%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP696-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 12:35:09 PM UTC 2026
% Result : Unsatisfiable 9.45s 1.91s
% Output : CNFRefutation 9.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 94 ( 94 unt; 8 def)
% Number of atoms : 94 ( 93 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-2 aty)
% Number of variables : 114 ( 114 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : mult(A,ld(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : ld(A,mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : mult(A,i(mult(B,A))) = i(B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : mult(A,mult(B,C)) = mult(rd(mult(A,B),A),mult(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,C),ld(C,mult(B,C))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] : mult(X0,ld(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1] : ld(X0,mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
! [X0,X1] : mult(X0,i(mult(X1,X0))) = i(X1),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] : mult(X0,mult(X1,X2)) = mult(rd(mult(X0,X1),X0),mult(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,X2),ld(X2,mult(X1,X2))),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f23,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f24,plain,
mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f25,definition,
sF2_fnc = mult(a,b),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f26,definition,
sF1_fnc = mult(sF2_fnc,a),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f27,definition,
sF3_fnc = mult(a,c),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f28,definition,
sF0_fnc = mult(sF1_fnc,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f29,definition,
sF7_fnc = mult(b,a),
introduced(definition,[new_symbols(definition,[sF7_fnc])],[function_definition]) ).
fof(f30,definition,
sF6_fnc = mult(sF7_fnc,a),
introduced(definition,[new_symbols(definition,[sF6_fnc])],[function_definition]) ).
fof(f31,definition,
sF5_fnc = mult(sF6_fnc,c),
introduced(definition,[new_symbols(definition,[sF5_fnc])],[function_definition]) ).
fof(f32,definition,
sF4_fnc = mult(a,sF5_fnc),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f33,plain,
sF0_fnc != sF4_fnc,
inference(definition_folding,[],[f24,f32,f31,f30,f29,f28,f27,f26,f25]) ).
fof(f59,plain,
! [X0,X1] : ld(rd(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f15,f14]) ).
fof(f79,plain,
i(unit) = unit,
inference(paramodulation,[status(thm)],[f17,f22]) ).
fof(f91,plain,
! [X0] : mult(X0,i(unit)) = i(i(X0)),
inference(paramodulation,[status(thm)],[f22,f19]) ).
fof(f92,plain,
! [X0,X1] : mult(X0,i(X1)) = i(rd(X1,X0)),
inference(paramodulation,[status(thm)],[f15,f19]) ).
fof(f102,plain,
! [X0,X1] : mult(i(mult(X0,X1)),i(i(X0))) = i(X1),
inference(paramodulation,[status(thm)],[f19,f19]) ).
fof(f107,plain,
! [X0,X1] : rd(i(X0),i(mult(X0,X1))) = X1,
inference(paramodulation,[status(thm)],[f19,f16]) ).
fof(f108,plain,
! [X0,X1] : ld(X0,i(X1)) = i(mult(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f109,plain,
! [X0] : mult(X0,unit) = i(i(X0)),
inference(forward_demodulation,[status(thm)],[f79,f91]) ).
fof(f110,plain,
! [X0] : X0 = i(i(X0)),
inference(forward_demodulation,[status(thm)],[f17,f109]) ).
fof(f127,plain,
! [X0,X1,X2] : mult(X0,mult(i(mult(X1,X0)),X2)) = mult(rd(i(X1),X0),mult(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f131,plain,
! [X0,X1] : mult(i(X0),mult(X1,X0)) = mult(rd(mult(i(X0),X1),i(X0)),unit),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f141,plain,
! [X0] : mult(a,mult(X0,c)) = mult(rd(mult(a,X0),a),sF3_fnc),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f156,plain,
! [X0,X1] : mult(i(X0),mult(X1,X0)) = rd(mult(i(X0),X1),i(X0)),
inference(forward_demodulation,[status(thm)],[f17,f131]) ).
fof(f162,plain,
! [X0,X1] : mult(mult(i(X0),X1),X0) = mult(unit,ld(X0,mult(X1,X0))),
inference(paramodulation,[status(thm)],[f22,f21]) ).
fof(f175,plain,
! [X0,X1] : mult(mult(X0,X1),i(X0)) = mult(unit,ld(i(X0),mult(X1,i(X0)))),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f202,plain,
! [X0,X1] : mult(mult(i(X0),X1),X0) = ld(X0,mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f18,f162]) ).
