%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV390+1 : TPTP v9.2.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 05:22:04 PM UTC 2026
% Result : Theorem 1.22s 1.72s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 10 unt; 0 def)
% Number of atoms : 52 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 51 ( 23 ~; 18 |; 4 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 76 ( 10 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax37,axiom,
! [X1,X2,X3,X4,X5] :
( less_than(X5,X4)
=> ( check_cpq(triple(X1,insert_slb(X2,pair(X4,X5)),X3))
<=> check_cpq(triple(X1,X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax37) ).
fof(ax42,axiom,
! [X1,X2,X3,X4] : insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax42) ).
fof(bottom_smallest,axiom,
! [X1] : less_than(bottom,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
fof(l26_li4142,lemma,
! [X1,X2,X3] :
( check_cpq(triple(X1,X2,X3))
<=> ! [X4,X5] :
( pair_in_list(X2,X4,X5)
=> less_than(X5,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l26_li4142) ).
fof(l26_co,conjecture,
! [X1,X2,X3] :
( ~ check_cpq(triple(X1,X2,X3))
=> ! [X4] : ~ check_cpq(insert_cpq(triple(X1,X2,X3),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l26_co) ).
fof(c_0_5,plain,
! [X192,X193,X194,X195,X196] :
( ( ~ check_cpq(triple(X192,insert_slb(X193,pair(X195,X196)),X194))
| check_cpq(triple(X192,X193,X194))
| ~ less_than(X196,X195) )
& ( ~ check_cpq(triple(X192,X193,X194))
| check_cpq(triple(X192,insert_slb(X193,pair(X195,X196)),X194))
| ~ less_than(X196,X195) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax37])])]) ).
fof(c_0_6,plain,
! [X211,X212,X213,X214] : insert_cpq(triple(X211,X212,X213),X214) = triple(insert_pqp(X211,X214),insert_slb(X212,pair(X214,bottom)),X213),
inference(variable_rename,[status(thm)],[ax42]) ).
fof(c_0_7,plain,
! [X140] : less_than(bottom,X140),
inference(variable_rename,[status(thm)],[bottom_smallest]) ).
fof(c_0_8,lemma,
! [X245,X246,X247,X248,X249,X250,X251,X254] :
( ( ~ check_cpq(triple(X245,X246,X247))
| ~ pair_in_list(X246,X248,X249)
| less_than(X249,X248) )
& ( pair_in_list(X251,esk1_2(X250,X251),esk2_2(X250,X251))
| check_cpq(triple(X250,X251,X254)) )
& ( ~ less_than(esk2_2(X250,X251),esk1_2(X250,X251))
| check_cpq(triple(X250,X251,X254)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[l26_li4142])])])])])]) ).
cnf(c_0_9,plain,
( check_cpq(triple(X1,X2,X5))
| ~ check_cpq(triple(X1,insert_slb(X2,pair(X3,X4)),X5))
| ~ less_than(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
insert_cpq(triple(X1,X2,X3),X4) = triple(insert_pqp(X1,X4),insert_slb(X2,pair(X4,bottom)),X3),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
less_than(bottom,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1,X2,X3] :
( ~ check_cpq(triple(X1,X2,X3))
=> ! [X4] : ~ check_cpq(insert_cpq(triple(X1,X2,X3),X4)) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l26_co])]) ).
cnf(c_0_13,lemma,
( less_than(X5,X4)
| ~ check_cpq(triple(X1,X2,X3))
| ~ pair_in_list(X2,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( check_cpq(triple(insert_pqp(X1,X2),X3,X4))
| ~ check_cpq(insert_cpq(triple(X1,X3,X4),X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]) ).
fof(c_0_15,negated_conjecture,
( ~ check_cpq(triple(esk3_0,esk4_0,esk5_0))
& check_cpq(insert_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_16,lemma,
( less_than(X1,X2)
| ~ check_cpq(insert_cpq(triple(X3,X4,X5),X6))
| ~ pair_in_list(X4,X2,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
check_cpq(insert_cpq(triple(esk3_0,esk4_0,esk5_0),esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( less_than(X1,X2)
| ~ pair_in_list(esk4_0,X2,X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,lemma,
( pair_in_list(X1,esk1_2(X2,X1),esk2_2(X2,X1))
| check_cpq(triple(X2,X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,lemma,
( check_cpq(triple(X1,X2,X3))
| ~ less_than(esk2_2(X1,X2),esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_21,negated_conjecture,
~ check_cpq(triple(esk3_0,esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,lemma,
check_cpq(triple(X1,esk4_0,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV390+1 : TPTP v9.2.1. Released v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.12/0.32 % Computer : n031.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 05:06:23 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.12/0.34 % start to proof: theBenchmark
% 1.22/1.72 % Version : CSE_E---1.7
% 1.22/1.72 % Problem : theBenchmark.p
% 1.22/1.72 % SZS status Theorem for theBenchmark.p
% 1.22/1.72 % SZS output start CNFRefutation
% See solution above
% 1.22/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------