%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:32:21 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 110 ( 23 unt; 13 def)
% Number of atoms : 245 ( 16 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 248 ( 113 ~; 122 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 14 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 108 ( 108 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
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,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f31,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f33,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f34,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [A] :
( subgroup_member(A)
| ! [B] :
( subgroup_member(B)
| product(A,element_in_O2(A,B),B) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f36,plain,
! [X0,X1] :
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
subgroup_member(b),
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,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f41,plain,
! [X0,X1] :
( X1 = identity
| ~ product(inverse(X0),X0,X1) ),
inference(resolution,[status(thm)],[f24,f20]) ).
fof(f49,plain,
! [X0] :
( subgroup_member(identity)
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(resolution,[status(thm)],[f31,f20]) ).
fof(f50,plain,
( subgroup_member(c)
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f31,f38]) ).
fof(f51,plain,
( subgroup_member(d)
| ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f31,f39]) ).
fof(f53,definition,
! [X0] :
( sQ0_spl
<=> ( ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f54,plain,
! [X0] :
( ~ sQ0_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ1_spl
| subgroup_member(identity) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f53,f56]) ).
fof(f60,definition,
( sQ2_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( sQ2_spl
| ~ subgroup_member(b) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ3_spl
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| subgroup_member(inverse(a)) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ3_spl
| ~ subgroup_member(inverse(a)) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ4_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f69,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f50,f60,f63,f66]) ).
fof(f70,definition,
( sQ5_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f73,definition,
( sQ6_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ6_spl
| subgroup_member(d) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f51,f70,f66,f73]) ).
fof(f78,plain,
! [X0] :
( ~ sQ0_spl
| ~ subgroup_member(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f29]) ).
fof(f79,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f40]) ).
fof(f80,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f37,f78]) ).
fof(f82,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f81]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( product(X0,identity,X3)
| ~ product(X2,X1,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f86,plain,
! [X0,X1,X2] :
( product(X0,c,X2)
| ~ product(X1,inverse(a),X2)
| ~ product(X0,b,X1) ),
inference(resolution,[status(thm)],[f26,f38]) ).
fof(f88,plain,
! [X0,X1,X2] :
( product(X0,d,X2)
| ~ product(X1,c,X2)
| ~ product(X0,a,X1) ),
inference(resolution,[status(thm)],[f26,f39]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,X2)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[f18,f26]) ).
fof(f125,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f19,f24]) ).
fof(f186,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(X0)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f31,f18]) ).
fof(f194,definition,
! [X0] :
( sQ8_spl
<=> ( subgroup_member(X0)
| ~ subgroup_member(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ8_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f186,f56,f194]) ).
fof(f205,plain,
! [X0] :
( product(X0,d,c)
| ~ product(X0,a,identity) ),
inference(resolution,[status(thm)],[f88,f18]) ).
fof(f208,plain,
! [X0,X1] :
( product(X0,d,multiply(X1,c))
| ~ product(X0,a,X1) ),
inference(resolution,[status(thm)],[f88,f22]) ).
fof(f209,plain,
product(inverse(a),d,c),
inference(resolution,[status(thm)],[f205,f20]) ).
fof(f218,plain,
! [X0] :
( X0 = c
| ~ product(inverse(a),d,X0) ),
inference(resolution,[status(thm)],[f209,f24]) ).
fof(f221,plain,
! [X0] :
( product(X0,c,inverse(a))
| ~ product(X0,b,identity) ),
inference(resolution,[status(thm)],[f86,f18]) ).
fof(f271,plain,
! [X0] :
( product(b,identity,X0)
| ~ product(c,a,X0) ),
inference(resolution,[status(thm)],[f84,f38]) ).
fof(f292,plain,
product(b,identity,multiply(c,a)),
inference(resolution,[status(thm)],[f271,f22]) ).
fof(f295,plain,
( subgroup_member(multiply(c,a))
| ~ subgroup_member(identity)
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f292,f31]) ).
