%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n017.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 11:11:53 AM UTC 2026
% Result : Unsatisfiable 9.01s 3.66s
% Output : CNFRefutation 9.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of formulae : 59 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 155 ( 81 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 137 ( 137 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ is_a_theorem > equivalent > #nlpp > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(a,type,
a: $i ).
tff(is_a_theorem,type,
is_a_theorem: $i > $o ).
tff(equivalent,type,
equivalent: ( $i * $i ) > $i ).
tff(f_35,axiom,
! [A,B,C] : is_a_theorem(equivalent(A,equivalent(equivalent(equivalent(A,B),equivalent(C,B)),C))),
file(unknown,unknown) ).
tff(f_32,axiom,
! [A,B] :
( ~ is_a_theorem(equivalent(A,B))
| ~ is_a_theorem(A)
| is_a_theorem(B) ),
file(unknown,unknown) ).
tff(f_38,axiom,
~ is_a_theorem(equivalent(a,a)),
file(unknown,unknown) ).
tff(c_8,plain,
! [A_8,B_9,C_10] : is_a_theorem(equivalent(A_8,equivalent(equivalent(equivalent(A_8,B_9),equivalent(C_10,B_9)),C_10))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_2,plain,
! [B_2,A_1] :
( is_a_theorem(B_2)
| ~ is_a_theorem(A_1)
| ~ is_a_theorem(equivalent(A_1,B_2)) ),
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_12,plain,
! [A_8,B_9,C_10] :
( is_a_theorem(equivalent(equivalent(equivalent(A_8,B_9),equivalent(C_10,B_9)),C_10))
| ~ is_a_theorem(A_8) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_4,plain,
! [A_3,B_4,C_5] : is_a_theorem(equivalent(A_3,equivalent(equivalent(equivalent(A_3,B_4),equivalent(C_5,B_4)),C_5))),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_13,plain,
! [A_11,B_12,C_13] :
( is_a_theorem(equivalent(equivalent(equivalent(A_11,B_12),equivalent(C_13,B_12)),C_13))
| ~ is_a_theorem(A_11) ),
inference(resolution,[status(thm)],[c_8,c_2]) ).
tff(c_18,plain,
! [C_14,A_15,B_16] :
( is_a_theorem(C_14)
| ~ is_a_theorem(equivalent(equivalent(A_15,B_16),equivalent(C_14,B_16)))
| ~ is_a_theorem(A_15) ),
inference(resolution,[status(thm)],[c_13,c_2]) ).
tff(c_23,plain,
! [A_15,C_5,B_4] :
( is_a_theorem(equivalent(equivalent(equivalent(A_15,C_5),B_4),equivalent(C_5,B_4)))
| ~ is_a_theorem(A_15) ),
inference(resolution,[status(thm)],[c_4,c_18]) ).
tff(c_24,plain,
! [A_17,C_18,B_19] :
( is_a_theorem(equivalent(equivalent(equivalent(A_17,C_18),B_19),equivalent(C_18,B_19)))
| ~ is_a_theorem(A_17) ),
inference(resolution,[status(thm)],[c_4,c_18]) ).
tff(c_46,plain,
! [C_22,B_23,A_24] :
( is_a_theorem(equivalent(C_22,B_23))
| ~ is_a_theorem(equivalent(equivalent(A_24,C_22),B_23))
| ~ is_a_theorem(A_24) ),
inference(resolution,[status(thm)],[c_24,c_2]) ).
tff(c_60,plain,
! [C_25,A_26,B_27,C_28] :
( is_a_theorem(equivalent(C_25,equivalent(equivalent(equivalent(equivalent(A_26,C_25),B_27),equivalent(C_28,B_27)),C_28)))
| ~ is_a_theorem(A_26) ),
inference(resolution,[status(thm)],[c_4,c_46]) ).
