%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 03:34:28 PM UTC 2026
% Result : Theorem 13.62s 2.23s
% Output : Proof 13.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 1
% Syntax : Number of formulae : 84 ( 4 unt; 0 def)
% Number of atoms : 360 ( 0 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 359 ( 83 ~; 206 |; 42 &)
% ( 8 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 167 ( 1 sgn 10 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X] :
? [Y1,Y2,Y3] :
! [Z] :
( ( big_f(Y1,Y2,Y3)
=> ( big_f(X,X,Z)
=> ( big_f(Y3,Y1,Y2)
| big_f(Y2,Y3,Y1) ) ) )
=> ( ( ( big_f(Y3,Y1,Y2)
=> ( big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) ) )
<=> big_f(Y2,Y1,Z) )
=> ( ( ( big_f(Y2,Y3,Y1)
=> ( big_f(Y3,Y1,Y2)
& big_f(Y1,Y2,Y3) ) )
<=> big_f(Y1,Z,Y2) )
=> ( ( ( ( big_f(Y3,Y1,Y2)
=> ~ big_f(Y2,Y3,Y1) )
=> big_f(Y1,Y2,Y3) )
<=> big_f(Z,Y2,Y1) )
=> ( ( big_f(Y3,Y1,Y2)
& big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) )
<=> big_f(Z,Z,Z) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',church_46_18_5) ).
fof(f0_neg,negated_conjecture,
~ ! [X] :
? [Y1,Y2,Y3] :
! [Z] :
( ( big_f(Y1,Y2,Y3)
=> ( big_f(X,X,Z)
=> ( big_f(Y3,Y1,Y2)
| big_f(Y2,Y3,Y1) ) ) )
=> ( ( ( big_f(Y3,Y1,Y2)
=> ( big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) ) )
<=> big_f(Y2,Y1,Z) )
=> ( ( ( big_f(Y2,Y3,Y1)
=> ( big_f(Y3,Y1,Y2)
& big_f(Y1,Y2,Y3) ) )
<=> big_f(Y1,Z,Y2) )
=> ( ( ( ( big_f(Y3,Y1,Y2)
=> ~ big_f(Y2,Y3,Y1) )
=> big_f(Y1,Y2,Y3) )
<=> big_f(Z,Y2,Y1) )
=> ( ( big_f(Y3,Y1,Y2)
& big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) )
<=> big_f(Z,Z,Z) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X] :
! [Y1,Y2,Y3] :
? [Z] :
( ( ( big_f(Z,Z,Z)
& ( ~ big_f(Y3,Y1,Y2)
| ~ big_f(Y2,Y3,Y1)
| ~ big_f(Y1,Y2,Y3) ) )
| ( ~ big_f(Z,Z,Z)
& big_f(Y3,Y1,Y2)
& big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) ) )
& ( ~ big_f(Z,Y2,Y1)
| big_f(Y1,Y2,Y3)
| ( big_f(Y2,Y3,Y1)
& big_f(Y3,Y1,Y2) ) )
& ( big_f(Z,Y2,Y1)
| ( ~ big_f(Y1,Y2,Y3)
& ( ~ big_f(Y2,Y3,Y1)
| ~ big_f(Y3,Y1,Y2) ) ) )
& ( ~ big_f(Y1,Z,Y2)
| ( big_f(Y3,Y1,Y2)
& big_f(Y1,Y2,Y3) )
| ~ big_f(Y2,Y3,Y1) )
& ( big_f(Y1,Z,Y2)
| ( ( ~ big_f(Y3,Y1,Y2)
| ~ big_f(Y1,Y2,Y3) )
& big_f(Y2,Y3,Y1) ) )
& ( ~ big_f(Y2,Y1,Z)
| ( big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) )
| ~ big_f(Y3,Y1,Y2) )
& ( big_f(Y2,Y1,Z)
| ( ( ~ big_f(Y2,Y3,Y1)
| ~ big_f(Y1,Y2,Y3) )
& big_f(Y3,Y1,Y2) ) )
& ( big_f(Y3,Y1,Y2)
| big_f(Y2,Y3,Y1)
| ~ big_f(X,X,Z)
| ~ big_f(Y1,Y2,Y3) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y1,Y2,Y3] :
( ( ( big_f(sk1(Y1,Y2,Y3),sk1(Y1,Y2,Y3),sk1(Y1,Y2,Y3))
& ( ~ big_f(Y3,Y1,Y2)
| ~ big_f(Y2,Y3,Y1)
| ~ big_f(Y1,Y2,Y3) ) )
| ( ~ big_f(sk1(Y1,Y2,Y3),sk1(Y1,Y2,Y3),sk1(Y1,Y2,Y3))
& big_f(Y3,Y1,Y2)
& big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) ) )
& ( ~ big_f(sk1(Y1,Y2,Y3),Y2,Y1)
| big_f(Y1,Y2,Y3)
| ( big_f(Y2,Y3,Y1)
& big_f(Y3,Y1,Y2) ) )
& ( big_f(sk1(Y1,Y2,Y3),Y2,Y1)
| ( ~ big_f(Y1,Y2,Y3)
