%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SYO038-1.003.003 : TPTP v9.0.0. Released v5.3.0.
% 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 : n032.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 10:37:01 PM UTC 2025
% Result : Unsatisfiable 5.03s 2.12s
% Output : CNFRefutation 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 50 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 15 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 28 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ d > f > #nlpp > s > one
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(d,type,
d: $i > $o ).
tff(s,type,
s: $i > $i ).
tff(one,type,
one: $i ).
tff(f,type,
f: ( $i * $i ) > $i ).
tff(f_36,axiom,
d(one),
file(unknown,unknown) ).
tff(f_41,axiom,
! [X] :
( ~ d(X)
| d(s(X)) ),
file(unknown,unknown) ).
tff(f_31,axiom,
! [N] : ( f(N,one) = s(one) ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [X] : ( f(one,s(X)) = s(s(f(one,X))) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [N,X] : ( f(s(N),s(X)) = f(N,f(s(N),X)) ),
file(unknown,unknown) ).
tff(f_43,axiom,
~ d(f(s(s(one)),s(s(one)))),
file(unknown,unknown) ).
tff(c_8,plain,
d(one),
inference(cnfTransformation,[status(thm)],[f_36]) ).
tff(c_10,plain,
! [X_5] :
( d(s(X_5))
| ~ d(X_5) ),
inference(cnfTransformation,[status(thm)],[f_41]) ).
tff(c_2,plain,
! [N_1] : ( f(N_1,one) = s(one) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_21,plain,
! [X_8] : ( s(s(f(one,X_8))) = f(one,s(X_8)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_34,plain,
s(s(s(one))) = f(one,s(one)),
inference(superposition,[status(thm),theory(equality)],[c_2,c_21]) ).
tff(c_88,plain,
( d(f(one,s(one)))
| ~ d(s(s(one))) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_10]) ).
tff(c_122,plain,
~ d(s(s(one))),
inference(splitLeft,[status(thm)],[c_88]) ).
tff(c_133,plain,
~ d(s(one)),
inference(resolution,[status(thm)],[c_10,c_122]) ).
tff(c_136,plain,
~ d(one),
inference(resolution,[status(thm)],[c_10,c_133]) ).
tff(c_140,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8,c_136]) ).
tff(c_141,plain,
d(f(one,s(one))),
inference(splitRight,[status(thm)],[c_88]) ).
tff(c_27,plain,
! [X_8] :
( d(f(one,s(X_8)))
| ~ d(s(f(one,X_8))) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_10]) ).
tff(c_143,plain,
! [X_13] :
( d(f(one,s(X_13)))
| ~ d(s(f(one,X_13))) ),
inference(superposition,[status(thm),theory(equality)],[c_21,c_10]) ).
tff(c_146,plain,
( d(f(one,f(one,s(one))))
| ~ d(s(f(one,s(s(one))))) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_143]) ).
tff(c_342,plain,
~ d(s(f(one,s(s(one))))),
inference(splitLeft,[status(thm)],[c_146]) ).
tff(c_346,plain,
~ d(f(one,s(s(one)))),
inference(resolution,[status(thm)],[c_10,c_342]) ).
tff(c_411,plain,
~ d(s(f(one,s(one)))),
inference(resolution,[status(thm)],[c_27,c_346]) ).
tff(c_414,plain,
~ d(f(one,s(one))),
inference(resolution,[status(thm)],[c_10,c_411]) ).
tff(c_418,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_141,c_414]) ).
tff(c_419,plain,
d(f(one,f(one,s(one)))),
inference(splitRight,[status(thm)],[c_146]) ).
tff(c_4,plain,
! [X_2] : ( s(s(f(one,X_2))) = f(one,s(X_2)) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_421,plain,
! [X_20] :
( d(f(one,f(one,s(X_20))))
| ~ d(s(f(one,s(f(one,X_20))))) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_143]) ).
tff(c_429,plain,
! [X_20] :
( d(f(one,f(one,s(X_20))))
| ~ d(f(one,s(f(one,X_20)))) ),
inference(resolution,[status(thm)],[c_10,c_421]) ).
