%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET002^7 : TPTP v9.2.1. Released v5.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n009.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 08:46:52 AM UTC 2026 % Result : Theorem 0.37s 0.66s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET002^7 : TPTP v9.2.1. Released v5.5.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n009.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 14:39:59 EDT 2026 % 0.17/0.34 % CPUTime : % 0.27/0.51 %----Proving TH0 % 0.37/0.66 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.66 % SZS status Theorem % 0.37/0.66 % SZS output start Proof % 0.37/0.66 ( % 0.37/0.66 (declare-sort tptp.mu 0) % 0.37/0.66 (declare-sort $$unsorted 0) % 0.37/0.66 (declare-const tptp.exists_in_world (-> tptp.mu $$unsorted Bool)) % 0.37/0.66 (declare-const tptp.rel_s4 (-> $$unsorted $$unsorted Bool)) % 0.37/0.66 (declare-const tptp.subset (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.37/0.66 (declare-const tptp.member (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.37/0.66 (declare-const tptp.qmltpeq (-> tptp.mu tptp.mu $$unsorted Bool)) % 0.37/0.66 (declare-const tptp.union (-> tptp.mu tptp.mu tptp.mu)) % 0.37/0.66 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.66 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.66 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.37/0.66 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.37/0.66 (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ _let_4 _let_3) _let_1)) (_ _let_2 _let_1))))))))) % 0.37/0.66 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.37/0.66 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.66 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mor (_ tptp.mnot _let_3)) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.66 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.66 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.66 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.66 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mequiv _let_3) _let_2)) _let_1)))))) % 0.37/0.66 (define tptp.mdia () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ tptp.mnot (_ (_ tptp.mbox _let_3) (_ tptp.mnot _let_2))) _let_1)))))) % 0.37/0.66 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.exists_in_world _let_2) _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.66 (define tptp.mexists_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.66 (define tptp.mexists_prop () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.37/0.66 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.66 (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)))))))) % 0.37/0.66 (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)))))))) % 0.37/0.66 (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" $$unsorted))) (lambda (@list _let_3) (forall (@list _let_2 _let_5 _let_1) (=> (and (_ _let_4 _let_5) (_ (_ _let_3 _let_5) _let_1)) (_ _let_4 _let_1)))))))))) % 0.37/0.66 (define tptp.meuclidean () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.66 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (= _let_2 _let_1)))))))))) % 0.37/0.66 (define tptp.mfunctional () (let ((_let_1 (@var "U" $$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))))))))))))) % 0.37/0.66 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_5 _let_2) (_ (_ _let_3 _let_2) _let_1)))))))))))) % 0.37/0.66 (define tptp.mweakly_connected () (let ((_let_1 (@var "T" $$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))))))))))) % 0.37/0.66 (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))))))))))))) % 0.37/0.66 (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)))))) % 0.37/0.66 (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)))))) % 0.37/0.66 (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))))))) % 0.37/0.66 (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))))))) % 0.37/0.66 (define tptp.mbox_s4 () (let ((_let_1 (@var "V" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "W" $$unsorted))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (or (not (_ (_ tptp.rel_s4 _let_3) _let_1)) (_ _let_2 _let_1)))))))) % 0.37/0.66 (define tptp.mdia_s4 () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ tptp.mbox_s4 (_ tptp.mnot _let_2))) _let_1))))) % 0.37/0.66 (define @t1 () (@var "V" $$unsorted)) % 0.37/0.66 (define @t2 () (@var "X" tptp.mu)) % 0.37/0.66 (define @t3 () (_ tptp.exists_in_world @t2)) % 0.37/0.66 (define @t4 () (_ @t3 @t1)) % 0.37/0.66 (define @t5 () (@list @t2)) % 0.37/0.66 (define @t6 () (@list @t1)) % 0.37/0.66 (define @t7 () (@var "W" $$unsorted)) % 0.37/0.66 (define @t8 () (_ @t3 @t7)) % 0.37/0.66 (define @t9 () (@var "V1" tptp.mu)) % 0.37/0.66 (define @t10 () (@var "V2" tptp.mu)) % 0.37/0.66 (define @t11 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.66 (define @t12 () (_ tptp.qmltpeq @t2)) % 0.37/0.66 (define @t13 () (@list @t2 @t11)) % 0.37/0.66 (define @t14 () (@var "Y" tptp.mu)) % 0.37/0.66 (define @t15 () (_ tptp.qmltpeq @t14)) % 0.37/0.66 (define @t16 () (_ @t12 @t14)) % 0.37/0.66 (define @t17 () (@list @t14 @t11)) % 0.37/0.66 (define @t18 () (@var "Z" tptp.mu)) % 0.37/0.66 (define @t19 () (@var "C" tptp.mu)) % 0.37/0.66 (define @t20 () (@var "B" tptp.mu)) % 0.37/0.66 (define @t21 () (_ tptp.union @t20)) % 0.37/0.66 (define @t22 () (_ @t21 @t19)) % 0.37/0.66 (define @t23 () (@var "A" tptp.mu)) % 0.37/0.66 (define @t24 () (_ (_ tptp.qmltpeq @t23) @t20)) % 0.37/0.66 (define @t25 () (_ tptp.mimplies @t24)) % 0.37/0.66 (define @t26 () (@list @t19 @t11)) % 0.37/0.66 (define @t27 () (@list @t20 @t11)) % 0.37/0.66 (define @t28 () (@list @t23 @t11)) % 0.37/0.66 (define @t29 () (_ tptp.union @t19)) % 0.37/0.66 (define @t30 () (_ @t29 @t20)) % 0.37/0.66 (define @t31 () (_ tptp.mand @t24)) % 0.37/0.66 (define @t32 () (_ tptp.member @t19)) % 0.37/0.66 (define @t33 () (_ tptp.subset @t20)) % 0.37/0.66 (define @t34 () (_ @t33 @t19)) % 0.37/0.66 (define @t35 () (_ tptp.subset @t19)) % 0.37/0.66 (define @t36 () (_ @t35 @t20)) % 0.37/0.66 (define @t37 () (_ tptp.qmltpeq @t22)) % 0.37/0.66 (define @t38 () (_ @t37 @t19)) % 0.37/0.66 (define @t39 () (lambda @t26 (_ (_ (_ tptp.mimplies @t34) @t38) @t11))) % 0.37/0.66 (define @t40 () (lambda @t27 (_ (_ tptp.mforall_ind @t39) @t11))) % 0.37/0.66 (define @t41 () (@var "D" tptp.mu)) % 0.37/0.66 (define @t42 () (_ tptp.member @t41)) % 0.37/0.66 (define @t43 () (_ @t42 @t19)) % 0.37/0.66 (define @t44 () (_ @t42 @t20)) % 0.37/0.66 (define @t45 () (@list @t41 @t11)) % 0.37/0.66 (define @t46 () (_ tptp.mequiv (_ (_ tptp.qmltpeq @t20) @t19))) % 0.37/0.66 (define @t47 () (lambda @t27 (_ (_ @t33 @t20) @t11))) % 0.37/0.66 (define @t48 () (lambda @t27 (_ (_ (_ tptp.qmltpeq (_ @t21 @t20)) @t20) @t11))) % 0.37/0.66 (define @t49 () (not (_ tptp.mvalid (_ tptp.mforall_ind @t48)))) % 0.37/0.66 (define @t50 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.66 (define @t51 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.66 (define @t52 () (lambda (@list @t51 @t50 @t7) (= (_ @t51 @t7) (_ @t50 @t7)))) % 0.37/0.66 (define @t53 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.66 (define @t54 () (_ @t53 @t7)) % 0.37/0.66 (define @t55 () (not @t54)) % 0.37/0.66 (define @t56 () (@list @t53 @t7)) % 0.37/0.66 (define @t57 () (lambda @t56 @t55)) % 0.37/0.66 (define @t58 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.66 (define @t59 () (_ @t58 @t7)) % 0.37/0.66 (define @t60 () (lambda (@list @t53 @t58 @t7) (or @t54 @t59))) % 0.37/0.66 (define @t61 () (_ @t53 @t1)) % 0.37/0.66 (define @t62 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.66 (define @t63 () (lambda (@list @t62 @t53 @t7) (forall @t6 (or (not (_ (_ @t62 @t7) @t1)) @t61)))) % 0.37/0.66 (define @t64 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.66 (define @t65 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.66 (define @t66 () (_ @t65 @t64)) % 0.37/0.66 (define @t67 () (lambda (@list @t65 @t7) (forall (@list @t64) (_ @t66 @t7)))) % 0.37/0.66 (define @t68 () (@list @t7)) % 0.37/0.66 (define @t69 () (lambda @t68 true)) % 0.37/0.66 (define @t70 () (_ tptp.mnot @t58)) % 0.37/0.66 (define @t71 () (_ tptp.mnot @t53)) % 0.37/0.66 (define @t72 () (_ tptp.mor @t71)) % 0.37/0.66 (define @t73 () (@list @t53 @t58 @t11)) % 0.37/0.66 (define @t74 () (lambda @t73 (_ (_ tptp.mnot (_ @t72 @t70)) @t11))) % 0.37/0.66 (define @t75 () (lambda @t73 (_ (_ @t72 @t58) @t11))) % 0.37/0.66 (define @t76 () (lambda @t73 (_ (_ (_ tptp.mor @t70) @t53) @t11))) % 0.37/0.66 (define @t77 () (lambda @t73 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t53) @t58)) (_ (_ tptp.mimplies @t58) @t53)) @t11))) % 0.37/0.66 (define @t78 () (lambda @t73 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t53) @t58)) @t11))) % 0.37/0.66 (define @t79 () (lambda (@list @t62 @t53 @t11) (_ (_ tptp.mnot (_ (_ tptp.mbox @t62) @t71)) @t11))) % 0.37/0.66 (define @t80 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.66 (define @t81 () (_ @t80 @t2)) % 0.37/0.66 (define @t82 () (_ @t81 @t7)) % 0.37/0.66 (define @t83 () (forall @t5 (=> @t8 @t82))) % 0.37/0.66 (define @t84 () (@list @t80 @t7)) % 0.37/0.66 (define @t85 () (lambda @t84 @t83)) % 0.37/0.66 (define @t86 () (lambda (@list @t80 @t11) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mnot @t81) @t11)))) @t11))) % 0.37/0.66 (define @t87 () (lambda (@list @t65 @t11) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t64 @t11) (_ (_ tptp.mnot @t66) @t11)))) @t11))) % 0.37/0.66 (define @t88 () (@var "S" $$unsorted)) % 0.37/0.66 (define @t89 () (_ @t62 @t88)) % 0.37/0.66 (define @t90 () (@list @t88)) % 0.37/0.66 (define @t91 () (@list @t62)) % 0.37/0.66 (define @t92 () (lambda @t91 (forall @t90 (_ @t89 @t88)))) % 0.37/0.66 (define @t93 () (@var "T" $$unsorted)) % 0.37/0.66 (define @t94 () (_ @t62 @t93)) % 0.37/0.66 (define @t95 () (_ @t89 @t93)) % 0.37/0.66 (define @t96 () (lambda @t91 (forall (@list @t88 @t93) (=> @t95 (_ @t94 @t88))))) % 0.37/0.66 (define @t97 () (@list @t93)) % 0.37/0.66 (define @t98 () (lambda @t91 (forall @t90 (exists @t97 @t95)))) % 0.37/0.66 (define @t99 () (@var "U" $$unsorted)) % 0.37/0.66 (define @t100 () (_ @t89 @t99)) % 0.37/0.66 (define @t101 () (_ @t94 @t99)) % 0.37/0.66 (define @t102 () (@list @t88 @t93 @t99)) % 0.37/0.66 (define @t103 () (lambda @t91 (forall @t102 (=> (and @t95 @t101) @t100)))) % 0.37/0.66 (define @t104 () (and @t95 @t100)) % 0.37/0.66 (define @t105 () (lambda @t91 (forall @t102 (=> @t104 @t101)))) % 0.37/0.66 (define @t106 () (= @t93 @t99)) % 0.37/0.66 (define @t107 () (lambda @t91 (forall @t102 (=> @t104 @t106)))) % 0.37/0.66 (define @t108 () (@list @t99)) % 0.37/0.66 (define @t109 () (lambda @t91 (forall @t90 (exists @t97 (and @t95 (forall @t108 (=> @t100 @t106))))))) % 0.37/0.66 (define @t110 () (_ @t62 @t99)) % 0.37/0.66 (define @t111 () (_ @t110 @t93)) % 0.37/0.66 (define @t112 () (lambda @t91 (forall @t102 (=> @t95 (exists @t108 (and @t100 @t111)))))) % 0.37/0.66 (define @t113 () (lambda @t91 (forall @t102 (=> @t104 (or @t101 @t106 @t111))))) % 0.37/0.66 (define @t114 () (lambda @t91 (forall @t102 (=> @t104 (exists @t6 (and (_ @t94 @t1) (_ @t110 @t1))))))) % 0.37/0.66 (define @t115 () (forall @t68 @t54)) % 0.37/0.66 (define @t116 () (@list @t53)) % 0.37/0.66 (define @t117 () (lambda @t116 @t115)) % 0.37/0.66 (define @t118 () (lambda @t116 (exists @t68 @t54))) % 0.37/0.66 (define @t119 () (lambda @t116 (exists @t68 @t55))) % 0.37/0.66 (define @t120 () (lambda @t116 (forall @t68 @t55))) % 0.37/0.66 (define @t121 () (lambda @t56 (forall @t6 (or (not (_ (_ tptp.rel_s4 @t7) @t1)) @t61)))) % 0.37/0.66 (define @t122 () (lambda (@list @t53 @t11) (_ (_ tptp.mnot (_ tptp.mbox_s4 @t71)) @t11))) % 0.37/0.66 (define @t123 () (tptp.union @t2 @t2)) % 0.37/0.66 (define @t124 () (tptp.qmltpeq @t123 @t2 @t7)) % 0.37/0.66 (define @t125 () (tptp.exists_in_world @t2 @t7)) % 0.37/0.66 (define @t126 () (not @t125)) % 0.37/0.66 (define @t127 () (or @t126 @t124)) % 0.37/0.66 (define @t128 () (@list @t7 @t2)) % 0.37/0.66 (define @t129 () (forall @t128 @t127)) % 0.37/0.66 (define @t130 () (forall @t5 @t127)) % 0.37/0.66 (define @t131 () (lambda @t68 @t130)) % 0.37/0.66 (define @t132 () (_ @t131 @t7)) % 0.37/0.66 (define @t133 () (forall @t68 @t132)) % 0.37/0.66 (define @t134 () (_ @t53 @t7)) % 0.37/0.66 (define @t135 () (lambda @t116 (forall @t68 @t134))) % 0.37/0.66 (define @t136 () (_ (_ tptp.union @t2) @t2)) % 0.37/0.66 (define @t137 () (_ (_ (_ tptp.qmltpeq @t136) @t2) @t7)) % 0.37/0.66 (define @t138 () (or @t126 @t137)) % 0.37/0.66 (define @t139 () (_ @t48 @t2 @t7)) % 0.37/0.66 (define @t140 () (or @t126 @t139)) % 0.37/0.66 (define @t141 () (forall @t5 @t140)) % 0.37/0.66 (define @t142 () (lambda @t68 @t141)) % 0.37/0.66 (define @t143 () (_ @t80 @t2 @t7)) % 0.37/0.66 (define @t144 () (lambda @t84 (forall @t5 (or @t126 @t143)))) % 0.37/0.66 (define @t145 () (_ @t144 @t48)) % 0.37/0.66 (define @t146 () (not @t8)) % 0.37/0.66 (define @t147 () (or @t146 @t82)) % 0.37/0.66 (define @t148 () (@quantifiers_skolemize @t129 0)) % 0.37/0.66 (define @t149 () (@quantifiers_skolemize @t129 1)) % 0.37/0.66 (define @t150 () (tptp.exists_in_world @t149 @t148)) % 0.37/0.66 (define @t151 () (tptp.qmltpeq (tptp.union @t149 @t149) @t149 @t148)) % 0.37/0.66 (define @t152 () (not @t150)) % 0.37/0.66 (define @t153 () (or @t152 @t151)) % 0.37/0.66 (define @t154 () (@list true)) % 0.37/0.66 (define @t155 () (@list @t153)) % 0.37/0.66 (define @t156 () (tptp.subset @t2 @t2 @t7)) % 0.37/0.66 (define @t157 () (or @t126 @t156)) % 0.37/0.66 (define @t158 () (forall @t5 @t157)) % 0.37/0.66 (define @t159 () (lambda @t68 @t158)) % 0.37/0.66 (define @t160 () (_ @t159 @t7)) % 0.37/0.66 (define @t161 () (forall @t68 @t160)) % 0.37/0.66 (define @t162 () (_ (_ (_ tptp.subset @t2) @t2) @t7)) % 0.37/0.66 (define @t163 () (or @t126 @t162)) % 0.37/0.66 (define @t164 () (_ @t47 @t2 @t7)) % 0.37/0.66 (define @t165 () (or @t126 @t164)) % 0.37/0.66 (define @t166 () (forall @t5 @t165)) % 0.37/0.66 (define @t167 () (lambda @t68 @t166)) % 0.37/0.66 (define @t168 () (@var "BOUND_VARIABLE_10096" tptp.mu)) % 0.37/0.66 (define @t169 () (tptp.qmltpeq (tptp.union @t2 @t168) @t168 @t7)) % 0.37/0.66 (define @t170 () (not (tptp.subset @t2 @t168 @t7))) % 0.37/0.66 (define @t171 () (not (tptp.exists_in_world @t168 @t7))) % 0.37/0.66 (define @t172 () (or @t126 @t171 @t170 @t169)) % 0.37/0.66 (define @t173 () (@list @t2 @t168)) % 0.37/0.66 (define @t174 () (forall @t173 @t172)) % 0.37/0.66 (define @t175 () (lambda @t68 @t174)) % 0.37/0.66 (define @t176 () (_ @t175 @t7)) % 0.37/0.66 (define @t177 () (forall @t68 @t176)) % 0.37/0.66 (define @t178 () (or @t171 @t170 @t169)) % 0.37/0.66 (define @t179 () (or @t126 @t178)) % 0.37/0.66 (define @t180 () (forall @t173 @t179)) % 0.37/0.66 (define @t181 () (@list @t168)) % 0.37/0.66 (define @t182 () (forall @t181 @t179)) % 0.37/0.66 (define @t183 () (forall @t181 @t178)) % 0.37/0.66 (define @t184 () (@var "BOUND_VARIABLE_10073" tptp.mu)) % 0.37/0.66 (define @t185 () (@list @t184)) % 0.37/0.66 (define @t186 () (or @t126 @t183)) % 0.37/0.66 (define @t187 () (@list @t184)) % 0.37/0.66 (define @t188 () (forall @t187 (or (not (tptp.exists_in_world @t184 @t7)) (not (tptp.subset @t2 @t184 @t7)) (tptp.qmltpeq (tptp.union @t2 @t184) @t184 @t7)))) % 0.37/0.66 (define @t189 () (tptp.union @t20 @t2)) % 0.37/0.66 (define @t190 () (forall @t5 (or (not (tptp.exists_in_world @t2 @t11)) (not (tptp.subset @t20 @t2 @t11)) (tptp.qmltpeq @t189 @t2 @t11)))) % 0.37/0.66 (define @t191 () (lambda @t27 @t190)) % 0.37/0.66 (define @t192 () (or @t126 (_ @t191 @t2 @t7))) % 0.37/0.66 (define @t193 () (forall @t5 @t192)) % 0.37/0.66 (define @t194 () (lambda @t68 @t193)) % 0.37/0.66 (define @t195 () (tptp.qmltpeq @t189 @t2 @t7)) % 0.37/0.66 (define @t196 () (tptp.subset @t20 @t2 @t7)) % 0.37/0.66 (define @t197 () (_ @t21 @t2)) % 0.37/0.66 (define @t198 () (_ (_ (_ tptp.qmltpeq @t197) @t2) @t7)) % 0.37/0.66 (define @t199 () (_ (_ @t33 @t2) @t7)) % 0.37/0.66 (define @t200 () (not @t199)) % 0.37/0.66 (define @t201 () (or @t126 @t200 @t198)) % 0.37/0.66 (define @t202 () (or @t200 @t198)) % 0.37/0.66 (define @t203 () (not (_ @t34 @t11))) % 0.37/0.66 (define @t204 () (or @t203 (_ @t38 @t11))) % 0.37/0.66 (define @t205 () (lambda @t26 @t204)) % 0.37/0.66 (define @t206 () (_ @t205 @t2 @t7)) % 0.37/0.66 (define @t207 () (or @t126 @t206)) % 0.37/0.66 (define @t208 () (forall @t5 @t207)) % 0.37/0.66 (define @t209 () (lambda @t68 @t208)) % 0.37/0.66 (define @t210 () (lambda (@list @t11) @t204)) % 0.37/0.66 (define @t211 () (_ @t58 @t11)) % 0.37/0.66 (define @t212 () (lambda (@list @t58 @t11) (or @t203 @t211))) % 0.37/0.66 (define @t213 () (or (not (_ @t53 @t11)) @t211)) % 0.37/0.66 (define @t214 () (_ (lambda @t73 @t213) @t34)) % 0.37/0.66 (define @t215 () (lambda @t26 (_ (_ @t214 @t38) @t11))) % 0.37/0.66 (define @t216 () (or @t55 @t59)) % 0.37/0.66 (define @t217 () (lambda @t68 @t216)) % 0.37/0.66 (define @t218 () (@list @t58 @t7)) % 0.37/0.66 (define @t219 () (lambda @t68 @t55)) % 0.37/0.66 (define @t220 () (_ @t219 @t7)) % 0.37/0.66 (define @t221 () (or @t220 @t59)) % 0.37/0.66 (define @t222 () (lambda @t218 @t221)) % 0.37/0.66 (define @t223 () (tptp.subset @t149 @t149 @t148)) % 0.37/0.66 (define @t224 () (not @t223)) % 0.37/0.66 (define @t225 () (or @t152 @t152 @t224 @t151)) % 0.37/0.66 (define @t226 () (or @t152 @t223)) % 0.37/0.66 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.66 (assume @p2 (forall @t6 (exists @t5 @t4))) % 0.37/0.66 (assume @p3 (_ tptp.mreflexive tptp.rel_s4)) % 0.37/0.66 (assume @p4 (_ tptp.mtransitive tptp.rel_s4)) % 0.37/0.66 (assume @p5 (forall (@list @t2 @t1 @t7) (=> (and @t4 (_ (_ tptp.rel_s4 @t1) @t7)) @t8))) % 0.37/0.66 (assume @p6 (forall (@list @t1 @t10 @t9) (_ (_ tptp.exists_in_world (_ (_ tptp.union @t10) @t9)) @t1))) % 0.37/0.66 (assume @p7 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t13 (_ (_ @t12 @t2) @t11))))) % 0.37/0.66 (assume @p8 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mforall_ind (lambda @t17 (_ (_ (_ tptp.mimplies @t16) (_ @t15 @t2)) @t11))) @t11))))) % 0.37/0.66 (assume @p9 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t13 (_ (_ tptp.mforall_ind (lambda @t17 (_ (_ tptp.mforall_ind (lambda (@list @t18 @t11) (_ (_ (_ tptp.mimplies (_ (_ tptp.mand @t16) (_ @t15 @t18))) (_ @t12 @t18)) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p10 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t28 (_ (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ @t25 (_ (_ tptp.qmltpeq (_ (_ tptp.union @t23) @t19)) @t22)) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p11 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t28 (_ (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ @t25 (_ (_ tptp.qmltpeq (_ @t29 @t23)) @t30)) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p12 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t28 (_ (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ (_ tptp.mimplies (_ @t31 (_ (_ tptp.member @t23) @t19))) (_ (_ tptp.member @t20) @t19)) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p13 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t28 (_ (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ (_ tptp.mimplies (_ @t31 (_ @t32 @t23))) (_ @t32 @t20)) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p14 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t28 (_ (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ (_ tptp.mimplies (_ @t31 (_ (_ tptp.subset @t23) @t19))) @t34) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p15 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t28 (_ (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ (_ tptp.mimplies (_ @t31 (_ @t35 @t23))) @t36) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p16 (_ tptp.mvalid (_ tptp.mforall_ind @t40))) % 0.37/0.67 (assume @p17 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ tptp.mforall_ind (lambda @t45 (_ (_ (_ tptp.mequiv (_ @t42 @t22)) (_ (_ tptp.mor @t44) @t43)) @t11))) @t11))) @t11))))) % 0.37/0.67 (assume @p18 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ @t46 (_ (_ tptp.mand @t34) @t36)) @t11))) @t11))))) % 0.37/0.67 (assume @p19 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ @t37 @t30) @t11))) @t11))))) % 0.37/0.67 (assume @p20 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ (_ tptp.mequiv @t34) (_ tptp.mforall_ind (lambda @t45 (_ (_ (_ tptp.mimplies @t44) @t43) @t11)))) @t11))) @t11))))) % 0.37/0.67 (assume @p21 (_ tptp.mvalid (_ tptp.mforall_ind @t47))) % 0.37/0.67 (assume @p22 (_ tptp.mvalid (_ tptp.mforall_ind (lambda @t27 (_ (_ tptp.mforall_ind (lambda @t26 (_ (_ @t46 (_ tptp.mforall_ind (lambda @t45 (_ (_ (_ tptp.mequiv @t44) @t43) @t11)))) @t11))) @t11))))) % 0.37/0.67 (assume @p23 @t49) % 0.37/0.67 (assume @p24 true) % 0.37/0.67 (step @p25 (= tptp.meq_prop @t52) :rule refl :args (@t52)) % 0.37/0.67 (step @p26 (= tptp.mnot @t57) :rule refl :args (@t57)) % 0.37/0.67 (step @p27 (= tptp.mor @t60) :rule refl :args (@t60)) % 0.37/0.67 (step @p28 (= tptp.mbox @t63) :rule refl :args (@t63)) % 0.37/0.67 (step @p29 (= tptp.mforall_prop @t67) :rule refl :args (@t67)) % 0.37/0.67 (step @p30 (= tptp.mtrue @t69) :rule refl :args (@t69)) % 0.37/0.67 (step @p31 (= tptp.mand @t74) :rule refl :args (@t74)) % 0.37/0.67 (step @p32 (= tptp.mimplies @t75) :rule refl :args (@t75)) % 0.37/0.67 (step @p33 (= tptp.mimplied @t76) :rule refl :args (@t76)) % 0.37/0.67 (step @p34 (= tptp.mequiv @t77) :rule refl :args (@t77)) % 0.37/0.67 (step @p35 (= tptp.mxor @t78) :rule refl :args (@t78)) % 0.37/0.67 (step @p36 (= tptp.mdia @t79) :rule refl :args (@t79)) % 0.37/0.67 (step @p37 (= tptp.mforall_ind @t85) :rule refl :args (@t85)) % 0.37/0.67 (step @p38 (= tptp.mexists_ind @t86) :rule refl :args (@t86)) % 0.37/0.67 (step @p39 (= tptp.mexists_prop @t87) :rule refl :args (@t87)) % 0.37/0.67 (step @p40 (= tptp.mreflexive @t92) :rule refl :args (@t92)) % 0.37/0.67 (step @p41 (= tptp.msymmetric @t96) :rule refl :args (@t96)) % 0.37/0.67 (step @p42 (= tptp.mserial @t98) :rule refl :args (@t98)) % 0.37/0.67 (step @p43 (= tptp.mtransitive @t103) :rule refl :args (@t103)) % 0.37/0.67 (step @p44 (= tptp.meuclidean @t105) :rule refl :args (@t105)) % 0.37/0.67 (step @p45 (= tptp.mpartially_functional @t107) :rule refl :args (@t107)) % 0.37/0.67 (step @p46 (= tptp.mfunctional @t109) :rule refl :args (@t109)) % 0.37/0.67 (step @p47 (= tptp.mweakly_dense @t112) :rule refl :args (@t112)) % 0.37/0.67 (step @p48 (= tptp.mweakly_connected @t113) :rule refl :args (@t113)) % 0.37/0.67 (step @p49 (= tptp.mweakly_directed @t114) :rule refl :args (@t114)) % 0.37/0.67 (step @p50 (= tptp.mvalid @t117) :rule refl :args (@t117)) % 0.37/0.67 (step @p51 (= tptp.msatisfiable @t118) :rule refl :args (@t118)) % 0.37/0.67 (step @p52 (= tptp.mcountersatisfiable @t119) :rule refl :args (@t119)) % 0.37/0.67 (step @p53 (= tptp.minvalid @t120) :rule refl :args (@t120)) % 0.37/0.67 (step @p54 (= tptp.mbox_s4 @t121) :rule refl :args (@t121)) % 0.37/0.67 (step @p55 (= tptp.mdia_s4 @t122) :rule refl :args (@t122)) % 0.37/0.67 (step @p56 :rule quant-merge-prenex :args ((= (forall @t68 @t130) @t129))) % 0.37/0.67 (step @p57 :rule beta-reduce :args ((= @t132 @t130))) % 0.37/0.67 (step @p58 :rule cong :premises (@p57) :args (@t133)) % 0.37/0.67 (step @p59 :rule trans :premises (@p58 @p56)) % 0.37/0.67 (step @p60 :rule beta-reduce :args ((= (_ @t135 @t131) @t133))) % 0.37/0.67 (step @p61 :rule trans :premises (@p60 @p59)) % 0.37/0.67 (step @p62 :rule refl :args ((tptp.qmltpeq @t136 @t2 @t7))) % 0.37/0.67 (step @p63 :rule refl :args (@t7)) % 0.37/0.67 (step @p64 :rule refl :args (@t2)) % 0.37/0.67 (step @p65 :rule refl :args (@t123)) % 0.37/0.67 (step @p66 :rule cong :premises (@p65 @p64 @p63) :args (@t124)) % 0.37/0.67 (step @p67 :rule trans :premises (@p66 @p62)) % 0.37/0.67 (step @p68 :rule refl :args (tptp.qmltpeq)) % 0.37/0.67 (step @p69 :rule ho_cong :premises (@p68 @p65)) % 0.37/0.67 (step @p70 :rule ho_cong :premises (@p69 @p64)) % 0.37/0.67 (step @p71 :rule ho_cong :premises (@p70 @p63)) % 0.37/0.67 (step @p72 :rule cong :premises (@p71 @p67) :args ((= (_ (_ (_ tptp.qmltpeq @t123) @t2) @t7) @t124))) % 0.37/0.67 (step @p73 :rule symm :premises (@p72)) % 0.37/0.67 (step @p74 :rule refl :args (@t137)) % 0.37/0.67 (step @p75 :rule eq_resolve :premises (@p74 @p73)) % 0.37/0.67 (step @p76 :rule refl :args (@t136)) % 0.37/0.67 (step @p77 :rule cong :premises (@p76 @p65) :args ((= @t136 @t123))) % 0.37/0.67 (step @p78 :rule symm :premises (@p77)) % 0.37/0.67 (step @p79 :rule eq_resolve :premises (@p76 @p78)) % 0.37/0.67 (step @p80 :rule ho_cong :premises (@p68 @p79)) % 0.37/0.67 (step @p81 :rule ho_cong :premises (@p80 @p64)) % 0.37/0.67 (step @p82 :rule ho_cong :premises (@p81 @p63)) % 0.37/0.67 (step @p83 :rule trans :premises (@p82 @p75)) % 0.37/0.67 (step @p84 :rule refl :args (@t126)) % 0.37/0.67 (step @p85 :rule nary_cong :premises (@p84 @p83) :args (@t138)) % 0.37/0.67 (step @p86 :rule cong :premises (@p85) :args ((forall @t5 @t138))) % 0.37/0.67 (step @p87 :rule beta-reduce :args ((= @t139 @t137))) % 0.37/0.67 (step @p88 :rule refl :args (@t126)) % 0.37/0.67 (step @p89 :rule nary_cong :premises (@p88 @p87) :args (@t140)) % 0.37/0.67 (step @p90 :rule cong :premises (@p89) :args (@t141)) % 0.37/0.67 (step @p91 :rule trans :premises (@p90 @p86)) % 0.37/0.67 (step @p92 :rule cong :premises (@p91) :args (@t142)) % 0.37/0.67 (step @p93 :rule beta-reduce :args ((= @t145 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(step @p255 :rule refl :args (@t58)) % 0.37/0.67 (step @p256 :rule refl :args (@t59)) % 0.37/0.67 (step @p257 :rule beta-reduce :args ((= @t220 @t55))) % 0.37/0.67 (step @p258 :rule nary_cong :premises (@p257 @p256) :args (@t221)) % 0.37/0.67 (step @p259 :rule cong :premises (@p258) :args (@t222)) % 0.37/0.67 (step @p260 :rule beta-reduce :args ((= (_ @t60 @t219) @t222))) % 0.37/0.67 (step @p261 :rule trans :premises (@p260 @p259)) % 0.37/0.67 (step @p262 :rule beta-reduce :args ((= (_ @t57 @t53) @t219))) % 0.37/0.67 (step @p263 :rule refl :args (@t60)) % 0.37/0.67 (step @p264 :rule ho_cong :premises (@p263 @p262)) % 0.37/0.67 (step @p265 :rule trans :premises (@p264 @p261)) % 0.37/0.67 (step @p266 :rule ho_cong :premises (@p265 @p255)) % 0.37/0.67 (step @p267 :rule trans :premises (@p266 @p254)) % 0.37/0.67 (step @p268 :rule ho_cong :premises (@p267 @p196)) % 0.37/0.67 (step @p269 :rule trans :premises (@p268 @p253)) % 0.37/0.67 (step @p270 :rule refl :args (@t53)) % 0.37/0.67 (step 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:args (false (@list true false false) (@list @t223 @t226 @t150))) % 0.37/0.67 ) % 0.37/0.67 % SZS output end Proof % 0.37/0.67 % cvc5 exiting %------------------------------------------------------------------------------