fof(f204,plain,
! [X0,X1] : mult(mult(X0,X1),i(X0)) = ld(i(X0),mult(X1,i(X0))),
inference(forward_demodulation,[status(thm)],[f18,f175]) ).
fof(f298,plain,
! [X0,X1] : mult(X0,X1) = i(rd(i(X1),X0)),
inference(paramodulation,[status(thm)],[f110,f92]) ).
fof(f393,plain,
! [X0,X1] : rd(X0,i(mult(i(X0),X1))) = X1,
inference(paramodulation,[status(thm)],[f110,f107]) ).
fof(f477,plain,
! [X0,X1] : rd(i(X0),X1) = i(mult(X1,X0)),
inference(paramodulation,[status(thm)],[f298,f110]) ).
fof(f529,plain,
! [X0,X1] : rd(X0,i(X1)) = ld(i(X0),X1),
inference(paramodulation,[status(thm)],[f13,f393]) ).
fof(f570,plain,
! [X0,X1] : i(rd(i(X0),i(mult(X0,X1)))) = i(X1),
inference(forward_demodulation,[status(thm)],[f92,f102]) ).
fof(f571,plain,
! [X0,X1] : mult(i(mult(X0,X1)),X0) = i(X1),
inference(forward_demodulation,[status(thm)],[f298,f570]) ).
fof(f593,plain,
! [X0,X1] : mult(i(X0),X1) = i(ld(X1,X0)),
inference(paramodulation,[status(thm)],[f13,f571]) ).
fof(f2258,plain,
! [X0,X1,X2] : mult(X0,mult(i(mult(X1,X0)),X2)) = mult(i(mult(X0,X1)),mult(X0,X2)),
inference(forward_demodulation,[status(thm)],[f477,f127]) ).
fof(f2264,plain,
! [X0,X1] : mult(X0,unit) = mult(i(mult(X0,X1)),mult(X0,mult(X1,X0))),
inference(paramodulation,[status(thm)],[f22,f2258]) ).
fof(f2382,plain,
! [X0,X1] : X0 = mult(i(mult(X0,X1)),mult(X0,mult(X1,X0))),
inference(forward_demodulation,[status(thm)],[f17,f2264]) ).
fof(f3253,plain,
! [X0,X1] : i(ld(mult(X0,X1),X1)) = rd(mult(i(X1),X0),i(X1)),
inference(forward_demodulation,[status(thm)],[f593,f156]) ).
fof(f3254,plain,
! [X0,X1] : i(ld(mult(X0,X1),X1)) = rd(i(ld(X0,X1)),i(X1)),
inference(forward_demodulation,[status(thm)],[f593,f3253]) ).
fof(f3255,plain,
! [X0,X1] : i(ld(mult(X0,X1),X1)) = i(mult(i(X1),ld(X0,X1))),
inference(forward_demodulation,[status(thm)],[f477,f3254]) ).
fof(f3256,plain,
! [X0,X1] : i(ld(mult(X0,X1),X1)) = i(i(ld(ld(X0,X1),X1))),
inference(forward_demodulation,[status(thm)],[f593,f3255]) ).
fof(f3257,plain,
! [X0,X1] : i(ld(mult(X0,X1),X1)) = ld(ld(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f110,f3256]) ).
fof(f3288,plain,
i(ld(sF1_fnc,a)) = ld(ld(sF2_fnc,a),a),
inference(paramodulation,[status(thm)],[f26,f3257]) ).
fof(f6803,plain,
! [X0,X1] : mult(i(ld(X0,X1)),X1) = ld(X1,mult(X0,X1)),
inference(forward_demodulation,[status(thm)],[f593,f202]) ).
fof(f6804,plain,
! [X0,X1] : i(ld(X0,ld(X1,X0))) = ld(X0,mult(X1,X0)),
inference(forward_demodulation,[status(thm)],[f593,f6803]) ).
fof(f8881,plain,
! [X0,X1] : X0 = i(ld(mult(X0,mult(X1,X0)),mult(X0,X1))),
inference(forward_demodulation,[status(thm)],[f593,f2382]) ).
fof(f8942,plain,
a = i(ld(mult(a,sF7_fnc),mult(a,b))),
inference(paramodulation,[status(thm)],[f29,f8881]) ).
