%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : GEG013^1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n019.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 08:15:59 AM UTC 2026 % Result : Theorem 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : GEG013^1 : TPTP v9.2.1. Released v4.1.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n019.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Mon Jun 1 23:03:34 EDT 2026 % 0.16/0.35 % CPUTime : % 0.28/0.51 %----Proving TH0 % 0.44/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort tptp.reg 0) % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-sort tptp.mu 0) % 0.44/0.63 (declare-const tptp.c (-> tptp.reg tptp.reg Bool)) % 0.44/0.63 (declare-const tptp.france tptp.reg) % 0.44/0.63 (declare-const tptp.catalunya tptp.reg) % 0.44/0.63 (declare-const tptp.a (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.spain tptp.reg) % 0.44/0.63 (declare-const tptp.fool (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.paris tptp.reg) % 0.44/0.63 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.44/0.63 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.44/0.63 (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)))))) % 0.44/0.63 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.44/0.63 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.44/0.63 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.44/0.63 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.44/0.63 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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))))))) % 0.44/0.63 (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)))))) % 0.44/0.63 (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)))))) % 0.44/0.63 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.44/0.63 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.44/0.63 (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)))))) % 0.44/0.63 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.44/0.63 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.63 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.44/0.63 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.44/0.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.44/0.63 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.44/0.63 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.44/0.63 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.44/0.63 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.44/0.63 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.44/0.63 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.44/0.63 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.44/0.63 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.44/0.63 (define tptp.dc () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "X" tptp.reg))) (lambda (@list _let_2 _let_1) (not (_ (_ tptp.c _let_2) _let_1)))))) % 0.44/0.63 (define tptp.p () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.c _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (forall (@list _let_2) (=> (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 0.44/0.63 (define tptp.eq () (let ((_let_1 (@var "X" tptp.reg))) (let ((_let_2 (@var "Y" tptp.reg))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.p _let_1) _let_2) (_ (_ tptp.p _let_2) _let_1)))))) % 0.44/0.63 (define tptp.o () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.p _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (exists (@list _let_2) (and (_ _let_3 _let_4) (_ _let_3 _let_1))))))))) % 0.44/0.63 (define tptp.po () (let ((_let_1 (@var "X" tptp.reg))) (let ((_let_2 (@var "Y" tptp.reg))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.o _let_1) _let_2) (not (_ (_ tptp.p _let_1) _let_2)) (not (_ (_ tptp.p _let_2) _let_1))))))) % 