%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV251-2 : 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 : n014.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 08:58:33 AM UTC 2026
% Result : Unsatisfiable 3.97s 1.71s
% Output : Refutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of formulae : 27 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 47 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 290 ( 22 ~; 20 |; 0 &; 248 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 66 ( 0 ^; 66 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_minus_decl,type,
c_minus: $i > $i > $i > $i ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
tc_Message_Omsg @ ( v_G @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(14,plain,
tc_Message_Omsg @ ( v_G @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( C @ tc_set @ ( B @ ( A @ c_minus ) ) @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( A @ ( B @ c_minus ) ) @ ( A @ c_union ) ) )
= ( C @ ( B @ ( A @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,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(35,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)],[12]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__mono_0) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( B @ c_Message_Oanalz @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,negated_conjecture,
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz @ ( v_x @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(16,plain,
~ ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ c_Message_Oanalz @ ( v_x @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( D @ ( C @ ( B @ ( A @ c_union ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ tc_set @ ( B @ ( C @ ( D @ ( A @ c_insert ) ) @ c_minus ) ) )
= ( C @ tc_set @ ( B @ ( D @ c_minus ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ ( v_X @ c_insert ) ) @ c_Message_Oanalz @ ( v_x @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(15,plain,
tc_Message_Omsg @ ( tc_Message_Omsg @ ( v_H @ ( v_X @ c_insert ) ) @ c_Message_Oanalz @ ( v_x @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,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(33,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)],[11]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ tc_set @ ( B @ ( C @ ( A @ ( D @ c_union ) ) @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
thf(38,plain,
! [B: $i,A: $i] : ( B @ tc_set @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(112,plain,
$false,
inference(e,[status(thm)],[24,14,20,22,35,18,16,26,30,15,33,28,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV251-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % 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
% 0.14/0.42 % Computer : n014.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 13:22:48 UTC 2026
% 0.14/0.43 % CPUTime :
% 0.14/0.43 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
% 0.67/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.90/0.82 % [INFO] Parsing done (95ms).
% 0.90/0.83 % [INFO] Running in sequential loop mode.
% 1.15/1.01 % [INFO] eprover registered as external prover.
% 1.15/1.01 % [INFO] Scanning for conjecture ...
% 1.46/1.06 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 1.46/1.08 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.46/1.09 % [INFO] Problem is propositional (TPTP CNF).
% 1.46/1.09 % [INFO] Type checking passed.
% 1.46/1.10 % [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 ...
% 3.97/1.71 % External prover 'e' found a proof!
% 3.97/1.71 % [INFO] Killing All external provers ...
% 3.97/1.71 % Time passed: 1188ms (effective reasoning time: 883ms)
% 3.97/1.71 % Axioms used in derivation (10): cls_Set_Oinsert__Diff1_0, cls_Set_OUn__subset__iff_2, cls_Set_Osubset__refl_0, cls_Set_OUn__Diff__cancel2_0, cls_Set_OUn__subset__iff_0, cls_Message_Oanalz__mono_0, cls_Set_OUn__Diff__cancel_0, cls_Set_OUn__subset__iff_1, cls_Set_OsubsetD_0, cls_Set_Osubset__antisym_0
% 3.97/1.71 % No. of inferences in proof: 27
% 3.97/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1188 ms resp. 883 ms w/o parsing
% 3.97/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.97/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------