%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP039-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 0.23s 5.65s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 113 ( 32 unt; 8 def)
% Number of atoms : 245 ( 15 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 241 ( 109 ~; 124 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 139 ( 139 !; 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(f4,axiom,
! [X] : product(X,inverse(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(f8,axiom,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,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(f11,axiom,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,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(f13,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : product(identity,X0,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : product(X0,identity,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0] : product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0] : product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [Z,W] :
( Z = W
| ! [X,Y] :
( ~ product(X,Y,W)
| ~ product(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,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(f25,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)],[f24]) ).
fof(f26,plain,
! [U,Z,W] :
( product(U,Z,W)
| ! [X,V] :
( ~ product(X,V,W)
| ! [Y] :
( ~ product(Y,Z,V)
| ~ product(X,Y,U) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3,X4,X5] :
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0] :
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f29,plain,
! [C] :
( subgroup_member(C)
| ! [A,B] :
( ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f30,plain,
! [X0,X1,X2] :
( subgroup_member(X2)
| ~ product(X0,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)],[f11]) ).
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)],[f12]) ).
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(b),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f36,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f37,plain,
product(a,c,d),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f38,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
! [X0,X1] :
( X1 = identity
| ~ product(X0,inverse(X0),X1) ),
inference(resolution,[status(thm)],[f23,f20]) ).
fof(f47,plain,
! [X0,X1] :
( ~ product(X0,X1,d)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f30,f38]) ).
fof(f48,plain,
( ~ subgroup_member(c)
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f47,f37]) ).
fof(f49,definition,
( sQ0_spl
<=> subgroup_member(a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( sQ0_spl
| ~ subgroup_member(a) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ1_spl
<=> subgroup_member(c) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ1_spl
| subgroup_member(c) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( sQ1_spl
| ~ subgroup_member(c) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f49,f52]) ).
fof(f56,plain,
! [X0,X1] :
( sQ0_spl
| ~ product(X0,X1,a)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f51,f30]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( product(X0,identity,X3)
| ~ product(X2,X1,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f62,plain,
! [X0,X1,X2] :
( product(X0,d,X2)
| ~ product(X1,c,X2)
| ~ product(X0,a,X1) ),
inference(resolution,[status(thm)],[f25,f37]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( product(X2,X1,X3)
| ~ product(X0,identity,X3)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f27,f19]) ).
fof(f78,plain,
inverse(identity) = identity,
inference(resolution,[status(thm)],[f17,f42]) ).
fof(f80,plain,
( ~ subgroup_member(d)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f17,f47]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( product(X0,X3,X2)
| ~ product(X1,X2,X3)
| ~ product(X0,X1,identity) ),
inference(resolution,[status(thm)],[f17,f25]) ).
fof(f89,plain,
! [X0,X1] :
( X1 = X0
| ~ product(identity,X0,X1) ),
inference(resolution,[status(thm)],[f17,f23]) ).
fof(f90,definition,
( sQ2_spl
<=> subgroup_member(identity) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( sQ2_spl
| ~ subgroup_member(identity) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f94,definition,
( sQ3_spl
<=> subgroup_member(d) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f80,f90,f94]) ).
fof(f98,plain,
! [X0,X1] :
( sQ2_spl
| ~ product(X0,X1,identity)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f92,f30]) ).
fof(f110,plain,
! [X0,X1] :
( X1 = X0
| ~ product(X0,identity,X1) ),
inference(resolution,[status(thm)],[f18,f23]) ).
fof(f129,plain,
! [X0,X1,X2] :
( X2 = multiply(X0,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f21,f23]) ).
fof(f133,plain,
! [X0] : multiply(identity,X0) = X0,
inference(resolution,[status(thm)],[f89,f21]) ).
fof(f153,plain,
! [X0] :
( subgroup_member(X0)
| product(X0,element_in_O2(X0,d),d) ),
inference(resolution,[status(thm)],[f34,f38]) ).
fof(f159,plain,
! [X0] :
( sQ2_spl
| ~ subgroup_member(X0)
| ~ subgroup_member(inverse(X0)) ),
inference(resolution,[status(thm)],[f98,f19]) ).
fof(f163,plain,
! [X0] :
( sQ2_spl
| ~ subgroup_member(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f28]) ).
fof(f168,plain,
( sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f163]) ).
fof(f171,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f201,plain,
! [X0] :
( product(b,identity,X0)
| ~ product(c,a,X0) ),
inference(resolution,[status(thm)],[f58,f36]) ).
fof(f247,plain,
( sQ0_spl
| product(a,element_in_O2(a,d),d) ),
inference(resolution,[status(thm)],[f153,f51]) ).
fof(f250,plain,
( sQ0_spl
| d = multiply(a,element_in_O2(a,d)) ),
inference(resolution,[status(thm)],[f247,f129]) ).
fof(f284,plain,
product(b,identity,multiply(c,a)),
inference(resolution,[status(thm)],[f201,f21]) ).
fof(f285,plain,
multiply(c,a) = b,
inference(resolution,[status(thm)],[f284,f110]) ).
fof(f296,plain,
product(c,a,b),
inference(paramodulation,[status(thm)],[f285,f21]) ).
fof(f306,plain,
! [X0] :
( product(X0,d,c)
| ~ product(X0,a,identity) ),
inference(resolution,[status(thm)],[f62,f17]) ).