0.44/0.63 (define tptp.ec () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "X" tptp.reg))) (lambda (@list _let_2 _let_1) (and (_ (_ tptp.c _let_2) _let_1) (not (_ (_ tptp.o _let_2) _let_1))))))) % 0.44/0.63 (define tptp.pp () (let ((_let_1 (@var "X" tptp.reg))) (let ((_let_2 (@var "Y" tptp.reg))) (lambda (@list _let_1 _let_2) (and (_ (_ tptp.p _let_1) _let_2) (not (_ (_ tptp.p _let_2) _let_1))))))) % 0.44/0.63 (define tptp.tpp () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.ec _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (and (_ (_ tptp.pp _let_4) _let_1) (exists (@list _let_2) (and (_ _let_3 _let_4) (_ _let_3 _let_1)))))))))) % 0.44/0.63 (define tptp.ntpp () (let ((_let_1 (@var "Y" tptp.reg))) (let ((_let_2 (@var "Z" tptp.reg))) (let ((_let_3 (_ tptp.ec _let_2))) (let ((_let_4 (@var "X" tptp.reg))) (lambda (@list _let_4 _let_1) (and (_ (_ tptp.pp _let_4) _let_1) (not (exists (@list _let_2) (and (_ _let_3 _let_4) (_ _let_3 _let_1))))))))))) % 0.44/0.63 (define @t1 () (@var "X" tptp.reg)) % 0.44/0.63 (define @t2 () (_ tptp.c @t1)) % 0.44/0.63 (define @t3 () (@var "Y" tptp.reg)) % 0.44/0.63 (define @t4 () (_ @t2 @t3)) % 0.44/0.63 (define @t5 () (@list @t1 @t3)) % 0.44/0.63 (define @t6 () (@var "__flatten_var_0" $$unsorted)) % 0.44/0.63 (define @t7 () (@var "A" (-> $$unsorted Bool))) % 0.44/0.63 (define @t8 () (_ tptp.mbox tptp.fool)) % 0.44/0.63 (define @t9 () (_ @t8 @t7)) % 0.44/0.63 (define @t10 () (_ tptp.mimplies @t9)) % 0.44/0.63 (define @t11 () (@list @t7 @t6)) % 0.44/0.63 (define @t12 () (@var "Phi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t13 () (_ tptp.mbox tptp.a)) % 0.44/0.63 (define @t14 () (@list (@var "X" $$unsorted))) % 0.44/0.63 (define @t15 () (lambda @t14 (_ (_ tptp.tpp tptp.catalunya) tptp.spain))) % 0.44/0.63 (define @t16 () (@var "Z" tptp.reg)) % 0.44/0.63 (define @t17 () (not (_ (_ tptp.eq @t16) @t3))) % 0.44/0.63 (define @t18 () (@list @t16 @t3)) % 0.44/0.63 (define @t19 () (exists @t18 @t17)) % 0.44/0.63 (define @t20 () (lambda @t14 @t19)) % 0.44/0.63 (define @t21 () (not (_ tptp.mvalid (_ @t13 @t20)))) % 0.44/0.63 (define @t22 () (@var "Y" tptp.mu)) % 0.44/0.63 (define @t23 () (@var "X" tptp.mu)) % 0.44/0.63 (define @t24 () (@var "W" $$unsorted)) % 0.44/0.63 (define @t25 () (lambda (@list @t23 @t22 @t24) (= @t23 @t22))) % 0.44/0.63 (define @t26 () (@var "Y" (-> $$unsorted Bool))) % 0.44/0.63 (define @t27 () (@var "X" (-> $$unsorted Bool))) % 0.44/0.63 (define @t28 () (lambda (@list @t27 @t26 @t24) (= (_ @t27 @t24) (_ @t26 @t24)))) % 0.44/0.63 (define @t29 () (_ @t12 @t24)) % 0.44/0.63 (define @t30 () (not @t29)) % 0.44/0.63 (define @t31 () (@list @t12 @t24)) % 0.44/0.63 (define @t32 () (lambda @t31 @t30)) % 0.44/0.63 (define @t33 () (@var "Psi" (-> $$unsorted Bool))) % 0.44/0.63 (define @t34 () (lambda (@list @t12 @t33 @t24) (or @t29 (_ @t33 @t24)))) % 0.44/0.63 (define @t35 () (_ tptp.mnot @t33)) % 0.44/0.63 (define @t36 () (_ tptp.mnot @t12)) % 0.44/0.63 (define @t37 () (_ tptp.mor @t36)) % 0.44/0.63 (define @t38 () (@list @t12 @t33 @t6)) % 0.44/0.63 (define @t39 () (lambda @t38 (_ (_ tptp.mnot (_ @t37 @t35)) @t6))) % 0.44/0.63 (define @t40 () (lambda @t38 (_ (_ @t37 @t33) @t6))) % 0.44/0.63 (define @t41 () (lambda @t38 (_ (_ (_ tptp.mor @t35) @t12) @t6))) % 0.44/0.63 (define @t42 () (lambda @t38 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t12) @t33)) (_ (_ tptp.mimplies @t33) @t12)) @t6))) % 0.44/0.63 (define @t43 () (lambda @t38 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t12) @t33)) @t6))) % 0.44/0.63 (define @t44 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.44/0.63 (define @t45 () (_ @t44 @t23)) % 0.44/0.63 (define @t46 () (lambda (@list @t44 @t24) (forall (@list @t23) (_ @t45 @t24)))) % 0.44/0.63 (define @t47 () (@var "P" (-> $$unsorted