%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV415+2 : 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 : n027.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 09:01:23 AM UTC 2026 % Result : Theorem 0.39s 0.81s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWV415+2 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n027.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 20:07:06 EDT 2026 % 0.18/0.36 % CPUTime : % 0.29/0.53 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.81 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.81 % SZS status Theorem % 0.39/0.81 % SZS output start Proof % 0.39/0.81 ( % 0.39/0.81 (declare-sort $$unsorted 0) % 0.39/0.81 (declare-const tptp.phi (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.pi_removemin (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.pi_sharp_removemin (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.pi_find_min (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.pi_remove (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.i (-> $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.removemin_cpq_res (-> $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.insert_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.ok (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.findmin_pqp_res (-> $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.removemin_pq_res (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.removemin_pq_eff (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.pi_sharp_remove (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.check_cpq (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.remove_pq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.insert_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.findmin_pq_res (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.remove_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.issmallestelement_pq (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.strictly_less_than (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.isnonempty_pq (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.findmin_pq_eff (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.contains_pq (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.isnonempty_slb (-> $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.remove_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.findmin_cpq_eff (-> $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.pi_sharp_find_min (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.create_pq $$unsorted) % 0.39/0.81 (declare-const tptp.lookup_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.bottom $$unsorted) % 0.39/0.81 (declare-const tptp.insert_pq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.update_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.contains_cpq (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.create_slb $$unsorted) % 0.39/0.81 (declare-const tptp.less_than (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.bad $$unsorted) % 0.39/0.81 (declare-const tptp.insert_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.contains_slb (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.pair_in_list (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.remove_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.findmin_cpq_res (-> $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.succ_cpq (-> $$unsorted $$unsorted Bool)) % 0.39/0.81 (declare-const tptp.removemin_cpq_eff (-> $$unsorted $$unsorted)) % 0.39/0.81 (declare-const tptp.triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.81 (define @t1 () (@var "W" $$unsorted)) % 0.39/0.81 (define @t2 () (@var "U" $$unsorted)) % 0.39/0.81 (define @t3 () (@var "V" $$unsorted)) % 0.39/0.81 (define @t4 () (tptp.less_than @t3 @t1)) % 0.39/0.81 (define @t5 () (tptp.less_than @t2 @t3)) % 0.39/0.81 (define @t6 () (@list @t2 @t3 @t1)) % 0.39/0.81 (define @t7 () (tptp.less_than @t3 @t2)) % 0.39/0.81 (define @t8 () (@list @t2 @t3)) % 0.39/0.81 (define @t9 () (@list @t2)) % 0.39/0.81 (define @t10 () (tptp.insert_pq @t2 @t3)) % 0.39/0.81 (define @t11 () (= @t3 @t1)) % 0.39/0.81 (define @t12 () (tptp.contains_pq @t2 @t1)) % 0.39/0.81 (define @t13 () (tptp.issmallestelement_pq @t2 @t3)) % 0.39/0.81 (define @t14 () (not @t11)) % 0.39/0.81 (define @t15 () (tptp.contains_pq @t2 @t3)) % 0.39/0.81 (define @t16 () (and @t15 @t13)) % 0.39/0.81 (define @t17 () (tptp.pair @t3 @t1)) % 0.39/0.81 (define @t18 () (tptp.insert_slb @t2 @t17)) % 0.39/0.81 (define @t19 () (tptp.contains_slb @t2 @t1)) % 0.39/0.81 (define @t20 () (@var "X" $$unsorted)) % 0.39/0.81 (define @t21 () (tptp.pair @t3 @t20)) % 0.39/0.81 (define @t22 () (tptp.insert_slb @t2 @t21)) % 0.39/0.81 (define @t23 () (@list @t2 @t3 @t1 @t20)) % 0.39/0.81 (define @t24 () (@var "Y" $$unsorted)) % 0.39/0.81 (define @t25 () (@list @t2 @t3 @t1 @t20 @t24)) % 0.39/0.81 (define @t26 () (and @t14 @t19)) % 0.39/0.81 (define @t27 () (tptp.update_slb @t2 @t1)) % 0.39/0.81 (define @t28 () (tptp.update_slb @t22 @t1)) % 0.39/0.81 (define @t29 () (tptp.succ_cpq @t2 @t3)) % 0.39/0.81 (define @t30 () (tptp.triple @t2 tptp.create_slb @t3)) % 0.39/0.81 (define @t31 () (tptp.triple @t2 @t3 @t1)) % 0.39/0.81 (define @t32 () (tptp.triple @t2 (tptp.insert_slb @t3 (tptp.pair @t20 @t24)) @t1)) % 0.39/0.81 (define @t33 () (tptp.check_cpq @t32)) % 0.39/0.81 (define @t34 () (tptp.contains_slb @t3 @t20)) % 0.39/0.81 (define @t35 () (tptp.triple @t2 @t3 tptp.bad)) % 0.39/0.81 (define @t36 () (tptp.insert_cpq @t31 @t20)) % 0.39/0.81 (define @t37 () (tptp.remove_cpq @t31 @t20)) % 0.39/0.81 (define @t38 () (tptp.remove_slb @t3 @t20)) % 0.39/0.81 (define @t39 () (tptp.remove_pqp @t2 @t20)) % 0.39/0.81 (define @t40 () (tptp.lookup_slb @t3 @t20)) % 0.39/0.81 (define @t41 () (tptp.findmin_pqp_res @t2)) % 0.39/0.81 (define @t42 () (tptp.update_slb @t3 @t41)) % 0.39/0.81 (define @t43 () (tptp.findmin_cpq_eff @t31)) % 0.39/0.81 (define @t44 () (= @t43 (tptp.triple @t2 @t42 tptp.bad))) % 0.39/0.81 (define @t45 () (tptp.contains_slb @t3 @t41)) % 0.39/0.81 (define @t46 () (not (= @t3 tptp.create_slb))) % 0.39/0.81 (define @t47 () (tptp.lookup_slb @t3 @t41)) % 0.39/0.81 (define @t48 () (tptp.findmin_cpq_res @t2)) % 0.39/0.81 (define @t49 () (tptp.i @t30)) % 0.39/0.81 (define @t50 () (forall @t8 (= @t49 tptp.create_pq))) % 0.39/0.81 (define @t51 () (tptp.insert_pq (tptp.i @t31) @t20)) % 0.39/0.81 (define @t52 () (tptp.i @t2)) % 0.39/0.81 (define @t53 () (@list @t3)) % 0.39/0.81 (define @t54 () (exists @t53 (tptp.pi_sharp_find_min @t52 @t3))) % 0.39/0.81 (define @t55 () (@var "X14" $$unsorted)) % 0.39/0.81 (define @t56 () (@var "X12" $$unsorted)) % 0.39/0.81 (define @t57 () (@var "X11" $$unsorted)) % 0.39/0.81 (define @t58 () (@var "X13" $$unsorted)) % 0.39/0.81 (define @t59 () (@var "X10" $$unsorted)) % 