& ( ~ big_f(Y2,Y3,Y1)
| ~ big_f(Y3,Y1,Y2) ) ) )
& ( ~ big_f(Y1,sk1(Y1,Y2,Y3),Y2)
| ( big_f(Y3,Y1,Y2)
& big_f(Y1,Y2,Y3) )
| ~ big_f(Y2,Y3,Y1) )
& ( big_f(Y1,sk1(Y1,Y2,Y3),Y2)
| ( ( ~ big_f(Y3,Y1,Y2)
| ~ big_f(Y1,Y2,Y3) )
& big_f(Y2,Y3,Y1) ) )
& ( ~ big_f(Y2,Y1,sk1(Y1,Y2,Y3))
| ( big_f(Y2,Y3,Y1)
& big_f(Y1,Y2,Y3) )
| ~ big_f(Y3,Y1,Y2) )
& ( big_f(Y2,Y1,sk1(Y1,Y2,Y3))
| ( ( ~ big_f(Y2,Y3,Y1)
| ~ big_f(Y1,Y2,Y3) )
& big_f(Y3,Y1,Y2) ) )
& ( big_f(Y3,Y1,Y2)
| big_f(Y2,Y3,Y1)
| ~ big_f(sk0,sk0,sk1(Y1,Y2,Y3))
| ~ big_f(Y1,Y2,Y3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c0,plain,
( big_f(X3,X1,X2)
| big_f(X2,X3,X1)
| ~ big_f(sk0,sk0,sk1(X1,X2,X3))
| ~ big_f(X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c1,plain,
( big_f(X2,X1,sk1(X1,X2,X3))
| big_f(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p65,plain,
( big_f(X2,X1,X0)
| big_f(sk1(X1,X0,X2),X0,X1)
| big_f(X1,sk1(X1,X0,X2),X0)
| ~ big_f(sk0,sk0,sk1(X0,X1,sk1(X1,X0,X2))) ),
inference(resolution,[status(thm)],[c0,c1]) ).
cnf(p274,plain,
( big_f(sk1(sk0,sk0,X0),sk0,sk0)
| big_f(X0,sk0,sk0)
| big_f(sk1(sk0,sk0,X0),sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(resolution,[status(thm)],[p65,c1]) ).
cnf(p275,plain,
( big_f(X0,sk0,sk0)
| big_f(sk1(sk0,sk0,X0),sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(factoring,[status(thm)],[p274]) ).
cnf(c11,plain,
( ~ big_f(sk1(X1,X2,X3),X2,X1)
| big_f(X1,X2,X3)
| big_f(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p279,plain,
( big_f(sk0,sk0,X0)
| big_f(X0,sk0,sk0)
| big_f(X0,sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(resolution,[status(thm)],[p275,c11]) ).
cnf(p281,plain,
( big_f(sk0,sk0,X0)
| big_f(X0,sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(factoring,[status(thm)],[p279]) ).
cnf(c7,plain,
( ~ big_f(X1,sk1(X1,X2,X3),X2)
| big_f(X1,X2,X3)
| ~ big_f(X2,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c5,plain,
( big_f(X1,sk1(X1,X2,X3),X2)
| big_f(X2,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p39,plain,
( big_f(X0,X2,X1)
| ~ big_f(X0,sk1(X0,X1,sk1(X1,X0,X2)),X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(p288,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk1(sk0,sk0,X0),sk0,sk0) ),
inference(resolution,[status(thm)],[p281,p39]) ).
cnf(p323,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk1(sk0,sk0,X0),sk0,sk0) ),
inference(factoring,[status(thm)],[p288]) ).
cnf(c9,plain,
( big_f(sk1(X1,X2,X3),X2,X1)
| ~ big_f(X2,X3,X1)
| ~ big_f(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p327,plain,
( big_f(sk1(sk0,sk0,sk1(sk0,sk0,X0)),sk0,sk0)
| ~ big_f(sk0,sk1(sk0,sk0,X0),sk0)
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p323,c9]) ).
cnf(p429,plain,
( big_f(sk0,X0,sk0)
| big_f(sk1(sk0,sk0,sk1(sk0,sk0,X0)),sk0,sk0)
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p327,c5]) ).
cnf(p431,plain,
( big_f(sk1(sk0,sk0,sk1(sk0,sk0,X0)),sk0,sk0)
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p429]) ).