Bool))) % 0.44/0.63 (define @t48 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.44/0.63 (define @t49 () (_ @t48 @t47)) % 0.44/0.63 (define @t50 () (lambda (@list @t48 @t24) (forall (@list @t47) (_ @t49 @t24)))) % 0.44/0.63 (define @t51 () (lambda (@list @t44 @t6) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t23 @t6) (_ (_ tptp.mnot @t45) @t6)))) @t6))) % 0.44/0.63 (define @t52 () (lambda (@list @t48 @t6) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t47 @t6) (_ (_ tptp.mnot @t49) @t6)))) @t6))) % 0.44/0.63 (define @t53 () (@list @t24)) % 0.44/0.63 (define @t54 () (lambda @t53 true)) % 0.44/0.63 (define @t55 () (@var "V" $$unsorted)) % 0.44/0.63 (define @t56 () (_ @t12 @t55)) % 0.44/0.63 (define @t57 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.44/0.63 (define @t58 () (_ (_ @t57 @t24) @t55)) % 0.44/0.63 (define @t59 () (not @t58)) % 0.44/0.63 (define @t60 () (or @t59 @t56)) % 0.44/0.63 (define @t61 () (@list @t55)) % 0.44/0.63 (define @t62 () (forall @t61 @t60)) % 0.44/0.63 (define @t63 () (@list @t57 @t12 @t24)) % 0.44/0.63 (define @t64 () (lambda @t63 @t62)) % 0.44/0.63 (define @t65 () (lambda (@list @t57 @t12 @t6) (_ (_ tptp.mnot (_ (_ tptp.mbox @t57) @t36)) @t6))) % 0.44/0.63 (define @t66 () (@var "S" $$unsorted)) % 0.44/0.63 (define @t67 () (_ @t57 @t66)) % 0.44/0.63 (define @t68 () (@list @t66)) % 0.44/0.63 (define @t69 () (@list @t57)) % 0.44/0.63 (define @t70 () (lambda @t69 (forall @t68 (_ @t67 @t66)))) % 0.44/0.63 (define @t71 () (@var "T" $$unsorted)) % 0.44/0.63 (define @t72 () (_ @t57 @t71)) % 0.44/0.63 (define @t73 () (_ @t67 @t71)) % 0.44/0.63 (define @t74 () (lambda @t69 (forall (@list @t66 @t71) (=> @t73 (_ @t72 @t66))))) % 0.44/0.63 (define @t75 () (@list @t71)) % 0.44/0.63 (define @t76 () (lambda @t69 (forall @t68 (exists @t75 @t73)))) % 0.44/0.63 (define @t77 () (@var "U" $$unsorted)) % 0.44/0.63 (define @t78 () (_ @t67 @t77)) % 0.44/0.63 (define @t79 () (_ @t72 @t77)) % 0.44/0.63 (define @t80 () (@list @t66 @t71 @t77)) % 0.44/0.63 (define @t81 () (lambda @t69 (forall @t80 (=> (and @t73 @t79) @t78)))) % 0.44/0.63 (define @t82 () (and @t73 @t78)) % 0.44/0.63 (define @t83 () (lambda @t69 (forall @t80 (=> @t82 @t79)))) % 0.44/0.63 (define @t84 () (= @t71 @t77)) % 0.44/0.63 (define @t85 () (lambda @t69 (forall @t80 (=> @t82 @t84)))) % 0.44/0.63 (define @t86 () (@list @t77)) % 0.44/0.63 (define @t87 () (lambda @t69 (forall @t68 (exists @t75 (and @t73 (forall @t86 (=> @t78 @t84))))))) % 0.44/0.63 (define @t88 () (_ @t57 @t77)) % 0.44/0.63 (define @t89 () (_ @t88 @t71)) % 0.44/0.63 (define @t90 () (lambda @t69 (forall @t80 (=> @t73 (exists @t86 (and @t78 @t89)))))) % 0.44/0.63 (define @t91 () (lambda @t69 (forall @t80 (=> @t82 (or @t79 @t84 @t89))))) % 0.44/0.63 (define @t92 () (lambda @t69 (forall @t80 (=> @t82 (exists @t61 (and (_ @t72 @t55) (_ @t88 @t55))))))) % 0.44/0.63 (define @t93 () (forall @t53 @t29)) % 0.44/0.63 (define @t94 () (@list @t12)) % 0.44/0.63 (define @t95 () (lambda @t94 @t93)) % 0.44/0.63 (define @t96 () (lambda @t94 (forall @t53 @t30))) % 0.44/0.63 (define @t97 () (lambda @t94 (exists @t53 @t29))) % 0.44/0.63 (define @t98 () (lambda @t94 (exists @t53 @t30))) % 0.44/0.63 (define @t99 () (lambda @t5 (not @t4))) % 0.44/0.63 (define @t100 () (_ tptp.c @t16)) % 0.44/0.63 (define @t101 () (_ @t100 @t3)) % 0.44/0.63 (define @t102 () (_ @t100 @t1)) % 0.44/0.63 (define @t103 () (@list @t16)) % 0.44/0.63 (define @t104 () (forall @t103 (=> @t102 @t101))) % 0.44/0.63 (define @t105 () (lambda @t5 @t104)) % 0.44/0.63 (define @t106 () (_ (_ tptp.p @t3) @t1)) % 0.44/0.63 (define @t107 () (_ (_ tptp.p @t1) @t3)) % 0.44/0.63 (define @t108 () (and @t107 @t106)) % 0.44/0.63 (define @t109 () (lambda @t5 @t108)) % 0.44/0.63 (define @t110 () (_ tptp.p @t16)) % 0.44/0.63 (define @t111 () (and (_ @t110 @t1) (_ @t110 @t3))) % 0.44/0.63 (define @t112 () (exists @t103 @t111)) % 0.44/0.63 (define @t113 () (lambda @t5 @t112)) % 0.44/0.63 (define @t114 () (not @t106)) % 0.44/0.63 (define @t115 () (_ (_ tptp.o @t1) @t3)) % 0.44/0.63 (define @t116 () (lambda @t5 (and @t115 (not @t107) @t114))) % 0.44/0.63 (define @t117 () (not @t115)) % 0.44/0.63 (define @t118 () (and @t4 @t117)) % 0.44/0.63 (define @t119 () (lambda @t5 @t118)) % 0.44/0.63 (define @t120 () (and @t107 @t114)) % 0.44/0.63 (define @t121 () (lambda @t5 @t120)) % 0.44/0.63 (define @t122 () (_ tptp.ec @t16)) % 0.44/0.63 (define @t123 () (and (_ @t122 @t1) (_ @t122 @t3))) % 0.44/0.63 (define @t124 () (exists @t103 @t123)) % 0.44/0.63 (define @t125 () (_ (_ tptp.pp @t1) @t3)) % 0.44/0.63 (define @t126 () (and @t125 @t124)) % 0.44/0.63 (define @t127 () (lambda @t5 @t126)) % 0.44/0.63 (define @t128 () (lambda @t5 (and @t125 (not @t124)))) % 0.44/0.63 (define @t129 () (not (tptp.a @t24 @t55))) % 0.44/0.63 (define @t130 () (forall (@list @t24 @t55) @t129)) % 0.44/0.63 (define @t131 () (forall @t61 @t129)) % 0.44/0.63 (define @t132 () (forall @t53 @t131)) % 0.44/0.63 (define @t133 () (@var "BOUND_VARIABLE_9141" tptp.reg)) % 0.44/0.63 (define @t134 () (@var "BOUND_VARIABLE_9094" tptp.reg)) % 0.44/0.63 (define @t135 () (@var "BOUND_VARIABLE_9143" tptp.reg)) % 0.44/0.63 (define @t136 () (or (not (tptp.c @t134 @t135)) (tptp.c @t134 @t133))) % 0.44/0.63 (define @t137 () (forall (@list @t133 @t135 @t134) @t136)) % 0.44/0.63 (define @t138 () (not @t137)) % 0.44/0.63 (define @t139 () (@var "BOUND_VARIABLE_9132" tptp.reg)) % 0.44/0.63 (define @t140 () (@var "BOUND_VARIABLE_9102" tptp.reg)) % 0.44/0.63 (define @t141 () (@var "BOUND_VARIABLE_9130" tptp.reg)) % 0.44/0.63 (define @t142 () (or (not (tptp.c @t140 @t141)) (tptp.c @t140 @t139))) % 0.44/0.63 (define @t143 () (forall (@list @t141 @t139 @t140) @t142)) % 0.44/0.63 (define @t144 () (not @t143)) % 0.44/0.63 (define @t145 () (or @t144 @t138 @t132)) % 0.44/0.63 (define @t146 () (or @t144 @t138 @t131)) % 0.44/0.63 (define @t147 () (lambda @t53 @t146)) % 0.44/0.63 (define @t148 () (_ @t147 @t24)) % 0.44/0.63 (define @t149 () (forall @t53 @t148)) % 0.44/0.63 (define @t150 () (_ @t12 @t24)) % 0.44/0.63 (define @t151 () (lambda @t94 (forall @t53 @t150))) % 0.44/0.63 (define @t152 () (or @t144 @t138 @t129)) % 0.44/0.63 (define @t153 () (or @t129 @t144 @t138)) % 0.44/0.63 (define @t154 () (not (and @t143 @t137))) % 0.44/0.63 (define @t155 () (or @t129 @t154)) % 0.44/0.63 (define @t156 () (lambda @t14 @t154)) % 0.44/0.63 (define @t157 () (_ @t156 @t55)) % 0.44/0.63 (define @t158 () (or @t129 @t157)) % 0.44/0.63 (define @t159 () (forall @t61 @t158)) % 0.44/0.63 (define @t160 () (lambda @t53 @t159)) % 0.44/0.63 (define @t161 () (_ @t12 @t55)) % 0.44/0.63 (define @t162 () (lambda @t31 (forall @t61 (or @t129 @t161)))) % 0.44/0.63 (define @t163 () (@list @t134)) % 0.44/0.63 (define @t164 () (forall (@list @t133 @t135) (forall @t163 @t136))) % 0.44/0.63 (define @t165 () (@list @t140)) % 0.44/0.63 (define @t166 () (forall (@list @t141 @t139) (forall @t165 @t142))) % 0.44/0.63 (define @t167 () (not (tptp.c @t134 @t3))) % 0.44/0.63 (define @t168 () (forall @t163 (or @t167 (tptp.c @t134 @t16)))) % 0.44/0.63 (define @t169 () (forall @t18 @t168)) % 0.44/0.63 (define @t170 () (@list @t16 @t3)) % 0.44/0.63 (define @t171 () (tptp.c @t140 @t3)) % 0.44/0.63 (define @t172 () (forall @t165 (or (not (tptp.c @t140 @t16)) @t171))) % 0.44/0.63 (define @t173 () (forall @t18 @t172)) % 0.44/0.63 (define @t174 () (and @t173 @t169)) % 0.44/0.63 (define @t175 () (and @t172 @t168)) % 0.44/0.63 (define @t176 () (not @t175)) % 0.44/0.63 (define @t177 () (forall @t18 (not @t176))) % 0.44/0.63 (define @t178 () (not @t177)) % 0.44/0.63 (define @t179 () (@list @t3)) % 0.44/0.63 (define @t180 () (lambda @t179 @t175)) % 0.44/0.63 (define @t181 () (tptp.c @t16 @t1)) % 0.44/0.63 (define @t182 () (tptp.c @t16 @t3)) % 0.44/0.63 (define @t183 () (not @t182)) % 0.44/0.63 (define @t184 () (forall @t103 (or @t183 @t181))) % 0.44/0.63 (define @t185 () (@list @t16)) % 0.44/0.63 (define @t186 () (not @t181)) % 0.44/0.63 (define @t187 () (forall @t103 (or @t186 @t182))) % 0.44/0.63 (define @t188 () (and @t187 @t184)) % 0.44/0.63 (define @t189 () (lambda @t5 @t188)) % 0.44/0.63 (define @t190 () (not (_ (_ @t189 @t16) @t3))) % 0.44/0.63 (define @t191 () (exists @t18 @t190)) % 0.44/0.63 (define @t192 () (lambda @t14 @t191)) % 0.44/0.63 (define @t193 () (_ @t57 @t24 @t55)) % 0.44/0.63 (define @t194 () (_ (lambda @t63 (forall @t61 (or (not @t193) @t161))) tptp.a)) % 0.44/0.63 (define @t195 () (@var "BOUND_VARIABLE_8289" tptp.reg)) % 0.44/0.63 (define @t196 () (tptp.c @t16 @t195)) % 0.44/0.63 (define @t197 () (lambda (@list @t195) (forall @t103 (or @t183 @t196)))) % 0.44/0.63 (define @t198 () (lambda @t5 @t187)) % 0.44/0.63 (define @t199 () (lambda @t179 @t187)) % 0.44/0.63 (define @t200 () (_ @t198 @t1)) % 0.44/0.63 (define @t201 () (_ (_ @t198 @t3) @t1)) % 0.44/0.63 (define @t202 () (_ @t200 @t3)) % 0.44/0.63 (define @t203 () (not @t102)) % 0.44/0.63 (define @t204 () (or @t203 @t101)) % 0.44/0.63 (define @t205 () (tptp.c @t16 tptp.catalunya)) % 0.44/0.63 (define @t206 () (tptp.c @t16 tptp.spain)) % 0.44/0.63 (define @t207 () (not @t206)) % 0.44/0.63 (define @t208 () (forall @t103 (or @t207 @t205))) % 0.44/0.63 (define @t209 () (not @t208)) % 0.44/0.63 (define @t210 () (not @t205)) % 0.44/0.63 (define @t211 () (@var "BOUND_VARIABLE_8327" tptp.reg)) % 0.44/0.63 (define @t212 () (@var "BOUND_VARIABLE_8440" tptp.reg)) % 0.44/0.63 (define @t213 () (not (tptp.c @t211 @t212))) % 0.44/0.63 (define @t214 () (@list @t211)) % 0.44/0.63 (define @t215 () (tptp.c @t211 @t16)) % 0.44/0.63 (define @t216 () (not (forall @t214 (or @t213 @t215)))) % 0.44/0.63 (define @t217 () (@list @t212)) % 0.44/0.63 (define @t218 () (not (forall @t217 (or @t216 (not (forall @t214 (or @t213 (tptp.c @t211 tptp.catalunya)))))))) % 0.44/0.63 (define @t219 () (and (not (forall @t103 (or @t210 @t218 @t207 (not (forall @t217 (or @t216 (not (forall @t214 (or @t213 (tptp.c @t211 tptp.spain)))))))))) (forall @t103 (or @t210 @t206)) @t209)) % 0.44/0.63 (define @t220 () (or @t219 @t132)) % 0.44/0.63 (define @t221 () (or @t219 @t131)) % 0.44/0.63 (define @t222 () (lambda @t53 @t221)) % 0.44/0.63 (define @t223 () (_ @t222 @t24)) % 0.44/0.63 (define @t224 () (forall @t53 @t223)) % 0.44/0.63 (define @t225 () (or @t219 @t129)) % 0.44/0.63 (define @t226 () (or @t129 @t219)) % 0.44/0.63 (define @t227 () (lambda @t14 @t219)) % 0.44/0.63 (define @t228 () (_ @t227 @t55)) % 0.44/0.63 (define @t229 () (or @t129 @t228)) % 0.44/0.63 (define @t230 () (forall @t61 @t229)) % 0.44/0.63 (define @t231 () (lambda @t53 @t230)) % 0.44/0.63 (define @t232 () (tptp.c @t211 @t3)) % 0.44/0.63 (define @t233 () (not (forall @t214 (or @t213 @t232)))) % 0.44/0.63 (define @t234 () (forall @t217 (or @t216 @t233))) % 0.44/0.63 (define @t235 () (not @t234)) % 0.44/0.63 (define @t236 () (lambda @t179 (and (not (forall @t103 (or @t210 @t218 @t183 @t235))) (forall @t103 (or @t210 @t182)) (not (forall @t103 (or @t183 @t205)))))) % 0.44/0.63 (define @t237 () (not @t184)) % 0.44/0.63 (define @t238 () (tptp.c @t211 @t1)) % 0.44/0.63 (define @t239 () (not (forall @t214 (or @t213 @t238)))) % 0.44/0.63 (define @t240 () (forall @t217 (or @t216 @t239))) % 0.44/0.63 (define @t241 () (not @t240)) % 0.44/0.63 (define @t242 () (not (forall @t103 (or @t186 @t241 @t183 @t235)))) % 0.44/0.63 (define @t243 () (and @t242 @t187 @t237)) % 0.44/0.63 (define @t244 () (_ (lambda @t5 @t243) tptp.catalunya)) % 0.44/0.63 (define @t245 () (and @t187 @t237)) % 0.44/0.63 (define @t246 () (not @t101)) % 0.44/0.63 (define @t247 () (or @t203 @t241 @t246 @t235)) % 0.44/0.63 (define @t248 () (and @t101 @t234)) % 0.44/0.63 (define @t249 () (and @t102 @t240 @t101 @t234)) % 0.44/0.63 (define @t250 () (forall @t103 (not @t249))) % 0.44/0.63 (define @t251 () (not @t250)) % 0.44/0.63 (define @t252 () (and @t102 @t240)) % 0.44/0.63 (define @t253 () (lambda @t179 @t248)) % 0.44/0.63 (define @t254 () (not @t215)) % 0.44/0.63 (define @t255 () (forall @t214 (or @t254 @t232))) % 0.44/0.63 (define @t256 () (forall @t214 (or @t254 @t238))) % 0.44/0.63 (define @t257 () (forall @t103 (or (not @t256) (not @t255)))) % 0.44/0.63 (define @t258 () (and @t4 @t257)) % 0.44/0.63 (define @t259 () (lambda @t5 @t258)) % 0.44/0.63 (define @t260 () (_ @t259 @t16)) % 0.44/0.63 (define @t261 () (and (_ @t260 @t1) (_ @t260 @t3))) % 0.44/0.63 (define @t262 () (exists @t103 @t261)) % 0.44/0.63 (define @t263 () (lambda @t179 @t245)) % 0.44/0.63 (define @t264 () (_ (lambda @t5 @t245) @t1)) % 0.44/0.63 (define @t265 () (not @t257)) % 0.44/0.63 (define @t266 () (lambda @t179 @t265)) % 0.44/0.63 (define @t267 () (_ (lambda @t5 @t265) @t1)) % 0.44/0.63 (define @t268 () (not (_ @t267 @t3))) % 0.44/0.63 (define @t269 () (and @t256 @t255)) % 0.44/0.63 (define @t270 () (forall @t103 (not @t269))) % 0.44/0.63 (define @t271 () (not @t270)) % 0.44/0.63 (define @t272 () (lambda @t179 @t255)) % 0.44/0.63 (define @t273 () (_ @t198 @t16)) % 0.44/0.63 (define @t274 () (and (_ @t273 @t1) (_ @t273 @t3))) % 0.44/0.63 (define @t275 () (not @t201)) % 0.44/0.63 (define @t276 () (@quantifiers_skolemize @t208 0)) % 0.44/0.63 (define @t277 () (or (not (tptp.c @t276 tptp.spain)) (tptp.c @t276 tptp.catalunya))) % 0.44/0.63 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.44/0.63 (assume @p2 (forall (@list @t1) (_ @t2 @t1))) % 0.44/0.63 (assume @p3 (forall @t5 (=> @t4 (_ (_ tptp.c @t3) @t1)))) % 0.44/0.63 (assume @p4 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t11 (_ (_ @t10 @t7) @t6))))) % 0.44/0.63 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_prop (lambda @t11 (_ (_ @t10 (_ @t8 @t9)) @t6))))) % 0.44/0.63 (assume @p6 (_ tptp.mvalid (_ tptp.mforall_prop (lambda (@list @t12 @t6) (_ (_ (_ tptp.mimplies (_ @t8 @t12)) (_ @t13 @t12)) @t6))))) % 0.44/0.63 (assume @p7 (_ tptp.mvalid (_ @t13 @t15))) % 0.44/0.63 (assume @p8 (_ tptp.mvalid (_ @t8 (lambda @t14 (_ (_ tptp.ec tptp.spain) tptp.france))))) % 0.44/0.63 (assume @p9 (_ tptp.mvalid (_ @t13 (lambda @t14 (_ (_ tptp.ntpp tptp.paris) tptp.france))))) % 0.44/0.63 (assume @p10 @t21) % 0.44/0.63 (assume @p11 true) % 0.44/0.63 (step @p12 (= tptp.meq_ind @t25) :rule refl :args (@t25)) % 0.44/0.63 (step @p13 (= tptp.meq_prop @t28) :rule refl :args (@t28)) % 0.44/0.63 (step @p14 (= tptp.mnot @t32) :rule refl :args (@t32)) % 0.44/0.63 (step @p15 (= tptp.mor @t34) :rule refl :args (@t34)) % 0.44/0.63 (step @p16 (= tptp.mand @t39) :rule refl :args (@t39)) % 0.44/0.63 (step @p17 (= tptp.mimplies @t40) :rule refl :args (@t40)) % 0.44/0.63 (step @p18 (= tptp.mimplied @t41) :rule refl :args (@t41)) % 0.44/0.63 (step @p19 (= tptp.mequiv @t42) :rule refl :args (@t42)) % 0.44/0.63 (step @p20 (= tptp.mxor @t43) :rule refl :args (@t43)) % 0.44/0.63 (step @p21 (= tptp.mforall_ind @t46) :rule refl :args (@t46)) % 0.44/0.63 (step @p22 (= tptp.mforall_prop @t50) :rule refl :args (@t50)) % 0.44/0.63 (step @p23 (= tptp.mexists_ind @t51) :rule refl :args (@t51)) % 0.44/0.63 (step @p24 (= tptp.mexists_prop @t52) :rule refl :args (@t52)) % 0.44/0.63 (step @p25 (= tptp.mtrue @t54) :rule refl :args (@t54)) % 0.44/0.63 (step @p26 (= tptp.mbox @t64) :rule refl :args (@t64)) % 0.44/0.63 (step @p27 (= tptp.mdia @t65) :rule refl :args (@t65)) % 