%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 12:32:18 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.37s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 38
% Syntax : Number of formulae : 192 ( 39 unt; 16 def)
% Number of atoms : 470 ( 89 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 553 ( 275 ~; 262 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 17 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-1 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Xg] : group_member(identity_for(Xg),Xg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Xg,X] : product(Xg,identity_for(Xg),X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Xg,X] : product(Xg,X,identity_for(Xg),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Xg,X,Y,Z,W] :
( W = Z
| ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
group_member(a,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
group_member(b,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
group_member(c,g2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
group_member(d,g2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
! [X] :
( X = b
| X = a
| ~ group_member(X,g1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
! [X] :
( X = d
| X = c
| ~ group_member(X,g2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
product(g1,a,b,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(g1,b,b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
product(g2,c,c,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
product(g2,c,d,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
product(g2,d,d,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
an_isomorphism(a) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
an_isomorphism(b) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
group_member(d1,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
group_member(d2,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
group_member(d3,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] : group_member(identity_for(X0),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0,X1] : product(X0,identity_for(X0),X1,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f35,plain,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f41,plain,
! [Z,W] :
( W = Z
| ! [Xg,X,Y] :
( ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X3
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f47,plain,
group_member(a,g1),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f48,plain,
group_member(b,g1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f49,plain,
group_member(c,g2),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f50,plain,
group_member(d,g2),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
! [X0] :
( X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f52,plain,
! [X0] :
( X0 = d
| X0 = c
| ~ group_member(X0,g2) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
product(g1,a,b,b),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f56,plain,
product(g1,b,b,a),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
product(g2,c,c,c),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f58,plain,
product(g2,c,d,d),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f60,plain,
product(g2,d,d,c),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f61,plain,
an_isomorphism(a) = c,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f62,plain,
an_isomorphism(b) = d,
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f63,plain,
group_member(d1,g1),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f64,plain,
group_member(d2,g1),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f65,plain,
group_member(d3,g1),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f66,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f67,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f83,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f34,f42]) ).
fof(f92,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f35,f42]) ).
fof(f124,plain,
! [X0] :
( a = X0
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f56,f42]) ).
fof(f163,plain,
! [X0] :
( c = X0
| ~ product(g2,d,d,X0) ),
inference(resolution,[status(thm)],[f60,f42]) ).
fof(f165,plain,
( identity_for(g2) = d
| identity_for(g2) = c ),
inference(resolution,[status(thm)],[f52,f33]) ).
fof(f166,plain,
( d = d
| d = c ),
inference(resolution,[status(thm)],[f52,f50]) ).
fof(f167,plain,
( c = d
| c = c ),
inference(resolution,[status(thm)],[f52,f49]) ).
fof(f168,definition,
( sQ0_spl
<=> identity_for(g2) = c ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ0_spl
| identity_for(g2) = c ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,definition,
( sQ1_spl
<=> identity_for(g2) = d ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( ~ sQ1_spl
| identity_for(g2) = d ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f165,f168,f171]) ).
fof(f175,definition,
( sQ2_spl
<=> d = c ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ2_spl
| d = c ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( sQ2_spl
| d != c ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
( sQ3_spl
<=> d = d ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f166,f175,f178]) ).
fof(f182,definition,
( sQ4_spl
<=> c = c ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f167,f182,f175]) ).
fof(f186,plain,
! [X0] :
( ~ sQ2_spl
| X0 = c
| X0 = c
| ~ group_member(X0,g2) ),
inference(backward_demodulation,[status(thm)],[f176,f52]) ).
fof(f190,plain,
( ~ sQ2_spl
| an_isomorphism(b) = c ),
inference(backward_demodulation,[status(thm)],[f176,f62]) ).
fof(f192,plain,
! [X0] :
( ~ sQ2_spl
| X0 = c
| ~ group_member(X0,g2) ),
inference(duplicate_literals_removal,[status(thm)],[f186]) ).
fof(f198,plain,
! [X0] :
( ~ sQ0_spl
| product(g2,X0,c,X0) ),
inference(paramodulation,[status(thm)],[f169,f35]) ).
