%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU293+1 : TPTP v9.2.1. Released v3.3.0. % 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 08:51:16 AM UTC 2026 % Result : Theorem 28.05s 28.20s % Output : Proof 28.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU293+1 : TPTP v9.2.1. Released v3.3.0. % 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.16/0.35 % Computer : n009.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Tue Jun 2 16:53:29 EDT 2026 % 0.16/0.35 % CPUTime : % 0.29/0.51 %----Proving TF0_NAR, FOF, or CNF % 28.05/28.20 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 28.05/28.20 --- Run --no-e-matching --full-saturate-quant at 6... % 28.05/28.20 --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 6... % 28.05/28.20 --- Run --finite-model-find --uf-ss=no-minimal at 6... % 28.05/28.20 % SZS status Theorem % 28.05/28.20 % SZS output start Proof % 28.05/28.20 ( % 28.05/28.20 (declare-sort $$unsorted 0) % 28.05/28.20 (declare-const tptp.relation_of2_as_subset (-> $$unsorted $$unsorted $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.relation_dom_as_subset (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 28.05/28.20 (declare-const tptp.powerset (-> $$unsorted $$unsorted)) % 28.05/28.20 (declare-const tptp.empty (-> $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.relation (-> $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.cartesian_product2 (-> $$unsorted $$unsorted $$unsorted)) % 28.05/28.20 (declare-const tptp.relation_of2 (-> $$unsorted $$unsorted $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.element (-> $$unsorted $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.quasi_total (-> $$unsorted $$unsorted $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.empty_set $$unsorted) % 28.05/28.20 (declare-const tptp.one_to_one (-> $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.relation_empty_yielding (-> $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.apply (-> $$unsorted $$unsorted $$unsorted)) % 28.05/28.20 (declare-const tptp.relation_dom (-> $$unsorted $$unsorted)) % 28.05/28.20 (declare-const tptp.function (-> $$unsorted Bool)) % 28.05/28.20 (declare-const tptp.relation_inverse_image (-> $$unsorted $$unsorted $$unsorted)) % 28.05/28.20 (define @t1 () (@var "A" $$unsorted)) % 28.05/28.20 (define @t2 () (@var "B" $$unsorted)) % 28.05/28.20 (define @t3 () (tptp.in @t1 @t2)) % 28.05/28.20 (define @t4 () (@list @t1 @t2)) % 28.05/28.20 (define @t5 () (tptp.function @t1)) % 28.05/28.20 (define @t6 () (tptp.empty @t1)) % 28.05/28.20 (define @t7 () (@list @t1)) % 28.05/28.20 (define @t8 () (tptp.relation @t1)) % 28.05/28.20 (define @t9 () (@var "C" $$unsorted)) % 28.05/28.20 (define @t10 () (tptp.relation @t9)) % 28.05/28.20 (define @t11 () (tptp.cartesian_product2 @t1 @t2)) % 28.05/28.20 (define @t12 () (tptp.element @t9 (tptp.powerset @t11))) % 28.05/28.20 (define @t13 () (@list @t1 @t2 @t9)) % 28.05/28.20 (define @t14 () (forall @t13 (=> @t12 @t10))) % 28.05/28.20 (define @t15 () (tptp.one_to_one @t1)) % 28.05/28.20 (define @t16 () (and @t8 @t5 @t15)) % 28.05/28.20 (define @t17 () (and @t8 @t6 @t5)) % 28.05/28.20 (define @t18 () (@var "D" $$unsorted)) % 28.05/28.20 (define @t19 () (tptp.apply @t1 @t18)) % 28.05/28.20 (define @t20 () (tptp.relation_dom @t1)) % 28.05/28.20 (define @t21 () (tptp.in @t18 @t20)) % 28.05/28.20 (define @t22 () (@list @t18)) % 28.05/28.20 (define @t23 () (forall (@list @t2 @t9) (= (= @t9 (tptp.relation_inverse_image @t1 @t2)) (forall @t22 (= (tptp.in @t18 @t9) (and @t21 (tptp.in @t19 @t2))))))) % 28.05/28.20 (define @t24 () (and @t8 @t5)) % 28.05/28.20 (define @t25 () (forall @t7 (=> @t24 @t23))) % 28.05/28.20 (define @t26 () (tptp.quasi_total @t9 @t1 @t2)) % 28.05/28.20 (define @t27 () (= @t26 (= @t9 tptp.empty_set))) % 28.05/28.20 (define @t28 () (= @t1 tptp.empty_set)) % 28.05/28.20 (define @t29 () (or @t28 @t27)) % 28.05/28.20 (define @t30 () (= @t2 tptp.empty_set)) % 28.05/28.20 (define @t31 () (tptp.relation_dom_as_subset @t1 @t2 @t9)) % 28.05/28.20 (define @t32 () (= @t26 (= @t1 @t31))) % 28.05/28.20 (define @t33 () (=> @t30 @t28)) % 28.05/28.20 (define @t34 () (and (=> @t33 @t32) (=> @t30 @t29))) % 28.05/28.20 (define @t35 () (tptp.relation_of2_as_subset @t9 @t1 @t2)) % 28.05/28.20 (define @t36 () (forall @t13 (=> @t35 @t34))) % 28.05/28.20 (define @t37 () (tptp.powerset @t1)) % 28.05/28.20 (define @t38 () (tptp.relation_of2 @t9 @t1 @t2)) % 28.05/28.20 (define @t39 () (forall @t13 (=> @t35 @t12))) % 28.05/28.20 (define @t40 () (@list @t9)) % 28.05/28.20 (define @t41 () (@list @t2)) % 28.05/28.20 (define @t42 () (tptp.relation tptp.empty_set)) % 28.05/28.20 (define @t43 () (tptp.empty tptp.empty_set)) % 28.05/28.20 (define @t44 () (tptp.empty @t2)) % 28.05/28.20 (define @t45 () (not @t44)) % 28.05/28.20 (define @t46 () (not @t6)) % 28.05/28.20 (define @t47 () (tptp.empty @t20)) % 28.05/28.20 (define @t48 () (and @t46 @t8)) % 28.05/28.20 (define @t49 () (tptp.function @t9)) % 28.05/28.20 (define @t50 () (tptp.element @t2 @t37)) % 28.05/28.20 (define @t51 () (tptp.relation_empty_yielding @t1)) % 28.05/28.20 (define @t52 () (= @t31 (tptp.relation_dom @t9))) % 28.05/28.20 (define @t53 () (forall @t13 (=> @t38 @t52))) % 28.05/28.20 (define @t54 () (tptp.element @t1 @t2)) % 28.05/28.20 (define @t55 () (@var "E" $$unsorted)) % 28.05/28.20 (define @t56 () (tptp.relation_inverse_image @t18 @t9)) % 28.05/28.20 (define @t57 () (forall (@list @t55) (= (tptp.in @t55 @t56) (and (tptp.in @t55 @t1) (tptp.in (tptp.apply @t18 @t55) @t9))))) % 28.05/28.20 (define @t58 () (not @t30)) % 28.05/28.20 (define @t59 () (=> @t58 @t57)) % 28.05/28.20 (define @t60 () (tptp.relation_of2_as_subset @t18 @t1 @t2)) % 28.05/28.20 (define @t61 () (tptp.quasi_total @t18 @t1 @t2)) % 28.05/28.20 (define @t62 () (tptp.function @t18)) % 28.05/28.20 (define @t63 () (and @t62 @t61 @t60)) % 28.05/28.20 (define @t64 () (@list @t1 @t2 @t9 @t18)) % 28.05/28.20 (define @t65 () (forall @t64 (=> @t63 @t59))) % 28.05/28.20 (define @t66 () (not @t65)) % 28.05/28.20 (define @t67 () (tptp.element @t2 (tptp.powerset @t9))) % 28.05/28.20 (define @t68 () (or @t58 @t28 @t27)) % 28.05/28.20 (define @t69 () (not @t35)) % 28.05/28.20 (define @t70 () (@var "BOUND_VARIABLE_7828" $$unsorted)) % 28.05/28.20 (define @t71 () (= (tptp.in @t70 @t56) (and (tptp.in @t70 @t1) (tptp.in (tptp.apply @t18 @t70) @t9)))) % 28.05/28.20 (define @t72 () (not @t60)) % 28.05/28.20 (define @t73 () (not @t61)) % 28.05/28.20 (define @t74 () (not @t62)) % 28.05/28.20 (define @t75 () (or @t74 @t73 @t72 @t30 @t71)) % 28.05/28.20 (define @t76 () (forall (@list @t1 @t2 @t9 @t18 @t70) @t75)) % 28.05/28.20 (define @t77 () (@quantifiers_skolemize @t76 3)) % 28.05/28.20 (define @t78 () (@quantifiers_skolemize @t76 1)) % 28.05/28.20 (define @t79 () (@quantifiers_skolemize @t76 0)) % 28.05/28.20 (define @t80 () (tptp.quasi_total @t77 @t79 @t78)) % 28.05/28.20 (define @t81 () (= @t80 (= @t77 tptp.empty_set))) % 28.05/28.20 (define @t82 () (= @t78 tptp.empty_set)) % 28.05/28.20 (define @t83 () (not @t82)) % 28.05/28.20 (define @t84 () (= @t79 tptp.empty_set)) % 28.05/28.20 (define @t85 () (or @t83 @t84 @t81)) % 28.05/28.20 (define @t86 () (tptp.relation_dom_as_subset @t79 @t78 @t77)) % 28.05/28.20 (define @t87 () (= @t79 @t86)) % 28.05/28.20 (define @t88 () (= @t80 @t87)) % 28.05/28.20 (define @t89 () (not @t84)) % 28.05/28.20 (define @t90 () (and @t82 @t89)) % 28.05/28.20 (define @t91 () (or @t90 @t88)) % 28.05/28.20 (define @t92 () (and @t91 @t85)) % 28.05/28.20 (define @t93 () (tptp.relation_of2_as_subset @t77 @t79 @t78)) % 28.05/28.20 (define @t94 () (not @t93)) % 28.05/28.20 (define @t95 () (or @t94 @t92)) % 28.05/28.20 (define @t96 () (forall @t13 (or @t69 (and (or (and @t30 (not @t28)) @t32) @t68)))) % 28.05/28.20 (define @t97 () (@list @t79 @t78 @t77)) % 28.05/28.20 (define @t98 () (= tptp.empty_set @t79)) % 28.05/28.20 (define @t99 () (= tptp.empty_set @t78)) % 28.05/28.20 (define @t100 () (not @t99)) % 28.05/28.20 (define @t101 () (and @t99 (not @t98))) % 28.05/28.20 (define @t102 () (or @t101 @t88)) % 28.05/28.20 (define @t103 () (and @t102 (or @t100 @t98 (= @t80 (= tptp.empty_set @t77))))) % 28.05/28.20 (define @t104 () (or @t94 @t103)) % 28.05/28.20 (define @t105 () (@list false)) % 28.05/28.20 (define @t106 () (@list @t70)) % 28.05/28.20 (define @t107 () (forall @t106 @t75)) % 28.05/28.20 (define @t108 () (forall @t106 @t71)) % 28.05/28.20 (define @t109 () (or @t74 @t73 @t72 @t30 @t108)) % 28.05/28.20 (define @t110 () (or @t74 @t73 @t72 @t30 @t57)) % 28.05/28.20 (define @t111 () (or @t74 @t73 @t72)) % 28.05/28.20 (define @t112 () (@quantifiers_skolemize @t76 2)) % 28.05/28.20 (define @t113 () (@quantifiers_skolemize @t76 4)) % 28.05/28.20 (define @t114 () (tptp.in (tptp.apply @t77 @t113) @t112)) % 28.05/28.20 (define @t115 () (tptp.in @t113 @t79)) % 28.05/28.20 (define @t116 () (and @t115 @t114)) % 28.05/28.20 (define @t117 () (tptp.relation_inverse_image @t77 @t112)) % 28.05/28.20 (define @t118 () (tptp.in @t113 @t117)) % 28.05/28.20 (define @t119 () (= @t118 @t116)) % 28.05/28.20 (define @t120 () (not @t80)) % 28.05/28.20 (define @t121 () (tptp.function @t77)) % 28.05/28.20 (define @t122 () (not @t121)) % 28.05/28.20 (define @t123 () (or @t122 @t120 @t94 @t99 @t119)) % 28.05/28.20 (define @t124 () (not @t123)) % 28.05/28.20 (define @t125 () (not @t76)) % 28.05/28.20 (define @t126 () (or @t122 @t120 @t94 @t82 @t119)) % 28.05/28.20 (define @t127 () (not @t126)) % 28.05/28.20 (define @t128 () (@list true)) % 28.05/28.20 (define @t129 () (@list @t123)) % 28.05/28.20 (define @t130 () (@list false false)) % 28.05/28.20 (define @t131 () (not @t101)) % 28.05/28.20 (define @t132 () (@list true false)) % 28.05/28.20 (define @t133 () (tptp.relation_dom @t77)) % 28.05/28.20 (define @t134 () (tptp.relation_of2 @t77 @t79 @t78)) % 28.05/28.20 (define @t135 () (not @t134)) % 28.05/28.20 (define @t136 () (or @t135 (= @t86 @t133))) % 28.05/28.20 (define @t137 () (forall @t13 (or (not @t38) @t52))) % 28.05/28.20 (define @t138 () (= @t133 @t86)) % 28.05/28.20 (define @t139 () (or @t135 @t138)) % 28.05/28.20 (define @t140 () (= @t93 @t134)) % 28.05/28.20 (define @t141 () (@var "BOUND_VARIABLE_7649" $$unsorted)) % 28.05/28.20 (define @t142 () (@var "BOUND_VARIABLE_7651" $$unsorted)) % 28.05/28.20 (define @t143 () (= (= @t142 (tptp.relation_inverse_image @t1 @t141)) (forall @t22 (= (tptp.in @t18 @t142) (and @t21 (tptp.in @t19 @t141)))))) % 28.05/28.20 (define @t144 () (not @t5)) % 28.05/28.20 (define @t145 () (not @t8)) % 28.05/28.20 (define @t146 () (or @t145 @t144 @t143)) % 28.05/28.20 (define @t147 () (forall (@list @t1 @t141 @t142) @t146)) % 28.05/28.20 (define @t148 () (@list @t141 @t142)) % 28.05/28.20 (define @t149 () (forall @t148 @t146)) % 28.05/28.20 (define @t150 () (forall @t148 @t143)) % 28.05/28.20 (define @t151 () (or @t145 @t144 @t150)) % 28.05/28.20 (define @t152 () (or @t145 @t144 @t23)) % 28.05/28.20 (define @t153 () (forall @t22 (= (tptp.in @t18 @t117) (and (tptp.in @t18 @t133) (tptp.in (tptp.apply @t77 @t18) @t112))))) % 28.05/28.20 (define @t154 () (= (= @t117 @t117) @t153)) % 28.05/28.20 (define @t155 () (tptp.relation @t77)) % 28.05/28.20 (define @t156 () (not @t155)) % 28.05/28.20 (define @t157 () (or @t156 @t122 @t154)) % 28.05/28.20 (define @t158 () (or @t156 @t122 @t153)) % 28.05/28.20 (define @t159 () (tptp.element @t77 (tptp.powerset (tptp.cartesian_product2 @t79 @t78)))) % 28.05/28.20 (define @t160 () (or @t94 @t159)) % 28.05/28.20 (define @t161 () (not @t159)) % 28.05/28.20 (define @t162 () (or @t161 @t155)) % 28.05/28.20 (define @t163 () (tptp.in @t113 @t133)) % 28.05/28.20 (define @t164 () (and @t163 @t114)) % 28.05/28.20 (define @t165 () (= @t118 @t164)) % 28.05/28.20 (define @t166 () (not @t165)) % 28.05/28.20 (define @t167 () (not @t118)) % 28.05/28.20 (define @t168 () (not @t164)) % 28.05/28.20 (define @t169 () (and @t163 @t87 @t138)) % 28.05/28.20 (define @t170 () (not @t138)) % 28.05/28.20 (define @t171 () (not @t87)) % 28.05/28.20 (define @t172 () (not @t163)) % 28.05/28.20 (define @t173 () (not @t116)) % 28.05/28.20 (define @t174 () (@list @t116)) % 28.05/28.20 (define @t175 () (and @t115 @t87 @t138)) % 28.05/28.20 (assume @p1 (forall @t4 (=> @t3 (not (tptp.in @t2 @t1))))) % 28.05/28.20 (assume @p2 (forall @t7 (=> @t6 @t5))) % 28.05/28.20 (assume @p3 (forall @t7 (=> @t6 @t8))) % 28.05/28.20 (assume @p4 @t14) % 28.05/28.20 (assume @p5 (forall @t7 (=> @t17 @t16))) % 28.05/28.20 (assume @p6 @t25) % 28.05/28.20 (assume @p7 @t36) % 28.05/28.20 (assume @p8 true) % 28.05/28.20 (assume @p9 (forall @t13 (=> @t38 (tptp.element @t31 @t37)))) % 28.05/28.20 (assume @p10 @t39) % 28.05/28.20 (assume @p11 (forall @t4 (exists @t40 @t38))) % 28.05/28.20 (assume @p12 (forall @t7 (exists @t41 (tptp.element @t2 @t1)))) % 28.05/28.20 (assume @p13 (forall @t4 (exists @t40 @t35))) % 28.05/28.20 (assume @p14 (and @t43 @t42 (tptp.relation_empty_yielding tptp.empty_set))) % 28.05/28.20 (assume @p15 (forall @t7 (not (tptp.empty @t37)))) % 28.05/28.20 (assume @p16 @t43) % 28.05/28.20 (assume @p17 (and @t43 @t42)) % 28.05/28.20 (assume @p18 (forall @t4 (=> (and @t46 @t45) (not (tptp.empty @t11))))) % 28.05/28.20 (assume @p19 (forall @t7 (=> @t48 (not @t47)))) % 28.05/28.20 (assume @p20 (forall @t7 (=> @t6 (and @t47 (tptp.relation @t20))))) % 28.05/28.20 (assume @p21 (exists @t7 @t24)) % 28.05/28.20 (assume @p22 (forall @t4 (exists @t40 (and @t38 @t10 @t49 @t26)))) % 28.05/28.20 (assume @p23 (exists @t7 (and @t8 @t5 @t15 @t6))) % 28.05/28.20 (assume @p24 (exists @t7 (and @t6 @t8))) % 28.05/28.20 (assume @p25 (forall @t7 (=> @t46 (exists @t41 (and @t50 @t45))))) % 28.05/28.20 (assume @p26 (exists @t7 @t6)) % 28.05/28.20 (assume @p27 (exists @t7 @t17)) % 28.05/28.20 (assume @p28 (forall @t4 (exists @t40 (and @t38 @t10 @t49)))) % 28.05/28.20 (assume @p29 (exists @t7 @t48)) % 28.05/28.20 (assume @p30 (forall @t7 (exists @t41 (and @t50 @t44)))) % 28.05/28.20 (assume @p31 (exists @t7 @t46)) % 28.05/28.20 (assume @p32 (exists @t7 @t16)) % 28.05/28.20 (assume @p33 (exists @t7 (and @t8 @t51))) % 28.05/28.20 (assume @p34 (exists @t7 (and @t8 @t51 @t5))) % 28.05/28.20 (assume @p35 @t53) % 28.05/28.20 (assume @p36 (forall @t13 (= @t35 @t38))) % 28.05/28.20 (assume @p37 (forall @t4 (tptp.subset @t1 @t1))) % 28.05/28.20 (assume @p38 (forall @t4 (=> @t3 @t54))) % 28.05/28.20 (assume @p39 (forall @t4 (=> @t54 (or @t44 @t3)))) % 28.05/28.20 (assume @p40 (forall @t4 (= (tptp.element @t1 (tptp.powerset @t2)) (tptp.subset @t1 @t2)))) % 28.05/28.20 (assume @p41 @t66) % 28.05/28.20 (assume @p42 (forall @t13 (=> (and @t3 @t67) (tptp.element @t1 @t9)))) % 28.05/28.20 (assume @p43 (forall @t13 (not (and @t3 @t67 (tptp.empty @t9))))) % 28.05/28.20 (assume @p44 (forall @t7 (=> @t6 @t28))) % 28.05/28.20 (assume @p45 (forall @t4 (not (and @t3 @t44)))) % 28.05/28.20 (assume @p46 (forall @t4 (not (and @t6 (not (= @t1 @t2)) @t44)))) % 28.05/28.20 (step @p47 :rule aci_norm :args ((= (or @t58 @t29) @t68))) % 28.05/28.20 (step @p48 :rule bool-impl-elim :args (@t30 @t29)) % 28.05/28.20 (step @p49 :rule trans :premises (@p48 @p47)) % 28.05/28.20 (step @p50 :rule refl :args (@t32)) % 28.05/28.20 (step @p51 :rule bool-implies-de-morgan :args (@t30 @t28)) % 28.05/28.20 (step @p52 :rule nary_cong :premises (@p51 @p50) :args ((or (not @t33) @t32))) % 28.05/28.20 (step @p53 :rule bool-impl-elim :args (@t33 @t32)) % 28.05/28.20 (step @p54 :rule trans :premises (@p53 @p52)) % 28.05/28.20 (step @p55 :rule nary_cong :premises (@p54 @p49) :args (@t34)) % 28.05/28.20 (step @p56 :rule refl :args (@t69)) % 28.05/28.20 (step @p57 :rule nary_cong :premises (@p56 @p55) :args ((or @t69 @t34))) % 28.05/28.20 (step @p58 :rule bool-impl-elim :args (@t35 @t34)) % 28.05/28.20 (step @p59 :rule trans :premises (@p58 @p57)) % 28.05/28.20 (step @p60 :rule cong :premises (@p59) :args (@t36)) % 28.05/28.20 (step @p61 :rule eq_resolve :premises (@p7 @p60)) % 28.05/28.20 (step @p62 :rule eq-symm :args (@t77 tptp.empty_set)) % 28.05/28.20 (step @p63 :rule refl :args (@t80)) % 28.05/28.20 (step @p64 :rule cong :premises (@p63 @p62) :args (@t81)) % 28.05/28.20 (step @p65 :rule eq-symm :args (@t79 tptp.empty_set)) % 28.05/28.20 (step @p66 :rule eq-symm :args (@t78 tptp.empty_set)) % 28.05/28.20 (step @p67 :rule cong :premises (@p66) :args (@t83)) % 28.05/28.20 (step @p68 :rule nary_cong :premises (@p67 @p65 @p64) :args (@t85)) % 28.05/28.20 (step @p69 :rule refl :args (@t88)) % 28.05/28.20 (step @p70 :rule cong :premises (@p65) :args (@t89)) % 28.05/28.20 (step @p71 :rule nary_cong :premises (@p66 @p70) :args (@t90)) % 28.05/28.20 (step @p72 :rule nary_cong :premises (@p71 @p69) :args (@t91)) % 28.05/28.20 (step @p73 :rule nary_cong :premises (@p72 @p68) :args (@t92)) % 28.05/28.20 (step @p74 :rule refl :args (@t94)) % 28.05/28.20 (step @p75 :rule nary_cong :premises (@p74 @p73) :args (@t95)) % 28.05/28.20 (step @p76 :rule refl :args (@t96)) % 28.05/28.20 (step @p77 :rule cong :premises (@p76 @p75) :args ((=> @t96 @t95))) % 28.05/28.20 (assume-push @p329 @t96) % 28.05/28.20 (step @p79 :rule instantiate :premises (@p61) :args (@t97)) % 28.05/28.20 (step-pop @p330 :rule scope :premises (@p79)) % 28.05/28.20 (step @p80 :rule process_scope :premises (@p330) :args (@t95)) % 28.05/28.20 (step @p82 :rule eq_resolve :premises (@p80 @p77)) % 28.05/28.20 (step @p83 :rule implies_elim :premises (@p82)) % 28.05/28.20 (step @p84 :rule chain_m_resolution :premises (@p83 @p61) :args (@t104 @t105 (@list @t96))) % 28.05/28.20 (step @p85 :rule quant-merge-prenex :args ((= (forall @t64 @t107) @t76))) % 28.05/28.20 (step @p86 :rule alpha_equiv :args (@t108 (@list @t70) (@list @t55))) % 28.05/28.20 (step @p87 :rule refl :args (@t30)) % 28.05/28.20 (step @p88 :rule refl :args (@t72)) % 28.05/28.20 (step 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@t72)) @t111))) % 28.05/28.20 (step @p104 :rule bool-and-de-morgan :args (@t61 @t60 true)) % 28.05/28.20 (step @p105 :rule nary_cong :premises (@p90 @p104) :args ((or @t74 (not (and @t61 @t60))))) % 28.05/28.20 (step @p106 :rule bool-and-de-morgan :args (@t62 @t61 (and @t60))) % 28.05/28.20 (step @p107 :rule trans :premises (@p106 @p105)) % 28.05/28.20 (step @p108 :rule trans :premises (@p107 @p103)) % 28.05/28.20 (step @p109 :rule nary_cong :premises (@p108 @p102) :args ((or (not @t63) @t59))) % 28.05/28.20 (step @p110 :rule trans :premises (@p109 @p97)) % 28.05/28.20 (step @p111 :rule bool-impl-elim :args (@t63 @t59)) % 28.05/28.20 (step @p112 :rule trans :premises (@p111 @p110)) % 28.05/28.20 (step @p113 :rule cong :premises (@p112) :args (@t65)) % 28.05/28.20 (step @p114 :rule trans :premises (@p113 @p96)) % 28.05/28.20 (step @p115 :rule cong :premises (@p114) :args (@t66)) % 28.05/28.20 (step @p116 :rule eq_resolve :premises (@p41 @p115)) % 28.05/28.20 (step @p117 :rule refl :args 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(@p131)) % 28.05/28.20 (step @p133 :rule eq_resolve :premises (@p132 @p119)) % 28.05/28.20 (step @p134 :rule chain_m_resolution :premises (@p133 @p116) :args (@t124 @t128 (@list @t76))) % 28.05/28.20 (step @p135 :rule bool-double-not-elim :args (@t93)) % 28.05/28.20 (step @p136 :rule refl :args (@t123)) % 28.05/28.20 (step @p137 :rule nary_cong :premises (@p136 @p135) :args ((or @t123 (not @t94)))) % 28.05/28.20 (step @p138 :rule cnf_or_neg :args (@t123 2)) % 28.05/28.20 (step @p139 :rule eq_resolve :premises (@p138 @p137)) % 28.05/28.20 (step @p140 :rule reordering :premises (@p139) :args ((or @t93 @t123))) % 28.05/28.20 (step @p141 :rule chain_m_resolution :premises (@p140 @p134) :args (@t93 @t128 @t129)) % 28.05/28.20 (step @p142 :rule cnf_or_pos :args (@t104)) % 28.05/28.20 (step @p143 :rule reordering :premises (@p142) :args ((or @t94 @t103 (not @t104)))) % 28.05/28.20 (step @p144 :rule chain_m_resolution :premises (@p143 @p141 @p84) :args (@t103 @t130 (@list @t93 @t104))) % 28.05/28.20 (step @p145 :rule cnf_and_pos :args (@t103 0)) % 28.05/28.20 (step @p146 :rule reordering :premises (@p145) :args ((or @t102 (not @t103)))) % 28.05/28.20 (step @p147 :rule chain_m_resolution :premises (@p146 @p144) :args (@t102 @t105 (@list @t103))) % 28.05/28.20 (step @p148 :rule cnf_or_neg :args (@t123 3)) % 28.05/28.20 (step @p149 :rule chain_m_resolution :premises (@p148 @p134) :args (@t100 @t128 @t129)) % 28.05/28.20 (step @p150 :rule cnf_and_pos :args (@t101 0)) % 28.05/28.20 (step @p151 :rule reordering :premises (@p150) :args ((or @t99 @t131))) % 28.05/28.20 (step @p152 :rule chain_m_resolution :premises (@p151 @p149) :args (@t131 @t128 (@list @t99))) % 28.05/28.20 (step @p153 :rule cnf_or_pos :args (@t102)) % 28.05/28.20 (step @p154 :rule reordering :premises (@p153) :args ((or @t88 @t101 (not @t102)))) % 28.05/28.20 (step @p155 :rule chain_m_resolution :premises (@p154 @p152 @p147) :args (@t88 @t132 (@list @t101 @t102))) % 28.05/28.20 (step @p156 :rule bool-double-not-elim :args (@t80)) % 28.05/28.20 (step @p157 :rule nary_cong :premises (@p136 @p156) :args ((or @t123 (not @t120)))) % 28.05/28.20 (step @p158 :rule cnf_or_neg :args (@t123 1)) % 28.05/28.20 (step @p159 :rule eq_resolve :premises (@p158 @p157)) % 28.05/28.20 (step @p160 :rule reordering :premises (@p159) :args ((or @t80 @t123))) % 28.05/28.20 (step @p161 :rule chain_m_resolution :premises (@p160 @p134) :args (@t80 @t128 @t129)) % 28.05/28.20 (step @p162 :rule cnf_equiv_pos1 :args (@t88)) % 28.05/28.20 (step @p163 :rule reordering :premises (@p162) :args ((or @t120 @t87 (not @t88)))) % 28.05/28.20 (step @p164 :rule chain_m_resolution :premises (@p163 @p161 @p155) :args (@t87 @t130 (@list @t80 @t88))) % 28.05/28.20 (step @p165 :rule bool-impl-elim :args (@t38 @t52)) % 28.05/28.20 (step @p166 :rule cong :premises (@p165) :args (@t53)) % 28.05/28.20 (step @p167 :rule eq_resolve :premises (@p35 @p166)) % 28.05/28.20 (step @p168 :rule eq-symm :args (@t86 @t133)) % 28.05/28.20 (step @p169 :rule refl :args (@t135)) % 28.05/28.20 (step @p170 :rule nary_cong :premises (@p169 @p168) :args (@t136)) % 28.05/28.20 (step @p171 :rule refl :args (@t137)) % 28.05/28.20 (step @p172 :rule cong :premises (@p171 @p170) :args ((=> @t137 @t136))) % 28.05/28.20 (assume-push @p333 @t137) % 28.05/28.20 (step @p174 :rule instantiate :premises (@p167) :args (@t97)) % 28.05/28.20 (step-pop @p334 :rule scope :premises (@p174)) % 28.05/28.20 (step @p175 :rule process_scope :premises (@p334) :args (@t136)) % 28.05/28.20 (step @p177 :rule eq_resolve :premises (@p175 @p172)) % 28.05/28.20 (step @p178 :rule implies_elim :premises (@p177)) % 28.05/28.20 (step @p179 :rule chain_m_resolution :premises (@p178 @p167) :args (@t139 @t105 (@list @t137))) % 28.05/28.20 (step @p180 :rule instantiate :premises (@p36) :args (@t97)) % 28.05/28.20 (step @p181 :rule cnf_equiv_pos1 :args (@t140)) % 28.05/28.20 (step @p182 :rule reordering :premises (@p181) :args ((or @t94 @t134 (not @t140)))) % 28.05/28.20 (step @p183 :rule chain_m_resolution :premises (@p182 @p141 @p180) :args (@t134 @t130 (@list @t93 @t140))) % 28.05/28.20 (step @p184 :rule cnf_or_pos :args (@t139)) % 28.05/28.20 (step @p185 :rule reordering :premises (@p184) :args ((or @t135 @t138 (not @t139)))) % 28.05/28.20 (step @p186 :rule chain_m_resolution :premises (@p185 @p183 @p179) :args (@t138 @t130 (@list @t134 @t139))) % 28.05/28.20 (step @p187 :rule cnf_or_neg :args (@t123 4)) % 28.05/28.20 (step @p188 :rule chain_m_resolution :premises (@p187 @p134) :args ((not @t119) @t128 @t129)) % 28.05/28.20 (step @p189 :rule cnf_equiv_neg2 :args (@t119)) % 28.05/28.20 (step @p190 :rule quant-merge-prenex :args ((= (forall @t7 @t149) @t147))) % 28.05/28.20 (step @p191 :rule alpha_equiv :args (@t150 (@list @t141 @t142) (@list @t2 @t9))) % 28.05/28.20 (step @p192 :rule refl :args (@t144)) % 28.05/28.20 (step @p193 :rule refl :args (@t145)) % 28.05/28.20 (step @p194 :rule nary_cong :premises (@p193 @p192 @p191) :args (@t151)) % 28.05/28.20 (step @p195 :rule quant-miniscope-or :args ((= @t149 @t151))) % 28.05/28.20 (step @p196 :rule trans :premises (@p195 @p194)) % 28.05/28.20 (step @p197 :rule symm :premises (@p196)) % 28.05/28.20 (step @p198 :rule cong :premises (@p197) :args ((forall @t7 @t152))) % 28.05/28.20 (step @p199 :rule trans :premises (@p198 @p190)) % 28.05/28.20 (step @p200 :rule aci_norm :args ((= (or (or @t145 @t144) @t23) @t152))) % 28.05/28.20 (step @p201 :rule refl :args (@t23)) % 28.05/28.20 (step @p202 :rule bool-and-de-morgan :args (@t8 @t5 true)) % 28.05/28.20 (step @p203 :rule nary_cong :premises (@p202 @p201) :args ((or (not @t24) @t23))) % 28.05/28.20 (step @p204 :rule trans :premises (@p203 @p200)) % 28.05/28.20 (step @p205 :rule bool-impl-elim :args (@t24 @t23)) % 28.05/28.20 (step @p206 :rule trans :premises (@p205 @p204)) % 28.05/28.20 (step @p207 :rule cong :premises (@p206) :args (@t25)) % 28.05/28.20 (step @p208 :rule trans :premises (@p207 @p199)) % 28.05/28.20 (step @p209 :rule eq_resolve :premises (@p6 @p208)) % 28.05/28.20 (step @p210 :rule bool-eq-true :args (@t153)) % 28.05/28.20 (step @p211 :rule eq-symm :args (true @t153)) % 28.05/28.20 (step @p212 :rule trans :premises (@p211 @p210)) % 28.05/28.20 (step @p213 :rule refl :args (@t153)) % 28.05/28.20 (step @p214 :rule eq-refl :args (@t117)) % 28.05/28.20 (step @p215 :rule cong :premises (@p214 @p213) :args (@t154)) % 28.05/28.20 (step @p216 :rule trans :premises (@p215 @p212)) % 28.05/28.20 (step @p217 :rule refl :args (@t156)) % 28.05/28.20 (step @p218 :rule