%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PUZ085^1 : 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 : n001.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 08:44:10 AM UTC 2026 % Result : Theorem 0.37s 0.61s % Output : Proof 0.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PUZ085^1 : 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 : n001.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 : Tue Jun 2 13:18:05 EDT 2026 % 0.16/0.34 % CPUTime : % 0.28/0.50 %----Proving TH0 % 0.37/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.37/0.61 % SZS status Theorem % 0.37/0.61 % SZS output start Proof % 0.37/0.61 ( % 0.37/0.61 (declare-sort $$unsorted 0) % 0.37/0.61 (declare-sort tptp.mu 0) % 0.37/0.61 (declare-const tptp.wife (-> (-> $$unsorted $$unsorted Bool) $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.john (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.peter (-> $$unsorted $$unsorted Bool)) % 0.37/0.61 (declare-const tptp.mfalse (-> $$unsorted Bool)) % 0.37/0.61 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.37/0.61 (define tptp.meq_prop () (let ((_let_1 (@var "W" $$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))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (define tptp.mor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.mand () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (define tptp.mimplies () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (_ (_ (_ tptp.mor (_ tptp.mnot _let_3)) _let_2) _let_1)))))) % 0.37/0.61 (define tptp.mimplied () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (define tptp.mequiv () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (_ (_ (_ tptp.mand (_ (_ tptp.mimplies _let_2) _let_3)) (_ (_ tptp.mimplies _let_3) _let_2)) _let_1)))))) % 0.37/0.61 (define tptp.mxor () (let ((_let_1 (@var "__flatten_var_0" $$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)))))) % 0.37/0.61 (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))))))) % 0.37/0.61 (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))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.37/0.61 (define tptp.mbox () (let ((_let_1 (@var "V" $$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))))))))) % 0.37/0.61 (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)))))) % 0.37/0.61 (define tptp.mreflexive () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ (_ _let_2 _let_1) _let_1)))))) % 0.37/0.61 (define tptp.msymmetric () (let ((_let_1 (@var "S" $$unsorted))) (let ((_let_2 (@var "T" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_1 _let_2) (=> (_ (_ _let_3 _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mserial () (let ((_let_1 (@var "T" $$unsorted))) (let ((_let_2 (@var "S" $$unsorted))) (let ((_let_3 (@var "R" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_3) (forall (@list _let_2) (exists (@list _let_1) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.37/0.61 (define tptp.mtransitive () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_2 _let_1) (=> (and (_ _let_5 _let_2) (_ _let_5 _let_1)) (_ (_ _let_3 _let_2) _let_1)))))))))) % 0.37/0.61 (define tptp.mpartially_functional () (let ((_let_1 (@var "U" $$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)))))))))) % 0.37/0.61 (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 $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_3))) (lambda (@list _let_4) (forall (@list _let_3) (exists (@list _let_2) (and (_ _let_5 _let_2) (forall (@list _let_1) (=> (_ _let_5 _let_1) (= _let_2 _let_1))))))))))))) % 0.37/0.61 (define tptp.mweakly_dense () (let ((_let_1 (@var "T" $$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)))))))))))) % 0.37/0.61 (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" $$unsorted))) (let ((_let_5 (_ _let_3 _let_4))) (lambda (@list _let_3) (forall (@list _let_4 _let_1 _let_2) (=> (and (_ _let_5 _let_1) (_ _let_5 _let_2)) (or (_ (_ _let_3 _let_1) _let_2) (= _let_1 _let_2) (_ (_ _let_3 _let_2) _let_1))))))))))) % 0.37/0.61 (define tptp.mweakly_directed () (let ((_let_1 (@var "V" $$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" $$unsorted))) (let ((_let_6 (_ _let_3 _let_5))) (lambda (@list _let_3) (forall (@list _let_5 _let_4 _let_2) (=> (and (_ _let_6 _let_4) (_ _let_6 _let_2)) (exists (@list _let_1) (and (_ (_ _let_3 _let_4) _let_1) (_ (_ _let_3 _let_2) _let_1))))))))))))) % 0.37/0.61 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.61 (define tptp.msatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (_ _let_2 _let_1)))))) % 0.37/0.61 (define tptp.mcountersatisfiable () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (exists (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.37/0.61 (define @t1 () (_ tptp.wife tptp.peter)) % 0.37/0.61 (define @t2 () (@var "__flatten_var_0" $$unsorted)) % 0.37/0.61 (define @t3 () (@var "A" (-> $$unsorted Bool))) % 0.37/0.61 (define @t4 () (_ tptp.mbox @t1)) % 0.37/0.61 (define @t5 () (_ @t4 @t3)) % 0.37/0.61 (define @t6 () (@list @t3 @t2)) % 0.37/0.61 (define @t7 () (lambda @t6 (_ (_ (_ tptp.mimplies @t5) (_ @t4 @t5)) @t2))) % 0.37/0.61 (define @t8 () (not (_ tptp.mvalid (_ tptp.mforall_prop @t7)))) % 0.37/0.61 (define @t9 () (@var "Y" tptp.mu)) % 0.37/0.61 (define @t10 () (@var "X" tptp.mu)) % 0.37/0.61 (define @t11 () (@var "W" $$unsorted)) % 0.37/0.61 (define @t12 () (lambda (@list @t10 @t9 @t11) (= @t10 @t9))) % 0.37/0.61 (define @t13 () (@var "Y" (-> $$unsorted Bool))) % 0.37/0.61 (define @t14 () (@var "X" (-> $$unsorted Bool))) % 0.37/0.61 (define @t15 () (lambda (@list @t14 @t13 @t11) (= (_ @t14 @t11) (_ @t13 @t11)))) % 0.37/0.61 (define @t16 () (@var "Phi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t17 () (_ @t16 @t11)) % 0.37/0.61 (define @t18 () (not @t17)) % 0.37/0.61 (define @t19 () (@list @t16 @t11)) % 0.37/0.61 (define @t20 () (lambda @t19 @t18)) % 0.37/0.61 (define @t21 () (@var "Psi" (-> $$unsorted Bool))) % 0.37/0.61 (define @t22 () (_ @t21 @t11)) % 0.37/0.61 (define @t23 () (lambda (@list @t16 @t21 @t11) (or @t17 @t22))) % 0.37/0.61 (define @t24 () (_ tptp.mnot @t21)) % 0.37/0.61 (define @t25 () (_ tptp.mnot @t16)) % 0.37/0.61 (define @t26 () (_ tptp.mor @t25)) % 0.37/0.61 (define @t27 () (@list @t16 @t21 @t2)) % 0.37/0.61 (define @t28 () (lambda @t27 (_ (_ tptp.mnot (_ @t26 @t24)) @t2))) % 0.37/0.61 (define @t29 () (lambda @t27 (_ (_ @t26 @t21) @t2))) % 0.37/0.61 (define @t30 () (lambda @t27 (_ (_ (_ tptp.mor @t24) @t16) @t2))) % 0.37/0.61 (define @t31 () (lambda @t27 (_ (_ (_ tptp.mand (_ (_ tptp.mimplies @t16) @t21)) (_ (_ tptp.mimplies @t21) @t16)) @t2))) % 0.37/0.61 (define @t32 () (lambda @t27 (_ (_ tptp.mnot (_ (_ tptp.mequiv @t16) @t21)) @t2))) % 0.37/0.61 (define @t33 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.37/0.61 (define @t34 () (_ @t33 @t10)) % 0.37/0.61 (define @t35 () (lambda (@list @t33 @t11) (forall (@list @t10) (_ @t34 @t11)))) % 0.37/0.61 (define @t36 () (@var "P" (-> $$unsorted Bool))) % 0.37/0.61 (define @t37 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.37/0.61 (define @t38 () (_ @t37 @t36)) % 0.37/0.61 (define @t39 () (_ @t38 @t11)) % 0.37/0.61 (define @t40 () (@list @t36)) % 0.37/0.61 (define @t41 () (forall @t40 @t39)) % 0.37/0.61 (define @t42 () (@list @t37 @t11)) % 0.37/0.61 (define @t43 () (lambda @t42 @t41)) % 0.37/0.61 (define @t44 () (lambda (@list @t33 @t2) (_ (_ tptp.mnot (_ tptp.mforall_ind (lambda (@list @t10 @t2) (_ (_ tptp.mnot @t34) @t2)))) @t2))) % 0.37/0.61 (define @t45 () (lambda (@list @t37 @t2) (_ (_ tptp.mnot (_ tptp.mforall_prop (lambda (@list @t36 @t2) (_ (_ tptp.mnot @t38) @t2)))) @t2))) % 0.37/0.61 (define @t46 () (@list @t11)) % 0.37/0.61 (define @t47 () (lambda @t46 true)) % 0.37/0.61 (define @t48 () (@var "V" $$unsorted)) % 0.37/0.61 (define @t49 () (_ @t16 @t48)) % 0.37/0.61 (define @t50 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.37/0.61 (define @t51 () (_ (_ @t50 @t11) @t48)) % 0.37/0.61 (define @t52 () (not @t51)) % 0.37/0.61 (define @t53 () (or @t52 @t49)) % 0.37/0.61 (define @t54 () (@list @t48)) % 0.37/0.61 (define @t55 () (forall @t54 @t53)) % 0.37/0.61 (define @t56 () (@list @t50 @t16 @t11)) % 0.37/0.61 (define @t57 () (lambda @t56 @t55)) % 0.37/0.61 (define @t58 () (lambda (@list @t50 @t16 @t2) (_ (_ tptp.mnot (_ (_ tptp.mbox @t50) @t25)) @t2))) % 0.37/0.61 (define @t59 () (@var "S" $$unsorted)) % 0.37/0.61 (define @t60 () (_ @t50 @t59)) % 0.37/0.61 (define @t61 () (@list @t59)) % 0.37/0.61 (define @t62 () (@list @t50)) % 0.37/0.61 (define @t63 () (lambda @t62 (forall @t61 (_ @t60 @t59)))) % 0.37/0.61 (define @t64 () (@var "T" $$unsorted)) % 0.37/0.61 (define @t65 () (_ @t50 @t64)) % 0.37/0.61 (define @t66 () (_ @t60 @t64)) % 0.37/0.61 (define @t67 () (lambda @t62 (forall (@list @t59 @t64) (=> @t66 (_ @t65 @t59))))) % 0.37/0.61 (define @t68 () (@list @t64)) % 0.37/0.61 (define @t69 () (lambda @t62 (forall @t61 (exists @t68 @t66)))) % 0.37/0.61 (define @t70 () (@var "U" $$unsorted)) % 0.37/0.61 (define @t71 () (_ @t60 @t70)) % 0.37/0.61 (define @t72 () (_ @t65 @t70)) % 0.37/0.61 (define @t73 () (and @t66 @t72)) % 0.37/0.61 (define @t74 () (@list @t59 @t64 @t70)) % 0.37/0.61 (define @t75 () (forall @t74 (=> @t73 @t71))) % 0.37/0.61 (define @t76 () (lambda @t62 @t75)) % 0.37/0.61 (define @t77 () (and @t66 @t71)) % 0.37/0.61 (define @t78 () (lambda @t62 (forall @t74 (=> @t77 @t72)))) % 0.37/0.61 (define @t79 () (= @t64 @t70)) % 0.37/0.61 (define @t80 () (lambda @t62 (forall @t74 (=> @t77 @t79)))) % 0.37/0.61 (define @t81 () (@list @t70)) % 0.37/0.61 (define @t82 () (lambda @t62 (forall @t61 (exists @t68 (and @t66 (forall @t81 (=> @t71 @t79))))))) % 0.37/0.61 (define @t83 () (_ @t50 @t70)) % 0.37/0.61 (define @t84 () (_ @t83 @t64)) % 0.37/0.61 (define @t85 () (lambda @t62 (forall @t74 (=> @t66 (exists @t81 (and @t71 @t84)))))) % 0.37/0.61 (define @t86 () (lambda @t62 (forall @t74 (=> @t77 (or @t72 @t79 @t84))))) % 0.37/0.61 (define @t87 () (lambda @t62 (forall @t74 (=> @t77 (exists @t54 (and (_ @t65 @t48) (_ @t83 @t48))))))) % 0.37/0.61 (define @t88 () (forall @t46 @t17)) % 0.37/0.61 (define @t89 () (@list @t16)) % 0.37/0.61 (define @t90 () (lambda @t89 @t88)) % 0.37/0.61 (define @t91 () (lambda @t89 (forall @t46 @t18))) % 0.37/0.61 (define @t92 () (lambda @t89 (exists @t46 @t17))) % 0.37/0.61 (define @t93 () (lambda @t89 (exists @t46 @t18))) % 0.37/0.61 (define @t94 () (@var "BOUND_VARIABLE_8500" $$unsorted)) % 0.37/0.61 (define @t95 () (_ @t36 @t94)) % 0.37/0.61 (define @t96 () (@var "BOUND_VARIABLE_8498" $$unsorted)) % 0.37/0.61 (define @t97 () (not (tptp.wife tptp.peter @t96 @t94))) % 0.37/0.61 (define @t98 () (not (tptp.wife tptp.peter @t11 @t96))) % 0.37/0.61 (define @t99 () (tptp.wife tptp.peter @t11 @t48)) % 0.37/0.61 (define @t100 () (not @t99)) % 0.37/0.61 (define @t101 () (not (forall @t54 (or @t100 (_ @t36 @t48))))) % 0.37/0.61 (define @t102 () (or @t101 @t98 @t97 @t95)) % 0.37/0.61 (define @t103 () (forall (@list @t11 @t36 @t96 @t94) @t102)) % 0.37/0.61 (define @t104 () (@list @t36 @t96 @t94)) % 0.37/0.61 (define @t105 () (forall @t104 @t102)) % 0.37/0.61 (define @t106 () (lambda @t46 @t105)) % 0.37/0.61 (define @t107 () (_ @t106 @t11)) % 0.37/0.61 (define @t108 () (forall @t46 @t107)) % 0.37/0.61 (define @t109 () (_ @t16 @t11)) % 0.37/0.61 (define @t110 () (lambda @t89 (forall @t46 @t109))) % 0.37/0.61 (define @t111 () (or @t98 @t97 @t95)) % 0.37/0.61 (define @t112 () (or @t101 @t111)) % 0.37/0.61 (define @t113 () (forall @t104 @t112)) % 0.37/0.61 (define @t114 () (@list @t96 @t94)) % 0.37/0.61 (define @t115 () (forall @t114 @t112)) % 0.37/0.61 (define @t116 () (forall @t114 @t111)) % 0.37/0.61 (define @t117 () (@var "BOUND_VARIABLE_8462" $$unsorted)) % 0.37/0.61 (define @t118 () (or @t101 @t116)) % 0.37/0.61 (define @t119 () (not (tptp.wife tptp.peter @t48 @t117))) % 0.37/0.61 (define @t120 () (@list @t48 @t117)) % 0.37/0.61 (define @t121 () (or @t101 (forall @t120 (or @t100 @t119 (_ @t36 @t117))))) % 0.37/0.61 (define @t122 () (_ @t3 @t117)) % 0.37/0.61 (define @t123 () (not (tptp.wife tptp.peter @t2 @t48))) % 0.37/0.61 (define @t124 () (forall @t120 (or @t123 @t119 @t122))) % 0.37/0.61 (define @t125 () (_ @t3 @t48)) % 0.37/0.61 (define @t126 () (forall @t54 (or @t123 @t125))) % 0.37/0.61 (define @t127 () (not @t126)) % 0.37/0.61 (define @t128 () (or @t127 @t124)) % 0.37/0.61 (define @t129 () (lambda @t6 @t128)) % 0.37/0.61 (define @t130 () (_ @t129 @t36 @t11)) % 0.37/0.61 (define @t131 () (forall @t40 @t130)) % 0.37/0.61 (define @t132 () (lambda @t46 @t131)) % 0.37/0.61 (define @t133 () (_ @t37 @t36 @t11)) % 0.37/0.61 (define @t134 () (lambda @t42 (forall @t40 @t133))) % 0.37/0.61 (define @t135 () (@list @t2)) % 0.37/0.61 (define @t136 () (or @t100 @t119 @t122)) % 0.37/0.61 (define @t137 () (lambda @t46 (forall @t120 @t136))) % 0.37/0.61 (define @t138 () (_ @t137 @t2)) % 0.37/0.61 (define @t139 () (or @t127 @t138)) % 0.37/0.61 (define @t140 () (lambda @t135 @t139)) % 0.37/0.61 (define @t141 () (_ @t21 @t2)) % 0.37/0.61 (define @t142 () (@list @t21 @t2)) % 0.37/0.61 (define @t143 () (or @t119 @t122)) % 0.37/0.61 (define @t144 () (or @t100 @t143)) % 0.37/0.61 (define @t145 () (forall @t120 @t144)) % 0.37/0.61 (define @t146 () (@list @t117)) % 0.37/0.61 (define @t147 () (forall @t146 @t144)) % 0.37/0.61 (define @t148 () (forall @t146 @t143)) % 0.37/0.61 (define @t149 () (@var "BOUND_VARIABLE_8446" $$unsorted)) % 0.37/0.61 (define @t150 () (@list @t149)) % 0.37/0.61 (define @t151 () (or @t100 @t148)) % 0.37/0.61 (define @t152 () (_ @t3 @t149)) % 0.37/0.61 (define @t153 () (@list @t149)) % 0.37/0.61 (define @t154 () (forall @t153 (or (not (tptp.wife tptp.peter @t48 @t149)) @t152))) % 0.37/0.61 (define @t155 () (forall @t54 (or @t100 @t125))) % 0.37/0.61 (define @t156 () (lambda @t46 @t155)) % 0.37/0.61 (define @t157 () (or @t100 (_ @t156 @t48))) % 0.37/0.61 (define @t158 () (forall @t54 @t157)) % 0.37/0.61 (define @t159 () (lambda @t46 @t158)) % 0.37/0.61 (define @t160 () (_ @t16 @t48)) % 0.37/0.61 (define @t161 () (lambda @t19 (forall @t54 (or @t100 @t160)))) % 0.37/0.61 (define @t162 () (_ (_ @t1 @t11) @t48)) % 0.37/0.61 (define @t163 () (not @t162)) % 0.37/0.61 (define @t164 () (or @t163 @t160)) % 0.37/0.61 (define @t165 () (_ @t1 @t11 @t48)) % 0.37/0.61 (define @t166 () (not @t165)) % 0.37/0.61 (define @t167 () (or @t166 @t160)) % 0.37/0.61 (define @t168 () (forall @t54 @t167)) % 0.37/0.61 (define @t169 () (lambda @t19 @t168)) % 0.37/0.61 (define @t170 () (_ @t50 @t11 @t48)) % 0.37/0.61 (define @t171 () (_ (lambda @t56 (forall @t54 (or (not @t170) @t160))) @t1)) % 0.37/0.61 (define @t172 () (_ @t156 @t2)) % 0.37/0.61 (define @t173 () (not @t172)) % 0.37/0.61 (define @t174 () (or @t173 @t141)) % 0.37/0.61 (define @t175 () (lambda @t142 @t174)) % 0.37/0.61 (define @t176 () (or (not (_ @t16 @t2)) @t141)) % 0.37/0.61 (define @t177 () (lambda @t27 @t176)) % 0.37/0.61 (define @t178 () (_ @t171 @t3)) % 0.37/0.61 (define @t179 () (lambda @t6 (_ (_ (_ @t177 @t178) (_ @t171 @t178)) @t2))) % 0.37/0.61 (define @t180 () (or @t18 @t22)) % 0.37/0.61 (define @t181 () (lambda @t46 @t180)) % 0.37/0.61 (define @t182 () (@list @t21 @t11)) % 0.37/0.61 (define @t183 () (lambda @t46 @t18)) % 0.37/0.61 (define @t184 () (_ @t183 @t11)) % 0.37/0.61 (define @t185 () (or @t184 @t22)) % 0.37/0.61 (define @t186 () (lambda @t182 @t185)) % 0.37/0.61 (define @t187 () (@quantifiers_skolemize @t103 3)) % 0.37/0.61 (define @t188 () (@quantifiers_skolemize @t103 1)) % 0.37/0.61 (define @t189 () (_ @t188 @t187)) % 0.37/0.61 (define @t190 () (@quantifiers_skolemize @t103 2)) % 0.37/0.61 (define @t191 () (tptp.wife tptp.peter @t190 @t187)) % 0.37/0.61 (define @t192 () (not @t191)) % 0.37/0.61 (define @t193 () (@quantifiers_skolemize @t103 0)) % 0.37/0.61 (define @t194 () (tptp.wife tptp.peter @t193 @t190)) % 0.37/0.61 (define @t195 () (not @t194)) % 0.37/0.61 (define @t196 () (forall @t54 (or (not (tptp.wife tptp.peter @t193 @t48)) (_ @t188 @t48)))) % 0.37/0.61 (define @t197 () (not @t196)) % 0.37/0.61 (define @t198 () (or @t197 @t195 @t192 @t189)) % 0.37/0.61 (define @t199 () (@list true)) % 0.37/0.61 (define @t200 () (@list @t198)) % 0.37/0.61 (define @t201 () (tptp.wife tptp.peter @t59 @t70)) % 0.37/0.61 (define @t202 () (_ @t1 @t59)) % 0.37/0.61 (define @t203 () (_ @t202 @t70)) % 0.37/0.61 (define @t204 () (tptp.wife tptp.peter @t64 @t70)) % 0.37/0.61 (define @t205 () (_ (_ @t1 @t64) @t70)) % 0.37/0.61 (define @t206 () (not @t205)) % 0.37/0.61 (define @t207 () (tptp.wife tptp.peter @t59 @t64)) % 0.37/0.61 (define @t208 () (_ @t202 @t64)) % 0.37/0.61 (define @t209 () (not @t208)) % 0.37/0.61 (define @t210 () (or @t209 @t206 @t203)) % 0.37/0.61 (define @t211 () (_ @t1 @t59 @t70)) % 0.37/0.61 (define @t212 () (_ @t1 @t64 @t70)) % 0.37/0.61 (define @t213 () (not @t212)) % 0.37/0.61 (define @t214 () (_ @t1 @t59 @t64)) % 0.37/0.61 (define @t215 () (not @t214)) % 0.37/0.61 (define @t216 () (or @t215 @t213 @t211)) % 0.37/0.61 (define @t217 () (forall @t74 @t216)) % 0.37/0.61 (define @t218 () (_ @t50 @t59 @t70)) % 0.37/0.61 (define @t219 () (_ @t50 @t64 @t70)) % 0.37/0.61 (define @t220 () (_ @t50 @t59 @t64)) % 0.37/0.61 (define @t221 () (not @t72)) % 0.37/0.61 (define @t222 () (not @t66)) % 0.37/0.61 (define @t223 () (or @t222 @t221 @t71)) % 0.37/0.61 (define @t224 () (tptp.wife tptp.peter @t193 @t187)) % 0.37/0.61 (define @t225 () (or @t195 @t192 @t224)) % 0.37/0.61 (define @t226 () (not @t224)) % 0.37/0.61 (define @t227 () (or @t226 @t189)) % 0.37/0.61 (assume @p1 (= tptp.mfalse (_ tptp.mnot tptp.mtrue))) % 0.37/0.61 (assume @p2 (_ tptp.mreflexive tptp.peter)) % 0.37/0.61 (assume @p3 (_ tptp.mreflexive tptp.john)) % 0.37/0.61 (assume @p4 (_ tptp.mreflexive @t1)) % 0.37/0.61 (assume @p5 (_ tptp.mtransitive tptp.peter)) % 0.37/0.61 (assume @p6 (_ tptp.mtransitive tptp.john)) % 0.37/0.61 (assume @p7 (_ tptp.mtransitive @t1)) % 0.37/0.61 (assume @p8 @t8) % 0.37/0.61 (assume @p9 true) % 0.37/0.61 (step @p10 (= tptp.meq_ind @t12) :rule refl :args (@t12)) % 0.37/0.61 (step @p11 (= tptp.meq_prop @t15) :rule refl :args (@t15)) % 0.37/0.61 (step @p12 (= tptp.mnot @t20) :rule refl :args (@t20)) % 0.37/0.61 (step @p13 (= tptp.mor @t23) :rule refl :args (@t23)) % 0.37/0.61 (step @p14 (= tptp.mand @t28) :rule refl :args (@t28)) % 0.37/0.61 (step @p15 (= tptp.mimplies @t29) :rule refl :args (@t29)) % 0.37/0.61 (step @p16 (= tptp.mimplied @t30) :rule refl :args (@t30)) % 0.37/0.61 (step @p17 (= tptp.mequiv @t31) :rule refl :args (@t31)) % 0.37/0.61 (step @p18 (= tptp.mxor @t32) :rule refl :args (@t32)) % 0.37/0.61 (step @p19 (= tptp.mforall_ind @t35) :rule refl :args (@t35)) % 0.37/0.61 (step @p20 (= tptp.mforall_prop @t43) :rule refl :args (@t43)) % 0.37/0.61 (step @p21 (= tptp.mexists_ind @t44) :rule refl :args (@t44)) % 0.37/0.61 (step @p22 (= tptp.mexists_prop @t45) :rule refl :args (@t45)) % 0.37/0.61 (step @p23 (= tptp.mtrue @t47) :rule refl :args (@t47)) % 0.37/0.61 (step @p24 (= tptp.mbox @t57) :rule