%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 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 : Sun Sep 27 06:57:52 AM UTC 2026
% Result : Unsatisfiable 2.35s 6.35s
% Output : Refutation 2.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 304 ( 20 ~; 20 |; 0 &; 264 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 15 usr; 5 con; 0-3 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_F_decl,type,
v_F: $i ).
thf(c_UNITY_Oconstrains_decl,type,
c_UNITY_Oconstrains: $i > $i > $i > $i ).
thf(v_A_decl,type,
v_A: $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(v_B_decl,type,
v_B: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(tc_UNITY_Oprogram_decl,type,
tc_UNITY_Oprogram: $i > $i ).
thf(c_WFair_Otransient_decl,type,
c_WFair_Otransient: $i > $i > $i ).
thf(c_WFair_OleadsTo_decl,type,
c_WFair_OleadsTo: $i > $i > $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_WFair_Oensures_decl,type,
c_WFair_Oensures: $i > $i > $i > $i ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_OleadsTo ) ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_OleadsTo__Basis_0) ).
thf(25,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_OleadsTo ) ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( E @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_set @ ( B @ ( E @ c_lessequals ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNITY_Oconstrains__weaken__L_0) ).
thf(21,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( E @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_set @ ( B @ ( E @ c_lessequals ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
~ ( t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_B @ ( v_A @ c_WFair_OleadsTo ) ) @ ( v_F @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,plain,
~ ( t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_B @ ( v_A @ c_WFair_OleadsTo ) ) @ ( v_F @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_UNITY_Oprogram @ ( C @ ( D @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ c_WFair_Otransient ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_Otransient__strengthen_0) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_UNITY_Oprogram @ ( C @ ( D @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_UNITY_Oprogram @ ( C @ ( B @ c_WFair_Otransient ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_A @ c_WFair_Otransient ) @ ( v_F @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(12,plain,
t_a @ tc_UNITY_Oprogram @ ( t_a @ ( v_A @ c_WFair_Otransient ) @ ( v_F @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
t_a @ tc_UNITY_Oprogram @ ( t_a @ ( t_a @ ( v_B @ ( v_A @ c_union ) ) @ ( v_A @ c_UNITY_Oconstrains ) ) @ ( v_F @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(11,plain,
t_a @ tc_UNITY_Oprogram @ ( t_a @ ( t_a @ ( v_B @ ( v_A @ c_union ) ) @ ( v_A @ c_UNITY_Oconstrains ) ) @ ( v_F @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_WFair_OensuresI_0) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_UNITY_Oprogram @ ( D @ ( C @ ( B @ c_WFair_Oensures ) ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_WFair_Otransient ) @ ( A @ c_in ) ) )
| ~ ( D @ tc_UNITY_Oprogram @ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ c_UNITY_Oconstrains ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( C @ ( B @ ( A @ c_Main_OsubsetI__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffE_1) ).
thf(15,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ tc_set @ ( C @ ( B @ c_minus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
$false,
inference(e,[status(thm)],[25,21,13,17,27,12,11,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM011-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/5.39 % Computer : n019.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Sat Sep 26 23:21:11 UTC 2026
% 0.16/5.40 % CPUTime :
% 0.16/5.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.16/5.68 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.16/5.77 % [INFO] Parsing done (92ms).
% 0.16/5.78 % [INFO] Running in sequential loop mode.
% 0.16/5.96 % [INFO] eprover registered as external prover.
% 0.16/5.97 % [INFO] Scanning for conjecture ...
% 0.16/6.01 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 1.48/6.03 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.48/6.04 % [INFO] Problem is propositional (TPTP CNF).
% 1.48/6.04 % [INFO] Type checking passed.
% 1.48/6.05 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 2.35/6.35 % External prover 'e' found a proof!
% 2.35/6.35 % [INFO] Killing All external provers ...
% 2.35/6.35 % Time passed: 864ms (effective reasoning time: 562ms)
% 2.35/6.35 % Axioms used in derivation (7): cls_Set_OsubsetI_1, cls_UNITY_Oconstrains__weaken__L_0, cls_Set_OsubsetI_0, cls_WFair_OensuresI_0, cls_WFair_Otransient__strengthen_0, cls_WFair_OleadsTo__Basis_0, cls_Set_ODiffE_1
% 2.35/6.35 % No. of inferences in proof: 21
% 2.35/6.35 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 864 ms resp. 562 ms w/o parsing
% 2.35/6.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.35/6.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------