%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV224+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:12:32 PM UTC 2026
% Result : Theorem 6.98s 1.81s
% Output : Proof 6.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 55 ( 19 unt; 0 def)
% Number of atoms : 415 ( 362 equ)
% Maximal formula atoms : 83 ( 7 avg)
% Number of connectives : 646 ( 286 ~; 112 |; 238 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 48 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-4 aty)
% Number of variables : 26 ( 0 sgn 23 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,conjecture,
( ( ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
=> ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> ( ( n4 = E
& n3 = F
& n3 = E
& n0 = F
& ~ ( n5 = F
& n5 = E )
& ~ ( n5 = E
& n4 = F )
& ~ ( n5 = F
& n4 = E )
& ~ ( n4 = F
& n4 = E )
& ~ ( n5 = E
& n3 = F )
& ~ ( n4 = E
& n3 = F )
& ~ ( n5 = F
& n3 = E )
& ~ ( n4 = F
& n3 = E )
& ~ ( n3 = F
& n3 = E )
& ~ ( n5 = E
& n2 = F )
& ~ ( n4 = E
& n2 = F )
& ~ ( n3 = E
& n2 = F )
& ~ ( n5 = F
& n2 = E )
& ~ ( n4 = F
& n2 = E )
& ~ ( n3 = F
& n2 = E )
& ~ ( n2 = F
& n2 = E )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n3 = E
& n1 = F )
& ~ ( n2 = E
& n1 = F )
& ~ ( n5 = F
& n1 = E )
& ~ ( n4 = F
& n1 = E )
& ~ ( n3 = F
& n1 = E )
& ~ ( n2 = F
& n1 = E )
& ~ ( n1 = F
& n1 = E )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E )
& ~ ( n2 = F
& n0 = E )
& ~ ( n1 = F
& n0 = E ) )
=> a_select2(xinit_noise,n3) = n0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0521) ).
fof(f52_neg,negated_conjecture,
~ ( ( ! [C,D] :
( ( leq(D,n2)
& leq(C,n2)
& leq(n0,D)
& leq(n0,C) )
=> a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C) )
& ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A) ) )
=> ! [E,F] :
( ( leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
=> ( ( n4 = E
& n3 = F
& n3 = E
& n0 = F
& ~ ( n5 = F
& n5 = E )
& ~ ( n5 = E
& n4 = F )
& ~ ( n5 = F
& n4 = E )
& ~ ( n4 = F
& n4 = E )
& ~ ( n5 = E
& n3 = F )
& ~ ( n4 = E
& n3 = F )
& ~ ( n5 = F
& n3 = E )
& ~ ( n4 = F
& n3 = E )
& ~ ( n3 = F
& n3 = E )
& ~ ( n5 = E
& n2 = F )
& ~ ( n4 = E
& n2 = F )
& ~ ( n3 = E
& n2 = F )
& ~ ( n5 = F
& n2 = E )
& ~ ( n4 = F
& n2 = E )
& ~ ( n3 = F
& n2 = E )
& ~ ( n2 = F
& n2 = E )
& ~ ( n5 = E
& n1 = F )
& ~ ( n4 = E
& n1 = F )
& ~ ( n3 = E
& n1 = F )
& ~ ( n2 = E
& n1 = F )
& ~ ( n5 = F
& n1 = E )
& ~ ( n4 = F
& n1 = E )
& ~ ( n3 = F
& n1 = E )
& ~ ( n2 = F
& n1 = E )
& ~ ( n1 = F
& n1 = E )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E )
& ~ ( n2 = F
& n0 = E )
& ~ ( n1 = F
& n0 = E ) )
=> a_select2(xinit_noise,n3) = n0 ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [E,F] :
( a_select2(xinit_noise,n3) != n0
& n4 = E
& n3 = F
& n3 = E
& n0 = F
& ( n5 != F
| n5 != E )
& ( n5 != E
| n4 != F )
& ( n5 != F
| n4 != E )
& ( n4 != F
| n4 != E )
& ( n5 != E
| n3 != F )
& ( n4 != E
| n3 != F )
& ( n5 != F
| n3 != E )
& ( n4 != F
| n3 != E )
& ( n3 != F
| n3 != E )
& ( n5 != E
| n2 != F )
& ( n4 != E
| n2 != F )
& ( n3 != E
| n2 != F )
& ( n5 != F
| n2 != E )
& ( n4 != F
| n2 != E )
& ( n3 != F
| n2 != E )
& ( n2 != F
| n2 != E )
& ( n5 != E
| n1 != F )
& ( n4 != E
| n1 != F )
& ( n3 != E
| n1 != F )
& ( n2 != E
| n1 != F )
& ( n5 != F
| n1 != E )
& ( n4 != F
| n1 != E )
& ( n3 != F
| n1 != E )
& ( n2 != F
| n1 != E )
& ( n1 != F
| n1 != E )
& ( n5 != E
| n0 != F )
& ( n4 != E
| n0 != F )
& ( n5 != F
| n0 != E )
& ( n4 != F
| n0 != E )
& ( n3 != F
| n0 != E )
& ( n2 != F
| n0 != E )
& ( n1 != F
| n0 != E )
& leq(F,n5)
& leq(E,n5)
& leq(n0,F)
& leq(n0,E) )
& ! [C,D] :
( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ! [A,B] :
( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) ) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
! [A,B,C,D] :
( a_select2(xinit_noise,n3) != n0
& n4 = sk27
& n3 = sk28
& n3 = sk27
& n0 = sk28
& ( n5 != sk28
| n5 != sk27 )
& ( n5 != sk27
| n4 != sk28 )
& ( n5 != sk28
| n4 != sk27 )
& ( n4 != sk28
| n4 != sk27 )
& ( n5 != sk27
| n3 != sk28 )
& ( n4 != sk27
| n3 != sk28 )
& ( n5 != sk28
| n3 != sk27 )
& ( n4 != sk28
| n3 != sk27 )
& ( n3 != sk28
| n3 != sk27 )
& ( n5 != sk27
| n2 != sk28 )
& ( n4 != sk27
| n2 != sk28 )
& ( n3 != sk27
| n2 != sk28 )
& ( n5 != sk28
| n2 != sk27 )
& ( n4 != sk28
| n2 != sk27 )
& ( n3 != sk28
| n2 != sk27 )
& ( n2 != sk28
| n2 != sk27 )
& ( n5 != sk27
| n1 != sk28 )
& ( n4 != sk27
| n1 != sk28 )
& ( n3 != sk27
| n1 != sk28 )
& ( n2 != sk27
| n1 != sk28 )
& ( n5 != sk28
| n1 != sk27 )
& ( n4 != sk28
| n1 != sk27 )
& ( n3 != sk28
| n1 != sk27 )
& ( n2 != sk28
| n1 != sk27 )
& ( n1 != sk28
| n1 != sk27 )
& ( n5 != sk27
| n0 != sk28 )
& ( n4 != sk27
| n0 != sk28 )
& ( n5 != sk28
| n0 != sk27 )
& ( n4 != sk28
| n0 != sk27 )
& ( n3 != sk28
