%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEV420^1 : TPTP v9.2.1. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n025.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 08:55:56 AM UTC 2026 % Result : Theorem 0.62s 0.86s % Output : Proof 0.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEV420^1 : TPTP v9.2.1. Released v4.1.0. % 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n025.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 18:32:16 EDT 2026 % 0.17/0.34 % CPUTime : % 0.30/0.49 %----Proving TH0 % 0.62/0.86 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.62/0.86 % SZS status Theorem % 0.62/0.86 % SZS output start Proof % 0.62/0.86 ( % 0.62/0.86 (declare-sort $$unsorted 0) % 0.62/0.86 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.62/0.86 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.62/0.86 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.62/0.86 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.62/0.86 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.62/0.86 (define tptp.union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (or (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.62/0.86 (define tptp.excl_union () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (_ _let_2 _let_1))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.62/0.86 (define tptp.intersection () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))) % 0.62/0.86 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.62/0.86 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.62/0.86 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.62/0.86 (define tptp.subset () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (forall (@list _let_1) (=> (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.62/0.86 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.62/0.86 (define tptp.misses () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (not (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1))))))))) % 0.62/0.86 (define tptp.is_function () (let ((_let_1 (@var "E" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_2 _let_3) (forall (@list _let_1) (=> (_ _let_4 _let_1) (_ _let_3 (_ _let_2 _let_1)))))))))) % 0.62/0.86 (define tptp.injection () (let ((_let_1 (@var "E2" $$unsorted))) (let ((_let_2 (@var "E1" $$unsorted))) (let ((_let_3 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (@var "Y" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_3 _let_5) (=> (_ (_ (_ tptp.is_function _let_4) _let_3) _let_5) (forall (@list _let_2 _let_1) (=> (and (_ _let_4 _let_2) (_ _let_4 _let_1) (= (_ _let_3 _let_2) (_ _let_3 _let_1))) (= _let_2 _let_1))))))))))) % 0.62/0.86 (define tptp.surjection () (let ((_let_1 (@var "E1" $$unsorted))) (let ((_let_2 (@var "E2" $$unsorted))) (let ((_let_3 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "X" (-> $$unsorted Bool)))) (let ((_let_5 (@var "Y" (-> $$unsorted Bool)))) (lambda (@list _let_4 _let_3 _let_5) (=> (_ (_ (_ tptp.is_function _let_4) _let_3) _let_5) (forall (@list _let_1) (=> (_ _let_5 _let_1) (exists (@list _let_2) (and (_ _let_4 _let_2) (= (_ _let_3 _let_2) _let_1))))))))))))) % 0.62/0.86 (define tptp.bijection () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ (_ (_ tptp.injection _let_3) _let_2) _let_1) (_ (_ (_ tptp.surjection _let_3) _let_2) _let_1))))))) % 0.62/0.86 (define tptp.equinumerous () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ (_ tptp.bijection _let_3) _let_2) _let_1))))))) % 0.62/0.86 (define tptp.embedding () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_1) (exists (@list _let_2) (_ (_ (_ tptp.injection _let_3) _let_2) _let_1))))))) % 0.62/0.86 (define @t1 () (@var "Bp" (-> $$unsorted Bool))) % 0.62/0.86 (define @t2 () (@var "Ap" (-> $$unsorted Bool))) % 0.62/0.86 (define @t3 () (@var "B" (-> $$unsorted Bool))) % 0.62/0.86 (define @t4 () (@var "A" (-> $$unsorted Bool))) % 0.62/0.86 (define @t5 () (= (_ (_ tptp.intersection @t2) @t1) tptp.emptyset)) % 0.62/0.86 (define @t6 () (and (_ (_ tptp.equinumerous @t4) @t2) (_ (_ tptp.equinumerous @t3) @t1) @t5)) % 0.62/0.86 (define @t7 () (=> @t6 (_ (_ tptp.embedding (_ (_ tptp.union @t4) @t3)) (_ (_ tptp.union @t2) @t1)))) % 0.62/0.86 (define @t8 () (@list @t4 @t2 @t3 @t1)) % 0.62/0.86 (define @t9 () (forall @t8 @t7)) % 0.62/0.86 (define @t10 () (not @t9)) % 0.62/0.86 (define @t11 () (@var "X" $$unsorted)) % 0.62/0.86 (define @t12 () (@var "M" (-> $$unsorted Bool))) % 0.62/0.86 (define @t13 () (lambda (@list @t11 @t12) (_ @t12 @t11))) % 0.62/0.86 (define @t14 () (lambda (@list @t11) false)) % 0.62/0.86 (define @t15 () (@var "Y" $$unsorted)) % 0.62/0.86 (define @t16 () (@var "U" $$unsorted)) % 0.62/0.86 (define @t17 () (= @t16 @t11)) % 0.62/0.86 (define @t18 () (lambda (@list @t11 @t15 @t16) (or @t17 (= @t16 @t15)))) % 0.62/0.86 (define @t19 () (lambda (@list @t11 @t16) @t17)) % 0.62/0.86 (define @t20 () (@var "Y" (-> $$unsorted Bool))) % 0.62/0.86 (define @t21 () (_ @t20 @t16)) % 0.62/0.86 (define @t22 () (@var "X" (-> $$unsorted Bool))) % 0.62/0.86 (define @t23 () (_ @t22 @t16)) % 0.62/0.86 (define @t24 () (@list @t22 @t20 @t16)) % 0.62/0.86 (define @t25 () (lambda @t24 (or @t23 @t21))) % 0.62/0.86 (define @t26 () (not @t23)) % 0.62/0.86 (define @t27 () (and @t23 (not @t21))) % 0.62/0.86 (define @t28 () (lambda @t24 (or @t27 (and @t26 @t21)))) % 0.62/0.86 (define @t29 () (and @t23 @t21)) % 0.62/0.86 (define @t30 () (lambda @t24 @t29)) % 0.62/0.86 (define @t31 () (lambda @t24 @t27)) % 0.62/0.86 (define @t32 () (lambda (@list @t22 @t16) @t26)) % 0.62/0.86 (define @t33 () (@list @t22 @t20)) % 0.62/0.86 (define @t34 () (lambda @t33 (= (_ (_ tptp.intersection @t22) @t20) tptp.emptyset))) % 0.62/0.86 (define @t35 () (@list @t16)) % 0.62/0.86 (define @t36 () (lambda @t33 (forall @t35 (=> @t23 @t21)))) % 0.62/0.86 (define @t37 () (exists @t35 @t29)) % 0.62/0.86 (define @t38 () (lambda @t33 @t37)) % 0.62/0.86 (define @t39 () (lambda @t33 (not @t37))) % 0.62/0.86 (define @t40 () (@var "E" $$unsorted)) % 0.62/0.86 (define @t41 () (@var "F" (-> $$unsorted $$unsorted))) % 0.62/0.86 (define @t42 () (_ @t41 @t40)) % 0.62/0.86 (define @t43 () (_ @t20 @t42)) % 0.62/0.86 (define @t44 () (_ @t22 @t40)) % 0.62/0.86 (define @t45 () (@list @t40)) % 0.62/0.86 (define @t46 () (forall @t45 (=> @t44 @t43))) % 0.62/0.86 (define @t47 () (@list @t22 @t41 @t20)) % 0.62/0.86 (define @t48 () (lambda @t47 @t46)) % 0.62/0.86 (define @t49 () (@var "E2" $$unsorted)) % 0.62/0.86 (define @t50 () (@var "E1" $$unsorted)) % 0.62/0.86 (define @t51 () (= @t50 @t49)) % 0.62/0.86 (define @t52 () (_ @t41 @t49)) % 0.62/0.86 (define @t53 () (_ @t41 @t50)) % 0.62/0.86 (define @t54 () (= @t53 @t52)) % 0.62/0.86 (define @t55 () (_ @t22 @t49)) % 0.62/0.86 (define @t56 () (_ @t22 @t50)) % 0.62/0.86 (define @t57 () (and @t56 @t55 @t54)) % 0.62/0.86 (define @t58 () (@list @t50 @t49)) % 0.62/0.86 (define @t59 () (forall @t58 (=> @t57 @t51))) % 0.62/0.86 (define @t60 () (_ (_ (_ tptp.is_function @t22) @t41) @t20)) % 0.62/0.86 (define @t61 () (=> @t60 @t59)) % 0.62/0.86 (define @t62 () (lambda @t47 @t61)) % 0.62/0.86 (define @t63 () (and @t55 (= @t52 @t50))) % 0.62/0.86 (define @t64 () (@list @t49)) % 0.62/0.86 (define @t65 () (exists @t64 @t63)) % 0.62/0.86 (define @t66 () (_ @t20 @t50)) % 0.62/0.86 (define @t67 () (=> @t66 @t65)) % 0.62/0.86 (define @t68 () (@list @t50)) % 0.62/0.86 (define @t69 () (forall @t68 @t67)) % 0.62/0.86 (define @t70 () (=> @t60 @t69)) % 0.62/0.86 (define @t71 () (lambda @t47 @t70)) % 0.62/0.86 (define @t72 () (_ (_ (_ tptp.injection @t22) @t41) @t20)) % 0.62/0.86 (define @t73 () (and @t72 (_ (_ (_ tptp.surjection @t22) @t41) @t20))) % 0.62/0.86 (define @t74 () (lambda @t47 @t73)) % 0.62/0.86 (define @t75 () (@list @t41)) % 0.62/0.86 (define @t76 () (exists @t75 (_ (_ (_ tptp.bijection @t22) @t41) @t20))) % 0.62/0.86 (define @t77 () (lambda @t33 @t76)) % 0.62/0.86 (define @t78 () (exists @t75 @t72)) % 0.62/0.86 (define @t79 () (lambda @t33 @t78)) % 0.62/0.86 (define @t80 () (@var "BOUND_VARIABLE_8178" (-> $$unsorted $$unsorted))) % 0.62/0.86 (define @t81 () (_ @t80 @t49)) % 0.62/0.86 (define @t82 () (_ @t3 @t49)) % 0.62/0.86 (define @t83 () (not @t82)) % 0.62/0.86 (define @t84 () (not (_ @t1 @t50))) % 0.62/0.86 (define @t85 () (@var "BOUND_VARIABLE_8182" $$unsorted)) % 0.62/0.86 (define @t86 () (and (or (not (_ @t3 @t85)) (_ @t1 (_ @t80 @t85))) (not (forall @t68 (or @t84 (not (forall @t64 (or @t83 (not (= @t50 @t81)))))))))) % 0.62/0.86 (define @t87 () (_ @t3 @t50)) % 0.62/0.86 (define @t88 () (not @t87)) % 0.62/0.86 (define @t89 () (@var "BOUND_VARIABLE_8180" $$unsorted)) % 0.62/0.86 (define @t90 () (and (or (not (_ @t3 @t89)) (_ @t1 (_ @t80 @t89))) (not (forall @t58 (or @t88 @t83 (not (= (_ @t80 @t50) @t81)) @t51))))) % 0.62/0.86 (define @t91 () (@var "BOUND_VARIABLE_8144" (-> $$unsorted $$unsorted))) % 0.62/0.86 (define @t92 () (_ @t91 @t49)) % 0.62/0.86 (define @t93 () (_ @t4 @t49)) % 0.62/0.86 (define @t94 () (not @t93)) % 0.62/0.86 (define @t95 () (not (_ @t2 @t50))) % 0.62/0.86 (define @t96 () (@var "BOUND_VARIABLE_8148" $$unsorted)) % 0.62/0.86 (define @t97 () (and (or (not (_ @t4 @t96)) (_ @t2 (_ @t91 @t96))) (not (forall @t68 (or @t95 (not (forall @t64 (or @t94 (not (= @t50 @t92)))))))))) % 0.62/0.86 (define @t98 () (_ @t4 @t50)) % 0.62/0.86 (define @t99 () (not @t98)) % 0.62/0.86 (define @t100 () (@var "BOUND_VARIABLE_8146" $$unsorted)) % 0.62/0.86 (define @t101 () (and (or (not (_ @t4 @t100)) (_ @t2 (_ @t91 @t100))) (not (forall @t58 (or @t99 @t94 (not (= (_ @t91 @t50) @t92)) @t51))))) % 