%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV372+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 : n011.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 0.36s 0.62s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWV372+1 : TPTP v9.2.1. Released v3.3.0. % 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.34 % Computer : n011.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue Jun 2 20:05:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.27/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.36/0.62 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.36/0.62 % SZS status Theorem % 0.36/0.62 % SZS output start Proof % 0.36/0.62 ( % 0.36/0.62 (declare-sort $$unsorted 0) % 0.36/0.62 (declare-const tptp.phi (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.pi_removemin (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.pi_sharp_removemin (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.pi_find_min (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.pi_remove (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.i (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.removemin_cpq_res (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.insert_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.ok (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.findmin_pqp_res (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.removemin_pq_res (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.removemin_pq_eff (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.pi_sharp_remove (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.check_cpq (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.remove_pq (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.insert_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.findmin_pq_res (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.remove_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.issmallestelement_pq (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.strictly_less_than (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.isnonempty_pq (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.findmin_pq_eff (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.contains_pq (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.isnonempty_slb (-> $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.remove_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.findmin_cpq_eff (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.pi_sharp_find_min (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.create_pq $$unsorted) % 0.36/0.62 (declare-const tptp.lookup_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.bottom $$unsorted) % 0.36/0.62 (declare-const tptp.insert_pq (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.update_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.contains_cpq (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.create_slb $$unsorted) % 0.36/0.62 (declare-const tptp.less_than (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.pair (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.bad $$unsorted) % 0.36/0.62 (declare-const tptp.insert_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.contains_slb (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.pair_in_list (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.remove_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.findmin_cpq_res (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.succ_cpq (-> $$unsorted $$unsorted Bool)) % 0.36/0.62 (declare-const tptp.removemin_cpq_eff (-> $$unsorted $$unsorted)) % 0.36/0.62 (declare-const tptp.triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.36/0.62 (define @t1 () (@var "W" $$unsorted)) % 0.36/0.62 (define @t2 () (@var "U" $$unsorted)) % 0.36/0.62 (define @t3 () (@var "V" $$unsorted)) % 0.36/0.62 (define @t4 () (tptp.less_than @t3 @t1)) % 0.36/0.62 (define @t5 () (tptp.less_than @t2 @t3)) % 0.36/0.62 (define @t6 () (@list @t2 @t3 @t1)) % 0.36/0.62 (define @t7 () (tptp.less_than @t3 @t2)) % 0.36/0.62 (define @t8 () (@list @t2 @t3)) % 0.36/0.62 (define @t9 () (@list @t2)) % 0.36/0.62 (define @t10 () (tptp.insert_pq @t2 @t3)) % 0.36/0.62 (define @t11 () (= @t3 @t1)) % 0.36/0.62 (define @t12 () (tptp.contains_pq @t2 @t1)) % 0.36/0.62 (define @t13 () (tptp.issmallestelement_pq @t2 @t3)) % 0.36/0.62 (define @t14 () (not @t11)) % 0.36/0.62 (define @t15 () (tptp.contains_pq @t2 @t3)) % 0.36/0.62 (define @t16 () (and @t15 @t13)) % 0.36/0.62 (define @t17 () (tptp.pair @t3 @t1)) % 0.36/0.62 (define @t18 () (tptp.insert_slb @t2 @t17)) % 0.36/0.62 (define @t19 () (tptp.contains_slb @t2 @t1)) % 0.36/0.62 (define @t20 () (@var "X" $$unsorted)) % 0.36/0.62 (define @t21 () (tptp.pair @t3 @t20)) % 0.36/0.62 (define @t22 () (tptp.insert_slb @t2 @t21)) % 0.36/0.62 (define @t23 () (@list @t2 @t3 @t1 @t20)) % 0.36/0.62 (define @t24 () (@var "Y" $$unsorted)) % 0.36/0.62 (define @t25 () (@list @t2 @t3 @t1 @t20 @t24)) % 0.36/0.62 (define @t26 () (and @t14 @t19)) % 0.36/0.62 (define @t27 () (tptp.update_slb tptp.create_slb @t2)) % 0.36/0.62 (define @t28 () (forall @t9 (= @t27 tptp.create_slb))) % 0.36/0.62 (define @t29 () (tptp.update_slb @t2 @t1)) % 0.36/0.62 (define @t30 () (tptp.update_slb @t22 @t1)) % 0.36/0.62 (define @t31 () (tptp.succ_cpq @t2 @t3)) % 0.36/0.62 (define @t32 () (tptp.triple @t2 tptp.create_slb @t3)) % 0.36/0.62 (define @t33 () (tptp.triple @t2 @t3 @t1)) % 0.36/0.62 (define @t34 () (tptp.triple @t2 (tptp.insert_slb @t3 (tptp.pair @t20 @t24)) @t1)) % 0.36/0.62 (define @t35 () (tptp.check_cpq @t34)) % 0.36/0.62 (define @t36 () (tptp.contains_slb @t3 @t20)) % 0.36/0.62 (define @t37 () (tptp.contains_cpq @t33 @t20)) % 0.36/0.62 (define @t38 () (tptp.triple @t2 @t3 tptp.bad)) % 0.36/0.62 (define @t39 () (tptp.ok @t38)) % 0.36/0.62 (define @t40 () (forall @t8 (= @t39 false))) % 0.36/0.62 (define @t41 () (tptp.ok @t33)) % 0.36/0.62 (define @t42 () (not @t41)) % 0.36/0.62 (define @t43 () (tptp.remove_cpq @t33 @t20)) % 0.36/0.62 (define @t44 () (tptp.remove_slb @t3 @t20)) % 0.36/0.62 (define @t45 () (tptp.remove_pqp @t2 @t20)) % 0.36/0.62 (define @t46 () (tptp.lookup_slb @t3 @t20)) % 0.36/0.62 (define @t47 () (tptp.findmin_pqp_res @t2)) % 0.36/0.62 (define @t48 () (tptp.update_slb @t3 @t47)) % 0.36/0.62 (define @t49 () (tptp.findmin_cpq_eff @t33)) % 0.36/0.62 (define @t50 () (= @t49 (tptp.triple @t2 @t48 tptp.bad))) % 0.36/0.62 (define @t51 () (tptp.contains_slb @t3 @t47)) % 0.36/0.62 (define @t52 () (not @t51)) % 0.36/0.62 (define @t53 () (= @t3 tptp.create_slb)) % 0.36/0.62 (define @t54 () (not @t53)) % 0.36/0.62 (define @t55 () (and @t54 @t52)) % 0.36/0.62 (define @t56 () (forall @t23 (=> @t55 @t50))) % 0.36/0.62 (define @t57 () (tptp.lookup_slb @t3 @t47)) % 0.36/0.62 (define @t58 () (tptp.findmin_cpq_res @t33)) % 0.36/0.62 (define @t59 () (=> @t54 (= @t58 @t47))) % 0.36/0.62 (define @t60 () (forall @t23 @t59)) % 0.36/0.62 (define @t61 () (tptp.findmin_cpq_res @t2)) % 0.36/0.62 (define @t62 () (tptp.i @t33)) % 0.36/0.62 (define @t63 () (tptp.i @t2)) % 0.36/0.62 (define @t64 () (@list @t3)) % 0.36/0.62 (define @t65 () (exists @t64 (tptp.pi_sharp_find_min @t63 @t3))) % 0.36/0.62 (define @t66 () (forall @t23 (= @t37 (tptp.contains_pq @t62 @t20)))) % 0.36/0.62 (define @t67 () (not (tptp.phi @t33))) % 0.36/0.62 (define @t68 () (forall @t6 (=> @t42 @t67))) % 0.36/0.62 (define @t69 () (tptp.contains_pq @t62 @t58)) % 0.36/0.62 (define @t70 () (tptp.phi @t49)) % 0.36/0.62 (define @t71 () (forall @t6 (=> @t70 @t69))) % 0.36/0.62 (define @t72 () (not @t71)) % 0.36/0.62 (define @t73 () (forall @t6 (or (not @t70) @t69))) % 0.36/0.62 (define @t74 () (@quantifiers_skolemize @t73 2)) % 0.36/0.62 (define @t75 () (@quantifiers_skolemize @t73 1)) % 0.36/0.62 (define @t76 () (@quantifiers_skolemize @t73 0)) % 0.36/0.62 (define @t77 () (tptp.triple @t76 @t75 @t74)) % 0.36/0.62 (define @t78 () (tptp.findmin_cpq_res @t77)) % 0.36/0.62 (define @t79 () (@list @t76 @t75 @t74 @t78)) % 0.36/0.62 (define @t80 () (tptp.contains_cpq @t77 @t78)) % 0.36/0.62 (define @t81 () (tptp.contains_pq (tptp.i @t77) @t78)) % 0.36/0.62 (define @t82 () (= @t80 @t81)) % 0.36/0.62 (define @t83 () (= @t81 @t80)) % 0.36/0.62 (define @t84 () (@list false)) % 0.36/0.62 (define @t85 () (tptp.findmin_cpq_eff @t77)) % 0.36/0.62 (define @t86 () (tptp.phi @t85)) % 0.36/0.62 (define @t87 () (not @t86)) % 0.36/0.62 (define @t88 () (or @t87 @t81)) % 0.36/0.62 (define @t89 () (@list true)) % 0.36/0.62 (define @t90 () (@list @t88)) % 0.36/0.62 (define @t91 () (not @t80)) % 0.36/0.62 (define @t92 () (@list true false)) % 0.36/0.62 (define @t93 () (tptp.contains_slb @t75 @t78)) % 0.36/0.62 (define @t94 () (= @t80 @t93)) % 0.36/0.62 (define @t95 () (not @t93)) % 0.36/0.62 (define @t96 () (= @t47 @t58)) % 0.36/0.62 (define @t97 () (or @t53 @t96)) % 0.36/0.62 (define @t98 () (forall @t6 @t97)) % 0.36/0.62 (define @t99 () (not @t54)) % 0.36/0.62 (define @t100 () (tptp.findmin_pqp_res @t76)) % 0.36/0.62 (define @t101 () (= @t75 tptp.create_slb)) % 0.36/0.62 (define @t102 () (or @t101 (= @t100 @t78))) % 0.36/0.62 (define @t103 () (@list @t76 @t75 @t74)) % 0.36/0.62 (define @t104 () (= @t78 @t100)) % 0.36/0.62 (define @t105 () (= tptp.create_slb @t75)) % 0.36/0.62 (define @t106 () (or @t105 @t104)) % 0.36/0.62 (define @t107 () (tptp.update_slb @t75 @t100)) % 0.36/0.62 (define @t108 () (tptp.triple @t76 @t107 tptp.bad)) % 0.36/0.62 (define @t109 () (tptp.phi @t108)) % 0.36/0.62 (define @t110 () (not @t109)) % 0.36/0.62 (define @t111 () (tptp.ok @t108)) % 0.36/0.62 (define @t112 () (or @t111 @t110)) % 0.36/0.62 (define @t113 () (= @t85 @t108)) % 0.36/0.62 (define @t114 () (not @t113)) % 0.36/0.62 (define @t115 () (= true false)) % 0.36/0.62 (define @t116 () (and @t110 @t113 @t86)) % 0.36/0.62 (define @t117 () (tptp.update_slb tptp.create_slb @t100)) % 0.36/0.62 (define @t118 () (= tptp.create_slb @t117)) % 0.36/0.62 (define @t119 () (tptp.triple @t76 tptp.create_slb tptp.bad)) % 0.36/0.62 (define @t120 () (= (tptp.findmin_cpq_eff (tptp.triple @t76 tptp.create_slb @t74)) @t119)) % 0.36/0.62 (define @t121 () (and @t105 @t118 @t120)) % 0.36/0.62 (define @t122 () (not @t105)) % 0.36/0.62 (define @t123 () (or @t53 @t51 @t50)) % 0.36/0.62 (define @t124 () (forall @t6 @t123)) % 0.36/0.62 (define @t125 () (tptp.contains_slb @t75 @t100)) % 0.36/0.62 (define @t126 () (or @t101 @t125 @t113)) % 0.36/0.62 (define @t127 () (or @t105 @t125 @t113)) % 0.36/0.62 (define @t128 () (not @t104)) % 0.36/0.62 (define @t129 () (not @t125)) % 0.36/0.62 (define @t130 () (and @t95 @t104 @t125)) % 0.36/0.62 (assume @p1 (forall @t6 (=> (and @t5 @t4) (tptp.less_than @t2 @t1)))) % 0.36/0.62 (assume @p2 (forall @t8 (or @t5 @t7))) % 0.36/0.62 (assume @p3 (forall @t9 (tptp.less_than @t2 @t2))) % 0.36/0.62 (assume @p4 (forall @t8 (= (tptp.strictly_less_than @t2 @t3) (and @t5 (not @t7))))) % 0.36/0.62 (assume @p5 (forall @t9 (tptp.less_than tptp.bottom @t2))) % 0.36/0.62 (assume @p6 (not (tptp.isnonempty_pq tptp.create_pq))) % 0.36/0.62 (assume @p7 (forall @t8 (tptp.isnonempty_pq @t10))) % 0.36/0.62 (assume @p8 (forall @t9 (not (tptp.contains_pq tptp.create_pq @t2)))) % 0.36/0.62 (assume @p9 (forall @t6 (= (tptp.contains_pq @t10 @t1) (or @t12 @t11)))) % 0.36/0.62 (assume @p10 (forall @t8 (= @t13 (forall (@list @t1) (=> @t12 @t4))))) % 0.36/0.62 (assume @p11 (forall @t8 (= (tptp.remove_pq @t10 @t3) @t2))) % 0.36/0.62 (assume @p12 (forall @t6 (=> (and @t12 @t14) (= (tptp.remove_pq @t10 @t1) (tptp.insert_pq (tptp.remove_pq @t2 @t1) @t3))))) % 0.36/0.62 (assume @p13 (forall @t8 (=> @t16 (= (tptp.findmin_pq_eff @t2 @t3) @t2)))) % 0.36/0.62 (assume @p14 (forall @t8 (=> @t16 (= (tptp.findmin_pq_res @t2 @t3) @t3)))) % 0.36/0.62 (assume @p15 (forall @t8 (=> @t16 (= (tptp.removemin_pq_eff @t2 @t3) (tptp.remove_pq @t2 @t3))))) % 0.36/0.62 (assume @p16 (forall @t8 (=> @t16 (= (tptp.removemin_pq_res @t2 @t3) @t3)))) % 0.36/0.62 (assume @p17 (forall @t6 (= (tptp.insert_pq @t10 @t1) (tptp.insert_pq (tptp.insert_pq @t2 @t1) @t3)))) % 0.36/0.62 (assume @p18 (not (tptp.isnonempty_slb tptp.create_slb))) % 0.36/0.62 (assume @p19 (forall @t6 (tptp.isnonempty_slb @t18))) % 0.36/0.62 (assume @p20 (forall @t9 (not (tptp.contains_slb tptp.create_slb @t2)))) % 0.36/0.62 (assume @p21 (forall @t23 (= (tptp.contains_slb @t22 @t1) (or @t19 @t11)))) % 0.36/0.62 (assume @p22 (forall @t8 (not (tptp.pair_in_list tptp.create_slb @t2 @t3)))) % 0.36/0.62 (assume @p23 (forall @t25 (= (tptp.pair_in_list @t22 @t1 @t24) (or (tptp.pair_in_list @t2 @t1 @t24) (and @t11 (= @t20 @t24)))))) % 0.36/0.62 (assume @p24 (forall @t6 (= (tptp.remove_slb @t18 @t3) @t2))) % 0.36/0.62 (assume @p25 (forall @t23 (=> @t26 (= (tptp.remove_slb @t22 @t1) (tptp.insert_slb (tptp.remove_slb @t2 @t1) @t21))))) % 0.36/0.62 (assume @p26 (forall @t6 (= (tptp.lookup_slb @t18 @t3) @t1))) % 0.36/0.62 (assume @p27 (forall @t23 (=> @t26 (= (tptp.lookup_slb @t22 @t1) (tptp.lookup_slb @t2 @t1))))) % 0.36/0.62 (assume @p28 @t28) % 0.36/0.62 (assume @p29 (forall @t23 (=> (tptp.strictly_less_than @t20 @t1) (= @t30 (tptp.insert_slb @t29 @t17))))) % 0.36/0.62 (assume @p30 (forall @t23 (=> (tptp.less_than @t1 @t20) (= @t30 (tptp.insert_slb @t29 @t21))))) % 0.36/0.62 (assume @p31 (forall @t9 (tptp.succ_cpq @t2 @t2))) % 0.36/0.62 (assume @p32 (forall @t6 (=> @t31 (tptp.succ_cpq @t2 (tptp.insert_cpq @t3 @t1))))) % 0.36/0.62 (assume @p33 (forall @t6 (=> @t31 (tptp.succ_cpq @t2 (tptp.remove_cpq @t3 @t1))))) % 0.36/0.62 (assume @p34 (forall @t8 (=> @t31 (tptp.succ_cpq @t2 (tptp.findmin_cpq_eff @t3))))) % 0.36/0.62 (assume @p35 (forall @t8 (=> @t31 (tptp.succ_cpq @t2 (tptp.removemin_cpq_eff @t3))))) % 0.36/0.62 (assume @p36 (forall @t8 (tptp.check_cpq @t32))) % 0.36/0.62 (assume @p37 (forall @t25 (=> (tptp.less_than @t24 @t20) (= @t35 (tptp.check_cpq @t33))))) % 0.36/0.62 (assume @p38 (forall @t25 (=> (tptp.strictly_less_than @t20 @t24) (= @t35 false)))) % 0.36/0.62 (assume @p39 (forall @t23 (= @t37 @t36))) % 0.36/0.62 (assume @p40 @t40) % 0.36/0.62 (assume @p41 (forall @t6 (=> @t42 (= @t1 tptp.bad)))) % 0.36/0.62 (assume @p42 (forall @t23 (= (tptp.insert_cpq @t33 @t20) (tptp.triple (tptp.insert_pqp @t2 @t20) (tptp.insert_slb @t3 (tptp.pair @t20 tptp.bottom)) @t1)))) % 0.36/0.62 (assume @p43 (forall @t23 (=> (not @t36) (= @t43 @t38)))) % 0.36/0.62 (assume @p44 (forall @t23 (=> (and @t36 (tptp.less_than @t46 @t20)) (= @t43 (tptp.triple @t45 @t44 @t1))))) % 0.36/0.62 (assume @p45 (forall @t23 (=> (and @t36 (tptp.strictly_less_than @t20 @t46)) (= @t43 (tptp.triple @t45 @t44 tptp.bad))))) % 0.36/0.62 (assume @p46 (forall @t8 (= (tptp.findmin_cpq_eff @t32) (tptp.triple @t2 tptp.create_slb tptp.bad)))) % 0.36/0.62 (assume @p47 @t56) % 0.36/0.62 (assume @p48 (forall @t23 (=> (and @t54 @t51 (tptp.strictly_less_than @t47 @t57)) @t50))) % 0.36/0.62 (assume @p49 (forall @t23 (=> (and @t54 @t51 (tptp.less_than @t57 @t47)) (= @t49 (tptp.triple @t2 @t48 @t1))))) % 0.36/0.62 (assume @p50 (forall @t8 (= (tptp.findmin_cpq_res @t32) tptp.bottom))) % 0.36/0.62 (assume @p51 @t60) % 0.36/0.62 (assume @p52 (forall @t9 (= (tptp.removemin_cpq_eff @t2) (tptp.remove_cpq (tptp.findmin_cpq_eff @t2) @t61)))) % 0.36/0.62 (assume @p53 (forall @t9 (= (tptp.removemin_cpq_res @t2) @t61))) % 0.36/0.62 (assume @p54 (forall @t8 (= (tptp.i @t32) tptp.create_pq))) % 0.36/0.62 (assume @p55 (forall @t25 (= (tptp.i @t34) (tptp.insert_pq @t62 @t20)))) % 0.36/0.62 (assume @p56 (forall @t8 (= (tptp.pi_sharp_remove @t2 @t3) @t15))) % 0.36/0.62 (assume @p57 (forall @t8 (= (tptp.pi_remove @t2 @t3) (tptp.pi_sharp_remove @t63 @t3)))) % 0.36/0.62 (assume @p58 (forall @t8 (= (tptp.pi_sharp_find_min @t2 @t3) @t16))) % 0.36/0.62 (assume @p59 (forall @t9 (= (tptp.pi_find_min @t2) @t65))) % 0.36/0.62 (assume @p60 (forall @t8 (= (tptp.pi_sharp_removemin @t2 @t3) @t16))) % 0.36/0.62 (assume @p61 (forall @t9 (= (tptp.pi_removemin @t2) @t65))) % 0.36/0.62 (assume @p62 (forall @t9 (= (tptp.phi @t2) (exists @t64 (and @t31 (tptp.ok @t3) (tptp.check_cpq @t3)))))) % 0.36/0.62 (assume @p63 @t66) % 0.36/0.62 (assume @p64 (forall @t6 (=> (not (tptp.contains_cpq @t33 @t58)) (not (tptp.ok @t49))))) % 0.36/0.62 (assume @p65 @t68) % 0.36/0.62 (assume @p66 @t72) % 0.36/0.62 (assume @p67 true) % 0.36/0.62 (step @p68 :rule instantiate :premises (@p39) :args (@t79)) % 0.36/0.62 (step @p69 :rule eq-symm :args (@t80 @t81)) % 0.36/0.62 (step @p70 :rule refl :args (@t66)) % 0.36/0.62 (step @p71 :rule cong :premises (@p70 @p69) :args ((=> @t66 @t82))) % 0.36/0.62 (assume-push @p272 @t66) % 0.36/0.62 (step @p73 :rule instantiate :premises (@p63) :args (@t79)) % 0.36/0.62 (step-pop @p273 :rule scope :premises (@p73)) % 0.36/0.62 (step @p74 :rule process_scope :premises (@p273) :args (@t82)) % 0.36/0.62 (step @p76 :rule eq_resolve :premises (@p74 @p71)) % 0.36/0.62 (step @p77 :rule implies_elim :premises (@p76)) % 0.36/0.62 (step @p78 :rule chain_m_resolution :premises (@p77 @p63) :args (@t83 @t84 (@list @t66))) % 0.36/0.62 (step @p79 :rule bool-impl-elim :args (@t70 @t69)) % 0.36/0.62 (step @p80 :rule cong :premises (@p79) :args (@t71)) % 0.36/0.62 (step @p81 :rule cong :premises (@p80) :args (@t72)) % 0.36/0.62 (step @p82 :rule eq_resolve :premises (@p66 @p81)) % 0.36/0.62 (step @p83 :rule skolemize :premises (@p82)) % 0.36/0.62 (step @p84 :rule cnf_or_neg :args (@t88 1)) % 0.36/0.62 (step @p85 :rule chain_m_resolution :premises (@p84 @p83) :args ((not @t81) @t89 @t90)) % 0.36/0.62 (step @p86 :rule cnf_equiv_pos2 :args (@t83)) % 0.36/0.62 (step @p87 :rule reordering :premises (@p86) :args ((or @t81 @t91 (not @t83)))) % 0.36/0.62 (step @p88 :rule chain_m_resolution :premises (@p87 @p85 @p78) :args (@t91 @t92 (@list @t81 @t83))) % 0.36/0.62 (step @p89 :rule cnf_equiv_pos2 :args (@t94)) % 0.36/0.62 (step @p90 :rule reordering :premises (@p89) :args ((or @t80 @t95 (not @t94)))) % 0.36/0.62 (step @p91 :rule chain_m_resolution :premises (@p90 @p88 @p68) :args (@t95 @t92 (@list @t80 @t94))) % 0.36/0.62 (step @p92 :rule quant-unused-vars :args ((= (forall @t23 @t97) @t98))) % 0.36/0.62 (step @p93 :rule refl :args (@t96)) % 0.36/0.62 (step @p94 :rule bool-double-not-elim :args (@t53)) % 0.36/0.62 (step @p95 :rule nary_cong :premises (@p94 @p93) :args ((or @t99 @t96))) % 0.36/0.62 (step @p96 :rule bool-impl-elim :args (@t54 @t96)) % 0.36/0.62 (step @p97 :rule trans :premises (@p96 @p95)) % 0.36/0.62 (step @p98 :rule cong :premises (@p97) :args ((forall @t23 (=> @t54 @t96)))) % 0.36/0.62 (step @p99 :rule trans :premises (@p98 @p92)) % 0.36/0.62 (step @p100 :rule eq-symm :args (@t58 @t47)) % 0.36/0.62 (step @p101 :rule refl :args (@t54)) % 0.36/0.62 (step @p102 :rule cong :premises (@p101 @p100) :args (@t59)) % 0.36/0.62 (step @p103 :rule cong :premises (@p102) :args (@t60)) % 0.36/0.62 (step @p104 :rule trans :premises (@p103 @p99)) % 0.36/0.62 (step @p105 :rule eq_resolve :premises (@p51 @p104)) % 