%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 12:06:35 PM UTC 2026
% Result : Unsatisfiable 52.88s 7.35s
% Output : CNFRefutation 52.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 43 unt; 5 def)
% Number of atoms : 100 ( 63 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 59 ( 26 ~; 28 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 155 ( 155 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z,U,V,W,V6] : multiply(multiply(X,inverse(X),Y),inverse(multiply(multiply(Z,U,V),W,multiply(Z,U,V6))),multiply(U,multiply(V6,W,V),Z)) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
( multiply(inverse(b),b,a) != a
| multiply(a,a,b) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,X4),X5,multiply(X2,X3,X6))),multiply(X3,multiply(X6,X5,X4),X2)) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
( multiply(inverse(b),b,a) != a
| multiply(a,a,b) != a
| multiply(a,b,inverse(b)) != a
| multiply(b,a,a) != a
| multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f5,definition,
( sQ0_spl
<=> multiply(multiply(d,e,a),b,multiply(d,e,c)) = multiply(d,e,multiply(a,b,c)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f7,plain,
( sQ0_spl
| multiply(multiply(d,e,a),b,multiply(d,e,c)) != multiply(d,e,multiply(a,b,c)) ),
inference(component_clause,[status(thm)],[f5]) ).
fof(f8,definition,
( sQ1_spl
<=> multiply(b,a,a) = a ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f10,plain,
( sQ1_spl
| multiply(b,a,a) != a ),
inference(component_clause,[status(thm)],[f8]) ).
fof(f11,definition,
( sQ2_spl
<=> multiply(a,b,inverse(b)) = a ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f13,plain,
( sQ2_spl
| multiply(a,b,inverse(b)) != a ),
inference(component_clause,[status(thm)],[f11]) ).
fof(f14,definition,
( sQ3_spl
<=> multiply(a,a,b) = a ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f16,plain,
( sQ3_spl
| multiply(a,a,b) != a ),
inference(component_clause,[status(thm)],[f14]) ).
fof(f17,definition,
( sQ4_spl
<=> multiply(inverse(b),b,a) = a ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f19,plain,
( sQ4_spl
| multiply(inverse(b),b,a) != a ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f4,f5,f8,f11,f14,f17]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] : multiply(multiply(X0,X1,X2),inverse(multiply(multiply(X3,X4,X5),X6,multiply(X3,X4,X7))),multiply(X4,multiply(X7,X6,X5),X3)) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X8)),X8),X0),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f24,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,X3,multiply(X4,multiply(X5,X6,X7),X8)),inverse(multiply(multiply(X8,X4,X7),X6,multiply(X8,X4,X5))),multiply(X2,X3,multiply(X9,inverse(X9),X10)))),multiply(X3,X10,X2)) = X1,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f25,plain,
! [X0,X1,X2] : X0 = multiply(inverse(X1),multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),X1),
inference(paramodulation,[status(thm)],[f3,f21]) ).
fof(f48,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] : multiply(multiply(X0,multiply(multiply(X1,X2,X3),inverse(multiply(multiply(X1,X2,X4),X0,X5)),X5),multiply(X1,X2,X4)),inverse(multiply(multiply(X6,X7,X8),X9,multiply(X6,X7,X10))),multiply(X7,multiply(X10,X9,X8),X6)) = multiply(X2,multiply(X3,X0,X4),X1),
inference(paramodulation,[status(thm)],[f21,f3]) ).
fof(f62,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(multiply(X2,inverse(X2),X3),inverse(multiply(X2,inverse(X2),X3)),multiply(X2,inverse(X2),X4))),X4) = X1,
inference(paramodulation,[status(thm)],[f25,f3]) ).
fof(f1251,plain,
! [X0,X1,X2,X3,X4,X5,X6] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(inverse(X2),multiply(multiply(X3,inverse(X3),multiply(X4,inverse(X4),X5)),inverse(multiply(X2,inverse(X2),X6)),X6),X2)),multiply(inverse(X3),X5,X3)) = X1,
inference(paramodulation,[status(thm)],[f62,f24]) ).
