%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 12:32:50 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 24
% Syntax : Number of formulae : 93 ( 12 unt; 15 def)
% Number of atoms : 317 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 388 ( 164 ~; 209 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 19 ( 18 usr; 16 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 85 ( 85 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] :
( product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1] :
( product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [Y,X,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f24,plain,
! [X0,X1,X2] :
( product(e_2,X1,X2)
| ~ product(X1,X2,X0)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f14,f22]) ).
fof(f25,plain,
! [X0,X1] :
( product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f24,f14]) ).
fof(f26,definition,
( sQ0_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f28,plain,
( sQ0_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f26]) ).
fof(f29,definition,
! [X0,X1] :
( sQ1_spl
<=> ( product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0,X1] :
( ~ sQ1_spl
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f25,f26,f29]) ).
fof(f33,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f11]) ).
fof(f34,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( ~ sQ1_spl
| product(X0,X1,e_1)
| ~ group_element(X1)
| product(e_2,X0,X1)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f30]) ).
fof(f36,plain,
! [X0,X1] :
( ~ sQ1_spl
| product(e_2,e_2,X0)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1)
| product(X0,X1,e_1)
| ~ group_element(X1)
| product(e_2,X0,X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f35,f24]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| equalish(X2,e_1)
| ~ product(e_2,X0,X2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| product(e_2,X0,X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f35,f16]) ).
fof(f39,definition,
! [X0,X1] :
( sQ2_spl
<=> ( product(e_2,e_2,X0)
| product(X0,X1,e_1)
| ~ group_element(X1)
| product(e_2,X0,X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f42,definition,
( sQ3_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ3_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,definition,
( sQ4_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( ~ sQ4_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( ~ sQ1_spl
| sQ4_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f36,f39,f42,f26,f45,f29]) ).
fof(f49,plain,
( ~ sQ4_spl
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f46,f24]) ).
fof(f52,definition,
( sQ5_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ5_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ6_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ6_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f57,plain,
( sQ6_spl
| ~ product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( ~ sQ4_spl
| sQ6_spl
| sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f49,f42,f52,f55,f45]) ).
fof(f59,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f10]) ).
fof(f60,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
( ~ sQ6_spl
| product(e_2,e_2,e_1)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f56,f24]) ).
fof(f64,definition,
( sQ7_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( ~ sQ7_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( ~ sQ6_spl
| sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f26,f64,f55]) ).
fof(f68,plain,
( ~ sQ7_spl
| product(e_2,e_2,e_2)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f65,f24]) ).
fof(f69,plain,
! [X0] :
( ~ sQ7_spl
| equalish(X0,e_1)
| ~ product(e_2,e_2,X0) ),
inference(resolution,[status(thm)],[f65,f16]) ).
fof(f71,definition,
( sQ8_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ8_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( ~ sQ7_spl
| sQ8_spl
| sQ4_spl
| ~ sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f68,f42,f26,f45,f71,f64]) ).
fof(f78,definition,
( sQ9_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ9_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f87,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ7_spl
| product(e_2,X0,e_1)
| ~ group_element(X0)
| product(e_2,e_2,X0)
| ~ group_element(e_2)
| equalish(e_1,e_1) ),
inference(resolution,[status(thm)],[f69,f35]) ).
fof(f89,definition,
( sQ10_spl
<=> equalish(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f92,definition,
! [X0] :
( sQ11_spl
<=> ( product(e_2,X0,e_1)
| ~ group_element(X0)
| product(e_2,e_2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| sQ11_spl
| ~ sQ0_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f87,f89,f26,f92,f64,f29]) ).
fof(f96,definition,
( sQ12_spl
<=> equalish(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ12_spl
| equalish(e_2,e_1) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f107,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| product(X0,X2,e_1)
| ~ group_element(X2)
| product(e_2,X0,X2)
| ~ group_element(X0)
| equalish(e_1,e_1)
| product(X0,X1,e_1)
| ~ group_element(X1)
| product(e_2,X0,X1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f37,f35]) ).
fof(f110,definition,
! [X0,X1,X2] :
( sQ13_spl
<=> ( product(X0,X2,e_1)
| ~ group_element(X2)
| product(e_2,X0,X2)
| ~ group_element(X0)
| product(X0,X1,e_1)
| ~ group_element(X1)
| product(e_2,X0,X1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ1_spl
| sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f107,f110,f89,f29]) ).
fof(f117,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_2)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f18,f46]) ).
fof(f123,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f117,f53]) ).
fof(f124,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f12]) ).
fof(f125,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f124]) ).
fof(f126,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f72,f69]) ).
fof(f133,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f13]) ).
fof(f134,plain,
( ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f142,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ6_spl
| equalish(e_2,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0)
| product(e_2,e_1,X0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f56,f37]) ).
fof(f148,definition,
! [X0] :
( sQ14_spl
<=> ( product(e_1,X0,e_1)
| ~ group_element(X0)
| product(e_2,e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| sQ12_spl
| sQ14_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f142,f42,f148,f96,f55,f29]) ).
fof(f160,plain,
( sQ6_spl
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f57,f14]) ).
fof(f161,plain,
( sQ6_spl
| sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f160,f26,f42,f78,f55]) ).
fof(f162,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f13]) ).
fof(f163,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f192,plain,
! [X0] :
( ~ sQ4_spl
| equalish(X0,e_1)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f20,f46]) ).
fof(f218,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ9_spl
| equalish(e_1,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0)
| product(e_2,e_1,X0)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f79,f37]) ).
fof(f222,plain,
( ~ sQ9_spl
| product(e_2,e_2,e_1)
| product(e_1,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f79,f24]) ).
fof(f225,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| sQ10_spl
| sQ14_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f218,f42,f148,f89,f78,f29]) ).
fof(f227,plain,
( ~ sQ9_spl
| sQ7_spl
| sQ4_spl
| ~ sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f222,f42,f26,f45,f64,f78]) ).
fof(f272,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f192,f65]) ).
fof(f273,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ4_spl
| product(e_2,X0,e_1)
| ~ group_element(X0)
| product(e_2,e_2,X0)
| ~ group_element(e_2)
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f192,f35]) ).
fof(f274,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f272,f96,f45,f64]) ).
fof(f275,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| sQ11_spl
| ~ sQ0_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f273,f96,f26,f92,f45,f29]) ).
fof(f276,plain,
$false,
inference(sat_refutation,[status(thm)],[f32,f34,f48,f58,f60,f67,f74,f95,f113,f125,f134,f151,f161,f163,f225,f227,f274,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:02:32 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.10/0.44 % Refutation found
% 0.10/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.084735 seconds
% 0.10/0.45 % CPU time: 0.466031 seconds
% 0.10/0.45 % Total memory used: 17.964 MB
% 0.10/0.45 % Net memory used: 17.573 MB
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