0.62/0.86 (define @t102 () (@var "BOUND_VARIABLE_7815" (-> $$unsorted $$unsorted))) % 0.62/0.86 (define @t103 () (not (= (_ @t102 @t50) (_ @t102 @t49)))) % 0.62/0.86 (define @t104 () (@list @t102)) % 0.62/0.86 (define @t105 () (forall @t104 (not (forall @t58 (or (and @t99 @t88) (and @t94 @t83) @t103 @t51))))) % 0.62/0.86 (define @t106 () (not @t105)) % 0.62/0.86 (define @t107 () (@var "BOUND_VARIABLE_7807" (-> $$unsorted $$unsorted))) % 0.62/0.86 (define @t108 () (_ @t107 @t40)) % 0.62/0.86 (define @t109 () (_ @t1 @t108)) % 0.62/0.86 (define @t110 () (_ @t2 @t108)) % 0.62/0.86 (define @t111 () (_ @t3 @t40)) % 0.62/0.86 (define @t112 () (_ @t4 @t40)) % 0.62/0.86 (define @t113 () (and (not @t112) (not @t111))) % 0.62/0.86 (define @t114 () (@list @t107 @t40)) % 0.62/0.86 (define @t115 () (forall @t114 (or @t113 @t110 @t109))) % 0.62/0.86 (define @t116 () (not @t115)) % 0.62/0.86 (define @t117 () (_ @t1 @t16)) % 0.62/0.86 (define @t118 () (_ @t2 @t16)) % 0.62/0.86 (define @t119 () (@var "BOUND_VARIABLE_8470" $$unsorted)) % 0.62/0.86 (define @t120 () (lambda (@list @t119) false)) % 0.62/0.86 (define @t121 () (not (= @t120 (lambda @t35 (and @t118 @t117))))) % 0.62/0.86 (define @t122 () (or @t121 @t116 @t106 @t101 @t97 @t90 @t86)) % 0.62/0.86 (define @t123 () (or @t90 @t86)) % 0.62/0.86 (define @t124 () (or @t101 @t97)) % 0.62/0.86 (define @t125 () (or @t124 @t123 @t121 @t116 @t106)) % 0.62/0.86 (define @t126 () (@list @t4 @t2 @t3 @t1 @t91 @t100 @t96 @t80 @t89 @t85)) % 0.62/0.86 (define @t127 () (forall @t126 @t125)) % 0.62/0.86 (define @t128 () (forall (@list @t91 @t100 @t96 @t80 @t89 @t85) @t125)) % 0.62/0.86 (define @t129 () (forall (@list @t80 @t89 @t85) @t123)) % 0.62/0.86 (define @t130 () (@var "BOUND_VARIABLE_7778" $$unsorted)) % 0.62/0.86 (define @t131 () (@var "BOUND_VARIABLE_7770" $$unsorted)) % 0.62/0.86 (define @t132 () (@list @t41 @t131 @t130)) % 0.62/0.86 (define @t133 () (forall (@list @t91 @t100 @t96) @t124)) % 0.62/0.86 (define @t134 () (or @t133 @t129 @t121 @t116 @t106)) % 0.62/0.86 (define @t135 () (_ @t41 @t49)) % 0.62/0.86 (define @t136 () (not (= @t50 @t135))) % 0.62/0.86 (define @t137 () (not (forall @t64 (or @t83 @t136)))) % 0.62/0.86 (define @t138 () (_ @t41 @t130)) % 0.62/0.86 (define @t139 () (not (_ @t3 @t130))) % 0.62/0.86 (define @t140 () (_ @t41 @t50)) % 0.62/0.86 (define @t141 () (not (= @t140 @t135))) % 0.62/0.86 (define @t142 () (not (forall @t58 (or @t88 @t83 @t141 @t51)))) % 0.62/0.86 (define @t143 () (_ @t41 @t131)) % 0.62/0.86 (define @t144 () (not (_ @t3 @t131))) % 0.62/0.86 (define @t145 () (@list @t41 @t131 @t130)) % 0.62/0.86 (define @t146 () (forall @t145 (or (and (or @t144 (_ @t1 @t143)) @t142) (and (or @t139 (_ @t1 @t138)) (not (forall @t68 (or @t84 @t137))))))) % 0.62/0.86 (define @t147 () (not (forall @t64 (or @t94 @t136)))) % 0.62/0.86 (define @t148 () (not (_ @t4 @t130))) % 0.62/0.86 (define @t149 () (not (forall @t58 (or @t99 @t94 @t141 @t51)))) % 0.62/0.86 (define @t150 () (not (_ @t4 @t131))) % 0.62/0.86 (define @t151 () (forall @t145 (or (and (or @t150 (_ @t2 @t143)) @t149) (and (or @t148 (_ @t2 @t138)) (not (forall @t68 (or @t95 @t147))))))) % 0.62/0.86 (define @t152 () (_ @t1 @t16)) % 0.62/0.86 (define @t153 () (_ @t2 @t16)) % 0.62/0.86 (define @t154 () (and @t153 @t152)) % 0.62/0.86 (define @t155 () (lambda @t35 @t154)) % 0.62/0.86 (define @t156 () (= @t120 @t155)) % 0.62/0.86 (define @t157 () (not @t156)) % 0.62/0.86 (define @t158 () (or @t151 @t146 @t157 @t116 @t106)) % 0.62/0.86 (define @t159 () (not @t146)) % 0.62/0.86 (define @t160 () (not @t159)) % 0.62/0.86 (define @t161 () (not @t151)) % 0.62/0.86 (define @t162 () (not @t161)) % 0.62/0.86 (define @t163 () (or @t162 @t160 @t157)) % 0.62/0.86 (define @t164 () (not (and @t115 @t105))) % 0.62/0.86 (define @t165 () (and @t161 @t159 @t156)) % 0.62/0.86 (define @t166 () (_ @t107 @t40)) % 0.62/0.86 (define @t167 () (_ @t1 @t108)) % 0.62/0.86 (define @t168 () (_ @t2 @t108)) % 0.62/0.86 (define @t169 () (or @t113 @t168 @t167)) % 0.62/0.86 (define @t170 () (or @t168 @t167)) % 0.62/0.86 (define @t171 () (lambda @t35 (or @t153 @t152))) % 0.62/0.86 (define @t172 () (_ @t171 @t108)) % 0.62/0.86 (define @t173 () (or @t113 @t172)) % 0.62/0.86 (define @t174 () (forall @t114 @t173)) % 0.62/0.86 (define @t175 () (and @t174 @t105)) % 0.62/0.86 (define @t176 () (not @t175)) % 0.62/0.86 (define @t177 () (_ @t20 @t108)) % 0.62/0.86 (define @t178 () (@list @t20)) % 0.62/0.86 (define @t179 () (@list @t20 @t16)) % 0.62/0.86 (define @t180 () (lambda @t179 (or @t153 @t21))) % 0.62/0.86 (define @t181 () (_ @t25 @t2)) % 0.62/0.86 (define @t182 () (_ @t3 @t49)) % 0.62/0.86 (define @t183 () (not @t182)) % 0.62/0.86 (define @t184 () (_ @t4 @t49)) % 0.62/0.86 (define @t185 () (not @t184)) % 0.62/0.86 (define @t186 () (and @t185 @t183)) % 0.62/0.86 (define @t187 () (_ @t3 @t50)) % 0.62/0.86 (define @t188 () (not @t187)) % 0.62/0.86 (define @t189 () (_ @t4 @t50)) % 0.62/0.86 (define @t190 () (not @t189)) % 0.62/0.86 (define @t191 () (and @t190 @t188)) % 0.62/0.86 (define @t192 () (or @t191 @t186 @t103 @t51)) % 0.62/0.86 (define @t193 () (or @t184 @t182)) % 0.62/0.86 (define @t194 () (or @t189 @t187)) % 0.62/0.86 (define @t195 () (or (not @t194) (not @t193) @t103 @t51)) % 0.62/0.86 (define @t196 () (_ @t4 @t16)) % 0.62/0.86 (define @t197 () (lambda @t35 (or @t196 (_ @t3 @t16)))) % 0.62/0.86 (define @t198 () (_ @t197 @t49)) % 0.62/0.86 (define @t199 () (not @t198)) % 0.62/0.86 (define @t200 () (_ @t197 @t50)) % 0.62/0.86 (define @t201 () (not @t200)) % 0.62/0.86 (define @t202 () (or @t201 @t199 @t103 @t51)) % 0.62/0.86 (define @t203 () (forall @t58 @t202)) % 0.62/0.86 (define @t204 () (not @t203)) % 0.62/0.86 (define @t205 () (forall @t104 @t204)) % 0.62/0.86 (define @t206 () (_ @t3 @t40)) % 0.62/0.86 (define @t207 () (not @t206)) % 0.62/0.86 (define @t208 () (_ @t4 @t40)) % 0.62/0.86 (define @t209 () (not @t208)) % 0.62/0.86 (define @t210 () (and @t209 @t207)) % 0.62/0.86 (define @t211 () (or @t210 @t177)) % 0.62/0.86 (define @t212 () (or @t208 @t206)) % 0.62/0.86 (define @t213 () (or (not @t212) @t177)) % 0.62/0.86 (define @t214 () (_ @t197 @t40)) % 0.62/0.86 (define @t215 () (not @t214)) % 0.62/0.86 (define @t216 () (or @t215 @t177)) % 0.62/0.86 (define @t217 () (forall @t114 @t216)) % 0.62/0.86 (define @t218 () (and @t217 @t205)) % 0.62/0.86 (define @t219 () (not @t218)) % 0.62/0.86 (define @t220 () (lambda @t178 @t219)) % 0.62/0.86 (define @t221 () (_ @t22 @t49)) % 0.62/0.86 (define @t222 () (not @t221)) % 0.62/0.86 (define @t223 () (_ @t22 @t50)) % 0.62/0.86 (define @t224 () (not @t223)) % 0.62/0.86 (define @t225 () (forall @t104 (not (forall @t58 (or @t224 @t222 @t103 @t51))))) % 0.62/0.86 (define @t226 () (_ @t22 @t40)) % 0.62/0.86 (define @t227 () (not @t226)) % 0.62/0.86 (define @t228 () (or @t227 @t177)) % 0.62/0.86 (define @t229 () (forall @t114 @t228)) % 0.62/0.86 (define @t230 () (lambda @t33 (not (and @t229 @t225)))) % 0.62/0.86 (define @t231 () (lambda @t179 (or @t196 @t21))) % 0.62/0.86 (define @t232 () (_ @t25 @t4)) % 0.62/0.86 (define @t233 () (lambda @t179 (and @t153 @t21))) % 0.62/0.86 (define @t234 () (_ @t30 @t2)) % 0.62/0.86 (define @t235 () (= (_ @t234 @t1) @t14)) % 0.62/0.86 (define @t236 () (_ @t20 @t50)) % 0.62/0.86 (define @t237 () (not @t236)) % 0.62/0.86 (define @t238 () (_ @t20 @t138)) % 0.62/0.86 (define @t239 () (_ @t20 @t143)) % 0.62/0.86 (define @t240 () (lambda @t178 (not (forall @t145 (or (and (or @t144 @t239) @t142) (and (or @t139 @t238) (not (forall @t68 (or @t237 @t137))))))))) % 0.62/0.86 (define @t241 () (not (forall @t64 (or @t222 @t136)))) % 0.62/0.86 (define @t242 () (forall @t68 (or @t237 @t241))) % 0.62/0.86 (define @t243 () (not @t242)) % 0.62/0.86 (define @t244 () (or (not (_ @t22 @t130)) @t238)) % 0.62/0.86 (define @t245 () (and @t244 @t243)) % 0.62/0.86 (define @t246 () (forall @t58 (or @t224 @t222 @t141 @t51))) % 0.62/0.86 (define @t247 () (not @t246)) % 0.62/0.86 (define @t248 () (or (not (_ @t22 @t131)) @t239)) % 0.62/0.86 (define @t249 () (and @t248 @t247)) % 0.62/0.86 (define @t250 () (or @t249 @t245)) % 0.62/0.86 (define @t251 () (forall @t145 @t250)) % 0.62/0.86 (define @t252 () (lambda @t33 (not @t251))) % 0.62/0.86 (define @t253 () (_ @t252 @t3)) % 0.62/0.86 (define @t254 () (lambda @t178 (not (forall @t145 (or (and (or @t150 @t239) @t149) (and (or @t148 @t238) (not (forall @t68 (or @t237 @t147))))))))) % 0.62/0.86 (define @t255 () (_ @t252 @t4)) % 0.62/0.86 (define @t256 () (and (_ @t255 @t2) (_ @t253 @t1) @t235)) % 0.62/0.86 (define @t257 () (=> @t256 (_ (_ @t230 (_ @t232 @t3)) (_ @t181 @t1)))) % 0.62/0.86 (define @t258 () (forall @t8 @t257)) % 0.62/0.86 (define @t259 () (forall (@list @t107) (forall @t45 @t228))) % 0.62/0.86 (define @t260 () (forall @t75 @t247)) % 0.62/0.86 (define @t261 () (@list @t41)) % 0.62/0.86 (define @t262 () (_ @t41 @t40)) % 0.62/0.86 (define @t263 () (_ @t20 @t262)) % 0.62/0.86 (define @t264 () (forall @t45 (or @t227 @t263))) % 0.62/0.86 (define @t265 () (forall @t75 @t264)) % 0.62/0.86 (define @t266 () (and @t265 @t260)) % 0.62/0.86 (define @t267 () (and @t264 @t247)) % 0.62/0.86 (define @t268 () (=> @t264 @t246)) % 0.62/0.86 (define @t269 () (not @t268)) % 0.62/0.86 (define @t270 () (forall @t75 @t269)) % 0.62/0.86 (define @t271 () (not @t270)) % 0.62/0.86 (define @t272 () (lambda @t178 @t268)) % 0.62/0.86 (define @t273 () (@list @t41 @t20)) % 0.62/0.86 (define @t274 () (lambda @t273 @t268)) % 0.62/0.86 (define @t275 () (_ (lambda @t47 @t268) @t22)) % 0.62/0.86 (define @t276 () (_ (_ @t275 @t41) @t20)) % 0.62/0.86 (define @t277 () (not @t54)) % 0.62/0.86 (define @t278 () (not @t55)) % 0.62/0.86 (define @t279 () (not @t56)) % 0.62/0.86 (define @t280 () (or @t279 @t278 @t277 @t51)) % 0.62/0.86 (define @t281 () (or @t279 @t278 @t277)) % 0.62/0.86 (define @t282 () (lambda @t178 @t264)) % 0.62/0.86 (define @t283 () (lambda @t273 @t264)) % 0.62/0.86 (define @t284 () (_ (lambda @t47 @t264) @t22)) % 0.62/0.86 (define @t285 () (_ (_ @t284 @t41) @t20)) % 0.62/0.86 (define @t286 () (not @t44)) % 0.62/0.86 (define @t287 () (or @t286 @t43)) % 0.62/0.86 (define @t288 () (forall (@list @t131 @t130) @t250)) % 0.62/0.86 (define @t289 () (@list @t130)) % 0.62/0.86 (define @t290 () (forall @t289 @t243)) % 0.62/0.86 (define @t291 () (forall @t289 @t244)) % 0.62/0.86 (define @t292 () (@list @t40)) % 0.62/0.86 (define @t293 () (and @t291 @t290)) % 0.62/0.86 (define @t294 () (forall @t289 @t245)) % 0.62/0.86 (define @t295 () (@list @t131)) % 0.62/0.86 (define @t296 () (forall @t295 @t247)) % 0.62/0.86 (define @t297 () (forall @t295 @t248)) % 0.62/0.86 (define @t298 () (and @t297 @t296)) % 0.62/0.86 (define @t299 () (forall @t295 @t249)) % 0.62/0.86 (define @t300 () (or @t299 @t294)) % 0.62/0.86 (define @t301 () (=> @t264 @t242)) % 0.62/0.86 (define @t302 () (and @t268 @t301)) % 0.62/0.86 (define @t303 () (forall @t75 (not @t302))) % 0.62/0.86 (define @t304 () (not @t303)) % 0.62/0.86 (define @t305 () (lambda @t178 @t302)) % 0.62/0.86 (define @t306 () (lambda @t273 @t302)) % 0.62/0.86 (define @t307 () (_ (lambda @t47 @t302) @t22)) % 0.62/0.86 (define @t308 () (lambda @t178 @t301)) % 0.62/0.86 (define @t309 () (lambda @t273 @t301)) % 0.62/0.86 (define @t310 () (_ (lambda @t47 @t301) @t22)) % 0.62/0.86 (define @t311 () (not @t66)) % 0.62/0.86 (define @t312 () (or @t311 @t241)) % 0.62/0.86 (define @t313 () (= @t50 @t52)) % 0.62/0.86 (define @t314 () (not @t313)) % 0.62/0.86 (define @t315 () (or @t278 @t314)) % 0.62/0.86 (define @t316 () (and @t55 @t313)) % 0.62/0.86 (define @t317 () (forall @t64 (not @t316))) % 0.62/0.86 (define @t318 () (not @t317)) % 0.62/0.86 (define @t319 () (forall @t126 @t122)) % 0.62/0.86 (define @t320 () (@quantifiers_skolemize @t319 7)) % 0.62/0.86 (define @t321 () (_ @t320 @t49)) % 0.62/0.86 (define @t322 () (@quantifiers_skolemize @t319 2)) % 0.62/0.86 (define @t323 () (not (_ @t322 @t49))) % 0.62/0.86 (define @t324 () (@quantifiers_skolemize @t319 3)) % 0.62/0.86 (define @t325 () (@quantifiers_skolemize @t319 9)) % 0.62/0.86 (define @t326 () (and (or (not (_ @t322 @t325)) (_ @t324 (_ @t320 @t325))) (not (forall @t68 (or (not (_ @t324 @t50)) (not (forall @t64 (or @t323 (not (= @t50 @t321)))))))))) % 0.62/0.86 (define @t327 () (not (_ @t322 @t50))) % 0.62/0.86 (define @t328 () (@quantifiers_skolemize @t319 8)) % 0.62/0.86 (define @t329 () (and (or (not (_ @t322 @t328)) (_ @t324 (_ @t320 @t328))) (not (forall @t58 (or @t327 @t323 (not (= (_ @t320 @t50) @t321)) @t51))))) % 0.62/0.86 (define @t330 () (@quantifiers_skolemize @t319 4)) % 0.62/0.86 (define @t331 () (_ @t330 @t49)) % 0.62/0.86 (define @t332 () (@quantifiers_skolemize @t319 0)) % 0.62/0.86 (define @t333 () (not (_ @t332 @t49))) % 0.62/0.86 (define @t334 () (@quantifiers_skolemize @t319 1)) % 0.62/0.86 (define @t335 () (@quantifiers_skolemize @t319 6)) % 0.62/0.86 (define @t336 () (and (or (not (_ @t332 @t335)) (_ @t334 (_ @t330 @t335))) (not (forall @t68 (or (not (_ @t334 @t50)) (not (forall @t64 (or @t333 (not (= @t50 @t331)))))))))) % 0.62/0.86 (define @t337 () (not (_ @t332 @t50))) % 0.62/0.86 (define @t338 () (@quantifiers_skolemize @t319 5)) % 0.62/0.86 (define @t339 () (and (or (not (_ @t332 @t338)) (_ @t334 (_ @t330 @t338))) (not (forall @t58 (or @t337 @t333 (not (= (_ @t330 @t50) @t331)) @t51))))) % 0.62/0.86 (define @t340 () (and @t333 @t323)) % 0.62/0.86 (define @t341 () (and @t337 @t327)) % 0.62/0.86 (define @t342 () (forall @t104 (not (forall @t58 (or @t341 @t340 @t103 @t51))))) % 0.62/0.86 (define @t343 () (not @t342)) % 0.62/0.86 (define @t344 () (not (forall @t114 (or (and (not (_ @t332 @t40)) (not (_ @t322 @t40))) (_ @t334 @t108) (_ @t324 @t108))))) % 0.62/0.86 (define @t345 () (@purify @t120)) % 0.62/0.86 (define @t346 () (lambda @t35 (and (_ @t334 @t16) (_ @t324 @t16)))) % 0.62/0.86 (define @t347 () (@purify @t346)) % 0.62/0.86 (define @t348 () (or (not (= @t347 @t345)) @t344 @t343 @t339 @t336 @t329 @t326)) % 0.62/0.86 (define @t349 () (not @t348)) % 0.62/0.86 (define @t350 () (not @t319)) % 0.62/0.86 (define @t351 () (= @t120 @t346)) % 0.62/0.86 (define @t352 () (not @t351)) % 0.62/0.86 (define @t353 () (or @t352 @t344 @t343 @t339 @t336 @t329 @t326)) % 0.62/0.86 (define @t354 () (not @t353)) % 0.62/0.86 (define @t355 () (@list true)) % 0.62/0.86 (define @t356 () (@var "BOUND_VARIABLE_55488" $$unsorted)) % 0.62/0.86 (define @t357 () (lambda (@list @t356) @t356)) % 0.62/0.86 (define @t358 () (_ @t357 @t49)) % 0.62/0.86 (define @t359 () (_ @t357 @t50)) % 0.62/0.86 (define @t360 () (= @t359 @t358)) % 0.62/0.86 (define @t361 () (not @t360)) % 0.62/0.86 (define @t362 () (or @t341 @t340 @t361 @t51)) % 0.62/0.86 (define @t363 () (forall @t58 @t362)) % 0.62/0.86 (define @t364 () (not @t363)) % 0.62/0.86 (assume @p1 @t10) % 0.62/0.86 (assume @p2 true) % 0.62/0.86 (step @p3 (= tptp.in @t13) :rule refl :args (@t13)) % 0.62/0.86 (step @p4 (= tptp.is_a @t13) :rule refl :args (@t13)) % 0.62/0.86 (step @p5 (= tptp.emptyset @t14) :rule refl :args (@t14)) % 0.62/0.86 (step @p6 (= tptp.unord_pair @t18) :rule refl :args (@t18)) % 0.62/0.86 (step @p7 (= tptp.singleton @t19) :rule refl :args (@t19)) % 0.62/0.86 (step @p8 (= tptp.union @t25) :rule refl :args (@t25)) % 0.62/0.86 (step @p9 (= tptp.excl_union @t28) :rule refl :args (@t28)) % 0.62/0.86 (step @p10 (= tptp.intersection @t30) :rule refl :args (@t30)) % 0.62/0.86 (step @p11 (= tptp.setminus @t31) :rule refl :args (@t31)) % 0.62/0.86 (step @p12 (= tptp.complement @t32) :rule refl :args (@t32)) % 0.62/0.86 (step @p13 (= tptp.disjoint @t34) :rule refl :args (@t34)) % 0.62/0.86 (step @p14 (= tptp.subset @t36) :rule refl :args (@t36)) % 0.62/0.86 (step @p15 (= tptp.meets @t38) :rule refl :args (@t38)) % 0.62/0.86 (step @p16 (= tptp.misses @t39) :rule refl :args (@t39)) % 0.62/0.86 (step @p17 (= tptp.is_function @t48) :rule refl :args (@t48)) % 0.62/0.86 (step @p18 (= tptp.injection @t62) :rule refl :args (@t62)) % 0.62/0.86 (step @p19 (= tptp.surjection @t71) :rule refl :args (@t71)) % 0.62/0.86 (step @p20 (= tptp.bijection @t74) :rule refl :args (@t74)) % 0.62/0.86 (step @p21 (= tptp.equinumerous @t77) :rule refl :args (@t77)) % 0.62/0.86 (step @p22 (= tptp.embedding @t79) :rule refl :args (@t79)) % 0.62/0.86 (step @p23 :rule aci_norm :args ((= @t125 @t122))) % 0.62/0.86 (step @p24 :rule cong :premises (@p23) :args (@t127)) % 0.62/0.86 (step @p25 :rule quant-merge-prenex :args ((= (forall @t8 @t128) @t127))) % 0.62/0.86 (step @p26 :rule refl :args (@t106)) % 0.62/0.86 (step @p27 :rule refl :args (@t116)) % 0.62/0.86 (step @p28 :rule refl :args (@t121)) % 0.62/0.86 (step @p29 :rule alpha_equiv :args (@t129 (@list @t80 @t89 @t85) @t132)) % 0.62/0.86 (step @p30 :rule alpha_equiv :args (@t133 (@list @t91 @t100 @t96) @t132)) % 0.62/0.86 (step @p31 :rule nary_cong :premises (@p30 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@t43)) % 0.62/0.86 (step @p335 :rule cong :premises (@p334) :args (@t46)) % 0.62/0.86 (step @p336 :rule trans :premises (@p335 @p333)) % 0.62/0.86 (step @p337 :rule cong :premises (@p336) :args (@t48)) % 0.62/0.86 (step @p338 :rule trans :premises (@p17 @p337)) % 0.62/0.86 (step @p339 :rule ho_cong :premises (@p338 @p260)) % 0.62/0.86 (step @p340 :rule ho_cong :premises (@p339 @p252)) % 0.62/0.86 (step @p341 :rule ho_cong :premises (@p340 @p250)) % 0.62/0.86 (step @p342 :rule cong :premises (@p341 @p309) :args (@t61)) % 0.62/0.86 (step @p343 :rule trans :premises (@p342 @p308)) % 0.62/0.86 (step @p344 :rule cong :premises (@p343) :args (@t62)) % 0.62/0.86 (step @p345 :rule trans :premises (@p18 @p344)) % 0.62/0.86 (step @p346 :rule ho_cong :premises (@p345 @p260)) % 0.62/0.86 (step @p347 :rule ho_cong :premises (@p346 @p252)) % 0.62/0.86 (step @p348 :rule ho_cong :premises (@p347 @p250)) % 0.62/0.86 (step @p349 :rule cong :premises (@p348) :args (@t78)) % 0.62/0.86 (step @p350 :rule 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@t247))) % 0.62/0.86 (step @p365 :rule alpha_equiv :args (@t297 (@list @t131) @t292)) % 0.62/0.86 (step @p366 :rule nary_cong :premises (@p365 @p364) :args (@t298)) % 0.62/0.86 (step @p367 :rule quant-miniscope-and :args ((= @t299 @t298))) % 0.62/0.86 (step @p368 :rule trans :premises (@p367 @p366)) % 0.62/0.86 (step @p369 :rule nary_cong :premises (@p368 @p363) :args (@t300)) % 0.62/0.86 (step @p370 :rule quant-miniscope-or :args ((= @t288 @t300))) % 0.62/0.86 (step @p371 :rule trans :premises (@p370 @p369)) % 0.62/0.86 (step @p372 :rule symm :premises (@p371)) % 0.62/0.86 (step @p373 :rule cong :premises (@p372) :args ((forall @t75 (or @t267 (and @t264 @t243))))) % 0.62/0.86 (step @p374 :rule trans :premises (@p373 @p358)) % 0.62/0.86 (step @p375 :rule bool-implies-de-morgan :args (@t264 @t242)) % 0.62/0.86 (step @p376 :rule nary_cong :premises (@p243 @p375) :args ((or @t269 (not @t301)))) % 0.62/0.86 (step @p377 :rule bool-and-de-morgan :args (@t268 @t301 true)) % 0.62/0.86 (step @p378 :rule trans :premises (@p377 @p376)) % 0.62/0.86 (step @p379 :rule cong :premises (@p378) :args (@t303)) % 0.62/0.86 (step @p380 :rule trans :premises (@p379 @p374)) % 0.62/0.86 (step @p381 :rule cong :premises (@p380) :args (@t304)) % 0.62/0.86 (step @p382 :rule exists-elim :args ((= (exists @t75 @t302) @t304))) % 0.62/0.86 (step @p383 :rule trans :premises (@p382 @p381)) % 0.62/0.86 (step @p384 :rule beta-reduce :args ((= (_ @t305 @t20) @t302))) % 0.62/0.86 (step @p385 :rule beta-reduce :args ((= (_ @t306 @t41) @t305))) % 0.62/0.86 (step @p386 :rule beta-reduce :args ((= @t307 @t306))) % 0.62/0.86 (step @p387 :rule ho_cong :premises (@p386 @p252)) % 0.62/0.86 (step @p388 :rule trans :premises (@p387 @p385)) % 0.62/0.86 (step @p389 :rule ho_cong :premises (@p388 @p250)) % 0.62/0.86 (step @p390 :rule trans :premises (@p389 @p384)) % 0.62/0.86 (step @p391 :rule cong :premises (@p390) :args ((exists @t75 (_ (_ @t307 @t41) @t20)))) % 0.62/0.86 (step @p392 :rule trans :premises (@p391 @p383)) % 0.62/0.86 (step @p393 :rule beta-reduce :args ((= (_ @t308 @t20) @t301))) % 0.62/0.86 (step @p394 :rule beta-reduce :args ((= (_ @t309 @t41) @t308))) % 0.62/0.86 (step @p395 :rule beta-reduce :args ((= @t310 @t309))) % 0.62/0.86 (step @p396 :rule ho_cong :premises (@p395 @p252)) % 0.62/0.86 (step @p397 :rule trans :premises (@p396 @p394)) % 0.62/0.86 (step @p398 :rule ho_cong :premises (@p397 @p250)) % 0.62/0.86 (step @p399 :rule trans :premises (@p398 @p393)) % 0.62/0.86 (step @p400 :rule nary_cong :premises (@p257 @p399) :args ((and @t276 (_ (_ @t310 @t41) @t20)))) % 0.62/0.86 (step @p401 :rule refl :args (@t241)) % 0.62/0.86 (step @p402 :rule refl :args (@t236)) % 0.62/0.86 (step @p403 :rule refl :args (@t66)) % 0.62/0.86 (step @p404 :rule cong :premises (@p403 @p402) :args ((= @t66 @t236))) % 0.62/0.86 (step @p405 :rule symm :premises (@p404)) % 0.62/0.86 (step @p406 :rule eq_resolve :premises (@p403 @p405)) % 0.62/0.86 (step @p407 :rule cong :premises (@p406) :args (@t311)) % 0.62/0.86 (step @p408 :rule nary_cong :premises (@p407 @p401) :args (@t312)) % 0.62/0.86 (step @p409 :rule cong :premises (@p408) :args ((forall @t68 @t312))) % 0.62/0.86 (step @p410 :rule bool-impl-elim :args (@t66 @t241)) % 0.62/0.86 (step @p411 :rule cong :premises (@p410) :args ((forall @t68 (=> @t66 @t241)))) % 0.62/0.86 (step @p412 :rule trans :premises (@p411 @p409)) % 0.62/0.86 (step @p413 :rule refl :args (@t50)) % 0.62/0.86 (step @p414 :rule cong :premises (@p413 @p265) :args (@t313)) % 0.62/0.86 (step @p415 :rule cong :premises (@p414) :args (@t314)) % 0.62/0.86 (step @p416 :rule nary_cong :premises (@p278 @p415) :args (@t315)) % 0.62/0.86 (step @p417 :rule cong :premises (@p416) :args ((forall @t64 @t315))) % 0.62/0.86 (step @p418 :rule bool-and-de-morgan :args (@t55 @t313 true)) % 0.62/0.86 (step @p419 :rule cong :premises (@p418) :args (@t317)) % 0.62/0.86 (step @p420 :rule trans :premises (@p419 @p417)) % 0.62/0.86 (step @p421 :rule cong :premises 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0.62/0.86 (step @p437 :rule cong :premises (@p436) :args (@t71)) % 0.62/0.86 (step @p438 :rule trans :premises (@p19 @p437)) % 0.62/0.86 (step @p439 :rule ho_cong :premises (@p438 @p260)) % 0.62/0.86 (step @p440 :rule ho_cong :premises (@p439 @p252)) % 0.62/0.86 (step @p441 :rule ho_cong :premises (@p440 @p250)) % 0.62/0.86 (step @p442 :rule nary_cong :premises (@p348 @p441) :args (@t73)) % 0.62/0.86 (step @p443 :rule trans :premises (@p442 @p400)) % 0.62/0.86 (step @p444 :rule cong :premises (@p443) :args (@t74)) % 0.62/0.86 (step @p445 :rule trans :premises (@p20 @p444)) % 0.62/0.86 (step @p446 :rule ho_cong :premises (@p445 @p260)) % 0.62/0.86 (step @p447 :rule ho_cong :premises (@p446 @p252)) % 0.62/0.86 (step @p448 :rule ho_cong :premises (@p447 @p250)) % 0.62/0.86 (step @p449 :rule cong :premises (@p448) :args (@t76)) % 0.62/0.86 (step @p450 :rule trans :premises (@p449 @p392)) % 0.62/0.86 (step @p451 :rule cong :premises (@p450) :args (@t77)) % 0.62/0.86 (step @p452 :rule trans :premises (@p21 @p451)) % 0.62/0.86 (step @p453 :rule ho_cong :premises (@p452 @p195)) % 0.62/0.86 (step @p454 :rule ho_cong :premises (@p453 @p113)) % 0.62/0.86 (step @p455 :rule ho_cong :premises (@p452 @p231)) % 0.62/0.86 (step @p456 :rule ho_cong :premises (@p455 @p220)) % 0.62/0.86 (step @p457 :rule nary_cong :premises (@p456 @p454 @p357) :args (@t6)) % 0.62/0.86 (step @p458 :rule cong :premises (@p457 @p354) :args (@t7)) % 0.62/0.86 (step @p459 :rule cong :premises (@p458) :args (@t9)) % 0.62/0.86 (step @p460 :rule cong :premises (@p459) :args (@t10)) % 0.62/0.86 (step @p461 :rule trans :premises (@p460 @p228)) % 0.62/0.86 (step @p462 :rule eq_resolve :premises (@p1 @p461)) % 0.62/0.86 (step @p463 :rule refl :args (@t349)) % 0.62/0.86 (step @p464 :rule bool-double-not-elim :args (@t319)) % 0.62/0.86 (step @p465 :rule nary_cong :premises (@p464 @p463) :args ((or (not @t350) @t349))) % 0.62/0.86 (step @p466 :rule refl :args (@t326)) % 0.62/0.86 (step @p467 :rule refl :args (@t329)) % 0.62/0.86 (step @p468 :rule refl :args (@t336)) % 0.62/0.86 (step @p469 :rule refl :args (@t339)) % 0.62/0.86 (step @p470 :rule refl :args (@t343)) % 0.62/0.86 (step @p471 :rule refl :args (@t344)) % 0.62/0.86 (step @p472 :rule eq-symm :args (@t345 @t347)) % 0.62/0.86 (step @p473 :rule eq-refl :args (@t346)) % 0.62/0.86 (step @p474 :rule skolem_intro :args (@t347)) % 0.62/0.86 (step @p475 :rule refl :args (@t346)) % 0.62/0.86 (step @p476 :rule cong :premises (@p475 @p474) :args ((= @t346 @t347))) % 0.62/0.86 (step @p477 :rule trans :premises (@p476 @p473)) % 0.62/0.86 (step @p478 :rule true_elim :premises (@p477)) % 0.62/0.86 (step @p479 :rule eq-refl :args (@t120)) % 0.62/0.86 (step @p480 :rule refl :args (@t120)) % 0.62/0.86 (step @p481 :rule cong :premises (@p480 @p206) :args ((= @t120 @t120))) % 0.62/0.86 (step @p482 :rule trans :premises (@p481 @p479)) % 0.62/0.86 (step @p483 :rule skolem_intro :args (@t345)) % 0.62/0.86 (step @p484 :rule cong :premises (@p480 @p483) :args ((= @t120 @t345))) % 0.62/0.86 (step @p485 :rule trans :premises (@p484 @p482)) % 0.62/0.86 (step @p486 :rule true_elim :premises (@p485)) % 0.62/0.86 (step @p487 :rule cong :premises (@p486 @p478) :args (@t351)) % 0.62/0.86 (step @p488 :rule trans :premises (@p487 @p472)) % 0.62/0.86 (step @p489 :rule cong :premises (@p488) :args (@t352)) % 0.62/0.86 (step @p490 :rule nary_cong :premises (@p489 @p471 @p470 @p469 @p468 @p467 @p466) :args (@t353)) % 0.62/0.86 (step @p491 :rule cong :premises (@p490) :args (@t354)) % 0.62/0.86 (step @p492 :rule refl :args (@t350)) % 0.62/0.86 (step @p493 :rule cong :premises (@p492 @p491) :args ((=> @t350 @t354))) % 0.62/0.86 (assume-push @p535 @t350) % 0.62/0.86 (step @p495 :rule skolemize :premises (@p462)) % 0.62/0.86 (step-pop @p536 :rule scope :premises (@p495)) % 0.62/0.86 (step @p496 :rule process_scope :premises (@p536) :args (@t354)) % 0.62/0.86 (step @p498 :rule eq_resolve :premises (@p496 @p493)) % 0.62/0.86 (step @p499 :rule implies_elim :premises (@p498)) % 0.62/0.86 (step @p500 :rule eq_resolve :premises (@p499 @p465)) % 0.62/0.86 (step @p501 :rule chain_m_resolution :premises (@p500 @p462) :args (@t349 @t355 (@list @t319))) % 0.62/0.86 (step @p502 :rule bool-double-not-elim :args (@t342)) % 0.62/0.86 (step @p503 :rule refl :args (@t348)) % 0.62/0.86 (step @p504 :rule nary_cong :premises (@p503 @p502) :args ((or @t348 (not @t343)))) % 0.62/0.86 (step @p505 :rule cnf_or_neg :args (@t348 2)) % 0.62/0.86 (step @p506 :rule eq_resolve :premises (@p505 @p504)) % 0.62/0.86 (step @p507 :rule reordering :premises (@p506) :args ((or @t342 @t348))) % 0.62/0.86 (step @p508 :rule chain_m_resolution :premises (@p507 @p501) :args (@t342 @t355 (@list @t348))) % 0.62/0.86 (step @p509 :rule bool-impl-false1 :args (@t342)) % 0.62/0.86 (step @p510 :rule evaluate :args ((not true))) % 0.62/0.86 (step @p511 :rule quant-unused-vars :args ((= (forall @t58 true) true))) % 0.62/0.86 (step @p512 :rule bool-or-taut2 :args ((or @t341 @t340) @t51 false false)) % 0.62/0.86 (step @p513 :rule cong :premises (@p512) :args ((forall @t58 (or @t341 @t340 (not @t51) @t51)))) % 0.62/0.86 (step @p514 :rule trans :premises (@p513 @p511)) % 0.62/0.86 (step @p515 :rule beta-reduce :args ((= @t358 @t49))) % 0.62/0.86 (step @p516 :rule beta-reduce :args ((= @t359 @t50))) % 0.62/0.86 (step @p517 :rule cong :premises (@p516 @p515) :args (@t360)) % 0.62/0.86 (step @p518 :rule cong :premises (@p517) :args (@t361)) % 0.62/0.86 (step @p519 :rule refl :args (@t340)) % 0.62/0.86 (step @p520 :rule refl :args (@t341)) % 0.62/0.86 (step @p521 :rule nary_cong :premises (@p520 @p519 @p518 @p152) :args (@t362)) % 0.62/0.86 (step @p522 :rule cong :premises (@p521) :args (@t363)) % 0.62/0.86 (step @p523 :rule trans :premises (@p522 @p514)) % 0.62/0.86 (step @p524 :rule cong :premises (@p523) :args (@t364)) % 0.62/0.86 (step @p525 :rule trans :premises (@p524 @p510)) % 0.62/0.86 (step @p526 :rule refl :args (@t342)) % 0.62/0.86 (step @p527 :rule cong :premises (@p526 @p525) :args ((=> @t342 @t364))) % 0.62/0.86 (step @p528 :rule trans :premises (@p527 @p509)) % 0.62/0.86 (assume-push @p537 @t342) % 0.62/0.86 (step @p530 :rule instantiate :premises (@p508) :args ((@list @t357))) % 0.62/0.86 (step-pop @p538 :rule scope :premises (@p530)) % 0.62/0.86 (step @p531 :rule process_scope :premises (@p538) :args (@t364)) % 0.62/0.86 (step @p533 :rule eq_resolve :premises (@p531 @p528)) % 0.62/0.86 (step @p534 false :rule chain_m_resolution :premises (@p533 @p508) :args (false (@list false) (@list @t342))) % 0.62/0.86 ) % 0.62/0.86 % SZS output end Proof % 0.62/0.86 % cvc5 exiting %------------------------------------------------------------------------------