fof(f1423,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f25,f1251]) ).
fof(f1452,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),multiply(X3,inverse(X3),X4))),multiply(inverse(X2),X4,X2)) = multiply(inverse(X5),X1,X5),
inference(paramodulation,[status(thm)],[f1423,f1423]) ).
fof(f1553,plain,
! [X0,X1] : X0 = multiply(inverse(X1),X0,X1),
inference(forward_demodulation,[status(thm)],[f1423,f1452]) ).
fof(f1602,plain,
! [X0,X1,X2] : X0 = multiply(X0,inverse(multiply(X1,inverse(X1),X2)),X2),
inference(backward_demodulation,[status(thm)],[f1553,f25]) ).
fof(f2201,plain,
! [X0,X1] : inverse(X0) = inverse(multiply(X1,inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f1553,f1602]) ).
fof(f2361,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,inverse(X0),X1),inverse(multiply(X2,inverse(X2),X3)),X3) = X1,
inference(backward_demodulation,[status(thm)],[f2201,f62]) ).
fof(f2365,plain,
! [X0,X1] : X0 = multiply(X0,inverse(X1),X1),
inference(backward_demodulation,[status(thm)],[f2201,f1602]) ).
fof(f2402,plain,
! [X0,X1,X2] : multiply(multiply(X0,inverse(X0),X1),inverse(X2),X2) = X1,
inference(forward_demodulation,[status(thm)],[f2201,f2361]) ).
fof(f4074,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,inverse(multiply(multiply(X1,X2,X3),X4,multiply(X1,X2,X5))),multiply(X2,multiply(X5,X4,X3),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f4075,f3]) ).
fof(f4075,plain,
! [X0,X1] : multiply(X0,inverse(X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f2365,f2402]) ).
fof(f4077,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f1553,f4075]) ).
fof(f4244,plain,
! [X0,X1] : multiply(inverse(X0),X0,X1) = X1,
inference(paramodulation,[status(thm)],[f4077,f4075]) ).
fof(f4245,plain,
! [X0,X1] : X0 = multiply(X0,X1,inverse(X1)),
inference(paramodulation,[status(thm)],[f4077,f2365]) ).
fof(f4246,plain,
! [X0,X1] : X0 = multiply(X1,X0,inverse(X1)),
inference(paramodulation,[status(thm)],[f4077,f1553]) ).
fof(f4249,plain,
! [X0,X1,X2,X3] : multiply(X0,X1,X2) = multiply(X1,multiply(X2,inverse(multiply(X0,X1,X3)),X3),X0),
inference(backward_demodulation,[status(thm)],[f4074,f21]) ).
fof(f4262,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,X2,multiply(X3,inverse(X3),X4))),multiply(inverse(X3),multiply(X4,X2,X1),X3)) = X0,
inference(paramodulation,[status(thm)],[f4075,f4074]) ).
fof(f4301,plain,
! [X0,X1,X2,X3,X4] : multiply(X0,inverse(multiply(X1,X2,X3)),multiply(inverse(X4),multiply(X3,X2,X1),X4)) = X0,
inference(forward_demodulation,[status(thm)],[f4075,f4262]) ).
fof(f4302,plain,
! [X0,X1,X2,X3] : multiply(X0,inverse(multiply(X1,X2,X3)),multiply(X3,X2,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f1553,f4301]) ).
fof(f4316,plain,
( sQ4_spl
| a != a ),
inference(backward_demodulation,[status(thm)],[f4244,f19]) ).
fof(f4342,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4316]) ).
fof(f4343,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f4342]) ).
fof(f4636,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = inverse(inverse(multiply(X2,X1,X0))),
inference(paramodulation,[status(thm)],[f4244,f4302]) ).
fof(f4693,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X2,X1,X0),
inference(forward_demodulation,[status(thm)],[f4077,f4636]) ).
