%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 12:51:10 PM UTC 2026
% Result : Unsatisfiable 46.34s 7.22s
% Output : Proof 46.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 20 unt; 0 def)
% Number of atoms : 74 ( 4 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 43 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
f(X,f(Y,Z)) = f(f(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_is_associative) ).
fof(f0_nnf,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : f(X,f(Y,Z)) = f(f(X,Y),Z),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
f(X0,f(X1,X2)) = f(f(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f4,hypothesis,
d(a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d_not_empty) ).
fof(f4_nnf,plain,
d(a2),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
d(a2),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(f6,negated_conjecture,
( ~ d(Y)
| ~ d(X)
| c(f(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ d(Y)
| ~ d(X)
| c(f(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ d(Y)
| ~ d(X)
| c(f(X,Y)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ d(X1)
| ~ d(X0)
| c(f(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p8,plain,
( ~ d(X0)
| c(f(X0,X0)) ),
inference(factoring,[status(thm)],[c6]) ).
cnf(p42,plain,
c(f(a2,a2)),
inference(resolution,[status(thm)],[c4,p8]) ).
cnf(f5,negated_conjecture,
( ~ c(Y)
| ~ c(X)
| d(f(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
fof(f5_nnf,plain,
! [X,Y] :
( ~ c(Y)
| ~ c(X)
| d(f(X,Y)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( ~ c(Y)
| ~ c(X)
| d(f(X,Y)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ c(X1)
| ~ c(X0)
| d(f(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p44,plain,
( ~ c(X0)
| d(f(f(a2,a2),X0)) ),
inference(resolution,[status(thm)],[p42,c5]) ).
cnf(f3,hypothesis,
c(a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_c_not_empty) ).
fof(f3_nnf,plain,
c(a1),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
c(a1),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(p174,plain,
d(f(f(a2,a2),a1)),
inference(resolution,[status(thm)],[p44,c3]) ).
cnf(p189,plain,
d(f(a2,f(a2,a1))),
inference(superposition,[status(thm)],[c0,p174]) ).
cnf(p41,plain,
( ~ d(X0)
| c(f(a2,X0)) ),
inference(resolution,[status(thm)],[c4,c6]) ).
cnf(f1,axiom,
( d(X)
| c(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_union) ).
fof(f1_nnf,plain,
! [X] :
( d(X)
| c(X) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] :
( d(X)
| c(X) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( d(X0)
| c(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p68,plain,
( c(X0)
| c(f(a2,X0)) ),
inference(resolution,[status(thm)],[p41,c1]) ).
cnf(f2,hypothesis,
( ~ d(X)
| ~ c(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive) ).
fof(f2_nnf,plain,
! [X] :
( ~ d(X)
| ~ c(X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] :
( ~ d(X)
| ~ c(X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ d(X0)
| ~ c(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p85,plain,
( ~ d(f(a2,X0))
| c(X0) ),
inference(resolution,[status(thm)],[p68,c2]) ).
cnf(p205,plain,
c(f(a2,a1)),
inference(resolution,[status(thm)],[p189,p85]) ).
cnf(p7,plain,
( ~ c(X0)
| d(f(X0,X0)) ),
inference(factoring,[status(thm)],[c5]) ).
cnf(p208,plain,
d(f(f(a2,a1),f(a2,a1))),
inference(resolution,[status(thm)],[p205,p7]) ).
cnf(p251,plain,
d(f(a2,f(a1,f(a2,a1)))),
inference(superposition,[status(thm)],[c0,p208]) ).
cnf(p279,plain,
c(f(a1,f(a2,a1))),
inference(resolution,[status(thm)],[p251,p85]) ).
cnf(p289,plain,
~ d(f(a1,f(a2,a1))),
inference(resolution,[status(thm)],[p279,c2]) ).
cnf(p9,plain,
( ~ c(X0)
| d(f(a1,X0)) ),
inference(resolution,[status(thm)],[c3,c5]) ).
cnf(p209,plain,
d(f(a1,f(a2,a1))),
inference(resolution,[status(thm)],[p205,p9]) ).
cnf(p294,plain,
$false,
inference(resolution,[status(thm)],[p289,p209]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG011-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 04:34:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 46.34/7.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 46.34/7.22 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------