%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n015.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 11:11:20 AM UTC 2026
% Result : Unsatisfiable 3.76s 2.08s
% Output : CNFRefutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 21 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 7 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ ordered > implies > big_hat > big_V > #nlpp > not > z > y > x > truth
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(truth,type,
truth: $i ).
tff(big_V,type,
big_V: ( $i * $i ) > $i ).
tff(ordered,type,
ordered: ( $i * $i ) > $o ).
tff(x,type,
x: $i ).
tff(y,type,
y: $i ).
tff(not,type,
not: $i > $i ).
tff(big_hat,type,
big_hat: ( $i * $i ) > $i ).
tff(z,type,
z: $i ).
tff(implies,type,
implies: ( $i * $i ) > $i ).
tff(f_47,axiom,
! [X] : ( implies(truth,X) = X ),
file(unknown,unknown) ).
tff(f_95,axiom,
ordered(x,y),
file(unknown,unknown) ).
tff(f_87,axiom,
! [X,Y] :
( ~ ordered(X,Y)
| ( implies(X,Y) = truth ) ),
file(unknown,unknown) ).
tff(f_49,axiom,
! [X,Y,Z] : ( implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))) = truth ),
file(unknown,unknown) ).
tff(f_92,axiom,
! [X,Y] :
( ( implies(X,Y) != truth )
| ordered(X,Y) ),
file(unknown,unknown) ).
tff(f_97,axiom,
~ ordered(implies(z,x),implies(z,y)),
file(unknown,unknown) ).
tff(c_2,plain,
! [X_1] : ( implies(truth,X_1) = X_1 ),
inference(cnfTransformation,[status(thm)],[f_47]) ).
tff(c_18,plain,
ordered(x,y),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_64,plain,
! [X_20,Y_21] :
( ( implies(X_20,Y_21) = truth )
| ~ ordered(X_20,Y_21) ),
inference(cnfTransformation,[status(thm)],[f_87]) ).
tff(c_68,plain,
implies(x,y) = truth,
inference(resolution,[status(thm)],[c_18,c_64]) ).
tff(c_281,plain,
! [X_33,Y_34,Z_35] : ( implies(implies(X_33,Y_34),implies(implies(Y_34,Z_35),implies(X_33,Z_35))) = truth ),
inference(cnfTransformation,[status(thm)],[f_49]) ).
tff(c_380,plain,
! [X_33] : ( implies(implies(X_33,x),implies(truth,implies(X_33,y))) = truth ),
inference(superposition,[status(thm),theory(equality)],[c_68,c_281]) ).
tff(c_404,plain,
! [X_33] : ( implies(implies(X_33,x),implies(X_33,y)) = truth ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_380]) ).
tff(c_69,plain,
! [X_22,Y_23] :
( ordered(X_22,Y_23)
| ( implies(X_22,Y_23) != truth ) ),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_20,plain,
~ ordered(implies(z,x),implies(z,y)),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_77,plain,
implies(implies(z,x),implies(z,y)) != truth,
inference(resolution,[status(thm)],[c_69,c_20]) ).
tff(c_923,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_404,c_77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL143-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.09/0.36 % Computer : n015.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 4 23:47:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 3.76/2.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.76/2.09
% 3.76/2.09 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------