fof(f199,plain,
! [X0] :
( ~ sQ0_spl
| product(g2,c,X0,X0) ),
inference(paramodulation,[status(thm)],[f169,f34]) ).
fof(f202,plain,
( ~ sQ2_spl
| identity_for(g2) = c ),
inference(resolution,[status(thm)],[f192,f33]) ).
fof(f266,plain,
( b = b
| b = a ),
inference(resolution,[status(thm)],[f51,f48]) ).
fof(f267,plain,
( a = b
| a = a ),
inference(resolution,[status(thm)],[f51,f47]) ).
fof(f268,plain,
( identity_for(g1) = b
| identity_for(g1) = a ),
inference(resolution,[status(thm)],[f51,f33]) ).
fof(f269,plain,
( d3 = b
| d3 = a ),
inference(resolution,[status(thm)],[f51,f65]) ).
fof(f270,plain,
( d2 = b
| d2 = a ),
inference(resolution,[status(thm)],[f51,f64]) ).
fof(f271,plain,
( d1 = b
| d1 = a ),
inference(resolution,[status(thm)],[f51,f63]) ).
fof(f272,definition,
( sQ6_spl
<=> b = a ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ6_spl
| b = a ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ7_spl
<=> b = b ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f266,f272,f275]) ).
fof(f279,definition,
( sQ8_spl
<=> a = a ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f267,f279,f272]) ).
fof(f283,definition,
( sQ9_spl
<=> identity_for(g1) = a ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ9_spl
| identity_for(g1) = a ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,definition,
( sQ10_spl
<=> identity_for(g1) = b ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ10_spl
| identity_for(g1) = b ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f268,f283,f286]) ).
fof(f290,definition,
( sQ11_spl
<=> d3 = a ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( ~ sQ11_spl
| d3 = a ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f292,plain,
( sQ11_spl
| d3 != a ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
( sQ12_spl
<=> d3 = b ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ12_spl
| d3 = b ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f295,plain,
( sQ12_spl
| d3 != b ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f269,f290,f293]) ).
fof(f297,definition,
( sQ13_spl
<=> d2 = a ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ13_spl
| d2 = a ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,definition,
( sQ14_spl
<=> d2 = b ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ14_spl
| d2 = b ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f270,f297,f300]) ).
fof(f304,definition,
( sQ15_spl
<=> d1 = a ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f305,plain,
( ~ sQ15_spl
| d1 = a ),
inference(component_clause,[status(thm)],[f304]) ).
fof(f307,definition,
( sQ16_spl
<=> d1 = b ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( ~ sQ16_spl
| d1 = b ),
inference(component_clause,[status(thm)],[f307]) ).
fof(f310,plain,
( sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f271,f304,f307]) ).
fof(f327,plain,
( ~ sQ15_spl
| product(g1,a,d2,d3) ),
inference(backward_demodulation,[status(thm)],[f305,f66]) ).
fof(f329,plain,
( ~ sQ15_spl
| ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(backward_demodulation,[status(thm)],[f305,f67]) ).
fof(f330,plain,
( ~ sQ15_spl
| ~ product(g2,c,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f61,f329]) ).
fof(f331,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ product(g2,c,an_isomorphism(a),an_isomorphism(d3)) ),
inference(backward_demodulation,[status(thm)],[f298,f330]) ).
fof(f333,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ product(g2,c,c,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f61,f331]) ).
fof(f334,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ product(g2,c,c,an_isomorphism(a)) ),
inference(backward_demodulation,[status(thm)],[f291,f333]) ).
fof(f336,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ product(g2,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f61,f334]) ).
fof(f337,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f336,f199]) ).
fof(f338,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f342,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f202,f168,f175]) ).
fof(f377,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| d2 = a ),
inference(backward_demodulation,[status(thm)],[f273,f301]) ).
fof(f378,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| d3 = a ),
inference(forward_demodulation,[status(thm)],[f273,f294]) ).
fof(f379,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f292]) ).
fof(f380,plain,
( ~ sQ12_spl
| ~ sQ6_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f384,plain,
! [X0,X1] :
( ~ sQ9_spl
| X0 = X1
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f284,f83]) ).
