%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV224+1 : TPTP v9.2.1. Bugfixed 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 : n010.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 05:21:07 PM UTC 2026
% Result : Theorem 1.32s 1.73s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 360 ( 283 equ)
% Maximal formula atoms : 104 ( 27 avg)
% Number of connectives : 551 ( 204 ~; 72 |; 262 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 15 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-3 aty)
% Number of variables : 26 ( 4 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_symm_0521,conjecture,
( ( ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n5)
& leq(X18,n5) )
=> a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,n2) )
=> a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) ) )
=> ! [X21,X22] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( ~ ( n0 = X21
& n1 = X22 )
& ~ ( n0 = X21
& n2 = X22 )
& ~ ( n0 = X21
& n3 = X22 )
& ~ ( n0 = X21
& n4 = X22 )
& ~ ( n0 = X21
& n5 = X22 )
& ~ ( n0 = X22
& n4 = X21 )
& ~ ( n0 = X22
& n5 = X21 )
& ~ ( n1 = X21
& n1 = X22 )
& ~ ( n1 = X21
& n2 = X22 )
& ~ ( n1 = X21
& n3 = X22 )
& ~ ( n1 = X21
& n4 = X22 )
& ~ ( n1 = X21
& n5 = X22 )
& ~ ( n1 = X22
& n2 = X21 )
& ~ ( n1 = X22
& n3 = X21 )
& ~ ( n1 = X22
& n4 = X21 )
& ~ ( n1 = X22
& n5 = X21 )
& ~ ( n2 = X21
& n2 = X22 )
& ~ ( n2 = X21
& n3 = X22 )
& ~ ( n2 = X21
& n4 = X22 )
& ~ ( n2 = X21
& n5 = X22 )
& ~ ( n2 = X22
& n3 = X21 )
& ~ ( n2 = X22
& n4 = X21 )
& ~ ( n2 = X22
& n5 = X21 )
& ~ ( n3 = X21
& n3 = X22 )
& ~ ( n3 = X21
& n4 = X22 )
& ~ ( n3 = X21
& n5 = X22 )
& ~ ( n3 = X22
& n4 = X21 )
& ~ ( n3 = X22
& n5 = X21 )
& ~ ( n4 = X21
& n4 = X22 )
& ~ ( n4 = X21
& n5 = X22 )
& ~ ( n4 = X22
& n5 = X21 )
& ~ ( n5 = X21
& n5 = X22 )
& n0 = X22
& n3 = X21
& n3 = X22
& n4 = X21 )
=> a_select2(xinit_noise,n3) = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0521) ).
fof(c_0_1,plain,
! [X22,X21] :
( epred3_2(X21,X22)
<=> ( ~ ( n0 = X21
& n1 = X22 )
& ~ ( n0 = X21
& n2 = X22 )
& ~ ( n0 = X21
& n3 = X22 )
& ~ ( n0 = X21
& n4 = X22 )
& ~ ( n0 = X21
& n5 = X22 )
& ~ ( n0 = X22
& n4 = X21 )
& ~ ( n0 = X22
& n5 = X21 )
& ~ ( n1 = X21
& n1 = X22 )
& ~ ( n1 = X21
& n2 = X22 )
& ~ ( n1 = X21
& n3 = X22 )
& ~ ( n1 = X21
& n4 = X22 )
& ~ ( n1 = X21
& n5 = X22 )
& ~ ( n1 = X22
& n2 = X21 )
& ~ ( n1 = X22
& n3 = X21 )
& ~ ( n1 = X22
& n4 = X21 )
& ~ ( n1 = X22
& n5 = X21 )
& ~ ( n2 = X21
& n2 = X22 )
& ~ ( n2 = X21
& n3 = X22 )
& ~ ( n2 = X21
& n4 = X22 )
& ~ ( n2 = X21
& n5 = X22 )
& ~ ( n2 = X22
& n3 = X21 )
& ~ ( n2 = X22
& n4 = X21 )
& ~ ( n2 = X22
& n5 = X21 )
& ~ ( n3 = X21
& n3 = X22 )
& ~ ( n3 = X21
& n4 = X22 )
& ~ ( n3 = X21
& n5 = X22 )
& ~ ( n3 = X22
& n4 = X21 )
& ~ ( n3 = X22
& n5 = X21 )
& ~ ( n4 = X21
& n4 = X22 )
& ~ ( n4 = X21
& n5 = X22 )
& ~ ( n4 = X22
& n5 = X21 )
& ~ ( n5 = X21
& n5 = X22 )
& n0 = X22
& n3 = X21
& n3 = X22
& n4 = X21 ) ),
introduced(definition) ).
fof(c_0_2,plain,
( epred2_0
<=> ( ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n5)
& leq(X18,n5) )
=> a_select3(q_ds1_filter,X14,X18) = a_select3(q_ds1_filter,X18,X14) )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,n2) )
=> a_select3(r_ds1_filter,X4,X20) = a_select3(r_ds1_filter,X20,X4) ) ) ),
introduced(definition) ).
