args (@t157))
% 0.36/0.62  (step @p102 :rule cong :premises (@p101) :args ((forall @t42 @t157)))
% 0.36/0.62  (step @p103 :rule aci_norm :args ((= (or @t117 @t158) @t157)))
% 0.36/0.62  (step @p104 :rule bool-double-not-elim :args (@t158))
% 0.36/0.62  (step @p105 :rule beta-reduce :args ((= @t161 (not @t158))))
% 0.36/0.62  (step @p106 :rule cong :premises (@p105) :args (@t162))
% 0.36/0.62  (step @p107 :rule trans :premises (@p106 @p104))
% 0.36/0.62  (step @p108 :rule refl :args (@t117))
% 0.36/0.62  (step @p109 :rule nary_cong :premises (@p108 @p107) :args (@t163))
% 0.36/0.62  (step @p110 :rule trans :premises (@p109 @p103))
% 0.36/0.62  (step @p111 :rule cong :premises (@p110) :args (@t164))
% 0.36/0.62  (step @p112 :rule trans :premises (@p111 @p102))
% 0.36/0.62  (step @p113 :rule cong :premises (@p112) :args (@t165))
% 0.36/0.62  (step @p114 :rule cong :premises (@p113) :args (@t166))
% 0.36/0.62  (step @p115 :rule beta-reduce :args ((= (_ @t138 @t160) @t166)))
% 0.36/0.62  (step @p116 :rule trans :premises (@p115 @p114))
% 0.36/0.62  (step @p117 :rule beta-reduce :args ((= (_ @t168 tptp.r) @t160)))
% 0.36/0.62  (step @p118 :rule refl :args (tptp.r))
% 0.36/0.62  (step @p119 :rule beta-reduce :args ((= @t170 @t168)))
% 0.36/0.62  (step @p120 :rule ho_cong :premises (@p119 @p118))
% 0.36/0.62  (step @p121 :rule trans :premises (@p120 @p117))
% 0.36/0.62  (step @p122 :rule refl :args (@t138))
% 0.36/0.62  (step @p123 :rule ho_cong :premises (@p122 @p121))
% 0.36/0.62  (step @p124 :rule trans :premises (@p123 @p116))
% 0.36/0.62  (step @p125 :rule refl :args (@t16))
% 0.36/0.62  (step @p126 :rule beta-reduce :args ((= @t172 @t114)))
% 0.36/0.62  (step @p127 :rule nary_cong :premises (@p126 @p125) :args (@t173))
% 0.36/0.62  (step @p128 :rule cong :premises (@p127) :args (@t174))
% 0.36/0.62  (step @p129 :rule beta-reduce :args ((= (_ @t17 @t171) @t174)))
% 0.36/0.62  (step @p130 :rule trans :premises (@p129 @p128))
% 0.36/0.62  (step @p131 :rule refl :args (@t110))
% 0.36/0.62  (step @p132 :rule refl :args (@t175))
% 0.36/0.62  (step @p133 :rule cong :premises (@p132 @p131) :args ((= @t175 @t110)))
% 0.36/0.62  (step @p134 :rule symm :premises (@p133))
% 0.36/0.62  (step @p135 :rule eq_resolve :premises (@p132 @p134))
% 0.36/0.62  (step @p136 :rule cong :premises (@p135) :args (@t176))
% 0.36/0.62  (step @p137 :rule nary_cong :premises (@p100 @p99 @p136) :args (@t177))
% 0.36/0.62  (step @p138 :rule cong :premises (@p137) :args ((forall @t42 @t177)))
% 0.36/0.62  (step @p139 :rule aci_norm :args ((= (or @t117 @t178) @t177)))
% 0.36/0.62  (step @p140 :rule bool-double-not-elim :args (@t178))
% 0.36/0.62  (step @p141 :rule beta-reduce :args ((= @t180 (not @t178))))
% 0.36/0.62  (step @p142 :rule cong :premises (@p141) :args (@t181))
% 0.36/0.62  (step @p143 :rule trans :premises (@p142 @p140))
% 0.36/0.62  (step @p144 :rule nary_cong :premises (@p108 @p143) :args (@t182))
% 0.36/0.62  (step @p145 :rule trans :premises (@p144 @p139))
% 0.36/0.62  (step @p146 :rule cong :premises (@p145) :args (@t183))
% 0.36/0.62  (step @p147 :rule trans :premises (@p146 @p138))
% 0.36/0.62  (step @p148 :rule cong :premises (@p147) :args (@t184))
% 0.36/0.62  (step @p149 :rule cong :premises (@p148) :args (@t185))