tff(c_17,plain,
! [C_13,A_11,B_12] :
( is_a_theorem(C_13)
| ~ is_a_theorem(equivalent(equivalent(A_11,B_12),equivalent(C_13,B_12)))
| ~ is_a_theorem(A_11) ),
inference(resolution,[status(thm)],[c_13,c_2]) ).
tff(c_137,plain,
! [A_43,A_44,C_45,B_46] :
( is_a_theorem(equivalent(equivalent(equivalent(A_43,equivalent(A_44,C_45)),B_46),equivalent(C_45,B_46)))
| ~ is_a_theorem(A_44)
| ~ is_a_theorem(A_43) ),
inference(resolution,[status(thm)],[c_60,c_17]) ).
tff(c_171,plain,
! [C_51,A_52,A_53] :
( is_a_theorem(C_51)
| ~ is_a_theorem(equivalent(A_52,equivalent(A_53,C_51)))
| ~ is_a_theorem(A_53)
| ~ is_a_theorem(A_52) ),
inference(resolution,[status(thm)],[c_137,c_17]) ).
tff(c_207,plain,
! [B_54,C_55,A_56] :
( is_a_theorem(B_54)
| ~ is_a_theorem(C_55)
| ~ is_a_theorem(equivalent(equivalent(A_56,C_55),B_54))
| ~ is_a_theorem(A_56) ),
inference(resolution,[status(thm)],[c_23,c_171]) ).
tff(c_243,plain,
! [C_57,B_58,A_59] :
( is_a_theorem(equivalent(C_57,B_58))
| ~ is_a_theorem(B_58)
| ~ is_a_theorem(equivalent(A_59,C_57))
| ~ is_a_theorem(A_59) ),
inference(resolution,[status(thm)],[c_23,c_207]) ).
tff(c_267,plain,
! [A_3,B_4,C_5,B_58] :
( is_a_theorem(equivalent(equivalent(equivalent(equivalent(A_3,B_4),equivalent(C_5,B_4)),C_5),B_58))
| ~ is_a_theorem(B_58)
| ~ is_a_theorem(A_3) ),
inference(resolution,[status(thm)],[c_4,c_243]) ).
tff(c_75,plain,
! [B_29,C_30,A_31] :
( is_a_theorem(equivalent(B_29,equivalent(C_30,B_29)))
| ~ is_a_theorem(equivalent(A_31,C_30))
| ~ is_a_theorem(A_31) ),
inference(resolution,[status(thm)],[c_23,c_46]) ).
tff(c_328,plain,
! [B_67,C_68,A_69,B_70] :
( is_a_theorem(equivalent(B_67,equivalent(C_68,B_67)))
| ~ is_a_theorem(equivalent(equivalent(A_69,B_70),equivalent(C_68,B_70)))
| ~ is_a_theorem(A_69) ),
inference(resolution,[status(thm)],[c_12,c_75]) ).
tff(c_350,plain,
! [B_67,A_69,C_5,B_4] :
( is_a_theorem(equivalent(B_67,equivalent(equivalent(equivalent(equivalent(A_69,C_5),B_4),equivalent(C_5,B_4)),B_67)))
| ~ is_a_theorem(A_69) ),
inference(resolution,[status(thm)],[c_4,c_328]) ).
tff(c_300,plain,
! [C_64,B_65,A_66] :
( is_a_theorem(C_64)
| ~ is_a_theorem(equivalent(C_64,B_65))
| ~ is_a_theorem(equivalent(A_66,B_65))
| ~ is_a_theorem(A_66) ),
inference(resolution,[status(thm)],[c_12,c_207]) ).
tff(c_984,plain,
! [A_133,A_134,B_135,C_136] :
( is_a_theorem(A_133)
| ~ is_a_theorem(equivalent(A_134,equivalent(equivalent(equivalent(A_133,B_135),equivalent(C_136,B_135)),C_136)))
| ~ is_a_theorem(A_134) ),
inference(resolution,[status(thm)],[c_4,c_300]) ).