0.44/0.63 (step @p28 (= tptp.mreflexive @t70) :rule refl :args (@t70)) % 0.44/0.63 (step @p29 (= tptp.msymmetric @t74) :rule refl :args (@t74)) % 0.44/0.63 (step @p30 (= tptp.mserial @t76) :rule refl :args (@t76)) % 0.44/0.63 (step @p31 (= tptp.mtransitive @t81) :rule refl :args (@t81)) % 0.44/0.63 (step @p32 (= tptp.meuclidean @t83) :rule refl :args (@t83)) % 0.44/0.63 (step @p33 (= tptp.mpartially_functional @t85) :rule refl :args (@t85)) % 0.44/0.63 (step @p34 (= tptp.mfunctional @t87) :rule refl :args (@t87)) % 0.44/0.63 (step @p35 (= tptp.mweakly_dense @t90) :rule refl :args (@t90)) % 0.44/0.63 (step @p36 (= tptp.mweakly_connected @t91) :rule refl :args (@t91)) % 0.44/0.63 (step @p37 (= tptp.mweakly_directed @t92) :rule refl :args (@t92)) % 0.44/0.63 (step @p38 (= tptp.mvalid @t95) :rule refl :args (@t95)) % 0.44/0.63 (step @p39 (= tptp.minvalid @t96) :rule refl :args (@t96)) % 0.44/0.63 (step @p40 (= tptp.msatisfiable @t97) :rule refl :args (@t97)) % 0.44/0.63 (step @p41 (= tptp.mcountersatisfiable @t98) :rule refl :args (@t98)) % 0.44/0.63 (step @p42 (= tptp.dc @t99) :rule refl :args (@t99)) % 0.44/0.63 (step @p43 (= tptp.p @t105) :rule refl :args (@t105)) % 0.44/0.63 (step @p44 (= tptp.eq @t109) :rule refl :args (@t109)) % 0.44/0.63 (step @p45 (= tptp.o @t113) :rule refl :args (@t113)) % 0.44/0.63 (step @p46 (= tptp.po @t116) :rule refl :args (@t116)) % 0.44/0.63 (step @p47 (= tptp.ec @t119) :rule refl :args (@t119)) % 0.44/0.63 (step @p48 (= tptp.pp @t121) :rule refl :args (@t121)) % 0.44/0.63 (step @p49 (= 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@t263))) % 0.44/0.63 (step @p270 :rule ho_cong :premises (@p269 @p97)) % 0.44/0.63 (step @p271 :rule trans :premises (@p270 @p268)) % 0.44/0.63 (step @p272 :rule nary_cong :premises (@p271 @p267) :args ((and (_ @t264 @t3) @t262))) % 0.44/0.63 (step @p273 :rule trans :premises (@p272 @p229)) % 0.44/0.63 (step @p274 :rule bool-double-not-elim :args (@t257)) % 0.44/0.63 (step @p275 :rule beta-reduce :args ((= (_ @t266 @t3) @t265))) % 0.44/0.63 (step @p276 :rule beta-reduce :args ((= @t267 @t266))) % 0.44/0.63 (step @p277 :rule ho_cong :premises (@p276 @p97)) % 0.44/0.63 (step @p278 :rule trans :premises (@p277 @p275)) % 0.44/0.63 (step @p279 :rule cong :premises (@p278) :args (@t268)) % 0.44/0.63 (step @p280 :rule trans :premises (@p279 @p274)) % 0.44/0.63 (step @p281 :rule refl :args (@t4)) % 0.44/0.63 (step @p282 :rule nary_cong :premises (@p281 @p280) :args ((and @t4 @t268))) % 0.44/0.63 (step @p283 :rule bool-and-de-morgan :args (@t256 @t255 true)) % 0.44/0.63 (step @p284 :rule cong :premises (@p283) :args (@t270)) % 0.44/0.63 (step @p285 :rule cong :premises (@p284) :args (@t271)) % 0.44/0.63 (step @p286 :rule exists-elim :args ((= (exists @t103 @t269) @t271))) % 0.44/0.63 (step @p287 :rule trans :premises (@p286 @p285)) % 0.44/0.63 (step @p288 :rule beta-reduce :args ((= (_ @t272 @t3) @t255))) % 0.44/0.63 (step @p289 :rule beta-reduce :args ((= (_ (lambda @t5 (forall @t214 (or (not @t238) @t232))) @t16) @t272))) % 0.44/0.63 (step @p290 :rule alpha_equiv :args (@t187 @t185 (@list @t211))) % 0.44/0.63 (step @p291 :rule cong :premises (@p290) :args (@t198)) % 0.44/0.63 (step @p292 :rule ho_cong :premises (@p291 @p99)) % 0.44/0.63 (step @p293 :rule trans :premises (@p292 @p289)) % 0.44/0.63 (step @p294 :rule ho_cong :premises (@p293 @p97)) % 0.44/0.63 (step @p295 :rule trans :premises (@p294 @p288)) % 0.44/0.63 (step @p296 :rule beta-reduce :args ((= (_ @t272 @t1) @t256))) % 0.44/0.63 (step @p297 :rule ho_cong :premises (@p293 @p121)) % 0.44/0.63 (step @p298 :rule trans :premises (@p297 @p296)) % 0.44/0.63 (step @p299 :rule nary_cong :premises (@p298 @p295) :args (@t274)) % 0.44/0.63 (step @p300 :rule cong :premises (@p299) :args ((exists @t103 @t274))) % 