refl :args (@t57)) % 0.37/0.61 (step @p25 (= tptp.mdia @t58) :rule refl :args (@t58)) % 0.37/0.61 (step @p26 (= tptp.mreflexive @t63) :rule refl :args (@t63)) % 0.37/0.61 (step @p27 (= tptp.msymmetric @t67) :rule refl :args (@t67)) % 0.37/0.61 (step @p28 (= tptp.mserial @t69) :rule refl :args (@t69)) % 0.37/0.61 (step @p29 (= tptp.mtransitive @t76) :rule refl :args (@t76)) % 0.37/0.61 (step @p30 (= tptp.meuclidean @t78) :rule refl :args (@t78)) % 0.37/0.61 (step @p31 (= tptp.mpartially_functional @t80) :rule refl :args (@t80)) % 0.37/0.61 (step @p32 (= tptp.mfunctional @t82) :rule refl :args (@t82)) % 0.37/0.61 (step @p33 (= tptp.mweakly_dense @t85) :rule refl :args (@t85)) % 0.37/0.61 (step @p34 (= tptp.mweakly_connected @t86) :rule refl :args (@t86)) % 0.37/0.61 (step @p35 (= tptp.mweakly_directed @t87) :rule refl :args (@t87)) % 0.37/0.61 (step @p36 (= tptp.mvalid @t90) :rule refl :args (@t90)) % 0.37/0.61 (step @p37 (= tptp.minvalid @t91) :rule refl :args (@t91)) % 0.37/0.61 (step @p38 (= tptp.msatisfiable @t92) :rule refl :args (@t92)) % 0.37/0.61 (step @p39 (= tptp.mcountersatisfiable @t93) :rule refl :args (@t93)) % 0.37/0.61 (step @p40 :rule quant-merge-prenex :args ((= (forall @t46 @t105) @t103))) % 0.37/0.61 (step @p41 :rule beta-reduce :args ((= @t107 @t105))) % 0.37/0.61 (step @p42 :rule cong :premises (@p41) :args (@t108)) % 0.37/0.61 (step @p43 :rule trans :premises (@p42 @p40)) % 0.37/0.61 (step @p44 :rule beta-reduce :args ((= (_ @t110 @t106) @t108))) % 0.37/0.61 (step @p45 :rule trans :premises (@p44 @p43)) % 0.37/0.61 (step @p46 :rule aci_norm :args ((= @t112 @t102))) % 0.37/0.61 (step @p47 :rule cong :premises (@p46) :args (@t113)) % 0.37/0.61 (step @p48 :rule quant-merge-prenex :args ((= (forall @t40 @t115) @t113))) % 0.37/0.61 (step @p49 :rule alpha_equiv :args (@t116 (@list @t96 @t94) (@list @t48 @t117))) % 0.37/0.61 (step @p50 :rule refl :args (@t101)) % 0.37/0.61 (step @p51 :rule nary_cong :premises (@p50 @p49) :args (@t118)) % 0.37/0.61 (step @p52 :rule quant-miniscope-or :args ((= @t115 @t118))) % 0.37/0.61 (step @p53 :rule trans :premises (@p52 @p51)) % 0.37/0.61 (step @p54 :rule symm :premises (@p53)) % 0.37/0.61 (step @p55 :rule cong :premises (@p54) :args ((forall @t40 @t121))) % 0.37/0.61 (step @p56 :rule trans :premises (@p55 @p48)) % 0.37/0.61 (step @p57 :rule trans :premises (@p56 @p47)) % 0.37/0.61 (step @p58 :rule beta-reduce :args ((= @t130 @t121))) % 0.37/0.61 (step @p59 :rule cong :premises (@p58) :args (@t131)) % 0.37/0.61 (step @p60 :rule trans :premises (@p59 @p57)) % 0.37/0.61 (step @p61 :rule cong :premises (@p60) :args (@t132)) % 0.37/0.61 (step @p62 :rule beta-reduce :args ((= (_ @t134 @t129) @t132))) % 0.37/0.61 (step @p63 :rule trans :premises (@p62 @p61)) % 0.37/0.61 (step @p64 :rule beta-reduce :args ((= (_ (lambda @t135 @t128) @t2) @t128))) % 0.37/0.61 (step @p65 :rule refl :args (@t2)) % 0.37/0.61 (step @p66 :rule beta-reduce :args ((= @t138 @t124))) % 0.37/0.61 (step @p67 :rule refl :args (@t127)) % 0.37/0.61 (step @p68 :rule nary_cong :premises (@p67 @p66) :args (@t139)) % 0.37/0.61 (step @p69 :rule cong :premises (@p68) :args (@t140)) % 0.37/0.61 (step @p70 :rule beta-reduce :args ((= (_ (lambda @t142 (or @t127 @t141)) @t137) @t140))) % 0.37/0.61 (step @p71 :rule trans :premises (@p70 @p69)) % 0.37/0.61 (step @p72 :rule aci_norm :args ((= @t144 @t136))) % 0.37/0.61 (step @p73 :rule cong :premises (@p72) :args (@t145)) % 0.37/0.61 (step @p74 :rule quant-merge-prenex :args ((= (forall @t54 @t147) @t145))) % 0.37/0.61 (step @p75 :rule alpha_equiv :args (@t148 (@list @t117) @t150)) % 0.37/0.61 (step @p76 :rule refl :args (@t100)) % 0.37/0.61 (step @p77 :rule nary_cong :premises (@p76 @p75) :args (@t151)) % 0.37/0.61 (step @p78 :rule quant-miniscope-or :args ((= @t147 @t151))) % 0.37/0.61 (step @p79 :rule trans :premises (@p78 @p77)) % 0.37/0.61 (step @p80 :rule symm :premises (@p79)) % 0.37/0.61 (step @p81 :rule cong :premises (@p80) :args ((forall @t54 (or @t100 @t154)))) % 0.37/0.61 (step @p82 :rule trans :premises (@p81 @p74)) % 0.37/0.61 (step @p83 :rule trans :premises (@p82 @p73)) % 0.37/0.61 (step @p84 :rule beta-reduce :args ((= (_ (lambda @t46 (forall @t153 (or (not (tptp.wife tptp.peter @t11 @t149)) @t152))) @t48) @t154))) % 0.37/0.61 (step @p85 :rule refl :args (@t48)) % 0.37/0.61 (step @p86 :rule alpha_equiv :args (@t155 (@list @t48) @t150)) % 0.37/0.61 (step @p87 :rule cong :premises (@p86) :args (@t156)) % 0.37/0.61 (step @p88 :rule ho_cong :premises (@p87 @p85)) % 0.37/0.61 (step @p89 :rule trans :premises (@p88 @p84)) % 0.37/0.61 (step @p90 :rule refl :args (@t100)) % 0.37/0.61 (step @p91 :rule nary_cong :premises (@p90 @p89) :args (@t157)) % 0.37/0.61 (step @p92 :rule