%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP685-11 : TPTP v9.0.0. Released v8.1.0.
% 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 : n018.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 06:26:59 PM UTC 2025
% Result : Unsatisfiable 8.69s 3.11s
% Output : CNFRefutation 8.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 94 ( 94 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ rd > mult > ld > #nlpp > x8 > x7 > x6
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(ld,type,
ld: ( $i * $i ) > $i ).
tff(rd,type,
rd: ( $i * $i ) > $i ).
tff(x7,type,
x7: $i ).
tff(x8,type,
x8: $i ).
tff(x6,type,
x6: $i ).
tff(mult,type,
mult: ( $i * $i ) > $i ).
tff(f_25,axiom,
! [A] : ( ld(A,mult(A,A)) = A ),
file(unknown,unknown) ).
tff(f_33,axiom,
! [A,B,C,D] : ( ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D) ),
file(unknown,unknown) ).
tff(f_29,axiom,
! [A,B] : ( mult(A,ld(A,B)) = ld(A,mult(A,B)) ),
file(unknown,unknown) ).
tff(f_31,axiom,
! [A,B] : ( mult(rd(A,B),B) = rd(mult(A,B),B) ),
file(unknown,unknown) ).
tff(f_27,axiom,
! [A] : ( rd(mult(A,A),A) = A ),
file(unknown,unknown) ).
tff(f_37,axiom,
! [A,B] : ( ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B) ),
file(unknown,unknown) ).
tff(f_35,axiom,
! [A,B,C,D] : ( rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)) ),
file(unknown,unknown) ).
tff(f_39,axiom,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
file(unknown,unknown) ).
tff(c_2,plain,
! [A_1] : ( ld(A_1,mult(A_1,A_1)) = A_1 ),
inference(cnfTransformation,[status(thm)],[f_25]) ).
tff(c_202,plain,
! [A_33,B_34,C_35,D_36] : ( ld(ld(A_33,B_34),mult(ld(A_33,B_34),mult(C_35,D_36))) = mult(ld(A_33,mult(A_33,C_35)),D_36) ),
inference(cnfTransformation,[status(thm)],[f_33]) ).
tff(c_256,plain,
! [A_1,C_35,D_36] : ( ld(A_1,mult(ld(A_1,mult(A_1,A_1)),mult(C_35,D_36))) = mult(ld(A_1,mult(A_1,C_35)),D_36) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_202]) ).
tff(c_327,plain,
! [A_39,C_40,D_41] : ( mult(ld(A_39,mult(A_39,C_40)),D_41) = ld(A_39,mult(A_39,mult(C_40,D_41))) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_256]) ).
tff(c_406,plain,
! [A_1,D_41] : ( ld(A_1,mult(A_1,mult(A_1,D_41))) = mult(A_1,D_41) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_327]) ).
tff(c_6,plain,
! [A_3,B_4] : ( mult(A_3,ld(A_3,B_4)) = ld(A_3,mult(A_3,B_4)) ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_49,plain,
! [A_21,B_22] : ( rd(mult(A_21,B_22),B_22) = mult(rd(A_21,B_22),B_22) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_4,plain,
! [A_2] : ( rd(mult(A_2,A_2),A_2) = A_2 ),
inference(cnfTransformation,[status(thm)],[f_27]) ).
tff(c_56,plain,
! [B_22] : ( mult(rd(B_22,B_22),B_22) = B_22 ),
inference(superposition,[status(thm),theory(equality)],[c_49,c_4]) ).
tff(c_105,plain,
! [A_26,B_27] : ( rd(mult(rd(A_26,A_26),B_27),B_27) = ld(A_26,mult(A_26,ld(B_27,B_27))) ),
inference(cnfTransformation,[status(thm)],[f_37]) ).
tff(c_121,plain,
! [B_22] : ( ld(B_22,mult(B_22,ld(B_22,B_22))) = rd(B_22,B_22) ),
inference(superposition,[status(thm),theory(equality)],[c_56,c_105]) ).
tff(c_136,plain,
! [B_22] : ( rd(B_22,B_22) = ld(B_22,B_22) ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_121]) ).
tff(c_8,plain,
! [A_5,B_6] : ( rd(mult(A_5,B_6),B_6) = mult(rd(A_5,B_6),B_6) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_125,plain,
! [A_26,B_6] : ( mult(rd(rd(A_26,A_26),B_6),B_6) = ld(A_26,mult(A_26,ld(B_6,B_6))) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_105]) ).
tff(c_175,plain,
! [A_26,B_6] : ( mult(rd(ld(A_26,A_26),B_6),B_6) = ld(A_26,mult(A_26,ld(B_6,B_6))) ),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_125]) ).
tff(c_1651,plain,
! [A_80,B_81] : ( rd(ld(A_80,mult(A_80,B_81)),ld(A_80,B_81)) = mult(rd(A_80,ld(A_80,B_81)),ld(A_80,B_81)) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_49]) ).
tff(c_1826,plain,
! [A_84] : ( mult(rd(A_84,ld(A_84,A_84)),ld(A_84,A_84)) = rd(A_84,ld(A_84,A_84)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1651]) ).
tff(c_139,plain,
! [B_22] : ( mult(ld(B_22,B_22),B_22) = B_22 ),
inference(demodulation,[status(thm),theory(equality)],[c_136,c_56]) ).
tff(c_12,plain,
! [A_11,B_12,C_13,D_14] : ( rd(mult(mult(A_11,B_12),rd(C_13,D_14)),rd(C_13,D_14)) = mult(A_11,rd(mult(B_12,D_14),D_14)) ),
inference(cnfTransformation,[status(thm)],[f_35]) ).
