%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SWV417+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n023.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 : Thu Aug 31 21:51:04 EDT 2023

% Result   : Theorem 0.21s 0.56s
% Output   : Proof 0.21s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : SWV417+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.13  % Command    : do_cvc5 %s %d
% 0.14/0.34  % Computer : n023.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Tue Aug 29 06:52:10 EDT 2023
% 0.14/0.34  % CPUTime    : 
% 0.21/0.48  %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.56  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.djI1QElgLB/cvc5---1.0.5_17669.p...
% 0.21/0.56  ------- get file name : TPTP file name is SWV417+1
% 0.21/0.56  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_17669.smt2...
% 0.21/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.56  % SZS status Theorem for SWV417+1
% 0.21/0.56  % SZS output start Proof for SWV417+1
% 0.21/0.56  (
% 0.21/0.56  (let ((_let_1 (not (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (=> (tptp.pi_find_min _let_1) (=> (tptp.phi (tptp.findmin_cpq_eff _let_1)) (exists ((X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (let ((_let_2 (tptp.i _let_1))) (and (tptp.pi_sharp_find_min _let_2 X) (= (tptp.findmin_cpq_res _let_1) (tptp.findmin_pq_res _let_2 X))))))))))))) (let ((_let_2 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (=> (tptp.phi (tptp.findmin_cpq_eff _let_1)) (tptp.pi_sharp_find_min (tptp.i _let_1) (tptp.findmin_cpq_res _let_1))))))) (let ((_let_3 (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_sharp_find_min U V) (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)))))) (let ((_let_4 (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.findmin_pq_res U V) V))))) (let ((_let_5 (forall ((U $$unsorted) (V $$unsorted)) (or (not (tptp.contains_pq U V)) (not (tptp.issmallestelement_pq U V)) (= V (tptp.findmin_pq_res U V)))))) (let ((_let_6 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_7 (tptp.findmin_cpq_res _let_6))) (let ((_let_8 (tptp.i _let_6))) (let ((_let_9 (= _let_7 (tptp.findmin_pq_res _let_8 _let_7)))) (let ((_let_10 (tptp.issmallestelement_pq _let_8 _let_7))) (let ((_let_11 (not _let_10))) (let ((_let_12 (tptp.contains_pq _let_8 _let_7))) (let ((_let_13 (not _let_12))) (let ((_let_14 (or _let_13 _let_11 _let_9))) (let ((_let_15 (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_16 (not _let_14))) (let ((_let_17 (and _let_12 _let_10))) (let ((_let_18 (tptp.pi_sharp_find_min _let_8 _let_7))) (let ((_let_19 (= _let_18 _let_17))) (let ((_let_20 (_let_3))) (let ((_let_21 (ASSUME :args _let_20))) (let ((_let_22 (tptp.phi (tptp.findmin_cpq_eff _let_6)))) (let ((_let_23 (not _let_22))) (let ((_let_24 (or _let_23 _let_18))) (let ((_let_25 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (or (not (tptp.phi (tptp.findmin_cpq_eff _let_1))) (tptp.pi_sharp_find_min (tptp.i _let_1) (tptp.findmin_cpq_res _let_1))))))) (let ((_let_26 (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_27 (forall ((X $$unsorted)) (let ((_let_1 (tptp.triple SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4))) (let ((_let_2 (tptp.i _let_1))) (or (not (tptp.pi_sharp_find_min _let_2 X)) (not (= (tptp.findmin_cpq_res _let_1) (tptp.findmin_pq_res _let_2 X))))))))) (let ((_let_28 (not _let_27))) (let ((_let_29 (or (not (tptp.pi_find_min _let_6)) _let_23 _let_28))) (let ((_let_30 (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (or (not (tptp.pi_find_min _let_1)) (not (tptp.phi (tptp.findmin_cpq_eff _let_1))) (not (forall ((X $$unsorted)) (let ((_let_1 (tptp.triple U V W))) (let ((_let_2 (tptp.i _let_1))) (or (not (tptp.pi_sharp_find_min _let_2 X)) (not (= (tptp.findmin_cpq_res _let_1) (tptp.findmin_pq_res _let_2 X))))))))))))) (let ((_let_31 (not _let_29))) (let ((_let_32 (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_33 (or))) (let ((_let_34 (not _let_30))) (let ((_let_35 (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (IMPLIES_ELIM (SCOPE (SKOLEMIZE _let_32) :args (_let_34))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_34) _let_30))) (REFL :args (_let_31)) :args _let_33)) _let_32 :args (_let_31 true _let_30)))) (let ((_let_36 (REFL :args (_let_29)))) (let ((_let_37 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_24)) :args ((or _let_23 _let_18 (not _let_24)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 1)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_23) _let_22))) :args _let_33)) :args ((or _let_22 _let_29))) _let_35 :args (_let_22 true _let_29)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_26 :args (SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_2 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_3 SKOLEM_FUN_QUANTIFIERS_SKOLEMIZE_4 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.triple