%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV225+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 : n017.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 3.82s 1.70s
% Output : Proof 3.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 53 ( 19 unt; 0 def)
% Number of atoms : 395 ( 342 equ)
% Maximal formula atoms : 79 ( 7 avg)
% Number of connectives : 612 ( 270 ~; 106 |; 226 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 46 ( 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) )
=> ( ( n3 = E
& n2 = F
& n1 = F
& n1 = E
& ~ ( 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 )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E )
& ~ ( n2 = F
& n0 = E ) )
=> n0 = a_select2(xinit_noise,n1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0561) ).
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) )
=> ( ( n3 = E
& n2 = F
& n1 = F
& n1 = E
& ~ ( 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 )
& ~ ( n5 = E
& n0 = F )
& ~ ( n4 = E
& n0 = F )
& ~ ( n5 = F
& n0 = E )
& ~ ( n4 = F
& n0 = E )
& ~ ( n3 = F
& n0 = E )
& ~ ( n2 = F
& n0 = E ) )
=> n0 = a_select2(xinit_noise,n1) ) ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
( ? [E,F] :
( n0 != a_select2(xinit_noise,n1)
& n3 = E
& n2 = F
& n1 = F
& n1 = E
& ( 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 )
& ( n5 != E
| n0 != F )
& ( n4 != E
| n0 != F )
& ( n5 != F
| n0 != E )
& ( n4 != F
| n0 != E )
& ( n3 != F
| n0 != E )
& ( n2 != 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] :
( n0 != a_select2(xinit_noise,n1)
& n3 = sk27
& n2 = sk28
& n1 = sk28
& n1 = sk27
& ( 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 )
& ( n5 != sk27
| n0 != sk28 )
& ( n4 != sk27
| n0 != sk28 )
& ( n5 != sk28
| n0 != sk27 )
& ( n4 != sk28
| n0 != sk27 )
& ( n3 != sk28
| n0 != sk27 )
& ( n2 != 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(c267,plain,
( n2 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi303,negated_conjecture,
ifeq(n1,sk27,ifeq(n2,sk28,false,trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c267]) ).
cnf(c291,plain,
n1 = sk27,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi259,negated_conjecture,
n1 = sk27,
inference(equality_encoding,[status(esa)],[c291]) ).
cnf(c293,plain,
n2 = sk28,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi261,negated_conjecture,
n2 = sk28,
inference(equality_encoding,[status(esa)],[c293]) ).
cnf(t4,plain,
trueq = false,
inference(hyper_resolution,[status(thm)],[hi303,hi259,hi261]) ).
cnf(t231,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,
( n2 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c262,plain,
( n3 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c263,plain,
( n4 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c264,plain,
( n5 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c265,plain,
( n4 != sk27
| n0 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c266,plain,
( n5 != sk27
| n0 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c268,plain,
( n3 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c269,plain,
( n4 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c270,plain,
( n5 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c271,plain,
( n2 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c272,plain,
( n3 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c273,plain,
( n4 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c274,plain,
( n5 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c275,plain,
( n2 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c276,plain,
( n3 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c277,plain,
( n4 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c278,plain,
( n5 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c279,plain,
( n3 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c280,plain,
( n4 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c281,plain,
( n5 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c282,plain,
( n3 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c283,plain,
( n4 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c284,plain,
( n5 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c285,plain,
( n4 != sk27
| n3 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c286,plain,
( n5 != sk27
| n3 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c287,plain,
( n4 != sk28
| n4 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c288,plain,
( n5 != sk28
| n4 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c289,plain,
( n5 != sk27
| n4 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c290,plain,
( n5 != sk28
| n5 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c295,plain,
n0 != a_select2(xinit_noise,n1),
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,c295]) ).
cnf(g0_0,plain,
trueq != trueq,
inference(rw,[status(thm)],[goal_0,t231]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV225+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.34 % Computer : n017.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 18:43:32 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.82/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.82/1.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------