%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV205+1 : TPTP v9.2.1. Bugfixed 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 : n018.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 05:21:04 PM UTC 2026
% Result : Theorem 1.36s 1.74s
% Output : CNFRefutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 12 unt; 0 def)
% Number of atoms : 258 ( 171 equ)
% Maximal formula atoms : 66 ( 8 avg)
% Number of connectives : 276 ( 50 ~; 77 |; 136 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 16 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(quaternion_ds1_inuse_0016,conjecture,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n2)
& leq(X18,n998) )
=> a_select3(u_defuse,X14,X18) = use )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,n998) )
=> a_select3(z_defuse,X4,X20) = use ) )
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n5) )
=> a_select2(sigma_defuse,X21) = use ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quaternion_ds1_inuse_0016) ).
fof(finite_domain_5,axiom,
! [X1] :
( ( leq(n0,X1)
& leq(X1,n5) )
=> ( X1 = n0
| X1 = n1
| X1 = n2
| X1 = n3
| X1 = n4
| X1 = n5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',finite_domain_5) ).
fof(c_0_2,plain,
( epred2_0
<=> ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n2)
& leq(X18,n998) )
=> a_select3(u_defuse,X14,X18) = use )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,n998) )
=> a_select3(z_defuse,X4,X20) = use ) ) ),
introduced(definition) ).
fof(c_0_3,negated_conjecture,
~ ( epred2_0
=> ! [X21] :
( ( leq(n0,X21)
& leq(X21,n5) )
=> a_select2(sigma_defuse,X21) = use ) ),
inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[quaternion_ds1_inuse_0016]),c_0_2]) ).
fof(c_0_4,plain,
( epred2_0
=> ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& ! [X14,X18] :
( ( leq(n0,X14)
& leq(n0,X18)
& leq(X14,n2)
& leq(X18,n998) )
=> a_select3(u_defuse,X14,X18) = use )
& ! [X4,X20] :
( ( leq(n0,X4)
& leq(n0,X20)
& leq(X4,n2)
& leq(X20,n998) )
=> a_select3(z_defuse,X4,X20) = use ) ) ),
inference(split_equiv,[status(thm)],[c_0_2]) ).
fof(c_0_5,plain,
! [X361] :
( ~ leq(n0,X361)
| ~ leq(X361,n5)
| X361 = n0
| X361 = n1
| X361 = n2
| X361 = n3
| X361 = n4
| X361 = n5 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[finite_domain_5])]) ).
fof(c_0_6,negated_conjecture,
( epred2_0
& leq(n0,esk24_0)
& leq(esk24_0,n5)
& a_select2(sigma_defuse,esk24_0) != use ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_7,plain,
! [X374,X375,X376,X377] :
( ( a_select2(rho_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(rho_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(rho_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(sigma_defuse,n5) = use
| ~ epred2_0 )
& ( a_select3(u_defuse,n0,n0) = use
| ~ epred2_0 )
& ( a_select3(u_defuse,n1,n0) = use
| ~ epred2_0 )
& ( a_select3(u_defuse,n2,n0) = use
| ~ epred2_0 )
& ( a_select2(xinit_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(xinit_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(xinit_defuse,n5) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(xinit_mean_defuse,n5) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n0) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n1) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n2) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n3) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n4) = use
| ~ epred2_0 )
& ( a_select2(xinit_noise_defuse,n5) = use
| ~ epred2_0 )
& ( ~ leq(n0,X374)
| ~ leq(n0,X375)
| ~ leq(X374,n2)
| ~ leq(X375,n998)
| a_select3(u_defuse,X374,X375) = use
| ~ epred2_0 )
& ( ~ leq(n0,X376)
| ~ leq(n0,X377)
| ~ leq(X376,n2)
| ~ leq(X377,n998)
| a_select3(z_defuse,X376,X377) = use
| ~ epred2_0 ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_8,plain,
( X1 = n0
| X1 = n1
| X1 = n2
| X1 = n3
| X1 = n4
| X1 = n5
| ~ leq(n0,X1)
| ~ leq(X1,n5) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
leq(esk24_0,n5),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
leq(n0,esk24_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( a_select2(sigma_defuse,n5) = use
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
epred2_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
a_select2(sigma_defuse,esk24_0) != use,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( esk24_0 = n5
| esk24_0 = n4
| esk24_0 = n3
| esk24_0 = n2
| esk24_0 = n1
| esk24_0 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10])]) ).
cnf(c_0_15,plain,
a_select2(sigma_defuse,n5) = use,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_16,plain,
( a_select2(sigma_defuse,n4) = use
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( esk24_0 = n0
| esk24_0 = n1
| esk24_0 = n2
| esk24_0 = n3
| esk24_0 = n4 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_18,plain,
a_select2(sigma_defuse,n4) = use,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_12])]) ).
cnf(c_0_19,plain,
( a_select2(sigma_defuse,n3) = use
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
( esk24_0 = n3
| esk24_0 = n2
| esk24_0 = n1
| esk24_0 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_17]),c_0_18])]) ).
cnf(c_0_21,plain,
a_select2(sigma_defuse,n3) = use,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_12])]) ).
cnf(c_0_22,plain,
( a_select2(sigma_defuse,n2) = use
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( esk24_0 = n0
| esk24_0 = n1
| esk24_0 = n2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_20]),c_0_21])]) ).
cnf(c_0_24,plain,
a_select2(sigma_defuse,n2) = use,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_12])]) ).
cnf(c_0_25,plain,
( a_select2(sigma_defuse,n1) = use
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_26,negated_conjecture,
( esk24_0 = n1
| esk24_0 = n0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_23]),c_0_24])]) ).
cnf(c_0_27,plain,
a_select2(sigma_defuse,n1) = use,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_12])]) ).
cnf(c_0_28,plain,
( a_select2(sigma_defuse,n0) = use
| ~ epred2_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_29,negated_conjecture,
esk24_0 = n0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_26]),c_0_27])]) ).
cnf(c_0_30,plain,
a_select2(sigma_defuse,n0) = use,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_12])]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_29]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV205+1 : TPTP v9.2.1. Bugfixed 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
% 0.16/0.33 % Computer : n018.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:57:47 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.36/1.74 % Version : CSE_E---1.7
% 1.36/1.74 % Problem : theBenchmark.p
% 1.36/1.74 % SZS status Theorem for theBenchmark.p
% 1.36/1.74 % SZS output start CNFRefutation
% See solution above
% 1.36/1.74 % Total time : 1.373s
%------------------------------------------------------------------------------