%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% 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 : n001.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 08:10:07 AM UTC 2026
% Result : Theorem 3.72s 2.47s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 24 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 51 ( 36 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 161 ( 28 ~; 15 |; 4 &; 106 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 0 ^; 40 !; 18 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
thf(greater_decl,type,
greater: $i > $i > $o ).
thf(vd203_decl,type,
vd203: $i ).
thf(vd204_decl,type,
vd204: $i ).
thf(less_decl,type,
less: $i > $i > $o ).
thf(vplus_decl,type,
vplus: $i > $i > $i ).
thf(vsucc_decl,type,
vsucc: $i > $i ).
thf(v1_decl,type,
v1: $i ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( v1 @ ( A @ vplus ) )
= ( A @ vsucc ) )
& ( ( B @ vsucc @ ( A @ vplus ) )
= ( B @ ( A @ vplus ) @ vsucc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ greater ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
thf(28,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
=> ( A @ ( B @ greater ) ) )
& ( ( A @ ( B @ greater ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
( ~ ( vd204 @ ( vd203 @ less ) )
| ~ ( vd204 @ ( vd203 @ greater ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 1))') ).
thf(2,negated_conjecture,
~ ( ~ ( vd204 @ ( vd203 @ less ) )
| ~ ( vd204 @ ( vd203 @ greater ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ( ~ ( vd204 @ ( vd203 @ less ) )
| ~ ( vd204 @ ( vd203 @ greater ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
( ~ ( vd204 @ ( vd203 @ greater ) )
| ( vd203 != vd204 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','dis(ex(cond(conseq(131), 0), 0))') ).
thf(17,plain,
( ~ ( vd204 @ ( vd203 @ greater ) )
| ( vd203 != vd204 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
thf(39,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 2)') ).
thf(43,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 3)') ).
thf(47,plain,
! [A: $i,B: $i] :
( ~ ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ less ) )
<=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
thf(20,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
=> ( A @ ( B @ less ) ) )
& ( ( A @ ( B @ less ) )
=> ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ vplus ) @ vplus ) )
= ( C @ ( B @ vplus ) @ ( A @ vplus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
thf(36,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( B
= ( C @ ( A @ vplus ) ) )
| ? [C: $i] :
( A
= ( C @ ( B @ vplus ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
thf(51,plain,
! [A: $i,B: $i] :
( ( A != B )
=> ! [C: $i] :
( ( A @ ( C @ vplus ) )
!= ( B @ ( C @ vplus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[60,28,13,17,39,43,47,20,57,36,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM836+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % 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
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 04:16:42 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.43/1.21 % [INFO] Parsing done (209ms).
% 1.43/1.22 % [INFO] Running in sequential loop mode.
% 2.07/1.62 % [INFO] eprover registered as external prover.
% 2.07/1.63 % [INFO] Scanning for conjecture ...
% 2.23/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.23/1.75 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.23/1.79 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/1.80 % [INFO] Type checking passed.
% 2.41/1.81 % [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 ...
% 3.72/2.46 % External prover 'e' found a proof!
% 3.72/2.46 % [INFO] Killing All external provers ...
% 3.72/2.47 % Time passed: 1909ms (effective reasoning time: 1239ms)
% 3.72/2.47 % 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)>
% 3.72/2.47 % Axioms used in derivation (10): def(cond(conseq(axiom(3)), 11), 1), ass(cond(goal(88), 0), 1), ass(cond(goal(88), 0), 3), dis(ex(cond(conseq(131), 0), 0)), ass(cond(goal(88), 0), 2), qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), ass(cond(goal(88), 0), 0), ass(cond(33, 0), 0), def(cond(conseq(axiom(3)), 12), 1), ass(cond(81, 0), 0)
% 3.72/2.47 % No. of inferences in proof: 24
% 3.72/2.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1909 ms resp. 1239 ms w/o parsing
% 3.96/2.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.96/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------