tff(c_37,plain,
! [N_9,X_10] : ( f(s(N_9),s(X_10)) = f(N_9,f(s(N_9),X_10)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_73,plain,
! [N_9] : ( f(s(N_9),s(one)) = f(N_9,s(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_37]) ).
tff(c_6,plain,
! [N_3,X_4] : ( f(s(N_3),s(X_4)) = f(N_3,f(s(N_3),X_4)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_150,plain,
! [N_14,X_15] : ( f(s(N_14),s(s(X_15))) = f(N_14,f(N_14,f(s(N_14),X_15))) ),
inference(superposition,[status(thm),theory(equality)],[c_37,c_6]) ).
tff(c_195,plain,
! [N_14] : ( f(N_14,f(N_14,f(s(N_14),s(one)))) = f(s(N_14),f(one,s(one))) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_150]) ).
tff(c_234,plain,
! [N_14] : ( f(s(N_14),f(one,s(one))) = f(N_14,f(N_14,f(N_14,s(one)))) ),
inference(demodulation,[status(thm),theory(equality)],[c_73,c_195]) ).
tff(c_93,plain,
! [N_11] : ( f(s(N_11),s(one)) = f(N_11,s(one)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_37]) ).
tff(c_102,plain,
! [N_11] : ( f(s(N_11),s(s(one))) = f(N_11,f(N_11,s(one))) ),
inference(superposition,[status(thm),theory(equality)],[c_93,c_6]) ).
tff(c_12,plain,
~ d(f(s(s(one)),s(s(one)))),
inference(cnfTransformation,[status(thm)],[f_43]) ).
tff(c_241,plain,
~ d(f(s(one),f(s(one),s(one)))),
inference(demodulation,[status(thm),theory(equality)],[c_102,c_12]) ).
tff(c_242,plain,
~ d(f(s(one),f(one,s(one)))),
inference(demodulation,[status(thm),theory(equality)],[c_73,c_241]) ).
tff(c_739,plain,
~ d(f(one,f(one,f(one,s(one))))),
inference(demodulation,[status(thm),theory(equality)],[c_234,c_242]) ).
tff(c_505,plain,
! [X_22] :
( d(f(one,f(one,s(X_22))))
| ~ d(f(one,s(f(one,X_22)))) ),
inference(resolution,[status(thm)],[c_10,c_421]) ).
tff(c_508,plain,
( d(f(one,f(one,f(one,s(one)))))
| ~ d(f(one,s(f(one,s(s(one)))))) ),
inference(superposition,[status(thm),theory(equality)],[c_34,c_505]) ).
tff(c_2529,plain,
~ d(f(one,s(f(one,s(s(one)))))),
inference(negUnitSimplification,[status(thm)],[c_739,c_508]) ).
tff(c_2533,plain,
~ d(s(f(one,f(one,s(s(one)))))),
inference(resolution,[status(thm)],[c_27,c_2529]) ).
tff(c_2537,plain,
~ d(f(one,f(one,s(s(one))))),
inference(resolution,[status(thm)],[c_10,c_2533]) ).
tff(c_2541,plain,
~ d(f(one,s(f(one,s(one))))),
inference(resolution,[status(thm)],[c_429,c_2537]) ).
tff(c_2545,plain,
~ d(s(f(one,f(one,s(one))))),
inference(resolution,[status(thm)],[c_27,c_2541]) ).
tff(c_2548,plain,
~ d(f(one,f(one,s(one)))),
inference(resolution,[status(thm)],[c_10,c_2545]) ).
tff(c_2552,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_419,c_2548]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.08 % Problem : SYO038-1.003.003 : TPTP v9.0.0. Released v5.3.0.
% 0.06/0.08 % 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
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Wed Apr 9 08:46:16 EDT 2025
% 0.08/0.27 % CPUTime :
% 5.03/2.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.03/2.13
% 5.03/2.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------