tff(c_1038,plain,
! [A_137,B_138] :
( is_a_theorem(equivalent(A_137,B_138))
| ~ is_a_theorem(B_138)
| ~ is_a_theorem(A_137) ),
inference(resolution,[status(thm)],[c_350,c_984]) ).
tff(c_57,plain,
! [B_4,C_5,A_15] :
( is_a_theorem(equivalent(B_4,equivalent(C_5,B_4)))
| ~ is_a_theorem(equivalent(A_15,C_5))
| ~ is_a_theorem(A_15) ),
inference(resolution,[status(thm)],[c_23,c_46]) ).
tff(c_1125,plain,
! [B_4,B_138,A_137] :
( is_a_theorem(equivalent(B_4,equivalent(B_138,B_4)))
| ~ is_a_theorem(B_138)
| ~ is_a_theorem(A_137) ),
inference(resolution,[status(thm)],[c_1038,c_57]) ).
tff(c_1452,plain,
! [A_137] : ~ is_a_theorem(A_137),
inference(splitLeft,[status(thm)],[c_1125]) ).
tff(c_1494,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1452,c_4]) ).
tff(c_1496,plain,
! [B_153,B_154] :
( is_a_theorem(equivalent(B_153,equivalent(B_154,B_153)))
| ~ is_a_theorem(B_154) ),
inference(splitRight,[status(thm)],[c_1125]) ).
tff(c_327,plain,
! [A_3,A_66,B_4,C_5] :
( is_a_theorem(A_3)
| ~ is_a_theorem(equivalent(A_66,equivalent(equivalent(equivalent(A_3,B_4),equivalent(C_5,B_4)),C_5)))
| ~ is_a_theorem(A_66) ),
inference(resolution,[status(thm)],[c_4,c_300]) ).
tff(c_2090,plain,
! [A_177,B_178,B_179] :
( is_a_theorem(A_177)
| ~ is_a_theorem(B_178)
| ~ is_a_theorem(equivalent(equivalent(A_177,B_179),equivalent(B_178,B_179))) ),
inference(resolution,[status(thm)],[c_1496,c_327]) ).
tff(c_2494,plain,
! [A_193,C_194,B_195] :
( is_a_theorem(A_193)
| ~ is_a_theorem(equivalent(equivalent(equivalent(A_193,C_194),B_195),equivalent(C_194,B_195))) ),
inference(resolution,[status(thm)],[c_4,c_2090]) ).
tff(c_4377,plain,
! [A_255,B_256,C_257] :
( is_a_theorem(equivalent(A_255,B_256))
| ~ is_a_theorem(equivalent(equivalent(C_257,B_256),C_257))
| ~ is_a_theorem(A_255) ),
inference(resolution,[status(thm)],[c_267,c_2494]) ).
tff(c_5150,plain,
! [A_285,A_286,B_287] :
( is_a_theorem(equivalent(A_285,equivalent(equivalent(A_286,B_287),B_287)))
| ~ is_a_theorem(A_285)
| ~ is_a_theorem(A_286) ),
inference(resolution,[status(thm)],[c_12,c_4377]) ).
tff(c_31,plain,
! [C_18,A_17] :
( is_a_theorem(C_18)
| ~ is_a_theorem(equivalent(A_17,C_18))
| ~ is_a_theorem(A_17) ),
inference(resolution,[status(thm)],[c_24,c_17]) ).
tff(c_5338,plain,
! [A_286,B_287,A_285] :
( is_a_theorem(equivalent(equivalent(A_286,B_287),B_287))
| ~ is_a_theorem(A_285)
| ~ is_a_theorem(A_286) ),
inference(resolution,[status(thm)],[c_5150,c_31]) ).
tff(c_5340,plain,
! [A_285] : ~ is_a_theorem(A_285),
inference(splitLeft,[status(thm)],[c_5338]) ).
tff(c_58,plain,
! [C_10,B_9,A_8] :
( is_a_theorem(equivalent(equivalent(C_10,B_9),C_10))
| ~ is_a_theorem(equivalent(A_8,B_9))
| ~ is_a_theorem(A_8) ),
inference(resolution,[status(thm)],[c_12,c_46]) ).
