TSTP Solution File: SWV408+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SWV408+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 21:38:27 EDT 2023
% Result : Theorem 0.20s 0.62s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 36
% Syntax : Number of formulae : 57 ( 9 unt; 32 typ; 0 def)
% Number of atoms : 65 ( 10 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 62 ( 22 ~; 26 |; 10 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 25 >; 20 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 41 ( 3 sgn; 25 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
less_than: ( $i * $i ) > $o ).
tff(decl_23,type,
strictly_less_than: ( $i * $i ) > $o ).
tff(decl_24,type,
bottom: $i ).
tff(decl_25,type,
create_slb: $i ).
tff(decl_26,type,
isnonempty_slb: $i > $o ).
tff(decl_27,type,
pair: ( $i * $i ) > $i ).
tff(decl_28,type,
insert_slb: ( $i * $i ) > $i ).
tff(decl_29,type,
contains_slb: ( $i * $i ) > $o ).
tff(decl_30,type,
pair_in_list: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
remove_slb: ( $i * $i ) > $i ).
tff(decl_32,type,
lookup_slb: ( $i * $i ) > $i ).
tff(decl_33,type,
update_slb: ( $i * $i ) > $i ).
tff(decl_34,type,
succ_cpq: ( $i * $i ) > $o ).
tff(decl_35,type,
insert_cpq: ( $i * $i ) > $i ).
tff(decl_36,type,
remove_cpq: ( $i * $i ) > $i ).
tff(decl_37,type,
findmin_cpq_eff: $i > $i ).
tff(decl_38,type,
removemin_cpq_eff: $i > $i ).
tff(decl_39,type,
triple: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
check_cpq: $i > $o ).
tff(decl_41,type,
contains_cpq: ( $i * $i ) > $o ).
tff(decl_42,type,
bad: $i ).
tff(decl_43,type,
ok: $i > $o ).
tff(decl_44,type,
insert_pqp: ( $i * $i ) > $i ).
tff(decl_45,type,
remove_pqp: ( $i * $i ) > $i ).
tff(decl_46,type,
findmin_pqp_res: $i > $i ).
tff(decl_47,type,
findmin_cpq_res: $i > $i ).
tff(decl_48,type,
removemin_cpq_res: $i > $i ).
tff(decl_49,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk2_0: $i ).
tff(decl_51,type,
esk3_0: $i ).
tff(decl_52,type,
esk4_0: $i ).
tff(decl_53,type,
esk5_0: $i ).
fof(l44_co,conjecture,
! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
| ? [X5] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
& less_than(findmin_pqp_res(X1),X5) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(l44_l45,lemma,
! [X1,X2,X3] :
( ( contains_slb(X1,X2)
& strictly_less_than(X2,X3) )
=> ( pair_in_list(update_slb(X1,X3),X2,X3)
| ? [X4] :
( pair_in_list(update_slb(X1,X3),X2,X4)
& less_than(X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_l45) ).
fof(ax51,axiom,
! [X1,X2,X3,X4] :
( X2 != create_slb
=> findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(ax20,axiom,
! [X1] : ~ contains_slb(create_slb,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax20) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( contains_slb(X2,X4)
& strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3))) )
=> ( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1))
| ? [X5] :
( pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5)
& less_than(findmin_pqp_res(X1),X5) ) ) ),
inference(assume_negation,[status(cth)],[l44_co]) ).
fof(c_0_5,lemma,
! [X119,X120,X121] :
( ( pair_in_list(update_slb(X119,X121),X120,esk1_3(X119,X120,X121))
| pair_in_list(update_slb(X119,X121),X120,X121)
| ~ contains_slb(X119,X120)
| ~ strictly_less_than(X120,X121) )
& ( less_than(X121,esk1_3(X119,X120,X121))
| pair_in_list(update_slb(X119,X121),X120,X121)
| ~ contains_slb(X119,X120)
| ~ strictly_less_than(X120,X121) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l44_l45])])])]) ).
fof(c_0_6,negated_conjecture,
! [X127] :
( contains_slb(esk3_0,esk5_0)
& strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0)))
& ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0))
& ( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X127)
| ~ less_than(findmin_pqp_res(esk2_0),X127) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_7,plain,
! [X114,X115,X116] :
( X115 = create_slb
| findmin_cpq_res(triple(X114,X115,X116)) = findmin_pqp_res(X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
cnf(c_0_8,lemma,
( pair_in_list(update_slb(X1,X2),X3,esk1_3(X1,X3,X2))
| pair_in_list(update_slb(X1,X2),X3,X2)
| ~ contains_slb(X1,X3)
| ~ strictly_less_than(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
contains_slb(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,lemma,
( less_than(X1,esk1_3(X2,X3,X1))
| pair_in_list(update_slb(X2,X1),X3,X1)
| ~ contains_slb(X2,X3)
| ~ strictly_less_than(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk5_0,esk1_3(esk3_0,esk5_0,X1))
| pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
| ~ strictly_less_than(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( esk3_0 = create_slb
| strictly_less_than(esk5_0,findmin_pqp_res(esk2_0)) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,negated_conjecture,
~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,findmin_pqp_res(esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
| less_than(X1,esk1_3(esk3_0,esk5_0,X1))
| ~ strictly_less_than(esk5_0,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
fof(c_0_17,plain,
! [X1] : ~ contains_slb(create_slb,X1),
inference(fof_simplification,[status(thm)],[ax20]) ).
cnf(c_0_18,negated_conjecture,
( ~ pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,X1)
| ~ less_than(findmin_pqp_res(esk2_0),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( esk3_0 = create_slb
| pair_in_list(update_slb(esk3_0,findmin_pqp_res(esk2_0)),esk5_0,esk1_3(esk3_0,esk5_0,findmin_pqp_res(esk2_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( esk3_0 = create_slb
| less_than(findmin_pqp_res(esk2_0),esk1_3(esk3_0,esk5_0,findmin_pqp_res(esk2_0))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_15]) ).
fof(c_0_21,plain,
! [X18] : ~ contains_slb(create_slb,X18),
inference(variable_rename,[status(thm)],[c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk3_0 = create_slb,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,plain,
~ contains_slb(create_slb,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV408+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 09:45:23 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.62 % Version : CSE_E---1.5
% 0.20/0.62 % Problem : theBenchmark.p
% 0.20/0.62 % Proof found
% 0.20/0.62 % SZS status Theorem for theBenchmark.p
% 0.20/0.62 % SZS output start Proof
% See solution above
% 0.20/0.63 % Total time : 0.032000 s
% 0.20/0.63 % SZS output end Proof
% 0.20/0.63 % Total time : 0.036000 s
%------------------------------------------------------------------------------