0.39/0.81 (define @t60 () (forall (@list @t59 @t57 @t56 @t58 @t55) (= (tptp.i (tptp.triple @t59 @t56 @t58)) (tptp.i (tptp.triple @t57 @t56 @t55))))) % 0.39/0.81 (define @t61 () (@var "X7" $$unsorted)) % 0.39/0.81 (define @t62 () (@var "X9" $$unsorted)) % 0.39/0.81 (define @t63 () (@var "X8" $$unsorted)) % 0.39/0.81 (define @t64 () (tptp.insert_slb @t24 (tptp.pair @t63 @t62))) % 0.39/0.81 (define @t65 () (@var "X5" $$unsorted)) % 0.39/0.81 (define @t66 () (@var "X6" $$unsorted)) % 0.39/0.81 (define @t67 () (@var "X4" $$unsorted)) % 0.39/0.81 (define @t68 () (forall (@list @t67 @t65 @t66 @t61 @t63 @t62) (= (tptp.i (tptp.triple @t67 @t64 @t66)) (tptp.i (tptp.triple @t65 @t64 @t61))))) % 0.39/0.81 (define @t69 () (@var "X3" $$unsorted)) % 0.39/0.81 (define @t70 () (@var "X1" $$unsorted)) % 0.39/0.81 (define @t71 () (@var "X2" $$unsorted)) % 0.39/0.81 (define @t72 () (@var "Z" $$unsorted)) % 0.39/0.81 (define @t73 () (@list @t72 @t70 @t71 @t69)) % 0.39/0.81 (define @t74 () (forall @t73 (= (tptp.i (tptp.triple @t72 @t24 @t71)) (tptp.i (tptp.triple @t70 @t24 @t69))))) % 0.39/0.81 (define @t75 () (@list @t24)) % 0.39/0.81 (define @t76 () (forall @t75 (=> @t74 @t68))) % 0.39/0.81 (define @t77 () (forall @t23 (= (tptp.i (tptp.triple @t2 tptp.create_slb @t1)) (tptp.i (tptp.triple @t3 tptp.create_slb @t20))))) % 0.39/0.81 (define @t78 () (and @t77 @t76)) % 0.39/0.81 (define @t79 () (=> @t78 @t60)) % 0.39/0.81 (define @t80 () (tptp.i @t36)) % 0.39/0.81 (define @t81 () (forall @t23 (= @t80 @t51))) % 0.39/0.81 (define @t82 () (not @t81)) % 0.39/0.81 (define @t83 () (forall @t23 (= @t51 @t80))) % 0.39/0.81 (define @t84 () (@quantifiers_skolemize @t83 3)) % 0.39/0.81 (define @t85 () (@quantifiers_skolemize @t83 2)) % 0.39/0.81 (define @t86 () (@quantifiers_skolemize @t83 1)) % 0.39/0.81 (define @t87 () (@quantifiers_skolemize @t83 0)) % 0.39/0.81 (define @t88 () (tptp.insert_pqp @t87 @t84)) % 0.39/0.81 (define @t89 () (@var "BOUND_VARIABLE_8006" $$unsorted)) % 0.39/0.81 (define @t90 () (@var "BOUND_VARIABLE_8010" $$unsorted)) % 0.39/0.81 (define @t91 () (@var "BOUND_VARIABLE_8008" $$unsorted)) % 0.39/0.81 (define @t92 () (tptp.insert_slb @t24 (tptp.pair @t91 @t90))) % 0.39/0.81 (define @t93 () (@var "BOUND_VARIABLE_8002" $$unsorted)) % 0.39/0.81 (define @t94 () (@var "BOUND_VARIABLE_8004" $$unsorted)) % 0.39/0.81 (define @t95 () (@var "BOUND_VARIABLE_8000" $$unsorted)) % 0.39/0.81 (define @t96 () (= (tptp.i (tptp.triple @t95 @t92 @t94)) (tptp.i (tptp.triple @t93 @t92 @t89)))) % 0.39/0.81 (define @t97 () (not @t74)) % 0.39/0.81 (define @t98 () (or @t97 @t96)) % 0.39/0.81 (define @t99 () (forall (@list @t24 @t95 @t93 @t94 @t89 @t91 @t90) @t98)) % 0.39/0.81 (define @t100 () (@quantifiers_skolemize @t99 0)) % 0.39/0.81 (define @t101 () (forall @t73 (= (tptp.i (tptp.triple @t72 @t100 @t71)) (tptp.i (tptp.triple @t70 @t100 @t69))))) % 0.39/0.81 (define @t102 () (@quantifiers_skolemize @t99 4)) % 0.39/0.81 (define @t103 () (@quantifiers_skolemize @t99 6)) % 0.39/0.81 (define @t104 () (@quantifiers_skolemize @t99 5)) % 0.39/0.81 (define @t105 () (tptp.insert_slb @t100 (tptp.pair @t104 @t103))) % 0.39/0.81 (define @t106 () (@quantifiers_skolemize @t99 2)) % 0.39/0.81 (define @t107 () (tptp.i (tptp.triple @t106 @t105 @t102))) % 0.39/0.81 (define @t108 () (@quantifiers_skolemize @t99 3)) % 0.39/0.81 (define @t109 () (@quantifiers_skolemize @t99 1)) % 0.39/0.81 (define @t110 () (tptp.i (tptp.triple @t109 @t105 @t108))) % 0.39/0.81 (define @t111 () (= @t110 @t107)) % 0.39/0.81 (define @t112 () (not @t101)) % 0.39/0.81 (define @t113 () (or @t112 @t111)) % 0.39/0.81 (define @t114 () (tptp.i (tptp.triple @t109 @t100 @t108))) % 0.39/0.81 (define @t115 () (tptp.i (tptp.triple @t106 @t100 @t102))) % 0.39/0.81 (define @t116 () (= @t114 @t115)) % 0.39/0.81 (define @t117 () (= @t107 (tptp.insert_pq @t115 @t104))) % 0.39/0.81 (define @t118 () (tptp.insert_pq @t114 @t104)) % 0.39/0.81 (define @t119 () (= @t110 @t118)) % 0.39/0.81 (define @t120 () (= @t115 @t114)) % 0.39/0.81 (define @t121 () (and @t117 @t119 @t120)) % 0.39/0.81 (define @t122 () (not @t113)) % 0.39/0.81 (define @t123 () (not @t99)) % 0.39/0.81 (define @t124 () (@list false)) % 0.39/0.81 (define @t125 () (@quantifiers_skolemize @t77 3)) % 0.39/0.81 (define @t126 () (@quantifiers_skolemize @t77 1)) % 0.39/0.81 (define @t127 () (@quantifiers_skolemize @t77 2)) % 0.39/0.81 (define @t128 () (@quantifiers_skolemize @t77 0)) % 0.39/0.81 (define @t129 () (= (tptp.i (tptp.triple @t128 tptp.create_slb @t127)) (tptp.i (tptp.triple @t126 tptp.create_slb @t125)))) % 0.39/0.81 (define @t130 () (not @t129)) % 0.39/0.81 (define @t131 () (not @t77)) % 0.39/0.81 (define @t132 () (and @t77 @t99)) % 0.39/0.81 (define @t133 () (@list @t95 @t93 @t94 @t89 @t91 @t90)) % 0.39/0.81 (define @t134 () (forall @t133 @t98)) % 0.39/0.81 (define @t135 () (forall @t133 @t96)) % 0.39/0.81 (define @t136 () (or @t97 @t135)) % 0.39/0.81 (define @t137 () (tptp.i (tptp.triple @t88 @t86 @t85))) % 0.39/0.81 (define @t138 () (tptp.triple @t87 @t86 @t85)) % 0.39/0.81 (define @t139 () (tptp.i @t138)) % 0.39/0.81 (define @t140 () (= @t139 @t137)) % 0.39/0.81 (define @t141 () (tptp.triple @t88 (tptp.insert_slb @t86 (tptp.pair @t84 tptp.bottom)) @t85)) % 0.39/0.81 (define @t142 () (tptp.insert_cpq @t138 @t84)) % 0.39/0.81 (define @t143 () (= @t142 @t141)) % 0.39/0.81 (define @t144 () (tptp.i @t141)) % 0.39/0.81 (define @t145 () (= @t144 (tptp.insert_pq @t137 @t84))) % 0.39/0.81 (define @t146 () (tptp.insert_pq @t139 @t84)) % 0.39/0.81 (define @t147 () (= @t146 (tptp.i @t142))) % 0.39/0.81 (define @t148 () (and @t143 @t145 @t140)) % 0.39/0.81 (assume @p1 (forall @t6 (=> (and @t5 @t4) (tptp.less_than @t2 @t1)))) % 0.39/0.81 (assume @p2 (forall @t8 (or @t5 @t7))) % 0.39/0.81 (assume @p3 (forall @t9 (tptp.less_than @t2 @t2))) % 0.39/0.81 (assume @p4 (forall @t8 (= (tptp.strictly_less_than @t2 @t3) (and @t5 (not @t7))))) % 0.39/0.81 (assume @p5 (forall @t9 (tptp.less_than tptp.bottom @t2))) % 0.39/0.81 (assume @p6 (not (tptp.isnonempty_pq tptp.create_pq))) % 0.39/0.81 (assume @p7 (forall @t8 (tptp.isnonempty_pq @t10))) % 0.39/0.81 (assume @p8 (forall @t9 (not (tptp.contains_pq tptp.create_pq @t2)))) % 0.39/0.81 (assume @p9 (forall @t6 (= (tptp.contains_pq @t10 @t1) (or @t12 @t11)))) % 0.39/0.81 (assume @p10 (forall @t8 (= @t13 (forall (@list @t1) (=> @t12 @t4))))) % 0.39/0.81 (assume @p11 (forall @t8 (= (tptp.remove_pq @t10 @t3) @t2))) % 0.39/0.81 (assume @p12 (forall @t6 (=> (and @t12 @t14) (= (tptp.remove_pq @t10 @t1) (tptp.insert_pq (tptp.remove_pq @t2 @t1) @t3))))) % 0.39/0.81 (assume @p13 (forall @t8 (=> @t16 (= (tptp.findmin_pq_eff @t2 @t3) @t2)))) % 0.39/0.81 (assume @p14 (forall @t8 (=> @t16 (= (tptp.findmin_pq_res @t2 @t3) @t3)))) % 0.39/0.81 (assume @p15 (forall @t8 (=> @t16 (= (tptp.removemin_pq_eff @t2 @t3) (tptp.remove_pq @t2 @t3))))) % 0.39/0.81 (assume @p16 (forall @t8 (=> @t16 (= (tptp.removemin_pq_res @t2 @t3) @t3)))) % 0.39/0.81 (assume @p17 (forall @t6 (= (tptp.insert_pq @t10 @t1) (tptp.insert_pq (tptp.insert_pq @t2 @t1) @t3)))) % 0.39/0.81 (assume @p18 (not (tptp.isnonempty_slb tptp.create_slb))) % 0.39/0.81 (assume @p19 (forall @t6 (tptp.isnonempty_slb @t18))) % 0.39/0.81 (assume @p20 (forall @t9 (not (tptp.contains_slb tptp.create_slb @t2)))) % 0.39/0.81 (assume @p21 (forall @t23 (= (tptp.contains_slb @t22 @t1) (or @t19 @t11)))) % 0.39/0.81 (assume @p22 (forall @t8 (not (tptp.pair_in_list tptp.create_slb @t2 @t3)))) % 0.39/0.81 (assume @p23 (forall @t25 (= (tptp.pair_in_list @t22 @t1 @t24) (or (tptp.pair_in_list @t2 @t1 @t24) (and @t11 (= @t20 @t24)))))) % 0.39/0.81 (assume @p24 (forall @t6 (= (tptp.remove_slb @t18 @t3) @t2))) % 0.39/0.81 (assume @p25 (forall @t23 (=> @t26 (= (tptp.remove_slb @t22 @t1) (tptp.insert_slb (tptp.remove_slb @t2 @t1) @t21))))) % 0.39/0.81 (assume @p26 (forall @t6 (= (tptp.lookup_slb @t18 @t3) @t1))) % 0.39/0.81 (assume @p27 (forall @t23 (=> @t26 (= (tptp.lookup_slb @t22 @t1) (tptp.lookup_slb @t2 @t1))))) % 0.39/0.81 (assume @p28 (forall @t9 (= (tptp.update_slb tptp.create_slb @t2) tptp.create_slb))) % 0.39/0.81 (assume @p29 (forall @t23 (=> (tptp.strictly_less_than @t20 @t1) (= @t28 (tptp.insert_slb @t27 @t17))))) % 0.39/0.81 (assume @p30 (forall @t23 (=> (tptp.less_than @t1 @t20) (= @t28 (tptp.insert_slb @t27 @t21))))) % 0.39/0.81 (assume @p31 (forall @t9 (tptp.succ_cpq @t2 @t2))) % 0.39/0.81 (assume @p32 (forall @t6 (=> @t29 (tptp.succ_cpq @t2 (tptp.insert_cpq @t3 @t1))))) % 0.39/0.81 (assume @p33 (forall @t6 (=> @t29 (tptp.succ_cpq @t2 (tptp.remove_cpq @t3 @t1))))) % 0.39/0.81 (assume @p34 (forall @t8 (=> @t29 (tptp.succ_cpq @t2 (tptp.findmin_cpq_eff @t3))))) % 0.39/0.81 (assume @p35 (forall @t8 (=> @t29 (tptp.succ_cpq @t2 (tptp.removemin_cpq_eff @t3))))) % 0.39/0.81 (assume @p36 (forall @t8 (tptp.check_cpq @t30))) % 0.39/0.81 (assume @p37 (forall @t25 (=> (tptp.less_than @t24 @t20) (= @t33 (tptp.check_cpq @t31))))) % 0.39/0.81 (assume @p38 (forall @t25 (=> (tptp.strictly_less_than @t20 @t24) (= @t33 false)))) % 0.39/0.81 (assume @p39 (forall @t23 (= (tptp.contains_cpq @t31 @t20) @t34))) % 0.39/0.81 (assume @p40 (forall @t8 (= (tptp.ok @t35) false))) % 0.39/0.81 (assume @p41 (forall @t6 (=> (not (tptp.ok @t31)) (= @t1 tptp.bad)))) % 0.39/0.81 (assume @p42 (forall @t23 (= @t36 (tptp.triple (tptp.insert_pqp @t2 @t20) (tptp.insert_slb @t3 (tptp.pair @t20 tptp.bottom)) @t1)))) % 0.39/0.81 (assume @p43 (forall @t23 (=> (not @t34) (= @t37 @t35)))) % 0.39/0.81 (assume @p44 (forall @t23 (=> (and @t34 (tptp.less_than @t40 @t20)) (= @t37 (tptp.triple @t39 @t38 @t1))))) % 0.39/0.81 (assume @p45 (forall @t23 (=> (and @t34 (tptp.strictly_less_than @t20 @t40)) (= @t37 (tptp.triple @t39 @t38 tptp.bad))))) % 0.39/0.81 (assume @p46 (forall @t8 (= (tptp.findmin_cpq_eff @t30) (tptp.triple @t2 tptp.create_slb tptp.bad)))) % 0.39/0.81 (assume @p47 (forall @t23 (=> (and @t46 (not @t45)) @t44))) % 0.39/0.81 (assume @p48 (forall @t23 (=> (and @t46 @t45 (tptp.strictly_less_than @t41 @t47)) @t44))) % 0.39/0.81 (assume @p49 (forall @t23 (=> (and @t46 @t45 (tptp.less_than @t47 @t41)) (= @t43 (tptp.triple @t2 @t42 @t1))))) % 0.39/0.81 (assume @p50 (forall @t8 (= (tptp.findmin_cpq_res @t30) tptp.bottom))) % 0.39/0.81 (assume @p51 (forall @t23 (=> @t46 (= (tptp.findmin_cpq_res @t31) @t41)))) % 0.39/0.81 (assume @p52 (forall @t9 (= (tptp.removemin_cpq_eff @t2) (tptp.remove_cpq (tptp.findmin_cpq_eff @t2) @t48)))) % 0.39/0.81 (assume @p53 (forall @t9 (= (tptp.removemin_cpq_res @t2) @t48))) % 0.39/0.81 (assume @p54 @t50) % 0.39/0.81 (assume @p55 (forall @t25 (= (tptp.i @t32) @t51))) % 0.39/0.81 (assume @p56 (forall @t8 (= (tptp.pi_sharp_remove @t2 @t3) @t15))) % 0.39/0.81 (assume @p57 (forall @t8 (= (tptp.pi_remove @t2 @t3) (tptp.pi_sharp_remove @t52 @t3)))) % 0.39/0.81 (assume @p58 (forall @t8 (= (tptp.pi_sharp_find_min @t2 @t3) @t16))) % 0.39/0.81 (assume @p59 (forall @t9 (= (tptp.pi_find_min @t2) @t54))) % 0.39/0.81 (assume @p60 (forall @t8 (= (tptp.pi_sharp_removemin @t2 @t3) @t16))) % 0.39/0.81 (assume @p61 (forall @t9 (= (tptp.pi_removemin @t2) @t54))) % 0.39/0.81 (assume @p62 (forall @t9 (= (tptp.phi @t2) (exists @t53 (and @t29 (tptp.ok @t3) (tptp.check_cpq @t3)))))) % 0.39/0.81 (assume @p63 @t79) % 0.39/0.81 (assume @p64 @t82) % 0.39/0.81 (assume @p65 true) % 0.39/0.81 (step @p66 :rule eq-symm :args (@t80 @t51)) % 0.39/0.81 (step @p67 :rule cong :premises (@p66) :args (@t81)) % 0.39/0.81 (step @p68 :rule cong :premises (@p67) :args (@t82)) % 0.39/0.81 (step @p69 :rule eq_resolve :premises (@p64 @p68)) % 0.39/0.81 (step @p70 :rule skolemize :premises (@p69)) % 0.39/0.81 (step @p71 :rule instantiate :premises (@p42) :args ((@list @t87 @t86 @t85 @t84))) % 0.39/0.81 (step @p72 :rule instantiate :premises (@p55) :args ((@list @t88 @t86 @t85 @t84 tptp.bottom))) % 0.39/0.81 (step @p73 :rule bool-double-not-elim :args (@t101)) % 0.39/0.81 (step @p74 :rule refl :args (@t113)) % 0.39/0.81 (step @p75 :rule nary_cong :premises (@p74 @p73) :args ((or @t113 (not @t112)))) % 0.39/0.81 (step @p76 :rule cnf_or_neg :args (@t113 0)) % 0.39/0.81 (step @p77 :rule eq_resolve :premises (@p76 @p75)) % 0.39/0.81 (step @p78 :rule reordering :premises (@p77) :args ((or @t101 @t113))) % 0.39/0.81 (step @p79 :rule cnf_or_neg :args (@t113 1)) % 0.39/0.81 (step @p80 :rule eq-symm :args (@t114 @t115)) % 0.39/0.81 (step @p81 :rule refl :args (@t101)) % 0.39/0.81 (step @p82 :rule cong :premises (@p81 @p80) :args ((=> @t101 @t116))) % 0.39/0.81 (assume-push @p199 @t101) % 0.39/0.81 (step @p84 :rule instantiate :premises (@p199) :args ((@list @t109 @t106 @t108 @t102))) % 0.39/0.81 (step-pop @p200 :rule scope :premises (@p84)) % 0.39/0.81 (step @p85 :rule process_scope :premises (@p200) :args (@t116)) % 0.39/0.81 (step @p87 :rule eq_resolve :premises (@p85 @p82)) % 0.39/0.81 (step @p88 :rule implies_elim :premises (@p87)) % 0.39/0.81 (step @p89 :rule instantiate :premises (@p55) :args ((@list @t106 @t100 @t102 @t104 @t103))) % 0.39/0.81 (step @p90 :rule instantiate :premises (@p55) :args ((@list @t109 @t100 @t108 @t104 @t103))) % 0.39/0.81 (assume-push @p201 @t117) % 0.39/0.81 (assume-push @p202 @t119) % 0.39/0.81 (assume-push @p203 @t120) % 0.39/0.81 (assume-push @p204 @t117) % 0.39/0.81 (assume-push @p205 @t120) % 0.39/0.81 (assume-push @p206 @t119) % 0.39/0.81 (step @p97 :rule symm :premises (@p89)) % 0.39/0.81 (step @p98 :rule refl :args (@t104)) % 0.39/0.81 (step @p99 :rule symm :premises (@p203)) % 0.39/0.81 (step @p100 :rule cong :premises (@p99 @p98) :args (@t118)) % 0.39/0.81 (step @p101 :rule trans :premises (@p90 @p100 @p97)) % 0.39/0.81 (step-pop @p207 :rule scope :premises (@p101)) % 0.39/0.81 (step-pop @p208 :rule scope :premises (@p207)) % 