%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SWV376+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 : n020.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 0.41s 0.61s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.13 % Problem : SWV376+1 : TPTP v9.2.1. Released v3.3.0. % 0.13/0.14 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.35 % Computer : n020.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 20:06:41 EDT 2026 % 0.18/0.35 % CPUTime : % 0.33/0.51 %----Proving TF0_NAR, FOF, or CNF % 0.41/0.61 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15... % 0.41/0.61 % SZS status Theorem % 0.41/0.61 % SZS output start Proof % 0.41/0.61 ( % 0.41/0.61 (declare-sort $$unsorted 0) % 0.41/0.61 (declare-const tptp.findmin_cpq_res (-> $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.check_cpq (-> $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.triple (-> $$unsorted $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.im_succ_cpq (-> $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.removemin_cpq_eff (-> $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.findmin_cpq_eff (-> $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.remove_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.insert_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.insert_cpq (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.less_than (-> $$unsorted $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.strictly_less_than (-> $$unsorted $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.findmin_pqp_res (-> $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.bottom $$unsorted) % 0.41/0.61 (declare-const tptp.create_slb $$unsorted) % 0.41/0.61 (declare-const tptp.lookup_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.isnonempty_slb (-> $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.removemin_cpq_res (-> $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.remove_pqp (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.contains_cpq (-> $$unsorted $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.pair (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.insert_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.ok (-> $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.contains_slb (-> $$unsorted $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.succ_cpq (-> $$unsorted $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.pair_in_list (-> $$unsorted $$unsorted $$unsorted Bool)) % 0.41/0.61 (declare-const tptp.bad $$unsorted) % 0.41/0.61 (declare-const tptp.remove_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (declare-const tptp.update_slb (-> $$unsorted $$unsorted $$unsorted)) % 0.41/0.61 (define @t1 () (@var "W" $$unsorted)) % 0.41/0.61 (define @t2 () (@var "U" $$unsorted)) % 0.41/0.61 (define @t3 () (@var "V" $$unsorted)) % 0.41/0.61 (define @t4 () (tptp.less_than @t2 @t3)) % 0.41/0.61 (define @t5 () (@list @t2 @t3 @t1)) % 0.41/0.61 (define @t6 () (tptp.less_than @t3 @t2)) % 0.41/0.61 (define @t7 () (@list @t2 @t3)) % 0.41/0.61 (define @t8 () (@list @t2)) % 0.41/0.61 (define @t9 () (tptp.pair @t3 @t1)) % 0.41/0.61 (define @t10 () (tptp.insert_slb @t2 @t9)) % 0.41/0.61 (define @t11 () (= @t3 @t1)) % 0.41/0.61 (define @t12 () (tptp.contains_slb @t2 @t1)) % 0.41/0.61 (define @t13 () (@var "X" $$unsorted)) % 0.41/0.61 (define @t14 () (tptp.pair @t3 @t13)) % 0.41/0.61 (define @t15 () (tptp.insert_slb @t2 @t14)) % 0.41/0.61 (define @t16 () (@list @t2 @t3 @t1 @t13)) % 0.41/0.61 (define @t17 () (@var "Y" $$unsorted)) % 0.41/0.61 (define @t18 () (@list @t2 @t3 @t1 @t13 @t17)) % 0.41/0.61 (define @t19 () (and (not @t11) @t12)) % 0.41/0.61 (define @t20 () (tptp.update_slb @t2 @t1)) % 0.41/0.61 (define @t21 () (tptp.update_slb @t15 @t1)) % 0.41/0.61 (define @t22 () (tptp.succ_cpq @t2 @t3)) % 0.41/0.61 (define @t23 () (tptp.triple @t2 tptp.create_slb @t3)) % 0.41/0.61 (define @t24 () (tptp.triple @t2 @t3 @t1)) % 0.41/0.61 (define @t25 () (tptp.check_cpq (tptp.triple @t2 (tptp.insert_slb @t3 (tptp.pair @t13 @t17)) @t1))) % 0.41/0.61 (define @t26 () (tptp.contains_slb @t3 @t13)) % 0.41/0.61 (define @t27 () (tptp.triple @t2 @t3 tptp.bad)) % 0.41/0.61 (define @t28 () (tptp.ok @t24)) % 0.41/0.61 (define @t29 () (not @t28)) % 0.41/0.61 (define @t30 () (tptp.remove_cpq @t24 @t13)) % 0.41/0.61 (define @t31 () (tptp.remove_slb @t3 @t13)) % 0.41/0.61 (define @t32 () (tptp.remove_pqp @t2 @t13)) % 0.41/0.61 (define @t33 () (tptp.lookup_slb @t3 @t13)) % 0.41/0.61 (define @t34 () (tptp.findmin_pqp_res @t2)) % 0.41/0.61 (define @t35 () (tptp.update_slb @t3 @t34)) % 0.41/0.61 (define @t36 () (tptp.findmin_cpq_eff @t24)) % 0.41/0.61 (define @t37 () (= @t36 (tptp.triple @t2 @t35 tptp.bad))) % 0.41/0.61 (define @t38 () (tptp.contains_slb @t3 @t34)) % 0.41/0.61 (define @t39 () (not (= @t3 tptp.create_slb))) % 0.41/0.61 (define @t40 () (tptp.lookup_slb @t3 @t34)) % 0.41/0.61 (define @t41 () (tptp.findmin_cpq_res @t2)) % 0.41/0.61 (define @t42 () (@var "X6" $$unsorted)) % 0.41/0.61 (define @t43 () (@var "X5" $$unsorted)) % 0.41/0.61 (define @t44 () (@var "X4" $$unsorted)) % 0.41/0.61 (define @t45 () (tptp.triple @t44 @t43 @t42)) % 0.41/0.61 (define @t46 () (not (tptp.ok @t45))) % 0.41/0.61 (define @t47 () (@var "X3" $$unsorted)) % 0.41/0.61 (define @t48 () (@var "X2" $$unsorted)) % 0.41/0.61 (define @t49 () (@var "X1" $$unsorted)) % 0.41/0.61 (define @t50 () (tptp.triple @t49 @t48 @t47)) % 0.41/0.61 (define @t51 () (tptp.succ_cpq @t50 @t45)) % 0.41/0.61 (define @t52 () (@list @t44 @t43 @t42)) % 0.41/0.61 (define @t53 () (forall @t52 (=> @t51 @t46))) % 0.41/0.61 (define @t54 () (tptp.ok @t50)) % 0.41/0.61 (define @t55 () (not @t54)) % 0.41/0.61 (define @t56 () (=> @t55 @t53)) % 0.41/0.61 (define @t57 () (@list @t49 @t48 @t47)) % 0.41/0.61 (define @t58 () (forall @t57 @t56)) % 0.41/0.61 (define @t59 () (@var "Z" $$unsorted)) % 0.41/0.61 (define @t60 () (tptp.triple @t13 @t17 @t59)) % 0.41/0.61 (define @t61 () (not (tptp.ok (tptp.im_succ_cpq @t60)))) % 0.41/0.61 (define @t62 () (tptp.ok @t60)) % 0.41/0.61 (define @t63 () (not @t62)) % 0.41/0.61 (define @t64 () (=> @t63 @t61)) % 0.41/0.61 (define @t65 () (tptp.succ_cpq @t24 @t60)) % 0.41/0.61 (define @t66 () (@list @t2 @t3 @t1 @t13 @t17 @t59)) % 0.41/0.61 (define @t67 () (forall @t66 (=> @t65 @t64))) % 0.41/0.61 (define @t68 () (=> @t67 @t58)) % 0.41/0.61 (define @t69 () (not (tptp.ok (tptp.im_succ_cpq @t24)))) % 0.41/0.61 (define @t70 () (forall @t5 (=> @t29 @t69))) % 0.41/0.61 (define @t71 () (@list @t13 @t17 @t59)) % 0.41/0.61 (define @t72 () (forall @t71 (=> @t65 @t63))) % 0.41/0.61 (define @t73 () (=> @t29 @t72)) % 0.41/0.61 (define @t74 () (forall @t5 @t73)) % 0.41/0.61 (define @t75 () (not @t74)) % 0.41/0.61 (define @t76 () (not @t29)) % 0.41/0.61 (define @t77 () (@var "BOUND_VARIABLE_7849" $$unsorted)) % 0.41/0.61 (define @t78 () (@var "BOUND_VARIABLE_7847" $$unsorted)) % 0.41/0.61 (define @t79 () (@var "BOUND_VARIABLE_7845" $$unsorted)) % 0.41/0.61 (define @t80 () (tptp.triple @t79 @t78 @t77)) % 0.41/0.61 (define @t81 () (not (tptp.ok @t80))) % 0.41/0.61 (define @t82 () (not (tptp.succ_cpq @t24 @t80))) % 0.41/0.61 (define @t83 () (or @t28 @t82 @t81)) % 0.41/0.61 (define @t84 () (or @t82 @t81)) % 0.41/0.61 (define @t85 () (or @t28 @t84)) % 0.41/0.61 (define @t86 () (@list @t2 @t3 @t1 @t79 @t78 @t77)) % 0.41/0.61 (define @t87 () (forall @t86 @t85)) % 0.41/0.61 (define @t88 () (@list @t79 @t78 @t77)) % 0.41/0.61 (define @t89 () (forall @t88 @t85)) % 0.41/0.61 (define @t90 () (forall @t88 @t84)) % 0.41/0.61 (define @t91 () (or @t28 @t90)) % 0.41/0.61 (define @t92 () (not @t65)) % 0.41/0.61 (define @t93 () (forall @t71 (or @t92 @t63))) % 0.41/0.61 (define @t94 () (@var "BOUND_VARIABLE_7821" $$unsorted)) % 0.41/0.61 (define @t95 () (@var "BOUND_VARIABLE_7819" $$unsorted)) % 0.41/0.61 (define @t96 () (@var "BOUND_VARIABLE_7817" $$unsorted)) % 0.41/0.61 (define @t97 () (tptp.triple @t96 @t95 @t94)) % 0.41/0.61 (define @t98 () (not (tptp.ok @t97))) % 0.41/0.61 (define @t99 () (not (tptp.succ_cpq @t50 @t97))) % 0.41/0.61 (define @t100 () (or @t54 @t99 @t98)) % 0.41/0.61 (define @t101 () (@list @t49 @t48 @t47 @t96 @t95 @t94)) % 0.41/0.61 (define @t102 () (forall @t101 @t100)) % 0.41/0.61 (define @t103 () (not @t102)) % 0.41/0.61 (define @t104 () (forall @t86 @t83)) % 0.41/0.61 (define @t105 () (@list true)) % 0.41/0.61 (define @t106 () (or @t99 @t98)) % 0.41/0.61 (define @t107 () (or @t54 @t106)) % 0.41/0.61 (define @t108 () (forall @t101 @t107)) % 0.41/0.61 (define @t109 () (@list @t96 @t95 @t94)) % 0.41/0.61 (define @t110 () (forall @t109 @t107)) % 0.41/0.61 (define @t111 () (forall @t109 @t106)) % 0.41/0.61 (define @t112 () (or @t54 @t111)) % 0.41/0.61 (define @t113 () (forall @t52 (or (not @t51) @t46))) % 0.41/0.61 (define @t114 () (or @t92 @t62 @t61)) % 0.41/0.61 (define @t115 () (forall @t66 @t114)) % 0.41/0.61 (define @t116 () (not @t115)) % 0.41/0.61 (define @t117 () (@quantifiers_skolemize @t115 5)) % 0.41/0.61 (define @t118 () (@quantifiers_skolemize @t115 4)) % 0.41/0.61 (define @t119 () (@quantifiers_skolemize @t115 3)) % 0.41/0.61 (define @t120 () (tptp.triple @t119 @t118 @t117)) % 0.41/0.61 (define @t121 () (tptp.ok (tptp.im_succ_cpq @t120))) % 0.41/0.61 (define @t122 () (not @t121)) % 0.41/0.61 (define @t123 () (tptp.ok @t120)) % 0.41/0.61 (define @t124 () (or (not (tptp.succ_cpq (tptp.triple (@quantifiers_skolemize @t115 0) (@quantifiers_skolemize @t115 1) (@quantifiers_skolemize @t115 2)) @t120)) @t123 @t122)) % 0.41/0.61 (define @t125 () (@list @t124)) % 0.41/0.61 (define @t126 () (or @t123 @t122)) % 0.41/0.61 (define @t127 () (not @t126)) % 0.41/0.61 (define @t128 () (@list true false)) % 0.41/0.61 (define @t129 () (forall @t5 (or @t28 @t69))) % 0.41/0.61 (assume @p1 (forall @t5 (=> (and @t4 (tptp.less_than @t3 @t1)) (tptp.less_than @t2 @t1)))) % 0.41/0.61 (assume @p2 (forall @t7 (or @t4 @t6))) % 0.41/0.61 (assume @p3 (forall @t8 (tptp.less_than @t2 @t2))) % 0.41/0.61 (assume @p4 (forall @t7 (= (tptp.strictly_less_than @t2 @t3) (and @t4 (not @t6))))) % 0.41/0.61 (assume @p5 (forall @t8 (tptp.less_than tptp.bottom @t2))) % 0.41/0.61 (assume @p6 (not (tptp.isnonempty_slb tptp.create_slb))) % 0.41/0.61 (assume @p7 (forall @t5 (tptp.isnonempty_slb @t10))) % 0.41/0.61 (assume @p8 (forall @t8 (not (tptp.contains_slb tptp.create_slb @t2)))) % 0.41/0.61 (assume @p9 (forall @t16 (= (tptp.contains_slb @t15 @t1) (or @t12 @t11)))) % 0.41/0.61 (assume @p10 (forall @t7 (not (tptp.pair_in_list tptp.create_slb @t2 @t3)))) % 0.41/0.61 (assume @p11 (forall @t18 (= (tptp.pair_in_list @t15 @t1 @t17) (or (tptp.pair_in_list @t2 @t1 @t17) (and @t11 (= @t13 @t17)))))) % 0.41/0.61 (assume @p12 (forall @t5 (= (tptp.remove_slb @t10 @t3) @t2))) % 0.41/0.61 (assume @p13 (forall @t16 (=> @t19 (= (tptp.remove_slb @t15 @t1) (tptp.insert_slb (tptp.remove_slb @t2 @t1) @t14))))) % 0.41/0.61 (assume @p14 (forall @t5 (= (tptp.lookup_slb @t10 @t3) @t1))) % 0.41/0.61 (assume @p15 (forall @t16 (=> @t19 (= (tptp.lookup_slb @t15 @t1) (tptp.lookup_slb @t2 @t1))))) % 0.41/0.61 (assume @p16 (forall @t8 (= (tptp.update_slb tptp.create_slb @t2) tptp.create_slb))) % 0.41/0.61 (assume @p17 (forall @t16 (=> (tptp.strictly_less_than @t13 @t1) (= @t21 (tptp.insert_slb @t20 @t9))))) % 0.41/0.61 (assume @p18 (forall @t16 (=> (tptp.less_than @t1 @t13) (= @t21 (tptp.insert_slb @t20 @t14))))) % 0.41/0.61 (assume @p19 (forall @t8 (tptp.succ_cpq @t2 @t2))) % 0.41/0.61 (assume @p20 (forall @t5 (=> @t22 (tptp.succ_cpq @t2 (tptp.insert_cpq @t3 @t1))))) % 0.41/0.61 (assume @p21 (forall @t5 (=> @t22 (tptp.succ_cpq @t2 (tptp.remove_cpq @t3 @t1))))) % 0.41/0.61 (assume @p22 (forall @t7 (=> @t22 (tptp.succ_cpq @t2 (tptp.findmin_cpq_eff @t3))))) % 0.41/0.61 (assume @p23 (forall @t7 (=> @t22 (tptp.succ_cpq @t2 (tptp.removemin_cpq_eff @t3))))) % 0.41/0.61 (assume @p24 (forall @t7 (tptp.check_cpq @t23))) % 0.41/0.61 (assume @p25 (forall @t18 (=> (tptp.less_than @t17 @t13) (= @t25 (tptp.check_cpq @t24))))) % 0.41/0.61 (assume @p26 (forall @t18 (=> (tptp.strictly_less_than @t13 @t17) (= @t25 false)))) % 0.41/0.61 (assume @p27 (forall @t16 (= (tptp.contains_cpq @t24 @t13) @t26))) % 0.41/0.61 (assume @p28 (forall @t7 (= (tptp.ok @t27) false))) % 0.41/0.61 (assume @p29 (forall @t5 (=> @t29 (= @t1 tptp.bad)))) % 0.41/0.61 (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)))) % 0.41/0.61 (assume @p31 (forall @t16 (=> (not @t26) (= @t30 @t27)))) % 0.41/0.61 (assume @p32 (forall @t16 (=> (and @t26 (tptp.less_than @t33 @t13)) (= @t30 (tptp.triple @t32 @t31 @t1))))) % 0.41/0.61 (assume @p33 (forall @t16 (=> (and @t26 (tptp.strictly_less_than @t13 @t33)) (= @t30 (tptp.triple @t32 @t31 tptp.bad))))) % 0.41/0.61 (assume @p34 (forall @t7 (= (tptp.findmin_cpq_eff @t23) (tptp.triple @t2 tptp.create_slb tptp.bad)))) % 0.41/0.61 (assume @p35 (forall @t16 (=> (and @t39 (not @t38)) @t37))) % 0.41/0.61 (assume @p36 (forall @t16 (=> (and @t39 @t38 (tptp.strictly_less_than @t34 @t40)) @t37))) % 0.41/0.61 (assume @p37 (forall @t16 (=> (and @t39 @t38 (tptp.less_than @t40 @t34)) (= @t36 (tptp.triple @t2 @t35 @t1))))) % 0.41/0.61 (assume @p38 (forall @t7 (= (tptp.findmin_cpq_res @t23) tptp.bottom))) % 0.41/0.61 (assume @p39 (forall @t16 (=> @t39 (= (tptp.findmin_cpq_res @t24) @t34)))) % 0.41/0.61 (assume @p40 (forall @t8 (= (tptp.removemin_cpq_eff @t2) (tptp.remove_cpq (tptp.findmin_cpq_eff @t2) @t41)))) % 0.41/0.61 (assume @p41 (forall @t8 (= (tptp.removemin_cpq_res @t2) @t41))) % 0.41/0.61 (assume @p42 @t68) % 0.41/0.61 (assume @p43 @t70) % 0.41/0.61 (assume @p44 @t75) % 0.41/0.61 (assume @p45 true) % 0.41/0.61 (step @p46 :rule refl :args (@t69)) % 0.41/0.61 (step @p47 :rule bool-double-not-elim :args (@t28)) % 0.41/0.61 (step @p48 :rule nary_cong :premises (@p47 @p46) :args ((or @t76 @t69))) % 0.41/0.61 (step @p49 :rule bool-impl-elim :args (@t29 @t69)) % 0.41/0.61 (step @p50 :rule trans :premises (@p49 @p48)) % 0.41/0.61 (step @p51 :rule cong :premises (@p50) :args (@t70)) % 0.41/0.61 (step @p52 :rule eq_resolve :premises (@p43 @p51)) % 0.41/0.61 (step @p53 :rule aci_norm :args ((= @t85 @t83))) % 0.41/0.61 (step @p54 :rule cong :premises (@p53) :args (@t87)) % 0.41/0.61 (step @p55 :rule quant-merge-prenex :args ((= (forall @t5 @t89) @t87))) % 0.41/0.61 (step @p56 :rule alpha_equiv :args (@t90 (@list @t79 @t78 @t77) (@list @t13 @t17 @t59))) % 0.41/0.61 (step @p57 :rule refl :args (@t28)) % 0.41/0.61 (step @p58 :rule nary_cong :premises (@p57 @p56) :args (@t91)) % 0.41/0.61 (step @p59 :rule quant-miniscope-or :args ((= @t89 @t91))) % 0.41/0.61 (step @p60 :rule trans :premises (@p59 @p58)) % 0.41/0.61 (step @p61 :rule symm :premises (@p60)) % 0.41/0.61 (step @p62 :rule cong :premises (@p61) :args ((forall @t5 (or @t28 @t93)))) % 