%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU676^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n003.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 08:52:41 AM UTC 2026 % Result : Theorem 208.91s 209.27s % Output : Proof 208.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SEU676^2 : TPTP v9.2.1. Released v3.7.0. % 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n003.cluster.edu % 0.18/0.35 % Model : x86_64 x86_64 % 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.35 % Memory : 8042.1875MB % 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.35 % CPULimit : 300 % 0.18/0.35 % WCLimit : 300 % 0.18/0.35 % DateTime : Tue Jun 2 17:45:29 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.51 %----Proving TH0 % 208.91/209.27 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 208.91/209.27 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s... % 208.91/209.27 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s... % 208.91/209.27 --- Run --ho-elim --full-saturate-quant at 18s... % 208.91/209.27 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 208.91/209.27 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 208.91/209.27 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 208.91/209.27 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 208.91/209.27 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 208.91/209.27 % SZS status Theorem % 208.91/209.27 % SZS output start Proof % 208.91/209.27 ( % 208.91/209.27 (declare-sort $$unsorted 0) % 208.91/209.27 (declare-const tptp.emptyset $$unsorted) % 208.91/209.27 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 208.91/209.27 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 208.91/209.27 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 208.91/209.27 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 208.91/209.27 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 208.91/209.27 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 208.91/209.27 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 208.91/209.27 (declare-const tptp.setunion (-> $$unsorted $$unsorted)) % 208.91/209.27 (declare-const tptp.infuncsetfunc Bool) % 208.91/209.27 (declare-const tptp.app Bool) % 208.91/209.27 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 208.91/209.27 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 208.91/209.27 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 208.91/209.27 (define tptp.func () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 208.91/209.27 (define tptp.funcSet () (let ((_let_1 (@var "Xf" $$unsorted))) (let ((_let_2 (@var "B" $$unsorted))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ (_ tptp.dsetconstr (_ tptp.powerset (_ (_ tptp.cartprod _let_3) _let_2))) (lambda (@list _let_1) (_ (_ (_ tptp.func _let_3) _let_2) _let_1)))))))) % 208.91/209.27 (define tptp.ap () (let ((_let_1 (@var "Xf" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (lambda (@list (@var "A" $$unsorted) _let_4 _let_1 _let_3) (_ tptp.setunion (_ (_ tptp.dsetconstr _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1)))))))))) % 208.91/209.27 (define @t1 () (@var "B" $$unsorted)) % 208.91/209.27 (define @t2 () (@var "Xx" $$unsorted)) % 208.91/209.27 (define @t3 () (@var "Xf" $$unsorted)) % 208.91/209.27 (define @t4 () (@var "A" $$unsorted)) % 208.91/209.27 (define @t5 () (_ (_ tptp.in @t2) @t4)) % 208.91/209.27 (define @t6 () (=> @t5 (_ (_ tptp.in (_ (_ (_ (_ tptp.ap @t4) @t1) @t3) @t2)) @t1))) % 208.91/209.27 (define @t7 () (@list @t2)) % 208.91/209.27 (define @t8 () (forall @t7 @t6)) % 208.91/209.27 (define @t9 () (_ (_ (_ tptp.func @t4) @t1) @t3)) % 208.91/209.27 (define @t10 () (=> @t9 @t8)) % 208.91/209.27 (define @t11 () (@list @t4 @t1 @t3)) % 208.91/209.27 (define @t12 () (forall @t11 @t10)) % 208.91/209.27 (define @t13 () (= tptp.app @t12)) % 208.91/209.27 (define @t14 () (_ tptp.in @t3)) % 208.91/209.27 (define @t15 () (_ @t14 (_ (_ tptp.funcSet @t4) @t1))) % 208.91/209.27 (define @t16 () (=> @t15 @t9)) % 208.91/209.27 (define @t17 () (forall @t11 @t16)) % 208.91/209.27 (define @t18 () (= tptp.infuncsetfunc @t17)) % 208.91/209.27 (define @t19 () (=> @t15 @t8)) % 208.91/209.27 (define @t20 () (forall @t11 @t19)) % 208.91/209.27 (define @t21 () (=> tptp.infuncsetfunc @t20)) % 208.91/209.27 (define @t22 () (=> tptp.app @t21)) % 208.91/209.27 (define @t23 () (not @t22)) % 208.91/209.27 (define @t24 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 208.91/209.27 (define @t25 () (= @t4 @t24)) % 208.91/209.27 (define @t26 () (and @t5 @t25)) % 208.91/209.27 (define @t27 () (exists @t7 @t26)) % 208.91/209.27 (define @t28 () (@list @t4)) % 208.91/209.27 (define @t29 () (lambda @t28 @t27)) % 208.91/209.27 (define @t30 () (@var "Xphi" (-> $$unsorted Bool))) % 208.91/209.27 (define @t31 () (lambda @t7 (_ @t30 @t2))) % 208.91/209.27 (define @t32 () (_ tptp.dsetconstr @t4)) % 208.91/209.27 (define @t33 () (_ @t32 @t31)) % 208.91/209.27 (define @t34 () (@list @t4 @t30)) % 208.91/209.27 (define @t35 () (lambda @t34 (_ tptp.singleton @t33))) % 208.91/209.27 (define @t36 () (_ (_ tptp.cartprod @t4) @t1)) % 208.91/209.27 (define @t37 () (@var "C" $$unsorted)) % 208.91/209.27 (define @t38 () (_ (_ tptp.subset @t37) @t36)) % 208.91/209.27 (define @t39 () (lambda (@list @t4 @t1 @t37) @t38)) % 208.91/209.27 (define @t40 () (@var "R" $$unsorted)) % 208.91/209.27 (define @t41 () (@var "Xy" $$unsorted)) % 208.91/209.27 (define @t42 () (_ (_ tptp.kpair @t2) @t41)) % 208.91/209.27 (define @t43 () (_ tptp.in @t42)) % 208.91/209.27 (define @t44 () (_ @t43 @t40)) % 208.91/209.27 (define @t45 () (@list @t41)) % 208.91/209.27 (define @t46 () (lambda @t45 @t44)) % 208.91/209.27 (define @t47 () (=> @t5 (_ (_ tptp.ex1 @t1) @t46))) % 208.91/209.27 (define @t48 () (forall @t7 @t47)) % 208.91/209.27 (define @t49 () (and (_ (_ (_ tptp.breln @t4) @t1) @t40) @t48)) % 208.91/209.27 (define @t50 () (@list @t4 @t1 @t40)) % 208.91/209.27 (define @t51 () (lambda @t50 @t49)) % 208.91/209.27 (define @t52 () (@list @t3)) % 208.91/209.27 (define @t53 () (lambda @t52 @t9)) % 208.91/209.27 (define @t54 () (_ tptp.powerset @t36)) % 208.91/209.27 (define @t55 () (_ tptp.dsetconstr @t54)) % 208.91/209.27 (define @t56 () (@list @t4 @t1)) % 208.91/209.27 (define @t57 () (lambda @t56 (_ @t55 @t53))) % 208.91/209.27 (define @t58 () (_ @t43 @t3)) % 208.91/209.27 (define @t59 () (lambda @t45 @t58)) % 208.91/209.27 (define @t60 () (_ tptp.dsetconstr @t1)) % 208.91/209.27 (define @t61 () (_ @t60 @t59)) % 208.91/209.27 (define @t62 () (_ tptp.setunion @t61)) % 208.91/209.27 (define @t63 () (lambda (@list @t4 @t1 @t3 @t2) @t62)) % 208.91/209.27 (define @t64 () (@var "BOUND_VARIABLE_7931" $$unsorted)) % 208.91/209.27 (define @t65 () (tptp.in (tptp.setunion (tptp.dsetconstr @t1 (lambda @t45 (tptp.in (tptp.kpair @t64 @t41) @t3)))) @t1)) % 208.91/209.27 (define @t66 () (not (tptp.in @t64 @t4))) % 208.91/209.27 (define @t67 () (@var "BOUND_VARIABLE_7894" $$unsorted)) % 208.91/209.27 (define @t68 () (tptp.kpair @t2 @t41)) % 208.91/209.27 (define @t69 () (tptp.in @t68 @t67)) % 208.91/209.27 (define @t70 () (lambda @t45 @t69)) % 208.91/209.27 (define @t71 () (tptp.dsetconstr @t1 @t70)) % 208.91/209.27 (define @t72 () (@var "BOUND_VARIABLE_7580" $$unsorted)) % 208.91/209.27 (define @t73 () (tptp.setadjoin @t72 tptp.emptyset)) % 208.91/209.27 (define @t74 () (= @t73 @t71)) % 208.91/209.27 (define @t75 () (not @t74)) % 208.91/209.27 (define @t76 () (tptp.in @t72 @t71)) % 208.91/209.27 (define @t77 () (not @t76)) % 208.91/209.27 (define @t78 () (or @t77 @t75)) % 208.91/209.27 (define @t79 () (@list @t72)) % 208.91/209.27 (define @t80 () (forall @t79 @t78)) % 208.91/209.27 (define @t81 () (not @t80)) % 208.91/209.27 (define @t82 () (tptp.in @t2 @t4)) % 208.91/209.27 (define @t83 () (not @t82)) % 208.91/209.27 (define @t84 () (or @t83 @t81)) % 208.91/209.27 (define @t85 () (forall @t7 @t84)) % 208.91/209.27 (define @t86 () (tptp.cartprod @t4 @t1)) % 208.91/209.27 (define @t87 () (tptp.subset @t67 @t86)) % 208.91/209.27 (define @t88 () (and @t87 @t85)) % 208.91/209.27 (define @t89 () (@list @t67)) % 208.91/209.27 (define @t90 () (lambda @t89 @t88)) % 208.91/209.27 (define @t91 () (tptp.powerset @t86)) % 208.91/209.27 (define @t92 () (tptp.dsetconstr @t91 @t90)) % 208.91/209.27 (define @t93 () (tptp.in @t3 @t92)) % 208.91/209.27 (define @t94 () (not @t93)) % 208.91/209.27 (define @t95 () (or @t94 @t66 @t65)) % 208.91/209.27 (define @t96 () (@list @t4 @t1 @t3 @t64)) % 208.91/209.27 (define @t97 () (forall @t96 @t95)) % 208.91/209.27 (define @t98 () (@var "BOUND_VARIABLE_7865" $$unsorted)) % 208.91/209.27 (define @t99 () (tptp.dsetconstr @t1 (lambda @t45 (tptp.in (tptp.kpair @t98 @t41) @t3)))) % 208.91/209.27 (define @t100 () (or (not (tptp.in @t98 @t4)) (not (forall @t79 (or (not (tptp.in @t72 @t99)) (not (= @t73 @t99))))))) % 208.91/209.27 (define @t101 () (tptp.subset @t3 @t86)) % 208.91/209.27 (define @t102 () (and @t101 @t100)) % 208.91/209.27 (define @t103 () (@var "BOUND_VARIABLE_7824" $$unsorted)) % 208.91/209.27 (define @t104 () (tptp.in @t68 @t103)) % 208.91/209.27 (define @t105 () (lambda @t45 @t104)) % 208.91/209.27 (define @t106 () (tptp.dsetconstr @t1 @t105)) % 208.91/209.27 (define @t107 () (= @t73 @t106)) % 208.91/209.27 (define @t108 () (not @t107)) % 208.91/209.27 (define @t109 () (tptp.in @t72 @t106)) % 208.91/209.27 (define @t110 () (not @t109)) % 208.91/209.27 (define @t111 () (or @t110 @t108)) % 208.91/209.27 (define @t112 () (forall @t79 @t111)) % 208.91/209.27 (define @t113 () (not @t112)) % 208.91/209.27 (define @t114 () (or @t83 @t113)) % 208.91/209.27 (define @t115 () (forall @t7 @t114)) % 208.91/209.27 (define @t116 () (tptp.subset @t103 @t86)) % 208.91/209.27 (define @t117 () (and @t116 @t115)) % 208.91/209.27 (define @t118 () (@list @t103)) % 208.91/209.27 (define @t119 () (lambda @t118 @t117)) % 208.91/209.27 (define @t120 () (tptp.dsetconstr @t91 @t119)) % 208.91/209.27 (define @t121 () (tptp.in @t3 @t120)) % 208.91/209.27 (define @t122 () (not @t121)) % 208.91/209.27 (define @t123 () (or @t122 @t102)) % 208.91/209.27 (define @t124 () (forall (@list @t4 @t1 @t3 @t98) @t123)) % 208.91/209.27 (define @t125 () (@list @t98)) % 208.91/209.27 (define @t126 () (forall @t125 @t123)) % 208.91/209.27 (define @t127 () (forall @t125 @t100)) % 208.91/209.27 (define @t128 () (@list @t2)) % 208.91/209.27 (define @t129 () (forall @t125 @t101)) % 208.91/209.27 (define @t130 () (and @t129 @t127)) % 208.91/209.27 (define @t131 () (forall @t125 @t102)) % 208.91/209.27 (define @t132 () (or @t122 @t131)) % 208.91/209.27 (define @t133 () (tptp.in @t68 @t3)) % 208.91/209.27 (define @t134 () (lambda @t45 @t133)) % 208.91/209.27 (define @t135 () (tptp.dsetconstr @t1 @t134)) % 208.91/209.27 (define @t136 () (forall @t7 (or @t83 (not (forall @t79 (or (not (tptp.in @t72 @t135)) (not (= @t73 @t135)))))))) % 208.91/209.27 (define @t137 () (_ tptp.subset @t3)) % 208.91/209.27 (define @t138 () (_ @t137 @t36)) % 208.91/209.27 (define @t139 () (and @t138 @t136)) % 208.91/209.27 (define @t140 () (lambda @t45 (_ @t43 @t103))) % 208.91/209.27 (define @t141 () (_ @t60 @t140)) % 208.91/209.27 (define @t142 () (_ (_ tptp.setadjoin @t72) tptp.emptyset)) % 208.91/209.27 (define @t143 () (_ tptp.in @t72)) % 208.91/209.27 (define @t144 () (not @t5)) % 208.91/209.27 (define @t145 () (_ tptp.subset @t103)) % 208.91/209.27 (define @t146 () (_ @t145 @t36)) % 208.91/209.27 (define @t147 () (lambda @t118 (and @t146 (forall @t7 (or @t144 (not (forall @t79 (or (not (_ @t143 @t141)) (not (= @t142 @t141)))))))))) % 208.91/209.27 (define @t148 () (_ @t55 @t147)) % 208.91/209.27 (define @t149 () (_ tptp.dsetconstr @t91)) % 208.91/209.27 (define @t150 () (and @t146 @t115)) % 208.91/209.27 (define @t151 () (lambda @t118 @t150)) % 208.91/209.27 (define @t152 () (_ @t14 (_ @t55 @t151))) % 208.91/209.27 (define @t153 () (not @t152)) % 208.91/209.27 (define @t154 () (or @t153 @t139)) % 208.91/209.27 (define @t155 () (lambda @t52 @t139)) % 208.91/209.27 (define @t156 () (@list @t3)) % 208.91/209.27 (define @t157 () (_ @t55 @t155)) % 208.91/209.27 (define @t158 () (_ @t14 @t157)) % 208.91/209.27 (define @t159 () (=> @t158 @t139)) % 208.91/209.27 (define @t160 () (tptp.in @t68 @t40)) % 208.91/209.27 (define @t161 () (tptp.dsetconstr @t1 (lambda @t45 @t160))) % 208.91/209.27 (define @t162 () (not (forall @t79 (or (not (tptp.in @t72 @t161)) (not (= @t73 @t161)))))) % 208.91/209.27 (define @t163 () (_ (_ tptp.subset @t40) @t36)) % 208.91/209.27 (define @t164 () (and @t163 (forall @t7 (or @t83 @t162)))) % 208.91/209.27 (define @t165 () (lambda (@list @t40) @t164)) % 208.91/209.27 (define @t166 () (lambda (@list @t1 @t40) @t164)) % 208.91/209.27 (define @t167 () (_ (lambda @t50 @t164) @t4)) % 208.91/209.27 (define @t168 () (lambda (@list @t1) @t157)) % 208.91/209.27 (define @t169 () (_ (lambda @t56 @t157) @t4)) % 208.91/209.27 (define @t170 () (_ (_ @t167 @t1) @t3)) % 208.91/209.27 (define @t171 () (_ @t14 (_ @t169 @t1))) % 208.91/209.27 (define @t172 () (=> @t171 @t170)) % 208.91/209.27 (define @t173 () (forall @t11 @t172)) % 208.91/209.27 (define @t174 () (or @t144 @t162)) % 208.91/209.27 (define @t175 () (_ tptp.in @t68)) % 208.91/209.27 (define @t176 () (tptp.dsetconstr @t1 @t46)) % 208.91/209.27 (define @t177 () (= @t73 @t176)) % 208.91/209.27 (define @t178 () (not @t177)) % 208.91/209.27 (define @t179 () (tptp.in @t72 @t176)) % 208.91/209.27 (define @t180 () (not @t179)) % 208.91/209.27 (define @t181 () (or @t180 @t178)) % 208.91/209.27 (define @t182 () (not (= @t176 @t73))) % 208.91/209.27 (define @t183 () (or @t180 @t182)) % 208.91/209.27 (define @t184 () (forall @t79 @t183)) % 208.91/209.27 (define @t185 () (not @t184)) % 208.91/209.27 (define @t186 () (tptp.dsetconstr @t1 @t30)) % 208.91/209.27 (define @t187 () (not (tptp.in @t72 @t186))) % 208.91/209.27 (define @t188 () (@list @t30)) % 208.91/209.27 (define @t189 () (not (= @t73 @t186))) % 208.91/209.27 (define @t190 () (or @t187 @t189)) % 208.91/209.27 (define @t191 () (forall @t79 @t190)) % 208.91/209.27 (define @t192 () (not @t191)) % 208.91/209.27 (define @t193 () (tptp.setadjoin @t2 tptp.emptyset)) % 208.91/209.27 (define @t194 () (forall @t7 (or (not (tptp.in @t2 @t186)) (not (= @t193 @t186))))) % 208.91/209.27 (define @t195 () (not @t194)) % 208.91/209.27 (define @t196 () (lambda @t188 @t195)) % 208.91/209.27 (define @t197 () (tptp.dsetconstr @t4 @t30)) % 208.91/209.27 (define @t198 () (_ (lambda @t34 (not (forall @t7 (or (not (tptp.in @t2 @t197)) (not (= @t193 @t197)))))) @t1)) % 208.91/209.27 (define @t199 () (=> @t5 (_ @t198 @t46))) % 208.91/209.27 (define @t200 () (forall @t7 @t199)) % 208.91/209.27 (define @t201 () (lambda (@list @t37) @t38)) % 208.91/209.27 (define @t202 () (lambda (@list @t1 @t37) @t38)) % 208.91/209.27 (define @t203 () (_ @t39 @t4)) % 208.91/209.27 (define @t204 () (@var "BOUND_VARIABLE_7481" $$unsorted)) % 208.91/209.27 (define @t205 () (_ @t30 @t204)) % 208.91/209.27 (define @t206 () (@list @t204)) % 208.91/209.27 (define @t207 () (lambda @t206 @t205)) % 208.91/209.27 (define @t208 () (tptp.dsetconstr @t4 @t207)) % 208.91/209.27 (define @t209 () (= @t193 @t208)) % 208.91/209.27 (define @t210 () (not @t209)) % 208.91/209.27 (define @t211 () (tptp.in @t2 @t208)) % 208.91/209.27 (define @t212 () (not @t211)) % 208.91/209.27 (define @t213 () (or @t212 @t210)) % 208.91/209.27 (define @t214 () (_ @t30 @t204)) % 208.91/209.27 (define @t215 () (lambda @t206 @t214)) % 208.91/209.27 (define @t216 () (_ @t32 @t215)) % 208.91/209.27 (define @t217 () (= @t193 @t216)) % 208.91/209.27 (define @t218 () (not @t217)) % 208.91/209.27 (define @t219 () (tptp.in @t2 @t216)) % 208.91/209.27 (define @t220 () (not @t219)) % 208.91/209.27 (define @t221 () (or @t220 @t218)) % 208.91/209.27 (define @t222 () (= @t193 @t33)) % 208.91/209.27 (define @t223 () (not @t222)) % 208.91/209.27 (define @t224 () (tptp.in @t2 @t33)) % 208.91/209.27 (define @t225 () (not @t224)) % 208.91/209.27 (define @t226 () (or @t225 @t223)) % 208.91/209.27 (define @t227 () (not (= @t33 @t193))) % 208.91/209.27 (define @t228 () (or @t225 @t227)) % 208.91/209.27 (define @t229 () (forall @t7 @t228)) % 208.91/209.27 (define @t230 () (not @t229)) % 208.91/209.27 (define @t231 () (not @t25)) % 208.91/209.27 (define @t232 () (or @t144 @t231)) % 208.91/209.27 (define @t233 () (forall @t7 (not @t26))) % 208.91/209.27 (define @t234 () (not @t233)) % 208.91/209.27 (define @t235 () (=> tptp.infuncsetfunc @t97)) % 208.91/209.27 (define @t236 () (@var "BOUND_VARIABLE_7796" $$unsorted)) % 208.91/209.27 (define @t237 () (tptp.in (tptp.setunion (tptp.dsetconstr @t1 (lambda @t45 (tptp.in (tptp.kpair @t236 @t41) @t3)))) @t1)) % 208.91/209.27 (define @t238 () (not (tptp.in @t236 @t4))) % 208.91/209.27 (define @t239 () (not @t136)) % 208.91/209.27 (define @t240 () (not @t101)) % 208.91/209.27 (define @t241 () (or @t240 @t239 @t238 @t237)) % 208.91/209.27 (define @t242 () (or @t238 @t237)) % 208.91/209.27 (define @t243 () (or @t240 @t239 @t242)) % 208.91/209.27 (define @t244 () (@list @t4 @t1 @t3 @t236)) % 208.91/209.27 (define @t245 () (forall @t244 @t243)) % 208.91/209.27 (define @t246 () (@list @t236)) % 208.91/209.27 (define @t247 () (forall @t246 @t243)) % 208.91/209.27 (define @t248 () (forall @t246 @t242)) % 208.91/209.27 (define @t249 () (or @t240 @t239 @t248)) % 208.91/209.27 (define @t250 () (tptp.setunion @t135)) % 208.91/209.27 (define @t251 () (tptp.in @t250 @t1)) % 208.91/209.27 (define @t252 () (forall @t7 (or @t83 @t251))) % 208.91/209.27 (define @t253 () (not @t138)) % 208.91/209.27 (define @t254 () (or @t253 @t239 @t252)) % 208.91/209.27 (define @t255 () (_ (_ tptp.in @t62) @t1)) % 208.91/209.27 (define @t256 () (or @t144 @t255)) % 208.91/209.27 (define @t257 () (lambda @t7 @t62)) % 208.91/209.27 (define @t258 () (lambda (@list @t3 @t2) @t62)) % 208.91/209.27 (define @t259 () (lambda (@list @t1 @t3 @t2) @t62)) % 208.91/209.27 (define @t260 () (_ @t63 @t4)) % 208.91/209.27 (define @t261 () (=> @t5 (_ (_ tptp.in (_ (_ (_ @t260 @t1) @t3) @t2)) @t1))) % 208.91/209.27 (define @t262 () (forall @t7 @t261)) % 208.91/209.27 (define @t263 () (=> @t170 @t262)) % 208.91/209.27 (define @t264 () (forall @t11 @t263)) % 208.91/209.27 (define @t265 () (=> tptp.app @t235)) % 208.91/209.27 (define @t266 () (or @t66 @t65)) % 208.91/209.27 (define @t267 () (or @t94 @t266)) % 208.91/209.27 (define @t268 () (forall @t96 @t267)) % 208.91/209.27 (define @t269 () (@list @t64)) % 208.91/209.27 (define @t270 () (forall @t269 @t267)) % 208.91/209.27 (define @t271 () (forall @t269 @t266)) % 208.91/209.27 (define @t272 () (or @t94 @t271)) % 208.91/209.27 (define @t273 () (lambda @t45 (_ @t43 @t67))) % 208.91/209.27 (define @t274 () (_ @t60 @t273)) % 208.91/209.27 (define @t275 () (_ tptp.subset @t67)) % 208.91/209.27 (define @t276 () (_ @t275 @t36)) % 208.91/209.27 (define @t277 () (lambda @t89 (and @t276 (forall @t7 (or @t144 (not (forall @t79 (or (not (_ @t143 @t274)) (not (= @t142 @t274)))))))))) % 208.91/209.27 (define @t278 () (_ @t55 @t277)) % 208.91/209.27 (define @t279 () (and @t276 @t85)) % 208.91/209.27 (define @t280 () (lambda @t89 @t279)) % 208.91/209.27 (define @t281 () (_ @t14 (_ @t55 @t280))) % 208.91/209.27 (define @t282 () (not @t281)) % 208.91/209.27 (define @t283 () (or @t282 @t252)) % 208.91/209.27 (define @t284 () (=> @t158 @t252)) % 208.91/209.27 (define @t285 () (=> @t171 @t262)) % 208.91/209.27 (define @t286 () (forall @t11 @t285)) % 208.91/209.27 (define @t287 () (=> tptp.infuncsetfunc @t286)) % 208.91/209.27 (define @t288 () (=> tptp.app @t287)) % 208.91/209.27 (define @t289 () (@quantifiers_skolemize @t97 1)) % 208.91/209.27 (define @t290 () (@quantifiers_skolemize @t97 2)) % 208.91/209.27 (define @t291 () (@quantifiers_skolemize @t97 3)) % 208.91/209.27 (define @t292 () (lambda @t45 (tptp.in (tptp.kpair @t291 @t41) @t290))) % 208.91/209.27 (define @t293 () (@purify @t292)) % 208.91/209.27 (define @t294 () (tptp.in (tptp.setunion (tptp.dsetconstr @t289 @t293)) @t289)) % 208.91/209.27 (define @t295 () (@quantifiers_skolemize @t97 0)) % 208.91/209.27 (define @t296 () (tptp.in @t291 @t295)) % 208.91/209.27 (define @t297 () (not @t296)) % 208.91/209.27 (define @t298 () (tptp.dsetconstr @t289 @t70)) % 208.91/209.27 (define @t299 () (not (tptp.in @t2 @t295))) % 208.91/209.27 (define @t300 () (tptp.cartprod @t295 @t289)) % 208.91/209.27 (define @t301 () (and (tptp.subset @t67 @t300) (forall @t7 (or @t299 (not (forall @t79 (or (not (tptp.in @t72 @t298)) (not (= @t73 @t298))))))))) % 208.91/209.27 (define @t302 () (lambda @t89 @t301)) % 208.91/209.27 (define @t303 () (@purify @t302)) % 208.91/209.27 (define @t304 () (tptp.powerset @t300)) % 208.91/209.27 (define @t305 () (tptp.in @t290 (tptp.dsetconstr @t304 @t303))) % 208.91/209.27 (define @t306 () (not @t305)) % 208.91/209.27 (define @t307 () (or @t306 @t297 @t294)) % 208.91/209.27 (define @t308 () (not @t307)) % 208.91/209.27 (define @t309 () (not @t97)) % 208.91/209.27 (define @t310 () (tptp.dsetconstr @t289 @t292)) % 208.91/209.27 (define @t311 () (tptp.setunion @t310)) % 208.91/209.27 (define @t312 () (tptp.in @t311 @t289)) % 208.91/209.27 (define @t313 () (tptp.dsetconstr @t304 @t302)) % 208.91/209.27 (define @t314 () (tptp.in @t290 @t313)) % 208.91/209.27 (define @t315 () (not @t314)) % 208.91/209.27 (define @t316 () (or @t315 @t297 @t312)) % 208.91/209.27 (define @t317 () (not @t316)) % 208.91/209.27 (define @t318 () (@list true)) % 208.91/209.27 (define @t319 () (@list @t307)) % 208.91/209.27 (define @t320 () (tptp.subset @t290 @t300)) % 208.91/209.27 (define @t321 () (and @t320 (or @t297 (not (forall @t79 (or (not (tptp.in @t72 @t310)) (not (= @t73 @t310)))))))) % 208.91/209.27 (define @t322 () (tptp.dsetconstr @t289 @t105)) % 208.91/209.27 (define @t323 () (and (tptp.subset @t103 @t300) (forall @t7 (or @t299 (not (forall @t79 (or (not (tptp.in @t72 @t322)) (not (= @t73 @t322))))))))) % 208.91/209.27 (define @t324 () (lambda @t118 @t323)) % 208.91/209.27 (define @t325 () (@purify @t324)) % 208.91/209.27 (define @t326 () (tptp.dsetconstr @t304 @t324)) % 208.91/209.27 (define @t327 () (tptp.in @t290 @t326)) % 208.91/209.27 (define @t328 () (not @t327)) % 208.91/209.27 (define @t329 () (or @t328 @t321)) % 208.91/209.27 (define @t330 () (@list @t295 @t289 @t290 @t291)) % 208.91/209.27 (define @t331 () (tptp.dsetconstr @t304 @t325)) % 208.91/209.27 (define @t332 () (tptp.in @t290 @t331)) % 208.91/209.27 (define @t333 () (not @t332)) % 208.91/209.27 (define @t334 () (or @t333 @t321)) % 208.91/209.27 (define @t335 () (@list false)) % 208.91/209.27 (define @t336 () (@list @t124)) % 208.91/209.27 (define @t337 () (tptp.dsetconstr @t289 (lambda @t45 (tptp.in @t68 @t290)))) % 208.91/209.27 (define @t338 () (forall @t7 (or @t299 (not (forall @t79 (or (not (tptp.in @t72 @t337)) (not (= @t73 @t337)))))))) % 208.91/209.27 (define @t339 () (@quantifiers_skolemize @t338 0)) % 208.91/209.27 (define @t340 () (tptp.dsetconstr @t289 (lambda @t45 (tptp.in (tptp.kpair @t339 @t41) @t290)))) % 208.91/209.27 (define @t341 () (or (not (tptp.in @t339 @t295)) (not (forall @t79 (or (not (tptp.in @t72 @t340)) (not (= @t73 @t340))))))) % 208.91/209.27 (define @t342 () (and @t320 @t341)) % 208.91/209.27 (define @t343 () (or @t328 @t342)) % 208.91/209.27 (define @t344 () (or @t333 @t342)) % 208.91/209.27 (define @t345 () (not @t338)) % 208.91/209.27 (define @t346 () (not @t320)) % 208.91/209.27 (define @t347 () (or @t346 @t345 @t297 @t312)) % 208.91/209.27 (define @t348 () (forall @t244 @t241)) % 208.91/209.27 (define @t349 () (or @t346 @t345 @t297 @t294)) % 208.91/209.27 (define @t350 () (not @t341)) % 208.91/209.27 (define @t351 () (@const 0 $$unsorted)) % 208.91/209.27 (define @t352 () (_ @t325 @t351)) % 208.91/209.27 (define @t353 () (_ @t303 @t351)) % 208.91/209.27 (define @t354 () (= @t353 @t352)) % 208.91/209.27 (define @t355 () (_ @t303 @t67)) % 208.91/209.27 (define @t356 () (_ @t302 @t67)) % 208.91/209.27 (define @t357 () (= @t355 @t356)) % 208.91/209.27 (define @t358 () (forall @t89 @t357)) % 208.91/209.27 (define @t359 () (tptp.dsetconstr @t289 (lambda @t45 (tptp.in @t68 @t351)))) % 208.91/209.27 (define @t360 () (and (tptp.subset @t351 @t300) (forall @t7 (or @t299 (not (forall @t79 (or (not (tptp.in @t72 @t359)) (not (= @t73 @t359))))))))) % 208.91/209.27 (define @t361 () (forall @t89 (= @t301 @t355))) % 208.91/209.27 (define @t362 () (= @t360 @t353)) % 208.91/209.27 (define @t363 () (@list @t351)) % 208.91/209.27 (define @t364 () (= @t353 @t360)) % 208.91/209.27 (define @t365 () (not @t364)) % 208.91/209.27 (define @t366 () (not @t353)) % 208.91/209.27 (define @t367 () (_ @t325 @t103)) % 208.91/209.27 (define @t368 () (_ @t324 @t103)) % 208.91/209.27 (define @t369 () (= @t367 @t368)) % 208.91/209.27 (define @t370 () (forall @t118 @t369)) % 208.91/209.27 (define @t371 () (forall @t118 (= @t323 @t367))) % 208.91/209.27 (define @t372 () (= @t360 @t352)) % 208.91/209.27 (define @t373 () (= @t352 @t360)) % 208.91/209.27 (define @t374 () (not @t373)) % 208.91/209.27 (define @t375 () (not @t360)) % 208.91/209.27 (define @t376 () (= @t303 @t325)) % 208.91/209.27 (define @t377 () (not @t376)) % 208.91/209.27 (define @t378 () (and @t305 @t376 @t333)) % 208.91/209.27 (assume @p1 @t13) % 208.91/209.27 (assume @p2 @t18) % 208.91/209.27 (assume @p3 @t23) % 208.91/209.27 (assume @p4 true) % 208.91/209.27 (step @p5 (= tptp.singleton @t29) :rule refl :args (@t29)) % 208.91/209.27 (step @p6 (= tptp.ex1 @t35) :rule refl :args (@t35)) % 208.91/209.27 (step @p7 (= tptp.breln @t39) :rule refl :args (@t39)) % 208.91/209.27 (step @p8 (= tptp.func @t51) :rule refl :args (@t51)) % 208.91/209.27 (step @p9 (= tptp.funcSet @t57) :rule refl :args (@t57)) % 208.91/209.27 (step @p10 (= tptp.ap @t63) :rule refl :args (@t63)) % 208.91/209.27 (step @p11 :rule refl :args (@t97)) % 208.91/209.27 (step @p12 :rule quant-merge-prenex :args ((= (forall @t11 @t126) @t124))) % 208.91/209.27 (step @p13 :rule alpha_equiv :args (@t127 (@list @t98) @t128)) % 208.91/209.27 (step @p14 :rule quant-unused-vars :args ((= @t129 @t101))) % 208.91/209.27 (step @p15 :rule nary_cong :premises (@p14 @p13) :args (@t130)) % 208.91/209.27 (step @p16 :rule quant-miniscope-and :args ((= @t131 @t130))) % 208.91/209.27 (step @p17 :rule trans :premises (@p16 @p15)) % 208.91/209.27 (step @p18 :rule refl :args (@t122)) % 208.91/209.27 (step @p19 :rule nary_cong :premises (@p18 @p17) :args (@t132)) % 208.91/209.27 (step @p20 :rule quant-miniscope-or :args ((= @t126 @t132))) % 208.91/209.27 (step @p21 :rule trans :premises (@p20 @p19)) % 208.91/209.27 (step @p22 :rule symm :premises (@p21)) % 208.91/209.27 (step @p23 :rule cong :premises (@p22) :args ((forall @t11 (or @t122 (and @t101 @t136))))) % 208.91/209.27 (step @p24 :rule trans :premises (@p23 @p12)) % 208.91/209.27 (step @p25 :rule refl :args (@t136)) % 208.91/209.27 (step @p26 :rule refl :args ((tptp.subset @t3 @t36))) % 208.91/209.27 (step @p27 :rule refl :args (@t86)) % 208.91/209.27 (step @p28 :rule refl :args (@t3)) % 208.91/209.27 (step @p29 :rule cong :premises (@p28 @p27) :args (@t101)) % 208.91/209.27 (step @p30 :rule trans :premises (@p29 @p26)) % 208.91/209.27 (step @p31 :rule refl :args (@t137)) % 208.91/209.27 (step @p32 :rule ho_cong :premises (@p31 @p27)) % 208.91/209.27 (step @p33 :rule cong :premises (@p32 @p30) :args ((= (_ @t137 @t86) @t101))) % 208.91/209.27 (step @p34 :rule symm :premises (@p33)) % 208.91/209.27 (step @p35 :rule refl :args (@t138)) % 208.91/209.27 (step @p36 :rule eq_resolve :premises (@p35 @p34)) % 208.91/209.27 (step @p37 :rule refl :args (@t36)) % 208.91/209.27 (step @p38 :rule cong :premises (@p37 @p27) :args ((= @t36 @t86))) % 208.91/209.27 (step @p39 :rule symm :premises (@p38)) % 208.91/209.27 (step @p40 :rule eq_resolve :premises (@p37 @p39)) % 208.91/209.27 (step @p41 :rule ho_cong :premises (@p31 @p40)) % 208.91/209.27 (step @p42 :rule trans :premises (@p41 @p36)) % 208.91/209.27 (step @p43 :rule nary_cong :premises (@p42 @p25) :args (@t139)) % 208.91/209.27 (step @p44 :rule refl :args ((tptp.in @t3 @t148))) % 208.91/209.27 (step @p45 :rule refl :args ((tptp.dsetconstr @t54 @t147))) % 208.91/209.27 (step @p46 :rule refl :args ((tptp.dsetconstr @t1 @t140))) % 208.91/209.27 (step @p47 :rule refl :args ((tptp.in @t42 @t103))) % 208.91/209.27 (step @p48 :rule