nary_cong :premises (@p217 @p122 @p216) :args (@t157)) % 28.05/28.20 (step @p219 :rule refl :args (@t147)) % 28.05/28.20 (step @p220 :rule cong :premises (@p219 @p218) :args ((=> @t147 @t157))) % 28.05/28.20 (assume-push @p335 @t147) % 28.05/28.20 (step @p222 :rule instantiate :premises (@p209) :args ((@list @t77 @t112 @t117))) % 28.05/28.20 (step-pop @p336 :rule scope :premises (@p222)) % 28.05/28.20 (step @p223 :rule process_scope :premises (@p336) :args (@t157)) % 28.05/28.20 (step @p225 :rule eq_resolve :premises (@p223 @p220)) % 28.05/28.20 (step @p226 :rule implies_elim :premises (@p225)) % 28.05/28.20 (step @p227 :rule chain_m_resolution :premises (@p226 @p209) :args (@t158 @t105 (@list @t147))) % 28.05/28.20 (step @p228 :rule bool-impl-elim :args (@t12 @t10)) % 28.05/28.20 (step @p229 :rule cong :premises (@p228) :args (@t14)) % 28.05/28.20 (step @p230 :rule eq_resolve :premises (@p4 @p229)) % 28.05/28.20 (step @p231 :rule instantiate :premises (@p230) :args (@t97)) % 28.05/28.20 (step @p232 :rule bool-impl-elim :args (@t35 @t12)) % 28.05/28.20 (step @p233 :rule cong :premises (@p232) :args (@t39)) % 28.05/28.20 (step @p234 :rule eq_resolve :premises (@p10 @p233)) % 28.05/28.20 (step @p235 :rule instantiate :premises (@p234) :args (@t97)) % 28.05/28.20 (step @p236 :rule cnf_or_pos :args (@t160)) % 28.05/28.20 (step @p237 :rule reordering :premises (@p236) :args ((or @t94 @t159 (not @t160)))) % 28.05/28.20 (step @p238 :rule chain_m_resolution :premises (@p237 @p141 @p235) :args (@t159 @t130 (@list @t93 @t160))) % 28.05/28.20 (step @p239 :rule cnf_or_pos :args (@t162)) % 28.05/28.20 (step @p240 :rule reordering :premises (@p239) :args ((or @t155 @t161 (not @t162)))) % 28.05/28.20 (step @p241 :rule chain_m_resolution :premises (@p240 @p238 @p231) :args (@t155 @t130 (@list @t159 @t162))) % 28.05/28.20 (step @p242 :rule bool-double-not-elim :args (@t121)) % 28.05/28.20 (step @p243 :rule nary_cong :premises (@p136 @p242) :args ((or @t123 (not @t122)))) % 28.05/28.20 (step @p244 :rule cnf_or_neg :args (@t123 0)) % 28.05/28.20 (step @p245 :rule eq_resolve :premises (@p244 @p243)) % 28.05/28.20 (step @p246 :rule reordering :premises (@p245) :args ((or @t121 @t123))) % 28.05/28.20 (step @p247 :rule chain_m_resolution :premises (@p246 @p134) :args (@t121 @t128 @t129)) % 28.05/28.20 (step @p248 :rule cnf_or_pos :args (@t158)) % 28.05/28.20 (step @p249 :rule reordering :premises (@p248) :args ((or @t122 @t156 @t153 (not @t158)))) % 28.05/28.20 (step @p250 :rule chain_m_resolution :premises (@p249 @p247 @p241 @p227) :args (@t153 (@list false false false) (@list @t121 @t155 @t158))) % 28.05/28.20 (step @p251 :rule instantiate :premises (@p250) :args ((@list @t113))) % 28.05/28.20 (step @p252 :rule cnf_equiv_pos1 :args (@t165)) % 28.05/28.20 (step @p253 :rule reordering :premises (@p252) :args ((or @t167 @t164 @t166))) % 28.05/28.20 (step @p254 :rule cnf_and_pos :args (@t164 0)) % 28.05/28.20 (step @p255 :rule reordering :premises (@p254) :args ((or @t163 @t168))) % 28.05/28.20 (step @p256 :rule cnf_and_pos :args (@t164 1)) % 28.05/28.20 (step @p257 :rule reordering :premises (@p256) :args ((or @t114 @t168))) % 28.05/28.20 (step @p258 :rule cnf_and_neg :args (@t116)) % 28.05/28.20 (assume-push @p337 @t163) % 28.05/28.20 (assume-push @p338 @t87) % 28.05/28.20 (assume-push @p339 @t138) % 28.05/28.20 (assume-push @p340 @t163) % 28.05/28.20 (assume-push @p341 @t138) % 28.05/28.20 (assume-push @p342 @t87) % 28.05/28.20 (step @p265 :rule true_intro :premises (@p337)) % 28.05/28.20 (step @p266 :rule symm :premises (@p186)) % 28.05/28.20 (step @p267 :rule trans :premises (@p164 @p266)) % 28.05/28.20 (step @p268 :rule refl :args (@t113)) % 28.05/28.20 (step @p269 :rule cong :premises (@p268 @p267) :args (@t115)) % 28.05/28.20 (step @p270 :rule trans :premises (@p269 @p265)) % 28.05/28.20 (step @p271 :rule true_elim :premises (@p270)) % 28.05/28.20 (step-pop @p343 :rule scope :premises (@p271)) % 28.05/28.20 (step-pop @p344 :rule scope :premises (@p343)) % 28.05/28.20 (step-pop @p345 :rule scope :premises (@p344)) % 28.05/28.20 (step @p272 :rule process_scope :premises (@p345) :args (@t115)) % 28.05/28.20 (step @p276 :rule and_intro :premises (@p337 @p186 @p164)) % 28.05/28.20 (step @p277 :rule modus_ponens :premises (@p276 @p272)) % 28.05/28.20 (step-pop @p346 :rule scope :premises (@p277)) % 28.05/28.20 (step-pop @p347 :rule scope :premises (@p346)) % 28.05/28.20 (step-pop @p348 :rule scope :premises (@p347)) % 28.05/28.20 (step @p278 :rule process_scope :premises (@p348) :args (@t115)) % 28.05/28.20 (step @p282 :rule implies_elim :premises (@p278)) % 28.05/28.20 (step @p283 :rule cnf_and_neg :args (@t169)) % 28.05/28.20 (step @p284 :rule resolution :premises (@p283 @p282) :args (true @t169)) % 28.05/28.20 (step @p285 :rule reordering :premises (@p284) :args ((or @t115 @t172 @t171 @t170))) % 28.05/28.20 (step @p286 :rule chain_m_resolution :premises (@p285 @p186 @p164 @p258 @p257 @p255 @p253 @p251 @p189 @p188) :args (@t167 (@list false false true false false false false true true) (@list @t138 @t87 @t115 @t114 @t163 @t164 @t165 @t116 @t119))) % 28.05/28.20 (step @p287 :rule cnf_equiv_neg1 :args (@t119)) % 28.05/28.20 (step @p288 :rule reordering :premises (@p287) :args ((or @t118 @t116 @t119))) % 28.05/28.20 (step @p289 :rule chain_m_resolution :premises (@p288 @p286 @p188) :args (@t116 (@list true true) (@list @t118 @t119))) % 28.05/28.20 (step @p290 :rule cnf_and_pos :args (@t116 0)) % 28.05/28.20 (step @p291 :rule reordering :premises (@p290) :args ((or @t115 @t173))) % 28.05/28.21 (step @p292 :rule chain_m_resolution :premises (@p291 @p289) :args (@t115 @t105 @t174)) % 28.05/28.21 (step @p293 :rule cnf_equiv_pos2 :args (@t165)) % 28.05/28.21 (step @p294 :rule reordering :premises (@p293) :args ((or @t118 @t168 @t166))) % 28.05/28.21 (step @p295 :rule chain_m_resolution :premises (@p294 @p286 @p251) :args (@t168 @t132 (@list @t118 @t165))) % 28.05/28.21 (step @p296 :rule cnf_and_pos :args (@t116 1)) % 28.05/28.21 (step @p297 :rule reordering :premises (@p296) :args ((or @t114 @t173))) % 28.05/28.21 (step @p298 :rule chain_m_resolution :premises (@p297 @p289) :args (@t114 @t105 @t174)) % 28.05/28.21 (step @p299 :rule cnf_and_neg :args (@t164)) % 28.05/28.21 (step @p300 :rule reordering :premises (@p299) :args ((or (not @t114) @t164 @t172))) % 28.05/28.21 (step @p301 :rule chain_m_resolution :premises (@p300 @p298 @p295) :args (@t172 (@list false true) (@list @t114 @t164))) % 28.05/28.21 (assume-push @p349 @t115) % 28.05/28.21 (assume-push @p350 @t87) % 28.05/28.21 (assume-push @p351 @t138) % 28.05/28.21 (assume-push @p352 @t115) % 28.05/28.21 (assume-push @p353 @t87) % 28.05/28.21 (assume-push @p354 @t138) % 28.05/28.21 (step @p308 :rule true_intro :premises (@p349)) % 28.05/28.21 (step @p309 :rule symm :premises (@p164)) % 28.05/28.21 (step @p310 :rule trans :premises (@p186 @p309)) % 28.05/28.21 (step @p268 :rule refl :args (@t113)) % 28.05/28.21 (step @p311 :rule cong :premises (@p268 @p310) :args (@t163)) % 28.05/28.21 (step @p312 :rule trans :premises (@p311 @p308)) % 28.05/28.21 (step @p313 :rule true_elim :premises (@p312)) % 28.05/28.21 (step-pop @p355 :rule scope :premises (@p313)) % 28.05/28.21 (step-pop @p356 :rule scope :premises (@p355)) % 28.05/28.21 (step-pop @p357 :rule scope :premises (@p356)) % 28.05/28.21 (step @p314 :rule process_scope :premises (@p357) :args (@t163)) % 28.05/28.21 (step @p318 :rule and_intro :premises (@p349 @p164 @p186)) % 28.05/28.21 (step @p319 :rule modus_ponens :premises (@p318 @p314)) % 28.05/28.21 (step-pop @p358 :rule scope :premises (@p319)) % 28.05/28.21 (step-pop @p359 :rule scope :premises (@p358)) % 28.05/28.21 (step-pop @p360 :rule scope :premises (@p359)) % 28.05/28.21 (step @p320 :rule process_scope :premises (@p360) :args (@t163)) % 28.05/28.21 (step @p324 :rule implies_elim :premises (@p320)) % 28.05/28.21 (step @p325 :rule cnf_and_neg :args (@t175)) % 28.05/28.21 (step @p326 :rule resolution :premises (@p325 @p324) :args (true @t175)) % 28.05/28.21 (step @p327 :rule reordering :premises (@p326) :args ((or (not @t115) @t163 @t171 @t170))) % 28.05/28.21 (step @p328 false :rule chain_m_resolution :premises (@p327 @p301 @p292 @p186 @p164) :args (false (@list true false false false) (@list @t163 @t115 @t138 @t87))) % 28.05/28.21 ) % 28.05/28.21 % SZS output end Proof % 28.05/28.21 % cvc5 exiting %------------------------------------------------------------------------------