cnf(c3,plain,
( ~ big_f(X2,X1,sk1(X1,X2,X3))
| big_f(X1,X2,X3)
| ~ big_f(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p432,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0))))
| big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p431,c3]) ).
cnf(c12,plain,
( ~ big_f(sk1(X1,X2,X3),X2,X1)
| big_f(X1,X2,X3)
| big_f(X2,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p328,plain,
( big_f(sk0,sk0,X0)
| big_f(sk0,X0,sk0)
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p323,c12]) ).
cnf(p329,plain,
( big_f(sk0,sk0,X0)
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p328]) ).
cnf(p881,plain,
( big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)),sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p432,p329]) ).
cnf(p1503,plain,
( big_f(sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)),sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p881]) ).
cnf(p1507,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p1503,p39]) ).
cnf(p1515,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p1507]) ).
cnf(p1517,plain,
( big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p1515]) ).
cnf(p324,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p323,c3]) ).
cnf(p428,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p324]) ).
cnf(p1524,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(resolution,[status(thm)],[p1517,p428]) ).
cnf(p1529,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p1524]) ).
cnf(p1531,plain,
( big_f(sk0,X0,sk0)
| big_f(sk0,sk0,sk1(sk0,sk0,X0)) ),
inference(factoring,[status(thm)],[p1529]) ).
cnf(c4,plain,
( ~ big_f(X2,X1,sk1(X1,X2,X3))
| big_f(X2,X3,X1)
| ~ big_f(X3,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p277,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(sk0,sk1(sk0,sk0,X0),sk0)
| big_f(X0,sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(resolution,[status(thm)],[p275,c4]) ).
cnf(p400,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,sk1(sk0,sk0,X0)))
| big_f(X0,sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(factoring,[status(thm)],[p277]) ).
cnf(p1540,plain,
( big_f(X0,sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(resolution,[status(thm)],[p1531,p400]) ).
cnf(p1560,plain,
( big_f(X0,sk0,sk0)
| big_f(sk0,sk1(sk0,sk0,X0),sk0) ),
inference(factoring,[status(thm)],[p1540]) ).
cnf(c8,plain,
( ~ big_f(X1,sk1(X1,X2,X3),X2)
| big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p42,plain,
( big_f(X1,X2,X0)
| ~ big_f(X1,sk1(X1,X0,sk1(X0,X1,X2)),X0)
| big_f(sk1(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[c8,c5]) ).
cnf(p1568,plain,
( big_f(sk0,X0,sk0)
| big_f(sk1(sk0,sk0,X0),sk0,sk0)
| big_f(sk1(sk0,sk0,X0),sk0,sk0) ),
inference(resolution,[status(thm)],[p1560,p42]) ).
cnf(p1604,plain,
( big_f(sk0,X0,sk0)
| big_f(sk1(sk0,sk0,X0),sk0,sk0) ),
inference(factoring,[status(thm)],[p1568]) ).
cnf(p1610,plain,
( big_f(sk0,sk0,X0)
| big_f(sk0,X0,sk0)
| big_f(sk0,X0,sk0) ),
inference(resolution,[status(thm)],[p1604,c12]) ).
cnf(p1671,plain,
( big_f(sk0,sk0,X0)
| big_f(sk0,X0,sk0) ),
inference(factoring,[status(thm)],[p1610]) ).
cnf(p1677,plain,
( ~ big_f(sk0,sk1(sk0,sk0,X0),sk0)
| big_f(sk0,sk0,X0)
| big_f(sk0,sk0,X0) ),
inference(resolution,[status(thm)],[p1671,c7]) ).
cnf(p1700,plain,
( ~ big_f(sk0,sk1(sk0,sk0,X0),sk0)
| big_f(sk0,sk0,X0) ),
inference(factoring,[status(thm)],[p1677]) ).
cnf(p1701,plain,
( big_f(X0,sk0,sk0)
| big_f(sk0,sk0,X0) ),
inference(resolution,[status(thm)],[p1700,p1560]) ).
cnf(p1703,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,sk0,X0)
| big_f(sk0,sk0,X0) ),
inference(resolution,[status(thm)],[p1701,c3]) ).
cnf(p1750,plain,
( ~ big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,sk0,X0) ),
inference(factoring,[status(thm)],[p1703]) ).
cnf(p1702,plain,
( big_f(sk0,sk0,sk1(sk0,sk0,X0))
| big_f(sk0,sk0,X0) ),
inference(resolution,[status(thm)],[p1700,p1671]) ).
cnf(p1753,plain,
( big_f(sk0,sk0,X0)
| big_f(sk0,sk0,X0) ),
inference(resolution,[status(thm)],[p1750,p1702]) ).
cnf(p1754,plain,
big_f(sk0,sk0,X0),
inference(factoring,[status(thm)],[p1753]) ).
