%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LAT276-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 01:02:30 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 21
% Syntax : Number of formulae : 70 ( 8 unt; 9 def)
% Number of atoms : 170 ( 4 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 180 ( 80 ~; 91 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-4 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
! [V_V] :
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(V_V,v_S,t_a)
| c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [V_U] :
( c_in(v_xa,v_S,t_a)
| ~ c_in(V_U,v_S,t_a)
| c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_c,V_A,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_L,V_S] :
( c_in(v_sko__4mP(V_L,V_S,v_r),V_S,t_a)
| c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_L,v_A,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_L,V_S] :
( c_in(c_Pair(c_Tarski_Olub(V_S,v_cl,t_a),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(V_L,V_S,v_r),V_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(V_L,v_A,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [V_x,V_S] :
( c_in(c_Pair(V_x,c_Tarski_Olub(V_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(V_S,v_A,tc_set(t_a))
| ~ c_in(V_x,V_S,t_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
c_lessequals(v_S,v_A,tc_set(t_a)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ! [V_V] :
( ~ c_in(V_V,v_S,t_a)
| c_in(c_Pair(V_V,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0] :
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( c_in(v_xa,v_S,t_a)
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
( c_in(v_xa,v_S,t_a)
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f18,plain,
( ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a))
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
( c_in(v_xa,v_S,t_a)
| ! [V_U] :
( ~ c_in(V_U,v_S,t_a)
| c_in(c_Pair(V_U,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f20,plain,
! [X0] :
( c_in(v_xa,v_S,t_a)
| ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [V_c,T_a,V_B] :
( c_in(V_c,V_B,T_a)
| ! [V_A] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(V_c,V_A,T_a) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
! [X0,X1] :
( c_in(v_sko__4mP(X0,X1,v_r),X1,t_a)
| c_in(c_Pair(c_Tarski_Olub(X1,v_cl,t_a),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X0,v_A,t_a) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( c_in(c_Pair(c_Tarski_Olub(X1,v_cl,t_a),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(X0,X1,v_r),X0,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X0,v_A,t_a) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( c_in(c_Pair(X0,c_Tarski_Olub(X1,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_lessequals(X1,v_A,tc_set(t_a))
| ~ c_in(X0,X1,t_a) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,definition,
! [X0] :
( sQ0_spl
<=> ( ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f29,plain,
! [X0] :
( ~ sQ0_spl
| ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
( sQ1_spl
<=> c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( sQ1_spl
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f28,f31]) ).
fof(f35,definition,
( sQ2_spl
<=> c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ2_spl
| c_in(v_xa,c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ3_spl
<=> c_in(v_xa,v_S,t_a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f16,f35,f38]) ).
fof(f42,definition,
( sQ4_spl
<=> c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( sQ4_spl
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( sQ3_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f17,f42,f38]) ).
fof(f46,plain,
( ~ sQ1_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f18,f42,f31]) ).
fof(f47,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f20,f28,f38]) ).
fof(f48,plain,
( sQ4_spl
| ~ c_in(c_Pair(c_Tarski_Olub(v_S,v_cl,t_a),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(forward_demodulation,[status(thm)],[f27,f44]) ).
fof(f49,plain,
! [X0] :
( ~ sQ0_spl
| ~ c_in(X0,v_S,t_a)
| c_in(c_Pair(X0,v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(forward_demodulation,[status(thm)],[f27,f29]) ).
fof(f53,plain,
( sQ4_spl
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_xa,v_A,t_a) ),
inference(resolution,[status(thm)],[f25,f48]) ).
fof(f54,definition,
( sQ5_spl
<=> c_in(v_xa,v_A,t_a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f56,plain,
( sQ5_spl
| ~ c_in(v_xa,v_A,t_a) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ6_spl
<=> c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f59,plain,
( sQ6_spl
| ~ c_in(c_Pair(v_sko__4mP(v_xa,v_S,v_r),v_xa,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,definition,
( sQ7_spl
<=> c_lessequals(v_S,v_A,tc_set(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( sQ7_spl
| ~ c_lessequals(v_S,v_A,tc_set(t_a)) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f53,f54,f57,f60,f42]) ).
fof(f64,plain,
( sQ1_spl
| ~ c_in(c_Pair(v_xa,c_Tarski_Olub(v_S,v_cl,t_a),t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
inference(forward_demodulation,[status(thm)],[f27,f33]) ).
fof(f65,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f13]) ).
fof(f66,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f65]) ).
fof(f67,plain,
( sQ1_spl
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(v_xa,v_S,t_a) ),
inference(resolution,[status(thm)],[f64,f26]) ).
fof(f69,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f67,f38,f60,f31]) ).
fof(f70,plain,
( ~ sQ2_spl
| c_in(v_xa,v_A,t_a) ),
inference(forward_demodulation,[status(thm)],[f23,f36]) ).
fof(f71,plain,
( sQ5_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f70]) ).
fof(f72,plain,
( sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f71]) ).
fof(f75,plain,
( sQ4_spl
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a)
| ~ c_lessequals(v_S,v_A,tc_set(t_a))
| ~ c_in(v_xa,v_A,t_a) ),
inference(resolution,[status(thm)],[f48,f24]) ).
fof(f79,definition,
( sQ8_spl
<=> c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ8_spl
| c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ4_spl
| sQ8_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f75,f54,f60,f79,f42]) ).
fof(f97,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ c_in(v_sko__4mP(v_xa,v_S,v_r),v_S,t_a) ),
inference(resolution,[status(thm)],[f59,f49]) ).
fof(f99,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f80]) ).
fof(f100,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f99]) ).
fof(f103,plain,
! [X0] :
( sQ5_spl
| ~ c_lessequals(X0,v_A,tc_set(t_a))
| ~ c_in(v_xa,X0,t_a) ),
inference(resolution,[status(thm)],[f56,f22]) ).
fof(f105,plain,
( sQ5_spl
| ~ c_in(v_xa,v_S,t_a) ),
inference(resolution,[status(thm)],[f103,f13]) ).
fof(f106,plain,
( sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f105,f38,f54]) ).
fof(f107,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f41,f45,f46,f47,f63,f66,f69,f72,f82,f100,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT276-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 23:22:36 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.052590 seconds
% 0.13/0.43 % CPU time: 0.150030 seconds
% 0.13/0.43 % Total memory used: 102.052 MB
% 0.13/0.43 % Net memory used: 101.691 MB
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