%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 03:34:39 PM UTC 2026
% Result : Theorem 4.28s 1.10s
% Output : Proof 4.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 1
% Syntax : Number of formulae : 86 ( 13 unt; 0 def)
% Number of atoms : 247 ( 84 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 259 ( 98 ~; 135 |; 20 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 73 ( 11 sgn 16 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ( ! [Y,Z] :
( ( f(Z)
& f(Y) )
=> Y = Z )
& ? [X] : f(X) )
<=> ? [U] :
( ! [V] :
( f(V)
=> U = V )
& f(U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish317) ).
fof(f0_neg,negated_conjecture,
~ ( ( ! [Y,Z] :
( ( f(Z)
& f(Y) )
=> Y = Z )
& ? [X] : f(X) )
<=> ? [U] :
( ! [V] :
( f(V)
=> U = V )
& f(U) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ( ? [U] :
( ! [V] :
( U = V
| ~ f(V) )
& f(U) )
& ( ? [Y,Z] :
( Y != Z
& f(Z)
& f(Y) )
| ! [X] : ~ f(X) ) )
| ( ! [U] :
( ? [V] :
( U != V
& f(V) )
| ~ f(U) )
& ! [Y,Z] :
( Y = Z
| ~ f(Z)
| ~ f(Y) )
& ? [X] : f(X) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y,Z,U,X,V] :
( ( ( sk4 = V
| ~ f(V) )
& f(sk4)
& ( ( sk2 != sk3
& f(sk3)
& f(sk2) )
| ~ f(X) ) )
| ( ( ( U != sk1(U)
& f(sk1(U)) )
| ~ f(U) )
& ( Y = Z
| ~ f(Z)
| ~ f(Y) )
& f(sk0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f0_nnf]) ).
cnf(c9,plain,
( sk4 = X4
| ~ f(X4)
| X1 = X2
| ~ f(X2)
| ~ f(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( sk4 = X1
| X0 = X1
| ~ f(X1)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(p282,plain,
( sk4 = X0
| ~ f(X0)
| ~ f(sk4) ),
inference(factoring,[status(thm)],[p48]) ).
cnf(c4,plain,
( sk4 = X4
| ~ f(X4)
| f(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c0,plain,
( f(sk2)
| ~ f(X0)
| f(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
( f(sk4)
| f(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p20,plain,
( f(sk0)
| f(sk2)
| f(sk0) ),
inference(resolution,[status(thm)],[c0,c3]) ).
cnf(p22,plain,
( f(sk2)
| f(sk0) ),
inference(factoring,[status(thm)],[p20]) ).
cnf(p25,plain,
( f(sk0)
| sk4 = sk2
| f(sk0) ),
inference(resolution,[status(thm)],[c4,p22]) ).
cnf(p29,plain,
( sk4 = sk2
| f(sk0) ),
inference(factoring,[status(thm)],[p25]) ).
cnf(c1,plain,
( f(sk3)
| ~ f(X0)
| f(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( f(sk0)
| f(sk3)
| f(sk0) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(p24,plain,
( f(sk3)
| f(sk0) ),
inference(factoring,[status(thm)],[p21]) ).
cnf(p26,plain,
( f(sk0)
| sk4 = sk3
| f(sk0) ),
inference(resolution,[status(thm)],[c4,p24]) ).
cnf(p31,plain,
( sk4 = sk3
| f(sk0) ),
inference(factoring,[status(thm)],[p26]) ).
cnf(p33,plain,
( sk2 = sk3
| f(sk0)
| f(sk0) ),
inference(superposition,[status(thm)],[p29,p31]) ).
cnf(p37,plain,
( sk2 = sk3
| f(sk0) ),
inference(factoring,[status(thm)],[p33]) ).
cnf(c2,plain,
( sk2 != sk3
| ~ f(X0)
| f(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p23,plain,
( f(sk0)
| sk2 != sk3
| f(sk0) ),
inference(resolution,[status(thm)],[c2,c3]) ).
cnf(p28,plain,
( sk2 != sk3
| f(sk0) ),
inference(factoring,[status(thm)],[p23]) ).