fof(f387,plain,
! [X0] :
( ~ sQ9_spl
| product(g1,X0,a,X0) ),
inference(paramodulation,[status(thm)],[f284,f35]) ).
fof(f388,plain,
! [X0] :
( ~ sQ9_spl
| product(g1,a,X0,X0) ),
inference(paramodulation,[status(thm)],[f284,f34]) ).
fof(f402,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ product(g2,c,an_isomorphism(b),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f301,f330]) ).
fof(f403,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ product(g2,c,an_isomorphism(b),an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f294,f402]) ).
fof(f413,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ product(g2,c,an_isomorphism(b),c) ),
inference(backward_demodulation,[status(thm)],[f190,f403]) ).
fof(f414,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ product(g2,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f190,f413]) ).
fof(f415,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f414,f57]) ).
fof(f416,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f419,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| product(g1,a,d2,b) ),
inference(forward_demodulation,[status(thm)],[f294,f327]) ).
fof(f486,plain,
! [X0,X1] :
( ~ sQ9_spl
| X0 = X1
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f387,f42]) ).
fof(f496,plain,
! [X0,X1] :
( ~ sQ9_spl
| X0 = X1
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f388,f42]) ).
fof(f524,plain,
( ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ13_spl
| product(g1,a,a,b) ),
inference(forward_demodulation,[status(thm)],[f298,f419]) ).
fof(f525,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ13_spl
| a = b ),
inference(resolution,[status(thm)],[f524,f384]) ).
fof(f534,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f525,f272,f297,f293,f304,f283]) ).
fof(f547,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ product(g2,c,d,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f62,f403]) ).
fof(f548,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ product(g2,c,d,d) ),
inference(forward_demodulation,[status(thm)],[f62,f547]) ).
fof(f549,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f199]) ).
fof(f550,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f571,plain,
! [X0,X1] :
( ~ sQ10_spl
| X0 = X1
| ~ product(g1,X0,b,X1) ),
inference(paramodulation,[status(thm)],[f287,f92]) ).
fof(f644,plain,
( ~ sQ10_spl
| a = b ),
inference(resolution,[status(thm)],[f571,f54]) ).
fof(f650,plain,
( ~ sQ10_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f644,f272,f286]) ).
fof(f653,plain,
( ~ sQ13_spl
| product(g1,d1,a,d3) ),
inference(forward_demodulation,[status(thm)],[f298,f66]) ).
fof(f654,plain,
( ~ sQ13_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f298,f67]) ).
fof(f655,plain,
( ~ sQ13_spl
| ~ product(g2,an_isomorphism(d1),c,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f61,f654]) ).
fof(f675,plain,
( ~ sQ14_spl
| ~ sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f377,f297,f272,f300]) ).
fof(f677,plain,
( sQ12_spl
| ~ sQ11_spl
| a != b ),
inference(backward_demodulation,[status(thm)],[f291,f295]) ).
fof(f678,plain,
( sQ12_spl
| ~ sQ11_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f677,f272,f290,f293]) ).
fof(f680,plain,
( ~ sQ6_spl
| an_isomorphism(a) = d ),
inference(backward_demodulation,[status(thm)],[f273,f62]) ).
fof(f685,plain,
( ~ sQ6_spl
| c = d ),
inference(forward_demodulation,[status(thm)],[f61,f680]) ).
fof(f706,plain,
( ~ sQ6_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f685,f177]) ).
fof(f707,plain,
( ~ sQ6_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f709,plain,
( ~ sQ13_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f298,f67]) ).
fof(f710,plain,
( ~ sQ13_spl
| ~ product(g2,an_isomorphism(d1),c,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f61,f709]) ).
fof(f711,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ product(g2,an_isomorphism(b),c,an_isomorphism(d3)) ),
inference(backward_demodulation,[status(thm)],[f308,f710]) ).
fof(f730,plain,
( ~ sQ2_spl
| an_isomorphism(b) = c ),
inference(forward_demodulation,[status(thm)],[f176,f62]) ).
fof(f731,plain,
( ~ sQ16_spl
| product(g1,b,d2,d3) ),
inference(forward_demodulation,[status(thm)],[f308,f66]) ).
