%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:10:16 PM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 48 ( 9 unt; 3 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 101 ( 47 ~; 51 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_c,V_A,V_B,T_a] :
( c_in(V_c,V_A,T_a)
| ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_A,V_B,T_a] :
( c_lessequals(V_A,V_B,tc_set(T_a))
| ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [V_F,V_A,V_A_H,T_a,V_B] :
( c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [V_F,V_A,V_B,T_a] :
( c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Otransient(c_minus(V_A,V_B,tc_set(T_a)),T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_UNITY_Oconstrains(c_minus(V_A,V_B,tc_set(T_a)),c_union(V_A,V_B,T_a),T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [V_F,V_A,V_B,T_a] :
( c_in(V_F,c_WFair_OleadsTo(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_in(V_F,c_WFair_Oensures(V_A,V_B,T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [V_F,V_A,T_a,V_B] :
( c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,plain,
c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
c_in(v_F,c_WFair_Otransient(v_A,t_a),tc_UNITY_Oprogram(t_a)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f13,plain,
~ c_in(v_F,c_WFair_OleadsTo(v_A,v_B,t_a),tc_UNITY_Oprogram(t_a)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [V_c,V_A,T_a] :
( c_in(V_c,V_A,T_a)
| ! [V_B] : ~ c_in(V_c,c_minus(V_A,V_B,tc_set(T_a)),T_a) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( c_in(X0,X1,X3)
| ~ c_in(X0,c_minus(X1,X2,tc_set(X3)),X3) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0,X1,X2] :
( c_lessequals(X0,X1,tc_set(X2))
| ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [V_F,V_A_H,T_a,V_B] :
( c_in(V_F,c_UNITY_Oconstrains(V_B,V_A_H,T_a),tc_UNITY_Oprogram(T_a))
| ! [V_A] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_UNITY_Oconstrains(V_A,V_A_H,T_a),tc_UNITY_Oprogram(T_a)) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4] :
( c_in(X0,c_UNITY_Oconstrains(X4,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_lessequals(X4,X1,tc_set(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Oensures(X1,X2,X3),tc_UNITY_Oprogram(X3)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f22,plain,
! [V_F,T_a,V_B] :
( c_in(V_F,c_WFair_Otransient(V_B,T_a),tc_UNITY_Oprogram(T_a))
| ! [V_A] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_in(V_F,c_WFair_Otransient(V_A,T_a),tc_UNITY_Oprogram(T_a)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_WFair_Otransient(X3,X2),tc_UNITY_Oprogram(X2))
| ~ c_lessequals(X3,X1,tc_set(X2))
| ~ c_in(X0,c_WFair_Otransient(X1,X2),tc_UNITY_Oprogram(X2)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( c_in(X0,c_WFair_OleadsTo(X1,X2,X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_WFair_Otransient(c_minus(X1,X2,tc_set(X3)),X3),tc_UNITY_Oprogram(X3))
| ~ c_in(X0,c_UNITY_Oconstrains(c_minus(X1,X2,tc_set(X3)),c_union(X1,X2,X3),X3),tc_UNITY_Oprogram(X3)) ),
inference(resolution,[status(thm)],[f20,f21]) ).
fof(f27,plain,
( ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[f25,f13]) ).
fof(f28,definition,
( sQ0_spl
<=> c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( sQ0_spl
| ~ c_in(v_F,c_UNITY_Oconstrains(c_minus(v_A,v_B,tc_set(t_a)),c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,definition,
( sQ1_spl
<=> c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( sQ1_spl
| ~ c_in(v_F,c_WFair_Otransient(c_minus(v_A,v_B,tc_set(t_a)),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f27,f28,f31]) ).
fof(f35,plain,
! [X0] :
( sQ0_spl
| ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),X0,tc_set(t_a))
| ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[f30,f19]) ).
fof(f36,plain,
! [X0] :
( sQ0_spl
| ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),X0,t_a),X0,t_a) ),
inference(resolution,[status(thm)],[f17,f35]) ).
fof(f45,plain,
! [X0] :
( sQ0_spl
| ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),X0,t_a),c_minus(v_A,v_B,tc_set(t_a)),t_a) ),
inference(resolution,[status(thm)],[f16,f35]) ).
fof(f49,plain,
! [X0] :
( sQ0_spl
| c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),X0,t_a),v_A,t_a)
| ~ c_in(v_F,c_UNITY_Oconstrains(X0,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[f45,f15]) ).
fof(f51,plain,
( sQ0_spl
| ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a))
| ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[f49,f36]) ).
fof(f52,definition,
( sQ3_spl
<=> c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( sQ3_spl
| ~ c_in(v_F,c_UNITY_Oconstrains(v_A,c_union(v_A,v_B,t_a),t_a),tc_UNITY_Oprogram(t_a)) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f51,f52,f28]) ).
fof(f56,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f11]) ).
fof(f57,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f56]) ).
fof(f58,plain,
! [X0] :
( sQ1_spl
| ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),X0,tc_set(t_a))
| ~ c_in(v_F,c_WFair_Otransient(X0,t_a),tc_UNITY_Oprogram(t_a)) ),
inference(resolution,[status(thm)],[f33,f23]) ).
fof(f59,plain,
( sQ1_spl
| ~ c_lessequals(c_minus(v_A,v_B,tc_set(t_a)),v_A,tc_set(t_a)) ),
inference(resolution,[status(thm)],[f58,f12]) ).
fof(f61,plain,
( sQ1_spl
| c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),c_minus(v_A,v_B,tc_set(t_a)),t_a) ),
inference(resolution,[status(thm)],[f59,f16]) ).
fof(f62,plain,
( sQ1_spl
| ~ c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a) ),
inference(resolution,[status(thm)],[f59,f17]) ).
fof(f63,plain,
( sQ1_spl
| c_in(c_Main_OsubsetI__1(c_minus(v_A,v_B,tc_set(t_a)),v_A,t_a),v_A,t_a) ),
inference(resolution,[status(thm)],[f61,f15]) ).
fof(f64,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f62]) ).
fof(f65,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f66,plain,
$false,
inference(sat_refutation,[status(thm)],[f34,f55,f57,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n019.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Mon Sep 21 14:14:41 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.41 % Elapsed time: 0.041100 seconds
% 0.14/5.41 % CPU time: 0.123196 seconds
% 0.14/5.41 % Total memory used: 17.140 MB
% 0.14/5.41 % Net memory used: 16.681 MB
%------------------------------------------------------------------------------