0.41/0.61 (step @p63 :rule trans :premises (@p62 @p55)) % 0.41/0.61 (step @p64 :rule trans :premises (@p63 @p54)) % 0.41/0.61 (step @p65 :rule refl :args (@t93)) % 0.41/0.61 (step @p66 :rule nary_cong :premises (@p47 @p65) :args ((or @t76 @t93))) % 0.41/0.61 (step @p67 :rule bool-impl-elim :args (@t29 @t93)) % 0.41/0.61 (step @p68 :rule trans :premises (@p67 @p66)) % 0.41/0.61 (step @p69 :rule cong :premises (@p68) :args ((forall @t5 (=> @t29 @t93)))) % 0.41/0.61 (step @p70 :rule trans :premises (@p69 @p64)) % 0.41/0.61 (step @p71 :rule bool-impl-elim :args (@t65 @t63)) % 0.41/0.61 (step @p72 :rule cong :premises (@p71) :args (@t72)) % 0.41/0.61 (step @p73 :rule refl :args (@t29)) % 0.41/0.61 (step @p74 :rule cong :premises (@p73 @p72) :args (@t73)) % 0.41/0.61 (step @p75 :rule cong :premises (@p74) :args (@t74)) % 0.41/0.61 (step @p76 :rule trans :premises (@p75 @p70)) % 0.41/0.61 (step @p77 :rule cong :premises (@p76) :args (@t75)) % 0.41/0.61 (step @p78 :rule eq_resolve :premises (@p44 @p77)) % 0.41/0.61 (step @p79 :rule alpha_equiv :args (@t102 (@list @t49 @t48 @t47 @t96 @t95 @t94) (@list @t2 @t3 @t1 @t79 @t78 @t77))) % 0.41/0.61 (step @p80 :rule equiv_elim1 :premises (@p79)) % 0.41/0.61 (step @p81 :rule reordering :premises (@p80) :args ((or @t104 @t103))) % 0.41/0.61 (step @p82 :rule chain_m_resolution :premises (@p81 @p78) :args (@t103 @t105 (@list @t104))) % 0.41/0.61 (step @p83 :rule aci_norm :args ((= @t107 @t100))) % 0.41/0.61 (step @p84 :rule cong :premises (@p83) :args (@t108)) % 0.41/0.61 (step @p85 :rule quant-merge-prenex :args ((= (forall @t57 @t110) @t108))) % 0.41/0.61 (step @p86 :rule alpha_equiv :args (@t111 (@list @t96 @t95 @t94) (@list @t44 @t43 @t42))) % 0.41/0.61 (step @p87 :rule refl :args (@t54)) % 0.41/0.61 (step @p88 :rule nary_cong :premises (@p87 @p86) :args (@t112)) % 0.41/0.61 (step @p89 :rule quant-miniscope-or :args ((= @t110 @t112))) % 0.41/0.61 (step @p90 :rule trans :premises (@p89 @p88)) % 0.41/0.61 (step @p91 :rule symm :premises (@p90)) % 0.41/0.61 (step @p92 :rule cong :premises (@p91) :args ((forall @t57 (or @t54 @t113)))) % 0.41/0.61 (step @p93 :rule trans :premises (@p92 @p85)) % 0.41/0.61 (step @p94 :rule trans :premises (@p93 @p84)) % 0.41/0.61 (step @p95 :rule refl :args (@t113)) % 0.41/0.61 (step @p96 :rule bool-double-not-elim :args (@t54)) % 0.41/0.61 (step @p97 :rule nary_cong :premises (@p96 @p95) :args ((or (not @t55) @t113))) % 0.41/0.61 (step @p98 :rule bool-impl-elim :args (@t55 @t113)) % 0.41/0.61 (step @p99 :rule trans :premises (@p98 @p97)) % 0.41/0.61 (step @p100 :rule cong :premises (@p99) :args ((forall @t57 (=> @t55 @t113)))) % 0.41/0.61 (step @p101 :rule trans :premises (@p100 @p94)) % 0.41/0.61 (step @p102 :rule bool-impl-elim :args (@t51 @t46)) % 0.41/0.61 (step @p103 :rule cong :premises (@p102) :args (@t53)) % 0.41/0.61 (step @p104 :rule refl :args (@t55)) % 0.41/0.61 (step @p105 :rule cong :premises (@p104 @p103) :args (@t56)) % 