cnf(p38,plain,
( f(sk0)
| f(sk0) ),
inference(resolution,[status(thm)],[p37,p28]) ).
cnf(p39,plain,
f(sk0),
inference(factoring,[status(thm)],[p38]) ).
cnf(c8,plain,
( f(sk4)
| X1 = X2
| ~ f(X2)
| ~ f(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p41,plain,
( f(sk4)
| sk0 = X0
| ~ f(X0) ),
inference(resolution,[status(thm)],[p39,c8]) ).
cnf(c13,plain,
( f(sk4)
| f(sk1(X3))
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p40,plain,
( f(sk4)
| f(sk1(sk0)) ),
inference(resolution,[status(thm)],[p39,c13]) ).
cnf(p44,plain,
( f(sk4)
| f(sk4)
| sk0 = sk1(sk0) ),
inference(resolution,[status(thm)],[p41,p40]) ).
cnf(p59,plain,
( f(sk4)
| sk0 = sk1(sk0) ),
inference(factoring,[status(thm)],[p44]) ).
cnf(c18,plain,
( f(sk4)
| X3 != sk1(X3)
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p45,plain,
( f(sk4)
| sk0 != sk1(sk0) ),
inference(resolution,[status(thm)],[c18,p39]) ).
cnf(p61,plain,
( f(sk4)
| f(sk4) ),
inference(resolution,[status(thm)],[p59,p45]) ).
cnf(p62,plain,
f(sk4),
inference(factoring,[status(thm)],[p61]) ).
cnf(p332,plain,
( sk4 = X0
| ~ f(X0) ),
inference(resolution,[status(thm)],[p282,p62]) ).
cnf(p333,plain,
sk4 = sk0,
inference(resolution,[status(thm)],[p332,p39]) ).
cnf(p350,plain,
( sk0 = X0
| ~ f(X0) ),
inference(demodulation,[status(thm)],[p333,p332]) ).
cnf(c5,plain,
( f(sk2)
| ~ f(X0)
| X1 = X2
| ~ f(X2)
| ~ f(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p27,plain,
( f(sk2)
| X0 = X1
| ~ f(X1)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c5]) ).
cnf(p161,plain,
( f(sk2)
| sk0 = X0
| ~ f(X0) ),
inference(resolution,[status(thm)],[p27,p39]) ).
cnf(c10,plain,
( f(sk2)
| ~ f(X0)
| f(sk1(X3))
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p60,plain,
( f(sk2)
| f(sk1(X0))
| ~ f(X0) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p64,plain,
( f(sk2)
| f(sk1(sk0)) ),
inference(resolution,[status(thm)],[p60,p39]) ).
cnf(p181,plain,
( f(sk2)
| f(sk2)
| sk0 = sk1(sk0) ),
inference(resolution,[status(thm)],[p161,p64]) ).
cnf(p244,plain,
( f(sk2)
| sk0 = sk1(sk0) ),
inference(factoring,[status(thm)],[p181]) ).
cnf(c15,plain,
( f(sk2)
| ~ f(X0)
| X3 != sk1(X3)
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p105,plain,
( f(sk2)
| X0 != sk1(X0)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c15]) ).
cnf(p127,plain,
( f(sk2)
| sk0 != sk1(sk0) ),
inference(resolution,[status(thm)],[p105,p39]) ).
cnf(p245,plain,
( f(sk2)
| f(sk2) ),
inference(resolution,[status(thm)],[p244,p127]) ).
cnf(p247,plain,
f(sk2),
inference(factoring,[status(thm)],[p245]) ).
cnf(p353,plain,
sk0 = sk2,
inference(resolution,[status(thm)],[p350,p247]) ).
cnf(c7,plain,
( sk2 != sk3
| ~ f(X0)
| X1 = X2
| ~ f(X2)
| ~ f(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p35,plain,
( sk2 != sk3
| X0 = X1
| ~ f(X1)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c7]) ).
cnf(p268,plain,
( sk2 != sk3
| sk2 = X0
| ~ f(X0) ),
inference(resolution,[status(thm)],[p247,p35]) ).
