%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% 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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:56:33 PM UTC 2026
% Result : Theorem 2.71s 1.70s
% Output : CNFRefutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 8 ~; 3 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 22 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ drop > cons > #nlpp > tail > s > proj1S > head > z > nil
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(proj1S,type,
proj1S: $i > $i ).
tff(s,type,
s: $i > $i ).
tff(drop,type,
drop: ( $i * $i ) > $i ).
tff(cons,type,
cons: ( $i * $i ) > $i ).
tff(tail,type,
tail: $i > $i ).
tff(z,type,
z: $i ).
tff(head,type,
head: $i > $i ).
tff(nil,type,
nil: $i ).
tff(f_31,axiom,
! [X,X2] : ( nil != cons(X,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
tff(f_40,axiom,
! [Z,X2,X3] : ( drop(s(Z),cons(X2,X3)) = drop(Z,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_007) ).
tff(f_38,axiom,
! [Z] : ( drop(s(Z),nil) = nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
tff(f_48,negated_conjecture,
~ ? [N,Xs,Ys] :
~ ( ( drop(N,Xs) = drop(N,Ys) )
=> ( Xs = Ys ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_009) ).
tff(c_6,plain,
! [X_5,X2_6] : ( cons(X_5,X2_6) != nil ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_93,plain,
! [Z_32,X2_33,X3_34] : ( drop(s(Z_32),cons(X2_33,X3_34)) = drop(Z_32,X3_34) ),
inference(cnfTransformation,[status(thm)],[f_40]) ).
tff(c_12,plain,
! [Z_9] : ( drop(s(Z_9),nil) = nil ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_68,plain,
! [Ys_27,Xs_28,N_29] :
( ( Ys_27 = Xs_28 )
| ( drop(N_29,Ys_27) != drop(N_29,Xs_28) ) ),
inference(cnfTransformation,[status(thm)],[f_48]) ).
tff(c_71,plain,
! [Xs_28,Z_9] :
( ( nil = Xs_28 )
| ( drop(s(Z_9),Xs_28) != nil ) ),
inference(superposition,[status(thm),theory(equality)],[c_12,c_68]) ).
tff(c_99,plain,
! [X2_33,X3_34,Z_32] :
( ( cons(X2_33,X3_34) = nil )
| ( drop(Z_32,X3_34) != nil ) ),
inference(superposition,[status(thm),theory(equality)],[c_93,c_71]) ).
tff(c_110,plain,
! [Z_32,X3_34] : ( drop(Z_32,X3_34) != nil ),
inference(negUnitSimplification,[status(thm)],[c_6,c_99]) ).
tff(c_113,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_110,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX186+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % 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
% 0.17/0.34 % Computer : n023.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 09:37:23 EDT 2026
% 0.17/0.35 % CPUTime :
% 2.71/1.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.71/1.70
% 2.71/1.70 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------