0.41/0.61 (step @p106 :rule cong :premises (@p105) :args (@t58)) % 0.41/0.61 (step @p107 :rule trans :premises (@p106 @p101)) % 0.41/0.61 (step @p108 :rule aci_norm :args ((= (or @t92 (or @t62 @t61)) @t114))) % 0.41/0.61 (step @p109 :rule refl :args (@t61)) % 0.41/0.61 (step @p110 :rule bool-double-not-elim :args (@t62)) % 0.41/0.61 (step @p111 :rule nary_cong :premises (@p110 @p109) :args ((or (not @t63) @t61))) % 0.41/0.61 (step @p112 :rule bool-impl-elim :args (@t63 @t61)) % 0.41/0.61 (step @p113 :rule trans :premises (@p112 @p111)) % 0.41/0.61 (step @p114 :rule refl :args (@t92)) % 0.41/0.61 (step @p115 :rule nary_cong :premises (@p114 @p113) :args ((or @t92 @t64))) % 0.41/0.61 (step @p116 :rule trans :premises (@p115 @p108)) % 0.41/0.61 (step @p117 :rule bool-impl-elim :args (@t65 @t64)) % 0.41/0.61 (step @p118 :rule trans :premises (@p117 @p116)) % 0.41/0.61 (step @p119 :rule cong :premises (@p118) :args (@t67)) % 0.41/0.61 (step @p120 :rule cong :premises (@p119 @p107) :args (@t68)) % 0.41/0.61 (step @p121 :rule eq_resolve :premises (@p42 @p120)) % 0.41/0.61 (step @p122 :rule implies_elim :premises (@p121)) % 0.41/0.61 (step @p123 :rule reordering :premises (@p122) :args ((or @t102 @t116))) % 0.41/0.61 (step @p124 :rule chain_m_resolution :premises (@p123 @p82) :args (@t116 @t105 (@list @t102))) % 0.41/0.61 (step @p125 :rule skolemize :premises (@p124)) % 0.41/0.61 (step @p126 :rule bool-double-not-elim :args (@t121)) % 0.41/0.61 (step @p127 :rule refl :args (@t124)) % 0.41/0.61 (step @p128 :rule nary_cong :premises (@p127 @p126) :args ((or @t124 (not @t122)))) % 0.41/0.61 (step @p129 :rule cnf_or_neg :args (@t124 2)) % 0.41/0.61 (step @p130 :rule eq_resolve :premises (@p129 @p128)) % 0.41/0.61 (step @p131 :rule reordering :premises (@p130) :args ((or @t121 @t124))) % 0.41/0.61 (step @p132 :rule chain_m_resolution :premises (@p131 @p125) :args (@t121 @t105 @t125)) % 0.41/0.61 (step @p133 :rule cnf_or_neg :args (@t124 1)) % 0.41/0.61 (step @p134 :rule chain_m_resolution :premises (@p133 @p125) :args ((not @t123) @t105 @t125)) % 0.41/0.61 (step @p135 :rule cnf_or_pos :args (@t126)) % 0.41/0.61 (step @p136 :rule reordering :premises (@p135) :args ((or @t123 @t122 @t127))) % 0.41/0.61 (step @p137 :rule chain_m_resolution :premises (@p136 @p134 @p132) :args (@t127 @t128 (@list @t123 @t121))) % 0.41/0.61 (assume-push @p144 @t129) % 0.41/0.61 (step @p139 :rule instantiate :premises (@p52) :args ((@list @t119 @t118 @t117))) % 0.41/0.61 (step-pop @p145 :rule scope :premises (@p139)) % 0.41/0.61 (step @p140 :rule process_scope :premises (@p145) :args (@t126)) % 0.41/0.61 (step @p142 :rule implies_elim :premises (@p140)) % 0.41/0.61 (step @p143 false :rule chain_m_resolution :premises (@p142 @p137 @p52) :args (false @t128 (@list @t126 @t129))) % 0.41/0.61 ) % 0.41/0.61 % SZS output end Proof % 0.41/0.61 % cvc5 exiting %------------------------------------------------------------------------------