cnf(p382,plain,
( sk2 != sk3
| sk2 = sk0 ),
inference(resolution,[status(thm)],[p268,p39]) ).
cnf(p391,plain,
( sk0 != sk3
| sk2 = sk0 ),
inference(superposition,[status(thm)],[p353,p382]) ).
cnf(c11,plain,
( f(sk3)
| ~ f(X0)
| f(sk1(X3))
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p66,plain,
( f(sk3)
| f(sk1(X0))
| ~ f(X0) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p71,plain,
( f(sk3)
| f(sk1(sk0)) ),
inference(resolution,[status(thm)],[p66,p39]) ).
cnf(p351,plain,
( f(sk3)
| sk0 = sk1(sk0) ),
inference(resolution,[status(thm)],[p350,p71]) ).
cnf(c16,plain,
( f(sk3)
| ~ f(X0)
| X3 != sk1(X3)
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p111,plain,
( f(sk3)
| X0 != sk1(X0)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c16]) ).
cnf(p152,plain,
( f(sk3)
| sk0 != sk1(sk0) ),
inference(resolution,[status(thm)],[p111,p39]) ).
cnf(p360,plain,
( f(sk3)
| f(sk3) ),
inference(resolution,[status(thm)],[p351,p152]) ).
cnf(p361,plain,
f(sk3),
inference(factoring,[status(thm)],[p360]) ).
cnf(p364,plain,
sk0 = sk3,
inference(resolution,[status(thm)],[p361,p350]) ).
cnf(p397,plain,
sk2 = sk0,
inference(resolution,[status(thm)],[p391,p364]) ).
cnf(p363,plain,
( sk2 != sk3
| sk3 = X0
| ~ f(X0) ),
inference(resolution,[status(thm)],[p361,p35]) ).
cnf(p392,plain,
( sk2 != sk3
| sk3 = sk0 ),
inference(resolution,[status(thm)],[p363,p39]) ).
cnf(p410,plain,
( sk0 != sk3
| sk3 = sk0 ),
inference(demodulation,[status(thm)],[p397,p392]) ).
cnf(p413,plain,
sk3 = sk0,
inference(resolution,[status(thm)],[p410,p364]) ).
cnf(c17,plain,
( sk2 != sk3
| ~ f(X0)
| X3 != sk1(X3)
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p122,plain,
( sk2 != sk3
| X0 != sk1(X0)
| ~ f(X0) ),
inference(factoring,[status(thm)],[c17]) ).
cnf(p365,plain,
( sk2 != sk3
| sk0 != sk1(sk0) ),
inference(resolution,[status(thm)],[p122,p39]) ).
cnf(p402,plain,
( sk0 != sk3
| sk0 != sk1(sk0) ),
inference(demodulation,[status(thm)],[p397,p365]) ).
cnf(p417,plain,
( sk0 != sk0
| sk0 != sk1(sk0) ),
inference(demodulation,[status(thm)],[p413,p402]) ).
cnf(p422,plain,
sk0 != sk1(sk0),
inference(equality_resolution,[status(thm)],[p417]) ).
cnf(c12,plain,
( sk2 != sk3
| ~ f(X0)
| f(sk1(X3))
| ~ f(X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p77,plain,
( sk2 != sk3
| f(sk1(X0))
| ~ f(X0) ),
inference(factoring,[status(thm)],[c12]) ).
cnf(p99,plain,
( sk2 != sk3
| f(sk1(sk0)) ),
inference(resolution,[status(thm)],[p77,p39]) ).
cnf(p356,plain,
( sk0 != sk3
| f(sk1(sk0)) ),
inference(superposition,[status(thm)],[p353,p99]) ).
cnf(p370,plain,
f(sk1(sk0)),
inference(resolution,[status(thm)],[p356,p364]) ).
cnf(p373,plain,
sk0 = sk1(sk0),
inference(resolution,[status(thm)],[p370,p350]) ).
cnf(p423,plain,
$false,
inference(resolution,[status(thm)],[p422,p373]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN415+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 01:05:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.28/1.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.28/1.10 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------