%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:10:41 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 53 ( 12 unt; 4 def)
% Number of atoms : 108 ( 9 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 103 ( 48 ~; 51 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [T_a,V_x] :
( ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [V_c,V_A,T_a] :
( ~ c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [V_c,V_A,T_a] :
( c_in(V_c,c_uminus(V_A,tc_set(T_a)),T_a)
| c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_a,V_B,T_a,V_b] :
( c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_x,V_B,T_a] : c_in(V_x,c_insert(V_x,V_B,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_a,V_b,V_A,T_a] :
( V_a = V_b
| c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
c_less(v_a,v_b,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_less(v_b,v_c,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
! [V_U] :
( c_in(v_a,V_U,tc_IntDef_Oint)
| ~ c_in(v_b,V_U,tc_IntDef_Oint)
| c_in(v_c,V_U,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [T_a] :
( ! [V_x] : ~ c_less(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( ~ c_less(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1,X2] :
( c_in(X0,c_uminus(X1,tc_set(X2)),X2)
| c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [V_a,V_B,T_a] :
( ! [V_b] : c_in(V_a,c_insert(V_b,V_B,T_a),T_a)
| ~ c_in(V_a,V_B,T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_insert(X3,X1,X2),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] : c_in(X0,c_insert(X0,X1,X2),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [V_a,V_b] :
( V_a = V_b
| ! [V_A,T_a] :
( c_in(V_a,V_A,T_a)
| ~ c_in(V_a,c_insert(V_b,V_A,T_a),T_a) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| c_in(X0,X2,X3)
| ~ c_in(X0,c_insert(X1,X2,X3),X3) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
c_less(v_a,v_b,tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f21,plain,
c_less(v_b,v_c,tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f22,plain,
! [X0] :
( c_in(v_a,X0,tc_IntDef_Oint)
| ~ c_in(v_b,X0,tc_IntDef_Oint)
| c_in(v_c,X0,tc_IntDef_Oint) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f23,plain,
class_Orderings_Oorder(tc_IntDef_Oint),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0] :
( c_in(v_a,c_uminus(X0,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_c,c_uminus(X0,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f14,f22]) ).
fof(f28,plain,
! [X0] :
( ~ c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_a,c_uminus(X0,tc_set(tc_IntDef_Oint)),tc_IntDef_Oint)
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f26,f13]) ).
fof(f29,plain,
! [X0] :
( ~ c_in(v_a,X0,tc_IntDef_Oint)
| ~ c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f28,f13]) ).
fof(f34,plain,
! [X0,X1] :
( ~ c_in(v_c,X1,tc_IntDef_Oint)
| ~ c_in(v_a,c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_in(v_b,c_insert(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f29,f16]) ).
fof(f39,plain,
! [X0] :
( ~ c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_b,c_insert(v_a,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f34,f17]) ).
fof(f46,plain,
! [X0] :
( ~ c_in(v_c,X0,tc_IntDef_Oint)
| v_b = v_a
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f19,f39]) ).
fof(f53,definition,
! [X0] :
( sQ0_spl
<=> ( ~ c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_b,X0,tc_IntDef_Oint) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f54,plain,
! [X0] :
( ~ sQ0_spl
| ~ c_in(v_c,X0,tc_IntDef_Oint)
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> v_b = v_a ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f57,plain,
( ~ sQ1_spl
| v_b = v_a ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f53,f56]) ).
fof(f63,definition,
( sQ3_spl
<=> v_b = v_c ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ3_spl
| v_b = v_c ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f91,plain,
( ~ sQ3_spl
| c_less(v_b,v_b,tc_IntDef_Oint) ),
inference(backward_demodulation,[status(thm)],[f64,f21]) ).
fof(f93,plain,
( ~ sQ3_spl
| ~ class_Orderings_Oorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f91,f12]) ).
fof(f94,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f23]) ).
fof(f95,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f98,plain,
! [X0] :
( ~ sQ0_spl
| c_in(v_b,c_insert(v_c,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f54,f17]) ).
fof(f99,plain,
! [X0] :
( ~ sQ0_spl
| v_b = v_c
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f98,f19]) ).
fof(f100,definition,
! [X0] :
( sQ7_spl
<=> c_in(v_b,X0,tc_IntDef_Oint) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f101,plain,
! [X0] :
( ~ sQ7_spl
| c_in(v_b,X0,tc_IntDef_Oint) ),
inference(component_clause,[status(thm)],[f100]) ).
fof(f103,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f99,f100,f63,f53]) ).
fof(f104,plain,
( ~ sQ1_spl
| c_less(v_b,v_b,tc_IntDef_Oint) ),
inference(backward_demodulation,[status(thm)],[f57,f20]) ).
fof(f106,plain,
! [X0] :
( ~ sQ7_spl
| ~ c_in(v_b,X0,tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f101,f13]) ).
fof(f108,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f101]) ).
fof(f109,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( ~ sQ1_spl
| ~ class_Orderings_Oorder(tc_IntDef_Oint) ),
inference(resolution,[status(thm)],[f104,f12]) ).
fof(f111,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f23]) ).
fof(f112,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f113,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f95,f103,f109,f112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 05:39:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.43 % Elapsed time: 0.053284 seconds
% 0.10/0.43 % CPU time: 0.165967 seconds
% 0.10/0.43 % Total memory used: 80.813 MB
% 0.10/0.43 % Net memory used: 80.187 MB
%------------------------------------------------------------------------------