%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Sun Sep 27 07:31:11 AM UTC 2026
% Result : Unsatisfiable 0.17s 5.50s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 85 ( 85 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% 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 : 181 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c01,axiom,
! [VAR_0] : ld(VAR_0,mult(VAR_0,VAR_0)) = VAR_0,
file('theBenchmark.p',c01) ).
cnf(c_1,plain,
ld(A,mult(A,A)) = A,
inference(clausify,[status(thm)],[c01]) ).
fof(c02,axiom,
! [VAR_0] : rd(mult(VAR_0,VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',c02) ).
cnf(c_2,plain,
rd(mult(A,A),A) = A,
inference(clausify,[status(thm)],[c02]) ).
fof(c03,axiom,
! [VAR_0,VAR_1] : mult(VAR_0,ld(VAR_0,VAR_1)) = ld(VAR_0,mult(VAR_0,VAR_1)),
file('theBenchmark.p',c03) ).
cnf(c_3,plain,
mult(A,ld(A,B)) = ld(A,mult(A,B)),
inference(clausify,[status(thm)],[c03]) ).
cnf(c_4,plain,
ld(A,mult(A,B)) = mult(A,ld(A,B)),
inference(copy,[status(thm)],[c_3]) ).
fof(c04,axiom,
! [VAR_0,VAR_1] : mult(rd(VAR_0,VAR_1),VAR_1) = rd(mult(VAR_0,VAR_1),VAR_1),
file('theBenchmark.p',c04) ).
cnf(c_5,plain,
mult(rd(A,B),B) = rd(mult(A,B),B),
inference(clausify,[status(thm)],[c04]) ).
cnf(c_6,plain,
rd(mult(A,B),B) = mult(rd(A,B),B),
inference(copy,[status(thm)],[c_5]) ).
fof(c05,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : ld(ld(VAR_0,VAR_1),mult(ld(VAR_0,VAR_1),mult(VAR_2,VAR_3))) = mult(ld(VAR_0,mult(VAR_0,VAR_2)),VAR_3),
file('theBenchmark.p',c05) ).
cnf(c_7,plain,
ld(ld(A,B),mult(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(clausify,[status(thm)],[c05]) ).
cnf(c_258,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(ld(A,mult(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_7]) ).
cnf(c_8,plain,
mult(ld(A,B),ld(ld(A,B),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_258]) ).
fof(c06,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : rd(mult(mult(VAR_0,VAR_1),rd(VAR_2,VAR_3)),rd(VAR_2,VAR_3)) = mult(VAR_0,rd(mult(VAR_1,VAR_3),VAR_3)),
file('theBenchmark.p',c06) ).
cnf(c_9,plain,
rd(mult(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
inference(clausify,[status(thm)],[c06]) ).
cnf(c_259,plain,
mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,rd(mult(B,D),D)),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_10,plain,
mult(rd(mult(A,B),rd(C,D)),rd(C,D)) = mult(A,mult(rd(B,D),D)),
inference(paramod,[status(thm)],[c_6,c_259]) ).
fof(c07,axiom,
! [VAR_0,VAR_1] : ld(VAR_0,mult(VAR_0,ld(VAR_1,VAR_1))) = rd(mult(rd(VAR_0,VAR_0),VAR_1),VAR_1),
file('theBenchmark.p',c07) ).
cnf(c_11,plain,
ld(A,mult(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(clausify,[status(thm)],[c07]) ).
cnf(c_260,plain,
mult(A,ld(A,ld(B,B))) = rd(mult(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_4,c_11]) ).
cnf(c_261,plain,
mult(A,ld(A,ld(B,B))) = mult(rd(rd(A,A),B),B),
inference(paramod,[status(thm)],[c_6,c_260]) ).
cnf(c_12,plain,
mult(rd(rd(A,A),B),B) = mult(A,ld(A,ld(B,B))),
inference(copy,[status(thm)],[c_261]) ).
fof(goals,axiom,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('theBenchmark.p',goals) ).
cnf(c_13,plain,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
inference(clausify,[status(thm)],[goals]) ).
cnf(c_262,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_14,plain,
mult(rd(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
inference(paramod,[status(thm)],[c_6,c_262]) ).
cnf(c_15,plain,
mult(A,ld(A,A)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_16,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_2]) ).
cnf(c_263,plain,
mult(mult(A,ld(A,B)),ld(ld(A,mult(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_18,plain,
mult(mult(A,ld(A,B)),ld(mult(A,ld(A,B)),mult(C,D))) = mult(mult(A,ld(A,C)),D),
inference(paramod,[status(thm)],[c_4,c_263]) ).
cnf(c_264,plain,
mult(rd(mult(A,B),mult(rd(C,D),D)),rd(mult(C,D),D)) = mult(A,mult(rd(B,D),D)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_24,plain,
mult(rd(mult(A,B),mult(rd(C,D),D)),mult(rd(C,D),D)) = mult(A,mult(rd(B,D),D)),
inference(paramod,[status(thm)],[c_6,c_264]) ).
cnf(c_265,plain,
ld(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_15,c_4]) ).
