%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SET752^4 : TPTP v9.2.1. Released v3.6.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:48:34 AM UTC 2026 % Result : Theorem 0.40s 0.61s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET752^4 : TPTP v9.2.1. Released v3.6.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n009.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 16:10:29 EDT 2026 % 0.17/0.35 % CPUTime : % 0.29/0.51 %----Proving TH0 % 0.40/0.61 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.40/0.61 % SZS status Theorem % 0.40/0.61 % SZS output start Proof % 0.40/0.61 ( % 0.40/0.61 (declare-sort $$unsorted 0) % 0.40/0.61 (define tptp.in () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.40/0.61 (define tptp.is_a () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "M" (-> $$unsorted Bool)))) (lambda (@list _let_1 _let_2) (_ _let_2 _let_1))))) % 0.40/0.61 (define tptp.emptyset () (lambda (@list (@var "X" $$unsorted)) false)) % 0.40/0.61 (define tptp.unord_pair () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (let ((_let_3 (@var "X" $$unsorted))) (lambda (@list _let_3 _let_1 _let_2) (or (= _let_2 _let_3) (= _let_2 _let_1))))))) % 0.40/0.61 (define tptp.singleton () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "U" $$unsorted))) (lambda (@list _let_1 _let_2) (= _let_2 _let_1))))) % 0.40/0.61 (define tptp.union () (let ((_let_1 (@var "U" $$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))))))) % 0.40/0.61 (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" (-> $$unsorted Bool)))) (let ((_let_5 (_ _let_4 _let_1))) (lambda (@list _let_4 _let_2 _let_1) (or (and _let_5 (not _let_3)) (and (not _let_5) _let_3))))))))) % 0.40/0.61 (define tptp.intersection () (let ((_let_1 (@var "U" $$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))))))) % 0.40/0.61 (define tptp.setminus () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2 _let_1) (and (_ _let_3 _let_1) (not (_ _let_2 _let_1)))))))) % 0.40/0.61 (define tptp.complement () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (not (_ _let_2 _let_1)))))) % 0.40/0.61 (define tptp.disjoint () (let ((_let_1 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_2 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_1) (= (_ (_ tptp.intersection _let_2) _let_1) tptp.emptyset))))) % 0.40/0.61 (define tptp.subset () (let ((_let_1 (@var "U" $$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)))))))) % 0.40/0.61 (define tptp.meets () (let ((_let_1 (@var "U" $$unsorted))) (let ((_let_2 (@var "Y" (-> $$unsorted Bool)))) (let ((_let_3 (@var "X" (-> $$unsorted Bool)))) (lambda (@list _let_3 _let_2) (exists (@list _let_1) (and (_ _let_3 _let_1) (_ _let_2 _let_1)))))))) % 0.40/0.61 (define tptp.misses () (let ((_let_1 (@var "U" $$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))))))))) % 0.40/0.61 (define tptp.fun_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "A" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_3) (exists (@list _let_1) (and (_ _let_4 _let_1) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.40/0.61 (define tptp.fun_composition () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "G" (-> $$unsorted $$unsorted)))) (lambda (@list _let_2 _let_3 _let_1) (_ _let_3 (_ _let_2 _let_1))))))) % 0.40/0.61 (define tptp.fun_inv_image () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "B" (-> $$unsorted