%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n004.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 : Mon Sep 7 11:11:23 AM UTC 2026
% Result : Unsatisfiable 4.07s 2.51s
% Output : CNFRefutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 22 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ theorem > axiom > or > #nlpp > not > r > q > p
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(r,type,
r: $i ).
tff(theorem,type,
theorem: $i > $o ).
tff(or,type,
or: ( $i * $i ) > $i ).
tff(not,type,
not: $i > $i ).
tff(q,type,
q: $i ).
tff(axiom,type,
axiom: $i > $o ).
tff(p,type,
p: $i ).
tff(f_61,axiom,
! [A,B,C] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
file(unknown,unknown) ).
tff(f_66,axiom,
! [X] :
( theorem(X)
| ~ axiom(X) ),
file(unknown,unknown) ).
tff(f_59,axiom,
! [A,B,C] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
file(unknown,unknown) ).
tff(f_74,axiom,
! [X,Y] :
( theorem(X)
| ~ axiom(or(not(Y),X))
| ~ theorem(Y) ),
file(unknown,unknown) ).
tff(f_86,axiom,
~ theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))),
file(unknown,unknown) ).
tff(c_10,plain,
! [A_9,B_10,C_11] : axiom(or(not(or(not(A_9),B_10)),or(not(or(C_11,A_9)),or(C_11,B_10)))),
inference(cnfTransformation,[status(thm)],[f_61]) ).
tff(c_12,plain,
! [X_12] :
( ~ axiom(X_12)
| theorem(X_12) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_56,plain,
! [A_32,B_33,C_34] : axiom(or(not(or(A_32,or(B_33,C_34))),or(B_33,or(A_32,C_34)))),
inference(cnfTransformation,[status(thm)],[f_59]) ).
tff(c_14,plain,
! [Y_14,X_13] :
( ~ theorem(Y_14)
| ~ axiom(or(not(Y_14),X_13))
| theorem(X_13) ),
inference(cnfTransformation,[status(thm)],[f_74]) ).
tff(c_79,plain,
! [A_39,B_40,C_41] :
( ~ theorem(or(A_39,or(B_40,C_41)))
| theorem(or(B_40,or(A_39,C_41))) ),
inference(resolution,[status(thm)],[c_56,c_14]) ).
tff(c_505,plain,
! [B_86,A_87,C_88] :
( theorem(or(B_86,or(A_87,C_88)))
| ~ axiom(or(A_87,or(B_86,C_88))) ),
inference(resolution,[status(thm)],[c_12,c_79]) ).
tff(c_18,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_514,plain,
~ axiom(or(not(or(not(q),r)),or(not(or(not(p),q)),or(not(p),r)))),
inference(resolution,[status(thm)],[c_505,c_18]) ).
tff(c_538,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_10,c_514]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 02:42:14 UTC 2026
% 0.09/0.35 % CPUTime :
% 4.07/2.51 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.07/2.51
% 4.07/2.51 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------