%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV408+1 : 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 : 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 : Tue May 5 05:22:06 PM UTC 2026
% Result : Theorem 1.37s 1.74s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 83 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 78 ( 27 ~; 31 |; 14 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 54 ( 5 sgn 34 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(ax50,axiom,
! [X1,X2] : findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax50) ).
fof(bottom_smallest,axiom,
! [X1] : less_than(bottom,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
fof(c_0_6,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_7,lemma,
! [X245,X246,X247] :
( ( pair_in_list(update_slb(X245,X247),X246,esk1_3(X245,X246,X247))
| pair_in_list(update_slb(X245,X247),X246,X247)
| ~ contains_slb(X245,X246)
| ~ strictly_less_than(X246,X247) )
& ( less_than(X247,esk1_3(X245,X246,X247))
| pair_in_list(update_slb(X245,X247),X246,X247)
| ~ contains_slb(X245,X246)
| ~ strictly_less_than(X246,X247) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l44_l45])])])]) ).
fof(c_0_8,negated_conjecture,
! [X253] :
( 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,X253)
| ~ less_than(findmin_pqp_res(esk2_0),X253) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_9,plain,
! [X240,X241,X242] :
( X241 = create_slb
| findmin_cpq_res(triple(X240,X241,X242)) = findmin_pqp_res(X240) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).
fof(c_0_10,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( less_than(X1,X2)
& ~ less_than(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_0_11,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_7]) ).
cnf(c_0_12,negated_conjecture,
contains_slb(esk3_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
strictly_less_than(esk5_0,findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0))),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( X1 = create_slb
| findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,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_7]) ).
fof(c_0_16,plain,
! [X138,X139] :
( ( less_than(X138,X139)
| ~ strictly_less_than(X138,X139) )
& ( ~ less_than(X139,X138)
| ~ strictly_less_than(X138,X139) )
& ( ~ less_than(X138,X139)
| less_than(X139,X138)
| strictly_less_than(X138,X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_17,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_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( esk3_0 = create_slb
| strictly_less_than(esk5_0,findmin_pqp_res(esk2_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,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_8]) ).
cnf(c_0_20,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_15,c_0_12]) ).
cnf(c_0_21,plain,
( ~ less_than(X1,X2)
| ~ strictly_less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,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_8]) ).
cnf(c_0_23,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_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,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_20,c_0_18]),c_0_19]) ).
fof(c_0_25,plain,
! [X238,X239] : findmin_cpq_res(triple(X238,create_slb,X239)) = bottom,
inference(variable_rename,[status(thm)],[ax50]) ).
fof(c_0_26,plain,
! [X140] : less_than(bottom,X140),
inference(variable_rename,[status(thm)],[bottom_smallest]) ).
cnf(c_0_27,negated_conjecture,
~ less_than(findmin_cpq_res(triple(esk2_0,esk3_0,esk4_0)),esk5_0),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 = create_slb,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
findmin_cpq_res(triple(X1,create_slb,X2)) = bottom,
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
less_than(bottom,X1),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV408+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n027.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 05:06:50 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.37/1.74 % Version : CSE_E---1.7
% 1.37/1.74 % Problem : theBenchmark.p
% 1.37/1.74 % SZS status Theorem for theBenchmark.p
% 1.37/1.74 % SZS output start CNFRefutation
% See solution above
% 1.37/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------