fof(f338,plain,
product(inverse(a),d,c),
inference(resolution,[status(thm)],[f306,f19]) ).
fof(f339,plain,
c = multiply(inverse(a),d),
inference(resolution,[status(thm)],[f338,f129]) ).
fof(f432,definition,
( sQ8_spl
<=> subgroup_member(inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f434,plain,
( sQ8_spl
| ~ subgroup_member(inverse(a)) ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f440,plain,
! [X0,X1] :
( sQ1_spl
| ~ product(X0,X1,c)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f54,f30]) ).
fof(f441,plain,
( sQ8_spl
| ~ subgroup_member(a) ),
inference(resolution,[status(thm)],[f434,f28]) ).
fof(f453,plain,
! [X0,X1] :
( sQ8_spl
| ~ product(X0,X1,a)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[f441,f30]) ).
fof(f476,plain,
( sQ1_spl
| ~ subgroup_member(inverse(a))
| ~ subgroup_member(b) ),
inference(resolution,[status(thm)],[f440,f36]) ).
fof(f480,definition,
( sQ10_spl
<=> subgroup_member(b) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( sQ10_spl
| ~ subgroup_member(b) ),
inference(component_clause,[status(thm)],[f480]) ).
fof(f483,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f476,f480,f432,f52]) ).
fof(f495,plain,
( sQ8_spl
| ~ subgroup_member(a)
| ~ subgroup_member(identity) ),
inference(resolution,[status(thm)],[f453,f17]) ).
fof(f497,plain,
( sQ8_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f495,f90,f49,f432]) ).
fof(f499,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f482,f35]) ).
fof(f500,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f509,plain,
! [X0,X1,X2] :
( product(X2,X1,X0)
| ~ product(X0,inverse(X1),X2) ),
inference(resolution,[status(thm)],[f70,f18]) ).
fof(f584,plain,
! [X0,X1] : product(multiply(X0,inverse(X1)),X1,X0),
inference(resolution,[status(thm)],[f509,f21]) ).
fof(f611,plain,
! [X0] :
( ~ subgroup_member(X0)
| ~ subgroup_member(multiply(d,inverse(X0))) ),
inference(resolution,[status(thm)],[f584,f47]) ).
fof(f754,definition,
( sQ11_spl
<=> subgroup_member(inverse(c)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f756,plain,
( sQ11_spl
| ~ subgroup_member(inverse(c)) ),
inference(component_clause,[status(thm)],[f754]) ).
fof(f835,plain,
( ~ subgroup_member(identity)
| ~ subgroup_member(multiply(d,identity)) ),
inference(paramodulation,[status(thm)],[f78,f611]) ).
fof(f838,definition,
( sQ13_spl
<=> subgroup_member(multiply(d,identity)) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f841,plain,
( ~ sQ2_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f835,f838,f90]) ).
fof(f901,plain,
! [X0,X1,X2] :
( product(multiply(identity,inverse(X0)),X2,X1)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f86,f584]) ).
fof(f907,plain,
! [X0,X1,X2] :
( product(inverse(X0),X2,X1)
| ~ product(X0,X1,X2) ),
inference(forward_demodulation,[status(thm)],[f133,f901]) ).
fof(f1058,plain,
product(inverse(c),b,a),
inference(resolution,[status(thm)],[f907,f296]) ).
fof(f1069,plain,
! [X0,X1] : product(inverse(X0),multiply(X0,X1),X1),
inference(resolution,[status(thm)],[f907,f21]) ).
fof(f1076,plain,
( sQ0_spl
| ~ subgroup_member(b)
| ~ subgroup_member(inverse(c)) ),
inference(resolution,[status(thm)],[f1058,f56]) ).
fof(f1087,plain,
( sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1076,f754,f480,f49]) ).
fof(f1089,plain,
( sQ11_spl
| ~ subgroup_member(c) ),
inference(resolution,[status(thm)],[f756,f28]) ).
fof(f1114,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(resolution,[status(thm)],[f1069,f129]) ).
fof(f1166,plain,
( sQ0_spl
| element_in_O2(a,d) = multiply(inverse(a),d) ),
inference(paramodulation,[status(thm)],[f250,f1114]) ).
fof(f1180,plain,
( sQ0_spl
| element_in_O2(a,d) = c ),
inference(forward_demodulation,[status(thm)],[f339,f1166]) ).
fof(f1185,plain,
( sQ0_spl
| subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c) ),
inference(paramodulation,[status(thm)],[f1180,f32]) ).
fof(f1186,plain,
( sQ0_spl
| sQ3_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f1185,f52,f94,f49]) ).
fof(f1187,plain,
( ~ sQ1_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f1089]) ).
fof(f1188,plain,
( ~ sQ1_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1187]) ).
fof(f1189,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f97,f171,f483,f497,f500,f841,f1087,f1186,f1188]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP039-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n015.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sun Sep 20 19:58:26 UTC 2026
% 0.18/5.47 % CPUTime :
% 0.18/5.48 % Drodi V4.1.1
% 0.23/5.65 % Refutation found
% 0.23/5.65 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.23/5.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/5.69 % Elapsed time: 0.203274 seconds
% 0.23/5.69 % CPU time: 1.143476 seconds
% 0.23/5.69 % Total memory used: 89.713 MB
% 0.23/5.69 % Net memory used: 87.666 MB
%------------------------------------------------------------------------------