fof(f741,plain,
( ~ sQ2_spl
| product(g2,c,c,d) ),
inference(forward_demodulation,[status(thm)],[f176,f58]) ).
fof(f742,plain,
( ~ sQ2_spl
| product(g2,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f176,f741]) ).
fof(f755,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ product(g2,an_isomorphism(b),c,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f308,f655]) ).
fof(f756,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ product(g2,c,c,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f730,f755]) ).
fof(f757,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ product(g2,c,c,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f294,f756]) ).
fof(f758,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ product(g2,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f730,f757]) ).
fof(f759,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f742]) ).
fof(f760,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f759]) ).
fof(f761,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| product(g1,b,d2,b) ),
inference(forward_demodulation,[status(thm)],[f294,f731]) ).
fof(f762,plain,
( ~ sQ16_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f308,f67]) ).
fof(f790,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ14_spl
| product(g1,b,b,b) ),
inference(forward_demodulation,[status(thm)],[f301,f761]) ).
fof(f921,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ14_spl
| a = b ),
inference(resolution,[status(thm)],[f124,f790]) ).
fof(f922,plain,
( ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ14_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f921,f272,f300,f293,f307]) ).
fof(f923,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| product(g1,b,a,d3) ),
inference(forward_demodulation,[status(thm)],[f308,f653]) ).
fof(f925,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ product(g2,d,c,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f62,f711]) ).
fof(f926,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ12_spl
| ~ product(g2,d,c,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f294,f925]) ).
fof(f927,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ12_spl
| ~ product(g2,d,c,d) ),
inference(forward_demodulation,[status(thm)],[f62,f926]) ).
fof(f928,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f927,f198]) ).
fof(f929,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f928]) ).
fof(f940,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| product(g1,a,b,d3) ),
inference(forward_demodulation,[status(thm)],[f301,f327]) ).
fof(f941,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f291,f940]) ).
fof(f942,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| b = a ),
inference(resolution,[status(thm)],[f941,f496]) ).
fof(f950,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f942,f272,f290,f300,f304,f283]) ).
fof(f956,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ11_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f291,f923]) ).
fof(f957,plain,
( ~ sQ16_spl
| ~ product(g2,d,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f62,f762]) ).
fof(f958,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| ~ product(g2,d,an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f291,f957]) ).
fof(f959,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| ~ product(g2,d,an_isomorphism(d2),c) ),
inference(forward_demodulation,[status(thm)],[f61,f958]) ).
fof(f990,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ11_spl
| b = a ),
inference(resolution,[status(thm)],[f956,f486]) ).
fof(f1000,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f990,f272,f290,f307,f297,f283]) ).
fof(f1016,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ product(g2,d,an_isomorphism(b),c) ),
inference(forward_demodulation,[status(thm)],[f301,f959]) ).
fof(f1017,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ product(g2,d,d,c) ),
inference(forward_demodulation,[status(thm)],[f62,f1016]) ).
fof(f1018,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1017,f60]) ).
fof(f1019,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1018]) ).
fof(f1052,plain,
! [X0] :
( ~ sQ1_spl
| product(g2,X0,d,X0) ),
inference(paramodulation,[status(thm)],[f172,f35]) ).
fof(f1065,plain,
( ~ sQ1_spl
| c = d ),
inference(resolution,[status(thm)],[f1052,f163]) ).
fof(f1076,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1065,f175,f171]) ).
fof(f1077,plain,
$false,
inference(sat_refutation,[status(thm)],[f174,f181,f185,f278,f282,f289,f296,f303,f310,f338,f342,f380,f416,f534,f550,f650,f675,f678,f707,f760,f922,f929,f950,f1000,f1019,f1076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sun Sep 20 19:53:54 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.31 % Drodi V4.1.1
% 0.07/0.37 % Refutation found
% 0.07/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.38 % Elapsed time: 0.080485 seconds
% 0.07/0.38 % CPU time: 0.438805 seconds
% 0.07/0.38 % Total memory used: 111.264 MB
% 0.07/0.38 % Net memory used: 109.905 MB
%------------------------------------------------------------------------------