tff(c_1124,plain,
! [C_10,B_138,A_137] :
( is_a_theorem(equivalent(equivalent(C_10,B_138),C_10))
| ~ is_a_theorem(B_138)
| ~ is_a_theorem(A_137) ),
inference(resolution,[status(thm)],[c_1038,c_58]) ).
tff(c_1130,plain,
! [A_137] : ~ is_a_theorem(A_137),
inference(splitLeft,[status(thm)],[c_1124]) ).
tff(c_1167,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_1130,c_4]) ).
tff(c_1253,plain,
! [C_144,B_145] :
( is_a_theorem(equivalent(equivalent(C_144,B_145),C_144))
| ~ is_a_theorem(B_145) ),
inference(splitRight,[status(thm)],[c_1124]) ).
tff(c_1337,plain,
! [C_146,B_147] :
( is_a_theorem(C_146)
| ~ is_a_theorem(equivalent(C_146,B_147))
| ~ is_a_theorem(B_147) ),
inference(resolution,[status(thm)],[c_1253,c_31]) ).
tff(c_3185,plain,
! [A_219,C_220,B_221] :
( is_a_theorem(equivalent(equivalent(A_219,C_220),B_221))
| ~ is_a_theorem(equivalent(C_220,B_221))
| ~ is_a_theorem(A_219) ),
inference(resolution,[status(thm)],[c_23,c_1337]) ).
tff(c_3329,plain,
! [C_13,C_220,A_219] :
( is_a_theorem(C_13)
| ~ is_a_theorem(equivalent(C_220,equivalent(C_13,C_220)))
| ~ is_a_theorem(A_219) ),
inference(resolution,[status(thm)],[c_3185,c_17]) ).
tff(c_3330,plain,
! [A_219] : ~ is_a_theorem(A_219),
inference(splitLeft,[status(thm)],[c_3329]) ).
tff(c_3393,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3330,c_4]) ).
tff(c_3395,plain,
! [C_222,C_223] :
( is_a_theorem(C_222)
| ~ is_a_theorem(equivalent(C_223,equivalent(C_222,C_223))) ),
inference(splitRight,[status(thm)],[c_3329]) ).
tff(c_3455,plain,
! [C_5,B_4] : is_a_theorem(equivalent(equivalent(C_5,B_4),equivalent(C_5,B_4))),
inference(resolution,[status(thm)],[c_4,c_3395]) ).
tff(c_5421,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5340,c_3455]) ).
tff(c_5423,plain,
! [A_288,B_289] :
( is_a_theorem(equivalent(equivalent(A_288,B_289),B_289))
| ~ is_a_theorem(A_288) ),
inference(splitRight,[status(thm)],[c_5338]) ).
tff(c_32,plain,
! [C_18,B_19,A_17] :
( is_a_theorem(equivalent(C_18,B_19))
| ~ is_a_theorem(equivalent(equivalent(A_17,C_18),B_19))
| ~ is_a_theorem(A_17) ),
inference(resolution,[status(thm)],[c_24,c_2]) ).
tff(c_5570,plain,
! [B_289,A_288] :
( is_a_theorem(equivalent(B_289,B_289))
| ~ is_a_theorem(A_288) ),
inference(resolution,[status(thm)],[c_5423,c_32]) ).
tff(c_5711,plain,
! [A_288] : ~ is_a_theorem(A_288),
inference(splitLeft,[status(thm)],[c_5570]) ).
tff(c_5794,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_5711,c_3455]) ).
tff(c_5795,plain,
! [B_289] : is_a_theorem(equivalent(B_289,B_289)),
inference(splitRight,[status(thm)],[c_5570]) ).
tff(c_6,plain,
~ is_a_theorem(equivalent(a,a)),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_5799,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_5795,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL416-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % 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
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 5 12:06:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 9.01/3.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.01/3.67
% 9.01/3.67 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------