fof(f304,definition,
( sQ10_spl
<=> subgroup_member(multiply(c,a)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f295,f60,f56,f304]) ).
fof(f309,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f37]) ).
fof(f310,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( sQ3_spl
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f65,f29]) ).
fof(f352,plain,
! [X0,X1,X2] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f112,f20]) ).
fof(f411,plain,
! [X0] :
( subgroup_member(inverse(a))
| ~ subgroup_member(c)
| ~ subgroup_member(X0)
| ~ product(X0,b,identity) ),
inference(resolution,[status(thm)],[f221,f31]) ).
fof(f453,definition,
! [X0] :
( sQ23_spl
<=> ( ~ subgroup_member(X0)
| ~ product(X0,b,identity) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f454,plain,
! [X0] :
( ~ sQ23_spl
| ~ subgroup_member(X0)
| ~ product(X0,b,identity) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( sQ3_spl
| ~ sQ4_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f411,f453,f66,f63]) ).
fof(f462,plain,
( ~ sQ23_spl
| ~ subgroup_member(inverse(b)) ),
inference(resolution,[status(thm)],[f454,f20]) ).
fof(f463,plain,
( ~ sQ23_spl
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f462,f29]) ).
fof(f464,plain,
( ~ sQ23_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f463,f60,f453]) ).
fof(f483,plain,
! [X0] :
( X0 = c
| ~ product(a,X0,d) ),
inference(resolution,[status(thm)],[f352,f218]) ).
fof(f485,plain,
! [X0,X1] :
( X1 = identity
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f352,f41]) ).
fof(f497,plain,
! [X0,X1] :
( X1 = inverse(X0)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[f352,f125]) ).
fof(f523,plain,
! [X0] :
( ~ product(multiply(X0,c),a,X0)
| d = identity ),
inference(resolution,[status(thm)],[f485,f208]) ).
fof(f534,definition,
( sQ28_spl
<=> d = identity ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ28_spl
| d = identity ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,definition,
! [X0] :
( sQ29_spl
<=> ~ product(multiply(X0,c),a,X0) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f523,f534,f537]) ).
fof(f562,plain,
( ~ sQ28_spl
| ~ subgroup_member(identity) ),
inference(backward_demodulation,[status(thm)],[f535,f40]) ).
fof(f567,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f57]) ).
fof(f568,plain,
( ~ sQ28_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f625,plain,
( subgroup_member(a)
| subgroup_member(d)
| element_in_O2(a,d) = c ),
inference(resolution,[status(thm)],[f483,f36]) ).
fof(f626,definition,
( sQ31_spl
<=> element_in_O2(a,d) = c ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f627,plain,
( ~ sQ31_spl
| element_in_O2(a,d) = c ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,plain,
( sQ5_spl
| sQ6_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f625,f626,f73,f70]) ).
fof(f632,plain,
( ~ sQ31_spl
| subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramodulation,[status(thm)],[f627,f34]) ).
fof(f641,plain,
( ~ sQ31_spl
| sQ5_spl
| sQ6_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f632,f66,f73,f70,f626]) ).
fof(f642,plain,
( sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f311,f70,f63]) ).
fof(f762,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(resolution,[status(thm)],[f497,f20]) ).
fof(f782,plain,
! [X0] :
( subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f762,f29]) ).
fof(f787,plain,
( ~ sQ3_spl
| subgroup_member(a) ),
inference(resolution,[status(thm)],[f782,f64]) ).
fof(f791,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f787,f70,f63]) ).
fof(f793,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f69,f76,f80,f82,f197,f307,f310,f456,f464,f540,f568,f629,f641,f642,f791]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n004.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 19:55:34 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.075338 seconds
% 0.12/0.43 % CPU time: 0.322490 seconds
% 0.12/0.43 % Total memory used: 83.533 MB
% 0.12/0.43 % Net memory used: 82.628 MB
%------------------------------------------------------------------------------