fof(f9056,plain,
a = i(ld(mult(a,sF7_fnc),sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f25,f8942]) ).
fof(f9098,plain,
ld(mult(a,sF7_fnc),sF2_fnc) = i(a),
inference(paramodulation,[status(thm)],[f9056,f110]) ).
fof(f9112,plain,
mult(mult(a,sF7_fnc),i(a)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f9098,f13]) ).
fof(f9119,plain,
i(rd(a,mult(a,sF7_fnc))) = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f92,f9112]) ).
fof(f9652,plain,
! [X0,X1] : i(rd(X0,mult(X0,X1))) = ld(i(X0),mult(X1,i(X0))),
inference(forward_demodulation,[status(thm)],[f92,f204]) ).
fof(f9653,plain,
! [X0,X1] : i(rd(X0,mult(X0,X1))) = rd(X0,i(mult(X1,i(X0)))),
inference(forward_demodulation,[status(thm)],[f529,f9652]) ).
fof(f9654,plain,
! [X0,X1] : i(rd(X0,mult(X0,X1))) = rd(X0,i(i(rd(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f92,f9653]) ).
fof(f9655,plain,
rd(a,rd(a,sF7_fnc)) = sF2_fnc,
inference(backward_demodulation,[status(thm)],[f9656,f9119]) ).
fof(f9656,plain,
! [X0,X1] : i(rd(X0,mult(X0,X1))) = rd(X0,rd(X0,X1)),
inference(forward_demodulation,[status(thm)],[f110,f9654]) ).
fof(f10232,plain,
ld(sF2_fnc,a) = rd(a,sF7_fnc),
inference(paramodulation,[status(thm)],[f9655,f59]) ).
fof(f10245,plain,
i(ld(sF1_fnc,a)) = ld(rd(a,sF7_fnc),a),
inference(backward_demodulation,[status(thm)],[f10232,f3288]) ).
fof(f10251,plain,
i(ld(sF1_fnc,a)) = sF7_fnc,
inference(forward_demodulation,[status(thm)],[f59,f10245]) ).
fof(f10264,plain,
ld(sF1_fnc,a) = i(sF7_fnc),
inference(paramodulation,[status(thm)],[f10251,f110]) ).
fof(f10268,plain,
i(ld(a,i(sF7_fnc))) = ld(a,mult(sF1_fnc,a)),
inference(paramodulation,[status(thm)],[f10264,f6804]) ).
fof(f10283,plain,
i(i(mult(sF7_fnc,a))) = ld(a,mult(sF1_fnc,a)),
inference(forward_demodulation,[status(thm)],[f108,f10268]) ).
fof(f10284,plain,
mult(sF7_fnc,a) = ld(a,mult(sF1_fnc,a)),
inference(forward_demodulation,[status(thm)],[f110,f10283]) ).
fof(f10285,plain,
sF6_fnc = ld(a,mult(sF1_fnc,a)),
inference(forward_demodulation,[status(thm)],[f30,f10284]) ).
fof(f10530,plain,
mult(a,sF6_fnc) = mult(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f10285,f13]) ).
fof(f10750,plain,
mult(a,mult(sF6_fnc,c)) = mult(rd(mult(sF1_fnc,a),a),sF3_fnc),
inference(paramodulation,[status(thm)],[f10530,f141]) ).
fof(f10789,plain,
mult(a,sF5_fnc) = mult(rd(mult(sF1_fnc,a),a),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f31,f10750]) ).
fof(f10790,plain,
sF4_fnc = mult(rd(mult(sF1_fnc,a),a),sF3_fnc),
inference(forward_demodulation,[status(thm)],[f32,f10789]) ).
fof(f10791,plain,
sF4_fnc = mult(sF1_fnc,sF3_fnc),
inference(forward_demodulation,[status(thm)],[f16,f10790]) ).
fof(f10792,plain,
sF4_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f28,f10791]) ).
fof(f10793,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10792,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP696-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:33:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 9.45/1.91 % Refutation found
% 9.45/1.91 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.45/1.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.45/2.00 % Elapsed time: 1.608889 seconds
% 9.45/2.00 % CPU time: 11.989933 seconds
% 9.45/2.00 % Total memory used: 201.177 MB
% 9.45/2.00 % Net memory used: 197.444 MB
%------------------------------------------------------------------------------