%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SYN986+1.002 : TPTP v9.0.0. Released v4.0.0.
% 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 : 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 10:08:36 PM UTC 2025
% Result : Theorem 3.84s 2.60s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 38 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 42 ( 22 ~; 16 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 2 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 36 ( 33 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ r > #nlpp > succ > zero
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(r,type,
r: ( $i * $i * $i ) > $o ).
tff(succ,type,
succ: $i > $i ).
tff(zero,type,
zero: $i ).
tff(f_57,axiom,
! [Y] : r(Y,zero,succ(Y)),
file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp1) ).
tff(f_63,axiom,
! [Y,X,Z,Z1] :
( r(Y,X,Z)
=> ( r(Z,X,Z1)
=> r(Y,succ(X),Z1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SYN002+0.ax',hyp2) ).
tff(f_72,negated_conjecture,
~ ? [Z2,Z1,Z0] :
( r(zero,zero,Z2)
& r(zero,Z2,Z1)
& r(zero,Z1,Z0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ck) ).
tff(c_2,plain,
! [Y_1] : r(Y_1,zero,succ(Y_1)),
inference(cnfTransformation,[status(thm)],[f_57]) ).
tff(c_14,plain,
! [Y_14,X_15,Z1_16,Z_17] :
( r(Y_14,succ(X_15),Z1_16)
| ~ r(Z_17,X_15,Z1_16)
| ~ r(Y_14,X_15,Z_17) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_17,plain,
! [Y_14,Y_1] :
( r(Y_14,succ(zero),succ(Y_1))
| ~ r(Y_14,zero,Y_1) ),
inference(resolution,[status(thm)],[c_2,c_14]) ).
tff(c_18,plain,
! [Y_18,Y_19] :
( r(Y_18,succ(zero),succ(Y_19))
| ~ r(Y_18,zero,Y_19) ),
inference(resolution,[status(thm)],[c_2,c_14]) ).
tff(c_4,plain,
! [Y_2,X_3,Z1_5,Z_4] :
( r(Y_2,succ(X_3),Z1_5)
| ~ r(Z_4,X_3,Z1_5)
| ~ r(Y_2,X_3,Z_4) ),
inference(cnfTransformation,[status(thm)],[f_63]) ).
tff(c_47,plain,
! [Y_22,Y_23,Y_24] :
( r(Y_22,succ(succ(zero)),succ(Y_23))
| ~ r(Y_22,succ(zero),Y_24)
| ~ r(Y_24,zero,Y_23) ),
inference(resolution,[status(thm)],[c_18,c_4]) ).
tff(c_51,plain,
! [Y_25,Y_26,Y_27] :
( r(Y_25,succ(succ(zero)),succ(Y_26))
| ~ r(succ(Y_27),zero,Y_26)
| ~ r(Y_25,zero,Y_27) ),
inference(resolution,[status(thm)],[c_17,c_47]) ).
tff(c_56,plain,
! [Y_28,Y_29] :
( r(Y_28,succ(succ(zero)),succ(succ(succ(Y_29))))
| ~ r(Y_28,zero,Y_29) ),
inference(resolution,[status(thm)],[c_2,c_51]) ).
tff(c_6,plain,
! [Z1_7,Z0_8,Z2_6] :
( ~ r(zero,Z1_7,Z0_8)
| ~ r(zero,Z2_6,Z1_7)
| ~ r(zero,zero,Z2_6) ),
inference(cnfTransformation,[status(thm)],[f_72]) ).
tff(c_63,plain,
! [Z2_6,Y_29] :
( ~ r(zero,Z2_6,succ(succ(zero)))
| ~ r(zero,zero,Z2_6)
| ~ r(zero,zero,Y_29) ),
inference(resolution,[status(thm)],[c_56,c_6]) ).
tff(c_65,plain,
! [Y_30] : ~ r(zero,zero,Y_30),
inference(splitLeft,[status(thm)],[c_63]) ).
tff(c_70,plain,
$false,
inference(resolution,[status(thm)],[c_2,c_65]) ).
tff(c_72,plain,
! [Z2_31] :
( ~ r(zero,Z2_31,succ(succ(zero)))
| ~ r(zero,zero,Z2_31) ),
inference(splitRight,[status(thm)],[c_63]) ).
tff(c_76,plain,
~ r(zero,zero,succ(zero)),
inference(resolution,[status(thm)],[c_17,c_72]) ).
tff(c_80,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SYN986+1.002 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % 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
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Apr 9 08:44:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.84/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.84/2.61
% 3.84/2.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------