| n0 != sk27 )
& ( n2 != sk28
| n0 != sk27 )
& ( n1 != sk28
| n0 != sk27 )
& leq(sk28,n5)
& leq(sk27,n5)
& leq(n0,sk28)
& leq(n0,sk27)
& ( a_select3(r_ds1_filter,C,D) = a_select3(r_ds1_filter,D,C)
| ~ leq(D,n2)
| ~ leq(C,n2)
| ~ leq(n0,D)
| ~ leq(n0,C) )
& ( a_select3(q_ds1_filter,A,B) = a_select3(q_ds1_filter,B,A)
| ~ leq(B,n5)
| ~ leq(A,n5)
| ~ leq(n0,B)
| ~ leq(n0,A) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27,sk28])],[f52_nnf]) ).
cnf(c284,plain,
( n3 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi320,negated_conjecture,
ifeq(n3,sk27,ifeq(n3,sk28,false,trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c284]) ).
cnf(c294,plain,
n3 = sk27,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi260,negated_conjecture,
n3 = sk27,
inference(equality_encoding,[status(esa)],[c294]) ).
cnf(c295,plain,
n3 = sk28,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi261,negated_conjecture,
n3 = sk28,
inference(equality_encoding,[status(esa)],[c295]) ).
cnf(t4,plain,
trueq = false,
inference(hyper_resolution,[status(thm)],[hi320,hi260,hi261]) ).
cnf(t239,plain,
false = trueq,
inference(orient,[status(thm)],[t4]) ).
fof(f2,axiom,
! [X] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',irreflexivity_gt) ).
fof(f2_nnf,plain,
! [X] : ~ gt(X,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : ~ gt(X,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
~ gt(X0,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f51,axiom,
def != use,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',defuse) ).
fof(f51_nnf,plain,
def != use,
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
def != use,
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c254,plain,
def != use,
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(c261,plain,
( n1 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c262,plain,
( n2 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c263,plain,
( n3 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c264,plain,
( n4 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c265,plain,
( n5 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c266,plain,
( n4 != sk27
| n0 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c267,plain,
( n5 != sk27
| n0 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c268,plain,
( n1 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c269,plain,
( n2 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c270,plain,
( n3 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c271,plain,
( n4 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c272,plain,
( n5 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c273,plain,
( n2 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c274,plain,
( n3 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c275,plain,
( n4 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c276,plain,
( n5 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c277,plain,
( n2 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c278,plain,
( n3 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c279,plain,
( n4 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c280,plain,
( n5 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c281,plain,
( n3 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c282,plain,
( n4 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c283,plain,
( n5 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c285,plain,
( n4 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c286,plain,
( n5 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c287,plain,
( n4 != sk27
| n3 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c288,plain,
( n5 != sk27
| n3 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c289,plain,
( n4 != sk28
| n4 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c290,plain,
( n5 != sk28
| n4 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c291,plain,
( n5 != sk27
| n4 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c292,plain,
( n5 != sk28
| n5 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c297,plain,
a_select2(xinit_noise,n3) != n0,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
trueq != false,
inference(equality_encoding,[status(esa)],[c2,c254,c261,c262,c263,c264,c265,c266,c267,c268,c269,c270,c271,c272,c273,c274,c275,c276,c277,c278,c279,c280,c281,c282,c283,c284,c285,c286,c287,c288,c289,c290,c291,c292,c297]) ).
cnf(g0_0,plain,
trueq != trueq,
inference(rw,[status(thm)],[goal_0,t239]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV224+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 18:49:52 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.98/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.98/1.81 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------