%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : LCL702^1 : TPTP v9.3.1. Bugfixed v5.0.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:23:40 AM UTC 2026 % Result : Theorem 0.21s 0.56s % Output : Proof 0.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL702^1 : TPTP v9.3.1. Bugfixed v5.0.0. % 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.12/0.37 % Computer : n004.cluster.edu % 0.12/0.37 % Model : x86_64 x86_64 % 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.37 % Memory : 8046.5625MB % 0.12/0.37 % OS : Linux 6.8.0-71-generic % 0.12/0.37 % CPULimit : 300 % 0.12/0.37 % WCLimit : 300 % 0.12/0.37 % DateTime : Sat Sep 5 15:23:14 UTC 2026 % 0.12/0.37 % CPUTime : % 0.12/0.45 %----Proving TH0 % 0.21/0.56 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.21/0.56 % SZS status Theorem % 0.21/0.56 % SZS output start Proof % 0.21/0.56 ( % 0.21/0.56 (declare-sort $$unsorted 0) % 0.21/0.56 (declare-sort tptp.mu 0) % 0.21/0.56 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.21/0.56 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.21/0.56 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.21/0.56 (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)))))) % 0.21/0.56 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.21/0.56 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.56 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.21/0.56 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.56 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.21/0.56 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.21/0.56 (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))))))) % 0.21/0.56 (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))))))) % 0.21/0.56 (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)))))) % 0.21/0.56 (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)))))) % 0.21/0.56 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.21/0.56 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.21/0.56 (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)))))) % 0.21/0.56 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.21/0.56 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.21/0.56 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.21/0.56 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.21/0.56 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.21/0.56 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.21/0.56 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.21/0.56 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.21/0.56 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.21/0.56 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.21/0.56 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.56 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.56 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.21/0.56 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.21/0.56 (define @t1 () (@var "__flatten_var_0" $$unsorted)) % 0.21/0.56 (define @t2 () (@var "A" (-> $$unsorted Bool))) % 0.21/0.56 (define @t3 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.21/0.56 (define @t4 () (_ tptp.mbox @t3)) % 0.21/0.56 (define @t5 () (_ @t4 @t2)) % 0.21/0.56 (define @t6 () (@list @t2 @t1)) % 0.21/0.56 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mimplies @t5) (_ @t4 @t5)) @t1))) % 0.21/0.56 (define @t8 () (=> (_ tptp.mtransitive @t3) (_ tptp.mvalid (_ tptp.mforall_prop @t7)))) % 0.21/0.56 (define @t9 () (@list @t3)) % 0.21/0.56 (define @t10 () (forall @t9 @t8)) % 0.21/0.56 (define @t11 () (not @t10)) % 0.21/0.56 (define @t12 () (@var "Y" tptp.mu)) % 0.21/0.56 (define @t13 () (@var "X" tptp.mu)) % 0.21/0.56 (define @t14 () (@var "W" $$unsorted)) % 0.21/0.56 (define @t15 () (lambda (@list @t13 @t12 @t14) (= @t13 @t12))) % 0.21/0.56 (define @t16 () (@var "Y" (-> $$unsorted Bool))) % 0.21/0.56 (define @t17 () (@var "X" (-> $$unsorted Bool))) % 0.21/0.56 (define @t18 () (lambda (@list @t17 @t16 @t14) (= (_ @t17 @t14) (_ @t16 @t14)))) % 0.21/0.56 (define @t19 () (@var "Phi" (-> $$unsorted Bool))) % 0.21/0.56 (define @t20 () (_ @t19 @t14)) % 0.21/0.56 (define @t21 () (not @t20)) % 0.21/0.56 (define @t22 () (@list @t19 @t14)) % 0.21/0.56 (define @t23 () (lambda @t22 @t21)) % 0.21/0.56 (define @t24 () (@var "Psi" (-> $$unsorted Bool))) % 0.21/0.56 (define @t25 () (_ @t24 @t14)) % 0.21/0.56 (define @t26 () (lambda (@list @t19 @t24 @t14) (or @t20 @t25))) % 0.21/0.56 (define @t27 () (_ tptp.mnot @t24)) % 0.21/0.56 (define @t28 () (_ tptp.mnot @t19)) % 0.21/0.56 (define @t29 () (_ tptp.mor @t28)) % 0.21/0.56 (define @t30 () (@list @t19 @t24 @t1)) % 0.21/0.56 (define @t31 () (lambda @t30 (_ (_ tptp.mnot (_ @t29 @t27)) @t1))) % 0.21/0.56 (define @t32 () (lambda @t30 (_ (_ @t29 @t24) @t1))) % 0.21/0.56 (define @t33 () (lambda @t30 (_ (_ (_ tptp.mor @t27) @t19) @t1))) % 0.21/0.56 (define @t34 () (lambda @t30 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t19) @t24)) (_ (_ tptp.mimplies @t24) @t19)) @t1))) % 0.21/0.56 (define @t35 () (lambda @t30 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t19) @t24)) @t1))) % 0.21/0.56 (define @t36 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.21/0.56 (define @t37 () (_ @t36 @t13)) % 0.21/0.56 (define @t38 () (lambda (@list @t36 @t14) (forall (@list @t13) (_ @t37 @t14)))) % 0.21/0.56 (define @t39 () (@var "P" (-> $$unsorted Bool))) % 0.21/0.56 (define @t40 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.21/0.56 (define @t41 () (_ @t40 @t39)) % 0.21/0.56 (define @t42 () (_ @t41 @t14)) % 0.21/0.56 (define @t43 () (@list @t39)) % 0.21/0.56 (define @t44 () (forall @t43 @t42)) % 0.21/0.56 (define @t45 () (@list @t40 @t14)) % 0.21/0.56 (define @t46 () (lambda @t45 @t44)) % 0.21/0.56 (define @t47 () (lambda (@list @t36 @t1) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t13 @t1) (_ (_ tptp.mnot @t37) @t1)))) @t1))) % 0.21/0.56 (define @t48 () (lambda (@list @t40 @t1) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t39 @t1) (_ (_ tptp.mnot @t41) @t1)))) @t1))) % 0.21/0.56 (define @t49 () (@list @t14)) % 0.21/0.56 (define @t50 () (lambda @t49 true)) % 0.21/0.56 (define @t51 () (@var "V" $$unsorted)) % 0.21/0.56 (define @t52 () (_ @t19 @t51)) % 0.21/0.56 (define @t53 () (_ (_ @t3 @t14) @t51)) % 0.21/0.56 (define @t54 () (not @t53)) % 0.21/0.56 (define @t55 () (or @t54 @t52)) % 0.21/0.56 (define @t56 () (@list @t51)) % 0.21/0.56 (define @t57 () (forall @t56 @t55)) % 0.21/0.56 (define @t58 () (@list @t3 @t19 @t14)) % 0.21/0.56 (define @t59 () (lambda @t58 @t57)) % 0.21/0.56 (define @t60 () (lambda (@list @t3 @t19 @t1) (_ (_ tptp.mnot (_ @t4 @t28)) @t1))) % 0.21/0.56 (define @t61 () (@var "S" $$unsorted)) % 0.21/0.56 (define @t62 () (_ @t3 @t61)) % 0.21/0.56 (define @t63 () (@list @t61)) % 0.21/0.56 (define @t64 () (lambda @t9 (forall @t63 (_ @t62 @t61)))) % 0.21/0.56 (define @t65 () (@var "T" $$unsorted)) % 0.21/0.56 (define @t66 () (_ @t3 @t65)) % 0.21/0.56 (define @t67 () (_ @t62 @t65)) % 0.21/0.56 (define @t68 () (lambda @t9 (forall (@list @t61 @t65) (=> @t67 (_ @t66 @t61))))) % 0.21/0.56 (define @t69 () (@list @t65)) % 0.21/0.56 (define @t70 () (lambda @t9 (forall @t63 (exists @t69 @t67)))) % 0.21/0.56 (define @t71 () (@var "U" $$unsorted)) % 0.21/0.56 (define @t72 () (_ @t62 @t71)) % 0.21/0.56 (define @t73 () (_ @t66 @t71)) % 0.21/0.56 (define @t74 () (and @t67 @t73)) % 0.21/0.56 (define @t75 () (@list @t61 @t65 @t71)) % 0.21/0.56 (define @t76 () (forall @t75 (=> @t74 @t72))) % 0.21/0.56 (define @t77 () (lambda @t9 @t76)) % 0.21/0.56 (define @t78 () (and @t67 @t72)) % 0.21/0.56 (define @t79 () (lambda @t9 (forall @t75 (=> @t78 @t73)))) % 0.21/0.56 (define @t80 () (= @t65 @t71)) % 0.21/0.56 (define @t81 () (lambda @t9 (forall @t75 (=> @t78 @t80)))) % 0.21/0.56 (define @t82 () (@list @t71)) % 0.21/0.56 (define @t83 () (lambda @t9 (forall @t63 (exists @t69 (and @t67 (forall @t82 (=> @t72 @t80))))))) % 0.21/0.56 (define @t84 () (_ @t3 @t71)) % 0.21/0.56 (define @t85 () (_ @t84 @t65)) % 0.21/0.56 (define @t86 () (lambda @t9 (forall @t75 (=> @t67 (exists @t82 (and @t72 @t85)))))) % 0.21/0.56 (define @t87 () (lambda @t9 (forall @t75 (=> @t78 (or @t73 @t80 @t85))))) % 0.21/0.56 (define @t88 () (lambda @t9 (forall @t75 (=> @t78 (exists @t56 (and (_ @t66 @t51) (_ @t84 @t51))))))) % 0.21/0.56 (define @t89 () (forall @t49 @t20)) % 0.21/0.56 (define @t90 () (@list @t19)) % 0.21/0.56 (define @t91 () (lambda @t90 @t89)) % 0.21/0.56 (define @t92 () (lambda @t90 (forall @t49 @t21))) % 0.21/0.56 (define @t93 () (lambda @t90 (exists @t49 @t20))) % 0.21/0.56 (define @t94 () (lambda @t90 (exists @t49 @t21))) % 0.21/0.56 (define @t95 () (@var "BOUND_VARIABLE_8447" $$unsorted)) % 0.21/0.56 (define @t96 () (@var "BOUND_VARIABLE_8443" (-> $$unsorted Bool))) % 0.21/0.56 (define @t97 () (_ @t96 @t95)) % 0.21/0.56 (define @t98 () (@var "BOUND_VARIABLE_8445" $$unsorted)) % 0.21/0.56 (define @t99 () (not (_ @t3 @t98 @t95))) % 0.21/0.56 (define @t100 () (@var "BOUND_VARIABLE_8441" $$unsorted)) % 0.21/0.56 (define @t101 () (not (_ @t3 @t100 @t98))) % 0.21/0.56 (define @t102 () (not (forall @t56 (or (not (_ @t3 @t100 @t51)) (_ @t96 @t51))))) % 0.21/0.56 (define @t103 () (_ @t3 @t61 @t71)) % 0.21/0.56 (define @t104 () (_ @t3 @t65 @t71)) % 0.21/0.56 (define @t105 () (_ @t3 @t61 @t65)) % 0.21/0.56 (define @t106 () (forall @t75 (or (not @t105) (not @t104) @t103))) % 0.21/0.56 (define @t107 () (not @t106)) % 0.21/0.56 (define @t108 () (or @t107 @t102 @t101 @t99 @t97)) % 0.21/0.56 (define @t109 () (or @t102 @t101 @t99 @t97)) % 0.21/0.56 (define @t110 () (or @t107 @t109)) % 0.21/0.56 (define @t111 () (@list @t3 @t100 @t96 @t98 @t95)) % 0.21/0.56 (define @t112 () (forall @t111 @t110)) % 0.21/0.56 (define @t113 () (@list @t100 @t96 @t98 @t95)) % 0.21/0.56 (define @t114 () (forall @t113 @t110)) % 0.21/0.56 (define @t115 () (forall @t113 @t109)) % 0.21/0.56 (define @t116 () (@var "BOUND_VARIABLE_8416" $$unsorted)) % 0.21/0.56 (define @t117 () (@var "BOUND_VARIABLE_8414" $$unsorted)) % 0.21/0.56 (define @t118 () (or @t107 @t115)) % 0.21/0.56 (define @t119 () (_ @t39 @t116)) % 0.21/0.56 (define @t120 () (not (_ @t3 @t117 @t116))) % 0.21/0.56 (define @t121 () (not (_ @t3 @t14 @t117))) % 0.21/0.56 (define @t122 () (_ @t3 @t14 @t51)) % 0.21/0.56 (define @t123 () (not @t122)) % 0.21/0.56 (define @t124 () (not (forall @t56 (or @t123 (_ @t39 @t51))))) % 0.21/0.56 (define @t125 () (or @t124 @t121 @t120 @t119)) % 0.21/0.56 (define @t126 () (forall (@list @t14 @t39 @t117 @t116) @t125)) % 0.21/0.56 (define @t127 () (@list @t39 @t117 @t116)) % 0.21/0.56 (define @t128 () (forall @t127 @t125)) % 0.21/0.56 (define @t129 () (lambda @t49 @t128)) % 0.21/0.56 (define @t130 () (_ @t129 @t14)) % 0.21/0.56 (define @t131 () (forall @t49 @t130)) % 0.21/0.56 (define @t132 () (_ @t19 @t14)) % 0.21/0.56 (define @t133 () (lambda @t90 (forall @t49 @t132))) % 0.21/0.56 (define @t134 () (or @t121 @t120 @t119)) % 0.21/0.56 (define @t135 () (or @t124 @t134)) % 0.21/0.56 (define @t136 () (forall @t127 @t135)) % 0.21/0.56 (define @t137 () (@list @t117 @t116)) % 0.21/0.56 (define @t138 () (forall @t137 @t135)) % 0.21/0.56 (define @t139 () (forall @t137 @t134)) % 0.21/0.56 (define @t140 () (@var "BOUND_VARIABLE_8378" $$unsorted)) % 0.21/0.56 (define @t141 () (or @t124 @t139)) % 0.21/0.56 (define @t142 () (not (_ @t3 @t51 @t140))) % 0.21/0.56 (define @t143 () (@list @t51 @t140)) % 0.21/0.56 (define @t144 () (or @t124 (forall @t143 (or @t123 @t142 (_ @t39 @t140))))) % 0.21/0.56 (define @t145 () (_ @t2 @t140)) % 0.21/0.56 (define @t146 () (not (_ @t3 @t1 @t51))) % 0.21/0.56 (define @t147 () (forall @t143 (or @t146 @t142 @t145))) % 0.21/0.56 (define @t148 () (_ @t2 @t51)) % 0.21/0.56 (define @t149 () (forall @t56 (or @t146 @t148))) % 0.21/0.56 (define @t150 () (not @t149)) % 0.21/0.56 (define @t151 () (or @t150 @t147)) % 0.21/0.56 (define @t152 () (lambda @t6 @t151)) % 0.21/0.56 (define @t153 () (_ @t152 @t39 @t14)) % 0.21/0.56 (define @t154 () (forall @t43 @t153)) % 0.21/0.56 (define @t155 () (lambda @t49 @t154)) % 0.21/0.56 (define @t156 () (_ @t40 @t39 @t14)) % 0.21/0.56 (define @t157 () (lambda @t45 (forall @t43 @t156))) % 0.21/0.56 (define @t158 () (@list @t1)) % 0.21/0.56 (define @t159 () (or @t123 @t142 @t145)) % 0.21/0.56 (define @t160 () (lambda @t49 (forall @t143 @t159))) % 0.21/0.56 (define @t161 () (_ @t160 @t1)) % 0.21/0.56 (define @t162 () (or @t150 @t161)) % 0.21/0.56 (define @t163 () (lambda @t158 @t162)) % 0.21/0.56 (define @t164 () (_ @t24 @t1)) % 0.21/0.56 (define @t165 () (@list @t24 @t1)) % 0.21/0.56 (define @t166 () (or @t142 @t145)) % 0.21/0.56 (define @t167 () (or @t123 @t166)) % 0.21/0.56 (define @t168 () (forall @t143 @t167)) % 0.21/0.56 (define @t169 () (@list @t140)) % 0.21/0.56 (define @t170 () (forall @t169 @t167)) % 0.21/0.56 (define @t171 () (forall @t169 @t166)) % 0.21/0.56 (define @t172 () (@var "BOUND_VARIABLE_8362" $$unsorted)) % 0.21/0.56 (define @t173 () (@list @t172)) % 0.21/0.56 (define @t174 () (or @t123 @t171)) % 0.21/0.56 (define @t175 () (_ @t2 @t172)) % 0.21/0.56 (define @t176 () (@list @t172)) % 0.21/0.56 (define @t177 () (forall @t176 (or (not (_ @t3 @t51 @t172)) @t175))) % 0.21/0.56 (define @t178 () (forall @t56 (or @t123 @t148))) % 0.21/0.56 (define @t179 () (lambda @t49 @t178)) % 0.21/0.56 (define @t180 () (or @t123 (_ @t179 @t51))) % 0.21/0.56 (define @t181 () (forall @t56 @t180)) % 0.21/0.56 (define @t182 () (lambda @t49 @t181)) % 0.21/0.56 (define @t183 () (_ @t19 @t51)) % 0.21/0.56 (define @t184 () (forall @t56 (or @t123 @t183))) % 0.21/0.56 (define @t185 () (lambda @t22 @t184)) % 0.21/0.56 (define @t186 () (_ (lambda @t58 @t184) @t3)) % 0.21/0.56 (define @t187 () (_ @t179 @t1)) % 0.21/0.56 (define @t188 () (not @t187)) % 0.21/0.56 (define @t189 () (or @t188 @t164)) % 0.21/0.56 (define @t190 () (lambda @t165 @t189)) % 0.21/0.56 (define @t191 () (or (not (_ @t19 @t1)) @t164)) % 0.21/0.56 (define @t192 () (lambda @t30 @t191)) % 0.21/0.56 (define @t193 () (_ @t186 @t2)) % 0.21/0.56 (define @t194 () (lambda @t6 (_ (_ (_ @t192 @t193) (_ @t186 @t193)) @t1))) % 0.21/0.56 (define @t195 () (_ (lambda @t9 @t106) @t3)) % 0.21/0.56 (define @t196 () (=> @t195 (_ @t133 (_ @t157 @t194)))) % 0.21/0.56 (define @t197 () (forall @t9 @t196)) % 0.21/0.56 (define @t198 () (or @t21 @t25)) % 0.21/0.56 (define @t199 () (lambda @t49 @t198)) % 0.21/0.56 (define @t200 () (@list @t24 @t14)) % 0.21/0.56 (define @t201 () (lambda @t49 @t21)) % 0.21/0.56 (define @t202 () (_ @t201 @t14)) % 0.21/0.56 (define @t203 () (or @t202 @t25)) % 0.21/0.56 (define @t204 () (lambda @t200 @t203)) % 0.21/0.56 (define @t205 () (not @t73)) % 0.21/0.56 (define @t206 () (not @t67)) % 0.21/0.56 (define @t207 () (or @t206 @t205 @t72)) % 0.21/0.56 (define @t208 () (forall @t111 @t108)) % 0.21/0.56 (define @t209 () (@quantifiers_skolemize @t208 4)) % 0.21/0.56 (define @t210 () (@quantifiers_skolemize @t208 2)) % 0.21/0.56 (define @t211 () (_ @t210 @t209)) % 0.21/0.56 (define @t212 () (@quantifiers_skolemize @t208 3)) % 0.21/0.56 (define @t213 () (@quantifiers_skolemize @t208 0)) % 0.21/0.56 (define @t214 () (_ @t213 @t212 @t209)) % 0.21/0.56 (define @t215 () (not @t214)) % 0.21/0.56 (define @t216 () (@quantifiers_skolemize @t208 1)) % 0.21/0.56 (define @t217 () (_ @t213 @t216 @t212)) % 0.21/0.56 (define @t218 () (not @t217)) % 0.21/0.56 (define @t219 () (forall @t56 (or (not (_ @t213 @t216 @t51)) (_ @t210 @t51)))) % 0.21/0.56 (define @t220 () (not @t219)) % 0.21/0.56 (define @t221 () (forall @t75 (or (not (_ @t213 @t61 @t65)) (not (_ @t213 @t65 @t71)) (_ @t213 @t61 @t71)))) % 0.21/0.56 (define @t222 () (not @t221)) % 0.21/0.56 (define @t223 () (or @t222 @t220 @t218 @t215 @t211)) % 0.21/0.56 (define @t224 () (@list true)) % 0.21/0.56 (define @t225 () (@list @t223)) % 0.21/0.56 (define @t226 () (_ @t213 @t216 @t209)) % 0.21/0.56 (define @t227 () (or @t218 @t215 @t226)) % 0.21/0.56 (define @t228 () (not @t226)) % 0.21/0.56 (define @t229 () (or @t228 @t211)) % 0.21/0.56 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.21/0.56 (assume @p2 @t11) % 0.21/0.56 (assume @p3 true) % 0.21/0.56 (step @p4 (= tptp.meq_ind @t15) :rule refl :args (@t15)) % 0.21/0.56 (step @p5 (= tptp.meq_prop @t18) :rule refl :args (@t18)) % 0.21/0.56 (step @p6 (= tptp.mnot @t23) :rule refl :args (@t23)) % 0.21/0.56 (step @p7 (= tptp.mor @t26) :rule refl :args (@t26)) % 0.21/0.56 (step @p8 (= tptp.mand @t31) :rule refl :args (@t31)) % 0.21/0.56 (step @p9 (= tptp.mimplies @t32) :rule refl :args (@t32)) % 0.21/0.56 (step @p10 (= tptp.mimplied @t33) :rule refl :args (@t33)) % 0.21/0.56 (step @p11 (= tptp.mequiv @t34) :rule refl :args (@t34)) % 0.21/0.56 (step @p12 (= tptp.mxor @t35) :rule refl :args (@t35)) % 0.21/0.56 (step @p13 (= tptp.mforall_ind @t38) :rule refl :args (@t38)) % 0.21/0.56 (step @p14 (= tptp.mforall_prop @t46) :rule refl :args (@t46)) % 0.21/0.56 (step @p15 (= tptp.mexists_ind @t47) :rule refl :args (@t47)) % 0.21/0.56 (step @p16 (= tptp.mexists_prop @t48) :rule refl :args (@t48)) % 0.21/0.56 (step @p17 (= tptp.mtrue @t50) :rule refl :args (@t50)) % 0.21/0.56 (step @p18 (= tptp.mbox @t59) :rule refl :args (@t59)) % 0.21/0.56 (step @p19 (= tptp.mdia @t60) :rule refl :args (@t60)) % 0.21/0.56 (step @p20 (= tptp.mreflexive @t64) :rule refl :args (@t64)) % 0.21/0.56 (step @p21 (= tptp.msymmetric @t68) :rule refl :args (@t68)) % 0.21/0.56 (step @p22 (= tptp.mserial @t70) :rule refl :args (@t70)) % 0.21/0.56 (step @p23 (= tptp.mtransitive @t77) :rule refl :args (@t77)) % 0.21/0.56 (step @p24 (= tptp.meuclidean @t79) :rule refl :args (@t79)) % 0.21/0.56 (step @p25 (= tptp.mpartially_functional @t81) :rule refl :args (@t81)) % 0.21/0.56 (step @p26 (= tptp.mfunctional @t83) :rule refl :args (@t83)) % 0.21/0.56 (step @p27 (= tptp.mweakly_dense @t86) :rule refl :args (@t86)) % 0.21/0.56 (step @p28 (= tptp.mweakly_connected @t87) :rule refl :args (@t87)) % 0.21/0.56 (step @p29 (= tptp.mweakly_directed @t88) :rule refl :args (@t88)) % 0.21/0.56 (step @p30 (= tptp.mvalid @t91) :rule refl :args (@t91)) % 0.21/0.56 (step @p31 (= tptp.minvalid @t92) :rule refl :args (@t92)) % 0.21/0.56 (step @p32 (= tptp.msatisfiable @t93) :rule refl :args (@t93)) % 0.21/0.56 (step @p33 (= tptp.mcountersatisfiable @t94) :rule refl :args (@t94)) % 0.21/0.56 (step @p34 :rule aci_norm :args ((= @t110 @t108))) % 0.21/0.56 (step @p35 :rule cong :premises (@p34) :args (@t112)) % 0.21/0.56 (step @p36 :rule quant-merge-prenex :args ((= (forall @t9 @t114) @t112))) % 0.21/0.56 (step @p37 :rule alpha_equiv :args (@t115 (@list @t100 @t96 @t98 @t95) (@list @t14 @t39 @t117 @t116))) % 0.21/0.56 (step @p38 :rule refl :args (@t107)) % 0.21/0.56 (step @p39 :rule nary_cong :premises (@p38 @p37) :args (@t118)) % 0.21/0.56 (step @p40 :rule quant-miniscope-or :args ((= @t114 @t118))) % 0.21/0.56 (step @p41 :rule trans :premises (@p40 @p39)) % 0.21/0.56 (step @p42 :rule symm :premises (@p41)) % 0.21/0.56 (step @p43 :rule cong :premises (@p42) :args ((forall @t9 (or @t107 @t126)))) % 0.21/0.56 (step @p44 :rule trans :premises (@p43 @p36)) % 0.21/0.56 (step @p45 :rule trans :premises (@p44 @p35)) % 0.21/0.56 (step @p46 :rule bool-impl-elim :args (@t106 @t126)) % 0.21/0.56 (step @p47 :rule cong :premises (@p46) :args ((forall @t9 (=> @t106 @t126)))) % 0.21/0.56 (step @p48 :rule trans :premises (@p47 @p45)) % 0.21/0.56 (step @p49 :rule quant-merge-prenex :args ((= (forall @t49 @t128) @t126))) % 0.21/0.56 (step @p50 :rule beta-reduce :args ((= @t130 @t128))) % 0.21/0.56 (step @p51 :rule cong :premises (@p50) :args (@t131)) % 0.21/0.56 (step @p52 :rule trans :premises (@p51 @p49)) % 0.21/0.56 (step @p53 :rule beta-reduce :args ((= (_ @t133 @t129) @t131))) % 0.21/0.56 (step @p54 :rule trans :premises (@p53 @p52)) % 0.21/0.56 (step @p55 :rule aci_norm :args ((= @t135 @t125))) % 0.21/0.56 (step @p56 :rule cong :premises (@p55) :args (@t136)) % 0.21/0.56 (step @p57 :rule quant-merge-prenex :args ((= (forall @t43 @t138) @t136))) % 0.21/0.56 (step @p58 :rule alpha_equiv :args (@t139 (@list @t117 @t116) (@list @t51 @t140))) % 0.21/0.56 (step @p59 :rule refl :args (@t124)) % 0.21/0.56 (step @p60 :rule nary_cong :premises (@p59 @p58) :args (@t141)) % 0.21/0.56 (step @p61 :rule quant-miniscope-or :args ((= @t138 @t141))) % 0.21/0.56 (step @p62 :rule trans :premises (@p61 @p60)) % 0.21/0.56 (step @p63 :rule symm :premises (@p62)) % 0.21/0.56 (step @p64 :rule cong :premises (@p63) :args ((forall @t43 @t144))) % 0.21/0.56 (step @p65 :rule trans :premises (@p64 @p57)) % 0.21/0.56 (step @p66 :rule trans :premises (@p65 @p56)) % 0.21/0.56 (step @p67 :rule beta-reduce :args ((= @t153 @t144))) % 0.21/0.56 (step @p68 :rule cong :premises (@p67) :args (@t154)) % 0.21/0.56 (step @p69 :rule trans :premises (@p68 @p66)) % 0.21/0.56 (step @p70 :rule cong :premises (@p69) :args (@t155)) % 0.21/0.56 (step @p71 :rule beta-reduce :args ((= (_ @t157 @t152) @t155))) % 0.21/0.56 (step @p72 :rule trans :premises (@p71 @p70)) % 0.21/0.56 (step @p73 :rule beta-reduce :args ((= (_ (lambda @t158 @t151) @t1) @t151))) % 0.21/0.56 (step @p74 :rule refl :args (@t1)) % 0.21/0.56 (step @p75 :rule beta-reduce :args ((= @t161 @t147))) % 0.21/0.56 (step @p76 :rule refl :args (@t150)) % 0.21/0.56 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t162)) % 0.21/0.56 (step @p78 :rule cong :premises (@p77) :args (@t163)) % 0.21/0.56 (step @p79 :rule beta-reduce :args ((= (_ (lambda @t165 (or @t150 @t164)) @t160) @t163))) % 0.22/0.56 (step @p80 :rule trans :premises (@p79 @p78)) % 0.22/0.56 (step @p81 :rule aci_norm :args ((= @t167 @t159))) % 0.22/0.56 (step @p82 :rule cong :premises (@p81) :args (@t168)) % 0.22/0.56 (step @p83 :rule quant-merge-prenex :args ((= (forall @t56 @t170) @t168))) % 0.22/0.56 (step @p84 :rule alpha_equiv :args (@t171 (@list @t140) @t173)) % 0.22/0.56 (step @p85 :rule refl :args (@t123)) % 0.22/0.56 (step @p86 :rule nary_cong :premises (@p85 @p84) :args (@t174)) % 0.22/0.56 (step @p87 :rule quant-miniscope-or :args ((= @t170 @t174))) % 0.22/0.56 (step @p88 :rule trans :premises (@p87 @p86)) % 0.22/0.56 (step @p89 :rule symm :premises (@p88)) % 0.22/0.56 (step @p90 :rule cong :premises (@p89) :args ((forall @t56 (or @t123 @t177)))) % 0.22/0.56 (step @p91 :rule trans :premises (@p90 @p83)) % 0.22/0.56 (step @p92 :rule trans :premises (@p91 @p82)) % 0.22/0.56 (step @p93 :rule beta-reduce :args ((= (_ (lambda @t49 (forall @t176 (or (not (_ @t3 @t14 @t172)) @t175))) @t51) @t177))) % 0.22/0.56 (step @p94 :rule refl :args (@t51)) % 0.22/0.56 (step @p95 :rule alpha_equiv :args (@t178 (@list @t51) @t173)) % 0.22/0.56 (step @p96 :rule cong :premises (@p95) :args (@t179)) % 0.22/0.56 (step @p97 :rule ho_cong :premises (@p96 @p94)) % 0.22/0.56 (step @p98 :rule trans :premises (@p97 @p93)) % 0.22/0.56 (step @p99 :rule refl :args (@t123)) % 0.22/0.56 (step @p100 :rule nary_cong :premises (@p99 @p98) :args (@t180)) % 0.22/0.56 (step @p101 :rule cong :premises (@p100) :args (@t181)) % 0.22/0.56 (step @p102 :rule trans :premises (@p101 @p92)) % 0.22/0.56 (step @p103 :rule cong :premises (@p102) :args (@t182)) % 0.22/0.56 (step @p104 :rule beta-reduce :args ((= (_ @t185 @t179) @t182))) % 0.22/0.56 (step @p105 :rule trans :premises (@p104 @p103)) % 0.22/0.56 (step @p106 :rule beta-reduce :args ((= (_ @t185 @t2) @t179))) % 0.22/0.56 (step @p107 :rule refl :args (@t2)) % 0.22/0.56 (step @p108 :rule beta-reduce :args ((= @t186 @t185))) % 0.22/0.56 (step @p109 :rule ho_cong :premises (@p108 @p107)) % 0.22/0.56 (step @p110 :rule trans :premises (@p109 @p106)) % 0.22/0.56 (step @p111 :rule ho_cong :premises (@p108 @p110)) % 0.22/0.56 (step @p112 :rule trans :premises (@p111 @p105)) % 0.22/0.56 (step @p113 :rule refl :args (@t164)) % 0.22/0.56 (step @p114 :rule beta-reduce :args ((= @t187 @t149))) % 0.22/0.56 (step @p115 :rule cong :premises (@p114) :args (@t188)) % 0.22/0.56 (step @p116 :rule nary_cong :premises (@p115 @p113) :args (@t189)) % 0.22/0.56 (step @p117 :rule cong :premises (@p116) :args (@t190)) % 0.22/0.56 (step @p118 :rule beta-reduce :args ((= (_ @t192 @t179) @t190))) % 0.22/0.56 (step @p119 :rule trans :premises (@p118 @p117)) % 0.22/0.56 (step @p120 :rule refl :args (@t192)) % 0.22/0.56 (step @p121 :rule ho_cong :premises (@p120 @p110)) % 0.22/0.56 (step @p122 :rule trans :premises (@p121 @p119)) % 0.22/0.56 (step @p123 :rule ho_cong :premises (@p122 @p112)) % 0.22/0.56 (step @p124 :rule trans :premises (@p123 @p80)) % 0.22/0.56 (step @p125 :rule ho_cong :premises (@p124 @p74)) % 0.22/0.56 (step @p126 :rule trans :premises (@p125 @p73)) % 0.22/0.56 (step @p127 :rule cong :premises (@p126) :args (@t194)) % 0.22/0.56 (step @p128 :rule refl :args (@t157)) % 0.22/0.56 (step @p129 :rule ho_cong :premises (@p128 @p127)) % 0.22/0.56 (step @p130 :rule trans :premises (@p129 @p72)) % 0.22/0.56 (step @p131 :rule refl :args (@t133)) % 0.22/0.56 (step @p132 :rule ho_cong :premises (@p131 @p130)) % 0.22/0.56 (step @p133 :rule trans :premises (@p132 @p54)) % 0.22/0.56 (step @p134 :rule beta-reduce :args ((= @t195 @t106))) % 0.22/0.56 (step @p135 :rule cong :premises (@p134 @p133) :args (@t196)) % 0.22/0.56 (step @p136 :rule cong :premises (@p135) :args (@t197)) % 0.22/0.56 (step @p137 :rule trans :premises (@p136 @p48)) % 0.22/0.56 (step @p138 :rule cong :premises (@p137) :args ((not @t197))) % 0.22/0.56 (step @p139 :rule refl :args (@t3)) % 0.22/0.56 (step @p140 :rule refl :args (@t183)) % 0.22/0.56 (step @p141 :rule refl :args (@t52)) % 0.22/0.56 (step @p142 :rule cong :premises (@p141 @p140) :args ((= @t52 @t183))) % 0.22/0.56 (step @p143 :rule symm :premises (@p142)) % 0.22/0.56 (step @p144 :rule eq_resolve :premises (@p141 @p143)) % 0.22/0.56 (step @p145 :rule refl :args (@t122)) % 0.22/0.56 (step @p146 :rule refl :args (@t53)) % 0.22/0.56 (step @p147 :rule cong :premises (@p146 @p145) :args ((= @t53 @t122))) % 0.22/0.56 (step @p148 :rule symm :premises (@p147)) % 0.22/0.56 (step @p149 :rule eq_resolve :premises (@p146 @p148)) % 0.22/0.56 (step @p150 :rule cong :premises (@p149) :args (@t54)) % 0.22/0.56 (step @p151 :rule nary_cong :premises (@p150 @p144) :args (@t55)) % 0.22/0.56 (step @p152 :rule cong :premises (@p151) :args (@t57)) % 0.22/0.56 (step @p153 :rule cong :premises (@p152) :args (@t59)) % 0.22/0.56 (step @p154 :rule trans :premises (@p18 @p153)) % 0.22/0.56 (step @p155 :rule ho_cong :premises (@p154 @p139)) % 0.22/0.56 (step @p156 :rule ho_cong :premises (@p155 @p107)) % 0.22/0.56 (step @p157 :rule ho_cong :premises (@p155 @p156)) % 0.22/0.56 (step @p158 :rule beta-reduce :args ((= (_ @t199 @t1) @t191))) % 0.22/0.56 (step @p159 :rule beta-reduce :args ((= (_ (lambda @t200 @t198) @t24) @t199))) % 0.22/0.56 (step @p160 :rule refl :args (@t24)) % 0.22/0.56 (step @p161 :rule refl :args (@t25)) % 0.22/0.56 (step @p162 :rule beta-reduce :args ((= @t202 @t21))) % 0.22/0.56 (step @p163 :rule nary_cong :premises (@p162 @p161) :args (@t203)) % 0.22/0.56 (step @p164 :rule cong :premises (@p163) :args (@t204)) % 0.22/0.56 (step @p165 :rule beta-reduce :args ((= (_ @t26 @t201) @t204))) % 0.22/0.56 (step @p166 :rule trans :premises (@p165 @p164)) % 0.22/0.56 (step @p167 :rule beta-reduce :args ((= (_ @t23 @t19) @t201))) % 0.22/0.56 (step @p168 :rule refl :args (@t26)) % 0.22/0.56 (step @p169 :rule ho_cong :premises (@p168 @p167)) % 0.22/0.56 (step @p170 :rule trans :premises (@p169 @p166)) % 0.22/0.56 (step @p171 :rule ho_cong :premises (@p170 @p160)) % 0.22/0.56 (step @p172 :rule trans :premises (@p171 @p159)) % 0.22/0.56 (step @p173 :rule ho_cong :premises (@p172 @p74)) % 0.22/0.56 (step @p174 :rule trans :premises (@p173 @p158)) % 0.22/0.56 (step @p175 :rule refl :args (@t19)) % 0.22/0.56 (step @p176 :rule ho_cong :premises (@p6 @p175)) % 0.22/0.56 (step @p177 :rule ho_cong :premises (@p7 @p176)) % 0.22/0.56 (step @p178 :rule ho_cong :premises (@p177 @p160)) % 0.22/0.56 (step @p179 :rule ho_cong :premises (@p178 @p74)) % 0.22/0.56 (step @p180 :rule trans :premises (@p179 @p174)) % 0.22/0.56 (step @p181 :rule cong :premises (@p180) :args (@t32)) % 0.22/0.56 (step @p182 :rule trans :premises (@p9 @p181)) % 0.22/0.56 (step @p183 :rule ho_cong :premises (@p182 @p156)) % 0.22/0.56 (step @p184 :rule ho_cong :premises (@p183 @p157)) % 0.22/0.56 (step @p185 :rule ho_cong :premises (@p184 @p74)) % 0.22/0.56 (step @p186 :rule cong :premises (@p185) :args (@t7)) % 0.22/0.56 (step @p187 :rule refl :args (@t156)) % 0.22/0.56 (step @p188 :rule refl :args (@t42)) % 0.22/0.56 (step @p189 :rule cong :premises (@p188 @p187) :args ((= @t42 @t156))) % 0.22/0.56 (step @p190 :rule symm :premises (@p189)) % 0.22/0.56 (step @p191 :rule eq_resolve :premises (@p188 @p190)) % 0.22/0.56 (step @p192 :rule cong :premises (@p191) :args (@t44)) % 0.22/0.56 (step @p193 :rule cong :premises (@p192) :args (@t46)) % 0.22/0.56 (step @p194 :rule trans :premises (@p14 @p193)) % 0.22/0.56 (step @p195 :rule ho_cong :premises (@p194 @p186)) % 0.22/0.56 (step @p196 :rule refl :args (@t132)) % 0.22/0.56 (step @p197 :rule refl :args (@t20)) % 0.22/0.56 (step @p198 :rule cong :premises (@p197 @p196) :args ((= @t20 @t132))) % 0.22/0.56 (step @p199 :rule symm :premises (@p198)) % 0.22/0.56 (step @p200 :rule eq_resolve :premises (@p197 @p199)) % 0.22/0.56 (step @p201 :rule cong :premises (@p200) :args (@t89)) % 0.22/0.56 (step @p202 :rule cong :premises (@p201) :args (@t91)) % 0.22/0.56 (step @p203 :rule trans :premises (@p30 @p202)) % 0.22/0.56 (step @p204 :rule ho_cong :premises (@p203 @p195)) % 0.22/0.56 (step @p205 :rule refl :args (@t103)) % 0.22/0.56 (step @p206 :rule refl :args (@t72)) % 0.22/0.56 (step @p207 :rule cong :premises (@p206 @p205) :args ((= @t72 @t103))) % 0.22/0.56 (step @p208 :rule symm :premises (@p207)) % 0.22/0.56 (step @p209 :rule eq_resolve :premises (@p206 @p208)) % 0.22/0.56 (step @p210 :rule refl :args (@t104)) % 0.22/0.56 (step @p211 :rule refl :args (@t73)) % 0.22/0.56 (step @p212 :rule cong :premises (@p211 @p210) :args ((= @t73 @t104))) % 0.22/0.56 (step @p213 :rule symm :premises (@p212)) % 0.22/0.56 (step @p214 :rule eq_resolve :premises (@p211 @p213)) % 0.22/0.56 (step @p215 :rule cong :premises (@p214) :args (@t205)) % 0.22/0.56 (step @p216 :rule refl :args (@t105)) % 0.22/0.56 (step @p217 :rule refl :args (@t67)) % 0.22/0.56 (step @p218 :rule cong :premises (@p217 @p216) :args ((= @t67 @t105))) % 0.22/0.56 (step @p219 :rule symm :premises (@p218)) % 0.22/0.56 (step @p220 :rule eq_resolve :premises (@p217 @p219)) % 0.22/0.56 (step @p221 :rule cong :premises (@p220) :args (@t206)) % 0.22/0.56 (step @p222 :rule nary_cong :premises (@p221 @p215 @p209) :args (@t207)) % 0.22/0.56 (step @p223 :rule cong :premises (@p222) :args ((forall @t75 @t207))) % 0.22/0.56 (step @p224 :rule aci_norm :args ((= (or (or @t206 @t205) @t72) @t207))) % 0.22/0.56 (step @p225 :rule bool-and-de-morgan :args (@t67 @t73 true)) % 0.22/0.56 (step @p226 :rule nary_cong :premises (@p225 @p206) :args ((or (not @t74) @t72))) % 0.22/0.56 (step @p227 :rule trans :premises (@p226 @p224)) % 0.22/0.56 (step @p228 :rule bool-impl-elim :args (@t74 @t72)) % 0.22/0.56 (step @p229 :rule trans :premises (@p228 @p227)) % 0.22/0.56 (step @p230 :rule cong :premises (@p229) :args (@t76)) % 0.22/0.56 (step @p231 :rule trans :premises (@p230 @p223)) % 0.22/0.56 (step @p232 :rule cong :premises (@p231) :args (@t77)) % 0.22/0.56 (step @p233 :rule trans :premises (@p23 @p232)) % 0.22/0.56 (step @p234 :rule ho_cong :premises (@p233 @p139)) % 0.22/0.56 (step @p235 :rule cong :premises (@p234 @p204) :args (@t8)) % 0.22/0.56 (step @p236 :rule cong :premises (@p235) :args (@t10)) % 0.22/0.56 (step @p237 :rule cong :premises (@p236) :args (@t11)) % 0.22/0.56 (step @p238 :rule trans :premises (@p237 @p138)) % 0.22/0.56 (step @p239 :rule eq_resolve :premises (@p2 @p238)) % 0.22/0.56 (step @p240 :rule skolemize :premises (@p239)) % 0.22/0.56 (step @p241 :rule cnf_or_neg :args (@t223 4)) % 0.22/0.56 (step @p242 :rule chain_m_resolution :premises (@p241 @p240) :args ((not @t211) @t224 @t225)) % 0.22/0.56 (step @p243 :rule bool-double-not-elim :args (@t219)) % 0.22/0.56 (step @p244 :rule refl :args (@t223)) % 0.22/0.56 (step @p245 :rule nary_cong :premises (@p244 @p243) :args ((or @t223 (not @t220)))) % 0.22/0.56 (step @p246 :rule cnf_or_neg :args (@t223 1)) % 0.22/0.56 (step @p247 :rule eq_resolve :premises (@p246 @p245)) % 0.22/0.56 (step @p248 :rule reordering :premises (@p247) :args ((or @t219 @t223))) % 0.22/0.56 (step @p249 :rule chain_m_resolution :premises (@p248 @p240) :args (@t219 @t224 @t225)) % 0.22/0.56 (step @p250 :rule instantiate :premises (@p249) :args ((@list @t209))) % 0.22/0.56 (step @p251 :rule bool-double-not-elim :args (@t221)) % 0.22/0.56 (step @p252 :rule nary_cong :premises (@p244 @p251) :args ((or @t223 (not @t222)))) % 0.22/0.56 (step @p253 :rule cnf_or_neg :args (@t223 0)) % 0.22/0.56 (step @p254 :rule eq_resolve :premises (@p253 @p252)) % 0.22/0.56 (step @p255 :rule reordering :premises (@p254) :args ((or @t221 @t223))) % 0.22/0.56 (step @p256 :rule chain_m_resolution :premises (@p255 @p240) :args (@t221 @t224 @t225)) % 0.22/0.56 (step @p257 :rule instantiate :premises (@p256) :args ((@list @t216 @t212 @t209))) % 0.22/0.56 (step @p258 :rule bool-double-not-elim :args (@t214)) % 0.22/0.56 (step @p259 :rule nary_cong :premises (@p244 @p258) :args ((or @t223 (not @t215)))) % 0.22/0.56 (step @p260 :rule cnf_or_neg :args (@t223 3)) % 0.22/0.56 (step @p261 :rule eq_resolve :premises (@p260 @p259)) % 0.22/0.56 (step @p262 :rule reordering :premises (@p261) :args ((or @t214 @t223))) % 0.22/0.56 (step @p263 :rule chain_m_resolution :premises (@p262 @p240) :args (@t214 @t224 @t225)) % 0.22/0.56 (step @p264 :rule bool-double-not-elim :args (@t217)) % 0.22/0.56 (step @p265 :rule nary_cong :premises (@p244 @p264) :args ((or @t223 (not @t218)))) % 0.22/0.56 (step @p266 :rule cnf_or_neg :args (@t223 2)) % 0.22/0.56 (step @p267 :rule eq_resolve :premises (@p266 @p265)) % 0.22/0.56 (step @p268 :rule reordering :premises (@p267) :args ((or @t217 @t223))) % 0.22/0.56 (step @p269 :rule chain_m_resolution :premises (@p268 @p240) :args (@t217 @t224 @t225)) % 0.22/0.56 (step @p270 :rule cnf_or_pos :args (@t227)) % 0.22/0.56 (step @p271 :rule reordering :premises (@p270) :args ((or @t218 @t215 @t226 (not @t227)))) % 0.22/0.56 (step @p272 :rule chain_m_resolution :premises (@p271 @p269 @p263 @p257) :args (@t226 (@list false false false) (@list @t217 @t214 @t227))) % 0.22/0.56 (step @p273 :rule cnf_or_pos :args (@t229)) % 0.22/0.56 (step @p274 :rule reordering :premises (@p273) :args ((or @t211 @t228 (not @t229)))) % 0.22/0.56 (step @p275 false :rule chain_m_resolution :premises (@p274 @p272 @p250 @p242) :args (false (@list false false true) (@list @t226 @t229 @t211))) % 0.22/0.56 ) % 0.22/0.56 % SZS output end Proof % 0.22/0.56 % cvc5 exiting %------------------------------------------------------------------------------