0.44/0.63 (step @p301 :rule trans :premises (@p300 @p287)) % 0.44/0.63 (step @p302 :rule ho_cong :premises (@p151 @p119)) % 0.44/0.63 (step @p303 :rule ho_cong :premises (@p302 @p97)) % 0.44/0.63 (step @p304 :rule ho_cong :premises (@p302 @p121)) % 0.44/0.63 (step @p305 :rule nary_cong :premises (@p304 @p303) :args (@t111)) % 0.44/0.63 (step @p306 :rule cong :premises (@p305) :args (@t112)) % 0.44/0.63 (step @p307 :rule trans :premises (@p306 @p301)) % 0.44/0.63 (step @p308 :rule cong :premises (@p307) :args (@t113)) % 0.44/0.63 (step @p309 :rule trans :premises (@p45 @p308)) % 0.44/0.63 (step @p310 :rule ho_cong :premises (@p309 @p121)) % 0.44/0.63 (step @p311 :rule ho_cong :premises (@p310 @p97)) % 0.44/0.63 (step @p312 :rule cong :premises (@p311) :args (@t117)) % 0.44/0.63 (step @p313 :rule nary_cong :premises (@p281 @p312) :args (@t118)) % 0.44/0.63 (step @p314 :rule trans :premises (@p313 @p282)) % 0.44/0.63 (step @p315 :rule cong :premises (@p314) :args (@t119)) % 0.44/0.63 (step @p316 :rule trans :premises (@p47 @p315)) % 0.44/0.63 (step @p317 :rule ho_cong :premises (@p316 @p119)) % 0.44/0.63 (step @p318 :rule ho_cong :premises (@p317 @p97)) % 0.44/0.63 (step @p319 :rule ho_cong :premises (@p317 @p121)) % 0.44/0.63 (step @p320 :rule nary_cong :premises (@p319 @p318) :args (@t123)) % 0.44/0.63 (step @p321 :rule cong :premises (@p320) :args (@t124)) % 0.44/0.63 (step @p322 :rule cong :premises (@p128) :args (@t275)) % 0.44/0.63 (step @p323 :rule nary_cong :premises (@p132 @p322) :args ((and @t202 @t275))) % 0.44/0.63 (step @p324 :rule cong :premises (@p153) :args (@t114)) % 0.44/0.63 (step @p325 :rule nary_cong :premises (@p155 @p324) :args (@t120)) % 0.44/0.63 (step @p326 :rule trans :premises (@p325 @p323)) % 0.44/0.63 (step @p327 :rule cong :premises (@p326) :args (@t121)) % 0.44/0.63 (step @p328 :rule trans :premises (@p48 @p327)) % 0.44/0.63 (step @p329 :rule ho_cong :premises (@p328 @p121)) % 0.44/0.63 (step @p330 :rule ho_cong :premises (@p329 @p97)) % 0.44/0.63 (step @p331 :rule nary_cong :premises (@p330 @p321) :args (@t126)) % 0.44/0.63 (step @p332 :rule trans :premises (@p331 @p273)) % 0.44/0.63 (step @p333 :rule cong :premises (@p332) :args (@t127)) % 0.44/0.63 (step @p334 :rule trans :premises (@p49 @p333)) % 0.44/0.63 (step @p335 :rule ho_cong :premises (@p334 @p228)) % 0.44/0.63 (step @p336 :rule ho_cong :premises (@p335 @p219)) % 0.44/0.63 (step @p337 :rule cong :premises (@p336) :args (@t15)) % 0.44/0.63 (step @p338 :rule ho_cong :premises (@p181 @p337)) % 0.44/0.63 (step @p339 :rule ho_cong :premises (@p190 @p338)) % 0.44/0.63 (step @p340 :rule trans :premises (@p339 @p227)) % 0.44/0.63 (step @p341 :rule eq_resolve :premises (@p7 @p340)) % 0.44/0.63 (step @p342 :rule chain_m_resolution :premises (@p341 @p197) :args (@t219 (@list true) (@list @t130))) % 0.44/0.63 (step @p343 :rule cnf_and_pos :args (@t219 2)) % 0.44/0.63 (step @p344 :rule reordering :premises (@p343) :args ((or @t209 (not @t219)))) % 0.44/0.63 (step @p345 :rule chain_m_resolution :premises (@p344 @p342) :args (@t209 (@list false) (@list @t219))) % 0.44/0.63 (step @p346 :rule skolemize :premises (@p345)) % 0.44/0.63 (assume-push @p353 @t143) % 0.44/0.63 (step @p348 :rule instantiate :premises (@p196) :args ((@list tptp.spain tptp.catalunya @t276))) % 0.44/0.63 (step-pop @p354 :rule scope :premises (@p348)) % 0.44/0.63 (step @p349 :rule process_scope :premises (@p354) :args (@t277)) % 0.44/0.63 (step @p351 :rule implies_elim :premises (@p349)) % 0.44/0.63 (step @p352 false :rule chain_m_resolution :premises (@p351 @p346 @p196) :args (false (@list true false) (@list @t277 @t143))) % 0.44/0.63 ) % 0.44/0.63 % SZS output end Proof % 0.44/0.63 % cvc5 exiting %------------------------------------------------------------------------------