%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP728-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:35:14 PM UTC 2026
% Result : Unsatisfiable 8.38s 1.72s
% Output : CNFRefutation 8.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 17
% Syntax : Number of formulae : 89 ( 89 unt; 2 def)
% Number of atoms : 89 ( 88 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 152 ( 152 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] : mult(unit,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A] : mult(A,unit) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : mult(A,i(A)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : mult(i(A),A) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] : i(mult(A,B)) = mult(i(A),i(B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : mult(i(A),mult(A,B)) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] : rd(mult(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B] : mult(rd(A,B),B) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] : mult(mult(A,B),C) = mult(mult(A,mult(B,C)),asoc(A,B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] : mult(A,B) = mult(mult(B,A),op_k(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B,C] : op_l(A,B,C) = mult(i(mult(C,B)),mult(C,mult(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B] : op_t(A,B) = mult(i(B),mult(A,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B,C,D,E] : asoc(asoc(A,B,C),D,E) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A,B,C,D,E] : asoc(A,B,asoc(C,D,E)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
op_k(op_k(a,b),c) != unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] : mult(unit,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
! [X0] : mult(X0,unit) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
! [X0] : mult(X0,i(X0)) = unit,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
! [X0] : mult(i(X0),X0) = unit,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
! [X0,X1] : i(mult(X0,X1)) = mult(i(X0),i(X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
! [X0,X1] : mult(i(X0),mult(X0,X1)) = X1,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
! [X0,X1] : rd(mult(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0,X1] : mult(rd(X0,X1),X1) = X0,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f33,plain,
! [X0,X1,X2] : mult(mult(X0,X1),X2) = mult(mult(X0,mult(X1,X2)),asoc(X0,X1,X2)),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
! [X0,X1] : mult(X0,X1) = mult(mult(X1,X0),op_k(X0,X1)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f35,plain,
! [X0,X1,X2] : op_l(X0,X1,X2) = mult(i(mult(X2,X1)),mult(X2,mult(X1,X0))),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f37,plain,
! [X0,X1] : op_t(X0,X1) = mult(i(X1),mult(X0,X1)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] : asoc(asoc(X0,X1,X2),X3,X4) = unit,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] : asoc(X0,X1,asoc(X2,X3,X4)) = unit,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f46,plain,
op_k(op_k(a,b),c) != unit,
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f47,definition,
sF1_fnc = op_k(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f48,definition,
sF0_fnc = op_k(sF1_fnc,c),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f49,plain,
sF0_fnc != unit,
inference(definition_folding,[],[f46,f48,f47]) ).
fof(f52,plain,
i(unit) = unit,
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f60,plain,
! [X0] : mult(X0,unit) = mult(X0,op_k(X0,unit)),
inference(paramodulation,[status(thm)],[f24,f34]) ).
fof(f63,plain,
mult(sF1_fnc,c) = mult(mult(c,sF1_fnc),sF0_fnc),
inference(paramodulation,[status(thm)],[f48,f34]) ).
fof(f64,plain,
mult(a,b) = mult(mult(b,a),sF1_fnc),
inference(paramodulation,[status(thm)],[f47,f34]) ).
fof(f67,plain,
! [X0] : X0 = mult(X0,op_k(X0,unit)),
inference(forward_demodulation,[status(thm)],[f25,f60]) ).
fof(f179,plain,
! [X0] : rd(unit,X0) = i(X0),
inference(paramodulation,[status(thm)],[f27,f30]) ).
fof(f183,plain,
! [X0] : rd(unit,i(X0)) = X0,
inference(paramodulation,[status(thm)],[f26,f30]) ).
fof(f204,plain,
! [X0] : i(i(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f179,f183]) ).
fof(f229,plain,
! [X0,X1] : mult(X0,mult(i(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f204,f29]) ).
fof(f239,plain,
! [X0] : mult(i(X0),X0) = op_k(X0,unit),
inference(paramodulation,[status(thm)],[f67,f29]) ).
fof(f250,plain,
! [X0] : unit = op_k(X0,unit),
inference(forward_demodulation,[status(thm)],[f27,f239]) ).
fof(f345,plain,
! [X0,X1] : i(mult(X0,i(X1))) = mult(i(X0),X1),
inference(paramodulation,[status(thm)],[f204,f28]) ).
fof(f348,plain,
! [X0,X1] : mult(X0,i(mult(X0,X1))) = i(X1),
inference(paramodulation,[status(thm)],[f28,f229]) ).
fof(f425,plain,
! [X0,X1,X2,X3] : mult(mult(X0,mult(X1,mult(X2,X3))),asoc(X1,X2,X3)) = mult(mult(X0,mult(mult(X1,X2),X3)),asoc(X0,mult(X1,mult(X2,X3)),asoc(X1,X2,X3))),
inference(paramodulation,[status(thm)],[f33,f33]) ).
fof(f432,plain,
! [X0,X1] : mult(mult(X0,i(X1)),X1) = mult(mult(X0,unit),asoc(X0,i(X1),X1)),
inference(paramodulation,[status(thm)],[f27,f33]) ).
