%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SYO434^1 : 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 : n017.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 09:12:39 AM UTC 2026 % Result : Theorem 0.53s 0.79s % Output : Proof 0.53s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SYO434^1 : 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 % 0.16/0.34 % Computer : n017.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 : Wed Jun 3 00:06:16 EDT 2026 % 0.16/0.34 % CPUTime : % 0.29/0.49 %----Proving TH0 % 0.53/0.79 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.53/0.79 % SZS status Theorem % 0.53/0.79 % SZS output start Proof % 0.53/0.79 ( % 0.53/0.79 (declare-sort $$unsorted 0) % 0.53/0.79 (declare-sort tptp.mu 0) % 0.53/0.79 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.53/0.79 (declare-const tptp.p (-> $$unsorted Bool)) % 0.53/0.79 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.53/0.79 (define tptp.meq_ind () (let ((_let_1 (@var "Y" tptp.mu))) (let ((_let_2 (@var "X" tptp.mu))) (lambda (@list _let_2 _let_1 (@var "W" $$unsorted)) (= _let_2 _let_1))))) % 0.53/0.79 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.53/0.79 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.53/0.79 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.53/0.79 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.53/0.79 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.53/0.79 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.53/0.79 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.53/0.79 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.53/0.79 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.53/0.79 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.53/0.79 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.53/0.79 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.53/0.79 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.53/0.79 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.53/0.79 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.53/0.79 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.53/0.79 (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)))))))) % 0.53/0.79 (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)))))))) % 0.53/0.79 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.53/0.79 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.53/0.79 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.53/0.79 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.53/0.79 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.53/0.79 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.53/0.79 (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))))))))))))) % 0.53/0.79 (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)))))) % 0.53/0.79 (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))))))) % 0.53/0.79 (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)))))) % 0.53/0.79 (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))))))) % 0.53/0.79 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.53/0.79 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.53/0.79 (define @t1 () (_ tptp.mbox_s4 tptp.p)) % 0.53/0.79 (define @t2 () (not (_ tptp.mvalid (_ (_ tptp.mimplies @t1) (_ tptp.mbox_s4 (_ tptp.mdia_s4 @t1)))))) % 0.53/0.79 (define @t3 () (@var "Y" tptp.mu)) % 0.53/0.79 (define @t4 () (@var "X" tptp.mu)) % 0.53/0.79 (define @t5 () (@var "W" $$unsorted)) % 0.53/0.79 (define @t6 () (lambda (@list @t4 @t3 @t5) (= @t4 @t3))) % 0.53/0.79 (define @t7 () (@var "Y" (-> $$unsorted Bool))) % 0.53/0.79 (define @t8 () (@var "X" (-> $$unsorted Bool))) % 0.53/0.79 (define @t9 () (lambda (@list @t8 @t7 @t5) (= (_ @t8 @t5) (_ @t7 @t5)))) % 0.53/0.79 (define @t10 () (@var "Phi" (-> $$unsorted Bool))) % 0.53/0.79 (define @t11 () (_ @t10 @t5)) % 0.53/0.79 (define @t12 () (not @t11)) % 0.53/0.79 (define @t13 () (@list @t10 @t5)) % 0.53/0.79 (define @t14 () (lambda @t13 @t12)) % 0.53/0.79 (define @t15 () (@var "Psi" (-> $$unsorted Bool))) % 0.53/0.79 (define @t16 () (_ @t15 @t5)) % 0.53/0.79 (define @t17 () (lambda (@list @t10 @t15 @t5) (or @t11 @t16))) % 0.53/0.79 (define @t18 () (@var "__flatten_var_0" $$unsorted)) % 0.53/0.79 (define @t19 () (_ tptp.mnot @t15)) % 0.53/0.79 (define @t20 () (_ tptp.mnot @t10)) % 0.53/0.79 (define @t21 () (_ tptp.mor @t20)) % 0.53/0.79 (define @t22 () (@list @t10 @t15 @t18)) % 0.53/0.79 (define @t23 () (lambda @t22 (_ (_ tptp.mnot (_ @t21 @t19)) @t18))) % 0.53/0.79 (define @t24 () (lambda @t22 (_ (_ @t21 @t15) @t18))) % 0.53/0.79 (define @t25 () (lambda @t22 (_ (_ (_ tptp.mor @t19) @t10) @t18))) % 0.53/0.79 (define @t26 () (lambda @t22 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t10) @t15)) (_ (_ tptp.mimplies @t15) @t10)) @t18))) % 0.53/0.79 (define @t27 () (lambda @t22 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t10) @t15)) @t18))) % 0.53/0.79 (define @t28 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.53/0.79 (define @t29 () (_ @t28 @t4)) % 0.53/0.79 (define @t30 () (lambda (@list @t28 @t5) (forall (@list @t4) (_ @t29 @t5)))) % 0.53/0.79 (define @t31 () (@var "P" (-> $$unsorted Bool))) % 0.53/0.79 (define @t32 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.53/0.79 (define @t33 () (_ @t32 @t31)) % 0.53/0.79 (define @t34 () (lambda (@list @t32 @t5) (forall (@list @t31) (_ @t33 @t5)))) % 0.53/0.79 (define @t35 () (lambda (@list @t28 @t18) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t4 @t18) (_ (_ tptp.mnot @t29) @t18)))) @t18))) % 0.53/0.79 (define @t36 () (lambda (@list @t32 @t18) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t31 @t18) (_ (_ tptp.mnot @t33) @t18)))) @t18))) % 0.53/0.79 (define @t37 () (@list @t5)) % 0.53/0.79 (define @t38 () (lambda @t37 true)) % 0.53/0.79 (define @t39 () (@var "V" $$unsorted)) % 0.53/0.79 (define @t40 () (_ @t10 @t39)) % 0.53/0.79 (define @t41 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.53/0.79 (define @t42 () (@list @t39)) % 0.53/0.79 (define @t43 () (lambda (@list @t41 @t10 @t5) (forall @t42 (or (not (_ (_ @t41 @t5) @t39)) @t40)))) % 0.53/0.79 (define @t44 () (lambda (@list @t41 @t10 @t18) (_ (_ tptp.mnot (_ (_ tptp.mbox @t41) @t20)) @t18))) % 0.53/0.79 (define @t45 () (@var "S" $$unsorted)) % 0.53/0.79 (define @t46 () (_ @t41 @t45)) % 0.53/0.79 (define @t47 () (_ @t46 @t45)) % 0.53/0.79 (define @t48 () (@list @t45)) % 0.53/0.79 (define @t49 () (forall @t48 @t47)) % 0.53/0.79 (define @t50 () (@list @t41)) % 0.53/0.79 (define @t51 () (lambda @t50 @t49)) % 0.53/0.79 (define @t52 () (@var "T" $$unsorted)) % 0.53/0.79 (define @t53 () (_ @t41 @t52)) % 0.53/0.79 (define @t54 () (_ @t46 @t52)) % 0.53/0.79 (define @t55 () (lambda @t50 (forall (@list @t45 @t52) (=> @t54 (_ @t53 @t45))))) % 0.53/0.79 (define @t56 () (@list @t52)) % 0.53/0.79 (define @t57 () (lambda @t50 (forall @t48 (exists @t56 @t54)))) % 0.53/0.79 (define @t58 () (@var "U" $$unsorted)) % 0.53/0.79 (define @t59 () (_ @t46 @t58)) % 0.53/0.79 (define @t60 () (_ @t53 @t58)) % 0.53/0.79 (define @t61 () (and @t54 @t60)) % 0.53/0.79 (define @t62 () (@list @t45 @t52 @t58)) % 0.53/0.79 (define @t63 () (forall @t62 (=> @t61 @t59))) % 0.53/0.79 (define @t64 () (lambda @t50 @t63)) % 0.53/0.79 (define @t65 () (and @t54 @t59)) % 0.53/0.79 (define @t66 () (lambda @t50 (forall @t62 (=> @t65 @t60)))) % 0.53/0.79 (define @t67 () (= @t52 @t58)) % 0.53/0.79 (define @t68 () (lambda @t50 (forall @t62 (=> @t65 @t67)))) % 0.53/0.79 (define @t69 () (@list @t58)) % 0.53/0.79 (define @t70 () (lambda @t50 (forall @t48 (exists @t56 (and @t54 (forall @t69 (=> @t59 @t67))))))) % 0.53/0.79 (define @t71 () (_ @t41 @t58)) % 0.53/0.79 (define @t72 () (_ @t71 @t52)) % 0.53/0.79 (define @t73 () (lambda @t50 (forall @t62 (=> @t54 (exists @t69 (and @t59 @t72)))))) % 0.53/0.79 (define @t74 () (lambda @t50 (forall @t62 (=> @t65 (or @t60 @t67 @t72))))) % 0.53/0.79 (define @t75 () (lambda @t50 (forall @t62 (=> @t65 (exists @t42 (and (_ @t53 @t39) (_ @t71 @t39))))))) % 0.53/0.79 (define @t76 () (forall @t37 @t11)) % 0.53/0.79 (define @t77 () (@list @t10)) % 0.53/0.79 (define @t78 () (lambda @t77 @t76)) % 0.53/0.79 (define @t79 () (lambda @t77 (forall @t37 @t12))) % 0.53/0.79 (define @t80 () (lambda @t77 (exists @t37 @t11))) % 0.53/0.79 (define @t81 () (lambda @t77 (exists @t37 @t12))) % 0.53/0.79 (define @t82 () (_ (_ tptp.rel_s4 @t5) @t39)) % 0.53/0.79 (define @t83 () (not @t82)) % 0.53/0.79 (define @t84 () (or @t83 @t40)) % 0.53/0.79 (define @t85 () (forall @t42 @t84)) % 0.53/0.79 (define @t86 () (lambda @t13 @t85)) % 0.53/0.79 (define @t87 () (@list @t10 @t18)) % 0.53/0.79 (define @t88 () (lambda @t87 (_ (_ tptp.mnot (_ tptp.mbox_s4 @t20)) @t18))) % 0.53/0.79 (define @t89 () (forall @t62 (or (not (tptp.rel_s4 @t45 @t52)) (not (tptp.rel_s4 @t52 @t58)) (tptp.rel_s4 @t45 @t58)))) % 0.53/0.79 (define @t90 () (_ @t41 @t45 @t58)) % 0.53/0.79 (define @t91 () (_ @t41 @t52 @t58)) % 0.53/0.79 (define @t92 () (_ @t41 @t45 @t52)) % 0.53/0.79 (define @t93 () (not @t60)) % 0.53/0.79 (define @t94 () (not @t54)) % 0.53/0.79 (define @t95 () (or @t94 @t93 @t59)) % 0.53/0.79 (define @t96 () (@var "BOUND_VARIABLE_8434" $$unsorted)) % 0.53/0.79 (define @t97 () (tptp.p @t96)) % 0.53/0.79 (define @t98 () (@var "BOUND_VARIABLE_8458" $$unsorted)) % 0.53/0.79 (define @t99 () (@list @t96)) % 0.53/0.79 (define @t100 () (not (forall @t99 (or (not (tptp.rel_s4 @t98 @t96)) @t97)))) % 0.53/0.79 (define @t101 () (@var "BOUND_VARIABLE_8496" $$unsorted)) % 0.53/0.79 (define @t102 () (@list @t98)) % 0.53/0.79 (define @t103 () (not (forall @t102 (or (not (tptp.rel_s4 @t101 @t98)) @t100)))) % 0.53/0.79 (define @t104 () (not (tptp.rel_s4 @t5 @t101))) % 0.53/0.79 (define @t105 () (tptp.p @t39)) % 0.53/0.79 (define @t106 () (tptp.rel_s4 @t5 @t39)) % 0.53/0.79 (define @t107 () (not @t106)) % 0.53/0.79 (define @t108 () (forall @t42 (or @t107 @t105))) % 0.53/0.79 (define @t109 () (not @t108)) % 0.53/0.79 (define @t110 () (or @t109 @t104 @t103)) % 0.53/0.79 (define @t111 () (or @t104 @t103)) % 0.53/0.79 (define @t112 () (or @t109 @t111)) % 0.53/0.79 (define @t113 () (@list @t5 @t101)) % 0.53/0.79 (define @t114 () (forall @t113 @t112)) % 0.53/0.79 (define @t115 () (@list @t101)) % 0.53/0.79 (define @t116 () (forall @t115 @t112)) % 0.53/0.79 (define @t117 () (forall @t115 @t111)) % 0.53/0.79 (define @t118 () (@list @t39)) % 0.53/0.79 (define @t119 () (or @t109 @t117)) % 0.53/0.79 (define @t120 () (not (forall @t102 (or (not (tptp.rel_s4 @t39 @t98)) @t100)))) % 0.53/0.79 (define @t121 () (forall @t42 (or @t107 @t120))) % 0.53/0.79 (define @t122 () (or @t109 @t121)) % 0.53/0.79 (define @t123 () (not (tptp.rel_s4 @t18 @t39))) % 0.53/0.79 (define @t124 () (forall @t42 (or @t123 @t120))) % 0.53/0.79 (define @t125 () (forall @t42 (or @t123 @t105))) % 0.53/0.79 (define @t126 () (not @t125)) % 0.53/0.79 (define @t127 () (@list @t18)) % 0.53/0.79 (define @t128 () (lambda @t127 (or @t126 @t124))) % 0.53/0.79 (define @t129 () (_ @t128 @t5)) % 0.53/0.79 (define @t130 () (forall @t37 @t129)) % 0.53/0.79 (define @t131 () (_ @t10 @t5)) % 0.53/0.79 (define @t132 () (lambda @t77 (forall @t37 @t131))) % 0.53/0.79 (define @t133 () (lambda @t37 @t121)) % 0.53/0.79 (define @t134 () (_ @t133 @t18)) % 0.53/0.79 (define @t135 () (or @t126 @t134)) % 0.53/0.79 (define @t136 () (lambda @t127 @t135)) % 0.53/0.79 (define @t137 () (_ @t15 @t18)) % 0.53/0.79 (define @t138 () (@list @t15 @t18)) % 0.53/0.79 (define @t139 () (forall @t99 (or (not (tptp.rel_s4 @t39 @t96)) @t97))) % 0.53/0.79 (define @t140 () (forall @t42 (or @t123 (not @t139)))) % 0.53/0.79 (define @t141 () (not @t140)) % 0.53/0.79 (define @t142 () (lambda @t127 @t141)) % 0.53/0.79 (define @t143 () (or @t107 (_ @t142 @t39))) % 0.53/0.79 (define @t144 () (forall @t42 @t143)) % 0.53/0.79 (define @t145 () (lambda @t37 @t144)) % 0.53/0.79 (define @t146 () (_ @t10 @t39)) % 0.53/0.79 (define @t147 () (lambda @t13 (forall @t42 (or @t107 @t146)))) % 0.53/0.79 (define @t148 () (lambda @t37 @t108)) % 0.53/0.79 (define @t149 () (not (_ @t148 @t39))) % 0.53/0.79 (define @t150 () (or @t123 @t149)) % 0.53/0.79 (define @t151 () (forall @t42 @t150)) % 0.53/0.79 (define @t152 () (not @t151)) % 