%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV370+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 : n026.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 09:01:18 AM UTC 2026 % Result : Theorem 0.39s 0.65s % Output : Proof 0.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWV370+1 : 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 % 0.17/0.35 % Computer : n026.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Tue Jun 2 20:06:10 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.52 %----Proving TF0_NAR, FOF, or CNF % 0.39/0.65 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.39/0.65 % SZS status Theorem % 0.39/0.65 % SZS output start Proof % 0.39/0.65 ( % 0.39/0.65 (declare-sort $$unsorted 0) % 0.39/0.65 (declare-const tptp.phi (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.pi_removemin (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.pi_sharp_removemin (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.pi_find_min (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.pi_remove (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.i (-> $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.removemin_cpq_res (-> $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.insert_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.ok (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.findmin_pqp_res (-> $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.removemin_pq_res (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.removemin_pq_eff (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.pi_sharp_remove (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.check_cpq (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.remove_pq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.insert_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.findmin_pq_res (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.remove_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.issmallestelement_pq (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.strictly_less_than (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.isnonempty_pq (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.findmin_pq_eff (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.contains_pq (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.isnonempty_slb (-> $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.remove_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.findmin_cpq_eff (-> $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.pi_sharp_find_min (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.create_pq $$unsorted) % 0.39/0.65 (declare-const tptp.lookup_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.bottom $$unsorted) % 0.39/0.65 (declare-const tptp.insert_pq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.update_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.contains_cpq (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.create_slb $$unsorted) % 0.39/0.65 (declare-const tptp.less_than (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.pair (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.bad $$unsorted) % 0.39/0.65 (declare-const tptp.insert_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.contains_slb (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.pair_in_list (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.remove_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.findmin_cpq_res (-> $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.succ_cpq (-> $$unsorted $$unsorted Bool)) % 0.39/0.65 (declare-const tptp.removemin_cpq_eff (-> $$unsorted $$unsorted)) % 0.39/0.65 (declare-const tptp.triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.39/0.65 (define @t1 () (@var "W" $$unsorted)) % 0.39/0.65 (define @t2 () (@var "U" $$unsorted)) % 0.39/0.65 (define @t3 () (@var "V" $$unsorted)) % 0.39/0.65 (define @t4 () (tptp.less_than @t3 @t1)) % 0.39/0.65 (define @t5 () (tptp.less_than @t2 @t3)) % 0.39/0.65 (define @t6 () (@list @t2 @t3 @t1)) % 0.39/0.65 (define @t7 () (tptp.less_than @t3 @t2)) % 0.39/0.65 (define @t8 () (@list @t2 @t3)) % 0.39/0.65 (define @t9 () (@list @t2)) % 0.39/0.65 (define @t10 () (tptp.insert_pq @t2 @t3)) % 0.39/0.65 (define @t11 () (= @t3 @t1)) % 0.39/0.65 (define @t12 () (tptp.contains_pq @t2 @t1)) % 0.39/0.65 (define @t13 () (tptp.issmallestelement_pq @t2 @t3)) % 0.39/0.65 (define @t14 () (not @t11)) % 0.39/0.65 (define @t15 () (tptp.contains_pq @t2 @t3)) % 0.39/0.65 (define @t16 () (and @t15 @t13)) % 0.39/0.65 (define @t17 () (tptp.pair @t3 @t1)) % 0.39/0.65 (define @t18 () (tptp.insert_slb @t2 @t17)) % 0.39/0.65 (define @t19 () (tptp.contains_slb @t2 @t1)) % 0.39/0.65 (define @t20 () (@var "X" $$unsorted)) % 0.39/0.65 (define @t21 () (tptp.pair @t3 @t20)) % 0.39/0.65 (define @t22 () (tptp.insert_slb @t2 @t21)) % 0.39/0.65 (define @t23 () (@list @t2 @t3 @t1 @t20)) % 0.39/0.65 (define @t24 () (@var "Y" $$unsorted)) % 0.39/0.65 (define @t25 () (@list @t2 @t3 @t1 @t20 @t24)) % 0.39/0.65 (define @t26 () (and @t14 @t19)) % 0.39/0.65 (define @t27 () (tptp.update_slb @t2 @t1)) % 0.39/0.65 (define @t28 () (tptp.update_slb @t22 @t1)) % 0.39/0.65 (define @t29 () (tptp.succ_cpq @t2 @t3)) % 0.39/0.65 (define @t30 () (tptp.triple @t2 tptp.create_slb @t3)) % 0.39/0.65 (define @t31 () (tptp.triple @t2 @t3 @t1)) % 0.39/0.65 (define @t32 () (tptp.triple @t2 (tptp.insert_slb @t3 (tptp.pair @t20 @t24)) @t1)) % 0.39/0.65 (define @t33 () (tptp.check_cpq @t32)) % 0.39/0.65 (define @t34 () (tptp.contains_slb @t3 @t20)) % 0.39/0.65 (define @t35 () (forall @t23 (= (tptp.contains_cpq @t31 @t20) @t34))) % 0.39/0.65 (define @t36 () (tptp.triple @t2 @t3 tptp.bad)) % 0.39/0.65 (define @t37 () (tptp.remove_cpq @t31 @t20)) % 0.39/0.65 (define @t38 () (tptp.remove_slb @t3 @t20)) % 0.39/0.65 (define @t39 () (tptp.remove_pqp @t2 @t20)) % 0.39/0.65 (define @t40 () (tptp.lookup_slb @t3 @t20)) % 0.39/0.65 (define @t41 () (tptp.findmin_pqp_res @t2)) % 0.39/0.65 (define @t42 () (tptp.update_slb @t3 @t41)) % 0.39/0.65 (define @t43 () (tptp.findmin_cpq_eff @t31)) % 0.39/0.65 (define @t44 () (= @t43 (tptp.triple @t2 @t42 tptp.bad))) % 0.39/0.65 (define @t45 () (tptp.contains_slb @t3 @t41)) % 0.39/0.65 (define @t46 () (not (= @t3 tptp.create_slb))) % 0.39/0.65 (define @t47 () (tptp.lookup_slb @t3 @t41)) % 0.39/0.65 (define @t48 () (tptp.findmin_cpq_res @t2)) % 0.39/0.65 (define @t49 () (tptp.i @t2)) % 0.39/0.65 (define @t50 () (@list @t3)) % 0.39/0.65 (define @t51 () (exists @t50 (tptp.pi_sharp_find_min @t49 @t3))) % 0.39/0.65 (define @t52 () (@var "X3" $$unsorted)) % 0.39/0.65 (define @t53 () (@var "Z" $$unsorted)) % 0.39/0.65 (define @t54 () (@var "X2" $$unsorted)) % 0.39/0.65 (define @t55 () (@var "X1" $$unsorted)) % 0.39/0.65 (define @t56 () (tptp.triple @t24 (tptp.insert_slb @t2 (tptp.pair @t55 @t54)) @t53)) % 0.39/0.65 (define @t57 () (forall (@list @t24 @t53 @t55 @t54 @t52) (= (tptp.contains_cpq @t56 @t52) (tptp.contains_pq (tptp.i @t56) @t52)))) % 0.39/0.65 (define @t58 () (tptp.triple @t3 @t2 @t1)) % 0.39/0.65 (define @t59 () (@list @t3 @t1 @t20)) % 0.39/0.65 (define @t60 () (forall @t59 (= (tptp.contains_cpq @t58 @t20) (tptp.contains_pq (tptp.i @t58) @t20)))) % 0.39/0.65 (define @t61 () (forall @t9 (=> @t60 @t57))) % 0.39/0.65 (define @t62 () (not @t61)) % 0.39/0.65 (define @t63 () (@var "BOUND_VARIABLE_7978" $$unsorted)) % 0.39/0.65 (define @t64 () (@var "BOUND_VARIABLE_7972" $$unsorted)) % 0.39/0.65 (define @t65 () (@var "BOUND_VARIABLE_7976" $$unsorted)) % 0.39/0.65 (define @t66 () (@var "BOUND_VARIABLE_7974" $$unsorted)) % 0.39/0.65 (define @t67 () (@var "BOUND_VARIABLE_7970" $$unsorted)) % 0.39/0.65 (define @t68 () (tptp.triple @t67 (tptp.insert_slb @t2 (tptp.pair @t66 @t65)) @t64)) % 0.39/0.65 (define @t69 () (= (tptp.contains_cpq @t68 @t63) (tptp.contains_pq (tptp.i @t68) @t63))) % 0.39/0.65 (define @t70 () (not @t60)) % 0.39/0.65 (define @t71 () (or @t70 @t69)) % 0.39/0.65 (define @t72 () (forall (@list @t2 @t67 @t64 @t66 @t65 @t63) @t71)) % 0.39/0.65 (define @t73 () (@quantifiers_skolemize @t72 4)) % 0.39/0.65 (define @t74 () (@quantifiers_skolemize @t72 3)) % 0.39/0.65 (define @t75 () (@quantifiers_skolemize @t72 2)) % 0.39/0.65 (define @t76 () (@quantifiers_skolemize @t72 0)) % 0.39/0.65 (define @t77 () (@quantifiers_skolemize @t72 1)) % 0.39/0.65 (define @t78 () (@list @t67 @t64 @t66 @t65 @t63)) % 0.39/0.65 (define @t79 () (forall @t78 @t71)) % 0.39/0.65 (define @t80 () (forall @t78 @t69)) % 0.39/0.65 (define @t81 () (or @t70 @t80)) % 0.39/0.65 (define @t82 () (@quantifiers_skolemize @t72 5)) % 0.39/0.65 (define @t83 () (tptp.insert_slb @t76 (tptp.pair @t74 @t73))) % 0.39/0.65 (define @t84 () (tptp.triple @t77 @t83 @t75)) % 0.39/0.65 (define @t85 () (tptp.i @t84)) % 0.39/0.65 (define @t86 () (tptp.contains_pq @t85 @t82)) % 0.39/0.65 (define @t87 () (tptp.contains_cpq @t84 @t82)) % 0.39/0.65 (define @t88 () (= @t87 @t86)) % 0.39/0.65 (define @t89 () (tptp.triple @t3 @t76 @t1)) % 0.39/0.65 (define @t90 () (forall @t59 (= (tptp.contains_cpq @t89 @t20) (tptp.contains_pq (tptp.i @t89) @t20)))) % 0.39/0.65 (define @t91 () (not @t90)) % 0.39/0.65 (define @t92 () (or @t91 @t88)) % 0.39/0.65 (define @t93 () (@list true)) % 0.39/0.65 (define @t94 () (@list @t92)) % 0.39/0.65 (define @t95 () (tptp.triple @t77 @t76 @t75)) % 0.39/0.65 (define @t96 () (tptp.i @t95)) % 0.39/0.65 (define @t97 () (tptp.insert_pq @t96 @t74)) % 0.39/0.65 (define @t98 () (= @t85 @t97)) % 0.39/0.65 (define @t99 () (tptp.contains_pq @t97 @t82)) % 0.39/0.65 (define @t100 () (and @t98 @t99)) % 0.39/0.65 (define @t101 () (not @t99)) % 0.39/0.65 (define @t102 () (tptp.contains_slb @t83 @t82)) % 0.39/0.65 (define @t103 () (= @t87 @t102)) % 0.39/0.65 (define @t104 () (not @t103)) % 0.39/0.65 (define @t105 () (not @t87)) % 0.39/0.65 (define @t106 () (= @t74 @t82)) % 0.39/0.65 (define @t107 () (tptp.contains_pq @t96 @t82)) % 0.39/0.65 (define @t108 () (or @t107 @t106)) % 0.39/0.65 (define @t109 () (= @t99 @t108)) % 0.39/0.65 (define @t110 () (not @t109)) % 0.39/0.65 (define @t111 () (not @t108)) % 0.39/0.65 (define @t112 () (tptp.contains_slb @t76 @t82)) % 0.39/0.65 (define @t113 () (or @t112 @t106)) % 0.39/0.65 (define @t114 () (= @t102 @t113)) % 0.39/0.65 (define @t115 () (not @t114)) % 0.39/0.65 (define @t116 () (not @t102)) % 0.39/0.65 (define @t117 () (tptp.contains_cpq @t95 @t82)) % 0.39/0.65 (define @t118 () (= @t117 @t112)) % 0.39/0.65 (define @t119 () (= @t112 @t117)) % 0.39/0.65 (define @t120 () (@list false)) % 0.39/0.65 (define @t121 () (= @t117 @t107)) % 0.39/0.65 (define @t122 () (= @t107 @t117)) % 0.39/0.65 (define @t123 () (not @t122)) % 0.39/0.65 (define @t124 () (not @t107)) % 0.39/0.65 (define @t125 () (not @t119)) % 0.39/0.65 (define @t126 () (not @t117)) % 0.39/0.65 (define @t127 () (not @t113)) % 0.39/0.65 (define @t128 () (@list true false)) % 0.39/0.65 (define @t129 () (not @t112)) % 0.39/0.65 (define @t130 () (and @t86 @t98)) % 0.39/0.65 (assume @p1 (forall @t6 (=> (and @t5 @t4) (tptp.less_than @t2 @t1)))) % 0.39/0.65 (assume @p2 (forall @t8 (or @t5 @t7))) % 0.39/0.65 (assume @p3 (forall @t9 (tptp.less_than @t2 @t2))) % 0.39/0.65 (assume @p4 (forall @t8 (= (tptp.strictly_less_than @t2 @t3) (and @t5 (not @t7))))) % 0.39/0.65 (assume @p5 (forall @t9 (tptp.less_than tptp.bottom @t2))) % 0.39/0.65 (assume @p6 (not (tptp.isnonempty_pq tptp.create_pq))) % 0.39/0.65 (assume @p7 (forall @t8 (tptp.isnonempty_pq @t10))) % 0.39/0.65 (assume @p8 (forall @t9 (not (tptp.contains_pq tptp.create_pq @t2)))) % 0.39/0.65 (assume @p9 (forall @t6 (= (tptp.contains_pq @t10 @t1) (or @t12 @t11)))) % 0.39/0.65 (assume @p10 (forall @t8 (= @t13 (forall (@list @t1) (=> @t12 @t4))))) % 0.39/0.65 (assume @p11 (forall @t8 (= (tptp.remove_pq @t10 @t3) @t2))) % 0.39/0.65 (assume @p12 (forall @t6 (=> (and @t12 @t14) (= (tptp.remove_pq @t10 @t1) (tptp.insert_pq (tptp.remove_pq @t2 @t1) @t3))))) % 0.39/0.65 (assume @p13 (forall @t8 (=> @t16 (= (tptp.findmin_pq_eff @t2 @t3) @t2)))) % 0.39/0.65 (assume @p14 (forall @t8 (=> @t16 (= (tptp.findmin_pq_res @t2 @t3) @t3)))) % 0.39/0.65 (assume @p15 (forall @t8 (=> @t16 (= (tptp.removemin_pq_eff @t2 @t3) (tptp.remove_pq @t2 @t3))))) % 0.39/0.65 (assume @p16 (forall @t8 (=> @t16 (= (tptp.removemin_pq_res @t2 @t3) @t3)))) % 0.39/0.65 (assume @p17 (forall @t6 (= (tptp.insert_pq @t10 @t1) (tptp.insert_pq (tptp.insert_pq @t2 @t1) @t3)))) % 0.39/0.65 (assume @p18 (not (tptp.isnonempty_slb tptp.create_slb))) % 0.39/0.65 (assume @p19 (forall @t6 (tptp.isnonempty_slb @t18))) % 0.39/0.65 (assume @p20 (forall @t9 (not (tptp.contains_slb tptp.create_slb @t2)))) % 0.39/0.65 (assume @p21 (forall @t23 (= (tptp.contains_slb @t22 @t1) (or @t19 @t11)))) % 0.39/0.65 (assume @p22 (forall @t8 (not (tptp.pair_in_list tptp.create_slb @t2 @t3)))) % 0.39/0.65 (assume @p23 (forall @t25 (= (tptp.pair_in_list @t22 @t1 @t24) (or (tptp.pair_in_list @t2 @t1 @t24) (and @t11 (= @t20 @t24)))))) % 0.39/0.65 (assume @p24 (forall @t6 (= (tptp.remove_slb @t18 @t3) @t2))) % 0.39/0.65 (assume @p25 (forall @t23 (=> @t26 (= (tptp.remove_slb @t22 @t1) (tptp.insert_slb (tptp.remove_slb @t2 @t1) @t21))))) % 0.39/0.65 (assume @p26 (forall @t6 (= (tptp.lookup_slb @t18 @t3) @t1))) % 0.39/0.65 (assume @p27 (forall @t23 (=> @t26 (= (tptp.lookup_slb @t22 @t1) (tptp.lookup_slb @t2 @t1))))) % 0.39/0.65 (assume @p28 (forall @t9 (= (tptp.update_slb tptp.create_slb @t2) tptp.create_slb))) % 0.39/0.65 (assume @p29 (forall @t23 (=> (tptp.strictly_less_than @t20 @t1) (= @t28 (tptp.insert_slb @t27 @t17))))) % 0.39/0.65 (assume @p30 (forall @t23 (=> (tptp.less_than @t1 @t20) (= @t28 (tptp.insert_slb @t27 @t21))))) % 0.39/0.65 (assume @p31 (forall @t9 (tptp.succ_cpq @t2 @t2))) % 0.39/0.65 (assume @p32 (forall @t6 (=> @t29 (tptp.succ_cpq @t2 (tptp.insert_cpq @t3 @t1))))) % 0.39/0.65 (assume @p33 (forall @t6 (=> @t29 (tptp.succ_cpq @t2 (tptp.remove_cpq @t3 @t1))))) % 0.39/0.65 (assume @p34 (forall @t8 (=> @t29 (tptp.succ_cpq @t2 (tptp.findmin_cpq_eff @t3))))) % 0.39/0.65 (assume @p35 (forall @t8 (=> @t29 (tptp.succ_cpq @t2 (tptp.removemin_cpq_eff @t3))))) % 0.39/0.65 (assume @p36 (forall @t8 (tptp.check_cpq @t30))) % 0.39/0.65 (assume @p37 (forall @t25 (=> (tptp.less_than @t24 @t20) (= @t33 (tptp.check_cpq @t31))))) % 0.39/0.65 (assume @p38 (forall @t25 (=> (tptp.strictly_less_than @t20 @t24) (= @t33 false)))) % 0.39/0.65 (assume @p39 @t35) % 0.39/0.65 (assume @p40 (forall @t8 (= (tptp.ok @t36) false))) % 0.39/0.65 (assume @p41 (forall @t6 (=> (not (tptp.ok @t31)) (= @t1 tptp.bad)))) % 0.39/0.65 (assume @p42 (forall @t23 (= (tptp.insert_cpq @t31 @t20) (tptp.triple (tptp.insert_pqp @t2 @t20) (tptp.insert_slb @t3 (tptp.pair @t20 tptp.bottom)) @t1)))) % 0.39/0.65 (assume @p43 (forall @t23 (=> (not @t34) (= @t37 @t36)))) % 0.39/0.65 (assume @p44 (forall @t23 (=> (and @t34 (tptp.less_than @t40 @t20)) (= @t37 (tptp.triple @t39 @t38 @t1))))) % 0.39/0.65 (assume @p45 (forall @t23 (=> (and @t34 (tptp.strictly_less_than @t20 @t40)) (= @t37 (tptp.triple @t39 @t38 tptp.bad))))) % 0.39/0.65 (assume @p46 (forall @t8 (= (tptp.findmin_cpq_eff @t30) (tptp.triple @t2 tptp.create_slb tptp.bad)))) % 0.39/0.65 (assume @p47 (forall @t23 (=> (and @t46 (not @t45)) @t44))) % 0.39/0.65 (assume @p48 (forall @t23 (=> (and @t46 @t45 (tptp.strictly_less_than @t41 @t47)) @t44))) % 0.39/0.65 (assume @p49 (forall @t23 (=> (and @t46 @t45 (tptp.less_than @t47 @t41)) (= @t43 (tptp.triple @t2 @t42 @t1))))) % 0.39/0.65 (assume @p50 (forall @t8 (= (tptp.findmin_cpq_res @t30) tptp.bottom))) % 0.39/0.65 (assume @p51 (forall @t23 (=> @t46 (= (tptp.findmin_cpq_res @t31) @t41)))) % 0.39/0.65 (assume @p52 (forall @t9 (= (tptp.removemin_cpq_eff @t2) (tptp.remove_cpq (tptp.findmin_cpq_eff @t2) @t48)))) % 0.39/0.65 (assume @p53 (forall @t9 (= (tptp.removemin_cpq_res @t2) @t48))) % 0.39/0.65 (assume @p54 (forall @t8 (= (tptp.i @t30) tptp.create_pq))) % 0.39/0.65 (assume @p55 (forall @t25 (= (tptp.i @t32) (tptp.insert_pq (tptp.i @t31) @t20)))) % 0.39/0.65 (assume @p56 (forall @t8 (= (tptp.pi_sharp_remove @t2 @t3) @t15))) % 0.39/0.65 (assume @p57 (forall @t8 (= (tptp.pi_remove @t2 @t3) (tptp.pi_sharp_remove @t49 @t3)))) % 0.39/0.65 (assume @p58 (forall @t8 (= (tptp.pi_sharp_find_min @t2 @t3) @t16))) % 0.39/0.65 (assume @p59 (forall @t9 (= (tptp.pi_find_min @t2) @t51))) % 0.39/0.65 (assume @p60 (forall @t8 (= (tptp.pi_sharp_removemin @t2 @t3) @t16))) % 0.39/0.65 (assume @p61 (forall @t9 (= (tptp.pi_removemin @t2) @t51))) % 0.39/0.65 (assume @p62 (forall @t9 (= (tptp.phi @t2) (exists @t50 (and @t29 (tptp.ok @t3) (tptp.check_cpq @t3)))))) % 0.39/0.65 (assume @p63 @t62) % 0.39/0.65 (assume @p64 true) % 0.39/0.65 (step @p65 :rule instantiate :premises (@p55) :args ((@list @t77 @t76 @t75 @t74 @t73))) % 0.39/0.65 (step @p66 :rule quant-merge-prenex :args ((= (forall @t9 @t79) @t72))) % 0.39/0.65 (step @p67 :rule alpha_equiv :args (@t80 (@list @t67 @t64 @t66 @t65 @t63) (@list @t24 @t53 @t55 @t54 @t52))) % 0.39/0.65 (step @p68 :rule refl :args (@t70)) % 0.39/0.65 (step @p69 :rule nary_cong :premises (@p68 @p67) :args (@t81)) % 0.39/0.65 (step @p70 :rule quant-miniscope-or :args ((= @t79 @t81))) % 0.39/0.65 (step @p71 :rule trans :premises (@p70 @p69)) % 0.39/0.65 (step @p72 :rule symm :premises (@p71)) % 0.39/0.65 (step @p73 :rule cong :premises (@p72) :args ((forall @t9 (or @t70 @t57)))) % 0.39/0.65 (step @p74 :rule trans :premises (@p73 @p66)) % 0.39/0.65 (step @p75 :rule bool-impl-elim :args (@t60 @t57)) % 0.39/0.65 (step @p76 :rule cong :premises (@p75) :args (@t61)) % 0.39/0.65 (step @p77 :rule trans :premises (@p76 @p74)) % 0.39/0.65 (step @p78 :rule cong :premises (@p77) :args (@t62)) % 0.39/0.65 (step @p79 :rule eq_resolve :premises (@p63 @p78)) % 0.39/0.65 (step @p80 :rule skolemize :premises (@p79)) % 0.39/0.65 (step @p81 :rule cnf_or_neg :args (@t92 1)) % 0.39/0.65 (step @p82 :rule chain_m_resolution :premises (@p81 @p80) :args ((not @t88) @t93 @t94)) % 0.39/0.65 (step @p83 :rule cnf_equiv_neg1 :args (@t88)) % 0.39/0.65 (step @p84 :rule reordering :premises (@p83) :args ((or @t87 @t86 @t88))) % 0.39/0.65 (assume-push @p196 @t98) % 0.39/0.65 (assume-push @p197 @t99) % 0.39/0.65 (assume-push @p198 @t99) % 0.39/0.65 (assume-push @p199 @t98) % 0.39/0.65 (step @p89 :rule true_intro :premises (@p197)) % 0.39/0.65 (step @p90 :rule refl :args (@t82)) % 0.39/0.65 (step @p91 :rule cong :premises (@p65 @p90) :args (@t86)) % 0.39/0.65 (step @p92 :rule trans :premises (@p91 @p89)) % 0.39/0.65 (step @p93 :rule true_elim :premises (@p92)) % 0.39/0.65 (step-pop @p200 :rule scope :premises (@p93)) % 0.39/0.65 (step-pop @p201 :rule scope :premises (@p200)) % 0.39/0.65 (step @p94 :rule process_scope :premises (@p201) :args (@t86)) % 0.39/0.65 (step @p97 :rule and_intro :premises (@p197 @p65)) % 0.39/0.65 (step @p98 :rule modus_ponens :premises (@p97 @p94)) % 0.39/0.65 (step-pop @p202 :rule scope :premises (@p98)) % 0.39/0.65 (step-pop @p203 :rule scope :premises (@p202)) % 0.39/0.65 (step @p99 :rule process_scope :premises (@p203) :args (@t86)) % 0.39/0.65 (step @p102 :rule implies_elim :premises (@p99)) % 0.39/0.65 (step @p103 :rule cnf_and_neg :args (@t100)) % 0.39/0.65 (step @p104 :rule resolution :premises (@p103 @p102) :args (true @t100)) % 0.39/0.65 (step @p105 :rule reordering :premises (@p104) :args ((or @t86 (not @t98) @t101))) % 0.39/0.65 (step @p106 :rule instantiate :premises (@p39) :args ((@list @t77 @t83 @t75 @t82))) % 0.39/0.65 (step @p107 :rule cnf_equiv_pos1 :args (@t103)) % 0.39/0.65 (step @p108 :rule reordering :premises (@p107) :args ((or @t105 @t102 @t104))) % 0.39/0.65 (step @p109 :rule instantiate :premises (@p9) :args ((@list @t96 @t74 @t82))) % 0.39/0.65 (step @p110 :rule cnf_equiv_pos2 :args (@t109)) % 0.39/0.65 (step @p111 :rule reordering :premises (@p110) :args ((or @t99 @t111 @t110))) % 0.39/0.65 (step @p112 :rule instantiate :premises (@p21) :args ((@list @t76 @t74 @t82 @t73))) % 0.39/0.65 (step @p113 :rule cnf_equiv_pos1 :args (@t114)) % 0.39/0.65 (step @p114 :rule reordering :premises (@p113) :args ((or @t116 @t113 @t115))) % 