0.39/0.81 (step-pop @p209 :rule scope :premises (@p208)) % 0.39/0.81 (step @p102 :rule process_scope :premises (@p209) :args (@t111)) % 0.39/0.81 (step @p106 :rule and_intro :premises (@p89 @p203 @p90)) % 0.39/0.81 (step @p107 :rule modus_ponens :premises (@p106 @p102)) % 0.39/0.81 (step-pop @p210 :rule scope :premises (@p107)) % 0.39/0.81 (step-pop @p211 :rule scope :premises (@p210)) % 0.39/0.81 (step-pop @p212 :rule scope :premises (@p211)) % 0.39/0.81 (step @p108 :rule process_scope :premises (@p212) :args (@t111)) % 0.39/0.81 (step @p112 :rule implies_elim :premises (@p108)) % 0.39/0.81 (step @p113 :rule cnf_and_neg :args (@t121)) % 0.39/0.81 (step @p114 :rule resolution :premises (@p113 @p112) :args (true @t121)) % 0.39/0.81 (step @p115 :rule reordering :premises (@p114) :args ((or @t111 (not @t117) (not @t119) (not @t120)))) % 0.39/0.81 (step @p116 :rule chain_m_resolution :premises (@p115 @p90 @p89 @p88 @p79 @p78) :args (@t113 (@list false false false true false) (@list @t119 @t117 @t120 @t111 @t101))) % 0.39/0.81 (step @p117 :rule refl :args (@t122)) % 0.39/0.81 (step @p118 :rule bool-double-not-elim :args (@t99)) % 0.39/0.81 (step @p119 :rule nary_cong :premises (@p118 @p117) :args ((or (not @t123) @t122))) % 0.39/0.81 (assume-push @p213 @t123) % 0.39/0.81 (step @p121 :rule skolemize :premises (@p213)) % 0.39/0.81 (step-pop @p214 :rule scope :premises (@p121)) % 0.39/0.81 (step @p122 :rule process_scope :premises (@p214) :args (@t122)) % 0.39/0.81 (step @p124 :rule implies_elim :premises (@p122)) % 0.39/0.81 (step @p125 :rule eq_resolve :premises (@p124 @p119)) % 0.39/0.81 (step @p126 :rule chain_m_resolution :premises (@p125 @p116) :args (@t99 @t124 (@list @t113))) % 0.39/0.81 (step @p127 :rule eq-symm :args (@t49 tptp.create_pq)) % 0.39/0.81 (step @p128 :rule cong :premises (@p127) :args (@t50)) % 0.39/0.81 (step @p129 :rule eq_resolve :premises (@p54 @p128)) % 0.39/0.81 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t126 @t125))) % 0.39/0.81 (step @p131 :rule instantiate :premises (@p129) :args ((@list @t128 @t127))) % 0.39/0.81 (step @p132 :rule symm :premises (@p131)) % 0.39/0.81 (step @p133 :rule trans :premises (@p132 @p130)) % 0.39/0.81 (step @p134 :rule refl :args (@t130)) % 0.39/0.81 (step @p135 :rule bool-double-not-elim :args (@t77)) % 0.39/0.81 (step @p136 :rule nary_cong :premises (@p135 @p134) :args ((or (not @t131) @t130))) % 0.39/0.81 (assume-push @p215 @t131) % 0.39/0.81 (step @p138 :rule skolemize :premises (@p215)) % 0.39/0.81 (step-pop @p216 :rule scope :premises (@p138)) % 0.39/0.81 (step @p139 :rule process_scope :premises (@p216) :args (@t130)) % 0.39/0.81 (step @p141 :rule implies_elim :premises (@p139)) % 0.39/0.81 (step @p142 :rule eq_resolve :premises (@p141 @p136)) % 0.39/0.81 (step @p143 :rule chain_m_resolution :premises (@p142 @p133) :args (@t77 @t124 (@list @t129))) % 0.39/0.81 (step @p144 :rule cnf_and_neg :args (@t132)) % 0.39/0.81 (step @p145 :rule chain_m_resolution :premises (@p144 @p143 @p126) :args (@t132 (@list false false) (@list @t77 @t99))) % 0.39/0.81 (step @p146 :rule refl :args (@t60)) % 0.39/0.81 (step @p147 :rule quant-merge-prenex :args ((= (forall @t75 @t134) @t99))) % 0.39/0.81 (step @p148 :rule alpha_equiv :args (@t135 (@list @t95 @t93 @t94 @t89 @t91 @t90) (@list @t67 @t65 @t66 @t61 @t63 @t62))) % 0.39/0.81 (step @p149 :rule refl :args (@t97)) % 0.39/0.81 (step @p150 :rule nary_cong :premises (@p149 @p148) :args (@t136)) % 0.39/0.81 (step @p151 :rule quant-miniscope-or :args ((= @t134 @t136))) % 0.39/0.81 (step @p152 :rule trans :premises (@p151 @p150)) % 0.39/0.81 (step @p153 :rule symm :premises (@p152)) % 0.39/0.81 (step @p154 :rule cong :premises (@p153) :args ((forall @t75 (or @t97 @t68)))) % 0.39/0.81 (step @p155 :rule trans :premises (@p154 @p147)) % 0.39/0.81 (step @p156 :rule bool-impl-elim :args (@t74 @t68)) % 0.39/0.81 (step @p157 :rule cong :premises (@p156) :args (@t76)) % 0.39/0.81 (step @p158 :rule trans :premises (@p157 @p155)) % 0.39/0.81 (step @p159 :rule refl :args (@t77)) % 0.39/0.81 (step @p160 :rule nary_cong :premises (@p159 @p158) :args (@t78)) % 0.39/0.81 (step @p161 :rule cong :premises (@p160 @p146) :args (@t79)) % 0.39/0.81 (step @p162 :rule eq_resolve :premises (@p63 @p161)) % 0.39/0.82 (step @p163 :rule implies_elim :premises (@p162)) % 0.39/0.82 (step @p164 :rule reordering :premises (@p163) :args ((or @t60 (not @t132)))) % 0.39/0.82 (step @p165 :rule chain_m_resolution :premises (@p164 @p145) :args (@t60 @t124 (@list @t132))) % 0.39/0.82 (assume-push @p217 @t60) % 0.39/0.82 (step @p167 :rule instantiate :premises (@p217) :args ((@list @t87 @t88 @t86 @t85 @t85))) % 0.39/0.82 (step-pop @p218 :rule scope :premises (@p167)) % 0.39/0.82 (step @p168 :rule process_scope :premises (@p218) :args (@t140)) % 0.39/0.82 (step @p170 :rule implies_elim :premises (@p168)) % 0.39/0.82 (step @p171 :rule chain_m_resolution :premises (@p170 @p165) :args (@t140 @t124 (@list @t60))) % 0.39/0.82 (assume-push @p219 @t143) % 0.39/0.82 (assume-push @p220 @t145) % 0.39/0.82 (assume-push @p221 @t140) % 0.39/0.82 (assume-push @p222 @t143) % 0.39/0.82 (assume-push @p223 @t145) % 0.39/0.82 (assume-push @p224 @t140) % 0.39/0.82 (step @p178 :rule symm :premises (@p71)) % 0.39/0.82 (step @p179 :rule cong :premises (@p178) :args (@t144)) % 0.39/0.82 (step @p180 :rule symm :premises (@p72)) % 0.39/0.82 (step @p181 :rule refl :args (@t84)) % 0.39/0.82 (step @p182 :rule cong :premises (@p221 @p181) :args (@t146)) % 0.39/0.82 (step @p183 :rule trans :premises (@p182 @p180 @p179)) % 0.39/0.82 (step-pop @p225 :rule scope :premises (@p183)) % 0.39/0.82 (step-pop @p226 :rule scope :premises (@p225)) % 0.39/0.82 (step-pop @p227 :rule scope :premises (@p226)) % 0.39/0.82 (step @p184 :rule process_scope :premises (@p227) :args (@t147)) % 0.39/0.82 (step @p188 :rule and_intro :premises (@p71 @p72 @p221)) % 0.39/0.82 (step @p189 :rule modus_ponens :premises (@p188 @p184)) % 0.39/0.82 (step-pop @p228 :rule scope :premises (@p189)) % 0.39/0.82 (step-pop @p229 :rule scope :premises (@p228)) % 0.39/0.82 (step-pop @p230 :rule scope :premises (@p229)) % 0.39/0.82 (step @p190 :rule process_scope :premises (@p230) :args (@t147)) % 0.39/0.82 (step @p194 :rule implies_elim :premises (@p190)) % 0.39/0.82 (step @p195 :rule cnf_and_neg :args (@t148)) % 0.39/0.82 (step @p196 :rule resolution :premises (@p195 @p194) :args (true @t148)) % 0.39/0.82 (step @p197 :rule reordering :premises (@p196) :args ((or @t147 (not @t143) (not @t145) (not @t140)))) % 0.39/0.82 (step @p198 false :rule chain_m_resolution :premises (@p197 @p171 @p72 @p71 @p70) :args (false (@list false false false true) (@list @t140 @t145 @t143 @t147))) % 0.39/0.82 ) % 0.39/0.82 % SZS output end Proof % 0.39/0.82 % cvc5 exiting %------------------------------------------------------------------------------