%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV408+2 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n007.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 : Tue May 5 05:22:06 PM UTC 2026
% Result : Theorem 1.70s 1.86s
% Output : CNFRefutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 80 ( 30 ~; 30 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(l48_li3839,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& strictly_less_than(X3,X4) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
fof(l45_li4647,lemma,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X1,X2)
| less_than(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
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(l49_li3637,lemma,
! [X1,X2,X3,X4] :
( ( pair_in_list(X1,X2,X3)
& less_than(X4,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l49_li3637) ).
fof(c_0_6,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
fof(c_0_7,lemma,
! [X255,X256,X257,X258] :
( ~ pair_in_list(X255,X256,X257)
| ~ strictly_less_than(X257,X258)
| pair_in_list(update_slb(X255,X258),X256,X258) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l48_li3839])]) ).
fof(c_0_8,lemma,
! [X252,X253] :
( ~ contains_slb(X252,X253)
| pair_in_list(X252,X253,esk1_2(X252,X253)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])]) ).
fof(c_0_9,plain,
! [X145,X146] :
( ( less_than(X145,X146)
| ~ strictly_less_than(X145,X146) )
& ( ~ less_than(X146,X145)
| ~ strictly_less_than(X145,X146) )
& ( ~ less_than(X145,X146)
| less_than(X146,X145)
| strictly_less_than(X145,X146) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X142,X143] :
( less_than(X142,X143)
| less_than(X143,X142) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(c_0_11,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]) ).
cnf(c_0_12,lemma,
( pair_in_list(update_slb(X1,X4),X2,X4)
| ~ pair_in_list(X1,X2,X3)
| ~ strictly_less_than(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,lemma,
( pair_in_list(X1,X2,esk1_2(X1,X2))
| ~ contains_slb(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2)
| ~ less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
! [X267] :
( 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,X267)
| ~ less_than(findmin_pqp_res(esk2_0),X267) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
fof(c_0_17,lemma,
! [X259,X260,X261,X262] :
( ~ pair_in_list(X259,X260,X261)
| ~ less_than(X262,X261)
| pair_in_list(update_slb(X259,X262),X260,X261) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l49_li3637])]) ).
cnf(c_0_18,lemma,
( pair_in_list(update_slb(X1,X2),X3,X2)
| ~ contains_slb(X1,X3)
| ~ strictly_less_than(esk1_2(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,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_16]) ).
cnf(c_0_21,lemma,
( pair_in_list(update_slb(X1,X4),X2,X3)
| ~ pair_in_list(X1,X2,X3)
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,lemma,
( pair_in_list(update_slb(X1,X2),X3,X2)
| less_than(X2,esk1_2(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
contains_slb(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ pair_in_list(esk3_0,esk5_0,X1)
| ~ less_than(findmin_pqp_res(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( pair_in_list(update_slb(esk3_0,X1),esk5_0,X1)
| less_than(X1,esk1_2(esk3_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,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_16]) ).
cnf(c_0_27,negated_conjecture,
~ pair_in_list(esk3_0,esk5_0,esk1_2(esk3_0,esk5_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV408+2 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 05:05:53 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.70/1.86 % Version : CSE_E---1.7
% 1.70/1.86 % Problem : theBenchmark.p
% 1.70/1.86 % SZS status Theorem for theBenchmark.p
% 1.70/1.86 % SZS output start CNFRefutation
% See solution above
% 1.70/1.86 % Total time : 1.374s
%------------------------------------------------------------------------------