fof(f5742,plain,
! [X0,X1,X2] : multiply(X0,X1,inverse(inverse(multiply(X0,X1,X2)))) = multiply(X1,X2,X0),
inference(paramodulation,[status(thm)],[f4244,f4249]) ).
fof(f5817,plain,
! [X0,X1,X2] : multiply(X0,X1,multiply(X0,X1,X2)) = multiply(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f4077,f5742]) ).
fof(f5865,plain,
! [X0,X1] : multiply(X0,X1,X1) = multiply(X1,inverse(X0),X0),
inference(paramodulation,[status(thm)],[f4246,f5817]) ).
fof(f5915,plain,
! [X0,X1] : multiply(X0,X1,X1) = X1,
inference(forward_demodulation,[status(thm)],[f2365,f5865]) ).
fof(f5934,plain,
! [X0,X1] : multiply(X0,X0,X1) = X0,
inference(paramodulation,[status(thm)],[f4693,f5915]) ).
fof(f5961,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X1,multiply(X2,inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f5915,f4249]) ).
fof(f5993,plain,
! [X0,X1,X2] : multiply(X0,X1,X2) = multiply(X1,X2,X0),
inference(forward_demodulation,[status(thm)],[f2365,f5961]) ).
fof(f6106,plain,
( sQ3_spl
| a != a ),
inference(backward_demodulation,[status(thm)],[f5934,f16]) ).
fof(f6179,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6106]) ).
fof(f6180,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f6179]) ).
fof(f6264,plain,
( sQ2_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f4245,f13]) ).
fof(f6265,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6264]) ).
fof(f6266,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f6265]) ).
fof(f14173,plain,
! [X0,X1,X2,X3,X4,X5] : multiply(X0,multiply(multiply(X1,X2,X3),inverse(multiply(multiply(X1,X2,X4),X0,X5)),X5),multiply(X1,X2,X4)) = multiply(X2,multiply(X3,X0,X4),X1),
inference(forward_demodulation,[status(thm)],[f4074,f48]) ).
fof(f14174,plain,
( sQ0_spl
| multiply(e,multiply(c,b,a),d) != multiply(d,e,multiply(a,b,c)) ),
inference(backward_demodulation,[status(thm)],[f14182,f7]) ).
fof(f14182,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,X1,X2),X3,multiply(X0,X1,X4)) = multiply(X1,multiply(X4,X3,X2),X0),
inference(forward_demodulation,[status(thm)],[f4249,f14173]) ).
fof(f14475,plain,
( sQ0_spl
| multiply(e,multiply(a,b,c),d) != multiply(d,e,multiply(a,b,c)) ),
inference(paramodulation,[status(thm)],[f4693,f14174]) ).
fof(f14477,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14475,f5993]) ).
fof(f14478,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f14477]) ).
fof(f14479,plain,
( sQ1_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f5915,f10]) ).
fof(f14480,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f14479]) ).
fof(f14481,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f14480]) ).
fof(f14482,plain,
$false,
inference(sat_refutation,[status(thm)],[f20,f4343,f6180,f6266,f14478,f14481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : BOO035-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.51 % Computer : n006.cluster.edu
% 0.20/0.51 % Model : x86_64 x86_64
% 0.20/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.51 % Memory : 8046.5625MB
% 0.20/0.51 % OS : Linux 6.8.0-71-generic
% 0.20/0.51 % CPULimit : 300
% 0.20/0.51 % WCLimit : 300
% 0.20/0.51 % DateTime : Mon Sep 21 13:48:58 UTC 2026
% 0.20/0.52 % CPUTime :
% 0.26/0.54 % Drodi V4.1.1
% 52.88/7.35 % Refutation found
% 52.88/7.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 52.88/7.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 30.62/7.50 % Elapsed time: 6.945218 seconds
% 30.62/7.50 % CPU time: 54.376661 seconds
% 30.62/7.50 % Total memory used: 457.131 MB
% 30.62/7.50 % Net memory used: 449.038 MB
%------------------------------------------------------------------------------