%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN236-1 : TPTP v9.3.1. Released v1.1.0.
% 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 : n009.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 09:17:02 AM UTC 2026
% Result : Unsatisfiable 192.62s 99.57s
% Output : Refutation 192.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 56 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 14 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 348 ( 64 ~; 60 |; 0 &; 224 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 59 ( 0 ^; 59 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
thf(l3_decl,type,
l3: $i > $i > $o ).
thf(e_decl,type,
e: $i ).
thf(d_decl,type,
d: $i ).
thf(s1_decl,type,
s1: $i > $o ).
thf(p0_decl,type,
p0: $i > $i > $o ).
thf(s2_decl,type,
s2: $i > $o ).
thf(q2_decl,type,
q2: $i > $i > $i > $o ).
thf(p1_decl,type,
p1: $i > $i > $i > $o ).
thf(s0_decl,type,
s0: $i > $o ).
thf(b_decl,type,
b: $i ).
thf(n0_decl,type,
n0: $i > $i > $o ).
thf(l1_decl,type,
l1: $i > $i > $o ).
thf(60,axiom,
b @ s0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(481,plain,
b @ s0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ~ ( A @ s0 )
| ~ ( B @ s0 )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_072) ).
thf(402,plain,
! [B: $i,A: $i] :
( ~ ( A @ s0 )
| ~ ( B @ s0 )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(403,plain,
! [B: $i,A: $i] :
( ~ ( A @ s0 )
| ~ ( B @ s0 )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
inference(cnf,[status(esa)],[402]) ).
thf(2336,plain,
! [B: $i,A: $i] :
( ( ( b @ s0 )
!= ( A @ s0 ) )
| ~ $true
| ~ ( B @ s0 )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[481,403]) ).
thf(2337,plain,
! [B: $i,A: $i] :
( ( ( b @ s0 )
!= ( A @ s0 ) )
| ~ ( B @ s0 )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
inference(simp,[status(thm)],[2336]) ).
thf(2338,plain,
! [A: $i] :
( ~ ( A @ s0 )
| ( b @ ( b @ ( b @ p1 ) ) ) ),
inference(pattern_uni,[status(thm)],[2337:[bind(A,$thf( b ))]]) ).
thf(2356,plain,
! [A: $i] :
( ~ ( A @ s0 )
| ( b @ ( b @ ( b @ p1 ) ) ) ),
inference(simp,[status(thm)],[2338]) ).
thf(2388,plain,
! [A: $i] :
( ( ( b @ s0 )
!= ( A @ s0 ) )
| ~ $true
| ( b @ ( b @ ( b @ p1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[481,2356]) ).
thf(2389,plain,
! [A: $i] :
( ( ( b @ s0 )
!= ( A @ s0 ) )
| ( b @ ( b @ ( b @ p1 ) ) ) ),
inference(simp,[status(thm)],[2388]) ).
thf(2390,plain,
b @ ( b @ ( b @ p1 ) ),
inference(pattern_uni,[status(thm)],[2389:[bind(A,$thf( b ))]]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ p1 ) ) )
| ( A @ ( A @ ( A @ q2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_181) ).
thf(396,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ p1 ) ) )
| ( A @ ( A @ ( A @ q2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(397,plain,
! [A: $i] :
( ~ ( A @ ( A @ ( A @ p1 ) ) )
| ( A @ ( A @ ( A @ q2 ) ) ) ),
inference(cnf,[status(esa)],[396]) ).
thf(2405,plain,
! [A: $i] :
( ( ( b @ ( b @ ( b @ p1 ) ) )
!= ( A @ ( A @ ( A @ p1 ) ) ) )
| ~ $true
| ( A @ ( A @ ( A @ q2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[2390,397]) ).
thf(2406,plain,
! [A: $i] :
( ( ( b @ ( b @ ( b @ p1 ) ) )
!= ( A @ ( A @ ( A @ p1 ) ) ) )
| ( A @ ( A @ ( A @ q2 ) ) ) ),
inference(simp,[status(thm)],[2405]) ).
thf(2407,plain,
b @ ( b @ ( b @ q2 ) ),
inference(pattern_uni,[status(thm)],[2406:[bind(A,$thf( b ))]]) ).
thf(112,axiom,
! [A: $i] :
( ~ ( b @ s1 )
| ~ ( b @ ( A @ ( b @ q2 ) ) )
| ( A @ s2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_189) ).
thf(580,plain,
! [A: $i] :
( ~ ( b @ s1 )
| ~ ( b @ ( A @ ( b @ q2 ) ) )
| ( A @ s2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(581,plain,
! [A: $i] :
( ~ ( b @ s1 )
| ~ ( b @ ( A @ ( b @ q2 ) ) )
| ( A @ s2 ) ),
inference(cnf,[status(esa)],[580]) ).
thf(78,axiom,
! [A: $i] : ( A @ ( b @ p0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(515,plain,
! [A: $i] : ( A @ ( b @ p0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(9,axiom,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( A @ s1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_125) ).
thf(386,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( A @ s1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(387,plain,
! [A: $i] :
( ~ ( A @ ( A @ p0 ) )
| ( A @ s1 ) ),
inference(cnf,[status(esa)],[386]) ).
thf(1395,plain,
! [B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( B @ p0 ) ) )
| ~ $true
| ( B @ s1 ) ),
inference(paramod_ordered,[status(thm)],[515,387]) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( B @ p0 ) ) )
| ( B @ s1 ) ),
inference(simp,[status(thm)],[1395]) ).
thf(1397,plain,
b @ s1,
inference(pattern_uni,[status(thm)],[1396:[bind(A,$thf( b )),bind(B,$thf( b ))]]) ).