% 0.36/0.62  (step @p150 :rule beta-reduce :args ((= (_ @t138 @t179) @t185)))
% 0.36/0.62  (step @p151 :rule trans :premises (@p150 @p149))
% 0.36/0.62  (step @p152 :rule beta-reduce :args ((= (_ @t168 tptp.q) @t179)))
% 0.36/0.62  (step @p153 :rule refl :args (tptp.q))
% 0.36/0.62  (step @p154 :rule ho_cong :premises (@p119 @p153))
% 0.36/0.62  (step @p155 :rule trans :premises (@p154 @p152))
% 0.36/0.62  (step @p156 :rule ho_cong :premises (@p122 @p155))
% 0.36/0.62  (step @p157 :rule trans :premises (@p156 @p151))
% 0.36/0.62  (step @p158 :rule refl :args (@t17))
% 0.36/0.62  (step @p159 :rule ho_cong :premises (@p158 @p157))
% 0.36/0.62  (step @p160 :rule trans :premises (@p159 @p130))
% 0.36/0.62  (step @p161 :rule ho_cong :premises (@p160 @p124))
% 0.36/0.62  (step @p162 :rule trans :premises (@p161 @p87))
% 0.36/0.62  (step @p163 :rule refl :args (@t147))
% 0.36/0.62  (step @p164 :rule ho_cong :premises (@p163 @p162))
% 0.36/0.62  (step @p165 :rule trans :premises (@p164 @p81))
% 0.36/0.62  (step @p166 :rule ho_cong :premises (@p165 @p74))
% 0.36/0.62  (step @p167 :rule trans :premises (@p166 @p73))
% 0.36/0.62  (step @p168 :rule refl :args (@t128))
% 0.36/0.62  (step @p169 :rule ho_cong :premises (@p168 @p167))
% 0.36/0.62  (step @p170 :rule trans :premises (@p169 @p67))
% 0.36/0.62  (step @p171 :rule cong :premises (@p170) :args ((not (_ @t128 (_ (_ @t147 (_ (_ @t17 (_ @t138 (_ @t170 tptp.q))) (_ @t138 (_ @t170 tptp.r)))) @t139)))))
% 0.36/0.62  (step @p172 :rule refl :args (tptp.p))
% 0.36/0.62  (step @p173 :rule beta-reduce :args ((= (_ (lambda @t37 (not @t186)) @t18) @t137)))
% 0.36/0.62  (step @p174 :rule refl :args (@t18))
% 0.36/0.62  (step @p175 :rule beta-reduce :args ((= @t188 @t186)))
% 0.36/0.62  (step @p176 :rule cong :premises (@p175) :args (@t189))
% 0.36/0.62  (step @p177 :rule cong :premises (@p176) :args (@t190))
% 0.36/0.62  (step @p178 :rule beta-reduce :args ((= (_ @t14 @t187) @t190)))
% 0.36/0.62  (step @p179 :rule trans :premises (@p178 @p177))
% 0.36/0.62  (step @p180 :rule refl :args (@t135))
% 0.36/0.62  (step @p181 :rule refl :args (@t40))
% 0.36/0.62  (step @p182 :rule cong :premises (@p181 @p180) :args ((= @t40 @t135)))
% 0.36/0.62  (step @p183 :rule symm :premises (@p182))
% 0.36/0.62  (step @p184 :rule eq_resolve :premises (@p181 @p183))
% 0.36/0.62  (step @p185 :rule cong :premises (@p184) :args (@t191))
% 0.36/0.62  (step @p186 :rule refl :args (@t88))
% 0.36/0.62  (step @p187 :rule nary_cong :premises (@p186 @p185) :args (@t192))
% 0.36/0.62  (step @p188 :rule cong :premises (@p187) :args ((forall @t42 @t192)))
% 0.36/0.62  (step @p189 :rule beta-reduce :args ((= @t194 @t191)))
% 0.36/0.62  (step @p190 :rule refl :args (@t88))
% 0.36/0.62  (step @p191 :rule nary_cong :premises (@p190 @p189) :args (@t195))
% 0.36/0.62  (step @p192 :rule cong :premises (@p191) :args (@t196))
% 0.36/0.62  (step @p193 :rule trans :premises (@p192 @p188))
% 0.36/0.62  (step @p194 :rule cong :premises (@p193) :args (@t197))
% 0.36/0.62  (step @p195 :rule beta-reduce :args ((= (_ @t198 @t193) @t197)))
% 0.36/0.62  (step @p196 :rule trans :premises (@p195 @p194))
% 0.36/0.62  (step @p197 :rule beta-reduce :args ((= (_ @t14 @t10) @t193)))
