%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV219+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 : n012.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 03:12:31 PM UTC 2026
% Result : Theorem 8.96s 1.58s
% Output : Proof 8.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 171 ( 150 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 246 ( 110 ~; 36 |; 96 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 14 con; 0-4 aty)
% Number of variables : 10 ( 0 sgn 7 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f52,conjecture,
! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n4 = B
& n4 = A
& n3 = A
& ~ ( n5 = B
& n5 = A )
& ~ ( n5 = A
& n4 = B )
& ~ ( n5 = B
& n4 = A )
& ~ ( n4 = B
& n4 = A )
& ~ ( n5 = A
& n3 = B )
& ~ ( n5 = B
& n3 = A )
& ~ ( n5 = A
& n2 = B )
& ~ ( n5 = B
& n2 = A )
& ~ ( n5 = A
& n1 = B )
& ~ ( n5 = B
& n1 = A )
& ~ ( n5 = A
& n0 = B )
& ~ ( n5 = B
& n0 = A ) )
=> times(divide(n1,n400),a_select2(sigma,n4)) = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quaternion_ds1_symm_0321) ).
fof(f52_neg,negated_conjecture,
~ ! [A,B] :
( ( leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) )
=> ( ( n4 = B
& n4 = A
& n3 = A
& ~ ( n5 = B
& n5 = A )
& ~ ( n5 = A
& n4 = B )
& ~ ( n5 = B
& n4 = A )
& ~ ( n4 = B
& n4 = A )
& ~ ( n5 = A
& n3 = B )
& ~ ( n5 = B
& n3 = A )
& ~ ( n5 = A
& n2 = B )
& ~ ( n5 = B
& n2 = A )
& ~ ( n5 = A
& n1 = B )
& ~ ( n5 = B
& n1 = A )
& ~ ( n5 = A
& n0 = B )
& ~ ( n5 = B
& n0 = A ) )
=> times(divide(n1,n400),a_select2(sigma,n4)) = n0 ) ),
inference(negated_conjecture,[status(cth)],[f52]) ).
fof(f52_nnf,plain,
? [A,B] :
( times(divide(n1,n400),a_select2(sigma,n4)) != n0
& n4 = B
& n4 = A
& n3 = A
& ( n5 != B
| n5 != A )
& ( n5 != A
| n4 != B )
& ( n5 != B
| n4 != A )
& ( n4 != B
| n4 != A )
& ( n5 != A
| n3 != B )
& ( n5 != B
| n3 != A )
& ( n5 != A
| n2 != B )
& ( n5 != B
| n2 != A )
& ( n5 != A
| n1 != B )
& ( n5 != B
| n1 != A )
& ( n5 != A
| n0 != B )
& ( n5 != B
| n0 != A )
& leq(B,n5)
& leq(A,n5)
& leq(n0,B)
& leq(n0,A) ),
inference(nnf_transformation,[status(thm)],[f52_neg]) ).
fof(f52_sk,plain,
( times(divide(n1,n400),a_select2(sigma,n4)) != n0
& n4 = sk28
& n4 = sk27
& n3 = sk27
& ( n5 != sk28
| n5 != sk27 )
& ( n5 != sk27
| n4 != sk28 )
& ( n5 != sk28
| n4 != sk27 )
& ( n4 != sk28
| n4 != sk27 )
& ( n5 != sk27
| n3 != sk28 )
& ( n5 != sk28
| n3 != sk27 )
& ( n5 != sk27
| n2 != sk28 )
& ( n5 != sk28
| n2 != sk27 )
& ( n5 != sk27
| n1 != sk28 )
& ( n5 != sk28
| n1 != sk27 )
& ( n5 != sk27
| n0 != sk28 )
& ( n5 != sk28
| n0 != sk27 )
& leq(sk28,n5)
& leq(sk27,n5)
& leq(n0,sk28)
& leq(n0,sk27) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk27,sk28])],[f52_nnf]) ).
cnf(c267,plain,
( n4 != sk28
| n4 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi309,negated_conjecture,
ifeq(n4,sk27,ifeq(n4,sk28,false,trueq),trueq) = trueq,
inference(equality_encoding,[status(esa)],[c267]) ).
cnf(c272,plain,
n4 = sk27,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi258,negated_conjecture,
n4 = sk27,
inference(equality_encoding,[status(esa)],[c272]) ).
cnf(c273,plain,
n4 = sk28,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(hi259,negated_conjecture,
n4 = sk28,
inference(equality_encoding,[status(esa)],[c273]) ).
cnf(t3,plain,
trueq = false,
inference(hyper_resolution,[status(thm)],[hi309,hi258,hi259]) ).
cnf(t448,plain,
false = trueq,
inference(orient,[status(thm)],[t3]) ).
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(c259,plain,
( n5 != sk28
| n0 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c260,plain,
( n5 != sk27
| n0 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c261,plain,
( n5 != sk28
| n1 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c262,plain,
( n5 != sk27
| n1 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c263,plain,
( n5 != sk28
| n2 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c264,plain,
( n5 != sk27
| n2 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c265,plain,
( n5 != sk28
| n3 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c266,plain,
( n5 != sk27
| n3 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c268,plain,
( n5 != sk28
| n4 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c269,plain,
( n5 != sk27
| n4 != sk28 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c270,plain,
( n5 != sk28
| n5 != sk27 ),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(c274,plain,
times(divide(n1,n400),a_select2(sigma,n4)) != n0,
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
trueq != false,
inference(equality_encoding,[status(esa)],[c2,c254,c259,c260,c261,c262,c263,c264,c265,c266,c267,c268,c269,c270,c274]) ).
cnf(g0_0,plain,
trueq != trueq,
inference(rw,[status(thm)],[goal_0,t448]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV219+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 18:47:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.96/1.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.96/1.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------