cnf(p66,plain,
( big_f(X1,X2,X0)
| big_f(X1,X0,sk1(X0,X1,X2))
| big_f(sk1(X0,X1,X2),X1,X0)
| ~ big_f(sk0,sk0,sk1(X0,sk1(X0,X1,X2),X1)) ),
inference(resolution,[status(thm)],[c0,c5]) ).
cnf(p1764,plain,
( big_f(X1,X2,X0)
| big_f(X1,X0,sk1(X0,X1,X2))
| big_f(sk1(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[p1754,p66]) ).
cnf(p2028,plain,
( big_f(sk1(X0,X1,sk1(X1,X0,X2)),X1,X0)
| ~ big_f(X1,sk1(X1,X0,X2),X0)
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p1764,c9]) ).
cnf(p2555,plain,
( big_f(X0,X2,X1)
| big_f(sk1(X0,X1,sk1(X1,X0,X2)),X1,X0)
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p2028,c5]) ).
cnf(p2562,plain,
( big_f(sk1(X0,X1,sk1(X1,X0,X2)),X1,X0)
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p2555]) ).
cnf(p2563,plain,
( ~ big_f(X0,X1,sk1(X1,X0,sk1(X0,X1,sk1(X1,X0,X2))))
| big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p2562,c3]) ).
cnf(p2029,plain,
( big_f(X1,X0,X2)
| big_f(X0,X2,X1)
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p1764,c12]) ).
cnf(p2143,plain,
( big_f(X1,X0,X2)
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p2029]) ).
cnf(p3184,plain,
( big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,sk1(X0,X1,sk1(X1,X0,X2)),X1)
| big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p2563,p2143]) ).
cnf(p3930,plain,
( big_f(X0,sk1(X0,X1,sk1(X1,X0,X2)),X1)
| big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p3184]) ).
cnf(p3938,plain,
( big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2))
| big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p3930,p39]) ).
cnf(p3958,plain,
( big_f(X0,X2,X1)
| big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p3938]) ).
cnf(p3960,plain,
( big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p3958]) ).
cnf(p2025,plain,
( ~ big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X1,sk1(X1,X0,X2))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p1764,c3]) ).
cnf(p2554,plain,
( ~ big_f(X1,X0,sk1(X0,X1,sk1(X1,X0,X2)))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p2025]) ).
cnf(p3970,plain,
( big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2))
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(resolution,[status(thm)],[p3960,p2554]) ).
cnf(p3974,plain,
( big_f(X0,X2,X1)
| big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p3970]) ).
cnf(p3976,plain,
( big_f(X0,X2,X1)
| big_f(X0,X1,sk1(X1,X0,X2)) ),
inference(factoring,[status(thm)],[p3974]) ).
cnf(p28,plain,
( big_f(X2,X0,X1)
| ~ big_f(sk1(X0,X1,X2),X0,sk1(X0,sk1(X0,X1,X2),X1))
| big_f(sk1(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(p3982,plain,
( big_f(X2,X0,X1)
| big_f(sk1(X0,X1,X2),X1,X0)
| big_f(sk1(X0,X1,X2),X1,X0) ),
inference(resolution,[status(thm)],[p3976,p28]) ).
cnf(p4020,plain,
( big_f(X2,X0,X1)
| big_f(sk1(X0,X1,X2),X1,X0) ),
inference(factoring,[status(thm)],[p3982]) ).
cnf(p47,plain,
( ~ big_f(sk1(X0,X0,X0),X0,X0)
| big_f(X0,X0,X0) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p4025,plain,
( big_f(X0,X0,X0)
| big_f(X0,X0,X0) ),
inference(resolution,[status(thm)],[p4020,p47]) ).
cnf(p4030,plain,
big_f(X0,X0,X0),
inference(factoring,[status(thm)],[p4025]) ).
cnf(c19,plain,
( ~ big_f(X3,X1,X2)
| ~ big_f(X2,X3,X1)
| ~ big_f(X1,X2,X3)
| ~ big_f(sk1(X1,X2,X3),sk1(X1,X2,X3),sk1(X1,X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p211,plain,
( ~ big_f(X0,X0,X0)
| ~ big_f(X0,X0,X0)
| ~ big_f(sk1(X0,X0,X0),sk1(X0,X0,X0),sk1(X0,X0,X0)) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(p212,plain,
( ~ big_f(X0,X0,X0)
| ~ big_f(sk1(X0,X0,X0),sk1(X0,X0,X0),sk1(X0,X0,X0)) ),
inference(factoring,[status(thm)],[p211]) ).
cnf(p4035,plain,
~ big_f(X0,X0,X0),
inference(resolution,[status(thm)],[p4030,p212]) ).
cnf(p4036,plain,
$false,
inference(resolution,[status(thm)],[p4035,p1754]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN353+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n003.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 00:59:06 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.62/2.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.62/2.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------