0.39/0.65 (step @p115 :rule cnf_or_neg :args (@t108 1)) % 0.39/0.65 (step @p116 :rule eq-symm :args (@t117 @t112)) % 0.39/0.65 (step @p117 :rule refl :args (@t35)) % 0.39/0.65 (step @p118 :rule cong :premises (@p117 @p116) :args ((=> @t35 @t118))) % 0.39/0.65 (assume-push @p204 @t35) % 0.39/0.65 (step @p120 :rule instantiate :premises (@p39) :args ((@list @t77 @t76 @t75 @t82))) % 0.39/0.65 (step-pop @p205 :rule scope :premises (@p120)) % 0.39/0.65 (step @p121 :rule process_scope :premises (@p205) :args (@t118)) % 0.39/0.65 (step @p123 :rule eq_resolve :premises (@p121 @p118)) % 0.39/0.65 (step @p124 :rule implies_elim :premises (@p123)) % 0.39/0.65 (step @p125 :rule chain_m_resolution :premises (@p124 @p39) :args (@t119 @t120 (@list @t35))) % 0.39/0.65 (step @p126 :rule bool-double-not-elim :args (@t90)) % 0.39/0.65 (step @p127 :rule refl :args (@t92)) % 0.39/0.65 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t92 (not @t91)))) % 0.39/0.65 (step @p129 :rule cnf_or_neg :args (@t92 0)) % 0.39/0.65 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 0.39/0.65 (step @p131 :rule reordering :premises (@p130) :args ((or @t90 @t92))) % 0.39/0.65 (step @p132 :rule chain_m_resolution :premises (@p131 @p80) :args (@t90 @t93 @t94)) % 0.39/0.65 (step @p133 :rule eq-symm :args (@t117 @t107)) % 0.39/0.65 (step @p134 :rule refl :args (@t90)) % 0.39/0.65 (step @p135 :rule cong :premises (@p134 @p133) :args ((=> @t90 @t121))) % 0.39/0.65 (assume-push @p206 @t90) % 0.39/0.65 (step @p137 :rule instantiate :premises (@p132) :args ((@list @t77 @t75 @t82))) % 0.39/0.65 (step-pop @p207 :rule scope :premises (@p137)) % 0.39/0.65 (step @p138 :rule process_scope :premises (@p207) :args (@t121)) % 0.39/0.65 (step @p140 :rule eq_resolve :premises (@p138 @p135)) % 0.39/0.65 (step @p141 :rule implies_elim :premises (@p140)) % 0.39/0.65 (step @p142 :rule chain_m_resolution :premises (@p141 @p132) :args (@t122 @t120 (@list @t90))) % 0.39/0.65 (step @p143 :rule cnf_or_neg :args (@t108 0)) % 0.39/0.65 (step @p144 :rule cnf_equiv_pos1 :args (@t122)) % 0.39/0.65 (step @p145 :rule reordering :premises (@p144) :args ((or @t124 @t117 @t123))) % 0.39/0.65 (step @p146 :rule cnf_equiv_pos2 :args (@t119)) % 0.39/0.65 (step @p147 :rule reordering :premises (@p146) :args ((or @t112 @t126 @t125))) % 0.39/0.65 (step @p148 :rule cnf_or_neg :args (@t113 0)) % 0.39/0.65 (step @p149 :rule cnf_equiv_pos2 :args (@t114)) % 0.39/0.65 (step @p150 :rule reordering :premises (@p149) :args ((or @t102 @t127 @t115))) % 0.39/0.65 (step @p151 :rule cnf_equiv_pos2 :args (@t103)) % 0.39/0.65 (step @p152 :rule reordering :premises (@p151) :args ((or @t87 @t116 @t104))) % 0.39/0.65 (step @p153 :rule cnf_equiv_neg2 :args (@t88)) % 0.39/0.65 (step @p154 :rule chain_m_resolution :premises (@p105 @p65 @p153 @p82 @p152 @p106 @p150 @p112 @p148 @p147 @p125 @p111 @p109 @p145 @p142 @p143) :args (@t124 (@list false true true false false false false false false false false false false false false) (@list @t98 @t86 @t88 @t87 @t103 @t102 @t114 @t113 @t112 @t119 @t99 @t109 @t117 @t122 @t108))) % 0.39/0.65 (step @p155 :rule cnf_equiv_pos2 :args (@t122)) % 0.39/0.65 (step @p156 :rule reordering :premises (@p155) :args ((or @t107 @t126 @t123))) % 0.39/0.65 (step @p157 :rule chain_m_resolution :premises (@p156 @p154 @p142) :args (@t126 @t128 (@list @t107 @t122))) % 0.39/0.65 (step @p158 :rule cnf_equiv_pos1 :args (@t119)) % 0.39/0.65 (step @p159 :rule reordering :premises (@p158) :args ((or @t129 @t117 @t125))) % 0.39/0.65 (step @p160 :rule chain_m_resolution :premises (@p159 @p157 @p125) :args (@t129 @t128 (@list @t117 @t119))) % 0.39/0.65 (step @p161 :rule cnf_or_pos :args (@t113)) % 0.39/0.65 (step @p162 :rule reordering :premises (@p161) :args ((or @t106 @t112 @t127))) % 0.39/0.65 (step @p163 :rule chain_m_resolution :premises (@p162 @p160 @p115 @p114 @p112 @p111 @p109 @p108 @p106 @p105 @p65 @p84 @p82) :args (@t86 (@list true true false false true false false false true false false true) (@list @t112 @t106 @t113 @t114 @t108 @t109 @t102 @t103 @t99 @t98 @t87 @t88))) % 0.39/0.65 (step @p164 :rule chain_m_resolution :premises (@p153 @p82 @p163) :args (@t105 @t128 (@list @t88 @t86))) % 0.39/0.65 (step @p165 :rule chain_m_resolution :premises (@p152 @p164 @p106) :args (@t116 @t128 (@list @t87 @t103))) % 0.39/0.65 (step @p166 :rule chain_m_resolution :premises (@p150 @p165 @p112) :args (@t127 @t128 (@list @t102 @t114))) % 0.39/0.65 (step @p167 :rule cnf_or_neg :args (@t113 1)) % 0.39/0.65 (step @p168 :rule chain_m_resolution :premises (@p167 @p166) :args ((not @t106) @t93 (@list @t113))) % 0.39/0.65 (step @p169 :rule cnf_or_pos :args (@t108)) % 0.39/0.65 (step @p170 :rule reordering :premises (@p169) :args ((or @t107 @t106 @t111))) % 0.39/0.66 (step @p171 :rule chain_m_resolution :premises (@p170 @p154 @p168) :args (@t111 (@list true true) (@list @t107 @t106))) % 0.39/0.66 (step @p172 :rule cnf_equiv_pos1 :args (@t109)) % 0.39/0.66 (step @p173 :rule reordering :premises (@p172) :args ((or @t108 @t101 @t110))) % 0.39/0.66 (step @p174 :rule chain_m_resolution :premises (@p173 @p171 @p109) :args (@t101 @t128 (@list @t108 @t109))) % 0.39/0.66 (assume-push @p208 @t86) % 0.39/0.66 (assume-push @p209 @t98) % 0.39/0.66 (assume-push @p210 @t86) % 0.39/0.66 (assume-push @p211 @t98) % 0.39/0.66 (step @p179 :rule true_intro :premises (@p208)) % 0.39/0.66 (step @p90 :rule refl :args (@t82)) % 0.39/0.66 (step @p180 :rule symm :premises (@p65)) % 0.39/0.66 (step @p181 :rule cong :premises (@p180 @p90) :args (@t99)) % 0.39/0.66 (step @p182 :rule trans :premises (@p181 @p179)) % 0.39/0.66 (step @p183 :rule true_elim :premises (@p182)) % 0.39/0.66 (step-pop @p212 :rule scope :premises (@p183)) % 0.39/0.66 (step-pop @p213 :rule scope :premises (@p212)) % 0.39/0.66 (step @p184 :rule process_scope :premises (@p213) :args (@t99)) % 0.39/0.66 (step @p187 :rule and_intro :premises (@p208 @p65)) % 0.39/0.66 (step @p188 :rule modus_ponens :premises (@p187 @p184)) % 0.39/0.66 (step-pop @p214 :rule scope :premises (@p188)) % 0.39/0.66 (step-pop @p215 :rule scope :premises (@p214)) % 0.39/0.66 (step @p189 :rule process_scope :premises (@p215) :args (@t99)) % 0.39/0.66 (step @p192 :rule implies_elim :premises (@p189)) % 0.39/0.66 (step @p193 :rule cnf_and_neg :args (@t130)) % 0.39/0.66 (step @p194 :rule resolution :premises (@p193 @p192) :args (true @t130)) % 0.39/0.66 (step @p195 false :rule chain_m_resolution :premises (@p194 @p174 @p163 @p65) :args (false (@list true false false) (@list @t99 @t86 @t98))) % 0.39/0.66 ) % 0.39/0.66 % SZS output end Proof % 0.39/0.66 % cvc5 exiting %------------------------------------------------------------------------------