cong :premises (@p91) :args (@t158)) % 0.37/0.61 (step @p93 :rule trans :premises (@p92 @p83)) % 0.37/0.61 (step @p94 :rule cong :premises (@p93) :args (@t159)) % 0.37/0.61 (step @p95 :rule beta-reduce :args ((= (_ @t161 @t156) @t159))) % 0.37/0.61 (step @p96 :rule trans :premises (@p95 @p94)) % 0.37/0.61 (step @p97 :rule beta-reduce :args ((= (_ @t161 @t3) @t156))) % 0.37/0.61 (step @p98 :rule refl :args (@t3)) % 0.37/0.61 (step @p99 :rule refl :args (@t160)) % 0.37/0.61 (step @p100 :rule refl :args (@t99)) % 0.37/0.61 (step @p101 :rule refl :args (@t162)) % 0.37/0.61 (step @p102 :rule cong :premises (@p101 @p100) :args ((= @t162 @t99))) % 0.37/0.61 (step @p103 :rule symm :premises (@p102)) % 0.37/0.61 (step @p104 :rule eq_resolve :premises (@p101 @p103)) % 0.37/0.61 (step @p105 :rule cong :premises (@p104) :args (@t163)) % 0.37/0.61 (step @p106 :rule nary_cong :premises (@p105 @p99) :args (@t164)) % 0.37/0.61 (step @p107 :rule cong :premises (@p106) :args ((forall @t54 @t164))) % 0.37/0.61 (step @p108 :rule refl :args (@t160)) % 0.37/0.61 (step @p109 :rule refl :args (@t165)) % 0.37/0.61 (step @p110 :rule cong :premises (@p109) :args (@t166)) % 0.37/0.61 (step @p111 :rule nary_cong :premises (@p110 @p108) :args (@t167)) % 0.37/0.61 (step @p112 :rule cong :premises (@p111) :args (@t168)) % 0.37/0.61 (step @p113 :rule trans :premises (@p112 @p107)) % 0.37/0.61 (step @p114 :rule cong :premises (@p113) :args (@t169)) % 0.37/0.61 (step @p115 :rule beta-reduce :args ((= @t171 @t169))) % 0.37/0.61 (step @p116 :rule trans :premises (@p115 @p114)) % 0.37/0.61 (step @p117 :rule ho_cong :premises (@p116 @p98)) % 0.37/0.61 (step @p118 :rule trans :premises (@p117 @p97)) % 0.37/0.61 (step @p119 :rule ho_cong :premises (@p116 @p118)) % 0.37/0.61 (step @p120 :rule trans :premises (@p119 @p96)) % 0.37/0.61 (step @p121 :rule refl :args (@t141)) % 0.37/0.61 (step @p122 :rule beta-reduce :args ((= @t172 @t126))) % 0.37/0.61 (step @p123 :rule cong :premises (@p122) :args (@t173)) % 0.37/0.61 (step @p124 :rule nary_cong :premises (@p123 @p121) :args (@t174)) % 0.37/0.61 (step @p125 :rule cong :premises (@p124) :args (@t175)) % 0.37/0.61 (step @p126 :rule beta-reduce :args ((= (_ @t177 @t156) @t175))) % 0.37/0.61 (step @p127 :rule trans :premises (@p126 @p125)) % 0.37/0.61 (step @p128 :rule refl :args (@t177)) % 0.37/0.61 (step @p129 :rule ho_cong :premises (@p128 @p118)) % 0.37/0.61 (step @p130 :rule trans :premises (@p129 @p127)) % 0.37/0.61 (step @p131 :rule ho_cong :premises (@p130 @p120)) % 0.37/0.61 (step @p132 :rule trans :premises (@p131 @p71)) % 0.37/0.61 (step @p133 :rule ho_cong :premises (@p132 @p65)) % 0.37/0.61 (step @p134 :rule trans :premises (@p133 @p64)) % 0.37/0.61 (step @p135 :rule cong :premises (@p134) :args (@t179)) % 0.37/0.61 (step @p136 :rule refl :args (@t134)) % 0.37/0.61 (step @p137 :rule ho_cong :premises (@p136 @p135)) % 0.37/0.61 (step @p138 :rule trans :premises (@p137 @p63)) % 0.37/0.61 (step @p139 :rule refl :args (@t110)) % 0.37/0.61 (step @p140 :rule ho_cong :premises (@p139 @p138)) % 0.37/0.61 (step @p141 :rule trans :premises (@p140 @p45)) % 0.37/0.61 (step @p142 :rule cong :premises (@p141) :args ((not (_ @t110 (_ @t134 @t179))))) % 0.37/0.61 (step @p143 :rule refl :args (@t1)) % 0.37/0.61 (step @p144 :rule refl :args (@t160)) % 0.37/0.61 (step @p145 :rule refl :args (@t49)) % 0.37/0.61 (step @p146 :rule cong :premises (@p145 @p144) :args ((= @t49 @t160))) % 0.37/0.61 (step @p147 :rule symm :premises (@p146)) % 0.37/0.61 (step @p148 :rule eq_resolve :premises (@p145 @p147)) % 0.37/0.61 (step @p149 :rule refl :args (@t170)) % 0.37/0.61 (step @p150 :rule refl :args (@t51)) % 0.37/0.61 (step @p151 :rule cong :premises (@p150 @p149) :args ((= @t51 @t170))) % 0.37/0.61 (step @p152 :rule symm :premises (@p151)) % 0.37/0.61 (step @p153 :rule eq_resolve :premises (@p150 @p152)) % 0.37/0.61 (step @p154 :rule cong :premises (@p153) :args (@t52)) % 0.37/0.61 (step @p155 :rule nary_cong :premises (@p154 @p148) :args (@t53)) % 0.37/0.61 (step @p156 :rule cong :premises (@p155) :args (@t55)) % 0.37/0.61 (step @p157 :rule cong :premises (@p156) :args (@t57)) % 0.37/0.61 (step @p158 :rule trans :premises (@p24 @p157)) % 0.37/0.61 (step @p159 :rule ho_cong :premises (@p158 @p143)) % 0.37/0.61 (step @p160 :rule ho_cong :premises (@p159 @p98)) % 0.37/0.61 (step @p161 :rule ho_cong :premises (@p159 @p160)) % 0.37/0.61 (step @p162 :rule beta-reduce :args ((= (_ @t181 @t2) @t176))) % 0.37/0.61 (step @p163 :rule beta-reduce :args ((= (_ (lambda @t182 @t180) @t21) @t181))) % 0.37/0.61 (step @p164 :rule refl :args (@t21)) % 0.37/0.61 (step @p165 :rule refl :args (@t22)) % 0.37/0.61 (step @p166 :rule beta-reduce :args ((= @t184 @t18))) % 0.37/0.61 (step @p167 :rule nary_cong :premises (@p166 @p165) :args (@t185)) % 0.37/0.61 (step @p168 :rule cong :premises (@p167) :args (@t186)) % 0.37/0.61 (step @p169 :rule beta-reduce :args ((= (_ @t23 @t183) @t186))) % 0.37/0.61 (step @p170 :rule trans :premises (@p169 @p168)) % 0.37/0.61 (step @p171 :rule beta-reduce :args ((= (_ @t20 @t16) @t183))) % 0.37/0.61 (step @p172 :rule refl :args (@t23)) % 0.37/0.61 (step @p173 :rule ho_cong :premises (@p172 @p171)) % 0.37/0.61 (step @p174 :rule trans :premises (@p173 @p170)) % 0.37/0.61 (step @p175 :rule ho_cong :premises (@p174 @p164)) % 0.37/0.61 (step @p176 :rule trans :premises (@p175 @p163)) % 0.37/0.61 (step @p177 :rule ho_cong :premises (@p176 @p65)) % 0.37/0.61 (step @p178 :rule trans :premises (@p177 @p162)) % 0.37/0.61 (step @p179 :rule refl :args (@t16)) % 0.37/0.61 (step @p180 :rule ho_cong :premises (@p12 @p179)) % 0.37/0.61 (step @p181 :rule ho_cong :premises (@p13 @p180)) % 0.37/0.61 (step @p182 :rule ho_cong :premises (@p181 @p164)) % 0.37/0.61 (step @p183 :rule ho_cong :premises (@p182 @p65)) % 0.37/0.61 (step @p184 :rule trans :premises (@p183 @p178)) % 0.37/0.61 (step @p185 :rule cong :premises (@p184) :args (@t29)) % 0.37/0.61 (step @p186 :rule trans :premises (@p15 @p185)) % 0.37/0.61 (step @p187 :rule ho_cong :premises (@p186 @p160)) % 0.37/0.61 (step @p188 :rule ho_cong :premises (@p187 @p161)) % 0.37/0.61 (step @p189 :rule ho_cong :premises (@p188 @p65)) % 0.37/0.61 (step @p190 :rule cong :premises (@p189) :args (@t7)) % 0.37/0.61 (step @p191 :rule refl :args (@t133)) % 0.37/0.61 (step @p192 :rule refl :args (@t39)) % 0.37/0.61 (step @p193 :rule cong :premises (@p192 @p191) :args ((= @t39 @t133))) % 0.37/0.61 (step @p194 :rule symm :premises (@p193)) % 0.37/0.61 (step @p195 :rule eq_resolve :premises (@p192 @p194)) % 0.37/0.61 (step @p196 :rule cong :premises (@p195) :args (@t41)) % 0.37/0.61 (step @p197 :rule cong :premises (@p196) :args (@t43)) % 0.37/0.61 (step @p198 :rule trans :premises (@p20 @p197)) % 0.37/0.61 (step @p199 :rule ho_cong :premises (@p198 @p190)) % 0.37/0.61 (step @p200 :rule refl :args (@t109)) % 0.37/0.61 (step @p201 :rule refl :args (@t17)) % 0.37/0.61 (step @p202 :rule cong :premises (@p201 @p200) :args ((= @t17 @t109))) % 0.37/0.61 (step @p203 :rule symm :premises (@p202)) % 0.37/0.61 (step @p204 :rule eq_resolve :premises (@p201 @p203)) % 0.37/0.61 (step @p205 :rule cong :premises (@p204) :args (@t88)) % 0.37/0.61 (step @p206 :rule cong :premises (@p205) :args (@t90)) % 0.37/0.61 (step @p207 :rule trans :premises (@p36 @p206)) % 0.37/0.61 (step @p208 :rule ho_cong :premises (@p207 @p199)) % 0.37/0.61 (step @p209 :rule cong :premises (@p208) :args (@t8)) % 0.37/0.61 (step @p210 :rule trans :premises (@p209 @p142)) % 0.37/0.61 (step @p211 :rule eq_resolve :premises (@p8 @p210)) % 0.37/0.61 (step @p212 :rule skolemize :premises (@p211)) % 0.37/0.61 (step @p213 :rule cnf_or_neg :args (@t198 3)) % 0.37/0.61 (step @p214 :rule chain_m_resolution :premises (@p213 @p212) :args ((not @t189) @t199 @t200)) % 0.37/0.61 (step @p215 :rule bool-double-not-elim :args (@t196)) % 0.37/0.61 (step @p216 :rule refl :args (@t198)) % 0.37/0.61 (step @p217 :rule nary_cong :premises (@p216 @p215) :args ((or @t198 (not @t197)))) % 0.37/0.61 (step @p218 :rule cnf_or_neg :args (@t198 0)) % 0.37/0.61 (step @p219 :rule eq_resolve :premises (@p218 @p217)) % 0.37/0.61 (step @p220 :rule reordering :premises (@p219) :args ((or @t196 @t198))) % 0.37/0.61 (step @p221 :rule chain_m_resolution :premises (@p220 @p212) :args (@t196 @t199 @t200)) % 0.37/0.61 (step @p222 :rule instantiate :premises (@p221) :args ((@list @t187))) % 0.37/0.61 (step @p223 :rule refl :args (@t201)) % 0.37/0.61 (step @p224 :rule refl :args (@t203)) % 0.37/0.61 (step @p225 :rule cong :premises (@p224 @p223) :args ((= @t203 @t201))) % 0.37/0.61 (step @p226 :rule symm :premises (@p225)) % 0.37/0.61 (step @p227 :rule eq_resolve :premises (@p224 @p226)) % 0.37/0.61 (step @p228 :rule refl :args (@t204)) % 0.37/0.61 (step @p229 :rule refl :args (@t205)) % 0.37/0.61 (step @p230 :rule cong :premises (@p229 @p228) :args ((= @t205 @t204))) % 0.37/0.61 (step @p231 :rule symm :premises (@p230)) % 0.37/0.61 (step @p232 :rule eq_resolve :premises (@p229 @p231)) % 0.37/0.61 (step @p233 :rule cong :premises (@p232) :args (@t206)) % 0.37/0.61 (step @p234 :rule refl :args (@t207)) % 0.37/0.61 (step @p235 :rule refl :args (@t208)) % 0.37/0.61 (step @p236 :rule cong :premises (@p235 @p234) :args ((= @t208 @t207))) % 0.37/0.61 (step @p237 :rule symm :premises (@p236)) % 0.37/0.61 (step @p238 :rule eq_resolve :premises (@p235 @p237)) % 0.37/0.61 (step @p239 :rule cong :premises (@p238) :args (@t209)) % 0.37/0.61 (step @p240 :rule nary_cong :premises (@p239 @p233 @p227) :args (@t210)) % 0.37/0.61 (step @p241 :rule cong :premises (@p240) :args ((forall @t74 @t210))) % 0.37/0.61 (step @p242 :rule refl :args (@t211)) % 0.37/0.61 (step @p243 :rule refl :args (@t212)) % 0.37/0.61 (step @p244 :rule cong :premises (@p243) :args (@t213)) % 0.37/0.61 (step @p245 :rule refl :args (@t214)) % 0.37/0.61 (step @p246 :rule cong :premises (@p245) :args (@t215)) % 0.37/0.61 (step @p247 :rule nary_cong :premises (@p246 @p244 @p242) :args (@t216)) % 0.37/0.61 (step @p248 :rule cong :premises (@p247) :args (@t217)) % 0.37/0.61 (step @p249 :rule trans :premises (@p248 @p241)) % 0.37/0.61 (step @p250 :rule beta-reduce :args ((= (_ (lambda @t62 (forall @t74 (or (not @t220) (not @t219) @t218))) @t1) @t217))) % 0.37/0.61 (step @p251 :rule trans :premises (@p250 @p249)) % 0.37/0.61 (step @p252 :rule refl :args (@t218)) % 0.37/0.61 (step @p253 :rule refl :args (@t71)) % 0.37/0.61 (step @p254 :rule cong :premises (@p253 @p252) :args ((= @t71 @t218))) % 0.37/0.61 (step @p255 :rule symm :premises (@p254)) % 0.37/0.61 (step @p256 :rule eq_resolve :premises (@p253 @p255)) % 0.37/0.61 (step @p257 :rule refl :args (@t219)) % 0.37/0.61 (step @p258 :rule refl :args (@t72)) % 0.37/0.61 (step @p259 :rule cong :premises (@p258 @p257) :args ((= @t72 @t219))) % 0.37/0.61 (step @p260 :rule symm :premises (@p259)) % 0.37/0.61 (step @p261 :rule eq_resolve :premises (@p258 @p260)) % 0.37/0.61 (step @p262 :rule cong :premises (@p261) :args (@t221)) % 0.37/0.61 (step @p263 :rule refl :args (@t220)) % 0.37/0.61 (step @p264 :rule refl :args (@t66)) % 0.37/0.61 (step @p265 :rule cong :premises (@p264 @p263) :args ((= @t66 @t220))) % 0.37/0.61 (step @p266 :rule symm :premises (@p265)) % 0.37/0.61 (step @p267 :rule eq_resolve :premises (@p264 @p266)) % 0.37/0.61 (step @p268 :rule cong :premises (@p267) :args (@t222)) % 0.37/0.61 (step @p269 :rule nary_cong :premises (@p268 @p262 @p256) :args (@t223)) % 0.37/0.61 (step @p270 :rule cong :premises (@p269) :args ((forall @t74 @t223))) % 0.37/0.61 (step @p271 :rule aci_norm :args ((= (or (or @t222 @t221) @t71) @t223))) % 0.37/0.61 (step @p272 :rule bool-and-de-morgan :args (@t66 @t72 true)) % 0.37/0.61 (step @p273 :rule nary_cong :premises (@p272 @p253) :args ((or (not @t73) @t71))) % 0.37/0.61 (step @p274 :rule trans :premises (@p273 @p271)) % 0.37/0.61 (step @p275 :rule bool-impl-elim :args (@t73 @t71)) % 0.37/0.61 (step @p276 :rule trans :premises (@p275 @p274)) % 0.37/0.61 (step @p277 :rule cong :premises (@p276) :args (@t75)) % 0.37/0.61 (step @p278 :rule trans :premises (@p277 @p270)) % 0.37/0.61 (step @p279 :rule cong :premises (@p278) :args (@t76)) % 0.37/0.61 (step @p280 :rule trans :premises (@p29 @p279)) % 0.37/0.61 (step @p281 :rule ho_cong :premises (@p280 @p143)) % 0.37/0.61 (step @p282 :rule trans :premises (@p281 @p251)) % 0.37/0.61 (step @p283 :rule eq_resolve :premises (@p7 @p282)) % 0.37/0.61 (step @p284 :rule instantiate :premises (@p283) :args ((@list @t193 @t190 @t187))) % 0.37/0.61 (step @p285 :rule bool-double-not-elim :args (@t191)) % 0.37/0.61 (step @p286 :rule nary_cong :premises (@p216 @p285) :args ((or @t198 (not @t192)))) % 0.37/0.61 (step @p287 :rule cnf_or_neg :args (@t198 2)) % 0.37/0.61 (step @p288 :rule eq_resolve :premises (@p287 @p286)) % 0.37/0.61 (step @p289 :rule reordering :premises (@p288) :args ((or @t191 @t198))) % 0.37/0.61 (step @p290 :rule chain_m_resolution :premises (@p289 @p212) :args (@t191 @t199 @t200)) % 0.37/0.61 (step @p291 :rule bool-double-not-elim :args (@t194)) % 0.37/0.61 (step @p292 :rule nary_cong :premises (@p216 @p291) :args ((or @t198 (not @t195)))) % 0.37/0.61 (step @p293 :rule cnf_or_neg :args (@t198 1)) % 0.37/0.61 (step @p294 :rule eq_resolve :premises (@p293 @p292)) % 0.37/0.61 (step @p295 :rule reordering :premises (@p294) :args ((or @t194 @t198))) % 0.37/0.61 (step @p296 :rule chain_m_resolution :premises (@p295 @p212) :args (@t194 @t199 @t200)) % 0.37/0.61 (step @p297 :rule cnf_or_pos :args (@t225)) % 0.37/0.61 (step @p298 :rule reordering :premises (@p297) :args ((or @t195 @t192 @t224 (not @t225)))) % 0.37/0.61 (step @p299 :rule chain_m_resolution :premises (@p298 @p296 @p290 @p284) :args (@t224 (@list false false false) (@list @t194 @t191 @t225))) % 0.37/0.61 (step @p300 :rule cnf_or_pos :args (@t227)) % 0.37/0.61 (step @p301 :rule reordering :premises (@p300) :args ((or @t189 @t226 (not @t227)))) % 0.37/0.61 (step @p302 false :rule chain_m_resolution :premises (@p301 @p299 @p222 @p214) :args (false (@list false false true) (@list @t224 @t227 @t189))) % 0.37/0.61 ) % 0.37/0.61 % SZS output end Proof % 0.37/0.61 % cvc5 exiting %------------------------------------------------------------------------------