% 0.36/0.62  (step @p198 :rule refl :args (@t198))
% 0.36/0.62  (step @p199 :rule ho_cong :premises (@p198 @p197))
% 0.36/0.62  (step @p200 :rule trans :premises (@p199 @p196))
% 0.36/0.62  (step @p201 :rule refl :args (@t14))
% 0.36/0.62  (step @p202 :rule ho_cong :premises (@p201 @p200))
% 0.36/0.62  (step @p203 :rule trans :premises (@p202 @p179))
% 0.36/0.62  (step @p204 :rule ho_cong :premises (@p203 @p174))
% 0.36/0.62  (step @p205 :rule trans :premises (@p204 @p173))
% 0.36/0.62  (step @p206 :rule refl :args (@t10))
% 0.36/0.62  (step @p207 :rule ho_cong :premises (@p8 @p206))
% 0.36/0.62  (step @p208 :rule refl :args (@t87))
% 0.36/0.62  (step @p209 :rule refl :args (@t78))
% 0.36/0.62  (step @p210 :rule cong :premises (@p209 @p208) :args ((= @t78 @t87)))
% 0.36/0.62  (step @p211 :rule symm :premises (@p210))
% 0.36/0.62  (step @p212 :rule eq_resolve :premises (@p209 @p211))
% 0.36/0.62  (step @p213 :rule cong :premises (@p212) :args (@t79))
% 0.36/0.62  (step @p214 :rule nary_cong :premises (@p213 @p184) :args (@t80))
% 0.36/0.62  (step @p215 :rule cong :premises (@p214) :args (@t81))
% 0.36/0.62  (step @p216 :rule cong :premises (@p215) :args (@t82))
% 0.36/0.62  (step @p217 :rule trans :premises (@p36 @p216))
% 0.36/0.62  (step @p218 :rule ho_cong :premises (@p217 @p207))
% 0.36/0.62  (step @p219 :rule ho_cong :premises (@p8 @p218))
% 0.36/0.62  (step @p220 :rule ho_cong :premises (@p219 @p174))
% 0.36/0.62  (step @p221 :rule trans :premises (@p220 @p205))
% 0.36/0.62  (step @p222 :rule cong :premises (@p221) :args (@t84))
% 0.36/0.62  (step @p223 :rule trans :premises (@p37 @p222))
% 0.36/0.62  (step @p224 :rule ho_cong :premises (@p223 @p172))
% 0.36/0.62  (step @p225 :rule beta-reduce :args ((= (_ (lambda @t37 (not @t200)) @t18) @t169)))
% 0.36/0.62  (step @p226 :rule beta-reduce :args ((= @t202 @t200)))
% 0.36/0.62  (step @p227 :rule cong :premises (@p226) :args (@t203))
% 0.36/0.62  (step @p228 :rule cong :premises (@p227) :args (@t204))
% 0.36/0.62  (step @p229 :rule beta-reduce :args ((= (_ @t14 @t201) @t204)))
% 0.36/0.62  (step @p230 :rule trans :premises (@p229 @p228))
% 0.36/0.62  (step @p231 :rule beta-reduce :args ((= @t206 @t199)))
% 0.36/0.62  (step @p232 :rule refl :args (@t12))
% 0.36/0.62  (step @p233 :rule nary_cong :premises (@p232 @p231) :args (@t207))
% 0.36/0.62  (step @p234 :rule cong :premises (@p233) :args (@t208))
% 0.36/0.62  (step @p235 :rule beta-reduce :args ((= (_ @t210 @t205) @t208)))
% 0.36/0.62  (step @p236 :rule trans :premises (@p235 @p234))
% 0.36/0.62  (step @p237 :rule beta-reduce :args ((= (_ @t14 @t15) @t205)))
% 0.36/0.62  (step @p238 :rule beta-reduce :args ((= @t211 @t12)))
% 0.36/0.62  (step @p239 :rule nary_cong :premises (@p238 @p125) :args (@t212))
% 0.36/0.62  (step @p240 :rule cong :premises (@p239) :args (@t213))
% 0.36/0.62  (step @p241 :rule beta-reduce :args ((= (_ @t17 @t193) @t213)))
% 0.36/0.62  (step @p242 :rule trans :premises (@p241 @p240))
% 0.36/0.62  (step @p243 :rule ho_cong :premises (@p158 @p197))
% 0.36/0.62  (step @p244 :rule trans :premises (@p243 @p242))
% 0.36/0.62  (step @p245 :rule ho_cong :premises (@p244 @p237))
% 0.36/0.62  (step @p246 :rule trans :premises (@p245 @p236))
% 0.36/0.62  (step @p247 :rule ho_cong :premises (@p201 @p246))
