%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 08:31:02 AM UTC 2026
% Result : Unsatisfiable 5.01s 2.88s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 374 ( 42 ~; 48 |; 0 &; 284 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 52 ( 0 ^; 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_X_decl,type,
v_X: $i ).
thf(c_inter_decl,type,
c_inter: $i > $i > $i > $i ).
thf(v_Y_decl,type,
v_Y: $i ).
thf(v_Z_decl,type,
v_Z: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Main_OsubsetI__1_decl,type,
c_Main_OsubsetI__1: $i > $i > $i > $i ).
thf(12,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
thf(42,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)],[12]) ).
thf(5,negated_conjecture,
( ( v_X
!= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) )
| ~ ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_X @ ( v_x @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(14,plain,
( ( v_X
!= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) )
| ~ ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_X @ ( v_x @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( C @ tc_set @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,negated_conjecture,
( ( v_X
!= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) )
| ~ ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_Y @ ( v_x @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(18,plain,
( ( v_X
!= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) )
| ~ ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_Y @ ( v_x @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_Y @ ( A @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_X @ ( A @ c_lessequals ) ) )
| ( v_X
= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(16,plain,
! [A: $i] :
( ~ ( t_a @ tc_set @ ( v_Y @ ( A @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( A @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_X @ ( A @ c_lessequals ) ) )
| ( v_X
= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
thf(40,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)],[11]) ).
thf(1,negated_conjecture,
( ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ( v_X
= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(15,plain,
( ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ( v_X
= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,negated_conjecture,
( ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ( v_X
= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(17,plain,
( ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ( v_X
= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_0) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntE_1) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_inter ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OIntI_0) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_inter ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,negated_conjecture,
( ( v_X
!= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) )
| ~ ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_Z @ ( v_x @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(19,plain,
( ( v_X
!= ( t_a @ ( v_Z @ ( v_Y @ c_inter ) ) ) )
| ~ ( t_a @ tc_set @ ( v_Y @ ( v_X @ c_lessequals ) ) )
| ~ ( t_a @ tc_set @ ( v_Z @ ( v_X @ c_lessequals ) ) )
| ( t_a @ tc_set @ ( v_Z @ ( v_x @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(89,plain,
$false,
inference(e,[status(thm)],[42,14,38,44,18,16,40,15,17,32,34,36,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET831-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.23/0.48 % Computer : n020.cluster.edu
% 0.23/0.48 % Model : x86_64 x86_64
% 0.23/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.48 % Memory : 8046.5625MB
% 0.23/0.48 % OS : Linux 6.8.0-71-generic
% 0.23/0.48 % CPULimit : 300
% 0.23/0.48 % WCLimit : 300
% 0.23/0.48 % DateTime : Sat Sep 26 08:20:19 UTC 2026
% 0.23/0.48 % CPUTime :
% 0.23/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.20/1.18 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.62/1.42 % [INFO] Parsing done (241ms).
% 1.62/1.44 % [INFO] Running in sequential loop mode.
% 2.51/2.04 % [INFO] eprover registered as external prover.
% 2.51/2.05 % [INFO] Scanning for conjecture ...
% 2.81/2.14 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.04/2.18 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.04/2.19 % [INFO] Problem is propositional (TPTP CNF).
% 3.11/2.20 % [INFO] Type checking passed.
% 3.11/2.20 % [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 ...
% 5.01/2.87 % External prover 'e' found a proof!
% 5.01/2.88 % [INFO] Killing All external provers ...
% 5.01/2.88 % Time passed: 2188ms (effective reasoning time: 1422ms)
% 5.01/2.88 % Axioms used in derivation (7): cls_Set_OsubsetI_1, cls_Set_OsubsetI_0, cls_Set_OIntE_1, cls_Set_OIntI_0, cls_Set_OIntE_0, cls_Set_OsubsetD_0, cls_Set_Osubset__antisym_0
% 5.01/2.88 % No. of inferences in proof: 27
% 5.01/2.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2188 ms resp. 1422 ms w/o parsing
% 5.58/2.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.58/2.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------