%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET821-2 : 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 : n026.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 08:30:59 AM UTC 2026
% Result : Unsatisfiable 5.21s 8.16s
% Output : Refutation 5.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of formulae : 21 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 37 ( 2 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 154 ( 14 ~; 16 |; 0 &; 124 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_less_decl,type,
c_less: $i > $i > $i > $o ).
thf(v_a_decl,type,
v_a: $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(tc_IntDef_Oint_decl,type,
tc_IntDef_Oint: $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_uminus_decl,type,
c_uminus: $i > $i > $i ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertE_0) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_insert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_0) ).
thf(21,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_insert ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( v_a @ c_in ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( v_b @ c_in ) ) )
| ( tc_IntDef_Oint @ ( A @ ( v_c @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(13,plain,
! [A: $i] :
( ( tc_IntDef_Oint @ ( A @ ( v_a @ c_in ) ) )
| ~ ( tc_IntDef_Oint @ ( A @ ( v_b @ c_in ) ) )
| ( tc_IntDef_Oint @ ( A @ ( v_c @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplD__dest_0) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,axiom,
tc_IntDef_Oint @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
thf(27,plain,
tc_IntDef_Oint @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(2,negated_conjecture,
tc_IntDef_Oint @ ( v_c @ ( v_b @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(12,plain,
tc_IntDef_Oint @ ( v_c @ ( v_b @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1,negated_conjecture,
tc_IntDef_Oint @ ( v_b @ ( v_a @ c_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(11,plain,
tc_IntDef_Oint @ ( v_b @ ( v_a @ c_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OinsertCI_1) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_insert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OComplI_0) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_set @ ( B @ c_uminus ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl__iff1_0) ).
thf(15,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_less ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
$false,
inference(e,[status(thm)],[24,21,13,17,27,12,11,23,19,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET821-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.09 % 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
% 0.19/5.45 % Computer : n026.cluster.edu
% 0.19/5.45 % Model : x86_64 x86_64
% 0.19/5.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.45 % Memory : 8046.5625MB
% 0.19/5.45 % OS : Linux 6.8.0-71-generic
% 0.19/5.45 % CPULimit : 300
% 0.19/5.45 % WCLimit : 300
% 0.19/5.45 % DateTime : Sat Sep 26 08:21:32 UTC 2026
% 0.19/5.45 % CPUTime :
% 0.19/5.45 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
% 1.28/6.29 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.81/6.56 % [INFO] Parsing done (263ms).
% 1.81/6.58 % [INFO] Running in sequential loop mode.
% 2.93/7.19 % [INFO] eprover registered as external prover.
% 3.04/7.20 % [INFO] Scanning for conjecture ...
% 3.21/7.34 % [INFO] Found a conjecture (or negated_conjecture) and 7 axioms. Running axiom selection ...
% 3.21/7.40 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 3.37/7.42 % [INFO] Problem is propositional (TPTP CNF).
% 3.37/7.43 % [INFO] Type checking passed.
% 3.37/7.43 % [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 ...
% 5.21/8.15 % External prover 'e' found a proof!
% 5.21/8.15 % [INFO] Killing All external provers ...
% 5.21/8.16 % Time passed: 2507ms (effective reasoning time: 1567ms)
% 5.21/8.16 % Axioms used in derivation (7): cls_Set_OComplI_0, cls_Set_OinsertCI_0, cls_Set_OinsertE_0, cls_Set_OComplD__dest_0, clsarity_IntDef__Oint_31, cls_Orderings_Oorder__less__irrefl__iff1_0, cls_Set_OinsertCI_1
% 5.21/8.16 % No. of inferences in proof: 21
% 5.21/8.16 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2507 ms resp. 1567 ms w/o parsing
% 5.32/8.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.32/8.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------