% 0.36/0.62  (step @p248 :rule trans :premises (@p247 @p230))
% 0.36/0.62  (step @p249 :rule ho_cong :premises (@p248 @p174))
% 0.36/0.62  (step @p250 :rule trans :premises (@p249 @p225))
% 0.36/0.62  (step @p251 :rule refl :args (@t15))
% 0.36/0.62  (step @p252 :rule ho_cong :premises (@p8 @p251))
% 0.36/0.62  (step @p253 :rule ho_cong :premises (@p9 @p207))
% 0.36/0.62  (step @p254 :rule ho_cong :premises (@p253 @p252))
% 0.36/0.62  (step @p255 :rule ho_cong :premises (@p8 @p254))
% 0.36/0.62  (step @p256 :rule ho_cong :premises (@p255 @p174))
% 0.36/0.62  (step @p257 :rule trans :premises (@p256 @p250))
% 0.36/0.62  (step @p258 :rule cong :premises (@p257) :args (@t23))
% 0.36/0.62  (step @p259 :rule trans :premises (@p10 @p258))
% 0.36/0.62  (step @p260 :rule ho_cong :premises (@p259 @p172))
% 0.36/0.62  (step @p261 :rule ho_cong :premises (@p260 @p118))
% 0.36/0.62  (step @p262 :rule ho_cong :premises (@p223 @p261))
% 0.36/0.62  (step @p263 :rule ho_cong :premises (@p260 @p153))
% 0.36/0.62  (step @p264 :rule ho_cong :premises (@p223 @p263))
% 0.36/0.62  (step @p265 :rule ho_cong :premises (@p9 @p264))
% 0.36/0.62  (step @p266 :rule ho_cong :premises (@p265 @p262))
% 0.36/0.62  (step @p267 :rule beta-reduce :args ((= (_ @t214 @t18) @t146)))
% 0.36/0.62  (step @p268 :rule beta-reduce :args ((= (_ @t210 @t15) @t214)))
% 0.36/0.62  (step @p269 :rule ho_cong :premises (@p244 @p251))
% 0.36/0.62  (step @p270 :rule trans :premises (@p269 @p268))
% 0.36/0.62  (step @p271 :rule ho_cong :premises (@p270 @p174))
% 0.36/0.62  (step @p272 :rule trans :premises (@p271 @p267))
% 0.36/0.62  (step @p273 :rule ho_cong :premises (@p253 @p251))
% 0.36/0.62  (step @p274 :rule ho_cong :premises (@p273 @p174))
% 0.36/0.62  (step @p275 :rule trans :premises (@p274 @p272))
% 0.36/0.62  (step @p276 :rule cong :premises (@p275) :args (@t24))
% 0.36/0.62  (step @p277 :rule trans :premises (@p11 @p276))
% 0.36/0.62  (step @p278 :rule ho_cong :premises (@p277 @p266))
% 0.36/0.62  (step @p279 :rule ho_cong :premises (@p278 @p224))
% 0.36/0.62  (step @p280 :rule refl :args (@t127))
% 0.36/0.62  (step @p281 :rule refl :args (@t11))
% 0.36/0.62  (step @p282 :rule cong :premises (@p281 @p280) :args ((= @t11 @t127)))
% 0.36/0.62  (step @p283 :rule symm :premises (@p282))
% 0.36/0.62  (step @p284 :rule eq_resolve :premises (@p281 @p283))
% 0.36/0.62  (step @p285 :rule cong :premises (@p284) :args (@t72))
% 0.36/0.62  (step @p286 :rule cong :premises (@p285) :args (@t74))
% 0.36/0.62  (step @p287 :rule trans :premises (@p32 @p286))
% 0.36/0.62  (step @p288 :rule ho_cong :premises (@p287 @p279))
% 0.36/0.62  (step @p289 :rule cong :premises (@p288) :args (@t2))
% 0.36/0.62  (step @p290 :rule trans :premises (@p289 @p171))
% 0.36/0.62  (step @p291 :rule eq_resolve :premises (@p4 @p290))
% 0.36/0.62  (step @p292 :rule skolemize :premises (@p291))
% 0.36/0.62  (step @p293 :rule bool-double-not-elim :args (@t216))
% 0.36/0.62  (step @p294 :rule refl :args (@t231))
% 0.36/0.62  (step @p295 :rule nary_cong :premises (@p294 @p293) :args ((or @t231 (not @t217))))
% 0.36/0.62  (step @p296 :rule cnf_or_neg :args (@t231 1))
% 0.36/0.62  (step @p297 :rule eq_resolve :premises (@p296 @p295))
