%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : ARI691_1 : TPTP v9.0.0. Released v6.3.0.
% 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 : n003.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 : Wed Apr 9 05:40:51 PM UTC 2025
% Result : Theorem 2.58s 1.53s
% Output : CNFRefutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 8 ( 7 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 18 ( 0 atm; 14 fun; 0 num; 4 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 4 ( 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
%$ #nlpp > f
%Foreground sorts:
%Background operators:
tff(b,type,
b: $int ).
tff(a,type,
a: $int ).
%Foreground operators:
tff(f,type,
f: $int > $int ).
tff(f_64,axiom,
! [A: $int,B: $int] : ( $product(A,B) = $product(B,A) ),
file('/export/starexec/sandbox2/solver/bin/lemmas/mult_lemmas.p',mult_comm) ).
tff(f_30,axiom,
$product(a,b) = f($product(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq) ).
tff(f_32,negated_conjecture,
f(f($product(a,b))) != $product(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(c_45,plain,
! [B_7: $int,A_8: $int] : ( $product(B_7,A_8) = $product(A_8,B_7) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_49,plain,
f($product(a,b)) = $product(a,b),
inference(cnfTransformation,[status(thm)],[f_30]) ).
tff(c_31,plain,
$product(b,a) != f(f($product(a,b))),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_56,plain,
$product(b,a) != $product(a,b),
inference(demodulation,[status(thm),theory(equality)],[c_49,c_49,c_31]) ).
tff(c_63,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_45,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : ARI691_1 : TPTP v9.0.0. Released v6.3.0.
% 0.00/0.09 % 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
% 0.08/0.28 % Computer : n003.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Mon Apr 7 15:16:48 EDT 2025
% 0.08/0.28 % CPUTime :
% 2.58/1.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.58/1.53
% 2.58/1.53 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------