0.53/0.79 (define @t153 () (lambda @t127 @t152)) % 0.53/0.79 (define @t154 () (not @t146)) % 0.53/0.79 (define @t155 () (not (forall @t42 (or @t123 @t154)))) % 0.53/0.79 (define @t156 () (lambda @t87 @t155)) % 0.53/0.79 (define @t157 () (_ @t147 tptp.p)) % 0.53/0.79 (define @t158 () (_ @t148 @t18)) % 0.53/0.79 (define @t159 () (not @t158)) % 0.53/0.79 (define @t160 () (or @t159 @t137)) % 0.53/0.79 (define @t161 () (lambda @t138 @t160)) % 0.53/0.79 (define @t162 () (or (not (_ @t10 @t18)) @t137)) % 0.53/0.79 (define @t163 () (lambda @t22 @t162)) % 0.53/0.79 (define @t164 () (forall @t42 (or @t107 @t154))) % 0.53/0.79 (define @t165 () (lambda @t37 @t164)) % 0.53/0.79 (define @t166 () (_ @t165 @t5)) % 0.53/0.79 (define @t167 () (not @t166)) % 0.53/0.79 (define @t168 () (lambda @t37 @t167)) % 0.53/0.79 (define @t169 () (not @t40)) % 0.53/0.79 (define @t170 () (or @t107 @t169)) % 0.53/0.79 (define @t171 () (lambda @t37 @t12)) % 0.53/0.79 (define @t172 () (_ @t171 @t39)) % 0.53/0.79 (define @t173 () (or @t107 @t172)) % 0.53/0.79 (define @t174 () (forall @t42 @t173)) % 0.53/0.79 (define @t175 () (lambda @t37 @t174)) % 0.53/0.79 (define @t176 () (or @t12 @t16)) % 0.53/0.79 (define @t177 () (lambda @t37 @t176)) % 0.53/0.79 (define @t178 () (@list @t15 @t5)) % 0.53/0.79 (define @t179 () (_ @t171 @t5)) % 0.53/0.79 (define @t180 () (or @t179 @t16)) % 0.53/0.79 (define @t181 () (lambda @t178 @t180)) % 0.53/0.79 (define @t182 () (forall @t113 @t110)) % 0.53/0.79 (define @t183 () (@quantifiers_skolemize @t182 0)) % 0.53/0.79 (define @t184 () (forall @t42 (or (not (tptp.rel_s4 @t183 @t39)) @t105))) % 0.53/0.79 (define @t185 () (@quantifiers_skolemize @t182 1)) % 0.53/0.79 (define @t186 () (forall @t102 (or (not (tptp.rel_s4 @t185 @t98)) @t100))) % 0.53/0.79 (define @t187 () (not @t186)) % 0.53/0.79 (define @t188 () (tptp.rel_s4 @t183 @t185)) % 0.53/0.79 (define @t189 () (not @t188)) % 0.53/0.79 (define @t190 () (not @t184)) % 0.53/0.79 (define @t191 () (or @t190 @t189 @t187)) % 0.53/0.79 (define @t192 () (@list true)) % 0.53/0.79 (define @t193 () (@list @t191)) % 0.53/0.79 (define @t194 () (forall @t99 (or (not (tptp.rel_s4 @t185 @t96)) @t97))) % 0.53/0.79 (define @t195 () (@quantifiers_skolemize @t194 0)) % 0.53/0.79 (define @t196 () (@list @t185)) % 0.53/0.79 (define @t197 () (_ @t41 @t45 @t45)) % 0.53/0.79 (define @t198 () (not @t194)) % 0.53/0.79 (define @t199 () (tptp.rel_s4 @t185 @t185)) % 0.53/0.79 (define @t200 () (not @t199)) % 0.53/0.79 (define @t201 () (or @t200 @t198)) % 0.53/0.79 (define @t202 () (tptp.p @t195)) % 0.53/0.79 (define @t203 () (tptp.rel_s4 @t185 @t195)) % 0.53/0.79 (define @t204 () (not @t203)) % 0.53/0.79 (define @t205 () (or @t204 @t202)) % 0.53/0.79 (define @t206 () (@list @t205)) % 0.53/0.79 (define @t207 () (tptp.rel_s4 @t183 @t195)) % 0.53/0.79 (define @t208 () (not @t207)) % 0.53/0.79 (define @t209 () (or @t208 @t202)) % 0.53/0.79 (define @t210 () (@list true false)) % 0.53/0.79 (define @t211 () (or @t189 @t204 @t207)) % 0.53/0.79 (define @t212 () (not @t211)) % 0.53/0.79 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.53/0.79 (assume @p2 (_ tptp.mreflexive tptp.rel_s4)) % 0.53/0.79 (assume @p3 (_ tptp.mtransitive tptp.rel_s4)) % 0.53/0.79 (assume @p4 @t2) % 0.53/0.79 (assume @p5 true) % 0.53/0.79 (step @p6 (= tptp.meq_ind @t6) :rule refl :args (@t6)) % 0.53/0.79 (step @p7 (= tptp.meq_prop @t9) :rule refl :args (@t9)) % 0.53/0.79 (step @p8 (= tptp.mnot @t14) :rule refl :args (@t14)) % 0.53/0.79 (step @p9 (= tptp.mor @t17) :rule refl :args (@t17)) % 0.53/0.79 (step @p10 (= tptp.mand @t23) :rule refl :args (@t23)) % 0.53/0.79 (step @p11 (= tptp.mimplies @t24) :rule refl :args (@t24)) % 0.53/0.79 (step @p12 (= tptp.mimplied @t25) :rule refl :args (@t25)) % 0.53/0.79 (step @p13 (= tptp.mequiv @t26) :rule refl :args (@t26)) % 0.53/0.79 (step @p14 (= tptp.mxor @t27) :rule refl :args (@t27)) % 0.53/0.79 (step @p15 (= tptp.mforall_ind @t30) :rule refl :args (@t30)) % 0.53/0.79 (step @p16 (= tptp.mforall_prop @t34) :rule refl :args (@t34)) % 0.53/0.79 (step @p17 (= tptp.mexists_ind @t35) :rule refl :args (@t35)) % 0.53/0.79 (step @p18 (= tptp.mexists_prop @t36) :rule refl :args (@t36)) % 0.53/0.79 (step @p19 (= tptp.mtrue @t38) :rule refl :args (@t38)) % 0.53/0.79 (step @p20 (= tptp.mbox @t43) :rule refl :args (@t43)) % 0.53/0.79 (step @p21 (= tptp.mdia @t44) :rule refl :args (@t44)) % 0.53/0.79 (step @p22 (= tptp.mreflexive @t51) :rule refl :args (@t51)) % 0.53/0.79 (step @p23 (= tptp.msymmetric @t55) :rule refl :args (@t55)) % 0.53/0.79 (step @p24 (= tptp.mserial @t57) :rule refl :args (@t57)) % 0.53/0.79 (step @p25 (= tptp.mtransitive @t64) :rule refl :args (@t64)) % 0.53/0.79 (step @p26 (= tptp.meuclidean @t66) :rule refl :args (@t66)) % 0.53/0.79 (step @p27 (= tptp.mpartially_functional @t68) :rule refl :args (@t68)) % 0.53/0.79 (step @p28 (= tptp.mfunctional @t70) :rule refl :args (@t70)) % 0.53/0.79 (step @p29 (= tptp.mweakly_dense @t73) :rule refl :args (@t73)) % 0.53/0.79 (step @p30 (= tptp.mweakly_connected @t74) :rule refl :args (@t74)) % 0.53/0.79 (step @p31 (= tptp.mweakly_directed @t75) :rule refl :args (@t75)) % 0.53/0.79 (step @p32 (= tptp.mvalid @t78) :rule refl :args (@t78)) % 0.53/0.79 (step @p33 (= tptp.minvalid @t79) :rule refl :args (@t79)) % 0.53/0.79 (step @p34 (= tptp.msatisfiable @t80) :rule refl :args (@t80)) % 0.53/0.79 (step @p35 (= tptp.mcountersatisfiable @t81) :rule refl :args (@t81)) % 0.53/0.79 (step @p36 (= tptp.mbox_s4 @t86) :rule refl :args (@t86)) % 0.53/0.79 (step @p37 (= tptp.mdia_s4 @t88) :rule refl :args (@t88)) % 0.53/0.79 (step @p38 :rule beta-reduce :args ((= (_ (lambda @t50 (forall @t62 (or (not @t92) (not @t91) @t90))) tptp.rel_s4) @t89))) % 0.53/0.79 (step @p39 :rule refl :args (tptp.rel_s4)) % 0.53/0.79 (step @p40 :rule refl :args (@t90)) % 0.53/0.79 (step @p41 :rule refl :args (@t59)) % 0.53/0.79 (step @p42 :rule cong :premises (@p41 @p40) :args ((= @t59 @t90))) % 0.53/0.79 (step @p43 :rule symm :premises (@p42)) % 0.53/0.79 (step @p44 :rule eq_resolve :premises (@p41 @p43)) % 0.53/0.79 (step @p45 :rule refl :args (@t91)) % 0.53/0.79 (step @p46 :rule refl :args (@t60)) % 0.53/0.79 (step @p47 :rule cong :premises (@p46 @p45) :args ((= @t60 @t91))) % 0.53/0.79 (step @p48 :rule symm :premises (@p47)) % 0.53/0.79 (step @p49 :rule eq_resolve :premises (@p46 @p48)) % 0.53/0.79 (step @p50 :rule cong :premises (@p49) :args (@t93)) % 0.53/0.79 (step @p51 :rule refl :args (@t92)) % 0.53/0.79 (step @p52 :rule refl :args (@t54)) % 0.53/0.79 (step @p53 :rule cong :premises (@p52 @p51) :args ((= @t54 @t92))) % 0.53/0.79 (step @p54 :rule symm :premises (@p53)) % 0.53/0.79 (step @p55 :rule eq_resolve :premises (@p52 @p54)) % 0.53/0.79 (step @p56 :rule cong :premises (@p55) :args (@t94)) % 0.53/0.79 (step @p57 :rule nary_cong :premises (@p56 @p50 @p44) :args (@t95)) % 0.53/0.79 (step @p58 :rule cong :premises (@p57) :args ((forall @t62 @t95))) % 0.53/0.79 (step @p59 :rule aci_norm :args ((= (or (or @t94 @t93) @t59) @t95))) % 0.53/0.79 (step @p60 :rule bool-and-de-morgan :args (@t54 @t60 true)) % 0.53/0.79 (step @p61 :rule nary_cong :premises (@p60 @p41) :args ((or (not @t61) @t59))) % 0.53/0.79 (step @p62 :rule trans :premises (@p61 @p59)) % 0.53/0.79 (step @p63 :rule bool-impl-elim :args (@t61 @t59)) % 0.53/0.79 (step @p64 :rule trans :premises (@p63 @p62)) % 0.53/0.79 (step @p65 :rule cong :premises (@p64) :args (@t63)) % 0.53/0.79 (step @p66 :rule trans :premises (@p65 @p58)) % 0.53/0.79 (step @p67 :rule cong :premises (@p66) :args (@t64)) % 0.53/0.79 (step @p68 :rule trans :premises (@p25 @p67)) % 0.53/0.79 (step @p69 :rule ho_cong :premises (@p68 @p39)) % 0.53/0.79 (step @p70 :rule trans :premises (@p69 @p38)) % 0.53/0.79 (step @p71 :rule eq_resolve :premises (@p3 @p70)) % 0.53/0.79 (step @p72 :rule aci_norm :args ((= @t112 @t110))) % 0.53/0.79 (step @p73 :rule cong :premises (@p72) :args (@t114)) % 0.53/0.79 (step @p74 :rule quant-merge-prenex :args ((= (forall @t37 @t116) @t114))) % 0.53/0.79 (step @p75 :rule alpha_equiv :args (@t117 (@list @t101) @t118)) % 0.53/0.79 (step @p76 :rule refl :args (@t109)) % 0.53/0.79 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t119)) % 0.53/0.79 (step @p78 :rule quant-miniscope-or :args ((= @t116 @t119))) % 0.53/0.79 (step @p79 :rule trans :premises (@p78 @p77)) % 0.53/0.79 (step @p80 :rule symm :premises (@p79)) % 0.53/0.79 (step @p81 :rule cong :premises (@p80) :args ((forall @t37 @t122))) % 0.53/0.79 (step @p82 :rule trans :premises (@p81 @p74)) % 0.53/0.79 (step @p83 :rule trans :premises (@p82 @p73)) % 0.53/0.79 (step @p84 :rule beta-reduce :args ((= @t129 @t122))) % 0.53/0.79 (step @p85 :rule cong :premises (@p84) :args (@t130)) % 0.53/0.79 (step @p86 :rule trans :premises (@p85 @p83)) % 0.53/0.79 (step @p87 :rule beta-reduce :args ((= (_ @t132 @t128) @t130))) % 0.53/0.79 (step @p88 :rule trans :premises (@p87 @p86)) % 0.53/0.79 (step @p89 :rule beta-reduce :args ((= @t134 @t124))) % 0.53/0.79 (step @p90 :rule refl :args (@t126)) % 0.53/0.79 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t135)) % 0.53/0.79 (step @p92 :rule cong :premises (@p91) :args (@t136)) % 0.53/0.79 (step @p93 :rule beta-reduce :args ((= (_ (lambda @t138 (or @t126 @t137)) @t133) @t136))) % 0.53/0.79 (step @p94 :rule trans :premises (@p93 @p92)) % 0.53/0.79 (step @p95 :rule beta-reduce :args ((= (_ (lambda @t127 (not (forall @t102 (or (not (tptp.rel_s4 @t18 @t98)) @t100)))) @t39) @t120))) % 0.53/0.79 (step @p96 :rule refl :args (@t39)) % 0.53/0.79 (step @p97 :rule alpha_equiv :args (@t140 @t118 (@list @t98))) % 0.53/0.79 (step @p98 :rule cong :premises (@p97) :args (@t141)) % 0.53/0.79 (step @p99 :rule cong :premises (@p98) :args (@t142)) % 0.53/0.79 (step @p100 :rule ho_cong :premises (@p99 @p96)) % 0.53/0.79 (step @p101 :rule trans :premises (@p100 @p95)) % 0.53/0.79 (step @p102 :rule refl :args (@t107)) % 0.53/0.79 (step @p103 :rule nary_cong :premises (@p102 @p101) :args (@t143)) % 0.53/0.79 (step @p104 :rule cong :premises (@p103) :args (@t144)) % 0.53/0.79 (step @p105 :rule cong :premises (@p104) :args (@t145)) % 0.53/0.79 (step @p106 :rule beta-reduce :args ((= (_ @t147 @t142) @t145))) % 0.53/0.79 (step @p107 :rule trans :premises (@p106 @p105)) % 0.53/0.79 (step @p108 :rule beta-reduce :args ((= (_ (lambda @t37 (forall @t99 (or (not (tptp.rel_s4 @t5 @t96)) @t97))) @t39) @t139))) % 0.53/0.79 (step @p109 :rule alpha_equiv :args (@t108 @t118 (@list @t96))) % 0.53/0.79 (step @p110 :rule cong :premises (@p109) :args (@t148)) % 0.53/0.79 (step @p111 :rule ho_cong :premises (@p110 @p96)) % 0.53/0.79 (step @p112 :rule trans :premises (@p111 @p108)) % 0.53/0.79 (step @p113 :rule cong :premises (@p112) :args (@t149)) % 0.53/0.79 (step @p114 :rule refl :args (@t123)) % 0.53/0.79 (step @p115 :rule nary_cong :premises (@p114 @p113) :args (@t150)) % 0.53/0.79 (step @p116 :rule cong :premises (@p115) :args (@t151)) % 0.53/0.79 (step @p117 :rule cong :premises (@p116) :args (@t152)) % 0.53/0.79 (step @p118 :rule cong :premises (@p117) :args (@t153)) % 0.53/0.79 (step @p119 :rule beta-reduce :args ((= (_ @t156 @t148) @t153))) % 0.53/0.79 (step @p120 :rule trans :premises (@p119 @p118)) % 0.53/0.79 (step @p121 :rule beta-reduce :args ((= @t157 @t148))) % 0.53/0.79 (step @p122 :rule refl :args (@t156)) % 0.53/0.79 (step @p123 :rule ho_cong :premises (@p122 @p121)) % 0.53/0.79 (step @p124 :rule trans :premises (@p123 @p120)) % 0.53/0.79 (step @p125 :rule refl :args (@t147)) % 0.53/0.79 (step @p126 :rule ho_cong :premises (@p125 @p124)) % 0.53/0.79 (step @p127 :rule trans :premises (@p126 @p107)) % 0.53/0.79 (step @p128 :rule refl :args (@t137)) % 0.53/0.79 (step @p129 :rule beta-reduce :args ((= @t158 @t125))) % 0.53/0.79 (step @p130 :rule cong :premises (@p129) :args (@t159)) % 0.53/0.79 (step @p131 :rule nary_cong :premises (@p130 @p128) :args (@t160)) % 0.53/0.79 (step @p132 :rule cong :premises (@p131) :args (@t161)) % 0.53/0.79 (step @p133 :rule beta-reduce :args ((= (_ @t163 @t148) @t161))) % 0.53/0.79 (step @p134 :rule trans :premises (@p133 @p132)) % 0.53/0.79 (step @p135 :rule refl :args (@t163)) % 0.53/0.79 (step @p136 :rule ho_cong :premises (@p135 @p121)) % 0.53/0.79 (step @p137 :rule trans :premises (@p136 @p134)) % 0.53/0.79 (step @p138 :rule ho_cong :premises (@p137 @p127)) % 0.53/0.79 (step @p139 :rule trans :premises (@p138 @p94)) % 0.53/0.79 (step @p140 :rule refl :args (@t132)) % 0.53/0.79 (step @p141 :rule ho_cong :premises (@p140 @p139)) % 0.53/0.79 (step 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(step @p172 :rule beta-reduce :args ((= @t172 @t169))) % 0.53/0.79 (step @p173 :rule nary_cong :premises (@p102 @p172) :args (@t173)) % 0.53/0.79 (step @p174 :rule cong :premises (@p173) :args (@t174)) % 0.53/0.79 (step @p175 :rule trans :premises (@p174 @p171)) % 0.53/0.79 (step @p176 :rule cong :premises (@p175) :args (@t175)) % 0.53/0.79 (step @p177 :rule beta-reduce :args ((= (_ @t147 @t171) @t175))) % 0.53/0.79 (step @p178 :rule trans :premises (@p177 @p176)) % 0.53/0.79 (step @p179 :rule beta-reduce :args ((= (_ @t14 @t10) @t171))) % 0.53/0.79 (step @p180 :rule ho_cong :premises (@p125 @p179)) % 0.53/0.79 (step @p181 :rule trans :premises (@p180 @p178)) % 0.53/0.79 (step @p182 :rule refl :args (@t14)) % 0.53/0.79 (step @p183 :rule ho_cong :premises (@p182 @p181)) % 0.53/0.79 (step @p184 :rule trans :premises (@p183 @p167)) % 0.53/0.79 (step @p185 :rule ho_cong :premises (@p184 @p162)) % 0.53/0.79 (step @p186 :rule trans :premises (@p185 @p161)) % 0.53/0.79 (step @p187 :rule refl 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(step @p203 :rule cong :premises (@p202) :args (@t181)) % 0.53/0.79 (step @p204 :rule beta-reduce :args ((= (_ @t17 @t171) @t181))) % 0.53/0.79 (step @p205 :rule trans :premises (@p204 @p203)) % 0.53/0.79 (step @p206 :rule refl :args (@t17)) % 0.53/0.79 (step @p207 :rule ho_cong :premises (@p206 @p179)) % 0.53/0.79 (step @p208 :rule trans :premises (@p207 @p205)) % 0.53/0.79 (step @p209 :rule ho_cong :premises (@p208 @p199)) % 0.53/0.79 (step @p210 :rule trans :premises (@p209 @p198)) % 0.53/0.79 (step @p211 :rule ho_cong :premises (@p210 @p162)) % 0.53/0.79 (step @p212 :rule trans :premises (@p211 @p197)) % 0.53/0.79 (step @p213 :rule ho_cong :premises (@p9 @p188)) % 0.53/0.79 (step @p214 :rule ho_cong :premises (@p213 @p199)) % 0.53/0.79 (step @p215 :rule ho_cong :premises (@p214 @p162)) % 0.53/0.79 (step @p216 :rule trans :premises (@p215 @p212)) % 0.53/0.79 (step @p217 :rule cong :premises (@p216) :args (@t24)) % 0.53/0.79 (step @p218 :rule trans :premises (@p11 @p217)) % 0.53/0.79 (step @p219 :rule ho_cong :premises (@p218 @p160)) % 0.53/0.79 (step @p220 :rule ho_cong :premises (@p219 @p196)) % 0.53/0.79 (step @p221 :rule refl :args (@t131)) % 0.53/0.79 (step @p222 :rule refl :args (@t11)) % 0.53/0.79 (step @p223 :rule cong :premises (@p222 @p221) :args ((= @t11 @t131))) % 0.53/0.79 (step @p224 :rule symm :premises (@p223)) % 0.53/0.79 (step @p225 :rule eq_resolve :premises (@p222 @p224)) % 0.53/0.79 (step @p226 :rule cong :premises (@p225) :args (@t76)) % 0.53/0.79 (step @p227 :rule cong :premises (@p226) :args (@t78)) % 0.53/0.79 (step @p228 :rule trans :premises (@p32 @p227)) % 0.53/0.79 (step @p229 :rule ho_cong :premises (@p228 @p220)) % 0.53/0.79 (step @p230 :rule cong :premises (@p229) :args (@t2)) % 0.53/0.79 (step @p231 :rule trans :premises (@p230 @p143)) % 0.53/0.79 (step @p232 :rule eq_resolve :premises (@p4 @p231)) % 0.53/0.79 (step @p233 :rule skolemize :premises (@p232)) % 0.53/0.79 (step @p234 :rule bool-double-not-elim :args (@t184)) % 0.53/0.79 (step @p235 :rule refl :args (@t191)) % 0.53/0.79 (step @p236 :rule nary_cong :premises (@p235 @p234) :args ((or @t191 (not @t190)))) % 0.53/0.79 (step @p237 :rule cnf_or_neg :args (@t191 0)) % 0.53/0.79 (step @p238 :rule eq_resolve :premises (@p237 @p236)) % 0.53/0.79 (step @p239 :rule reordering :premises (@p238) :args ((or @t184 @t191))) % 0.53/0.79 (step @p240 :rule chain_m_resolution :premises (@p239 @p233) :args (@t184 @t192 @t193)) % 0.53/0.79 (step @p241 :rule instantiate :premises (@p240) :args ((@list @t195))) % 0.53/0.79 (step @p242 :rule bool-double-not-elim :args (@t186)) % 0.53/0.79 (step @p243 :rule nary_cong :premises (@p235 @p242) :args ((or @t191 (not @t187)))) % 0.53/0.79 (step @p244 :rule cnf_or_neg :args (@t191 2)) % 0.53/0.79 (step @p245 :rule eq_resolve :premises (@p244 @p243)) % 0.53/0.79 (step @p246 :rule reordering :premises (@p245) :args ((or @t186 @t191))) % 0.53/0.79 (step @p247 :rule chain_m_resolution :premises (@p246 @p233) :args (@t186 @t192 @t193)) % 0.53/0.79 (step @p248 :rule instantiate :premises (@p247) :args (@t196)) % 0.53/0.79 (step @p249 :rule beta-reduce :args ((= (_ (lambda @t50 (forall @t48 @t197)) tptp.rel_s4) (forall @t48 (tptp.rel_s4 @t45 @t45))))) % 0.53/0.79 (step @p250 :rule refl :args (@t197)) % 0.53/0.79 (step @p251 :rule refl :args (@t47)) % 0.53/0.79 (step @p252 :rule cong :premises (@p251 @p250) :args ((= @t47 @t197))) % 0.53/0.79 (step @p253 :rule symm :premises (@p252)) % 0.53/0.79 (step @p254 :rule eq_resolve :premises (@p251 @p253)) % 0.53/0.79 (step @p255 :rule cong :premises (@p254) :args (@t49)) % 0.53/0.79 (step @p256 :rule cong :premises (@p255) :args (@t51)) % 0.53/0.79 (step @p257 :rule trans :premises (@p22 @p256)) % 0.53/0.79 (step @p258 :rule ho_cong :premises (@p257 @p39)) % 0.53/0.79 (step @p259 :rule trans :premises (@p258 @p249)) % 0.53/0.79 (step @p260 :rule eq_resolve :premises (@p2 @p259)) % 0.53/0.79 (step @p261 :rule instantiate :premises (@p260) :args (@t196)) % 0.53/0.79 (step @p262 :rule cnf_or_pos :args (@t201)) % 0.53/0.79 (step @p263 :rule reordering :premises (@p262) :args ((or @t200 @t198 (not @t201)))) % 0.53/0.79 (step @p264 :rule chain_m_resolution :premises (@p263 @p261 @p248) :args (@t198 (@list false false) (@list @t199 @t201))) % 0.53/0.79 (step @p265 :rule skolemize :premises (@p264)) % 0.53/0.79 (step @p266 :rule cnf_or_neg :args (@t205 1)) % 0.53/0.79 (step @p267 :rule chain_m_resolution :premises (@p266 @p265) :args ((not @t202) @t192 @t206)) % 0.53/0.79 (step @p268 :rule cnf_or_pos :args (@t209)) % 0.53/0.79 (step @p269 :rule reordering :premises (@p268) :args ((or @t202 @t208 (not @t209)))) % 0.53/0.79 (step @p270 :rule chain_m_resolution :premises (@p269 @p267 @p241) :args (@t208 @t210 (@list @t202 @t209))) % 0.53/0.79 (step @p271 :rule bool-double-not-elim :args (@t203)) % 0.53/0.79 (step @p272 :rule refl :args (@t205)) % 0.53/0.79 (step @p273 :rule nary_cong :premises (@p272 @p271) :args ((or @t205 (not @t204)))) % 0.53/0.79 (step @p274 :rule cnf_or_neg :args (@t205 0)) % 0.53/0.79 (step @p275 :rule eq_resolve :premises (@p274 @p273)) % 0.53/0.79 (step @p276 :rule reordering :premises (@p275) :args ((or @t203 @t205))) % 0.53/0.79 (step @p277 :rule chain_m_resolution :premises (@p276 @p265) :args (@t203 @t192 @t206)) % 0.53/0.79 (step @p278 :rule bool-double-not-elim :args (@t188)) % 0.53/0.79 (step @p279 :rule nary_cong :premises (@p235 @p278) :args ((or @t191 (not @t189)))) % 0.53/0.79 (step @p280 :rule cnf_or_neg :args (@t191 1)) % 0.53/0.79 (step @p281 :rule eq_resolve :premises (@p280 @p279)) % 0.53/0.79 (step @p282 :rule reordering :premises (@p281) :args ((or @t188 @t191))) % 0.53/0.79 (step @p283 :rule chain_m_resolution :premises (@p282 @p233) :args (@t188 @t192 @t193)) % 0.53/0.79 (step @p284 :rule cnf_or_pos :args (@t211)) % 0.53/0.79 (step @p285 :rule reordering :premises (@p284) :args ((or @t189 @t204 @t207 @t212))) % 0.53/0.79 (step @p286 :rule chain_m_resolution :premises (@p285 @p283 @p277 @p270) :args (@t212 (@list false false true) (@list @t188 @t203 @t207))) % 0.53/0.79 (assume-push @p293 @t89) % 0.53/0.79 (step @p288 :rule instantiate :premises (@p71) :args ((@list @t183 @t185 @t195))) % 0.53/0.79 (step-pop @p294 :rule scope :premises (@p288)) % 0.53/0.79 (step @p289 :rule process_scope :premises (@p294) :args (@t211)) % 0.53/0.79 (step @p291 :rule implies_elim :premises (@p289)) % 0.53/0.79 (step @p292 false :rule chain_m_resolution :premises (@p291 @p286 @p71) :args (false @t210 (@list @t211 @t89))) % 0.53/0.79 ) % 0.53/0.79 % SZS output end Proof % 0.53/0.79 % cvc5 exiting %------------------------------------------------------------------------------