cnf(c_33,plain,
mult(A,ld(A,ld(A,A))) = ld(A,A),
inference(copy,[status(thm)],[c_265]) ).
cnf(c_266,plain,
rd(A,ld(A,A)) = mult(rd(A,ld(A,A)),ld(A,A)),
inference(paramod,[status(thm)],[c_15,c_6]) ).
cnf(c_34,plain,
mult(rd(A,ld(A,A)),ld(A,A)) = rd(A,ld(A,A)),
inference(copy,[status(thm)],[c_266]) ).
cnf(c_36,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(rd(ld(A,A),C),C)),
inference(paramod,[status(thm)],[c_15,c_10]) ).
cnf(c_267,plain,
rd(A,A) = mult(rd(rd(A,A),A),A),
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_268,plain,
rd(A,A) = mult(A,ld(A,ld(A,A))),
inference(paramod,[status(thm)],[c_12,c_267]) ).
cnf(c_38,plain,
rd(A,A) = ld(A,A),
inference(paramod,[status(thm)],[c_33,c_268]) ).
cnf(c_269,plain,
rd(mult(A,A),A) = A,
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_270,plain,
mult(rd(A,A),A) = A,
inference(paramod,[status(thm)],[c_6,c_269]) ).
cnf(c_39,plain,
mult(ld(A,A),A) = A,
inference(paramod,[status(thm)],[c_38,c_270]) ).
cnf(c_271,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(rd(A,A),mult(rd(A,C),C)),
inference(paramod,[status(thm)],[c_16,c_10]) ).
cnf(c_41,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(ld(A,A),mult(rd(A,C),C)),
inference(paramod,[status(thm)],[c_38,c_271]) ).
cnf(c_50,plain,
mult(rd(ld(A,A),B),B) = mult(A,ld(A,ld(B,B))),
inference(paramod,[status(thm)],[c_38,c_12]) ).
cnf(c_272,plain,
mult(ld(A,A),mult(rd(A,C),C)) = mult(A,mult(rd(ld(A,A),C),C)),
inference(paramod,[status(thm)],[c_41,c_36]) ).
cnf(c_51,plain,
mult(ld(A,A),mult(rd(A,B),B)) = mult(A,mult(A,ld(A,ld(B,B)))),
inference(paramod,[status(thm)],[c_50,c_272]) ).
cnf(c_54,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,mult(A,ld(A,ld(C,C)))),
inference(paramod,[status(thm)],[c_51,c_41]) ).
cnf(c_273,plain,
mult(A,ld(mult(A,ld(A,A)),mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_64,plain,
mult(A,ld(A,mult(B,C))) = mult(mult(A,ld(A,B)),C),
inference(paramod,[status(thm)],[c_15,c_273]) ).
cnf(c_274,plain,
mult(A,mult(A,ld(A,B))) = mult(mult(A,ld(A,A)),B),
inference(paramod,[status(thm)],[c_4,c_64]) ).
cnf(c_92,plain,
mult(A,mult(A,ld(A,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_15,c_274]) ).
cnf(c_105,plain,
mult(rd(A,rd(B,C)),rd(B,C)) = mult(A,ld(C,C)),
inference(paramod,[status(thm)],[c_92,c_54]) ).
cnf(c_275,plain,
mult(rd(A,mult(rd(B,C),C)),mult(rd(B,C),C)) = mult(A,mult(rd(ld(A,A),C),C)),
inference(paramod,[status(thm)],[c_15,c_24]) ).
cnf(c_276,plain,
mult(rd(A,mult(rd(B,C),C)),mult(rd(B,C),C)) = mult(A,mult(A,ld(A,ld(C,C)))),
inference(paramod,[status(thm)],[c_50,c_275]) ).
cnf(c_137,plain,
mult(rd(A,mult(rd(B,C),C)),mult(rd(B,C),C)) = mult(A,ld(C,C)),
inference(paramod,[status(thm)],[c_92,c_276]) ).
cnf(c_277,plain,
mult(rd(mult(A,B),mult(ld(C,C),C)),mult(rd(C,C),C)) = mult(A,mult(rd(B,C),C)),
inference(paramod,[status(thm)],[c_38,c_24]) ).
cnf(c_278,plain,
mult(rd(mult(A,B),C),mult(rd(C,C),C)) = mult(A,mult(rd(B,C),C)),
inference(paramod,[status(thm)],[c_39,c_277]) ).
cnf(c_279,plain,
mult(rd(mult(A,B),C),mult(ld(C,C),C)) = mult(A,mult(rd(B,C),C)),
inference(paramod,[status(thm)],[c_38,c_278]) ).
cnf(c_138,plain,
mult(rd(mult(A,B),C),C) = mult(A,mult(rd(B,C),C)),
inference(paramod,[status(thm)],[c_39,c_279]) ).
cnf(c_280,plain,
mult(rd(mult(A,B),mult(rd(C,B),B)),mult(rd(C,B),B)) = mult(A,mult(ld(B,B),B)),
inference(paramod,[status(thm)],[c_38,c_24]) ).