fof(f444,plain,
! [X0,X1,X2] : mult(asoc(X0,X1,X2),mult(X0,mult(X1,X2))) = mult(mult(mult(X0,X1),X2),op_k(asoc(X0,X1,X2),mult(X0,mult(X1,X2)))),
inference(paramodulation,[status(thm)],[f33,f34]) ).
fof(f452,plain,
! [X0,X1] : mult(mult(X0,i(X1)),X1) = mult(X0,asoc(X0,i(X1),X1)),
inference(forward_demodulation,[status(thm)],[f25,f432]) ).
fof(f680,plain,
! [X0,X1,X2,X3,X4] : mult(mult(X0,X1),asoc(X2,X3,X4)) = mult(mult(X0,mult(X1,asoc(X2,X3,X4))),unit),
inference(paramodulation,[status(thm)],[f45,f33]) ).
fof(f681,plain,
! [X0,X1,X2,X3,X4] : mult(mult(X0,X1),asoc(X2,X3,X4)) = mult(X0,mult(X1,asoc(X2,X3,X4))),
inference(forward_demodulation,[status(thm)],[f25,f680]) ).
fof(f734,plain,
! [X0,X1] : op_l(X0,i(X0),X1) = mult(i(mult(X1,i(X0))),mult(X1,unit)),
inference(paramodulation,[status(thm)],[f27,f35]) ).
fof(f773,plain,
! [X0,X1] : op_l(X0,i(X0),X1) = mult(i(mult(X1,i(X0))),X1),
inference(forward_demodulation,[status(thm)],[f25,f734]) ).
fof(f855,plain,
! [X0,X1] : op_t(rd(X0,X1),X1) = mult(i(X1),X0),
inference(paramodulation,[status(thm)],[f31,f37]) ).
fof(f1795,plain,
mult(mult(b,a),i(mult(a,b))) = i(sF1_fnc),
inference(paramodulation,[status(thm)],[f64,f348]) ).
fof(f1796,plain,
mult(mult(c,sF1_fnc),i(mult(sF1_fnc,c))) = i(sF0_fnc),
inference(paramodulation,[status(thm)],[f63,f348]) ).
fof(f10648,plain,
! [X0,X1,X2,X3] : mult(mult(X0,mult(X1,mult(X2,X3))),asoc(X1,X2,X3)) = mult(mult(X0,mult(mult(X1,X2),X3)),unit),
inference(forward_demodulation,[status(thm)],[f45,f425]) ).
fof(f10649,plain,
! [X0,X1,X2,X3] : mult(mult(X0,mult(X1,mult(X2,X3))),asoc(X1,X2,X3)) = mult(X0,mult(mult(X1,X2),X3)),
inference(forward_demodulation,[status(thm)],[f25,f10648]) ).
fof(f10668,plain,
! [X0,X1,X2] : mult(op_l(X0,X1,X2),asoc(X2,X1,X0)) = mult(i(mult(X2,X1)),mult(mult(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f35,f10649]) ).
fof(f10832,plain,
! [X0,X1,X2] : mult(op_l(X0,X1,X2),asoc(X2,X1,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f29,f10668]) ).
fof(f12093,plain,
! [X0,X1,X2,X3,X4] : mult(op_l(X0,X1,asoc(X2,X3,X4)),unit) = X0,
inference(paramodulation,[status(thm)],[f44,f10832]) ).
fof(f12154,plain,
! [X0,X1,X2,X3,X4] : op_l(X0,X1,asoc(X2,X3,X4)) = X0,
inference(forward_demodulation,[status(thm)],[f25,f12093]) ).
fof(f14186,plain,
mult(asoc(b,a,i(mult(a,b))),mult(b,mult(a,i(mult(a,b))))) = mult(i(sF1_fnc),op_k(asoc(b,a,i(mult(a,b))),mult(b,mult(a,i(mult(a,b)))))),
inference(paramodulation,[status(thm)],[f1795,f444]) ).
fof(f14453,plain,
mult(asoc(b,a,i(mult(a,b))),mult(b,i(b))) = mult(i(sF1_fnc),op_k(asoc(b,a,i(mult(a,b))),mult(b,mult(a,i(mult(a,b)))))),
inference(forward_demodulation,[status(thm)],[f348,f14186]) ).
fof(f14454,plain,
mult(asoc(b,a,i(mult(a,b))),unit) = mult(i(sF1_fnc),op_k(asoc(b,a,i(mult(a,b))),mult(b,mult(a,i(mult(a,b)))))),
inference(forward_demodulation,[status(thm)],[f26,f14453]) ).
fof(f14455,plain,
asoc(b,a,i(mult(a,b))) = mult(i(sF1_fnc),op_k(asoc(b,a,i(mult(a,b))),mult(b,mult(a,i(mult(a,b)))))),
inference(forward_demodulation,[status(thm)],[f25,f14454]) ).