tff(c_511,plain,
! [A_47,B_48,C_49,D_50] : ( rd(mult(mult(A_47,B_48),rd(C_49,D_50)),rd(C_49,D_50)) = mult(A_47,mult(rd(B_48,D_50),D_50)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_12]) ).
tff(c_571,plain,
! [A_47,B_48,A_2] : ( rd(mult(mult(A_47,B_48),A_2),rd(mult(A_2,A_2),A_2)) = mult(A_47,mult(rd(B_48,A_2),A_2)) ),
inference(superposition,[status(thm),theory(equality)],[c_4,c_511]) ).
tff(c_592,plain,
! [A_51,B_52,A_53] : ( mult(rd(mult(A_51,B_52),A_53),A_53) = mult(A_51,mult(rd(B_52,A_53),A_53)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_4,c_571]) ).
tff(c_641,plain,
! [A_5,B_6] : ( mult(mult(rd(A_5,B_6),B_6),B_6) = mult(A_5,mult(rd(B_6,B_6),B_6)) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_592]) ).
tff(c_659,plain,
! [A_5,B_6] : ( mult(mult(rd(A_5,B_6),B_6),B_6) = mult(A_5,B_6) ),
inference(demodulation,[status(thm),theory(equality)],[c_139,c_136,c_641]) ).
tff(c_1850,plain,
! [A_84] : ( mult(rd(A_84,ld(A_84,A_84)),ld(A_84,A_84)) = mult(A_84,ld(A_84,A_84)) ),
inference(superposition,[status(thm),theory(equality)],[c_1826,c_659]) ).
tff(c_1897,plain,
! [A_84] : ( mult(rd(A_84,ld(A_84,A_84)),ld(A_84,A_84)) = A_84 ),
inference(demodulation,[status(thm),theory(equality)],[c_2,c_6,c_1850]) ).
tff(c_1735,plain,
! [A_1] : ( mult(rd(A_1,ld(A_1,A_1)),ld(A_1,A_1)) = rd(A_1,ld(A_1,A_1)) ),
inference(superposition,[status(thm),theory(equality)],[c_2,c_1651]) ).
tff(c_1908,plain,
! [A_1] : ( rd(A_1,ld(A_1,A_1)) = A_1 ),
inference(demodulation,[status(thm),theory(equality)],[c_1897,c_1735]) ).
tff(c_2044,plain,
! [A_87] : ( mult(A_87,ld(A_87,A_87)) = A_87 ),
inference(demodulation,[status(thm),theory(equality)],[c_1908,c_1897]) ).
tff(c_18,plain,
! [A_11,B_12,C_13,D_14] : ( rd(mult(mult(A_11,B_12),rd(C_13,D_14)),rd(C_13,D_14)) = mult(A_11,mult(rd(B_12,D_14),D_14)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_12]) ).
tff(c_2076,plain,
! [A_87,C_13,D_14] : ( rd(mult(A_87,rd(C_13,D_14)),rd(C_13,D_14)) = mult(A_87,mult(rd(ld(A_87,A_87),D_14),D_14)) ),
inference(superposition,[status(thm),theory(equality)],[c_2044,c_18]) ).
tff(c_6599,plain,
! [A_155,C_156,D_157] : ( rd(mult(A_155,rd(C_156,D_157)),rd(C_156,D_157)) = mult(A_155,ld(D_157,D_157)) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_6,c_175,c_2076]) ).
tff(c_590,plain,
! [A_47,B_48,A_2] : ( mult(rd(mult(A_47,B_48),A_2),A_2) = mult(A_47,mult(rd(B_48,A_2),A_2)) ),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_4,c_571]) ).
tff(c_2073,plain,
! [A_87,A_2] : ( mult(A_87,mult(rd(ld(A_87,A_87),A_2),A_2)) = mult(rd(A_87,A_2),A_2) ),
inference(superposition,[status(thm),theory(equality)],[c_2044,c_590]) ).
tff(c_2118,plain,
! [A_87,A_2] : ( mult(rd(A_87,A_2),A_2) = mult(A_87,ld(A_2,A_2)) ),
inference(demodulation,[status(thm),theory(equality)],[c_406,c_6,c_175,c_2073]) ).
tff(c_2135,plain,
! [A_5,B_6] : ( rd(mult(A_5,B_6),B_6) = mult(A_5,ld(B_6,B_6)) ),
inference(demodulation,[status(thm),theory(equality)],[c_2118,c_8]) ).
tff(c_6632,plain,
! [A_155,C_156,D_157] : ( mult(A_155,ld(rd(C_156,D_157),rd(C_156,D_157))) = mult(A_155,ld(D_157,D_157)) ),
inference(superposition,[status(thm),theory(equality)],[c_6599,c_2135]) ).
tff(c_16,plain,
rd(mult(x6,rd(x7,x8)),rd(x7,x8)) != rd(mult(x6,x8),x8),
inference(cnfTransformation,[status(thm)],[f_39]) ).
tff(c_17,plain,
mult(rd(x6,rd(x7,x8)),rd(x7,x8)) != mult(rd(x6,x8),x8),
inference(demodulation,[status(thm),theory(equality)],[c_8,c_8,c_16]) ).
tff(c_2134,plain,
mult(x6,ld(rd(x7,x8),rd(x7,x8))) != mult(x6,ld(x8,x8)),
inference(demodulation,[status(thm),theory(equality)],[c_2118,c_2118,c_17]) ).
tff(c_10042,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_6632,c_2134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP685-11 : TPTP v9.0.0. Released v8.1.0.
% 0.11/0.13 % 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
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 22:26:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 8.69/3.11 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.72/3.12
% 8.72/3.12 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------