%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO498+1 : TPTP v9.3.1. Released v7.0.0.
% 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 07:13:25 AM UTC 2026
% Result : Theorem 5.46s 3.24s
% Output : Refutation 5.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of formulae : 18 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 19 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 114 ( 20 ~; 18 |; 0 &; 76 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 2 usr; 1 con; 0-3 aty)
% Number of variables : 48 ( 0 ^; 48 !; 0 ?; 48 :)
% Comments :
%------------------------------------------------------------------------------
thf(s_decl,type,
s: $i > $i > $i ).
thf(s_m_decl,type,
s_m: $i > $i > $i > $o ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_8) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( B = D )
| ( ( D @ ( A @ s ) )
!= C )
| ( ( B @ ( A @ s ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ s ) @ ( A @ s ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_7) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ s ) @ ( A @ s ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3b) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4b) ).
thf(26,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C = D )
| ~ ( D @ ( B @ ( A @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i] : ( A @ ( B @ s ) @ ( B @ ( A @ s_m ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_4a) ).
thf(32,plain,
! [A: $i,B: $i] : ( A @ ( B @ s ) @ ( B @ ( A @ s_m ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( B @ s ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_6) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( A @ ( B @ s ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_2) ).
thf(30,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ s_m ) ) )
| ~ ( C @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',aSatz7_3a) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( A @ s_m ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[10,37,22,26,32,34,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO498+1 : TPTP v9.3.1. Released v7.0.0.
% 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
% 0.22/0.48 % Computer : n026.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.49 % DateTime : Fri Sep 25 13:39:10 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.24/1.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.10/1.54 % [INFO] Parsing done (383ms).
% 2.10/1.56 % [INFO] Running in sequential loop mode.
% 3.25/2.12 % [INFO] eprover registered as external prover.
% 3.25/2.13 % [INFO] Scanning for conjecture ...
% 3.73/2.30 % [INFO] Found a conjecture (or negated_conjecture) and 109 axioms. Running axiom selection ...
% 3.73/2.38 % [INFO] Axiom selection finished. Selected 7 axioms (removed 102 axioms).
% 3.92/2.41 % [INFO] Problem is first-order (TPTP FOF).
% 3.92/2.42 % [INFO] Type checking passed.
% 3.92/2.42 % [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 ...
% 5.46/3.23 % External prover 'e' found a proof!
% 5.46/3.23 % [INFO] Killing All external provers ...
% 5.46/3.23 % Time passed: 2610ms (effective reasoning time: 1667ms)
% 5.46/3.23 % Solved by 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)>
% 5.46/3.24 % Axioms used in derivation (7): aSatz7_2, aSatz7_3b, aSatz7_7, aSatz7_4a, aSatz7_6, aSatz7_4b, aSatz7_3a
% 5.46/3.24 % No. of inferences in proof: 18
% 5.46/3.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2610 ms resp. 1667 ms w/o parsing
% 5.80/3.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.80/3.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------