0.36/0.62 (step @p106 :rule eq-symm :args (@t100 @t78)) % 0.36/0.62 (step @p107 :rule eq-symm :args (@t75 tptp.create_slb)) % 0.36/0.62 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t102)) % 0.36/0.62 (step @p109 :rule refl :args (@t98)) % 0.36/0.62 (step @p110 :rule cong :premises (@p109 @p108) :args ((=> @t98 @t102))) % 0.36/0.62 (assume-push @p274 @t98) % 0.36/0.62 (step @p112 :rule instantiate :premises (@p105) :args (@t103)) % 0.36/0.62 (step-pop @p275 :rule scope :premises (@p112)) % 0.36/0.62 (step @p113 :rule process_scope :premises (@p275) :args (@t102)) % 0.36/0.62 (step @p115 :rule eq_resolve :premises (@p113 @p110)) % 0.36/0.62 (step @p116 :rule implies_elim :premises (@p115)) % 0.36/0.62 (step @p117 :rule chain_m_resolution :premises (@p116 @p105) :args (@t106 @t84 (@list @t98))) % 0.36/0.62 (step @p118 :rule instantiate :premises (@p46) :args ((@list @t76 @t74))) % 0.36/0.62 (step @p119 :rule eq-symm :args (@t27 tptp.create_slb)) % 0.36/0.62 (step @p120 :rule cong :premises (@p119) :args (@t28)) % 0.36/0.62 (step @p121 :rule eq_resolve :premises (@p28 @p120)) % 0.36/0.62 (step @p122 :rule instantiate :premises (@p121) :args ((@list @t100))) % 0.36/0.62 (step @p123 :rule refl :args (@t67)) % 0.36/0.62 (step @p124 :rule bool-double-not-elim :args (@t41)) % 0.36/0.62 (step @p125 :rule nary_cong :premises (@p124 @p123) :args ((or (not @t42) @t67))) % 0.36/0.62 (step @p126 :rule bool-impl-elim :args (@t42 @t67)) % 0.36/0.62 (step @p127 :rule trans :premises (@p126 @p125)) % 0.36/0.62 (step @p128 :rule cong :premises (@p127) :args (@t68)) % 0.36/0.62 (step @p129 :rule eq_resolve :premises (@p65 @p128)) % 0.36/0.62 (step @p130 :rule instantiate :premises (@p129) :args ((@list @t76 @t107 tptp.bad))) % 0.36/0.62 (step @p131 :rule bool-eq-false :args (@t39)) % 0.36/0.62 (step @p132 :rule cong :premises (@p131) :args (@t40)) % 0.36/0.62 (step @p133 :rule eq_resolve :premises (@p40 @p132)) % 0.36/0.62 (step @p134 :rule instantiate :premises (@p133) :args ((@list @t76 @t107))) % 0.36/0.62 (step @p135 :rule cnf_or_pos :args (@t112)) % 0.36/0.62 (step @p136 :rule reordering :premises (@p135) :args ((or @t111 @t110 (not @t112)))) % 0.36/0.62 (step @p137 :rule chain_m_resolution :premises (@p136 @p134 @p130) :args (@t110 @t92 (@list @t111 @t112))) % 0.36/0.62 (step @p138 :rule bool-double-not-elim :args (@t86)) % 0.36/0.62 (step @p139 :rule refl :args (@t88)) % 0.36/0.62 (step @p140 :rule nary_cong :premises (@p139 @p138) :args ((or @t88 (not @t87)))) % 0.36/0.62 (step @p141 :rule cnf_or_neg :args (@t88 0)) % 0.36/0.62 (step @p142 :rule eq_resolve :premises (@p141 @p140)) % 0.36/0.62 (step @p143 :rule reordering :premises (@p142) :args ((or @t86 @t88))) % 0.36/0.62 (step @p144 :rule chain_m_resolution :premises (@p143 @p83) :args (@t86 @t89 @t90)) % 0.36/0.62 (step @p145 :rule bool-double-not-elim :args (@t109)) % 0.36/0.62 (step @p146 :rule refl :args (@t114)) % 0.36/0.62 (step @p147 :rule refl :args (@t87)) % 0.36/0.62 (step @p148 :rule nary_cong :premises (@p147 @p146 @p145) :args ((or @t87 @t114 (not @t110)))) % 0.36/0.62 (assume-push @p276 @t110) % 0.36/0.62 (assume-push @p277 @t113) % 0.36/0.62 (assume-push @p278 @t86) % 0.36/0.62 (step @p152 :rule evaluate :args (@t115)) % 0.36/0.62 (step @p153 :rule false_intro :premises (@p137)) % 0.36/0.62 (step @p154 :rule cong :premises (@p277) :args (@t86)) % 0.36/0.62 (step @p155 :rule true_intro :premises (@p144)) % 0.36/0.62 (step @p156 :rule symm :premises (@p155)) % 0.36/0.62 (step @p157 :rule trans :premises (@p156 @p154 @p153)) % 0.36/0.62 (step @p158 false :rule eq_resolve :premises (@p157 @p152)) % 0.36/0.62 (step-pop @p279 :rule scope :premises (@p158)) % 0.36/0.62 (step-pop @p280 :rule scope :premises (@p279)) % 0.36/0.62 (step-pop @p281 :rule scope :premises (@p280)) % 0.36/0.62 (step @p159 :rule process_scope :premises (@p281) :args (false)) % 0.36/0.62 (assume-push @p282 @t86) % 0.36/0.62 (assume-push @p283 @t113) % 0.36/0.62 (assume-push @p284 @t110) % 0.36/0.62 (step @p166 :rule and_intro :premises (@p137 @p283 @p144)) % 0.36/0.62 (step-pop @p285 :rule scope :premises (@p166)) % 0.36/0.62 (step-pop @p286 :rule scope :premises (@p285)) % 0.36/0.62 (step-pop @p287 :rule scope :premises (@p286)) % 0.36/0.62 (step @p167 :rule process_scope :premises (@p287) :args (@t116)) % 0.36/0.62 (step @p171 :rule implies_elim :premises (@p167)) % 0.36/0.62 (step @p172 :rule resolution :premises (@p171 @p159) :args (true @t116)) % 0.36/0.62 (step @p173 :rule not_and :premises (@p172)) % 0.36/0.62 (step @p174 :rule eq_resolve :premises (@p173 @p148)) % 0.36/0.62 (step @p175 :rule chain_m_resolution :premises (@p174 @p144 @p137) :args (@t114 (@list false true) (@list @t86 @t109))) % 0.36/0.62 (assume-push @p288 @t105) % 0.36/0.62 (assume-push @p289 @t118) % 0.36/0.62 (assume-push @p290 @t120) % 0.36/0.62 (assume-push @p291 @t105) % 0.36/0.62 (assume-push @p292 @t118) % 0.36/0.62 (assume-push @p293 @t120) % 0.36/0.62 (step @p182 :rule refl :args (tptp.bad)) % 0.36/0.62 (step @p183 :rule refl :args (@t100)) % 0.36/0.62 (step @p184 :rule cong :premises (@p288 @p183) :args (@t117)) % 0.36/0.62 (step @p185 :rule trans :premises (@p122 @p184)) % 0.36/0.62 (step @p186 :rule refl :args (@t76)) % 0.36/0.62 (step @p187 :rule cong :premises (@p186 @p185 @p182) :args (@t119)) % 0.36/0.62 (step @p188 :rule refl :args (@t74)) % 0.36/0.62 (step @p189 :rule symm :premises (@p288)) % 0.36/0.62 (step @p190 :rule cong :premises (@p186 @p189 @p188) :args (@t77)) % 0.36/0.62 (step @p191 :rule cong :premises (@p190) :args (@t85)) % 0.36/0.62 (step @p192 :rule trans :premises (@p191 @p118 @p187)) % 0.36/0.62 (step-pop @p294 :rule scope :premises (@p192)) % 0.36/0.62 (step-pop @p295 :rule scope :premises (@p294)) % 0.36/0.62 (step-pop @p296 :rule scope :premises (@p295)) % 0.36/0.62 (step @p193 :rule process_scope :premises (@p296) :args (@t113)) % 0.36/0.62 (step @p197 :rule and_intro :premises (@p288 @p122 @p118)) % 0.36/0.62 (step @p198 :rule modus_ponens :premises (@p197 @p193)) % 0.36/0.62 (step-pop @p297 :rule scope :premises (@p198)) % 0.36/0.62 (step-pop @p298 :rule scope :premises (@p297)) % 0.36/0.62 (step-pop @p299 :rule scope :premises (@p298)) % 0.36/0.62 (step @p199 :rule process_scope :premises (@p299) :args (@t113)) % 0.36/0.62 (step @p203 :rule implies_elim :premises (@p199)) % 0.36/0.62 (step @p204 :rule cnf_and_neg :args (@t121)) % 0.36/0.62 (step @p205 :rule resolution :premises (@p204 @p203) :args (true @t121)) % 0.36/0.62 (step @p206 :rule reordering :premises (@p205) :args ((or @t113 @t122 (not @t118) (not @t120)))) % 0.36/0.62 (step @p207 :rule chain_m_resolution :premises (@p206 @p175 @p122 @p118) :args (@t122 (@list true false false) (@list @t113 @t118 @t120))) % 0.36/0.62 (step @p208 :rule cnf_or_pos :args (@t106)) % 0.36/0.62 (step @p209 :rule reordering :premises (@p208) :args ((or @t105 @t104 (not @t106)))) % 0.36/0.62 (step @p210 :rule chain_m_resolution :premises (@p209 @p207 @p117) :args (@t104 @t92 (@list @t105 @t106))) % 0.36/0.62 (step @p211 :rule quant-unused-vars :args ((= (forall @t23 @t123) @t124))) % 0.36/0.62 (step @p212 :rule aci_norm :args ((= (or (or @t53 @t51) @t50) @t123))) % 0.36/0.62 (step @p213 :rule refl :args (@t50)) % 0.36/0.62 (step @p214 :rule bool-double-not-elim :args (@t51)) % 0.36/0.62 (step @p215 :rule nary_cong :premises (@p94 @p214) :args ((or @t99 (not @t52)))) % 0.36/0.62 (step @p216 :rule bool-and-de-morgan :args (@t54 @t52 true)) % 0.36/0.62 (step @p217 :rule trans :premises (@p216 @p215)) % 0.36/0.62 (step @p218 :rule nary_cong :premises (@p217 @p213) :args ((or (not @t55) @t50))) % 0.36/0.62 (step @p219 :rule trans :premises (@p218 @p212)) % 0.36/0.62 (step @p220 :rule bool-impl-elim :args (@t55 @t50)) % 0.36/0.62 (step @p221 :rule trans :premises (@p220 @p219)) % 0.36/0.62 (step @p222 :rule cong :premises (@p221) :args (@t56)) % 0.36/0.62 (step @p223 :rule trans :premises (@p222 @p211)) % 0.36/0.62 (step @p224 :rule eq_resolve :premises (@p47 @p223)) % 0.36/0.62 (step @p225 :rule refl :args (@t113)) % 0.36/0.62 (step @p226 :rule refl :args (@t125)) % 0.36/0.62 (step @p227 :rule nary_cong :premises (@p107 @p226 @p225) :args (@t126)) % 0.36/0.62 (step @p228 :rule refl :args (@t124)) % 0.36/0.62 (step @p229 :rule cong :premises (@p228 @p227) :args ((=> @t124 @t126))) % 0.36/0.62 (assume-push @p300 @t124) % 0.36/0.62 (step @p231 :rule instantiate :premises (@p224) :args (@t103)) % 0.36/0.62 (step-pop @p301 :rule scope :premises (@p231)) % 0.36/0.62 (step @p232 :rule process_scope :premises (@p301) :args (@t126)) % 0.36/0.62 (step @p234 :rule eq_resolve :premises (@p232 @p229)) % 0.36/0.62 (step @p235 :rule implies_elim :premises (@p234)) % 0.36/0.62 (step @p236 :rule chain_m_resolution :premises (@p235 @p224) :args (@t127 @t84 (@list @t124))) % 0.36/0.62 (step @p237 :rule cnf_or_pos :args (@t127)) % 0.36/0.62 (step @p238 :rule reordering :premises (@p237) :args ((or @t125 @t113 @t105 (not @t127)))) % 0.36/0.62 (step @p239 :rule chain_m_resolution :premises (@p238 @p175 @p207 @p236) :args (@t125 (@list true true false) (@list @t113 @t105 @t127))) % 0.36/0.62 (step @p240 :rule bool-double-not-elim :args (@t93)) % 0.36/0.62 (step @p241 :rule refl :args (@t128)) % 0.36/0.62 (step @p242 :rule refl :args (@t129)) % 0.36/0.62 (step @p243 :rule nary_cong :premises (@p242 @p241 @p240) :args ((or @t129 @t128 (not @t95)))) % 0.36/0.62 (assume-push @p302 @t95) % 0.36/0.62 (assume-push @p303 @t104) % 0.36/0.62 (assume-push @p304 @t125) % 0.36/0.62 (step @p152 :rule evaluate :args (@t115)) % 0.36/0.62 (step @p247 :rule false_intro :premises (@p91)) % 0.36/0.62 (step @p248 :rule symm :premises (@p303)) % 0.36/0.62 (step @p249 :rule refl :args (@t75)) % 0.36/0.62 (step @p250 :rule cong :premises (@p249 @p248) :args (@t125)) % 0.36/0.62 (step @p251 :rule true_intro :premises (@p304)) % 0.36/0.62 (step @p252 :rule symm :premises (@p251)) % 0.36/0.62 (step @p253 :rule trans :premises (@p252 @p250 @p247)) % 0.36/0.62 (step @p254 false :rule eq_resolve :premises (@p253 @p152)) % 0.36/0.62 (step-pop @p305 :rule scope :premises (@p254)) % 0.36/0.62 (step-pop @p306 :rule scope :premises (@p305)) % 0.36/0.62 (step-pop @p307 :rule scope :premises (@p306)) % 0.36/0.62 (step @p255 :rule process_scope :premises (@p307) :args (false)) % 0.36/0.62 (assume-push @p308 @t125) % 0.36/0.62 (assume-push @p309 @t104) % 0.36/0.62 (assume-push @p310 @t95) % 0.36/0.62 (step @p262 :rule and_intro :premises (@p91 @p309 @p308)) % 0.36/0.62 (step-pop @p311 :rule scope :premises (@p262)) % 0.36/0.62 (step-pop @p312 :rule scope :premises (@p311)) % 0.36/0.62 (step-pop @p313 :rule scope :premises (@p312)) % 0.36/0.62 (step @p263 :rule process_scope :premises (@p313) :args (@t130)) % 0.36/0.62 (step @p267 :rule implies_elim :premises (@p263)) % 0.36/0.62 (step @p268 :rule resolution :premises (@p267 @p255) :args (true @t130)) % 0.36/0.62 (step @p269 :rule not_and :premises (@p268)) % 0.36/0.62 (step @p270 :rule eq_resolve :premises (@p269 @p243)) % 0.36/0.62 (step @p271 false :rule chain_m_resolution :premises (@p270 @p239 @p210 @p91) :args (false (@list false false true) (@list @t125 @t104 @t93))) % 0.36/0.62 ) % 0.36/0.62 % SZS output end Proof % 0.36/0.62 % cvc5 exiting %------------------------------------------------------------------------------