U V W)))) :args (_let_25))) _let_26 :args (_let_24 false _let_25)) :args (_let_18 false _let_22 false _let_24)))) (let ((_let_38 (not _let_18))) (let ((_let_39 (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS1 :args (_let_19)) :args ((or _let_38 _let_17 (not _let_19)))) _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_21 :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((tptp.pi_sharp_find_min U V)))) :args _let_20)) _let_21 :args (_let_19 false _let_3)) :args (_let_17 false _let_18 false _let_19)))) (let ((_let_40 (not _let_17))) (let ((_let_41 (not _let_9))) (let ((_let_42 (or _let_38 _let_41))) (let ((_let_43 (_let_27))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_15 :args (_let_8 _let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.contains_pq U V) false))))) :args (_let_5))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_14)) :args ((or _let_9 _let_13 _let_11 _let_16))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_42)) :args ((or _let_38 _let_41 (not _let_42)))) _let_37 (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE (ASSUME :args _let_43) :args (_let_7 QUANTIFIERS_INST_E_MATCHING_SIMPLE ((not (= (tptp.pi_sharp_find_min _let_8 X) false))))) :args _let_43)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_OR_NEG :args (_let_29 2)) (CONG _let_36 (MACRO_SR_PRED_INTRO :args ((= (not _let_28) _let_27))) :args _let_33)) :args ((or _let_27 _let_29))) _let_35 :args (_let_27 true _let_29)) :args (_let_42 false _let_27)) :args (_let_41 false _let_18 false _let_42)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_17 0)) :args ((or _let_12 _let_40))) _let_39 :args (_let_12 false _let_17)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_AND_POS :args (_let_17 1)) :args ((or _let_10 _let_40))) _let_39 :args (_let_10 false _let_17)) :args (_let_16 true _let_9 false _let_12 false _let_10)) _let_15 :args (false true _let_14 false _let_5)) :args ((forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.less_than U V) (tptp.less_than V W)) (tptp.less_than U W))) (forall ((U $$unsorted) (V $$unsorted)) (or (tptp.less_than U V) (tptp.less_than V U))) (forall ((U $$unsorted)) (tptp.less_than U U)) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.strictly_less_than U V) (and (tptp.less_than U V) (not (tptp.less_than V U))))) (forall ((U $$unsorted)) (tptp.less_than tptp.bottom U)) (not (tptp.isnonempty_pq tptp.create_pq)) (forall ((U $$unsorted) (V $$unsorted)) (tptp.isnonempty_pq (tptp.insert_pq U V))) (forall ((U $$unsorted)) (not (tptp.contains_pq tptp.create_pq U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.contains_pq (tptp.insert_pq U V) W) (or (tptp.contains_pq U W) (= V W)))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.issmallestelement_pq U V) (forall ((W $$unsorted)) (=> (tptp.contains_pq U W) (tptp.less_than V W))))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.remove_pq (tptp.insert_pq U V) V) U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (and (tptp.contains_pq U W) (not (= V W))) (= (tptp.remove_pq (tptp.insert_pq U V) W) (tptp.insert_pq (tptp.remove_pq U W) V)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.findmin_pq_eff U V) U))) _let_4 (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.removemin_pq_eff U V) (tptp.remove_pq U V)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)) (= (tptp.removemin_pq_res U V) V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.insert_pq (tptp.insert_pq U V) W) (tptp.insert_pq (tptp.insert_pq U W) V))) (not (tptp.isnonempty_slb tptp.create_slb)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (tptp.isnonempty_slb (tptp.insert_slb U (tptp.pair V W)))) (forall ((U $$unsorted)) (not (tptp.contains_slb tptp.create_slb U))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.contains_slb (tptp.insert_slb U (tptp.pair V X)) W) (or (tptp.contains_slb U W) (= V W)))) (forall ((U $$unsorted) (V $$unsorted)) (not (tptp.pair_in_list tptp.create_slb U V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.pair_in_list (tptp.insert_slb U (tptp.pair V X)) W Y) (or (tptp.pair_in_list U W Y) (and (= V W) (= X Y))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.remove_slb (tptp.insert_slb U (tptp.pair V W)) V) U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.pair V X))) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.remove_slb (tptp.insert_slb U _let_1) W) (tptp.insert_slb (tptp.remove_slb U W) _let_1))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V W)) V) W)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (not (= V W)) (tptp.contains_slb U W)) (= (tptp.lookup_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.lookup_slb U W)))) (forall ((U $$unsorted)) (= (tptp.update_slb tptp.create_slb U) tptp.create_slb)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (tptp.strictly_less_than