fof(f14456,plain,
asoc(b,a,i(mult(a,b))) = mult(i(sF1_fnc),op_k(asoc(b,a,i(mult(a,b))),mult(b,i(b)))),
inference(forward_demodulation,[status(thm)],[f348,f14455]) ).
fof(f14457,plain,
asoc(b,a,i(mult(a,b))) = mult(i(sF1_fnc),op_k(asoc(b,a,i(mult(a,b))),unit)),
inference(forward_demodulation,[status(thm)],[f26,f14456]) ).
fof(f14458,plain,
asoc(b,a,i(mult(a,b))) = mult(i(sF1_fnc),unit),
inference(forward_demodulation,[status(thm)],[f250,f14457]) ).
fof(f14459,plain,
asoc(b,a,i(mult(a,b))) = i(sF1_fnc),
inference(forward_demodulation,[status(thm)],[f25,f14458]) ).
fof(f17172,plain,
! [X0,X1] : asoc(X0,X1,i(sF1_fnc)) = unit,
inference(paramodulation,[status(thm)],[f14459,f45]) ).
fof(f17226,plain,
! [X0] : mult(mult(X0,i(i(sF1_fnc))),i(sF1_fnc)) = mult(X0,unit),
inference(paramodulation,[status(thm)],[f17172,f452]) ).
fof(f17242,plain,
! [X0] : mult(mult(X0,sF1_fnc),i(sF1_fnc)) = mult(X0,unit),
inference(forward_demodulation,[status(thm)],[f204,f17226]) ).
fof(f17243,plain,
! [X0] : mult(mult(X0,sF1_fnc),i(sF1_fnc)) = X0,
inference(forward_demodulation,[status(thm)],[f25,f17242]) ).
fof(f17629,plain,
! [X0] : rd(X0,i(sF1_fnc)) = mult(X0,sF1_fnc),
inference(paramodulation,[status(thm)],[f17243,f30]) ).
fof(f25210,plain,
! [X0,X1] : op_l(X0,i(X0),X1) = mult(mult(i(X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f345,f773]) ).
fof(f25212,plain,
! [X0,X1,X2,X3] : X0 = mult(mult(i(asoc(X1,X2,X3)),X0),asoc(X1,X2,X3)),
inference(paramodulation,[status(thm)],[f12154,f25210]) ).
fof(f25346,plain,
! [X0,X1,X2,X3] : X0 = mult(i(asoc(X1,X2,X3)),mult(X0,asoc(X1,X2,X3))),
inference(forward_demodulation,[status(thm)],[f681,f25212]) ).
fof(f25347,plain,
! [X0,X1,X2,X3] : X0 = op_t(X0,asoc(X1,X2,X3)),
inference(forward_demodulation,[status(thm)],[f37,f25346]) ).
fof(f25442,plain,
! [X0] : X0 = op_t(X0,i(sF1_fnc)),
inference(paramodulation,[status(thm)],[f14459,f25347]) ).
fof(f25491,plain,
! [X0] : rd(X0,i(sF1_fnc)) = mult(i(i(sF1_fnc)),X0),
inference(paramodulation,[status(thm)],[f855,f25442]) ).
fof(f25535,plain,
! [X0] : mult(X0,sF1_fnc) = mult(i(i(sF1_fnc)),X0),
inference(forward_demodulation,[status(thm)],[f17629,f25491]) ).
fof(f25536,plain,
! [X0] : mult(X0,sF1_fnc) = mult(sF1_fnc,X0),
inference(forward_demodulation,[status(thm)],[f204,f25535]) ).
fof(f25783,plain,
mult(mult(c,sF1_fnc),i(mult(c,sF1_fnc))) = i(sF0_fnc),
inference(paramodulation,[status(thm)],[f25536,f1796]) ).
fof(f25876,plain,
unit = i(sF0_fnc),
inference(forward_demodulation,[status(thm)],[f26,f25783]) ).
fof(f25972,plain,
i(unit) = sF0_fnc,
inference(paramodulation,[status(thm)],[f25876,f204]) ).
fof(f26063,plain,
unit = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f52,f25972]) ).
fof(f26064,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f26063,f49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP728-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.39 % Computer : n012.cluster.edu
% 0.09/0.39 % Model : x86_64 x86_64
% 0.09/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.39 % Memory : 8046.5625MB
% 0.09/0.39 % OS : Linux 6.8.0-71-generic
% 0.09/0.39 % CPULimit : 300
% 0.09/0.39 % WCLimit : 300
% 0.09/0.39 % DateTime : Sun Sep 20 20:35:52 UTC 2026
% 0.09/0.39 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 8.38/1.72 % Refutation found
% 8.38/1.72 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.38/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.62/1.81 % Elapsed time: 1.407292 seconds
% 0.62/1.81 % CPU time: 9.548420 seconds
% 0.62/1.81 % Total memory used: 280.072 MB
% 0.62/1.81 % Net memory used: 276.071 MB
%------------------------------------------------------------------------------