refl :args (@t103)) % 208.91/209.27 (step @p49 :rule refl :args (@t68)) % 208.91/209.27 (step @p50 :rule cong :premises (@p49 @p48) :args (@t104)) % 208.91/209.27 (step @p51 :rule trans :premises (@p50 @p47)) % 208.91/209.27 (step @p52 :rule cong :premises (@p51) :args (@t105)) % 208.91/209.27 (step @p53 :rule refl :args (@t1)) % 208.91/209.27 (step @p54 :rule cong :premises (@p53 @p52) :args (@t106)) % 208.91/209.27 (step @p55 :rule trans :premises (@p54 @p46)) % 208.91/209.27 (step @p56 :rule refl :args (@t73)) % 208.91/209.27 (step @p57 :rule cong :premises (@p56 @p55) :args (@t107)) % 208.91/209.27 (step @p58 :rule cong :premises (@p57) :args (@t108)) % 208.91/209.27 (step @p59 :rule refl :args ((tptp.in @t72 @t141))) % 208.91/209.27 (step @p60 :rule refl :args (@t72)) % 208.91/209.27 (step @p61 :rule cong :premises (@p60 @p55) :args (@t109)) % 208.91/209.27 (step @p62 :rule trans :premises (@p61 @p59)) % 208.91/209.27 (step @p63 :rule cong :premises (@p62) :args (@t110)) % 208.91/209.27 (step @p64 :rule nary_cong :premises (@p63 @p58) :args (@t111)) % 208.91/209.27 (step @p65 :rule cong :premises (@p64) :args (@t112)) % 208.91/209.27 (step @p66 :rule cong :premises (@p65) :args (@t113)) % 208.91/209.27 (step @p67 :rule refl :args (@t82)) % 208.91/209.27 (step @p68 :rule cong :premises (@p67) :args (@t83)) % 208.91/209.27 (step @p69 :rule nary_cong :premises (@p68 @p66) :args (@t114)) % 208.91/209.27 (step @p70 :rule cong :premises (@p69) :args (@t115)) % 208.91/209.27 (step @p71 :rule refl :args ((tptp.subset @t103 @t36))) % 208.91/209.27 (step @p72 :rule cong :premises (@p48 @p27) :args (@t116)) % 208.91/209.27 (step @p73 :rule trans :premises (@p72 @p71)) % 208.91/209.27 (step @p74 :rule nary_cong :premises (@p73 @p70) :args (@t117)) % 208.91/209.27 (step @p75 :rule cong :premises (@p74) :args (@t119)) % 208.91/209.27 (step @p76 :rule refl :args ((tptp.powerset @t36))) % 208.91/209.27 (step @p77 :rule cong :premises (@p27) :args (@t91)) % 208.91/209.27 (step @p78 :rule trans :premises (@p77 @p76)) % 208.91/209.27 (step @p79 :rule cong :premises (@p78 @p75) :args (@t120)) % 208.91/209.27 (step @p80 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:premises (@p576) :args (@t315)) % 208.91/209.28 (step @p578 :rule nary_cong :premises (@p577 @p566 @p565) :args (@t316)) % 208.91/209.28 (step @p579 :rule cong :premises (@p578) :args (@t317)) % 208.91/209.28 (step @p580 :rule refl :args (@t309)) % 208.91/209.28 (step @p581 :rule cong :premises (@p580 @p579) :args ((=> @t309 @t317))) % 208.91/209.28 (assume-push @p773 @t309) % 208.91/209.28 (step @p583 :rule skolemize :premises (@p552)) % 208.91/209.28 (step-pop @p774 :rule scope :premises (@p583)) % 208.91/209.28 (step @p584 :rule process_scope :premises (@p774) :args (@t317)) % 208.91/209.28 (step @p586 :rule eq_resolve :premises (@p584 @p581)) % 208.91/209.28 (step @p587 :rule implies_elim :premises (@p586)) % 208.91/209.28 (step @p588 :rule eq_resolve :premises (@p587 @p555)) % 208.91/209.28 (step @p589 :rule chain_m_resolution :premises (@p588 @p552) :args (@t308 @t318 (@list @t97))) % 208.91/209.28 (step @p590 :rule bool-double-not-elim :args (@t305)) % 208.91/209.28 (step @p591 :rule refl :args (@t307)) % 208.91/209.28 (step @p592 :rule nary_cong :premises (@p591 @p590) :args ((or @t307 (not @t306)))) % 208.91/209.28 (step @p593 :rule cnf_or_neg :args (@t307 0)) % 208.91/209.28 (step @p594 :rule eq_resolve :premises (@p593 @p592)) % 208.91/209.28 (step @p595 :rule reordering :premises (@p594) :args ((or @t305 @t307))) % 208.91/209.28 (step @p596 :rule chain_m_resolution :premises (@p595 @p589) :args (@t305 @t318 @t319)) % 208.91/209.28 (step @p597 :rule not_implies_elim1 :premises (@p551)) % 208.91/209.28 (step @p598 :rule refl :args (@t321)) % 208.91/209.28 (step @p599 :rule eq-refl :args (@t324)) % 208.91/209.28 (step @p600 :rule skolem_intro :args (@t325)) % 208.91/209.28 (step @p601 :rule refl :args (@t324)) % 208.91/209.28 (step @p602 :rule cong :premises (@p601 @p600) :args ((= @t324 @t325))) % 208.91/209.28 (step @p603 :rule trans :premises (@p602 @p599)) % 208.91/209.28 (step @p604 :rule true_elim :premises (@p603)) % 208.91/209.28 (step @p605 :rule cong :premises (@p573 @p604) :args (@t326)) % 208.91/209.28 (step @p606 :rule cong :premises (@p575 @p605) :args (@t327)) % 208.91/209.28 (step @p607 :rule cong :premises (@p606) :args (@t328)) % 208.91/209.28 (step @p608 :rule nary_cong :premises (@p607 @p598) :args (@t329)) % 208.91/209.28 (step @p609 :rule refl :args (@t124)) % 208.91/209.28 (step @p610 :rule cong :premises (@p609 @p608) :args ((=> @t124 @t329))) % 208.91/209.28 (assume-push @p775 @t124) % 208.91/209.28 (step @p612 :rule instantiate :premises (@p597) :args (@t330)) % 208.91/209.28 (step-pop @p776 :rule scope :premises (@p612)) % 208.91/209.28 (step @p613 :rule process_scope :premises (@p776) :args (@t329)) % 208.91/209.28 (step @p615 :rule eq_resolve :premises (@p613 @p610)) % 208.91/209.28 (step @p616 :rule implies_elim :premises (@p615)) % 208.91/209.28 (step @p617 :rule chain_m_resolution :premises (@p616 @p597) :args (@t334 @t335 @t336)) % 208.91/209.28 (step @p618 :rule cnf_or_pos :args (@t334)) % 208.91/209.28 (step @p619 :rule reordering :premises (@p618) :args ((or @t321 @t333 (not @t334)))) % 208.91/209.28 (step @p620 :rule refl :args (@t342)) % 208.91/209.28 (step @p621 :rule nary_cong :premises (@p607 @p620) :args (@t343)) % 208.91/209.28 (step @p622 :rule cong :premises (@p609 @p621) :args ((=> @t124 @t343))) % 208.91/209.28 (assume-push @p777 @t124) % 208.91/209.28 (step @p624 :rule instantiate :premises (@p597) :args ((@list @t295 @t289 @t290 @t339))) % 208.91/209.28 (step-pop @p778 :rule scope :premises (@p624)) % 208.91/209.28 (step @p625 :rule process_scope :premises (@p778) :args (@t343)) % 208.91/209.28 (step @p627 :rule eq_resolve :premises (@p625 @p622)) % 208.91/209.28 (step @p628 :rule implies_elim :premises (@p627)) % 208.91/209.28 (step @p629 :rule chain_m_resolution :premises (@p628 @p597) :args (@t344 @t335 @t336)) % 208.91/209.28 (step @p630 :rule cnf_or_pos :args (@t344)) % 208.91/209.28 (step @p631 :rule reordering :premises (@p630) :args ((or @t333 @t342 (not @t344)))) % 208.91/209.28 (step @p632 :rule cnf_and_pos :args (@t321 0)) % 208.91/209.28 (step @p633 :rule reordering :premises (@p632) :args ((or @t320 (not @t321)))) % 208.91/209.28 (step @p634 :rule cnf_and_pos :args (@t342 1)) % 208.91/209.28 (step @p635 :rule reordering :premises (@p634) :args ((or @t341 (not @t342)))) % 208.91/209.28 (step @p636 :rule bool-double-not-elim :args (@t296)) % 208.91/209.28 (step @p637 :rule nary_cong :premises (@p591 @p636) :args ((or @t307 (not @t297)))) % 208.91/209.28 (step @p638 :rule cnf_or_neg :args (@t307 1)) % 208.91/209.28 (step @p639 :rule eq_resolve :premises (@p638 @p637)) % 208.91/209.28 (step @p640 :rule reordering :premises (@p639) :args ((or @t296 @t307))) % 208.91/209.28 (step @p641 :rule chain_m_resolution :premises (@p640 @p589) :args (@t296 @t318 @t319)) % 208.91/209.28 (step @p642 :rule cnf_or_neg :args (@t307 2)) % 208.91/209.28 (step @p643 :rule chain_m_resolution :premises (@p642 @p589) :args ((not @t294) @t318 @t319)) % 208.91/209.28 (step @p644 :rule not_implies_elim1 :premises (@p550)) % 208.91/209.28 (step @p645 :rule refl :args (@t345)) % 208.91/209.28 (step @p646 :rule refl :args (@t346)) % 208.91/209.28 (step @p647 :rule nary_cong :premises (@p646 @p645 @p566 @p565) :args (@t347)) % 208.91/209.28 (step @p648 :rule refl :args (@t348)) % 208.91/209.28 (step @p649 :rule cong :premises (@p648 @p647) :args ((=> @t348 @t347))) % 208.91/209.28 (assume-push @p779 @t348) % 208.91/209.28 (step @p651 :rule instantiate :premises (@p644) :args (@t330)) % 208.91/209.28 (step-pop @p780 :rule scope :premises (@p651)) % 208.91/209.28 (step @p652 :rule process_scope :premises (@p780) :args (@t347)) % 208.91/209.28 (step @p654 :rule eq_resolve :premises (@p652 @p649)) % 208.91/209.28 (step @p655 :rule implies_elim :premises (@p654)) % 208.91/209.28 (step @p656 :rule chain_m_resolution :premises (@p655 @p644) :args (@t349 @t335 (@list @t348))) % 208.91/209.28 (step @p657 :rule cnf_or_pos :args (@t349)) % 208.91/209.28 (step @p658 :rule reordering :premises (@p657) :args ((or @t297 @t294 @t346 @t345 (not @t349)))) % 208.91/209.28 (step @p659 :rule refl :args (@t350)) % 208.91/209.28 (step @p660 :rule bool-double-not-elim :args (@t338)) % 208.91/209.28 (step @p661 :rule nary_cong :premises (@p660 @p659) :args ((or (not @t345) @t350))) % 208.91/209.28 (assume-push @p781 @t345) % 208.91/209.28 (step @p663 :rule skolemize :premises (@p781)) % 208.91/209.28 (step-pop @p782 :rule scope :premises (@p663)) % 208.91/209.28 (step @p664 :rule process_scope :premises (@p782) :args (@t350)) % 208.91/209.28 (step @p666 :rule implies_elim :premises (@p664)) % 208.91/209.28 (step @p667 :rule eq_resolve :premises (@p666 @p661)) % 208.91/209.28 (step @p668 :rule chain_m_resolution :premises (@p667 @p658 @p656 @p643 @p641 @p635 @p633 @p631 @p629 @p619 @p617) :args (@t333 (@list true false true false false false false false false false) (@list @t338 @t349 @t294 @t296 @t341 @t320 @t342 @t344 @t321 @t334))) % 208.91/209.28 (step @p669 :rule cnf_equiv_neg2 :args (@t354)) % 208.91/209.28 (step @p670 :rule eq-symm :args (@t355 @t301)) % 208.91/209.28 (step @p671 :rule beta-reduce :args ((= @t356 @t301))) % 208.91/209.28 (step @p672 :rule refl :args (@t355)) % 208.91/209.28 (step @p673 :rule cong :premises (@p672 @p671) :args (@t357)) % 208.91/209.28 (step @p674 :rule trans :premises (@p673 @p670)) % 208.91/209.28 (step @p675 :rule cong :premises (@p674) :args (@t358)) % 208.91/209.28 (step @p676 :rule quant-unused-vars :args ((= (forall @t89 true) true))) % 208.91/209.28 (step @p677 :rule eq-refl :args (@t356)) % 208.91/209.28 (step @p678 :rule cong :premises (@p677) :args ((forall @t89 (= @t356 @t356)))) % 208.91/209.28 (step @p679 :rule trans :premises (@p678 @p676)) % 208.91/209.28 (step @p680 :rule refl :args (@t356)) % 208.91/209.28 (step @p681 :rule refl :args (@t67)) % 208.91/209.28 (step @p682 :rule ho_cong :premises (@p568 @p681)) % 208.91/209.28 (step @p683 :rule cong :premises (@p682 @p680) :args (@t357)) % 208.91/209.28 (step @p684 :rule cong :premises (@p683) :args (@t358)) % 208.91/209.28 (step @p685 :rule trans :premises (@p684 @p679)) % 208.91/209.28 (step @p686 :rule true_elim :premises (@p685)) % 208.91/209.28 (step @p687 :rule eq_resolve :premises (@p686 @p675)) % 208.91/209.28 (step @p688 :rule eq-symm :args (@t360 @t353)) % 208.91/209.28 (step @p689 :rule refl :args (@t361)) % 208.91/209.28 (step @p690 :rule cong :premises (@p689 @p688) :args ((=> @t361 @t362))) % 208.91/209.28 (assume-push @p783 @t361) % 208.91/209.28 (step @p692 :rule instantiate :premises (@p687) :args (@t363)) % 208.91/209.28 (step-pop @p784 :rule scope :premises (@p692)) % 208.91/209.28 (step @p693 :rule process_scope :premises (@p784) :args (@t362)) % 208.91/209.28 (step @p695 :rule eq_resolve :premises (@p693 @p690)) % 208.91/209.28 (step @p696 :rule implies_elim :premises (@p695)) % 208.91/209.28 (step @p697 :rule chain_m_resolution :premises (@p696 @p687) :args (@t364 @t335 (@list @t361))) % 208.91/209.28 (step @p698 :rule cnf_equiv_pos1 :args (@t364)) % 208.91/209.28 (step @p699 :rule reordering :premises (@p698) :args ((or @t366 @t360 @t365))) % 208.91/209.28 (step @p700 :rule eq-symm :args (@t367 @t323)) % 208.91/209.28 (step @p701 :rule beta-reduce :args ((= @t368 @t323))) % 208.91/209.28 (step @p702 :rule refl :args (@t367)) % 208.91/209.28 (step @p703 :rule cong :premises (@p702 @p701) :args (@t369)) % 208.91/209.28 (step @p704 :rule trans :premises (@p703 @p700)) % 208.91/209.28 (step @p705 :rule cong :premises (@p704) :args (@t370)) % 208.91/209.28 (step @p706 :rule quant-unused-vars :args ((= (forall @t118 true) true))) % 208.91/209.28 (step @p707 :rule eq-refl :args (@t368)) % 208.91/209.28 (step @p708 :rule cong :premises (@p707) :args ((forall @t118 (= @t368 @t368)))) % 208.91/209.28 (step @p709 :rule trans :premises (@p708 @p706)) % 208.91/209.28 (step @p710 :rule refl :args (@t368)) % 208.91/209.28 (step @p711 :rule refl :args (@t103)) % 208.91/209.28 (step @p712 :rule ho_cong :premises (@p600 @p711)) % 208.91/209.28 (step @p713 :rule cong :premises (@p712 @p710) :args (@t369)) % 208.91/209.28 (step @p714 :rule cong :premises (@p713) :args (@t370)) % 208.91/209.28 (step @p715 :rule trans :premises (@p714 @p709)) % 208.91/209.28 (step @p716 :rule true_elim :premises (@p715)) % 208.91/209.28 (step @p717 :rule eq_resolve :premises (@p716 @p705)) % 208.91/209.28 (step @p718 :rule eq-symm :args (@t360 @t352)) % 208.91/209.28 (step @p719 :rule refl :args (@t371)) % 208.91/209.28 (step @p720 :rule cong :premises (@p719 @p718) :args ((=> @t371 @t372))) % 208.91/209.28 (assume-push @p785 @t371) % 208.91/209.28 (step @p722 :rule instantiate :premises (@p717) :args (@t363)) % 208.91/209.28 (step-pop @p786 :rule scope :premises (@p722)) % 208.91/209.28 (step @p723 :rule process_scope :premises (@p786) :args (@t372)) % 208.91/209.28 (step @p725 :rule eq_resolve :premises (@p723 @p720)) % 208.91/209.28 (step @p726 :rule implies_elim :premises (@p725)) % 208.91/209.28 (step @p727 :rule chain_m_resolution :premises (@p726 @p717) :args (@t373 @t335 (@list @t371))) % 208.91/209.28 (step @p728 :rule cnf_equiv_pos2 :args (@t373)) % 208.91/209.28 (step @p729 :rule reordering :premises (@p728) :args ((or @t352 @t375 @t374))) % 208.91/209.28 (step @p730 :rule chain_m_resolution :premises (@p729 @p727 @p699 @p697 @p669) :args ((or @t354 @t366) (@list false false false true) (@list @t373 @t360 @t364 @t352))) % 208.91/209.28 (step @p731 :rule cnf_equiv_neg1 :args (@t354)) % 208.91/209.28 (step @p732 :rule reordering :premises (@p731) :args ((or @t353 @t352 @t354))) % 208.91/209.28 (step @p733 :rule cnf_equiv_pos2 :args (@t364)) % 208.91/209.28 (step @p734 :rule reordering :premises (@p733) :args ((or @t353 @t375 @t365))) % 208.91/209.28 (step @p735 :rule cnf_equiv_pos1 :args (@t373)) % 208.91/209.28 (step @p736 :rule reordering :premises (@p735) :args ((or (not @t352) @t360 @t374))) % 208.91/209.28 (step @p737 :rule chain_m_resolution :premises (@p736 @p727 @p734 @p697 @p732 @p730) :args (@t354 (@list false true false false true) (@list @t373 @t360 @t364 @t352 @t353))) % 208.91/209.28 ; WARNING: add trust step for TRUST % 208.91/209.28 ; trust TRUST THEORY_LEMMA % 208.91/209.28 (step @p738 :rule trust :premises () :args ((or @t376 (not @t354)))) % 208.91/209.28 (step @p739 :rule chain_m_resolution :premises (@p738 @p737) :args (@t376 @t335 (@list @t354))) % 208.91/209.28 (step @p740 :rule refl :args (@t377)) % 208.91/209.28 (step @p741 :rule bool-double-not-elim :args (@t332)) % 208.91/209.28 (step @p742 :rule refl :args (@t306)) % 208.91/209.28 (step @p743 :rule nary_cong :premises (@p742 @p741 @p740) :args ((or @t306 (not @t333) @t377))) % 208.91/209.28 (assume-push @p787 @t305) % 208.91/209.28 (assume-push @p788 @t376) % 208.91/209.28 (assume-push @p789 @t333) % 208.91/209.28 (step @p747 :rule evaluate :args ((= false true))) % 208.91/209.28 (step @p748 :rule true_intro :premises (@p596)) % 208.91/209.28 (step @p749 :rule symm :premises (@p739)) % 208.91/209.28 (step @p750 :rule cong :premises (@p573 @p749) :args (@t331)) % 208.91/209.28 (step @p751 :rule cong :premises (@p575 @p750) :args (@t332)) % 208.91/209.28 (step @p752 :rule false_intro :premises (@p789)) % 208.91/209.28 (step @p753 :rule symm :premises (@p752)) % 208.91/209.28 (step @p754 :rule trans :premises (@p753 @p751 @p748)) % 208.91/209.28 (step @p755 false :rule eq_resolve :premises (@p754 @p747)) % 208.91/209.28 (step-pop @p790 :rule scope :premises (@p755)) % 208.91/209.28 (step-pop @p791 :rule scope :premises (@p790)) % 208.91/209.28 (step-pop @p792 :rule scope :premises (@p791)) % 208.91/209.28 (step @p756 :rule process_scope :premises (@p792) :args (false)) % 208.91/209.28 (assume-push @p793 @t305) % 208.91/209.28 (assume-push @p794 @t333) % 208.91/209.28 (assume-push @p795 @t376) % 208.91/209.28 (step @p763 :rule and_intro :premises (@p596 @p739 @p794)) % 208.91/209.28 (step-pop @p796 :rule scope :premises (@p763)) % 208.91/209.28 (step-pop @p797 :rule scope :premises (@p796)) % 208.91/209.28 (step-pop @p798 :rule scope :premises (@p797)) % 208.91/209.28 (step @p764 :rule process_scope :premises (@p798) :args (@t378)) % 208.91/209.28 (step @p768 :rule implies_elim :premises (@p764)) % 208.91/209.28 (step @p769 :rule resolution :premises (@p768 @p756) :args (true @t378)) % 208.91/209.28 (step @p770 :rule not_and :premises (@p769)) % 208.91/209.28 (step @p771 :rule eq_resolve :premises (@p770 @p743)) % 208.91/209.28 (step @p772 false :rule chain_m_resolution :premises (@p771 @p739 @p668 @p596) :args (false (@list false true false) (@list @t376 @t332 @t305))) % 208.91/209.28 ) % 208.91/209.28 % SZS output end Proof % 208.91/209.28 % cvc5 exiting %------------------------------------------------------------------------------