%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : PHI043^2 : TPTP v9.2.1. Released v7.5.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n008.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 08:43:16 AM UTC 2026 % Result : Theorem 0.46s 0.69s % Output : Proof 0.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : PHI043^2 : TPTP v9.2.1. Released v7.5.0. % 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 : n008.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 % 0.17/0.35 % DateTime : Tue Jun 2 12:54:33 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.49 %----Proving TH0 % 0.46/0.69 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.46/0.69 % SZS status Theorem % 0.46/0.69 % SZS output start Proof % 0.46/0.69 ( % 0.46/0.69 (declare-sort $$unsorted 0) % 0.46/0.69 (declare-sort tptp.mu 0) % 0.46/0.69 (declare-const tptp.eiw_ind (-> $$unsorted tptp.mu Bool)) % 0.46/0.69 (declare-const tptp.p (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.mdia (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.mbox (-> (-> $$unsorted Bool) $$unsorted Bool)) % 0.46/0.69 (declare-const tptp.rel (-> $$unsorted $$unsorted Bool)) % 0.46/0.69 (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" $$unsorted)) (= _let_2 _let_1))))) % 0.46/0.69 (define tptp.mtrue () (lambda (@list (@var "W" $$unsorted)) true)) % 0.46/0.69 (define tptp.mfalse () (lambda (@list (@var "W" $$unsorted)) false)) % 0.46/0.69 (define tptp.mnot () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.46/0.69 (define tptp.mor () (let ((_let_1 (@var "W" $$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))))))) % 0.46/0.69 (define tptp.mand () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.69 (define tptp.mimplies () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.69 (define tptp.mimplied () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Psi" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_3 _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.69 (define tptp.mequiv () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (= (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.46/0.69 (define tptp.mxor () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Psi" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "Phi" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.46/0.69 (define tptp.mforall_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.69 (define tptp.mforall_indset () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> tptp.mu $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.69 (define tptp.mforall_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.69 (define tptp.mexists_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.69 (define tptp.mexists_indset () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" (-> tptp.mu $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.69 (define tptp.mexists_prop () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "P" (-> $$unsorted Bool)))) (let ((_let_3 (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ _let_3 _let_2) _let_1))))))) % 0.46/0.69 (define tptp.mbox_generic () (let ((_let_1 (@var "V" $$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))))))))) % 0.46/0.69 (define tptp.mdia_generic () (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 $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (exists (@list _let_1) (and (_ (_ _let_4 _let_3) _let_1) (_ _let_2 _let_1))))))))) % 0.46/0.69 (define tptp.mvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (_ _let_2 _let_1)))))) % 0.46/0.69 (define tptp.minvalid () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "Phi" (-> $$unsorted Bool)))) (lambda (@list _let_2) (forall (@list _let_1) (not (_ _let_2 _let_1))))))) % 0.46/0.69 (define tptp.mforall_eiw_ind () (let ((_let_1 (@var "W" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (forall (@list _let_2) (=> (_ (_ tptp.eiw_ind _let_1) _let_2) (_ (_ _let_3 _let_2) _let_1)))))))) % 0.46/0.69 (define tptp.mexists_eiw_ind () (let ((_let_1 (@var "__flatten_var_0" $$unsorted))) (let ((_let_2 (@var "X" tptp.mu))) (let ((_let_3 (@var "Phi" (-> tptp.mu $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (_ (_ tptp.mnot (_ tptp.mforall_eiw_ind (lambda (@list _let_2 _let_1) (_ (_ tptp.mnot (_ _let_3 _let_2)) _let_1)))) _let_1)))))) % 0.46/0.69 (define @t1 () (= tptp.mbox (_ tptp.mbox_generic tptp.rel))) % 0.46/0.69 (define @t2 () (= tptp.mdia (_ tptp.mdia_generic tptp.rel))) % 0.46/0.69 (define @t3 () (@var "X" tptp.mu)) % 0.46/0.69 (define @t4 () (@var "V" $$unsorted)) % 0.46/0.69 (define @t5 () (@list @t3)) % 0.46/0.69 (define @t6 () (@list @t4)) % 0.46/0.69 (define @t7 () (not (= @t3 @t3))) % 0.46/0.69 (define @t8 () (@var "W" $$unsorted)) % 0.46/0.69 (define @t9 () (@list @t3 @t8)) % 0.46/0.69 (define @t10 () (lambda @t9 @t7)) % 0.46/0.69 (define @t11 () (_ tptp.p @t10)) % 0.46/0.69 (define @t12 () (@var "__flatten_var_0" $$unsorted)) % 0.46/0.69 (define @t13 () (@var "Psi" (-> tptp.mu $$unsorted Bool))) % 0.46/0.69 (define @t14 () (_ tptp.p @t13)) % 0.46/0.69 (define @t15 () (@var "Phi" (-> tptp.mu $$unsorted Bool))) % 0.46/0.69 (define @t16 () (_ tptp.p @t15)) % 0.46/0.69 (define @t17 () (_ @t13 @t3)) % 0.46/0.69 (define @t18 () (_ @t15 @t3)) % 0.46/0.69 (define @t19 () (@list @t3 @t12)) % 0.46/0.69 (define @t20 () (lambda @t19 (_ (_ (_ tptp.mequiv @t18) @t17) @t12))) % 0.46/0.69 (define @t21 () (@list @t13 @t12)) % 0.46/0.69 (define @t22 () (lambda @t21 (_ (_ (_ tptp.mimplies (_ tptp.mbox (_ tptp.mforall_eiw_ind @t20))) (_ (_ tptp.mequiv @t16) @t14)) @t12))) % 0.46/0.69 (define @t23 () (@list @t15 @t12)) % 0.46/0.69 (define @t24 () (lambda @t23 (_ (_ tptp.mforall_indset @t22) @t12))) % 0.46/0.69 (define @t25 () (_ @t18 @t12)) % 0.46/0.69 (define @t26 () (lambda @t19 @t25)) % 0.46/0.69 (define @t27 () (lambda @t23 (_ (_ (_ tptp.mimplies @t16) (_ tptp.mdia (_ tptp.mexists_eiw_ind @t26))) @t12))) % 0.46/0.69 (define @t28 () (not (_ tptp.mvalid (_ tptp.mforall_indset @t27)))) % 0.46/0.69 (define @t29 () (@var "Y" tptp.mu)) % 0.46/0.69 (define @t30 () (lambda (@list @t3 @t29 @t8) (= @t3 @t29))) % 0.46/0.69 (define @t31 () (@list @t8)) % 0.46/0.69 (define @t32 () (lambda @t31 true)) % 0.46/0.69 (define @t33 () (lambda @t31 false)) % 0.46/0.69 (define @t34 () (@var "Phi" (-> $$unsorted Bool))) % 0.46/0.69 (define @t35 () (_ @t34 @t8)) % 0.46/0.69 (define @t36 () (not @t35)) % 0.46/0.69 (define @t37 () (@list @t34 @t8)) % 0.46/0.69 (define @t38 () (lambda @t37 @t36)) % 0.46/0.69 (define @t39 () (@var "Psi" (-> $$unsorted Bool))) % 0.46/0.69 (define @t40 () (_ @t39 @t8)) % 0.46/0.69 (define @t41 () (@list @t34 @t39 @t8)) % 0.46/0.69 (define @t42 () (lambda @t41 (or @t35 @t40))) % 0.46/0.69 (define @t43 () (lambda @t41 (and @t35 @t40))) % 0.46/0.69 (define @t44 () (lambda @t41 (=> @t35 @t40))) % 0.46/0.69 (define @t45 () (lambda @t41 (=> @t40 @t35))) % 0.46/0.69 (define @t46 () (lambda @t41 (= @t35 @t40))) % 0.46/0.69 (define @t47 () (lambda @t41 (or (and @t35 (not @t40)) (and @t36 @t40)))) % 0.46/0.69 (define @t48 () (_ @t18 @t8)) % 0.46/0.69 (define @t49 () (@list @t15 @t8)) % 0.46/0.69 (define @t50 () (lambda @t49 (forall @t5 @t48))) % 0.46/0.69 (define @t51 () (@var "X" (-> tptp.mu $$unsorted Bool))) % 0.46/0.69 (define @t52 () (@var "Phi" (-> (-> tptp.mu $$unsorted Bool) $$unsorted Bool))) % 0.46/0.69 (define @t53 () (_ (_ @t52 @t51) @t8)) % 0.46/0.69 (define @t54 () (@list @t51)) % 0.46/0.69 (define @t55 () (forall @t54 @t53)) % 0.46/0.69 (define @t56 () (@list @t52 @t8)) % 0.46/0.69 (define @t57 () (lambda @t56 @t55)) % 0.46/0.69 (define @t58 () (@var "P" (-> $$unsorted Bool))) % 0.46/0.69 (define @t59 () (@var "Phi" (-> (-> $$unsorted Bool) $$unsorted Bool))) % 0.46/0.69 (define @t60 () (_ (_ @t59 @t58) @t8)) % 0.46/0.69 (define @t61 () (@list @t58)) % 0.46/0.69 (define @t62 () (@list @t59 @t8)) % 0.46/0.69 (define @t63 () (lambda @t62 (forall @t61 @t60))) % 0.46/0.69 (define @t64 () (lambda @t49 (exists @t5 @t48))) % 0.46/0.69 (define @t65 () (lambda @t56 (exists @t54 @t53))) % 0.46/0.69 (define @t66 () (lambda @t62 (exists @t61 @t60))) % 0.46/0.69 (define @t67 () (_ @t34 @t4)) % 0.46/0.69 (define @t68 () (@var "R" (-> $$unsorted $$unsorted Bool))) % 0.46/0.69 (define @t69 () (_ (_ @t68 @t8) @t4)) % 0.46/0.69 (define @t70 () (not @t69)) % 0.46/0.69 (define @t71 () (or @t70 @t67)) % 0.46/0.69 (define @t72 () (forall @t6 @t71)) % 0.46/0.69 (define @t73 () (@list @t68 @t34 @t8)) % 0.46/0.69 (define @t74 () (lambda @t73 @t72)) % 0.46/0.69 (define @t75 () (and @t69 @t67)) % 0.46/0.69 (define @t76 () (exists @t6 @t75)) % 0.46/0.69 (define @t77 () (lambda @t73 @t76)) % 0.46/0.69 (define @t78 () (forall @t31 @t35)) % 0.46/0.69 (define @t79 () (@list @t34)) % 0.46/0.69 (define @t80 () (lambda @t79 @t78)) % 0.46/0.69 (define @t81 () (lambda @t79 (forall @t31 @t36))) % 0.46/0.69 (define @t82 () (_ (_ tptp.eiw_ind @t8) @t3)) % 0.46/0.69 (define @t83 () (forall @t5 (=> @t82 @t48))) % 0.46/0.69 (define @t84 () (lambda @t49 @t83)) % 0.46/0.69 (define @t85 () (lambda @t19 (_ (_ tptp.mnot @t18) @t12))) % 0.46/0.69 (define @t86 () (lambda @t23 (_ (_ tptp.mnot (_ tptp.mforall_eiw_ind @t85)) @t12))) % 0.46/0.69 (define @t87 () (@var "BOUND_VARIABLE_8205" tptp.mu)) % 0.46/0.69 (define @t88 () (not (_ @t51 @t87 @t4))) % 0.46/0.69 (define @t89 () (not (tptp.eiw_ind @t4 @t87))) % 0.46/0.69 (define @t90 () (not (tptp.rel @t8 @t4))) % 0.46/0.69 (define @t91 () (or @t90 @t89 @t88)) % 0.46/0.69 (define @t92 () (or @t89 @t88)) % 0.46/0.69 (define @t93 () (or @t90 @t92)) % 0.46/0.69 (define @t94 () (@list @t4 @t87)) % 0.46/0.69 (define @t95 () (forall @t94 @t93)) % 0.46/0.69 (define @t96 () (@list @t87)) % 0.46/0.69 (define @t97 () (forall @t96 @t93)) % 0.46/0.69 (define @t98 () (forall @t96 @t92)) % 0.46/0.69 (define @t99 () (@list @t3)) % 0.46/0.69 (define @t100 () (or @t90 @t98)) % 0.46/0.69 (define @t101 () (_ @t51 @t3 @t4)) % 0.46/0.69 (define @t102 () (not (tptp.eiw_ind @t4 @t3))) % 0.46/0.69 (define @t103 () (forall @t5 (or @t102 (not @t101)))) % 0.46/0.69 (define @t104 () (@var "BOUND_VARIABLE_8108" $$unsorted)) % 0.46/0.69 (define @t105 () (_ @t51 @t3 @t104)) % 0.46/0.69 (define @t106 () (not @t105)) % 0.46/0.69 (define @t107 () (tptp.eiw_ind @t104 @t3)) % 0.46/0.69 (define @t108 () (not @t107)) % 0.46/0.69 (define @t109 () (or @t108 @t106)) % 0.46/0.69 (define @t110 () (forall @t5 @t109)) % 0.46/0.69 (define @t111 () (not @t110)) % 0.46/0.69 (define @t112 () (@list @t104)) % 0.46/0.69 (define @t113 () (lambda @t112 @t111)) % 0.46/0.69 (define @t114 () (_ @t113 @t4)) % 0.46/0.69 (define @t115 () (not @t114)) % 0.46/0.69 (define @t116 () (or @t90 @t115)) % 0.46/0.69 (define @t117 () (forall @t6 @t116)) % 0.46/0.69 (define @t118 () (not @t117)) % 0.46/0.69 (define @t119 () (_ @t34 @t4)) % 0.46/0.69 (define @t120 () (not @t119)) % 0.46/0.69 (define @t121 () (lambda @t37 (not (forall @t6 (or @t90 @t120))))) % 0.46/0.69 (define @t122 () (_ @t121 @t113 @t8)) % 0.46/0.69 (define @t123 () (tptp.p @t51 @t8)) % 0.46/0.69 (define @t124 () (not @t123)) % 0.46/0.69 (define @t125 () (or @t124 @t122)) % 0.46/0.69 (define @t126 () (@list @t8 @t51)) % 0.46/0.69 (define @t127 () (forall @t126 @t125)) % 0.46/0.69 (define @t128 () (_ @t68 @t8 @t4)) % 0.46/0.69 (define @t129 () (not @t128)) % 0.46/0.69 (define @t130 () (_ (lambda @t73 (not (forall @t6 (or @t129 @t120)))) tptp.rel)) % 0.46/0.69 (define @t131 () (not @t67)) % 0.46/0.69 (define @t132 () (or @t70 @t131)) % 0.46/0.69 (define @t133 () (forall @t6 (not @t75))) % 0.46/0.69 (define @t134 () (not @t133)) % 0.46/0.69 (define @t135 () (tptp.mdia @t113 @t8)) % 0.46/0.69 (define @t136 () (or @t124 @t135)) % 0.46/0.69 (define @t137 () (forall @t126 @t136)) % 0.46/0.69 (define @t138 () (forall @t54 @t136)) % 0.46/0.69 (define @t139 () (lambda @t31 @t138)) % 0.46/0.69 (define @t140 () (_ @t139 @t8)) % 0.46/0.69 (define @t141 () (forall @t31 @t140)) % 0.46/0.69 (define @t142 () (_ @t34 @t8)) % 0.46/0.69 (define @t143 () (lambda @t79 (forall @t31 @t142))) % 0.46/0.69 (define @t144 () (_ @t51 @t3)) % 0.46/0.69 (define @t145 () (lambda @t112 (not (forall @t5 (or (not (_ (_ tptp.eiw_ind @t104) @t3)) (not (_ @t144 @t104))))))) % 0.46/0.69 (define @t146 () (_ (_ tptp.mdia @t113) @t8)) % 0.46/0.69 (define @t147 () (_ (_ tptp.p @t51) @t8)) % 0.46/0.69 (define @t148 () (not @t147)) % 0.46/0.69 (define @t149 () (or @t148 @t146)) % 0.46/0.69 (define @t150 () (=> @t147 @t146)) % 0.46/0.69 (define @t151 () (_ tptp.mdia (lambda @t112 (not (forall @t5 (or @t108 (not (_ @t15 @t3 @t104)))))))) % 0.46/0.69 (define @t152 () (_ @t16 @t12)) % 0.46/0.69 (define @t153 () (=> @t152 (_ @t151 @t12))) % 0.46/0.69 (define @t154 () (lambda @t23 @t153)) % 0.46/0.69 (define @t155 () (_ @t154 @t51 @t8)) % 0.46/0.69 (define @t156 () (forall @t54 @t155)) % 0.46/0.69 (define @t157 () (lambda @t31 @t156)) % 0.46/0.69 (define @t158 () (_ @t52 @t51 @t8)) % 0.46/0.69 (define @t159 () (lambda @t56 (forall @t54 @t158))) % 0.46/0.69 (define @t160 () (_ @t16 @t8)) % 0.46/0.69 (define @t161 () (_ @t15 @t3 @t12)) % 0.46/0.69 (define @t162 () (not (tptp.eiw_ind @t12 @t3))) % 0.46/0.69 (define @t163 () (not (forall @t5 (or @t162 (not @t161))))) % 0.46/0.69 (define @t164 () (@list @t12)) % 0.46/0.69 (define @t165 () (lambda @t164 @t163)) % 0.46/0.69 (define @t166 () (_ tptp.mdia @t165)) % 0.46/0.69 (define @t167 () (=> @t160 (_ @t166 @t8))) % 0.46/0.69 (define @t168 () (lambda @t31 @t167)) % 0.46/0.69 (define @t169 () (@list @t39 @t8)) % 0.46/0.69 (define @t170 () (lambda @t169 (=> @t160 @t40))) % 0.46/0.69 (define @t171 () (not @t25)) % 0.46/0.69 (define @t172 () (or @t162 @t171)) % 0.46/0.69 (define @t173 () (_ @t26 @t3 @t12)) % 0.46/0.69 (define @t174 () (not @t173)) % 0.46/0.69 (define @t175 () (or @t162 @t174)) % 0.46/0.69 (define @t176 () (forall @t5 @t175)) % 0.46/0.69 (define @t177 () (not @t176)) % 0.46/0.69 (define @t178 () (lambda @t164 @t177)) % 0.46/0.69 (define @t179 () (_ (lambda @t23 @t163) @t26)) % 0.46/0.69 (define @t180 () (_ @t44 @t16)) % 0.46/0.69 (define @t181 () (lambda @t23 (_ (_ @t180 (_ tptp.mdia @t179)) @t12))) % 0.46/0.69 (define @t182 () (_ @t15 @t3 @t8)) % 0.46/0.69 (define @t183 () (tptp.eiw_ind @t8 @t3)) % 0.46/0.69 (define @t184 () (not @t183)) % 0.46/0.69 (define @t185 () (forall @t5 (or @t184 (not @t182)))) % 0.46/0.69 (define @t186 () (lambda @t31 @t185)) % 0.46/0.69 (define @t187 () (_ @t186 @t8)) % 0.46/0.69 (define @t188 () (not @t187)) % 0.46/0.69 (define @t189 () (lambda @t31 @t188)) % 0.46/0.69 (define @t190 () (not @t48)) % 0.46/0.69 (define @t191 () (or @t184 @t190)) % 0.46/0.69 (define @t192 () (lambda @t19 @t171)) % 0.46/0.69 (define @t193 () (_ @t192 @t3 @t8)) % 0.46/0.69 (define @t194 () (or @t184 @t193)) % 0.46/0.69 (define @t195 () (forall @t5 @t194)) % 0.46/0.69 (define @t196 () (lambda @t31 @t195)) % 0.46/0.69 (define @t197 () (lambda @t49 (forall @t5 (or @t184 @t182)))) % 0.46/0.69 (define @t198 () (lambda @t31 @t190)) % 0.46/0.69 (define @t199 () (_ @t38 @t18)) % 0.46/0.69 (define @t200 () (not @t82)) % 0.46/0.69 (define @t201 () (or @t200 @t48)) % 0.46/0.69 (define @t202 () (forall @t126 (or @t124 (not (forall @t94 @t91))))) % 0.46/0.69 (define @t203 () (@quantifiers_skolemize @t202 1)) % 0.46/0.69 (define @t204 () (@quantifiers_skolemize @t202 0)) % 0.46/0.69 (define @t205 () (not (tptp.rel @t204 @t4))) % 0.46/0.69 (define @t206 () (forall @t94 (or @t205 @t89 (not (_ @t203 @t87 @t4))))) % 0.46/0.69 (define @t207 () (not @t206)) % 0.46/0.69 (define @t208 () (tptp.p @t203 @t204)) % 0.46/0.69 (define @t209 () (not @t208)) % 0.46/0.69 (define @t210 () (or @t209 @t207)) % 0.46/0.69 (define @t211 () (@list true)) % 0.46/0.69 (define @t212 () (@list @t210)) % 0.46/0.69 (define @t213 () (@var "BOUND_VARIABLE_8043" (-> tptp.mu $$unsorted Bool))) % 0.46/0.69 (define @t214 () (= @t123 (tptp.p @t213 @t8))) % 0.46/0.69 (define @t215 () (@var "BOUND_VARIABLE_8172" tptp.mu)) % 0.46/0.69 (define @t216 () (= (_ @t51 @t215 @t4) (_ @t213 @t215 @t4))) % 0.46/0.69 (define @t217 () (not (tptp.eiw_ind @t4 @t215))) % 0.46/0.69 (define @t218 () (or @t217 @t216)) % 0.46/0.69 (define @t219 () (or @t90 @t218)) % 0.46/0.69 (define @t220 () (@list @t4 @t215)) % 0.46/0.69 (define @t221 () (forall @t220 @t219)) % 0.46/0.69 (define @t222 () (@list @t215)) % 0.46/0.69 (define @t223 () (forall @t222 @t219)) % 0.46/0.69 (define @t224 () (forall @t222 @t218)) % 0.46/0.69 (define @t225 () (or @t90 @t224)) % 0.46/0.69 (define @t226 () (forall @t5 (or @t102 (= @t101 (_ @t213 @t3 @t4))))) % 0.46/0.69 (define @t227 () (@var "BOUND_VARIABLE_7960" $$unsorted)) % 