fof(c_0_3,plain,
! [X22,X21] :
( epred3_2(X21,X22)
=> ( ~ ( n0 = X21
& n1 = X22 )
& ~ ( n0 = X21
& n2 = X22 )
& ~ ( n0 = X21
& n3 = X22 )
& ~ ( n0 = X21
& n4 = X22 )
& ~ ( n0 = X21
& n5 = X22 )
& ~ ( n0 = X22
& n4 = X21 )
& ~ ( n0 = X22
& n5 = X21 )
& ~ ( n1 = X21
& n1 = X22 )
& ~ ( n1 = X21
& n2 = X22 )
& ~ ( n1 = X21
& n3 = X22 )
& ~ ( n1 = X21
& n4 = X22 )
& ~ ( n1 = X21
& n5 = X22 )
& ~ ( n1 = X22
& n2 = X21 )
& ~ ( n1 = X22
& n3 = X21 )
& ~ ( n1 = X22
& n4 = X21 )
& ~ ( n1 = X22
& n5 = X21 )
& ~ ( n2 = X21
& n2 = X22 )
& ~ ( n2 = X21
& n3 = X22 )
& ~ ( n2 = X21
& n4 = X22 )
& ~ ( n2 = X21
& n5 = X22 )
& ~ ( n2 = X22
& n3 = X21 )
& ~ ( n2 = X22
& n4 = X21 )
& ~ ( n2 = X22
& n5 = X21 )
& ~ ( n3 = X21
& n3 = X22 )
& ~ ( n3 = X21
& n4 = X22 )
& ~ ( n3 = X21
& n5 = X22 )
& ~ ( n3 = X22
& n4 = X21 )
& ~ ( n3 = X22
& n5 = X21 )
& ~ ( n4 = X21
& n4 = X22 )
& ~ ( n4 = X21
& n5 = X22 )
& ~ ( n4 = X22
& n5 = X21 )
& ~ ( n5 = X21
& n5 = X22 )
& n0 = X22
& n3 = X21
& n3 = X22
& n4 = X21 ) ),
inference(split_equiv,[status(thm)],[c_0_1]) ).
fof(c_0_4,negated_conjecture,
~ ( epred2_0
=> ! [X21,X22] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( epred3_2(X21,X22)
=> a_select2(xinit_noise,n3) = n0 ) ) ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_symm_0521]),c_0_2]),c_0_1]) ).
fof(c_0_5,plain,
! [X380,X381] :
( ( n0 != X381
| n1 != X380
| ~ epred3_2(X381,X380) )
& ( n0 != X381
| n2 != X380
| ~ epred3_2(X381,X380) )
& ( n0 != X381
| n3 != X380
| ~ epred3_2(X381,X380) )
& ( n0 != X381
| n4 != X380
| ~ epred3_2(X381,X380) )
& ( n0 != X381
| n5 != X380
| ~ epred3_2(X381,X380) )
& ( n0 != X380
| n4 != X381
| ~ epred3_2(X381,X380) )
& ( n0 != X380
| n5 != X381
| ~ epred3_2(X381,X380) )
& ( n1 != X381
| n1 != X380
| ~ epred3_2(X381,X380) )
& ( n1 != X381
| n2 != X380
| ~ epred3_2(X381,X380) )
& ( n1 != X381
| n3 != X380
| ~ epred3_2(X381,X380) )
& ( n1 != X381
| n4 != X380
| ~ epred3_2(X381,X380) )
& ( n1 != X381
| n5 != X380
| ~ epred3_2(X381,X380) )
& ( n1 != X380
| n2 != X381
| ~ epred3_2(X381,X380) )
& ( n1 != X380
| n3 != X381
| ~ epred3_2(X381,X380) )
& ( n1 != X380
| n4 != X381
| ~ epred3_2(X381,X380) )
& ( n1 != X380
| n5 != X381
| ~ epred3_2(X381,X380) )
& ( n2 != X381
| n2 != X380
| ~ epred3_2(X381,X380) )
& ( n2 != X381
| n3 != X380
| ~ epred3_2(X381,X380) )
& ( n2 != X381
| n4 != X380
| ~ epred3_2(X381,X380) )
& ( n2 != X381
| n5 != X380
| ~ epred3_2(X381,X380) )
& ( n2 != X380
| n3 != X381
| ~ epred3_2(X381,X380) )
& ( n2 != X380
| n4 != X381
| ~ epred3_2(X381,X380) )
& ( n2 != X380
| n5 != X381
| ~ epred3_2(X381,X380) )
& ( n3 != X381
| n3 != X380
| ~ epred3_2(X381,X380) )
& ( n3 != X381
| n4 != X380
| ~ epred3_2(X381,X380) )
& ( n3 != X381
| n5 != X380
| ~ epred3_2(X381,X380) )
& ( n3 != X380
| n4 != X381
| ~ epred3_2(X381,X380) )
& ( n3 != X380
| n5 != X381
| ~ epred3_2(X381,X380) )
& ( n4 != X381
| n4 != X380
| ~ epred3_2(X381,X380) )
& ( n4 != X381
| n5 != X380
| ~ epred3_2(X381,X380) )
& ( n4 != X380
| n5 != X381
| ~ epred3_2(X381,X380) )
& ( n5 != X381
| n5 != X380
| ~ epred3_2(X381,X380) )
& ( n0 = X380
| ~ epred3_2(X381,X380) )
& ( n3 = X381
| ~ epred3_2(X381,X380) )
& ( n3 = X380
| ~ epred3_2(X381,X380) )
& ( n4 = X381
| ~ epred3_2(X381,X380) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_6,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(n0,esk25_0)
& leq(esk24_0,n5)
& leq(esk25_0,n5)
& epred3_2(esk24_0,esk25_0)
& a_select2(xinit_noise,n3) != n0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( n0 != X1
| n4 != X2
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( n4 = X1
| ~ epred3_2(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( n0 = X1
| ~ epred3_2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
epred3_2(esk24_0,esk25_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
~ epred3_2(X1,X2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_10,c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV224+1 : TPTP v9.2.1. Bugfixed 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 : n010.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 04:57:51 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.32/1.73 % Version : CSE_E---1.7
% 1.32/1.73 % Problem : theBenchmark.p
% 1.32/1.73 % SZS status Theorem for theBenchmark.p
% 1.32/1.73 % SZS output start CNFRefutation
% See solution above
% 1.32/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------