X W) (= (tptp.update_slb (tptp.insert_slb U (tptp.pair V X)) W) (tptp.insert_slb (tptp.update_slb U W) (tptp.pair V W))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.pair V X))) (=> (tptp.less_than W X) (= (tptp.update_slb (tptp.insert_slb U _let_1) W) (tptp.insert_slb (tptp.update_slb U W) _let_1))))) (forall ((U $$unsorted)) (tptp.succ_cpq U U)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.insert_cpq V W)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.remove_cpq V W)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.findmin_cpq_eff V)))) (forall ((U $$unsorted) (V $$unsorted)) (=> (tptp.succ_cpq U V) (tptp.succ_cpq U (tptp.removemin_cpq_eff V)))) (forall ((U $$unsorted) (V $$unsorted)) (tptp.check_cpq (tptp.triple U tptp.create_slb V))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.less_than Y X) (= (tptp.check_cpq (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) (tptp.check_cpq (tptp.triple U V W))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (=> (tptp.strictly_less_than X Y) (= (tptp.check_cpq (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) false))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.contains_cpq (tptp.triple U V W) X) (tptp.contains_slb V X))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.ok (tptp.triple U V tptp.bad)) false)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted)) (=> (not (tptp.ok (tptp.triple U V W))) (= W tptp.bad))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (= (tptp.insert_cpq (tptp.triple U V W) X) (tptp.triple (tptp.insert_pqp U X) (tptp.insert_slb V (tptp.pair X tptp.bottom)) W))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (not (tptp.contains_slb V X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple U V tptp.bad)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.less_than (tptp.lookup_slb V X) X)) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) W)))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (and (tptp.contains_slb V X) (tptp.strictly_less_than X (tptp.lookup_slb V X))) (= (tptp.remove_cpq (tptp.triple U V W) X) (tptp.triple (tptp.remove_pqp U X) (tptp.remove_slb V X) tptp.bad)))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.findmin_cpq_eff (tptp.triple U tptp.create_slb V)) (tptp.triple U tptp.create_slb tptp.bad))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (=> (and (not (= V tptp.create_slb)) (not (tptp.contains_slb V _let_1))) (= (tptp.findmin_cpq_eff (tptp.triple U V W)) (tptp.triple U (tptp.update_slb V _let_1) tptp.bad))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (=> (and (not (= V tptp.create_slb)) (tptp.contains_slb V _let_1) (tptp.strictly_less_than _let_1 (tptp.lookup_slb V _let_1))) (= (tptp.findmin_cpq_eff (tptp.triple U V W)) (tptp.triple U (tptp.update_slb V _let_1) tptp.bad))))) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (let ((_let_1 (tptp.findmin_pqp_res U))) (=> (and (not (= V tptp.create_slb)) (tptp.contains_slb V _let_1) (tptp.less_than (tptp.lookup_slb V _let_1) _let_1)) (= (tptp.findmin_cpq_eff (tptp.triple U V W)) (tptp.triple U (tptp.update_slb V _let_1) W))))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.findmin_cpq_res (tptp.triple U tptp.create_slb V)) tptp.bottom)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted)) (=> (not (= V tptp.create_slb)) (= (tptp.findmin_cpq_res (tptp.triple U V W)) (tptp.findmin_pqp_res U)))) (forall ((U $$unsorted)) (= (tptp.removemin_cpq_eff U) (tptp.remove_cpq (tptp.findmin_cpq_eff U) (tptp.findmin_cpq_res U)))) (forall ((U $$unsorted)) (= (tptp.removemin_cpq_res U) (tptp.findmin_cpq_res U))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.i (tptp.triple U tptp.create_slb V)) tptp.create_pq)) (forall ((U $$unsorted) (V $$unsorted) (W $$unsorted) (X $$unsorted) (Y $$unsorted)) (= (tptp.i (tptp.triple U (tptp.insert_slb V (tptp.pair X Y)) W)) (tptp.insert_pq (tptp.i (tptp.triple U V W)) X))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_sharp_remove U V) (tptp.contains_pq U V))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_remove U V) (tptp.pi_sharp_remove (tptp.i U) V))) _let_3 (forall ((U $$unsorted)) (= (tptp.pi_find_min U) (exists ((V $$unsorted)) (tptp.pi_sharp_find_min (tptp.i U) V)))) (forall ((U $$unsorted) (V $$unsorted)) (= (tptp.pi_sharp_removemin U V) (and (tptp.contains_pq U V) (tptp.issmallestelement_pq U V)))) (forall ((U $$unsorted)) (= (tptp.pi_removemin U) (exists ((V $$unsorted)) (tptp.pi_sharp_find_min (tptp.i U) V)))) (forall ((U $$unsorted)) (= (tptp.phi U) (exists ((V $$unsorted)) (and (tptp.succ_cpq U V) (tptp.ok V) (tptp.check_cpq V))))) _let_2 _let_1 true))))))))))))))))))))))))))))))))))))))))))))))
% 0.21/0.57  )
% 0.21/0.57  % SZS output end Proof for SWV417+1
% 0.21/0.57  % cvc5---1.0.5 exiting
% 0.41/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------