0.46/0.69 (define @t228 () (_ @t213 @t3 @t227)) % 0.46/0.69 (define @t229 () (_ @t51 @t3 @t227)) % 0.46/0.69 (define @t230 () (tptp.eiw_ind @t227 @t3)) % 0.46/0.69 (define @t231 () (not @t230)) % 0.46/0.69 (define @t232 () (@list @t227)) % 0.46/0.69 (define @t233 () (lambda @t232 (forall @t5 (or @t231 (= @t229 @t228))))) % 0.46/0.69 (define @t234 () (_ @t233 @t4)) % 0.46/0.69 (define @t235 () (or @t90 @t234)) % 0.46/0.69 (define @t236 () (forall @t6 @t235)) % 0.46/0.69 (define @t237 () (lambda @t37 (forall @t6 (or @t90 @t119)))) % 0.46/0.69 (define @t238 () (_ @t237 @t233 @t8)) % 0.46/0.69 (define @t239 () (not @t238)) % 0.46/0.69 (define @t240 () (or @t239 @t214)) % 0.46/0.69 (define @t241 () (@list @t8 @t51 @t213)) % 0.46/0.69 (define @t242 () (_ (lambda @t73 (forall @t6 (or @t129 @t119))) tptp.rel)) % 0.46/0.69 (define @t243 () (not (tptp.mbox @t233 @t8))) % 0.46/0.69 (define @t244 () (or @t243 @t214)) % 0.46/0.69 (define @t245 () (forall @t241 @t244)) % 0.46/0.69 (define @t246 () (forall (@list @t51 @t213) @t244)) % 0.46/0.69 (define @t247 () (lambda @t31 @t246)) % 0.46/0.69 (define @t248 () (_ @t247 @t8)) % 0.46/0.69 (define @t249 () (forall @t31 @t248)) % 0.46/0.69 (define @t250 () (@list @t213)) % 0.46/0.69 (define @t251 () (forall @t250 @t244)) % 0.46/0.69 (define @t252 () (tptp.p @t15 @t12)) % 0.46/0.69 (define @t253 () (_ @t15 @t3 @t227)) % 0.46/0.69 (define @t254 () (= @t253 @t229)) % 0.46/0.69 (define @t255 () (or @t231 @t254)) % 0.46/0.69 (define @t256 () (forall @t5 @t255)) % 0.46/0.69 (define @t257 () (lambda @t232 @t256)) % 0.46/0.69 (define @t258 () (forall @t54 (or (not (tptp.mbox @t257 @t12)) (= @t252 (tptp.p @t51 @t12))))) % 0.46/0.69 (define @t259 () (lambda @t23 @t258)) % 0.46/0.69 (define @t260 () (forall @t54 (_ @t259 @t51 @t8))) % 0.46/0.69 (define @t261 () (lambda @t31 @t260)) % 0.46/0.69 (define @t262 () (tptp.p @t15 @t8)) % 0.46/0.69 (define @t263 () (tptp.mbox @t257 @t8)) % 0.46/0.69 (define @t264 () (= @t160 @t147)) % 0.46/0.69 (define @t265 () (lambda @t232 (forall @t5 (or (not (_ (_ tptp.eiw_ind @t227) @t3)) (= (_ @t18 @t227) (_ @t144 @t227)))))) % 0.46/0.69 (define @t266 () (_ (_ tptp.mbox @t257) @t8)) % 0.46/0.69 (define @t267 () (not @t266)) % 0.46/0.69 (define @t268 () (or @t267 @t264)) % 0.46/0.69 (define @t269 () (=> @t266 @t264)) % 0.46/0.69 (define @t270 () (_ tptp.mbox (lambda @t232 (forall @t5 (or @t231 (= @t253 (_ @t13 @t3 @t227))))))) % 0.46/0.69 (define @t271 () (=> (_ @t270 @t12) (= @t152 (_ @t14 @t12)))) % 0.46/0.69 (define @t272 () (lambda @t21 @t271)) % 0.46/0.69 (define @t273 () (_ @t272 @t51 @t8)) % 0.46/0.69 (define @t274 () (forall @t54 @t273)) % 0.46/0.69 (define @t275 () (lambda @t31 @t274)) % 0.46/0.69 (define @t276 () (_ @t14 @t8)) % 0.46/0.69 (define @t277 () (= @t160 @t276)) % 0.46/0.69 (define @t278 () (_ @t270 @t8)) % 0.46/0.69 (define @t279 () (lambda @t31 @t277)) % 0.46/0.69 (define @t280 () (_ @t279 @t8)) % 0.46/0.69 (define @t281 () (=> @t278 @t280)) % 0.46/0.69 (define @t282 () (lambda @t31 @t281)) % 0.46/0.69 (define @t283 () (lambda @t169 (=> @t278 @t40))) % 0.46/0.69 (define @t284 () (lambda @t31 (= @t276 @t160))) % 0.46/0.69 (define @t285 () (lambda @t169 (= @t160 @t40))) % 0.46/0.69 (define @t286 () (_ @t46 @t16)) % 0.46/0.69 (define @t287 () (_ @t13 @t3 @t8)) % 0.46/0.69 (define @t288 () (_ tptp.mbox (lambda @t31 (forall @t5 (or @t184 (= @t182 @t287)))))) % 0.46/0.69 (define @t289 () (lambda @t169 (=> (_ @t288 @t8) @t40))) % 0.46/0.69 (define @t290 () (_ @t17 @t8)) % 0.46/0.69 (define @t291 () (= @t48 @t290)) % 0.46/0.69 (define @t292 () (or @t184 @t291)) % 0.46/0.69 (define @t293 () (= @t25 (_ @t17 @t12))) % 0.46/0.69 (define @t294 () (lambda @t19 @t293)) % 0.46/0.69 (define @t295 () (_ @t294 @t3 @t8)) % 0.46/0.69 (define @t296 () (or @t184 @t295)) % 0.46/0.69 (define @t297 () (forall @t5 @t296)) % 0.46/0.69 (define @t298 () (lambda @t31 @t297)) % 0.46/0.69 (define @t299 () (lambda @t31 (= @t290 @t48))) % 0.46/0.69 (define @t300 () (lambda @t169 (= @t48 @t40))) % 0.46/0.69 (define @t301 () (_ @t46 @t18)) % 0.46/0.69 (define @t302 () (lambda @t19 (_ (_ @t301 @t17) @t12))) % 0.46/0.69 (define @t303 () (lambda @t21 (_ (_ (_ @t44 (_ tptp.mbox (_ @t197 @t302))) (_ @t286 @t14)) @t12))) % 0.46/0.69 (define @t304 () (@var "BOUND_VARIABLE_15399" $$unsorted)) % 0.46/0.69 (define @t305 () (@var "BOUND_VARIABLE_15397" tptp.mu)) % 0.46/0.69 (define @t306 () (lambda (@list @t305 @t304) false)) % 0.46/0.69 (define @t307 () (@purify @t306)) % 0.46/0.69 (define @t308 () (tptp.p @t306 @t8)) % 0.46/0.69 (define @t309 () (_ tptp.p @t306)) % 0.46/0.69 (define @t310 () (_ @t309 @t8)) % 0.46/0.69 (define @t311 () (not @t310)) % 0.46/0.69 (define @t312 () (lambda @t31 @t311)) % 0.46/0.69 (define @t313 () (_ @t312 @t8)) % 0.46/0.69 (define @t314 () (forall @t31 @t313)) % 0.46/0.69 (define @t315 () (tptp.p @t306 @t204)) % 0.46/0.69 (define @t316 () (not @t315)) % 0.46/0.69 (define @t317 () (forall @t31 (not @t308))) % 0.46/0.69 (define @t318 () (tptp.p @t307 @t204)) % 0.46/0.69 (define @t319 () (= @t208 @t318)) % 0.46/0.69 (define @t320 () (not @t319)) % 0.46/0.69 (define @t321 () (forall @t220 (or @t205 @t217 (= (_ @t203 @t215 @t4) (_ @t307 @t215 @t4))))) % 0.46/0.69 (define @t322 () (not @t321)) % 0.46/0.69 (define @t323 () (or @t322 @t319)) % 0.46/0.69 (define @t324 () (@list true false)) % 0.46/0.69 (define @t325 () (@quantifiers_skolemize @t321 0)) % 0.46/0.69 (define @t326 () (@quantifiers_skolemize @t321 1)) % 0.46/0.69 (define @t327 () (_ @t203 @t326 @t325)) % 0.46/0.69 (define @t328 () (not (tptp.eiw_ind @t325 @t326))) % 0.46/0.69 (define @t329 () (not (tptp.rel @t204 @t325))) % 0.46/0.69 (define @t330 () (or @t329 @t328 (not @t327))) % 0.46/0.69 (define @t331 () (not @t330)) % 0.46/0.69 (define @t332 () (_ @t306 @t326 @t325)) % 0.46/0.69 (define @t333 () (_ @t307 @t326 @t325)) % 0.46/0.69 (define @t334 () (= @t327 @t333)) % 0.46/0.69 (define @t335 () (or @t329 @t328 @t334)) % 0.46/0.69 (define @t336 () (not @t335)) % 0.46/0.69 (assume @p1 @t1) % 0.46/0.69 (assume @p2 @t2) % 0.46/0.69 (assume @p3 (forall @t6 (exists @t5 (_ (_ tptp.eiw_ind @t4) @t3)))) % 0.46/0.69 (assume @p4 (_ tptp.mvalid (_ tptp.mnot @t11))) % 0.46/0.69 (assume @p5 (_ tptp.mvalid (_ tptp.mforall_indset @t24))) % 0.46/0.69 (assume @p6 @t28) % 0.46/0.69 (assume @p7 true) % 0.46/0.69 (step @p8 (= tptp.meq_ind @t30) :rule refl :args (@t30)) % 0.46/0.69 (step @p9 (= tptp.mtrue @t32) :rule refl :args (@t32)) % 0.46/0.69 (step @p10 (= tptp.mfalse @t33) :rule refl :args (@t33)) % 0.46/0.69 (step @p11 (= tptp.mnot @t38) :rule refl :args (@t38)) % 0.46/0.69 (step @p12 (= tptp.mor @t42) :rule refl :args (@t42)) % 0.46/0.69 (step @p13 (= tptp.mand @t43) :rule refl :args (@t43)) % 0.46/0.69 (step @p14 (= tptp.mimplies @t44) :rule refl :args (@t44)) % 0.46/0.69 (step @p15 (= tptp.mimplied @t45) :rule refl :args (@t45)) % 0.46/0.69 (step @p16 (= tptp.mequiv @t46) :rule refl :args (@t46)) % 0.46/0.69 (step @p17 (= tptp.mxor @t47) :rule refl :args (@t47)) % 0.46/0.69 (step @p18 (= tptp.mforall_ind @t50) :rule refl :args (@t50)) % 0.46/0.69 (step @p19 (= tptp.mforall_indset @t57) :rule refl :args (@t57)) % 0.46/0.69 (step @p20 (= tptp.mforall_prop @t63) :rule refl :args (@t63)) % 0.46/0.69 (step @p21 (= tptp.mexists_ind @t64) :rule refl :args (@t64)) % 0.46/0.69 (step @p22 (= tptp.mexists_indset @t65) :rule refl :args (@t65)) % 0.46/0.69 (step @p23 (= tptp.mexists_prop @t66) :rule refl :args (@t66)) % 0.46/0.69 (step @p24 (= tptp.mbox_generic @t74) :rule refl :args (@t74)) % 0.46/0.69 (step @p25 (= tptp.mdia_generic @t77) :rule refl :args (@t77)) % 0.46/0.69 (step @p26 (= tptp.mvalid @t80) :rule refl :args (@t80)) % 0.46/0.69 (step @p27 (= tptp.minvalid @t81) :rule refl :args (@t81)) % 0.46/0.69 (step @p28 (= tptp.mforall_eiw_ind @t84) :rule refl :args (@t84)) % 0.46/0.69 (step @p29 (= tptp.mexists_eiw_ind @t86) :rule refl :args (@t86)) % 0.46/0.69 (step @p30 :rule aci_norm :args ((= @t93 @t91))) % 0.46/0.69 (step @p31 :rule cong :premises (@p30) :args (@t95)) % 0.46/0.69 (step @p32 :rule quant-merge-prenex :args ((= (forall @t6 @t97) @t95))) % 0.46/0.69 (step @p33 :rule alpha_equiv :args (@t98 (@list @t87) @t99)) % 0.46/0.69 (step @p34 :rule refl :args (@t90)) % 0.46/0.69 (step @p35 :rule nary_cong :premises (@p34 @p33) :args (@t100)) % 0.46/0.69 (step @p36 :rule quant-miniscope-or :args ((= @t97 @t100))) % 0.46/0.69 (step @p37 :rule trans :premises (@p36 @p35)) % 0.46/0.69 (step @p38 :rule symm :premises (@p37)) % 0.46/0.69 (step @p39 :rule cong :premises (@p38) :args ((forall @t6 (or @t90 @t103)))) % 0.46/0.69 (step @p40 :rule trans :premises (@p39 @p32)) % 0.46/0.69 (step @p41 :rule trans :premises (@p40 @p31)) % 0.46/0.69 (step @p42 :rule bool-double-not-elim :args (@t103)) % 0.46/0.69 (step @p43 :rule beta-reduce :args ((= @t114 (not @t103)))) % 0.46/0.69 (step @p44 :rule cong :premises (@p43) :args (@t115)) % 0.46/0.69 (step @p45 :rule trans :premises (@p44 @p42)) % 0.46/0.69 (step @p46 :rule refl :args (@t90)) % 0.46/0.69 (step @p47 :rule nary_cong :premises (@p46 @p45) :args (@t116)) % 0.46/0.69 (step @p48 :rule cong :premises (@p47) :args (@t117)) % 0.46/0.69 (step @p49 :rule trans :premises (@p48 @p41)) % 0.46/0.69 (step @p50 :rule cong :premises (@p49) :args (@t118)) % 0.46/0.69 (step @p51 :rule beta-reduce :args ((= @t122 @t118))) % 0.46/0.69 (step @p52 :rule trans :premises (@p51 @p50)) % 0.46/0.69 (step @p53 :rule refl :args (@t124)) % 0.46/0.69 (step @p54 :rule nary_cong :premises (@p53 @p52) :args (@t125)) % 0.46/0.69 (step @p55 :rule cong :premises (@p54) :args (@t127)) % 0.46/0.69 (step @p56 :rule cong :premises (@p55) :args ((not @t127))) % 0.46/0.69 (step @p57 :rule refl :args (@t8)) % 0.46/0.69 (step @p58 :rule refl :args (@t113)) % 0.46/0.69 (step @p59 :rule beta-reduce :args ((= @t130 @t121))) % 0.46/0.69 (step @p60 :rule refl :args (tptp.mdia)) % 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