% 0.36/0.62  (step @p298 :rule reordering :premises (@p297) :args ((or @t216 @t231)))
% 0.36/0.62  (step @p299 :rule chain_m_resolution :premises (@p298 @p292) :args (@t216 @t232 @t233))
% 0.36/0.62  (step @p300 :rule instantiate :premises (@p299) :args ((@list @t224)))
% 0.36/0.62  (step @p301 :rule bool-double-not-elim :args (@t221))
% 0.36/0.62  (step @p302 :rule refl :args (@t223))
% 0.36/0.62  (step @p303 :rule nary_cong :premises (@p302 @p301) :args ((or @t223 (not @t222))))
% 0.36/0.62  (step @p304 :rule cnf_or_neg :args (@t223 0))
% 0.36/0.62  (step @p305 :rule eq_resolve :premises (@p304 @p303))
% 0.36/0.62  (step @p306 :rule reordering :premises (@p305) :args ((or @t221 @t223)))
% 0.36/0.62  (step @p307 :rule bool-double-not-elim :args (@t219))
% 0.36/0.62  (step @p308 :rule nary_cong :premises (@p302 @p307) :args ((or @t223 (not @t220))))
% 0.36/0.62  (step @p309 :rule cnf_or_neg :args (@t223 1))
% 0.36/0.62  (step @p310 :rule eq_resolve :premises (@p309 @p308))
% 0.36/0.62  (step @p311 :rule reordering :premises (@p310) :args ((or @t219 @t223)))
% 0.36/0.62  (step @p312 :rule instantiate :premises (@p299) :args ((@list @t218)))
% 0.36/0.62  (step @p313 :rule cnf_or_pos :args (@t234))
% 0.36/0.62  (step @p314 :rule reordering :premises (@p313) :args ((or @t222 @t220 (not @t234))))
% 0.36/0.62  (step @p315 :rule chain_m_resolution :premises (@p314 @p312 @p311 @p306) :args (@t223 @t235 (@list @t234 @t219 @t221)))
% 0.36/0.62  (step @p316 :rule cnf_or_neg :args (@t231 0))
% 0.36/0.62  (step @p317 :rule chain_m_resolution :premises (@p316 @p292) :args ((not @t230) @t232 @t233))
% 0.36/0.62  (step @p318 :rule cnf_and_neg :args (@t230))
% 0.36/0.62  (step @p319 :rule chain_m_resolution :premises (@p318 @p317 @p315) :args ((not @t229) (@list true false) (@list @t230 @t223)))
% 0.36/0.62  (step @p320 :rule bool-double-not-elim :args (@t227))
% 0.36/0.62  (step @p321 :rule refl :args (@t229))
% 0.36/0.62  (step @p322 :rule nary_cong :premises (@p321 @p320) :args ((or @t229 (not @t228))))
% 0.36/0.62  (step @p323 :rule cnf_or_neg :args (@t229 0))
% 0.36/0.62  (step @p324 :rule eq_resolve :premises (@p323 @p322))
% 0.36/0.62  (step @p325 :rule reordering :premises (@p324) :args ((or @t227 @t229)))
% 0.36/0.62  (step @p326 :rule chain_m_resolution :premises (@p325 @p319) :args (@t227 @t232 @t236))
% 0.36/0.62  (step @p327 :rule bool-double-not-elim :args (@t225))
% 0.36/0.62  (step @p328 :rule nary_cong :premises (@p321 @p327) :args ((or @t229 (not @t226))))
% 0.36/0.62  (step @p329 :rule cnf_or_neg :args (@t229 1))
% 0.36/0.62  (step @p330 :rule eq_resolve :premises (@p329 @p328))
% 0.36/0.62  (step @p331 :rule reordering :premises (@p330) :args ((or @t225 @t229)))
% 0.36/0.62  (step @p332 :rule chain_m_resolution :premises (@p331 @p319) :args (@t225 @t232 @t236))
% 0.36/0.62  (step @p333 :rule cnf_or_pos :args (@t237))
% 0.36/0.62  (step @p334 :rule reordering :premises (@p333) :args ((or @t228 @t226 (not @t237))))
% 0.36/0.62  (step @p335 false :rule chain_m_resolution :premises (@p334 @p332 @p326 @p300) :args (false @t235 (@list @t225 @t227 @t237)))
% 0.36/0.62  )
% 0.36/0.62  % SZS output end Proof
% 0.36/0.62  % cvc5 exiting
%------------------------------------------------------------------------------