cnf(c_281,plain,
mult(mult(A,B),ld(B,B)) = mult(A,mult(ld(B,B),B)),
inference(paramod,[status(thm)],[c_137,c_280]) ).
cnf(c_139,plain,
mult(mult(A,B),ld(B,B)) = mult(A,B),
inference(paramod,[status(thm)],[c_39,c_281]) ).
cnf(c_282,plain,
mult(rd(mult(A,B),mult(rd(C,ld(B,B)),ld(B,B))),mult(rd(C,ld(B,B)),ld(B,B))) = mult(A,rd(B,ld(B,B))),
inference(paramod,[status(thm)],[c_34,c_24]) ).
cnf(c_142,plain,
mult(mult(A,B),ld(ld(B,B),ld(B,B))) = mult(A,rd(B,ld(B,B))),
inference(paramod,[status(thm)],[c_137,c_282]) ).
cnf(c_283,plain,
rd(mult(A,B),ld(B,B)) = mult(rd(mult(A,B),ld(B,B)),ld(B,B)),
inference(paramod,[status(thm)],[c_139,c_6]) ).
cnf(c_284,plain,
rd(mult(A,B),ld(B,B)) = mult(A,mult(rd(B,ld(B,B)),ld(B,B))),
inference(paramod,[status(thm)],[c_138,c_283]) ).
cnf(c_162,plain,
rd(mult(A,B),ld(B,B)) = mult(A,rd(B,ld(B,B))),
inference(paramod,[status(thm)],[c_34,c_284]) ).
cnf(c_285,plain,
mult(mult(A,B),ld(ld(B,B),ld(B,B))) = mult(mult(A,B),ld(B,B)),
inference(paramod,[status(thm)],[c_139,c_139]) ).
cnf(c_168,plain,
mult(mult(A,B),ld(ld(B,B),ld(B,B))) = mult(A,B),
inference(paramod,[status(thm)],[c_139,c_285]) ).
cnf(c_286,plain,
mult(A,B) = mult(A,rd(B,ld(B,B))),
inference(paramod,[status(thm)],[c_168,c_142]) ).
cnf(c_169,plain,
mult(A,rd(B,ld(B,B))) = mult(A,B),
inference(copy,[status(thm)],[c_286]) ).
cnf(c_170,plain,
rd(mult(A,B),ld(B,B)) = mult(A,B),
inference(paramod,[status(thm)],[c_169,c_162]) ).
cnf(c_287,plain,
rd(A,ld(A,A)) = mult(ld(A,A),A),
inference(paramod,[status(thm)],[c_39,c_170]) ).
cnf(c_173,plain,
rd(A,ld(A,A)) = A,
inference(paramod,[status(thm)],[c_39,c_287]) ).
cnf(c_288,plain,
mult(rd(A,mult(B,C)),rd(mult(B,C),ld(C,C))) = mult(A,ld(ld(C,C),ld(C,C))),
inference(paramod,[status(thm)],[c_170,c_105]) ).
cnf(c_245,plain,
mult(rd(A,mult(B,C)),mult(B,C)) = mult(A,ld(ld(C,C),ld(C,C))),
inference(paramod,[status(thm)],[c_170,c_288]) ).
cnf(c_289,plain,
mult(rd(A,B),rd(B,ld(B,B))) = mult(A,ld(ld(B,B),ld(B,B))),
inference(paramod,[status(thm)],[c_173,c_105]) ).
cnf(c_246,plain,
mult(rd(A,B),B) = mult(A,ld(ld(B,B),ld(B,B))),
inference(paramod,[status(thm)],[c_173,c_289]) ).
cnf(c_290,plain,
mult(a,ld(ld(mult(b,c),mult(b,c)),ld(mult(b,c),mult(b,c)))) != mult(rd(a,c),c),
inference(paramod,[status(thm)],[c_246,c_14]) ).
cnf(c_255,plain,
mult(a,ld(ld(mult(b,c),mult(b,c)),ld(mult(b,c),mult(b,c)))) != mult(a,ld(ld(c,c),ld(c,c))),
inference(paramod,[status(thm)],[c_246,c_290]) ).
cnf(c_256,plain,
mult(A,ld(ld(mult(B,C),mult(B,C)),ld(mult(B,C),mult(B,C)))) = mult(A,ld(ld(C,C),ld(C,C))),
inference(paramod,[status(thm)],[c_246,c_245]) ).
cnf(c_257,plain,
$false,
inference(resolve,[status(thm)],[c_256,c_255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP684-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n005.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 15:36:52 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.39 % Process 3856356 was started by sandbox2 on n005,
% 0.11/5.39 % Fri Sep 25 15:36:52 2026
% 0.11/5.39 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.17/5.50
% 0.17/5.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/5.50
% 0.17/5.50 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.17/5.50 % Length of proof is 44.
% 0.17/5.50 % Level of proof is 14.
% 0.17/5.50 % Maximum clause weight is 72.000.
% 0.17/5.50 % Given clauses 31.
% 0.17/5.50
% 0.17/5.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------