%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU817^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n004.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:53:20 AM UTC 2026 % Result : Theorem 0.44s 0.63s % Output : Proof 0.44s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU817^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n004.cluster.edu % 0.16/0.34 % Model : x86_64 x86_64 % 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.34 % Memory : 8042.1875MB % 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.34 % CPULimit : 300 % 0.16/0.34 % WCLimit : 300 % 0.16/0.34 % DateTime : Tue Jun 2 17:54:22 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.50 %----Proving TH0 % 0.44/0.63 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.44/0.63 % SZS status Theorem % 0.44/0.63 % SZS output start Proof % 0.44/0.63 ( % 0.44/0.63 (declare-sort $$unsorted 0) % 0.44/0.63 (declare-const tptp.emptyset $$unsorted) % 0.44/0.63 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.44/0.63 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 0.44/0.63 (declare-const tptp.subsetE Bool) % 0.44/0.63 (define tptp.nonempty () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (not (= _let_1 tptp.emptyset))))) % 0.44/0.63 (define tptp.transitiveset () (let ((_let_1 (@var "A" $$unsorted))) (let ((_let_2 (@var "X" $$unsorted))) (lambda (@list _let_1) (forall (@list _let_2) (=> (_ (_ tptp.in _let_2) _let_1) (_ (_ tptp.subset _let_2) _let_1))))))) % 0.44/0.63 (define tptp.stricttotalorderedByIn () (let ((_let_1 (@var "X" $$unsorted))) (let ((_let_2 (_ tptp.in _let_1))) (let ((_let_3 (@var "A" $$unsorted))) (let ((_let_4 (_ _let_2 _let_3))) (let ((_let_5 (@list _let_1))) (let ((_let_6 (@var "Y" $$unsorted))) (let ((_let_7 (_ tptp.in _let_6))) (let ((_let_8 (_ _let_2 _let_6))) (let ((_let_9 (_ _let_7 _let_3))) (let ((_let_10 (@list _let_6))) (let ((_let_11 (@var "Xx" $$unsorted))) (let ((_let_12 (_ tptp.in _let_11))) (lambda (@list _let_3) (and (forall (@list _let_11) (=> (_ _let_12 _let_3) (forall _let_5 (=> _let_4 (forall _let_10 (=> _let_9 (=> (and (_ _let_12 _let_1) _let_8) (_ _let_12 _let_6)))))))) (forall _let_5 (=> _let_4 (forall _let_10 (=> _let_9 (or (= _let_1 _let_6) _let_8 (_ _let_7 _let_1)))))) (forall _let_5 (=> _let_4 (not (_ _let_2 _let_1))))))))))))))))))) % 0.44/0.63 (define tptp.wellorderedByIn () (let ((_let_1 (@var "Y" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (_ tptp.in _let_2))) (let ((_let_4 (@var "X" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5) (and (_ tptp.stricttotalorderedByIn _let_5) (forall (@list _let_4) (=> (_ (_ tptp.in _let_4) (_ tptp.powerset _let_5)) (=> (_ tptp.nonempty _let_4) (exists (@list _let_2) (and (_ _let_3 _let_4) (forall (@list _let_1) (=> (_ (_ tptp.in _let_1) _let_4) (or (= _let_2 _let_1) (_ _let_3 _let_1))))))))))))))))) % 0.44/0.63 (define tptp.ordinal () (let ((_let_1 (@var "Xx" $$unsorted))) (lambda (@list _let_1) (and (_ tptp.transitiveset _let_1) (_ tptp.wellorderedByIn _let_1))))) % 0.44/0.63 (define @t1 () (@var "B" $$unsorted)) % 0.44/0.63 (define @t2 () (@var "Xx" $$unsorted)) % 0.44/0.63 (define @t3 () (_ tptp.in @t2)) % 0.44/0.63 (define @t4 () (_ @t3 @t1)) % 0.44/0.63 (define @t5 () (@var "A" $$unsorted)) % 0.44/0.63 (define @t6 () (_ @t3 @t5)) % 0.44/0.63 (define @t7 () (=> @t6 @t4)) % 0.44/0.63 (define @t8 () (_ (_ tptp.subset @t5) @t1)) % 0.44/0.63 (define @t9 () (@list @t5 @t1 @t2)) % 0.44/0.63 (define @t10 () (forall @t9 (=> @t8 @t7))) % 0.44/0.63 (define @t11 () (= tptp.subsetE @t10)) % 0.44/0.63 (define @t12 () (@var "X" $$unsorted)) % 0.44/0.63 (define @t13 () (_ @t3 @t12)) % 0.44/0.63 (define @t14 () (=> @t6 @t13)) % 0.44/0.63 (define @t15 () (_ (_ tptp.in @t5) @t12)) % 0.44/0.63 (define @t16 () (@list @t2 @t5)) % 0.44/0.63 (define @t17 () (forall @t16 (=> @t15 @t14))) % 0.44/0.63 (define @t18 () (=> (_ tptp.ordinal @t12) @t17)) % 0.44/0.63 (define @t19 () (@list @t12)) % 0.44/0.63 (define @t20 () (forall @t19 @t18)) % 0.44/0.63 (define @t21 () (=> tptp.subsetE @t20)) % 0.44/0.63 (define @t22 () (not @t21)) % 0.44/0.63 (define @t23 () (not (= @t2 tptp.emptyset))) % 0.44/0.63 (define @t24 () (@list @t2)) % 0.44/0.63 (define @t25 () (lambda @t24 @t23)) % 0.44/0.63 (define @t26 () (_ (_ tptp.subset @t12) @t5)) % 0.44/0.63 (define @t27 () (_ tptp.in @t12)) % 0.44/0.63 (define @t28 () (_ @t27 @t5)) % 0.44/0.63 (define @t29 () (forall @t19 (=> @t28 @t26))) % 0.44/0.63 (define @t30 () (@list @t5)) % 0.44/0.63 (define @t31 () (lambda @t30 @t29)) % 0.44/0.63 (define @t32 () (_ @t27 @t12)) % 0.44/0.63 (define @t33 () (not @t32)) % 0.44/0.63 (define @t34 () (forall @t19 (=> @t28 @t33))) % 0.44/0.63 (define @t35 () (@var "Y" $$unsorted)) % 0.44/0.63 (define @t36 () (_ tptp.in @t35)) % 0.44/0.63 (define @t37 () (_ @t36 @t12)) % 0.44/0.63 (define @t38 () (_ @t27 @t35)) % 0.44/0.63 (define @t39 () (= @t12 @t35)) % 0.44/0.63 (define @t40 () (or @t39 @t38 @t37)) % 0.44/0.63 (define @t41 () (_ @t36 @t5)) % 0.44/0.63 (define @t42 () (@list @t35)) % 0.44/0.63 (define @t43 () (forall @t42 (=> @t41 @t40))) % 0.44/0.63 (define @t44 () (=> @t28 @t43)) % 0.44/0.63 (define @t45 () (forall @t19 @t44)) % 0.44/0.63 (define @t46 () (_ @t3 @t35)) % 0.44/0.63 (define @t47 () (and @t13 @t38)) % 0.44/0.63 (define @t48 () (=> @t47 @t46)) % 0.44/0.63 (define @t49 () (forall @t42 (=> @t41 @t48))) % 0.44/0.63 (define @t50 () (=> @t28 @t49)) % 0.44/0.63 (define @t51 () (forall @t19 @t50)) % 0.44/0.63 (define @t52 () (=> @t6 @t51)) % 0.44/0.63 (define @t53 () (forall @t24 @t52)) % 0.44/0.63 (define @t54 () (and @t53 @t45 @t34)) % 0.44/0.63 (define @t55 () (lambda @t30 @t54)) % 0.44/0.63 (define @t56 () (= @t2 @t35)) % 0.44/0.63 (define @t57 () (or @t56 @t46)) % 0.44/0.63 (define @t58 () (forall @t42 (=> @t37 @t57))) % 0.44/0.63 (define @t59 () (and @t13 @t58)) % 0.44/0.63 (define @t60 () (exists @t24 @t59)) % 0.44/0.63 (define @t61 () (=> (_ tptp.nonempty @t12) @t60)) % 0.44/0.63 (define @t62 () (_ tptp.powerset @t5)) % 0.44/0.63 (define @t63 () (_ @t27 @t62)) % 0.44/0.63 (define @t64 () (=> @t63 @t61)) % 0.44/0.63 (define @t65 () (forall @t19 @t64)) % 0.44/0.63 (define @t66 () (and (_ tptp.stricttotalorderedByIn @t5) @t65)) % 0.44/0.63 (define @t67 () (lambda @t30 @t66)) % 0.44/0.63 (define @t68 () (and (_ tptp.transitiveset @t2) (_ tptp.wellorderedByIn @t2))) % 0.44/0.63 (define @t69 () (lambda @t24 @t68)) % 0.44/0.63 (define @t70 () (@var "BOUND_VARIABLE_7902" $$unsorted)) % 0.44/0.63 (define @t71 () (tptp.in @t70 @t12)) % 0.44/0.63 (define @t72 () (@var "BOUND_VARIABLE_7904" $$unsorted)) % 0.44/0.63 (define @t73 () (not (tptp.in @t70 @t72))) % 0.44/0.63 (define @t74 () (not (tptp.in @t72 @t12))) % 0.44/0.63 (define @t75 () (@var "BOUND_VARIABLE_7800" $$unsorted)) % 0.44/0.63 (define @t76 () (not (tptp.in @t75 @t75))) % 0.44/0.63 (define @t77 () (@list @t75)) % 0.44/0.63 (define @t78 () (forall @t77 (or (not (tptp.in @t75 @t12)) @t76))) % 0.44/0.63 (define @t79 () (not @t78)) % 0.44/0.63 (define @t80 () (@var "BOUND_VARIABLE_7809" $$unsorted)) % 0.44/0.63 (define @t81 () (@var "BOUND_VARIABLE_7579" $$unsorted)) % 0.44/0.63 (define @t82 () (tptp.in @t81 @t80)) % 0.44/0.63 (define @t83 () (tptp.in @t80 @t81)) % 0.44/0.63 (define @t84 () (= @t81 @t80)) % 0.44/0.63 (define @t85 () (tptp.in @t81 @t12)) % 0.44/0.63 (define @t86 () (@list @t80 @t81)) % 0.44/0.63 (define @t87 () (forall @t86 (or (not (tptp.in @t80 @t12)) (not @t85) @t84 @t83 @t82))) % 0.44/0.63 (define @t88 () (not @t87)) % 0.44/0.63 (define @t89 () (@var "BOUND_VARIABLE_7551" $$unsorted)) % 0.44/0.63 (define @t90 () (@var "BOUND_VARIABLE_7687" $$unsorted)) % 0.44/0.63 (define @t91 () (tptp.in @t90 @t89)) % 0.44/0.63 (define @t92 () (@var "BOUND_VARIABLE_7549" $$unsorted)) % 0.44/0.63 (define @t93 () (not (tptp.in @t92 @t89))) % 0.44/0.63 (define @t94 () (not (tptp.in @t90 @t92))) % 0.44/0.63 (define @t95 () (@list @t90 @t92 @t89)) % 0.44/0.63 (define @t96 () (forall @t95 (or (not (tptp.in @t90 @t12)) (not (tptp.in @t92 @t12)) @t94 (not (tptp.in @t89 @t12)) @t93 @t91))) % 0.44/0.63 (define @t97 () (not @t96)) % 0.44/0.63 (define @t98 () (@var "BOUND_VARIABLE_7697" $$unsorted)) % 0.44/0.63 (define @t99 () (tptp.in @t98 @t35)) % 0.44/0.63 (define @t100 () (= @t35 @t98)) % 0.44/0.63 (define @t101 () (@var "BOUND_VARIABLE_7819" $$unsorted)) % 0.44/0.63 (define @t102 () (@list @t98)) % 0.44/0.63 (define @t103 () (not (forall @t102 (or (not (tptp.in @t98 @t101)) (not (forall @t42 (or (not (tptp.in @t35 @t101)) @t100 @t99))))))) % 0.44/0.63 (define @t104 () (= tptp.emptyset @t101)) % 0.44/0.63 (define @t105 () (@list @t101)) % 0.44/0.63 (define @t106 () (forall @t105 (or (not (tptp.in @t101 (tptp.powerset @t12))) @t104 @t103))) % 0.44/0.63 (define @t107 () (not @t106)) % 0.44/0.63 (define @t108 () (@var "BOUND_VARIABLE_7837" $$unsorted)) % 0.44/0.63 (define @t109 () (@list @t108)) % 0.44/0.63 (define @t110 () (forall @t109 (or (not (tptp.in @t108 @t12)) (tptp.subset @t108 @t12)))) % 0.44/0.63 (define @t111 () (not @t110)) % 0.44/0.63 (define @t112 () (or @t111 @t107 @t97 @t88 @t79 @t74 @t73 @t71)) % 0.44/0.63 (define @t113 () (@list @t12 @t70 @t72)) % 0.44/0.63 (define @t114 () (forall @t113 @t112)) % 0.44/0.63 (define @t115 () (tptp.in @t2 @t1)) % 0.44/0.63 (define @t116 () (tptp.in @t2 @t5)) % 0.44/0.63 (define @t117 () (not @t6)) % 0.44/0.63 (define @t118 () (tptp.subset @t5 @t1)) % 0.44/0.63 (define @t119 () (not @t8)) % 0.44/0.63 (define @t120 () (or @t119 @t117 @t4)) % 0.44/0.63 (define @t121 () (=> tptp.subsetE @t114)) % 0.44/0.63 (define @t122 () (or @t74 @t73 @t71)) % 0.44/0.63 (define @t123 () (or @t111 @t107 @t97 @t88 @t79 @t122)) % 0.44/0.63 (define @t124 () (forall @t113 @t123)) % 0.44/0.63 (define @t125 () (@list @t70 @t72)) % 0.44/0.63 (define @t126 () (forall @t125 @t123)) % 0.44/0.63 (define @t127 () (forall @t125 @t122)) % 0.44/0.63 (define @t128 () (or @t111 @t107 @t97 @t88 @t79 @t127)) % 0.44/0.63 (define @t129 () (tptp.in @t2 @t12)) % 0.44/0.63 (define @t130 () (not @t116)) % 0.44/0.63 (define @t131 () (tptp.in @t5 @t12)) % 0.44/0.63 (define @t132 () (forall @t16 (or (not @t131) @t130 @t129))) % 0.44/0.63 (define @t133 () (or @t111 @t107 @t97 @t88 @t79 @t132)) % 0.44/0.63 (define @t134 () (or @t111 @t107 @t97 @t88 @t79)) % 0.44/0.63 (define @t135 () (and @t110 @t106 @t96 @t87 @t78)) % 0.44/0.63 (define @t136 () (not @t15)) % 0.44/0.63 (define @t137 () (or @t136 @t117 @t13)) % 0.44/0.63 (define @t138 () (forall @t77 (or (not (tptp.in @t75 @t2)) @t76))) % 0.44/0.63 (define @t139 () (not (tptp.in @t81 @t2))) % 0.44/0.63 (define @t140 () (not (tptp.in @t80 @t2))) % 0.44/0.63 (define @t141 () (forall @t95 (or (not (tptp.in @t90 @t2)) (not (tptp.in @t92 @t2)) @t94 (not (tptp.in @t89 @t2)) @t93 @t91))) % 0.44/0.63 (define @t142 () (tptp.powerset @t2)) % 0.44/0.63 (define @t143 () (forall @t105 (or (not (tptp.in @t101 @t142)) @t104 @t103))) % 0.44/0.63 (define @t144 () (forall @t109 (or (not (tptp.in @t108 @t2)) (tptp.subset @t108 @t2)))) % 0.44/0.63 (define @t145 () (or @t140 @t139 (= @t80 @t81) @t83 @t82)) % 0.44/0.63 (define @t146 () (forall @t86 @t145)) % 0.44/0.63 (define @t147 () (and @t144 @t143 @t141 @t146 @t138)) % 0.44/0.63 (define @t148 () (tptp.in @t12 @t12)) % 0.44/0.63 (define @t149 () (not @t148)) % 0.44/0.63 (define @t150 () (not (tptp.in @t12 @t2))) % 0.44/0.63 (define @t151 () (forall @t19 (or @t150 @t149))) % 0.44/0.63 (define @t152 () (@list @t12)) % 0.44/0.63 (define @t153 () (tptp.in @t12 @t81)) % 0.44/0.63 (define @t154 () (= @t12 @t81)) % 0.44/0.63 (define @t155 () (@list @t12 @t81)) % 0.44/0.63 (define @t156 () (forall @t155 (or @t150 @t139 @t154 @t153 @t85))) % 0.44/0.63 (define @t157 () (tptp.in @t35 @t12)) % 0.44/0.63 (define @t158 () (not @t157)) % 0.44/0.63 (define @t159 () (not (tptp.in @t98 @t12))) % 0.44/0.63 (define @t160 () (not (forall @t102 (or @t159 (not (forall @t42 (or @t158 @t100 @t99))))))) % 0.44/0.63 (define @t161 () (= tptp.emptyset @t12)) % 0.44/0.63 (define @t162 () (forall @t19 (or (not (tptp.in @t12 @t142)) @t161 @t160))) % 0.44/0.63 (define @t163 () (forall @t19 (or @t150 (tptp.subset @t12 @t2)))) % 0.44/0.63 (define @t164 () (and @t163 @t162 @t141 @t156 @t151)) % 0.44/0.63 (define @t165 () (lambda @t24 @t164)) % 0.44/0.63 (define @t166 () (=> (_ @t165 @t12) @t17)) % 0.44/0.63 (define @t167 () (forall @t19 @t166)) % 0.44/0.63 (define @t168 () (=> tptp.subsetE @t167)) % 0.44/0.63 (define @t169 () (and @t162 @t141 @t156 @t151)) % 0.44/0.63 (define @t170 () (tptp.in @t12 @t5)) % 0.44/0.63 (define @t171 () (not @t170)) % 0.44/0.63 (define @t172 () (forall @t19 (or @t171 @t149))) % 0.44/0.63 (define @t173 () (not (tptp.in @t81 @t5))) % 0.44/0.63 (define @t174 () (or @t171 @t173 @t154 @t153 @t85)) % 0.44/0.63 (define @t175 () (forall @t155 @t174)) % 0.44/0.63 (define @t176 () (not (tptp.in @t89 @t5))) % 0.44/0.63 (define @t177 () (not (tptp.in @t92 @t5))) % 0.44/0.63 (define @t178 () (forall @t95 (or (not (tptp.in @t90 @t5)) @t177 @t94 @t176 @t93 @t91))) % 0.44/0.63 (define @t179 () (tptp.powerset @t5)) % 0.44/0.63 (define @t180 () (tptp.in @t12 @t179)) % 0.44/0.63 (define @t181 () (not @t180)) % 0.44/0.63 (define @t182 () (or @t158 (= @t98 @t35) @t99)) % 0.44/0.63 (define @t183 () (forall @t42 @t182)) % 0.44/0.63 (define @t184 () (not @t183)) % 0.44/0.63 (define @t185 () (or @t159 @t184)) % 0.44/0.63 (define @t186 () (forall @t102 @t185)) % 0.44/0.63 (define @t187 () (not @t186)) % 0.44/0.63 (define @t188 () (or @t181 @t161 @t187)) % 0.44/0.63 (define @t189 () (forall @t19 @t188)) % 0.44/0.63 (define @t190 () (and @t189 @t178 @t175 @t172)) % 0.44/0.63 (define @t191 () (tptp.in @t2 @t89)) % 0.44/0.63 (define @t192 () (not (tptp.in @t2 @t92))) % 0.44/0.63 (define @t193 () (or @t130 @t177 @t192 @t176 @t93 @t191)) % 0.44/0.63 (define @t194 () (@list @t2 @t92 @t89)) % 0.44/0.63 (define @t195 () (forall @t194 @t193)) % 0.44/0.63 (define @t196 () (@list @t2)) % 0.44/0.63 (define @t197 () (tptp.in @t2 @t35)) % 0.44/0.63 (define @t198 () (forall @t42 (or @t158 @t56 @t197))) % 0.44/0.63 (define @t199 () (not @t198)) % 0.44/0.63 (define @t200 () (not @t129)) % 0.44/0.63 (define @t201 () (forall @t24 (or @t200 @t199))) % 0.44/0.63 (define @t202 () (not @t201)) % 0.44/0.63 (define @t203 () (or @t181 @t161 @t202)) % 0.44/0.63 (define @t204 () (forall @t19 @t203)) % 0.44/0.63 (define @t205 () (and @t204 @t195 @t175 @t172)) % 0.44/0.63 (define @t206 () (lambda @t30 @t205)) % 0.44/0.63 (define @t207 () (tptp.subset @t12 @t5)) % 0.44/0.63 (define @t208 () (_ (lambda @t30 (forall @t19 (or @t171 @t207))) @t2)) % 0.44/0.63 (define @t209 () (and @t195 @t175 @t172)) % 0.44/0.63 (define @t210 () (not @t63)) % 0.44/0.63 (define @t211 () (or @t210 @t161 @t202)) % 0.44/0.63 (define @t212 () (not @t161)) % 0.44/0.63 (define @t213 () (=> @t212 @t202)) % 0.44/0.63 (define @t214 () (not @t13)) % 0.44/0.63 (define @t215 () (or @t214 @t199)) % 0.44/0.63 (define @t216 () (and @t13 @t198)) % 0.44/0.63 (define @t217 () (forall @t24 (not @t216))) % 0.44/0.63 (define @t218 () (not @t217)) % 0.44/0.63 (define @t219 () (not @t37)) % 0.44/0.63 (define @t220 () (or @t219 @t56 @t46)) % 0.44/0.63 (define @t221 () (_ (lambda @t24 (not (= tptp.emptyset @t2))) @t12)) % 0.44/0.63 (define @t222 () (=> @t221 @t60)) % 0.44/0.63 (define @t223 () (=> @t63 @t222)) % 0.44/0.63 (define @t224 () (forall @t19 @t223)) % 0.44/0.63 (define @t225 () (_ (lambda @t30 @t209) @t5)) % 0.44/0.63 (define @t226 () (not @t28)) % 0.44/0.63 (define @t227 () (or @t226 @t33)) % 0.44/0.63 (define @t228 () (or @t173 @t154 @t153 @t85)) % 0.44/0.63 (define @t229 () (or @t171 @t228)) % 0.44/0.63 (define @t230 () (forall @t155 @t229)) % 0.44/0.63 (define @t231 () (@list @t81)) % 0.44/0.63 (define @t232 () (forall @t231 @t229)) % 0.44/0.63 (define @t233 () (forall @t231 @t228)) % 0.44/0.63 (define @t234 () (@list @t35)) % 0.44/0.63 (define @t235 () (or @t171 @t233)) % 0.44/0.63 (define @t236 () (tptp.in @t12 @t35)) % 0.44/0.63 (define @t237 () (tptp.in @t35 @t5)) % 0.44/0.63 (define @t238 () (not @t237)) % 0.44/0.63 (define @t239 () (forall @t42 (or @t238 @t39 @t236 @t157))) % 0.44/0.63 (define @t240 () (or @t226 @t239)) % 0.44/0.63 (define @t241 () (not @t41)) % 0.44/0.63 (define @t242 () (or @t241 @t39 @t38 @t37)) % 0.44/0.63 (define @t243 () (or @t177 @t192 @t176 @t93 @t191)) % 0.44/0.63 (define @t244 () (or @t130 @t243)) % 0.44/0.63 (define @t245 () (forall @t194 @t244)) % 0.44/0.63 (define @t246 () (@list @t92 @t89)) % 0.44/0.63 (define @t247 () (forall @t246 @t244)) % 0.44/0.63 (define @t248 () (forall @t246 @t243)) % 0.44/0.63 (define @t249 () (@var "BOUND_VARIABLE_7527" $$unsorted)) % 0.44/0.63 (define @t250 () (or @t130 @t248)) % 0.44/0.63 (define @t251 () (tptp.in @t2 @t249)) % 0.44/0.63 (define @t252 () (not (tptp.in @t12 @t249))) % 0.44/0.63 (define @t253 () (not (tptp.in @t249 @t5))) % 0.44/0.63 (define @t254 () (or @t171 @t200 @t253 @t252 @t251)) % 0.44/0.63 (define @t255 () (@list @t12 @t249)) % 0.44/0.63 (define @t256 () (forall @t255 @t254)) % 0.44/0.63 (define @t257 () (or @t117 @t256)) % 0.44/0.63 (define @t258 () (or @t253 @t252 @t251)) % 0.44/0.63 (define @t259 () (or @t171 @t200 @t258)) % 0.44/0.63 (define @t260 () (forall @t255 @t259)) % 0.44/0.63 (define @t261 () (@list @t249)) % 0.44/0.63 (define @t262 () (forall @t261 @t259)) % 0.44/0.63 (define @t263 () (forall @t261 @t258)) % 0.44/0.63 (define @t264 () (or @t171 @t200 @t263)) % 0.44/0.63 (define @t265 () (forall @t42 (or @t238 (not @t236) @t197))) % 0.44/0.63 (define @t266 () (or @t226 @t214 @t265)) % 0.44/0.63 (define @t267 () (or @t214 @t265)) % 0.44/0.63 (define @t268 () (not @t38)) % 0.44/0.63 (define @t269 () (or @t241 @t268 @t46)) % 0.44/0.63 (define @t270 () (forall @t42 @t269)) % 0.44/0.63 (define @t271 () (or @t214 @t270)) % 0.44/0.63 (define @t272 () (or @t214 @t269)) % 0.44/0.63 (define @t273 () (or @t241 @t214 @t268 @t46)) % 0.44/0.63 (define @t274 () (or @t214 @t268 @t46)) % 0.44/0.63 (define @t275 () (or @t226 @t26)) % 0.44/0.63 (define @t276 () (@quantifiers_skolemize @t114 0)) % 0.44/0.63 (define @t277 () (forall @t109 (or (not (tptp.in @t108 @t276)) (tptp.subset @t108 @t276)))) % 0.44/0.63 (define @t278 () (@quantifiers_skolemize @t114 1)) % 0.44/0.63 (define @t279 () (tptp.in @t278 @t276)) % 0.44/0.63 (define @t280 () (@quantifiers_skolemize @t114 2)) % 0.44/0.63 (define @t281 () (tptp.in @t278 @t280)) % 0.44/0.63 (define @t282 () (not @t281)) % 0.44/0.63 (define @t283 () (tptp.in @t280 @t276)) % 0.44/0.63 (define @t284 () (not @t283)) % 0.44/0.63 (define @t285 () (not @t277)) % 0.44/0.63 (define @t286 () (or @t285 (not (forall @t105 (or (not (tptp.in @t101 (tptp.powerset @t276))) @t104 @t103))) (not (forall @t95 (or (not (tptp.in @t90 @t276)) (not (tptp.in @t92 @t276)) @t94 (not (tptp.in @t89 @t276)) @t93 @t91))) (not (forall @t86 (or (not (tptp.in @t80 @t276)) (not (tptp.in @t81 @t276)) @t84 @t83 @t82))) (not (forall @t77 (or (not (tptp.in @t75 @t276)) @t76))) @t284 @t282 @t279)) % 0.44/0.63 (define @t287 () (@list true)) % 0.44/0.63 (define @t288 () (@list @t286)) % 0.44/0.63 (define @t289 () (tptp.subset @t280 @t276)) % 0.44/0.63 (define @t290 () (or @t284 @t289)) % 0.44/0.63 (define @t291 () (not @t289)) % 0.44/0.63 (define @t292 () (or @t291 @t282 @t279)) % 0.44/0.63 (define @t293 () (not @t292)) % 0.44/0.63 (define @t294 () (forall @t9 (or (not @t118) @t130 @t115))) % 0.44/0.63 (assume @p1 @t11) % 0.44/0.63 (assume @p2 @t22) % 0.44/0.63 (assume @p3 true) % 0.44/0.63 (step @p4 (= tptp.nonempty @t25) :rule refl :args (@t25)) % 0.44/0.63 (step @p5 (= tptp.transitiveset @t31) :rule refl :args (@t31)) % 0.44/0.63 (step @p6 (= tptp.stricttotalorderedByIn @t55) :rule refl :args (@t55)) % 0.44/0.63 (step @p7 (= tptp.wellorderedByIn @t67) :rule refl :args (@t67)) % 0.44/0.63 (step @p8 (= tptp.ordinal @t69) :rule refl :args (@t69)) % 0.44/0.63 (step @p9 :rule refl :args (@t114)) % 0.44/0.63 (step @p10 :rule refl :args (@t115)) % 0.44/0.63 (step @p11 :rule refl :args (@t4)) % 0.44/0.63 (step @p12 :rule cong :premises (@p11 @p10) :args ((= @t4 @t115))) % 0.44/0.63 (step @p13 :rule symm :premises (@p12)) % 0.44/0.63 (step @p14 :rule eq_resolve :premises (@p11 @p13)) % 0.44/0.63 (step @p15 :rule refl :args (@t116)) % 0.44/0.63 (step @p16 :rule refl :args (@t6)) % 0.44/0.63 (step @p17 :rule cong :premises (@p16 @p15) :args ((= @t6 @t116))) % 0.44/0.63 (step @p18 :rule symm :premises (@p17)) % 0.44/0.63 (step @p19 :rule eq_resolve :premises (@p16 @p18)) % 0.44/0.63 (step @p20 :rule cong :premises (@p19) :args (@t117)) % 0.44/0.63 (step @p21 :rule refl :args (@t118)) % 0.44/0.63 (step @p22 :rule refl :args (@t8)) % 0.44/0.63 (step @p23 :rule cong :premises (@p22 @p21) :args ((= @t8 @t118))) % 0.44/0.63 (step @p24 :rule symm :premises (@p23)) % 0.44/0.63 (step @p25 :rule eq_resolve :premises (@p22 @p24)) % 0.44/0.63 (step @p26 :rule cong :premises (@p25) :args (@t119)) % 0.44/0.63 (step @p27 :rule nary_cong :premises (@p26 @p20 @p14) :args (@t120)) % 0.44/0.63 (step @p28 :rule cong :premises (@p27) :args ((forall @t9 @t120))) % 0.44/0.63 (step @p29 :rule aci_norm :args ((= (or @t119 (or @t117 @t4)) @t120))) % 0.44/0.63 (step @p30 :rule bool-impl-elim :args (@t6 @t4)) % 0.44/0.63 (step @p31 :rule refl :args (@t119)) % 0.44/0.63 (step @p32 :rule nary_cong :premises (@p31 @p30) :args ((or @t119 @t7))) % 0.44/0.63 (step @p33 :rule trans :premises (@p32 @p29)) % 0.44/0.63 (step @p34 :rule bool-impl-elim :args (@t8 @t7)) % 0.44/0.63 (step @p35 :rule trans :premises (@p34 @p33)) % 0.44/0.63 (step @p36 :rule cong :premises (@p35) :args (@t10)) % 0.44/0.63 (step @p37 :rule trans :premises (@p36 @p28)) % 0.44/0.63 (step @p38 :rule refl :args (tptp.subsetE)) % 0.44/0.63 (step @p39 :rule cong :premises (@p38 @p37) :args (@t11)) % 0.44/0.63 (step @p40 :rule eq_resolve :premises (@p1 @p39)) % 0.44/0.63 (step @p41 :rule cong :premises (@p40 @p9) :args (@t121)) % 0.44/0.63 (step @p42 :rule cong :premises (@p41) :args ((not @t121))) % 0.44/0.63 (step @p43 :rule aci_norm :args ((= @t123 @t112))) % 0.44/0.63 (step @p44 :rule cong :premises (@p43) :args (@t124)) % 0.44/0.63 (step @p45 :rule quant-merge-prenex :args ((= (forall @t19 @t126) @t124))) % 0.44/0.63 (step @p46 :rule alpha_equiv :args (@t127 (@list @t70 @t72) (@list @t2 @t5))) % 0.44/0.63 (step @p47 :rule refl :args (@t79)) % 0.44/0.63 (step @p48 :rule refl :args (@t88)) % 0.44/0.63 (step @p49 :rule refl :args (@t97)) % 0.44/0.63 (step @p50 :rule refl :args (@t107)) % 0.44/0.63 (step @p51 :rule refl :args (@t111)) % 0.44/0.63 (step @p52 :rule nary_cong :premises (@p51 @p50 @p49 @p48 @p47 @p46) :args (@t128)) % 0.44/0.63 (step @p53 :rule quant-miniscope-or :args ((= @t126 @t128))) % 0.44/0.63 (step @p54 :rule trans :premises (@p53 @p52)) % 0.44/0.63 (step @p55 :rule symm :premises (@p54)) % 0.44/0.63 (step @p56 :rule cong :premises (@p55) :args ((forall @t19 @t133))) % 0.44/0.63 (step @p57 :rule trans :premises (@p56 @p45)) % 0.44/0.63 (step @p58 :rule trans :premises (@p57 @p44)) % 0.44/0.63 (step @p59 :rule aci_norm :args ((= (or @t134 @t132) @t133))) % 0.44/0.63 (step @p60 :rule refl :args (@t132)) % 0.44/0.63 (step @p61 :rule aci_norm :args ((= (or @t111 (or @t107 (or @t97 (or @t88 @t79)))) @t134))) % 0.44/0.63 (step @p62 :rule bool-and-de-morgan :args (@t87 @t78 true)) % 0.44/0.63 (step @p63 :rule nary_cong :premises (@p49 @p62) :args ((or @t97 (not (and @t87 @t78))))) % 0.44/0.63 (step @p64 :rule bool-and-de-morgan :args (@t96 @t87 (and @t78))) % 0.44/0.63 (step @p65 :rule trans :premises (@p64 @p63)) % 0.44/0.63 (step @p66 :rule nary_cong :premises (@p50 @p65) :args ((or @t107 (not (and @t96 @t87 @t78))))) % 0.44/0.63 (step @p67 :rule bool-and-de-morgan :args (@t106 @t96 (and @t87 @t78))) % 0.44/0.63 (step @p68 :rule trans :premises (@p67 @p66)) % 0.44/0.63 (step @p69 :rule nary_cong :premises (@p51 @p68) :args ((or @t111 (not (and @t106 @t96 @t87 @t78))))) % 0.44/0.63 (step @p70 :rule bool-and-de-morgan :args (@t110 @t106 (and @t96 @t87 @t78))) % 0.44/0.63 (step @p71 :rule trans :premises (@p70 @p69)) % 0.44/0.63 (step @p72 :rule trans :premises (@p71 @p61)) % 0.44/0.63 (step @p73 :rule nary_cong :premises (@p72 @p60) :args ((or (not @t135) @t132))) % 0.44/0.63 (step @p74 :rule trans :premises (@p73 @p59)) % 0.44/0.63 (step @p75 :rule bool-impl-elim :args (@t135 @t132)) % 0.44/0.63 (step @p76 :rule trans :premises (@p75 @p74)) % 0.44/0.63 (step @p77 :rule cong :premises (@p76) :args ((forall @t19 (=> @t135 @t132)))) % 0.44/0.63 (step @p78 :rule trans :premises (@p77 @p58)) % 0.44/0.63 (step @p79 :rule refl :args (@t129)) % 0.44/0.63 (step @p80 :rule refl :args (@t13)) % 0.44/0.63 (step @p81 :rule cong :premises (@p80 @p79) :args ((= @t13 @t129))) % 0.44/0.63 (step @p82 :rule symm :premises (@p81)) % 0.44/0.63 (step @p83 :rule eq_resolve :premises (@p80 @p82)) % 0.44/0.63 (step @p84 :rule refl :args (@t131)) % 0.44/0.63 (step @p85 :rule refl :args (@t15)) % 0.44/0.63 (step @p86 :rule cong :premises (@p85 @p84) :args ((= @t15 @t131))) % 0.44/0.63 (step @p87 :rule symm :premises (@p86)) % 0.44/0.63 (step @p88 :rule eq_resolve :premises (@p85 @p87)) % 0.44/0.63 (step @p89 :rule cong :premises (@p88) :args (@t136)) % 0.44/0.63 (step @p90 :rule nary_cong :premises (@p89 @p20 @p83) :args (@t137)) % 0.44/0.63 (step @p91 :rule cong :premises (@p90) :args ((forall @t16 @t137))) % 0.44/0.63 (step @p92 :rule aci_norm :args ((= (or @t136 (or @t117 @t13)) @t137))) % 0.44/0.63 (step @p93 :rule bool-impl-elim :args (@t6 @t13)) % 0.44/0.63 (step @p94 :rule refl :args (@t136)) % 0.44/0.63 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or @t136 @t14))) % 0.44/0.63 (step @p96 :rule trans :premises (@p95 @p92)) % 0.44/0.63 (step @p97 :rule bool-impl-elim :args (@t15 @t14)) % 0.44/0.63 (step @p98 :rule trans :premises (@p97 @p96)) % 0.44/0.63 (step @p99 :rule cong :premises (@p98) :args (@t17)) % 0.44/0.63 (step @p100 :rule trans :premises (@p99 @p91)) % 0.44/0.63 (step @p101 :rule beta-reduce :args ((= (_ (lambda @t24 (and @t144 @t143 @t141 (forall @t86 (or @t140 @t139 @t84 @t83 @t82)) @t138)) @t12) @t135))) % 0.44/0.63 (step @p102 :rule refl :args (@t12)) % 0.44/0.63 (step @p103 :rule refl :args (@t138)) % 0.44/0.63 (step @p104 :rule refl :args (@t82)) % 0.44/0.63 (step @p105 :rule refl :args (@t83)) % 0.44/0.63 (step @p106 :rule eq-symm :args (@t80 @t81)) % 0.44/0.63 (step @p107 :rule refl :args (@t139)) % 0.44/0.63 (step @p108 :rule refl :args (@t140)) % 0.44/0.63 (step @p109 :rule nary_cong :premises (@p108 @p107 @p106 @p105 @p104) :args (@t145)) % 0.44/0.63 (step @p110 :rule cong :premises (@p109) :args (@t146)) % 0.44/0.63 (step @p111 :rule refl :args (@t141)) % 0.44/0.63 (step @p112 :rule refl :args (@t143)) % 0.44/0.63 (step @p113 :rule refl :args (@t144)) % 0.44/0.63 (step @p114 :rule nary_cong :premises (@p113 @p112 @p111 @p110 @p103) :args (@t147)) % 0.44/0.63 (step @p115 :rule cong :premises (@p114) :args ((lambda @t24 @t147))) % 0.44/0.63 (step @p116 :rule ho_cong :premises (@p115 @p102)) % 0.44/0.63 (step @p117 :rule trans :premises (@p116 @p101)) % 0.44/0.63 (step @p118 :rule refl :args (@t12)) % 0.44/0.63 (step @p119 :rule alpha_equiv :args (@t151 @t152 (@list @t75))) % 0.44/0.63 (step @p120 :rule alpha_equiv :args (@t156 @t152 (@list @t80))) % 0.44/0.63 (step @p121 :rule refl :args (@t141)) % 0.44/0.63 (step @p122 :rule alpha_equiv :args (@t162 @t152 (@list @t101))) % 0.44/0.63 (step @p123 :rule alpha_equiv :args (@t163 @t152 (@list @t108))) % 0.44/0.63 (step @p124 :rule nary_cong :premises (@p123 @p122 @p121 @p120 @p119) :args (@t164)) % 0.44/0.63 (step @p125 :rule cong :premises (@p124) :args (@t165)) % 0.44/0.63 (step @p126 :rule ho_cong :premises (@p125 @p118)) % 0.44/0.63 (step @p127 :rule trans :premises (@p126 @p117)) % 0.44/0.63 (step @p128 :rule cong :premises (@p127 @p100) :args (@t166)) % 0.44/0.63 (step @p129 :rule cong :premises (@p128) :args (@t167)) % 0.44/0.63 (step @p130 :rule trans :premises (@p129 @p78)) % 0.44/0.63 (step @p131 :rule cong :premises (@p38 @p130) :args (@t168)) % 0.44/0.63 (step @p132 :rule cong :premises (@p131) :args ((not @t168))) % 0.44/0.63 (step @p133 :rule refl :args (@t17)) % 0.44/0.63 (step @p134 :rule aci_norm :args ((= (and @t163 @t169) @t164))) % 0.44/0.63 (step @p135 :rule beta-reduce :args ((= (_ (lambda @t30 (and (forall @t19 (or @t181 @t161 @t160)) @t178 @t175 @t172)) @t2) @t169))) % 0.44/0.63 (step @p136 :rule refl :args (@t2)) % 0.44/0.63 (step @p137 :rule refl :args (@t172)) % 0.44/0.63 (step @p138 :rule refl :args (@t175)) % 0.44/0.63 (step @p139 :rule refl :args (@t178)) % 0.44/0.63 (step @p140 :rule refl :args (@t99)) % 0.44/0.63 (step @p141 :rule eq-symm :args (@t98 @t35)) % 0.44/0.63 (step @p142 :rule refl :args (@t158)) % 0.44/0.63 (step @p143 :rule nary_cong :premises (@p142 @p141 @p140) :args (@t182)) % 0.44/0.63 (step @p144 :rule cong :premises (@p143) :args (@t183)) % 0.44/0.63 (step @p145 :rule cong :premises (@p144) :args (@t184)) % 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0.44/0.63 (step @p414 :rule cong :premises (@p413) :args (@t69)) % 0.44/0.63 (step @p415 :rule trans :premises (@p8 @p414)) % 0.44/0.63 (step @p416 :rule ho_cong :premises (@p415 @p102)) % 0.44/0.63 (step @p417 :rule cong :premises (@p416 @p133) :args (@t18)) % 0.44/0.63 (step @p418 :rule cong :premises (@p417) :args (@t20)) % 0.44/0.63 (step @p419 :rule cong :premises (@p38 @p418) :args (@t21)) % 0.44/0.63 (step @p420 :rule cong :premises (@p419) :args (@t22)) % 0.44/0.63 (step @p421 :rule trans :premises (@p420 @p132)) % 0.44/0.63 (step @p422 :rule trans :premises (@p421 @p42)) % 0.44/0.63 (step @p423 :rule eq_resolve :premises (@p2 @p422)) % 0.44/0.63 (step @p424 :rule not_implies_elim1 :premises (@p423)) % 0.44/0.63 (step @p425 :rule not_implies_elim2 :premises (@p423)) % 0.44/0.63 (step @p426 :rule skolemize :premises (@p425)) % 0.44/0.63 (step @p427 :rule bool-double-not-elim :args (@t277)) % 0.44/0.63 (step @p428 :rule refl :args (@t286)) % 0.44/0.63 (step @p429 :rule nary_cong :premises (@p428 @p427) :args ((or @t286 (not @t285)))) % 0.44/0.63 (step @p430 :rule cnf_or_neg :args (@t286 0)) % 0.44/0.63 (step @p431 :rule eq_resolve :premises (@p430 @p429)) % 0.44/0.63 (step @p432 :rule reordering :premises (@p431) :args ((or @t277 @t286))) % 0.44/0.63 (step @p433 :rule chain_m_resolution :premises (@p432 @p426) :args (@t277 @t287 @t288)) % 0.44/0.63 (step @p434 :rule instantiate :premises (@p433) :args ((@list @t280))) % 0.44/0.63 (step @p435 :rule bool-double-not-elim :args (@t283)) % 0.44/0.63 (step @p436 :rule nary_cong :premises (@p428 @p435) :args ((or @t286 (not @t284)))) % 0.44/0.63 (step @p437 :rule cnf_or_neg :args (@t286 5)) % 0.44/0.63 (step @p438 :rule eq_resolve :premises (@p437 @p436)) % 0.44/0.63 (step @p439 :rule reordering :premises (@p438) :args ((or @t283 @t286))) % 0.44/0.63 (step @p440 :rule chain_m_resolution :premises (@p439 @p426) :args (@t283 @t287 @t288)) % 0.44/0.63 (step @p441 :rule cnf_or_pos :args (@t290)) % 0.44/0.63 (step @p442 :rule reordering :premises (@p441) :args ((or @t284 @t289 (not @t290)))) % 0.44/0.63 (step @p443 :rule chain_m_resolution :premises (@p442 @p440 @p434) :args (@t289 (@list false false) (@list @t283 @t290))) % 0.44/0.63 (step @p444 :rule cnf_or_neg :args (@t286 7)) % 0.44/0.63 (step @p445 :rule chain_m_resolution :premises (@p444 @p426) :args ((not @t279) @t287 @t288)) % 0.44/0.63 (step @p446 :rule bool-double-not-elim :args (@t281)) % 0.44/0.63 (step @p447 :rule nary_cong :premises (@p428 @p446) :args ((or @t286 (not @t282)))) % 0.44/0.63 (step @p448 :rule cnf_or_neg :args (@t286 6)) % 0.44/0.63 (step @p449 :rule eq_resolve :premises (@p448 @p447)) % 0.44/0.63 (step @p450 :rule reordering :premises (@p449) :args ((or @t281 @t286))) % 0.44/0.63 (step @p451 :rule chain_m_resolution :premises (@p450 @p426) :args (@t281 @t287 @t288)) % 0.44/0.63 (step @p452 :rule cnf_or_pos :args (@t292)) % 0.44/0.63 (step @p453 :rule reordering :premises (@p452) :args ((or @t282 @t279 @t291 @t293))) % 0.44/0.63 (step @p454 :rule chain_m_resolution :premises (@p453 @p451 @p445 @p443) :args (@t293 (@list false true false) (@list @t281 @t279 @t289))) % 0.44/0.63 (assume-push @p461 @t294) % 0.44/0.63 (step @p456 :rule instantiate :premises (@p424) :args ((@list @t280 @t276 @t278))) % 0.44/0.63 (step-pop @p462 :rule scope :premises (@p456)) % 0.44/0.63 (step @p457 :rule process_scope :premises (@p462) :args (@t292)) % 0.44/0.63 (step @p459 :rule implies_elim :premises (@p457)) % 0.44/0.63 (step @p460 false :rule chain_m_resolution :premises (@p459 @p454 @p424) :args (false (@list true false) (@list @t292 @t294))) % 0.44/0.63 ) % 0.44/0.63 % SZS output end Proof % 0.44/0.63 % cvc5 exiting %------------------------------------------------------------------------------