%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET825-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:10:42 PM UTC 2026
% Result : Unsatisfiable 0.03s 0.38s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 8 unt; 3 def)
% Number of atoms : 62 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 26 ~; 27 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [V_a,T_a] : c_in(c_Pair(V_a,V_a,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_a,V_b,T_a] :
( V_a = V_b
| ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(V_U),v_xa(V_U),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(V_U)),c_Suc(v_xa(V_U)),tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),V_U,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f8,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [T_a] : ~ c_in(c_Pair(V_a,V_b,T_a,T_a),c_Relation_OId,tc_prod(T_a,T_a)) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ c_in(c_Pair(X0,X1,X2,X2),c_Relation_OId,tc_prod(X2,X2)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
v_Q(v_n),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
~ v_Q(v_m),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
! [X0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_x(X0),v_xa(X0),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0] :
( ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_x(X0)),c_Suc(v_xa(X0)),tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),X0,tc_prod(tc_nat,tc_nat)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
( ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolution,[status(thm)],[f7,f13]) ).
fof(f15,definition,
( sQ0_spl
<=> c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f16,plain,
( ~ sQ0_spl
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ1_spl
<=> c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( sQ1_spl
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_xa(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f15,f18]) ).
fof(f22,plain,
( ~ sQ0_spl
| v_n = v_m ),
inference(resolution,[status(thm)],[f9,f16]) ).
fof(f26,plain,
( ~ sQ0_spl
| ~ v_Q(v_n) ),
inference(backward_demodulation,[status(thm)],[f22,f11]) ).
fof(f28,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f10]) ).
fof(f29,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f28]) ).
fof(f30,plain,
( c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| c_in(c_Pair(v_n,v_m,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(resolution,[status(thm)],[f12,f7]) ).
fof(f31,definition,
( sQ2_spl
<=> c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f32,plain,
( ~ sQ2_spl
| c_in(c_Pair(v_x(c_Relation_OId),v_xa(c_Relation_OId),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f30,f15,f31]) ).
fof(f35,plain,
( ~ sQ2_spl
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(resolution,[status(thm)],[f32,f9]) ).
fof(f37,plain,
( sQ1_spl
| ~ sQ2_spl
| ~ c_in(c_Pair(c_Suc(v_x(c_Relation_OId)),c_Suc(v_x(c_Relation_OId)),tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(backward_demodulation,[status(thm)],[f35,f20]) ).
fof(f38,plain,
( sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f7]) ).
fof(f39,plain,
( sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f29,f34,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET825-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Mon Sep 21 05:40:04 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.37 % Drodi V4.1.1
% 0.03/0.38 % Refutation found
% 0.03/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.03/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.03/0.41 % Elapsed time: 0.041869 seconds
% 0.03/0.41 % CPU time: 0.119611 seconds
% 0.03/0.41 % Total memory used: 52.559 MB
% 0.03/0.41 % Net memory used: 52.256 MB
%------------------------------------------------------------------------------