Bool)))) (lambda (@list _let_2 _let_4 _let_1) (exists (@list _let_3) (and (_ _let_4 _let_3) (= _let_3 (_ _let_2 _let_1)))))))))) % 0.40/0.61 (define tptp.fun_injective () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (let ((_let_3 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_3) (forall (@list _let_2 _let_1) (=> (= (_ _let_3 _let_2) (_ _let_3 _let_1)) (= _let_2 _let_1)))))))) % 0.40/0.61 (define tptp.fun_surjective () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (lambda (@list _let_2) (forall (@list _let_3) (exists (@list _let_1) (= _let_3 (_ _let_2 _let_1))))))))) % 0.40/0.61 (define tptp.fun_bijective () (let ((_let_1 (@var "F" (-> $$unsorted $$unsorted)))) (lambda (@list _let_1) (and (_ tptp.fun_injective _let_1) (_ tptp.fun_surjective _let_1))))) % 0.40/0.61 (define tptp.fun_decreasing () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "Y" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_1 _let_3) (=> (_ (_ _let_4 _let_1) _let_3) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.40/0.61 (define tptp.fun_increasing () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "F" (-> $$unsorted $$unsorted)))) (let ((_let_3 (@var "X" $$unsorted))) (let ((_let_4 (@var "SMALLER" (-> $$unsorted $$unsorted Bool)))) (lambda (@list _let_2 _let_4) (forall (@list _let_3 _let_1) (=> (_ (_ _let_4 _let_3) _let_1) (_ (_ _let_4 (_ _let_2 _let_3)) (_ _let_2 _let_1)))))))))) % 0.40/0.61 (define @t1 () (@var "Y" (-> $$unsorted Bool))) % 0.40/0.61 (define @t2 () (@var "F" (-> $$unsorted $$unsorted))) % 0.40/0.61 (define @t3 () (_ tptp.fun_image @t2)) % 0.40/0.61 (define @t4 () (@var "X" (-> $$unsorted Bool))) % 0.40/0.61 (define @t5 () (= (_ @t3 (_ (_ tptp.union @t4) @t1)) (_ (_ tptp.union (_ @t3 @t4)) (_ @t3 @t1)))) % 0.40/0.61 (define @t6 () (@list @t4 @t1 @t2)) % 0.40/0.61 (define @t7 () (forall @t6 @t5)) % 0.40/0.61 (define @t8 () (not @t7)) % 0.40/0.61 (define @t9 () (@var "X" $$unsorted)) % 0.40/0.61 (define @t10 () (@var "M" (-> $$unsorted Bool))) % 0.40/0.61 (define @t11 () (lambda (@list @t9 @t10) (_ @t10 @t9))) % 0.40/0.61 (define @t12 () (@list @t9)) % 0.40/0.61 (define @t13 () (lambda @t12 false)) % 0.40/0.61 (define @t14 () (@var "Y" $$unsorted)) % 0.40/0.61 (define @t15 () (@var "U" $$unsorted)) % 0.40/0.61 (define @t16 () (= @t15 @t9)) % 0.40/0.61 (define @t17 () (lambda (@list @t9 @t14 @t15) (or @t16 (= @t15 @t14)))) % 0.40/0.61 (define @t18 () (lambda (@list @t9 @t15) @t16)) % 0.40/0.61 (define @t19 () (_ @t1 @t15)) % 0.40/0.61 (define @t20 () (_ @t4 @t15)) % 0.40/0.61 (define @t21 () (or @t20 @t19)) % 0.40/0.61 (define @t22 () (@list @t4 @t1 @t15)) % 0.40/0.61 (define @t23 () (lambda @t22 @t21)) % 0.40/0.61 (define @t24 () (not @t20)) % 0.40/0.61 (define @t25 () (and @t20 (not @t19))) % 0.40/0.61 (define @t26 () (lambda @t22 (or @t25 (and @t24 @t19)))) % 0.40/0.61 (define @t27 () (and @t20 @t19)) % 0.40/0.61 (define @t28 () (lambda @t22 @t27)) % 0.40/0.61 (define @t29 () (lambda @t22 @t25)) % 0.40/0.61 (define @t30 () (lambda (@list @t4 @t15) @t24)) % 0.40/0.61 (define @t31 () (@list @t4 @t1)) % 0.40/0.61 (define @t32 () (lambda @t31 (= (_ (_ tptp.intersection @t4) @t1) tptp.emptyset))) % 0.40/0.61 (define @t33 () (@list @t15)) % 0.40/0.61 (define @t34 () (lambda @t31 (forall @t33 (=> @t20 @t19)))) % 0.40/0.61 (define @t35 () (exists @t33 @t27)) % 0.40/0.61 (define @t36 () (lambda @t31 @t35)) % 0.40/0.61 (define @t37 () (lambda @t31 (not @t35))) % 0.40/0.61 (define @t38 () (_ @t2 @t9)) % 0.40/0.61 (define @t39 () (= @t14 @t38)) % 0.40/0.61 (define @t40 () (@var "A" (-> $$unsorted Bool))) % 0.40/0.61 (define @t41 () (_ @t40 @t9)) % 0.40/0.61 (define @t42 () (and @t41 @t39)) % 0.40/0.61 (define @t43 () (exists @t12 @t42)) % 0.40/0.61 (define @t44 () (@list @t2 @t40 @t14)) % 0.40/0.61 (define @t45 () (lambda @t44 @t43)) % 0.40/0.61 (define @t46 () (@var "G" (-> $$unsorted $$unsorted))) % 0.40/0.61 (define @t47 () (lambda (@list @t2 @t46 @t9) (_ @t46 @t38))) % 0.40/0.61 (define @t48 () (@var "B" (-> $$unsorted Bool))) % 0.40/0.61 (define @t49 () (@list @t14)) % 0.40/0.61 (define @t50 () (lambda (@list @t2 @t48 @t9) (exists @t49 (and (_ @t48 @t14) @t39)))) % 0.40/0.61 (define @t51 () (_ @t2 @t14)) % 0.40/0.61 (define @t52 () (@list @t9 @t14)) % 0.40/0.61 (define @t53 () (@list @t2)) % 0.40/0.61 (define @t54 () (lambda @t53 (forall @t52 (=> (= @t38 @t51) (= @t9 @t14))))) % 0.40/0.61 (define @t55 () (lambda @t53 (forall @t49 (exists @t12 @t39)))) % 0.40/0.61 (define @t56 () (lambda @t53 (and (_ tptp.fun_injective @t2) (_ tptp.fun_surjective @t2)))) % 0.40/0.61 (define @t57 () (@var "SMALLER" (-> $$unsorted $$unsorted Bool))) % 0.40/0.61 (define @t58 () (_ (_ @t57 @t9) @t14)) % 0.40/0.61 (define @t59 () (@list @t2 @t57)) % 0.40/0.61 (define @t60 () (lambda @t59 (forall @t52 (=> @t58 (_ (_ @t57 @t51) @t38))))) % 0.40/0.61 (define @t61 () (lambda @t59 (forall @t52 (=> @t58 (_ (_ @t57 @t38) @t51))))) % 0.40/0.61 (define @t62 () (_ @t2 @t9)) % 0.40/0.61 (define @t63 () (not (= @t15 @t62))) % 0.40/0.61 (define @t64 () (_ @t1 @t9)) % 0.40/0.61 (define @t65 () (not @t64)) % 0.40/0.61 (define @t66 () (not (forall @t12 (or @t65 @t63)))) % 0.40/0.61 (define @t67 () (not (= @t14 @t62))) % 0.40/0.61 (define @t68 () (lambda @t49 (not (forall @t12 (or @t65 @t67))))) % 0.40/0.61 (define @t69 () (_ @t68 @t15)) % 0.40/0.61 (define @t70 () (_ @t4 @t9)) % 0.40/0.61 (define @t71 () (not @t70)) % 0.40/0.61 (define @t72 () (not (forall @t12 (or @t71 @t63)))) % 0.40/0.61 (define @t73 () (or @t72 @t69)) % 0.40/0.61 (define @t74 () (lambda @t33 @t73)) % 0.40/0.61 (define @t75 () (@list @t1 @t15)) % 0.40/0.61 (define @t76 () (_ @t40 @t9)) % 0.40/0.61 (define @t77 () (not (forall @t12 (or (not @t76) @t67)))) % 0.40/0.61 (define @t78 () (lambda (@list @t40 @t14) @t77)) % 0.40/0.61 (define @t79 () (_ (lambda @t44 @t77) @t2)) % 0.40/0.61 (define @t80 () (lambda @t49 (not (forall @t12 (or @t71 @t67))))) % 0.40/0.61 (define @t81 () (_ @t80 @t15)) % 0.40/0.61 (define @t82 () (or @t81 @t19)) % 0.40/0.61 (define @t83 () (lambda @t75 @t82)) % 0.40/0.61 (define @t84 () (_ @t1 @t9)) % 0.40/0.61 (define @t85 () (not @t84)) % 0.40/0.61 (define @t86 () (_ @t4 @t9)) % 0.40/0.61 (define @t87 () (not @t86)) % 0.40/0.61 (define @t88 () (and @t87 @t85)) % 0.40/0.61 (define @t89 () (or @t88 @t67)) % 0.40/0.61 (define @t90 () (or @t86 @t84)) % 0.40/0.61 (define @t91 () (or (not @t90) @t67)) % 0.40/0.61 (define @t92 () (lambda @t33 @t21)) % 0.40/0.61 (define @t93 () (_ @t92 @t9)) % 0.40/0.61 (define @t94 () (not @t93)) % 0.40/0.61 (define @t95 () (or @t94 @t67)) % 0.40/0.61 (define @t96 () (forall @t12 @t95)) % 0.40/0.61 (define @t97 () (not @t96)) % 0.40/0.61 (define @t98 () (lambda @t49 @t97)) % 0.40/0.61 (define @t99 () (lambda @t75 @t21)) % 0.40/0.61 (define @t100 () (_ @t23 @t4)) % 0.40/0.61 (define @t101 () (= (_ @t79 (_ @t100 @t1)) (_ (_ @t23 (_ @t79 @t4)) (_ @t79 @t1)))) % 0.40/0.61 (define @t102 () (forall @t6 @t101)) % 0.40/0.61 (define @t103 () (not @t39)) % 0.40/0.61 (define @t104 () (not @t41)) % 0.40/0.61 (define @t105 () (or @t104 @t103)) % 0.40/0.61 (define @t106 () (forall @t12 (not @t42))) % 0.40/0.61 (define @t107 () (not @t106)) % 0.40/0.61 (define @t108 () (forall @t6 (= (lambda @t49 (not (forall @t12 (or (and @t71 @t65) @t67)))) (lambda @t33 (or @t72 @t66))))) % 0.40/0.61 (define @t109 () (@quantifiers_skolemize @t108 2)) % 0.40/0.61 (define @t110 () (_ @t109 @t9)) % 0.40/0.61 (define @t111 () (@quantifiers_skolemize @t108 1)) % 0.40/0.61 (define @t112 () (not (_ @t111 @t9))) % 0.40/0.61 (define @t113 () (@quantifiers_skolemize @t108 0)) % 0.40/0.61 (define @t114 () (not (_ @t113 @t9))) % 0.40/0.61 (define @t115 () (and @t114 @t112)) % 0.40/0.61 (define @t116 () (lambda @t49 (not (forall @t12 (or @t115 (not (= @t14 @t110))))))) % 0.40/0.61 (define @t117 () (@purify @t116)) % 0.40/0.61 (define @t118 () (not (= @t15 @t110))) % 0.40/0.61 (define @t119 () (lambda @t33 (or (not (forall @t12 (or @t114 @t118))) (not (forall @t12 (or @t112 @t118)))))) % 0.40/0.61 (define @t120 () (@purify @t119)) % 0.40/0.61 (define @t121 () (= @t120 @t117)) % 0.40/0.61 (define @t122 () (not @t121)) % 0.40/0.61 (define @t123 () (not @t108)) % 0.40/0.61 (define @t124 () (= @t116 @t119)) % 0.40/0.61 (define @t125 () (not @t124)) % 0.40/0.61 (define @t126 () (@list true)) % 0.40/0.61 (define @t127 () (@const 0 $$unsorted)) % 0.40/0.61 (define @t128 () (not (= @t110 @t127))) % 0.40/0.61 (define @t129 () (forall @t12 (or @t112 @t128))) % 0.40/0.61 (define @t130 () (not @t129)) % 0.40/0.61 (define @t131 () (forall @t12 (or @t114 @t128))) % 0.40/0.61 (define @t132 () (not @t131)) % 0.40/0.61 (define @t133 () (or @t132 @t130)) % 0.40/0.61 (define @t134 () (forall @t12 (or @t115 @t128))) % 0.40/0.61 (define @t135 () (not @t134)) % 0.40/0.61 (define @t136 () (not (= @t127 @t110))) % 0.40/0.61 (define @t137 () (or @t115 @t136)) % 0.40/0.61 (define @t138 () (forall @t12 @t137)) % 0.40/0.61 (define @t139 () (not @t138)) % 0.40/0.61 (define @t140 () (_ @t116 @t127)) % 0.40/0.61 (define @t141 () (_ @t117 @t127)) % 0.40/0.61 (define @t142 () (or @t112 @t136)) % 0.40/0.61 (define @t143 () (forall @t12 @t142)) % 0.40/0.61 (define @t144 () (not @t143)) % 0.40/0.61 (define @t145 () (or @t114 @t136)) % 0.40/0.61 (define @t146 () (forall @t12 @t145)) % 0.40/0.61 (define @t147 () (not @t146)) % 0.40/0.61 (define @t148 () (or @t147 @t144)) % 0.40/0.61 (define @t149 () (_ @t119 @t127)) % 0.40/0.61 (define @t150 () (_ @t120 @t127)) % 0.40/0.61 (define @t151 () (= @t150 @t141)) % 0.40/0.61 (define @t152 () (not @t151)) % 0.40/0.61 (define @t153 () (or @t121 @t152)) % 0.40/0.61 (define @t154 () (= @t135 @t133)) % 0.40/0.61 (define @t155 () (not @t133)) % 0.40/0.61 (define @t156 () (not @t135)) % 0.40/0.61 (define @t157 () (not @t132)) % 0.40/0.61 (define @t158 () (not @t130)) % 0.40/0.61 (define @t159 () (@quantifiers_skolemize @t134 0)) % 0.40/0.61 (define @t160 () (_ @t109 @t159)) % 0.40/0.61 (define @t161 () (= @t127 @t160)) % 0.40/0.61 (define @t162 () (not @t161)) % 0.40/0.61 (define @t163 () (_ @t111 @t159)) % 0.40/0.61 (define @t164 () (not @t163)) % 0.40/0.61 (define @t165 () (_ @t113 @t159)) % 0.40/0.61 (define @t166 () (not @t165)) % 0.40/0.61 (define @t167 () (and @t166 @t164)) % 0.40/0.61 (define @t168 () (or @t167 @t162)) % 0.40/0.61 (define @t169 () (not @t168)) % 0.40/0.61 (define @t170 () (not (= @t160 @t127))) % 0.40/0.61 (define @t171 () (or @t167 @t170)) % 0.40/0.61 (define @t172 () (not @t171)) % 0.40/0.61 (define @t173 () (or @t166 @t170)) % 0.40/0.61 (define @t174 () (@list @t159)) % 0.40/0.61 (define @t175 () (or @t166 @t162)) % 0.40/0.61 (define @t176 () (or @t164 @t162)) % 0.40/0.61 (define @t177 () (or @t164 @t170)) % 0.40/0.61 (define @t178 () (@quantifiers_skolemize @t131 0)) % 0.40/0.61 (define @t179 () (_ @t113 @t178)) % 0.40/0.61 (define @t180 () (_ @t109 @t178)) % 0.40/0.61 (define @t181 () (= @t127 @t180)) % 0.40/0.61 (define @t182 () (not @t181)) % 0.40/0.61 (define @t183 () (not @t179)) % 0.40/0.61 (define @t184 () (or @t183 @t182)) % 0.40/0.61 (define @t185 () (and @t183 (not (_ @t111 @t178)))) % 0.40/0.61 (define @t186 () (not (= @t180 @t127))) % 0.40/0.61 (define @t187 () (or @t185 @t186)) % 0.40/0.61 (define @t188 () (or @t185 @t182)) % 0.40/0.61 (define @t189 () (@list false)) % 0.40/0.61 (define @t190 () (@list @t134)) % 0.40/0.61 (define @t191 () (not @t184)) % 0.40/0.61 (define @t192 () (or @t183 @t186)) % 0.40/0.61 (define @t193 () (not @t192)) % 0.40/0.61 (define @t194 () (@quantifiers_skolemize @t129 0)) % 0.40/0.61 (define @t195 () (_ @t109 @t194)) % 0.40/0.61 (define @t196 () (= @t127 @t195)) % 0.40/0.61 (define @t197 () (not @t196)) % 0.40/0.61 (define @t198 () (_ @t111 @t194)) % 0.40/0.61 (define @t199 () (not @t198)) % 0.40/0.61 (define @t200 () (or @t199 @t197)) % 0.40/0.61 (define @t201 () (not @t200)) % 0.40/0.61 (define @t202 () (not (= @t195 @t127))) % 0.40/0.61 (define @t203 () (or @t199 @t202)) % 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@p198 :rule nary_cong :premises (@p197 @p196) :args (@t153)) % 0.40/0.61 ; WARNING: add trust step for TRUST % 0.40/0.61 ; trust TRUST THEORY_LEMMA % 0.40/0.61 (step @p199 :rule trust :premises () :args (@t153)) % 0.40/0.61 (step @p200 :rule eq_resolve :premises (@p199 @p198)) % 0.40/0.61 (step @p201 :rule chain_m_resolution :premises (@p200 @p156) :args ((not @t154) @t126 (@list @t121))) % 0.40/0.61 (step @p202 :rule refl :args (@t155)) % 0.40/0.61 (step @p203 :rule bool-double-not-elim :args (@t134)) % 0.40/0.61 (step @p204 :rule refl :args (@t154)) % 0.40/0.61 (step @p205 :rule nary_cong :premises (@p204 @p203 @p202) :args ((or @t154 @t156 @t155))) % 0.40/0.61 (step @p206 :rule cnf_equiv_neg2 :args (@t154)) % 0.40/0.61 (step @p207 :rule eq_resolve :premises (@p206 @p205)) % 0.40/0.61 (step @p208 :rule reordering :premises (@p207) :args ((or @t134 @t154 @t155))) % 0.40/0.61 (step @p209 :rule bool-double-not-elim :args (@t131)) % 0.40/0.61 (step @p210 :rule nary_cong :premises (@p176 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(@t171)) % 0.40/0.61 (step @p225 :rule cong :premises (@p224) :args (@t172)) % 0.40/0.61 (step @p226 :rule cong :premises (@p159 @p225) :args ((=> @t135 @t172))) % 0.40/0.61 (assume-push @p370 @t135) % 0.40/0.61 (step @p228 :rule skolemize :premises (@p370)) % 0.40/0.61 (step-pop @p371 :rule scope :premises (@p228)) % 0.40/0.61 (step @p229 :rule process_scope :premises (@p371) :args (@t172)) % 0.40/0.61 (step @p231 :rule eq_resolve :premises (@p229 @p226)) % 0.40/0.61 (step @p232 :rule implies_elim :premises (@p231)) % 0.40/0.61 (step @p233 :rule eq_resolve :premises (@p232 @p220)) % 0.40/0.61 (step @p234 :rule cnf_or_neg :args (@t168 0)) % 0.40/0.61 (step @p235 :rule bool-double-not-elim :args (@t161)) % 0.40/0.61 (step @p236 :rule refl :args (@t168)) % 0.40/0.61 (step @p237 :rule nary_cong :premises (@p236 @p235) :args ((or @t168 (not @t162)))) % 0.40/0.61 (step @p238 :rule cnf_or_neg :args (@t168 1)) % 0.40/0.61 (step @p239 :rule eq_resolve :premises (@p238 @p237)) % 0.40/0.61 (step @p240 :rule reordering :premises (@p239) :args ((or @t161 @t168))) % 0.40/0.61 (step @p241 :rule refl :args (@t166)) % 0.40/0.61 (step @p242 :rule nary_cong :premises (@p241 @p222) :args (@t173)) % 0.40/0.61 (step @p243 :rule refl :args (@t131)) % 0.40/0.61 (step @p244 :rule cong :premises (@p243 @p242) :args ((=> @t131 @t173))) % 0.40/0.61 (assume-push @p372 @t131) % 0.40/0.61 (step @p246 :rule instantiate :premises (@p372) :args (@t174)) % 0.40/0.61 (step-pop @p373 :rule scope :premises (@p246)) % 0.40/0.61 (step @p247 :rule process_scope :premises (@p373) :args (@t173)) % 0.40/0.61 (step @p249 :rule eq_resolve :premises (@p247 @p244)) % 0.40/0.61 (step @p250 :rule implies_elim :premises (@p249)) % 0.40/0.61 (step @p251 :rule cnf_or_pos :args (@t175)) % 0.40/0.61 (step @p252 :rule reordering :premises (@p251) :args ((or @t166 @t162 (not @t175)))) % 0.40/0.61 (step @p253 :rule bool-double-not-elim :args (@t163)) % 0.40/0.61 (step @p254 :rule bool-double-not-elim :args (@t165)) % 0.40/0.61 (step @p255 :rule nary_cong :premises (@p223 @p254 @p253) :args ((or @t167 (not @t166) (not @t164)))) % 0.40/0.61 (step @p256 :rule cnf_and_neg :args (@t167)) % 0.40/0.61 (step @p257 :rule eq_resolve :premises (@p256 @p255)) % 0.40/0.61 (step @p258 :rule reordering :premises (@p257) :args ((or @t165 @t163 @t167))) % 0.40/0.61 (step @p259 :rule cnf_or_pos :args (@t176)) % 0.40/0.61 (step @p260 :rule reordering :premises (@p259) :args ((or @t164 @t162 (not @t176)))) % 0.40/0.61 (step @p261 :rule refl :args (@t164)) % 0.40/0.61 (step @p262 :rule nary_cong :premises (@p261 @p222) :args (@t177)) % 0.40/0.61 (step @p263 :rule refl :args (@t129)) % 0.40/0.61 (step @p264 :rule cong :premises (@p263 @p262) :args ((=> @t129 @t177))) % 0.40/0.61 (assume-push @p374 @t129) % 0.40/0.61 (step @p266 :rule instantiate :premises (@p374) :args (@t174)) % 0.40/0.61 (step-pop @p375 :rule scope :premises (@p266)) % 0.40/0.61 (step @p267 :rule process_scope :premises (@p375) :args (@t177)) % 0.40/0.61 (step @p269 :rule eq_resolve :premises (@p267 @p264)) % 0.40/0.61 (step @p270 :rule implies_elim :premises (@p269)) % 0.40/0.61 (step @p271 :rule chain_m_resolution :premises (@p270 @p260 @p258 @p252 @p250 @p240 @p234 @p233 @p218 @p213 @p208 @p201) :args (@t134 (@list true false true false false true true false false true true) (@list @t176 @t163 @t165 @t175 @t161 @t167 @t168 @t129 @t131 @t133 @t154))) % 0.40/0.61 (step @p272 :rule cnf_equiv_neg1 :args (@t154)) % 0.40/0.61 (step @p273 :rule reordering :premises (@p272) :args ((or @t135 @t133 @t154))) % 0.40/0.61 (step @p274 :rule chain_m_resolution :premises (@p273 @p271 @p201) :args (@t133 (@list false true) (@list @t134 @t154))) % 0.40/0.61 (step @p275 :rule bool-double-not-elim :args (@t179)) % 0.40/0.61 (step @p276 :rule refl :args (@t184)) % 0.40/0.61 (step @p277 :rule nary_cong :premises (@p276 @p275) :args ((or @t184 (not @t183)))) % 0.40/0.61 (step @p278 :rule cnf_or_neg :args (@t184 0)) % 0.40/0.61 (step @p279 :rule eq_resolve :premises (@p278 @p277)) % 0.40/0.61 (step @p280 :rule reordering :premises (@p279) :args ((or @t179 @t184))) % 0.40/0.61 (step @p281 :rule bool-double-not-elim :args (@t181)) % 0.40/0.61 (step @p282 :rule nary_cong :premises (@p276 @p281) :args ((or @t184 (not @t182)))) % 0.40/0.61 (step @p283 :rule cnf_or_neg :args (@t184 1)) % 0.40/0.61 (step @p284 :rule eq_resolve :premises (@p283 @p282)) % 0.40/0.61 (step @p285 :rule reordering :premises (@p284) :args ((or @t181 @t184))) % 0.40/0.61 (step @p286 :rule cnf_and_pos :args (@t185 0)) % 0.40/0.61 (step @p287 :rule reordering :premises (@p286) :args ((or @t183 (not @t185)))) % 0.40/0.61 (step @p288 :rule eq-symm :args (@t180 @t127)) % 0.40/0.61 (step @p289 :rule cong :premises (@p288) :args (@t186)) % 0.40/0.61 (step @p290 :rule refl :args (@t185)) % 0.40/0.61 (step @p291 :rule nary_cong :premises (@p290 @p289) :args (@t187)) % 0.40/0.61 (step @p292 :rule refl :args (@t134)) % 0.40/0.61 (step @p293 :rule cong :premises (@p292 @p291) :args ((=> @t134 @t187))) % 0.40/0.61 (assume-push @p376 @t134) % 0.40/0.61 (step @p295 :rule instantiate :premises (@p376) :args ((@list @t178))) % 0.40/0.61 (step-pop @p377 :rule scope :premises (@p295)) % 0.40/0.61 (step @p296 :rule process_scope :premises (@p377) :args (@t187)) % 0.40/0.61 (step @p298 :rule eq_resolve :premises (@p296 @p293)) % 0.40/0.61 (step @p299 :rule implies_elim :premises (@p298)) % 0.40/0.61 (step @p300 :rule chain_m_resolution :premises (@p299 @p271) :args (@t188 @t189 @t190)) % 0.40/0.61 (step @p301 :rule cnf_or_pos :args (@t188)) % 0.40/0.61 (step @p302 :rule reordering :premises (@p301) :args ((or @t182 @t185 (not @t188)))) % 0.40/0.61 (step @p303 :rule chain_m_resolution :premises (@p302 @p300 @p287 @p285 @p280) :args (@t184 (@list false true false false) (@list @t188 @t185 @t181 @t179))) % 0.40/0.61 (step @p304 :rule refl :args (@t191)) % 0.40/0.61 (step @p305 :rule nary_cong :premises (@p209 @p304) :args ((or @t157 @t191))) % 0.40/0.61 (step @p306 :rule refl :args (@t183)) % 0.40/0.61 (step @p307 :rule nary_cong :premises (@p306 @p289) :args (@t192)) % 0.40/0.61 (step @p308 :rule cong :premises (@p307) :args (@t193)) % 0.40/0.61 (step @p309 :rule refl :args (@t132)) % 0.40/0.61 (step @p310 :rule cong :premises (@p309 @p308) :args ((=> @t132 @t193))) % 0.40/0.61 (assume-push @p378 @t132) % 0.40/0.61 (step @p312 :rule skolemize :premises (@p378)) % 0.40/0.61 (step-pop @p379 :rule scope :premises (@p312)) % 0.40/0.61 (step @p313 :rule process_scope :premises (@p379) :args (@t193)) % 0.40/0.61 (step @p315 :rule eq_resolve :premises (@p313 @p310)) % 0.40/0.61 (step @p316 :rule implies_elim :premises (@p315)) % 0.40/0.61 (step @p317 :rule eq_resolve :premises (@p316 @p305)) % 0.40/0.61 (step @p318 :rule chain_m_resolution :premises (@p317 @p303) :args (@t131 @t189 (@list @t184))) % 0.40/0.61 (step @p319 :rule cnf_or_pos :args (@t133)) % 0.40/0.61 (step @p320 :rule reordering :premises (@p319) :args ((or @t132 @t130 @t155))) % 0.40/0.61 (step @p321 :rule chain_m_resolution :premises (@p320 @p318 @p274) :args (@t130 (@list false false) (@list @t131 @t133))) % 0.40/0.61 (step @p322 :rule refl :args (@t201)) % 0.40/0.61 (step @p323 :rule nary_cong :premises (@p214 @p322) :args ((or @t158 @t201))) % 0.40/0.61 (step @p324 :rule eq-symm :args (@t195 @t127)) % 0.40/0.61 (step @p325 :rule cong :premises (@p324) :args (@t202)) % 0.40/0.61 (step @p326 :rule refl :args (@t199)) % 0.40/0.61 (step @p327 :rule nary_cong :premises (@p326 @p325) :args (@t203)) % 0.40/0.61 (step @p328 :rule cong :premises (@p327) :args (@t204)) % 0.40/0.61 (step @p329 :rule refl :args (@t130)) % 0.40/0.61 (step @p330 :rule cong :premises (@p329 @p328) :args ((=> @t130 @t204))) % 0.40/0.61 (assume-push @p380 @t130) % 0.40/0.61 (step @p332 :rule skolemize :premises (@p380)) % 0.40/0.61 (step-pop @p381 :rule scope :premises (@p332)) % 0.40/0.61 (step @p333 :rule process_scope :premises (@p381) :args (@t204)) % 0.40/0.61 (step @p335 :rule eq_resolve :premises (@p333 @p330)) % 0.40/0.61 (step @p336 :rule implies_elim :premises (@p335)) % 0.40/0.61 (step @p337 :rule eq_resolve :premises (@p336 @p323)) % 0.40/0.61 (step @p338 :rule chain_m_resolution :premises (@p337 @p321) :args (@t201 @t126 (@list @t129))) % 0.40/0.61 (step @p339 :rule bool-double-not-elim :args (@t196)) % 0.40/0.61 (step @p340 :rule refl :args (@t200)) % 0.40/0.61 (step @p341 :rule nary_cong :premises (@p340 @p339) :args ((or @t200 (not @t197)))) % 0.40/0.61 (step @p342 :rule cnf_or_neg :args (@t200 1)) % 0.40/0.61 (step @p343 :rule eq_resolve :premises (@p342 @p341)) % 0.40/0.61 (step @p344 :rule reordering :premises (@p343) :args ((or @t196 @t200))) % 0.40/0.61 (step @p345 :rule chain_m_resolution :premises (@p344 @p338) :args (@t196 @t126 @t205)) % 0.40/0.61 (step @p346 :rule bool-double-not-elim :args (@t198)) % 0.40/0.61 (step @p347 :rule nary_cong :premises (@p340 @p346) :args ((or @t200 (not @t199)))) % 0.40/0.61 (step @p348 :rule cnf_or_neg :args (@t200 0)) % 0.40/0.61 (step @p349 :rule eq_resolve :premises (@p348 @p347)) % 0.40/0.61 (step @p350 :rule reordering :premises (@p349) :args ((or @t198 @t200))) % 0.40/0.61 (step @p351 :rule chain_m_resolution :premises (@p350 @p338) :args (@t198 @t126 @t205)) % 0.40/0.61 (step @p352 :rule cnf_and_pos :args (@t206 1)) % 0.40/0.61 (step @p353 :rule reordering :premises (@p352) :args ((or @t199 @t207))) % 0.40/0.61 (step @p354 :rule chain_m_resolution :premises (@p353 @p351) :args (@t207 @t189 (@list @t198))) % 0.40/0.61 (step @p355 :rule refl :args (@t206)) % 0.40/0.61 (step @p356 :rule nary_cong :premises (@p355 @p325) :args (@t208)) % 0.40/0.61 (step @p357 :rule cong :premises (@p292 @p356) :args ((=> @t134 @t208))) % 0.40/0.61 (assume-push @p382 @t134) % 0.40/0.61 (step @p359 :rule instantiate :premises (@p382) :args ((@list @t194))) % 0.40/0.61 (step-pop @p383 :rule scope :premises (@p359)) % 0.40/0.61 (step @p360 :rule process_scope :premises (@p383) :args (@t208)) % 0.40/0.61 (step @p362 :rule eq_resolve :premises (@p360 @p357)) % 0.40/0.61 (step @p363 :rule implies_elim :premises (@p362)) % 0.40/0.61 (step @p364 :rule chain_m_resolution :premises (@p363 @p271) :args (@t209 @t189 @t190)) % 0.40/0.61 (step @p365 :rule cnf_or_pos :args (@t209)) % 0.40/0.61 (step @p366 :rule reordering :premises (@p365) :args ((or @t197 @t206 (not @t209)))) % 0.40/0.61 (step @p367 false :rule chain_m_resolution :premises (@p366 @p364 @p354 @p345) :args (false (@list false true false) (@list @t209 @t206 @t196))) % 0.40/0.61 ) % 0.40/0.61 % SZS output end Proof % 0.40/0.61 % cvc5 exiting %------------------------------------------------------------------------------