%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP309-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:33:22 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 42
% Syntax : Number of formulae : 200 ( 12 unt; 17 def)
% Number of atoms : 646 ( 236 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 830 ( 384 ~; 429 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 37 ( 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
multiply(sk_c5,sk_c6) = sk_c7,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
! [X3,X4,X1,X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f35,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
multiply(sk_c5,sk_c6) = sk_c7,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f38,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f42,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f43,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f50,plain,
! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c7
| ! [X3] :
( multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f51,plain,
! [X0,X1,X2,X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(sk_c7) != sk_c5
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f29,f52,f55]) ).
fof(f59,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f52,f59]) ).
fof(f63,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f31,f52,f63]) ).
fof(f67,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f52,f67]) ).
fof(f71,definition,
( sQ5_spl
<=> inverse(sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ5_spl
| inverse(sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f73,plain,
( sQ5_spl
| inverse(sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f74,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f33,f71,f55]) ).
fof(f75,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f34,f71,f59]) ).
fof(f76,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f35,f71,f63]) ).
fof(f77,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f36,f71,f67]) ).
fof(f78,definition,
( sQ6_spl
<=> multiply(sk_c7,sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f38,f78,f55]) ).
fof(f82,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f39,f78,f59]) ).
fof(f83,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f40,f78,f63]) ).
fof(f84,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f41,f78,f67]) ).
fof(f85,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f42,f85,f55]) ).
fof(f89,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f43,f85,f59]) ).
fof(f90,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f85,f63]) ).
fof(f91,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f85,f67]) ).
fof(f92,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f95,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f92,f55]) ).
fof(f96,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f92,f59]) ).
fof(f97,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f92,f63]) ).
fof(f98,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f92,f67]) ).
fof(f99,definition,
( sQ9_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ9_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
! [X0,X1] :
( sQ10_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f103,plain,
! [X0,X1] :
( ~ sQ10_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
! [X2] :
( sQ11_spl
<=> ( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f106,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,definition,
! [X3] :
( sQ12_spl
<=> ( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f52,f71,f99,f102,f105,f108]) ).
fof(f112,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f109,f64]) ).
fof(f114,plain,
( ~ sQ12_spl
| inverse(sk_c5) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramodulation,[status(thm)],[f37,f109]) ).
fof(f115,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f68,f112]) ).
fof(f116,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f115]) ).
fof(f117,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f118,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f106,f56]) ).
fof(f119,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7
| sk_c2 != sk_c6 ),
inference(paramodulation,[status(thm)],[f86,f106]) ).
fof(f121,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f60,f118]) ).
fof(f122,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f121]) ).
fof(f123,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f122]) ).
fof(f124,plain,
! [X0] :
( ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f103]) ).
fof(f125,plain,
( sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f37,f101]) ).
fof(f126,plain,
( sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f125]) ).
fof(f127,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f126]) ).
fof(f137,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7
| multiply(sk_c7,sk_c2) != sk_c6 ),
inference(paramodulation,[status(thm)],[f86,f124]) ).
fof(f138,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f56,f124]) ).
fof(f139,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f137,f78,f92,f102,f85]) ).
fof(f140,definition,
( sQ13_spl
<=> multiply(sk_c7,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( sQ13_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f138,f140,f59,f102,f55]) ).
fof(f144,definition,
( sQ14_spl
<=> sk_c2 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ14_spl
| sk_c2 != sk_c6 ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f119,f144,f92,f105,f85]) ).
fof(f151,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f68,f27]) ).
fof(f152,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f27,f28]) ).
fof(f153,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f152]) ).
fof(f170,plain,
( ~ sQ6_spl
| sk_c2 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f79,f153]) ).
fof(f171,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f86,f153]) ).
fof(f177,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f72,f170]) ).
fof(f178,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f37,f177]) ).
fof(f179,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f93,f171]) ).
fof(f180,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f79,f179]) ).
fof(f185,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f178,f53]) ).
fof(f186,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f178,f72]) ).
fof(f187,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c2,sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f178,f79]) ).
fof(f191,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f178,f180]) ).
fof(f192,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f146]) ).
fof(f193,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,definition,
( sQ15_spl
<=> sk_c7 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ15_spl
| sk_c7 != sk_c5 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,definition,
( sQ16_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ16_spl
| inverse(sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f114,f194,f197,f108]) ).
fof(f201,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c2 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f178,f196]) ).
fof(f205,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c2) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f191,f185]) ).
fof(f210,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f205,f187]) ).
fof(f211,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f213,f186]) ).
fof(f213,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f191,f210]) ).
fof(f214,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f213,f201]) ).
fof(f215,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f214]) ).
fof(f216,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f217,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f213,f199]) ).
fof(f218,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f191,f217]) ).
fof(f229,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f211,f218]) ).
fof(f230,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f229]) ).
fof(f231,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f60,f27]) ).
fof(f242,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f64,f153]) ).
fof(f244,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f68,f242]) ).
fof(f245,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c6) ),
inference(paramodulation,[status(thm)],[f56,f153]) ).
fof(f247,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f60,f245]) ).
fof(f280,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f244,f153]) ).
fof(f282,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f27,f280]) ).
fof(f283,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f282,f233]) ).
fof(f285,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f282,f151]) ).
fof(f287,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f282,f27]) ).
fof(f288,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f282,f26]) ).
fof(f289,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f288,f37]) ).
fof(f295,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f289,f142]) ).
fof(f296,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f289,f60]) ).
fof(f298,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f289,f247]) ).
fof(f299,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f289,f298]) ).
fof(f302,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f54]) ).
fof(f303,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f299,f302]) ).
fof(f330,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c3) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f283]) ).
fof(f343,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f299,f295]) ).
fof(f344,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f343]) ).
fof(f345,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f348,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f53]) ).
fof(f349,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f299,f348]) ).
fof(f351,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f289,f73]) ).
fof(f353,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f349,f285]) ).
fof(f354,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f349,f330]) ).
fof(f357,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f349,f296]) ).
fof(f362,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f288,f353]) ).
fof(f363,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f288,f354]) ).
fof(f368,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f362,f349]) ).
fof(f373,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f362,f363]) ).
fof(f374,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f362,f351]) ).
fof(f381,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f368,f374]) ).
fof(f382,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f373,f357]) ).
fof(f383,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f362,f382]) ).
fof(f390,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f383,f381]) ).
fof(f391,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f390]) ).
fof(f392,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f446,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f299,f153]) ).
fof(f448,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f287,f446]) ).
fof(f449,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f448,f303]) ).
fof(f450,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f451,plain,
$false,
inference(sat_refutation,[status(thm)],[f58,f62,f66,f70,f74,f75,f76,f77,f81,f82,f83,f84,f88,f89,f90,f91,f95,f96,f97,f98,f111,f117,f123,f127,f139,f143,f147,f193,f200,f216,f231,f345,f392,f450]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP309-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n007.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 20 20:06:50 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.48 % Elapsed time: 0.058026 seconds
% 0.22/0.48 % CPU time: 0.176597 seconds
% 0.22/0.48 % Total memory used: 103.325 MB
% 0.22/0.48 % Net memory used: 103.035 MB
%------------------------------------------------------------------------------