thf(24801,plain,
! [A: $i] :
( ~ $true
| ~ ( b @ ( A @ ( b @ q2 ) ) )
| ( A @ s2 ) ),
inference(rewrite,[status(thm)],[581,1397]) ).
thf(24802,plain,
! [A: $i] :
( ~ ( b @ ( A @ ( b @ q2 ) ) )
| ( A @ s2 ) ),
inference(simp,[status(thm)],[24801]) ).
thf(24835,plain,
! [A: $i] :
( ( ( b @ ( b @ ( b @ q2 ) ) )
!= ( b @ ( A @ ( b @ q2 ) ) ) )
| ~ $true
| ( A @ s2 ) ),
inference(paramod_ordered,[status(thm)],[2407,24802]) ).
thf(24836,plain,
! [A: $i] :
( ( ( b @ ( b @ ( b @ q2 ) ) )
!= ( b @ ( A @ ( b @ q2 ) ) ) )
| ( A @ s2 ) ),
inference(simp,[status(thm)],[24835]) ).
thf(24837,plain,
b @ s2,
inference(pattern_uni,[status(thm)],[24836:[bind(A,$thf( b ))]]) ).
thf(306,axiom,
e @ ( d @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(952,plain,
e @ ( d @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ n0 ) )
| ( A @ ( A @ l1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_002) ).
thf(468,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ n0 ) )
| ( A @ ( A @ l1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(469,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ n0 ) )
| ( A @ ( A @ l1 ) ) ),
inference(cnf,[status(esa)],[468]) ).
thf(12589,plain,
! [B: $i,A: $i] :
( ( ( e @ ( d @ n0 ) )
!= ( A @ ( B @ n0 ) ) )
| ~ $true
| ( A @ ( A @ l1 ) ) ),
inference(paramod_ordered,[status(thm)],[952,469]) ).
thf(12590,plain,
! [B: $i,A: $i] :
( ( ( e @ ( d @ n0 ) )
!= ( A @ ( B @ n0 ) ) )
| ( A @ ( A @ l1 ) ) ),
inference(simp,[status(thm)],[12589]) ).
thf(12591,plain,
e @ ( e @ l1 ),
inference(pattern_uni,[status(thm)],[12590:[bind(A,$thf( e )),bind(B,$thf( d ))]]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ l1 ) )
| ~ ( B @ s2 )
| ( A @ ( A @ l3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_220) ).
thf(934,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ l1 ) )
| ~ ( B @ s2 )
| ( A @ ( A @ l3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(935,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ l1 ) )
| ~ ( B @ s2 )
| ( A @ ( A @ l3 ) ) ),
inference(cnf,[status(esa)],[934]) ).
thf(50062,plain,
! [B: $i,A: $i] :
( ( ( e @ ( e @ l1 ) )
!= ( A @ ( A @ l1 ) ) )
| ~ $true
| ~ ( B @ s2 )
| ( A @ ( A @ l3 ) ) ),
inference(paramod_ordered,[status(thm)],[12591,935]) ).
thf(50063,plain,
! [B: $i,A: $i] :
( ( ( e @ ( e @ l1 ) )
!= ( A @ ( A @ l1 ) ) )
| ~ ( B @ s2 )
| ( A @ ( A @ l3 ) ) ),
inference(simp,[status(thm)],[50062]) ).
thf(50064,plain,
! [A: $i] :
( ~ ( A @ s2 )
| ( e @ ( e @ l3 ) ) ),
inference(pattern_uni,[status(thm)],[50063:[bind(A,$thf( e ))]]) ).
thf(50095,plain,
! [A: $i] :
( ~ ( A @ s2 )
| ( e @ ( e @ l3 ) ) ),
inference(simp,[status(thm)],[50064]) ).
thf(1,negated_conjecture,
~ ( e @ ( e @ l3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(370,plain,
~ ( e @ ( e @ l3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(371,plain,
~ ( e @ ( e @ l3 ) ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(50145,plain,
! [A: $i] :
( ~ ( A @ s2 )
| $false ),
inference(rewrite,[status(thm)],[50095,371]) ).
thf(50146,plain,
! [A: $i] :
~ ( A @ s2 ),
inference(simp,[status(thm)],[50145]) ).
thf(50155,plain,
$false,
inference(rewrite,[status(thm)],[24837,50146]) ).
thf(50156,plain,
$false,
inference(simp,[status(thm)],[50155]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN236-1 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.14/0.40 % Computer : n009.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 17:25:01 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.93/1.30 % [INFO] Parsing done (315ms).
% 1.93/1.31 % [INFO] Running in sequential loop mode.
% 2.90/1.71 % [INFO] eprover registered as external prover.
% 2.90/1.71 % [INFO] Scanning for conjecture ...
% 3.09/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 368 axioms. Running axiom selection ...
% 3.29/2.01 % [INFO] Axiom selection finished. Selected 368 axioms (removed 0 axioms).
% 4.25/2.20 % [INFO] Problem is propositional (TPTP CNF).
% 4.25/2.22 % [INFO] Type checking passed.
% 4.25/2.22 % [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 ...
% 192.62/99.56 % [INFO] Killing All external provers ...
% 192.62/99.56 % Time passed: 99017ms (effective reasoning time: 98242ms)
% 192.62/99.56 % Axioms used in derivation (9): rule_220, rule_125, axiom_3, rule_002, rule_189, rule_181, axiom_5, axiom_14, rule_072
% 192.62/99.56 % No. of inferences in proof: 56
% 192.62/99.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 99017 ms resp. 98242 ms w/o parsing
% 192.62/99.58 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 192.62/99.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------