%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV384+1 : TPTP v9.2.1. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % Computer : n017.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 09:01:19 AM UTC 2026 % Result : Theorem 0.40s 0.60s % Output : Proof 0.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV384+1 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.16/0.34 % Computer : n017.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 20:04:46 EDT 2026 % 0.16/0.35 % CPUTime : % 0.31/0.49 %----Proving TF0_NAR, FOF, or CNF % 0.40/0.60 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.40/0.60 % SZS status Theorem % 0.40/0.60 % SZS output start Proof % 0.40/0.60 ( % 0.40/0.60 (declare-sort $$unsorted 0) % 0.40/0.60 (declare-const tptp.findmin_cpq_res (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.check_cpq (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.im_succ_cpq (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.removemin_cpq_eff (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.findmin_cpq_eff (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.remove_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.insert_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.insert_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.less_than (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.strictly_less_than (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.findmin_pqp_res (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.bottom $$unsorted) % 0.40/0.60 (declare-const tptp.create_slb $$unsorted) % 0.40/0.60 (declare-const tptp.lookup_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.isnonempty_slb (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.removemin_cpq_res (-> $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.remove_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.contains_cpq (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.pair (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.insert_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.ok (-> $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.contains_slb (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.succ_cpq (-> $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.pair_in_list (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.40/0.60 (declare-const tptp.bad $$unsorted) % 0.40/0.60 (declare-const tptp.remove_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (declare-const tptp.update_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.40/0.60 (define @t1 () (@var "W" $$unsorted)) % 0.40/0.60 (define @t2 () (@var "U" $$unsorted)) % 0.40/0.60 (define @t3 () (@var "V" $$unsorted)) % 0.40/0.60 (define @t4 () (tptp.less_than @t2 @t3)) % 0.40/0.60 (define @t5 () (@list @t2 @t3 @t1)) % 0.40/0.60 (define @t6 () (tptp.less_than @t3 @t2)) % 0.40/0.60 (define @t7 () (@list @t2 @t3)) % 0.40/0.60 (define @t8 () (@list @t2)) % 0.40/0.60 (define @t9 () (tptp.pair @t3 @t1)) % 0.40/0.60 (define @t10 () (tptp.insert_slb @t2 @t9)) % 0.40/0.60 (define @t11 () (= @t3 @t1)) % 0.40/0.60 (define @t12 () (tptp.contains_slb @t2 @t1)) % 0.40/0.60 (define @t13 () (@var "X" $$unsorted)) % 0.40/0.60 (define @t14 () (tptp.pair @t3 @t13)) % 0.40/0.60 (define @t15 () (tptp.insert_slb @t2 @t14)) % 0.40/0.60 (define @t16 () (@list @t2 @t3 @t1 @t13)) % 0.40/0.60 (define @t17 () (@var "Y" $$unsorted)) % 0.40/0.60 (define @t18 () (@list @t2 @t3 @t1 @t13 @t17)) % 0.40/0.60 (define @t19 () (and (not @t11) @t12)) % 0.40/0.60 (define @t20 () (tptp.update_slb @t2 @t1)) % 0.40/0.60 (define @t21 () (tptp.update_slb @t15 @t1)) % 0.40/0.60 (define @t22 () (tptp.succ_cpq @t2 @t3)) % 0.40/0.60 (define @t23 () (tptp.triple @t2 tptp.create_slb @t3)) % 0.40/0.60 (define @t24 () (tptp.triple @t2 @t3 @t1)) % 0.40/0.60 (define @t25 () (tptp.check_cpq @t24)) % 0.40/0.60 (define @t26 () (tptp.check_cpq (tptp.triple @t2 (tptp.insert_slb @t3 (tptp.pair @t13 @t17)) @t1))) % 0.40/0.60 (define @t27 () (tptp.contains_slb @t3 @t13)) % 0.40/0.60 (define @t28 () (tptp.triple @t2 @t3 tptp.bad)) % 0.40/0.60 (define @t29 () (tptp.ok @t24)) % 0.40/0.60 (define @t30 () (not @t29)) % 0.40/0.60 (define @t31 () (tptp.remove_cpq @t24 @t13)) % 0.40/0.60 (define @t32 () (tptp.remove_slb @t3 @t13)) % 0.40/0.60 (define @t33 () (tptp.remove_pqp @t2 @t13)) % 0.40/0.60 (define @t34 () (tptp.lookup_slb @t3 @t13)) % 0.40/0.60 (define @t35 () (tptp.findmin_pqp_res @t2)) % 0.40/0.60 (define @t36 () (tptp.update_slb @t3 @t35)) % 0.40/0.60 (define @t37 () (tptp.findmin_cpq_eff @t24)) % 0.40/0.60 (define @t38 () (= @t37 (tptp.triple @t2 @t36 tptp.bad))) % 0.40/0.60 (define @t39 () (tptp.contains_slb @t3 @t35)) % 0.40/0.60 (define @t40 () (not (= @t3 tptp.create_slb))) % 0.40/0.60 (define @t41 () (tptp.lookup_slb @t3 @t35)) % 0.40/0.60 (define @t42 () (tptp.findmin_cpq_res @t2)) % 0.40/0.60 (define @t43 () (@var "X6" $$unsorted)) % 0.40/0.60 (define @t44 () (@var "X5" $$unsorted)) % 0.40/0.60 (define @t45 () (@var "X4" $$unsorted)) % 0.40/0.60 (define @t46 () (tptp.triple @t45 @t44 @t43)) % 0.40/0.60 (define @t47 () (not (tptp.check_cpq @t46))) % 0.40/0.60 (define @t48 () (not (tptp.ok @t46))) % 0.40/0.60 (define @t49 () (or @t48 @t47)) % 0.40/0.60 (define @t50 () (@var "X3" $$unsorted)) % 0.40/0.60 (define @t51 () (@var "X2" $$unsorted)) % 0.40/0.60 (define @t52 () (@var "X1" $$unsorted)) % 0.40/0.60 (define @t53 () (tptp.triple @t52 @t51 @t50)) % 0.40/0.60 (define @t54 () (tptp.succ_cpq @t53 @t46)) % 0.40/0.60 (define @t55 () (@list @t45 @t44 @t43)) % 0.40/0.60 (define @t56 () (forall @t55 (=> @t54 @t49))) % 0.40/0.60 (define @t57 () (tptp.ok @t53)) % 0.40/0.60 (define @t58 () (not @t57)) % 0.40/0.60 (define @t59 () (tptp.check_cpq @t53)) % 0.40/0.60 (define @t60 () (not @t59)) % 0.40/0.60 (define @t61 () (or @t60 @t58)) % 0.40/0.60 (define @t62 () (=> @t61 @t56)) % 0.40/0.60 (define @t63 () (@list @t52 @t51 @t50)) % 0.40/0.60 (define @t64 () (forall @t63 @t62)) % 0.40/0.60 (define @t65 () (@var "Z" $$unsorted)) % 0.40/0.60 (define @t66 () (tptp.triple @t13 @t17 @t65)) % 0.40/0.60 (define @t67 () (tptp.im_succ_cpq @t66)) % 0.40/0.60 (define @t68 () (not (tptp.ok @t67))) % 0.40/0.60 (define @t69 () (not (tptp.check_cpq @t67))) % 0.40/0.60 (define @t70 () (or @t69 @t68)) % 0.40/0.60 (define @t71 () (tptp.ok @t66)) % 0.40/0.60 (define @t72 () (not @t71)) % 0.40/0.60 (define @t73 () (tptp.check_cpq @t66)) % 0.40/0.60 (define @t74 () (not @t73)) % 0.40/0.60 (define @t75 () (or @t74 @t72)) % 0.40/0.60 (define @t76 () (=> @t75 @t70)) % 0.40/0.60 (define @t77 () (tptp.succ_cpq @t24 @t66)) % 0.40/0.60 (define @t78 () (@list @t2 @t3 @t1 @t13 @t17 @t65)) % 0.40/0.60 (define @t79 () (forall @t78 (=> @t77 @t76))) % 0.40/0.60 (define @t80 () (=> @t79 @t64)) % 0.40/0.60 (define @t81 () (tptp.im_succ_cpq @t24)) % 0.40/0.60 (define @t82 () (not (tptp.ok @t81))) % 0.40/0.60 (define @t83 () (not (tptp.check_cpq @t81))) % 0.40/0.60 (define @t84 () (or @t83 @t82)) % 0.40/0.60 (define @t85 () (not @t25)) % 0.40/0.60 (define @t86 () (or @t85 @t30)) % 0.40/0.60 (define @t87 () (forall @t5 (=> @t86 @t84))) % 0.40/0.60 (define @t88 () (or @t72 @t74)) % 0.40/0.60 (define @t89 () (@list @t13 @t17 @t65)) % 0.40/0.60 (define @t90 () (forall @t89 (=> @t77 @t88))) % 0.40/0.60 (define @t91 () (=> @t86 @t90)) % 0.40/0.60 (define @t92 () (forall @t5 @t91)) % 0.40/0.60 (define @t93 () (not @t92)) % 0.40/0.60 (define @t94 () (and @t25 @t29)) % 0.40/0.60 (define @t95 () (or @t94 @t83 @t82)) % 0.40/0.60 (define @t96 () (not @t86)) % 0.40/0.60 (define @t97 () (@var "BOUND_VARIABLE_7875" $$unsorted)) % 0.40/0.60 (define @t98 () (@var "BOUND_VARIABLE_7873" $$unsorted)) % 0.40/0.60 (define @t99 () (@var "BOUND_VARIABLE_7871" $$unsorted)) % 0.40/0.60 (define @t100 () (tptp.triple @t99 @t98 @t97)) % 0.40/0.60 (define @t101 () (not (tptp.check_cpq @t100))) % 0.40/0.60 (define @t102 () (not (tptp.ok @t100))) % 0.40/0.60 (define @t103 () (not (tptp.succ_cpq @t24 @t100))) % 0.40/0.60 (define @t104 () (or @t94 @t103 @t102 @t101)) % 0.40/0.60 (define @t105 () (or @t103 @t102 @t101)) % 0.40/0.60 (define @t106 () (or @t94 @t105)) % 0.40/0.60 (define @t107 () (@list @t2 @t3 @t1 @t99 @t98 @t97)) % 0.40/0.60 (define @t108 () (forall @t107 @t106)) % 0.40/0.60 (define @t109 () (@list @t99 @t98 @t97)) % 0.40/0.60 (define @t110 () (forall @t109 @t106)) % 0.40/0.60 (define @t111 () (forall @t109 @t105)) % 0.40/0.60 (define @t112 () (or @t94 @t111)) % 0.40/0.60 (define @t113 () (not @t77)) % 0.40/0.60 (define @t114 () (or @t113 @t72 @t74)) % 0.40/0.60 (define @t115 () (forall @t89 @t114)) % 0.40/0.60 (define @t116 () (@var "BOUND_VARIABLE_7843" $$unsorted)) % 0.40/0.60 (define @t117 () (@var "BOUND_VARIABLE_7841" $$unsorted)) % 0.40/0.60 (define @t118 () (@var "BOUND_VARIABLE_7839" $$unsorted)) % 0.40/0.60 (define @t119 () (tptp.triple @t118 @t117 @t116)) % 0.40/0.60 (define @t120 () (not (tptp.check_cpq @t119))) % 0.40/0.60 (define @t121 () (not (tptp.ok @t119))) % 0.40/0.60 (define @t122 () (not (tptp.succ_cpq @t53 @t119))) % 0.40/0.60 (define @t123 () (and @t59 @t57)) % 0.40/0.60 (define @t124 () (or @t123 @t122 @t121 @t120)) % 0.40/0.60 (define @t125 () (@list @t52 @t51 @t50 @t118 @t117 @t116)) % 0.40/0.60 (define @t126 () (forall @t125 @t124)) % 0.40/0.60 (define @t127 () (not @t126)) % 0.40/0.60 (define @t128 () (forall @t107 @t104)) % 0.40/0.60 (define @t129 () (@list true)) % 0.40/0.60 (define @t130 () (or @t122 @t121 @t120)) % 0.40/0.60 (define @t131 () (or @t123 @t130)) % 0.40/0.60 (define @t132 () (forall @t125 @t131)) % 0.40/0.60 (define @t133 () (@list @t118 @t117 @t116)) % 0.40/0.60 (define @t134 () (forall @t133 @t131)) % 0.40/0.60 (define @t135 () (forall @t133 @t130)) % 0.40/0.60 (define @t136 () (or @t123 @t135)) % 0.40/0.60 (define @t137 () (not @t54)) % 0.40/0.60 (define @t138 () (or @t137 @t48 @t47)) % 0.40/0.60 (define @t139 () (forall @t55 @t138)) % 0.40/0.60 (define @t140 () (and @t73 @t71)) % 0.40/0.60 (define @t141 () (or @t113 @t140 @t69 @t68)) % 0.40/0.60 (define @t142 () (or @t140 @t69 @t68)) % 0.40/0.60 (define @t143 () (forall @t78 @t141)) % 0.40/0.60 (define @t144 () (not @t143)) % 0.40/0.60 (define @t145 () (@quantifiers_skolemize @t143 5)) % 0.40/0.60 (define @t146 () (@quantifiers_skolemize @t143 4)) % 0.40/0.60 (define @t147 () (@quantifiers_skolemize @t143 3)) % 0.40/0.60 (define @t148 () (tptp.triple @t147 @t146 @t145)) % 0.40/0.60 (define @t149 () (tptp.im_succ_cpq @t148)) % 0.40/0.60 (define @t150 () (tptp.ok @t149)) % 0.40/0.60 (define @t151 () (not @t150)) % 0.40/0.60 (define @t152 () (tptp.check_cpq @t149)) % 0.40/0.60 (define @t153 () (not @t152)) % 0.40/0.60 (define @t154 () (and (tptp.check_cpq @t148) (tptp.ok @t148))) % 0.40/0.60 (define @t155 () (or (not (tptp.succ_cpq (tptp.triple (@quantifiers_skolemize @t143 0) (@quantifiers_skolemize @t143 1) (@quantifiers_skolemize @t143 2)) @t148)) @t154 @t153 @t151)) % 0.40/0.60 (define @t156 () (@list @t155)) % 0.40/0.60 (define @t157 () (or @t154 @t153 @t151)) % 0.40/0.60 (define @t158 () (not @t157)) % 0.40/0.60 (define @t159 () (forall @t5 @t95)) % 0.40/0.60 (assume @p1 (forall @t5 (=> (and @t4 (tptp.less_than @t3 @t1)) (tptp.less_than @t2 @t1)))) % 0.40/0.60 (assume @p2 (forall @t7 (or @t4 @t6))) % 0.40/0.60 (assume @p3 (forall @t8 (tptp.less_than @t2 @t2))) % 0.40/0.60 (assume @p4 (forall @t7 (= (tptp.strictly_less_than @t2 @t3) (and @t4 (not @t6))))) % 0.40/0.60 (assume @p5 (forall @t8 (tptp.less_than tptp.bottom @t2))) % 0.40/0.60 (assume @p6 (not (tptp.isnonempty_slb tptp.create_slb))) % 0.40/0.60 (assume @p7 (forall @t5 (tptp.isnonempty_slb @t10))) % 0.40/0.60 (assume @p8 (forall @t8 (not (tptp.contains_slb tptp.create_slb @t2)))) % 0.40/0.60 (assume @p9 (forall @t16 (= (tptp.contains_slb @t15 @t1) (or @t12 @t11)))) % 0.40/0.60 (assume @p10 (forall @t7 (not (tptp.pair_in_list tptp.create_slb @t2 @t3)))) % 0.40/0.60 (assume @p11 (forall @t18 (= (tptp.pair_in_list @t15 @t1 @t17) (or (tptp.pair_in_list @t2 @t1 @t17) (and @t11 (= @t13 @t17)))))) % 0.40/0.60 (assume @p12 (forall @t5 (= (tptp.remove_slb @t10 @t3) @t2))) % 0.40/0.60 (assume @p13 (forall @t16 (=> @t19 (= (tptp.remove_slb @t15 @t1) (tptp.insert_slb (tptp.remove_slb @t2 @t1) @t14))))) % 0.40/0.60 (assume @p14 (forall @t5 (= (tptp.lookup_slb @t10 @t3) @t1))) % 0.40/0.60 (assume @p15 (forall @t16 (=> @t19 (= (tptp.lookup_slb @t15 @t1) (tptp.lookup_slb @t2 @t1))))) % 0.40/0.60 (assume @p16 (forall @t8 (= (tptp.update_slb tptp.create_slb @t2) tptp.create_slb))) % 0.40/0.60 (assume @p17 (forall @t16 (=> (tptp.strictly_less_than @t13 @t1) (= @t21 (tptp.insert_slb @t20 @t9))))) % 0.40/0.60 (assume @p18 (forall @t16 (=> (tptp.less_than @t1 @t13) (= @t21 (tptp.insert_slb @t20 @t14))))) % 0.40/0.60 (assume @p19 (forall @t8 (tptp.succ_cpq @t2 @t2))) % 0.40/0.60 (assume @p20 (forall @t5 (=> @t22 (tptp.succ_cpq @t2 (tptp.insert_cpq @t3 @t1))))) % 0.40/0.60 (assume @p21 (forall @t5 (=> @t22 (tptp.succ_cpq @t2 (tptp.remove_cpq @t3 @t1))))) % 0.40/0.60 (assume @p22 (forall @t7 (=> @t22 (tptp.succ_cpq @t2 (tptp.findmin_cpq_eff @t3))))) % 0.40/0.60 (assume @p23 (forall @t7 (=> @t22 (tptp.succ_cpq @t2 (tptp.removemin_cpq_eff @t3))))) % 0.40/0.60 (assume @p24 (forall @t7 (tptp.check_cpq @t23))) % 0.40/0.60 (assume @p25 (forall @t18 (=> (tptp.less_than @t17 @t13) (= @t26 @t25)))) % 0.40/0.60 (assume @p26 (forall @t18 (=> (tptp.strictly_less_than @t13 @t17) (= @t26 false)))) % 0.40/0.60 (assume @p27 (forall @t16 (= (tptp.contains_cpq @t24 @t13) @t27))) % 0.40/0.60 (assume @p28 (forall @t7 (= (tptp.ok @t28) false))) % 0.40/0.60 (assume @p29 (forall @t5 (=> @t30 (= @t1 tptp.bad)))) % 0.40/0.60 (assume @p30 (forall @t16 (= (tptp.insert_cpq @t24 @t13) (tptp.triple (tptp.insert_pqp @t2 @t13) (tptp.insert_slb @t3 (tptp.pair @t13 tptp.bottom)) @t1)))) % 0.40/0.60 (assume @p31 (forall @t16 (=> (not @t27) (= @t31 @t28)))) % 0.40/0.60 (assume @p32 (forall @t16 (=> (and @t27 (tptp.less_than @t34 @t13)) (= @t31 (tptp.triple @t33 @t32 @t1))))) % 0.40/0.60 (assume @p33 (forall @t16 (=> (and @t27 (tptp.strictly_less_than @t13 @t34)) (= @t31 (tptp.triple @t33 @t32 tptp.bad))))) % 0.40/0.60 (assume @p34 (forall @t7 (= (tptp.findmin_cpq_eff @t23) (tptp.triple @t2 tptp.create_slb tptp.bad)))) % 0.40/0.60 (assume @p35 (forall @t16 (=> (and @t40 (not @t39)) @t38))) % 0.40/0.60 (assume @p36 (forall @t16 (=> (and @t40 @t39 (tptp.strictly_less_than @t35 @t41)) @t38))) % 0.40/0.60 (assume @p37 (forall @t16 (=> (and @t40 @t39 (tptp.less_than @t41 @t35)) (= @t37 (tptp.triple @t2 @t36 @t1))))) % 0.40/0.60 (assume @p38 (forall @t7 (= (tptp.findmin_cpq_res @t23) tptp.bottom))) % 0.40/0.60 (assume @p39 (forall @t16 (=> @t40 (= (tptp.findmin_cpq_res @t24) @t35)))) % 0.40/0.60 (assume @p40 (forall @t8 (= (tptp.removemin_cpq_eff @t2) (tptp.remove_cpq (tptp.findmin_cpq_eff @t2) @t42)))) % 0.40/0.60 (assume @p41 (forall @t8 (= (tptp.removemin_cpq_res @t2) @t42))) % 0.40/0.60 (assume @p42 @t80) % 0.40/0.60 (assume @p43 @t87) % 0.40/0.60 (assume @p44 @t93) % 0.40/0.60 (assume @p45 true) % 0.40/0.60 (step @p46 :rule aci_norm :args ((= (or @t94 @t84) @t95))) % 0.40/0.60 (step @p47 :rule refl :args (@t84)) % 0.40/0.60 (step @p48 :rule bool-double-not-elim :args (@t29)) % 0.40/0.60 (step @p49 :rule bool-double-not-elim :args (@t25)) % 0.40/0.60 (step @p50 :rule nary_cong :premises (@p49 @p48) :args ((and (not @t85) (not @t30)))) % 0.40/0.60 (step @p51 :rule bool-or-de-morgan :args (@t85 @t30 false)) % 0.40/0.60 (step @p52 :rule trans :premises (@p51 @p50)) % 0.40/0.60 (step @p53 :rule nary_cong :premises (@p52 @p47) :args ((or @t96 @t84))) % 0.40/0.60 (step @p54 :rule trans :premises (@p53 @p46)) % 0.40/0.60 (step @p55 :rule bool-impl-elim :args (@t86 @t84)) % 0.40/0.60 (step @p56 :rule trans :premises (@p55 @p54)) % 0.40/0.60 (step @p57 :rule cong :premises (@p56) :args (@t87)) % 0.40/0.60 (step @p58 :rule eq_resolve :premises (@p43 @p57)) % 0.40/0.60 (step @p59 :rule aci_norm :args ((= @t106 @t104))) % 0.40/0.60 (step @p60 :rule cong :premises (@p59) :args (@t108)) % 0.40/0.60 (step @p61 :rule quant-merge-prenex :args ((= (forall @t5 @t110) @t108))) % 0.40/0.60 (step @p62 :rule alpha_equiv :args (@t111 (@list @t99 @t98 @t97) (@list @t13 @t17 @t65))) % 0.40/0.60 (step @p63 :rule refl :args (@t94)) % 0.40/0.60 (step @p64 :rule nary_cong :premises (@p63 @p62) :args (@t112)) % 0.40/0.60 (step @p65 :rule quant-miniscope-or :args ((= @t110 @t112))) % 0.40/0.60 (step @p66 :rule trans :premises (@p65 @p64)) % 0.40/0.60 (step @p67 :rule symm :premises (@p66)) % 0.40/0.60 (step @p68 :rule cong :premises (@p67) :args ((forall @t5 (or @t94 @t115)))) % 0.40/0.60 (step @p69 :rule trans :premises (@p68 @p61)) % 0.40/0.60 (step @p70 :rule trans :premises (@p69 @p60)) % 0.40/0.60 (step @p71 :rule refl :args (@t115)) % 0.40/0.60 (step @p72 :rule nary_cong :premises (@p52 @p71) :args ((or @t96 @t115))) % 0.40/0.60 (step @p73 :rule bool-impl-elim :args (@t86 @t115)) % 0.40/0.60 (step @p74 :rule trans :premises (@p73 @p72)) % 0.40/0.60 (step @p75 :rule cong :premises (@p74) :args ((forall @t5 (=> @t86 @t115)))) % 0.40/0.60 (step @p76 :rule trans :premises (@p75 @p70)) % 0.40/0.60 (step @p77 :rule aci_norm :args ((= (or @t113 @t88) @t114))) % 0.40/0.60 (step @p78 :rule bool-impl-elim :args (@t77 @t88)) % 0.40/0.60 (step @p79 :rule trans :premises (@p78 @p77)) % 0.40/0.60 (step @p80 :rule cong :premises (@p79) :args (@t90)) % 0.40/0.60 (step @p81 :rule refl :args (@t86)) % 0.40/0.60 (step @p82 :rule cong :premises (@p81 @p80) :args (@t91)) % 0.40/0.60 (step @p83 :rule cong :premises (@p82) :args (@t92)) % 0.40/0.60 (step @p84 :rule trans :premises (@p83 @p76)) % 0.40/0.60 (step @p85 :rule cong :premises (@p84) :args (@t93)) % 0.40/0.60 (step @p86 :rule eq_resolve :premises (@p44 @p85)) % 0.40/0.60 (step @p87 :rule alpha_equiv :args (@t126 (@list @t52 @t51 @t50 @t118 @t117 @t116) (@list @t2 @t3 @t1 @t99 @t98 @t97))) % 0.40/0.60 (step @p88 :rule equiv_elim1 :premises (@p87)) % 0.40/0.60 (step @p89 :rule reordering :premises (@p88) :args ((or @t128 @t127))) % 0.40/0.60 (step @p90 :rule chain_m_resolution :premises (@p89 @p86) :args (@t127 @t129 (@list @t128))) % 0.40/0.60 (step @p91 :rule aci_norm :args ((= @t131 @t124))) % 0.40/0.60 (step @p92 :rule cong :premises (@p91) :args (@t132)) % 0.40/0.60 (step @p93 :rule quant-merge-prenex :args ((= (forall @t63 @t134) @t132))) % 0.40/0.60 (step @p94 :rule alpha_equiv :args (@t135 (@list @t118 @t117 @t116) (@list @t45 @t44 @t43))) % 0.40/0.60 (step @p95 :rule refl :args (@t123)) % 0.40/0.60 (step @p96 :rule nary_cong :premises (@p95 @p94) :args (@t136)) % 0.40/0.60 (step @p97 :rule quant-miniscope-or :args ((= @t134 @t136))) % 0.40/0.60 (step @p98 :rule trans :premises (@p97 @p96)) % 0.40/0.60 (step @p99 :rule symm :premises (@p98)) % 0.40/0.60 (step @p100 :rule cong :premises (@p99) :args ((forall @t63 (or @t123 @t139)))) % 0.40/0.60 (step @p101 :rule trans :premises (@p100 @p93)) % 0.40/0.60 (step @p102 :rule trans :premises (@p101 @p92)) % 0.40/0.60 (step @p103 :rule refl :args (@t139)) % 0.40/0.60 (step @p104 :rule bool-double-not-elim :args (@t57)) % 0.40/0.60 (step @p105 :rule bool-double-not-elim :args (@t59)) % 0.40/0.60 (step @p106 :rule nary_cong :premises (@p105 @p104) :args ((and (not @t60) (not @t58)))) % 0.40/0.60 (step @p107 :rule bool-or-de-morgan :args (@t60 @t58 false)) % 0.40/0.60 (step @p108 :rule trans :premises (@p107 @p106)) % 0.40/0.60 (step @p109 :rule nary_cong :premises (@p108 @p103) :args ((or (not @t61) @t139))) % 0.40/0.60 (step @p110 :rule bool-impl-elim :args (@t61 @t139)) % 0.40/0.60 (step @p111 :rule trans :premises (@p110 @p109)) % 0.40/0.60 (step @p112 :rule cong :premises (@p111) :args ((forall @t63 (=> @t61 @t139)))) % 0.40/0.60 (step @p113 :rule trans :premises (@p112 @p102)) % 0.40/0.60 (step @p114 :rule aci_norm :args ((= (or @t137 @t49) @t138))) % 0.40/0.60 (step @p115 :rule bool-impl-elim :args (@t54 @t49)) % 0.40/0.60 (step @p116 :rule trans :premises (@p115 @p114)) % 0.40/0.60 (step @p117 :rule cong :premises (@p116) :args (@t56)) % 0.40/0.60 (step @p118 :rule refl :args (@t61)) % 0.40/0.60 (step @p119 :rule cong :premises (@p118 @p117) :args (@t62)) % 0.40/0.60 (step @p120 :rule cong :premises (@p119) :args (@t64)) % 0.40/0.60 (step @p121 :rule trans :premises (@p120 @p113)) % 0.40/0.60 (step @p122 :rule aci_norm :args ((= (or @t113 @t142) @t141))) % 0.40/0.60 (step @p123 :rule aci_norm :args ((= (or @t140 @t70) @t142))) % 0.40/0.60 (step @p124 :rule refl :args (@t70)) % 0.40/0.60 (step @p125 :rule bool-double-not-elim :args (@t71)) % 0.40/0.60 (step @p126 :rule bool-double-not-elim :args (@t73)) % 0.40/0.60 (step @p127 :rule nary_cong :premises (@p126 @p125) :args ((and (not @t74) (not @t72)))) % 0.40/0.60 (step @p128 :rule bool-or-de-morgan :args (@t74 @t72 false)) % 0.40/0.60 (step @p129 :rule trans :premises (@p128 @p127)) % 0.40/0.60 (step @p130 :rule nary_cong :premises (@p129 @p124) :args ((or (not @t75) @t70))) % 0.40/0.60 (step @p131 :rule trans :premises (@p130 @p123)) % 0.40/0.60 (step @p132 :rule bool-impl-elim :args (@t75 @t70)) % 0.40/0.60 (step @p133 :rule trans :premises (@p132 @p131)) % 0.40/0.60 (step @p134 :rule refl :args (@t113)) % 0.40/0.60 (step @p135 :rule nary_cong :premises (@p134 @p133) :args ((or @t113 @t76))) % 0.40/0.60 (step @p136 :rule trans :premises (@p135 @p122)) % 0.40/0.60 (step @p137 :rule bool-impl-elim :args (@t77 @t76)) % 0.40/0.60 (step @p138 :rule trans :premises (@p137 @p136)) % 0.40/0.60 (step @p139 :rule cong :premises (@p138) :args (@t79)) % 0.40/0.60 (step @p140 :rule cong :premises (@p139 @p121) :args (@t80)) % 0.40/0.60 (step @p141 :rule eq_resolve :premises (@p42 @p140)) % 0.40/0.60 (step @p142 :rule implies_elim :premises (@p141)) % 0.40/0.60 (step @p143 :rule reordering :premises (@p142) :args ((or @t126 @t144))) % 0.40/0.60 (step @p144 :rule chain_m_resolution :premises (@p143 @p90) :args (@t144 @t129 (@list @t126))) % 0.40/0.60 (step @p145 :rule skolemize :premises (@p144)) % 0.40/0.60 (step @p146 :rule bool-double-not-elim :args (@t150)) % 0.40/0.60 (step @p147 :rule refl :args (@t155)) % 0.40/0.60 (step @p148 :rule nary_cong :premises (@p147 @p146) :args ((or @t155 (not @t151)))) % 0.40/0.60 (step @p149 :rule cnf_or_neg :args (@t155 3)) % 0.40/0.60 (step @p150 :rule eq_resolve :premises (@p149 @p148)) % 0.40/0.60 (step @p151 :rule reordering :premises (@p150) :args ((or @t150 @t155))) % 0.40/0.60 (step @p152 :rule chain_m_resolution :premises (@p151 @p145) :args (@t150 @t129 @t156)) % 0.40/0.60 (step @p153 :rule bool-double-not-elim :args (@t152)) % 0.40/0.60 (step @p154 :rule nary_cong :premises (@p147 @p153) :args ((or @t155 (not @t153)))) % 0.40/0.60 (step @p155 :rule cnf_or_neg :args (@t155 2)) % 0.40/0.60 (step @p156 :rule eq_resolve :premises (@p155 @p154)) % 0.40/0.60 (step @p157 :rule reordering :premises (@p156) :args ((or @t152 @t155))) % 0.40/0.60 (step @p158 :rule chain_m_resolution :premises (@p157 @p145) :args (@t152 @t129 @t156)) % 0.40/0.60 (step @p159 :rule cnf_or_neg :args (@t155 1)) % 0.40/0.60 (step @p160 :rule chain_m_resolution :premises (@p159 @p145) :args ((not @t154) @t129 @t156)) % 0.40/0.60 (step @p161 :rule cnf_or_pos :args (@t157)) % 0.40/0.60 (step @p162 :rule reordering :premises (@p161) :args ((or @t154 @t153 @t151 @t158))) % 0.40/0.60 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p158 @p152) :args (@t158 (@list true false false) (@list @t154 @t152 @t150))) % 0.40/0.60 (assume-push @p170 @t159) % 0.40/0.60 (step @p165 :rule instantiate :premises (@p58) :args ((@list @t147 @t146 @t145))) % 0.40/0.60 (step-pop @p171 :rule scope :premises (@p165)) % 0.40/0.60 (step @p166 :rule process_scope :premises (@p171) :args (@t157)) % 0.40/0.60 (step @p168 :rule implies_elim :premises (@p166)) % 0.40/0.60 (step @p169 false :rule chain_m_resolution :premises (@p168 @p163 @p58) :args (false (@list true false) (@list @t157 @t159))) % 0.40/0.60 ) % 0.40/0.60 % SZS output end Proof % 0.40/0.60 % cvc5 exiting %------------------------------------------------------------------------------