%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 34 ( 10 unt; 4 def)
% Number of atoms : 68 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 27 ~; 30 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f126,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(f131,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(f1358,negated_conjecture,
v_Q(v_n),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1359,negated_conjecture,
~ v_Q(v_m),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f1360,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(f1361,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(f1536,plain,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f1541,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)],[f131]) ).
fof(f1542,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)],[f1541]) ).
fof(f2837,plain,
v_Q(v_n),
inference(cnf_transformation,[status(thm)],[f1358]) ).
fof(f2838,plain,
~ v_Q(v_m),
inference(cnf_transformation,[status(thm)],[f1359]) ).
fof(f2839,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)],[f1360]) ).
fof(f2840,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)],[f1361]) ).
fof(f4136,plain,
( ~ c_in(c_Pair(c_0,c_0,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))
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(resolution,[status(thm)],[f1542,f2839]) ).
fof(f4141,definition,
( sQ55_spl
<=> v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f4142,plain,
( ~ sQ55_spl
| v_x(c_Relation_OId) = v_xa(c_Relation_OId) ),
inference(component_clause,[status(thm)],[f4141]) ).
fof(f4144,definition,
( sQ56_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,[sQ56_spl])],[split_symbol_definition]) ).
fof(f4145,plain,
( ~ sQ56_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)],[f4144]) ).
fof(f4147,definition,
( sQ57_spl
<=> c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f4149,plain,
( sQ57_spl
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat)) ),
inference(component_clause,[status(thm)],[f4147]) ).
fof(f4150,plain,
( ~ sQ57_spl
| sQ56_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f4136,f4141,f4144,f4147]) ).
fof(f4153,plain,
( sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4149,f1536]) ).
fof(f4154,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f4153]) ).
fof(f4156,plain,
( ~ sQ55_spl
| ~ c_in(c_Pair(c_0,c_0,tc_nat,tc_nat),c_Relation_OId,tc_prod(tc_nat,tc_nat))
| ~ c_in(c_Pair(c_Suc(v_xa(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(paramodulation,[status(thm)],[f4142,f2840]) ).
fof(f4161,definition,
( sQ59_spl
<=> c_in(c_Pair(c_Suc(v_xa(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,[sQ59_spl])],[split_symbol_definition]) ).
fof(f4163,plain,
( sQ59_spl
| ~ c_in(c_Pair(c_Suc(v_xa(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)],[f4161]) ).
fof(f4164,plain,
( ~ sQ55_spl
| ~ sQ57_spl
| ~ sQ59_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f4156,f4144,f4161,f4147,f4141]) ).
fof(f4165,plain,
( ~ sQ56_spl
| v_n = v_m ),
inference(resolution,[status(thm)],[f4145,f1542]) ).
fof(f4204,plain,
( ~ sQ56_spl
| v_Q(v_m) ),
inference(backward_demodulation,[status(thm)],[f4165,f2837]) ).
fof(f4205,plain,
( ~ sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4204,f2838]) ).
fof(f4206,plain,
~ sQ56_spl,
inference(contradiction_clause,[status(thm)],[f4205]) ).
fof(f4207,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4163,f1536]) ).
fof(f4208,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f4207]) ).
fof(f4209,plain,
$false,
inference(sat_refutation,[status(thm)],[f4150,f4154,f4164,f4206,f4208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET825-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n008.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 05:40:39 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.11/0.40 % Drodi V4.1.1
% 0.11/0.45 % Refutation found
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.48 % Elapsed time: 0.123784 seconds
% 0.11/0.48 % CPU time: 0.452143 seconds
% 0.11/0.48 % Total memory used: 128.654 MB
% 0.11/0.48 % Net memory used: 127.808 MB
%------------------------------------------------------------------------------