%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:32:22 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.54s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 27
% Syntax : Number of formulae : 102 ( 29 unt; 12 def)
% Number of atoms : 229 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 230 ( 103 ~; 115 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 13 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 104 ( 104 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : product(X,inverse(X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
~ subgroup_member(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
! [A] : inverse(inverse(A)) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [X,V,W] :
( product(X,V,W)
| ! [U,Z] :
( ~ product(U,Z,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,inverse(B),C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,inverse(X1),X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| product(A,element_in_O2(A,B),B) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f34,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
~ subgroup_member(a),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f36,plain,
subgroup_member(b),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f37,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f38,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f39,plain,
product(a,c,d),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f40,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f42,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(inverse(X1))
| ~ subgroup_member(X0) ),
inference(paramodulation,[status(thm)],[f40,f30]) ).
fof(f43,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f18,f30]) ).
fof(f44,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0))
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f18,f42]) ).
fof(f45,definition,
( sQ0_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f48,definition,
! [X0] :
( sQ1_spl
<=> ( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f49,plain,
! [X0] :
( ~ sQ1_spl
| subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(component_clause,[status(thm)],[f48]) ).
fof(f51,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f45,f48]) ).
fof(f52,definition,
! [X0] :
( sQ2_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f53,plain,
! [X0] :
( ~ sQ2_spl
| subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f45,f52]) ).
fof(f64,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(inverse(X0))) ),
inference(resolution,[status(thm)],[f20,f30]) ).
fof(f67,definition,
! [X0] :
( sQ5_spl
<=> ( ~ subgroup_member(X0)
| ~ subgroup_member(inverse(inverse(X0))) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f68,plain,
! [X0] :
( ~ sQ5_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(inverse(X0))) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ0_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f64,f67,f45]) ).
fof(f76,plain,
! [X0] :
( ~ sQ5_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(X0) ),
inference(forward_demodulation,[status(thm)],[f40,f68]) ).
fof(f77,plain,
( ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f80]) ).
fof(f80,plain,
! [X0] :
( ~ sQ5_spl
| ~ subgroup_member(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f76]) ).
fof(f81,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f77]) ).
fof(f108,definition,
( sQ8_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f111,definition,
( sQ9_spl
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( sQ9_spl
| ~ subgroup_member(inverse(c)) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,definition,
( sQ10_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ10_spl
| subgroup_member(d) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f118,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f37]) ).
fof(f119,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( subgroup_member(c)
| ~ subgroup_member(a)
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f38,f30]) ).
fof(f122,definition,
( sQ11_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( sQ11_spl
| ~ subgroup_member(b) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ12_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ12_spl
| subgroup_member(c) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f120,f122,f108,f125]) ).
fof(f134,plain,
! [X0] :
( X0 = d
| ~ product(a,c,X0) ),
inference(resolution,[status(thm)],[f24,f39]) ).
fof(f139,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f24,f22]) ).
fof(f173,plain,
multiply(a,c) = d,
inference(resolution,[status(thm)],[f134,f22]) ).
fof(f226,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,X2)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[f26,f18]) ).
fof(f353,plain,
! [X0,X1,X2] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f226,f20]) ).
fof(f356,plain,
! [X0,X1,X2] :
( product(X0,X2,X1)
| ~ product(inverse(X0),X1,X2) ),
inference(resolution,[status(thm)],[f226,f21]) ).
fof(f382,plain,
! [X0,X1,X2] :
( X1 = multiply(inverse(X0),X2)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f353,f139]) ).
fof(f384,plain,
! [X0,X1,X2] :
( subgroup_member(X1)
| ~ subgroup_member(inverse(X2))
| ~ subgroup_member(inverse(X0))
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f353,f42]) ).
fof(f414,plain,
( subgroup_member(inverse(a))
| ~ subgroup_member(inverse(c))
| ~ subgroup_member(inverse(b)) ),
inference(resolution,[status(thm)],[f384,f38]) ).
fof(f424,definition,
( sQ20_spl
<=> subgroup_member(inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( sQ20_spl
| ~ subgroup_member(inverse(b)) ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f427,definition,
( sQ21_spl
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f428,plain,
( ~ sQ21_spl
| subgroup_member(inverse(a)) ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,plain,
( sQ21_spl
| ~ sQ9_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f414,f424,f111,f427]) ).
fof(f446,plain,
( ~ sQ1_spl
| sQ9_spl
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f113,f49]) ).
fof(f447,plain,
( ~ sQ1_spl
| sQ9_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f126]) ).
fof(f448,plain,
( ~ sQ1_spl
| sQ9_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f36]) ).
fof(f450,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f467,plain,
( ~ sQ1_spl
| sQ20_spl
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f426,f49]) ).
fof(f468,plain,
( ~ sQ1_spl
| sQ20_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f467,f122,f424,f48]) ).
fof(f515,plain,
! [X0,X1] : product(X0,multiply(inverse(X0),X1),X1),
inference(resolution,[status(thm)],[f356,f22]) ).
fof(f534,plain,
! [X0,X1] : X0 = multiply(X1,multiply(inverse(X1),X0)),
inference(resolution,[status(thm)],[f515,f139]) ).
fof(f562,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f40,f534]) ).
fof(f612,plain,
c = multiply(inverse(a),d),
inference(paramodulation,[status(thm)],[f173,f562]) ).
fof(f653,plain,
! [X0] :
( X0 = c
| ~ product(a,X0,d) ),
inference(paramodulation,[status(thm)],[f612,f382]) ).
fof(f667,plain,
( subgroup_member(a)
| subgroup_member(d)
| element_in_O2(a,d) = c ),
inference(resolution,[status(thm)],[f653,f34]) ).
fof(f668,definition,
( sQ28_spl
<=> element_in_O2(a,d) = c ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( ~ sQ28_spl
| element_in_O2(a,d) = c ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,plain,
( sQ8_spl
| sQ10_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f667,f668,f114,f108]) ).
fof(f674,plain,
( ~ sQ28_spl
| subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramodulation,[status(thm)],[f669,f32]) ).
fof(f683,plain,
( ~ sQ28_spl
| sQ8_spl
| sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f674,f125,f114,f108,f668]) ).
fof(f705,plain,
( ~ sQ2_spl
| ~ sQ21_spl
| subgroup_member(a) ),
inference(resolution,[status(thm)],[f428,f53]) ).
fof(f706,plain,
( ~ sQ2_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f705,f35]) ).
fof(f707,plain,
( ~ sQ2_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f708,plain,
$false,
inference(sat_refutation,[status(thm)],[f51,f55,f70,f81,f119,f128,f430,f448,f450,f468,f671,f683,f707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP040-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:55:39 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.54 % Refutation found
% 0.13/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.06/0.56 % Elapsed time: 0.204885 seconds
% 1.06/0.56 % CPU time: 1.288007 seconds
% 1.06/0.56 % Total memory used: 114.025 MB
% 1.06/0.56 % Net memory used: 110.980 MB
%------------------------------------------------------------------------------