%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN114-1 : 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 : n008.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 09:16:50 AM UTC 2026
% Result : Unsatisfiable 186.90s 94.77s
% Output : Refutation 187.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 14 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 435 ( 78 ~; 61 |; 0 &; 296 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 130 ( 0 ^; 130 !; 0 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(k3_decl,type,
k3: $i > $i > $i > $o ).
thf(b_decl,type,
b: $i ).
thf(m0_decl,type,
m0: $i > $i > $i > $o ).
thf(p0_decl,type,
p0: $i > $i > $o ).
thf(e_decl,type,
e: $i ).
thf(d_decl,type,
d: $i ).
thf(q1_decl,type,
q1: $i > $i > $i > $o ).
thf(q0_decl,type,
q0: $i > $i > $o ).
thf(p1_decl,type,
p1: $i > $i > $i > $o ).
thf(k2_decl,type,
k2: $i > $i > $o ).
thf(n2_decl,type,
n2: $i > $o ).
thf(282,axiom,
! [A: $i] :
( ~ ( A @ n2 )
| ( A @ ( A @ ( A @ k3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_210) ).
thf(904,plain,
! [A: $i] :
( ~ ( A @ n2 )
| ( A @ ( A @ ( A @ k3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(905,plain,
! [A: $i] :
( ~ ( A @ n2 )
| ( A @ ( A @ ( A @ k3 ) ) ) ),
inference(cnf,[status(esa)],[904]) ).
thf(287,axiom,
! [A: $i] : ( A @ ( b @ p0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(914,plain,
! [A: $i] : ( A @ ( b @ p0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(150,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p0 ) )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_085) ).
thf(655,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p0 ) )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(656,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p0 ) )
| ( A @ ( A @ ( A @ p1 ) ) ) ),
inference(cnf,[status(esa)],[655]) ).
thf(25702,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( C @ p0 ) ) )
| ~ $true
| ( B @ ( B @ ( B @ p1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[914,656]) ).
thf(25703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( b @ p0 ) )
!= ( B @ ( C @ p0 ) ) )
| ( B @ ( B @ ( B @ p1 ) ) ) ),
inference(simp,[status(thm)],[25702]) ).
thf(25704,plain,
! [A: $i] : ( A @ ( A @ ( A @ p1 ) ) ),
inference(pattern_uni,[status(thm)],[25703:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( b ))]]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ p1 ) ) )
| ( A @ n2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_137) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ p1 ) ) )
| ( A @ n2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ p1 ) ) )
| ( A @ n2 ) ),
inference(cnf,[status(esa)],[537]) ).
thf(25725,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ p1 ) ) )
!= ( B @ ( D @ ( C @ p1 ) ) ) )
| ~ $true
| ( B @ n2 ) ),
inference(paramod_ordered,[status(thm)],[25704,538]) ).
thf(25726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ p1 ) ) )
!= ( B @ ( D @ ( C @ p1 ) ) ) )
| ( B @ n2 ) ),
inference(simp,[status(thm)],[25725]) ).
thf(25727,plain,
! [A: $i] : ( A @ n2 ),
inference(pattern_uni,[status(thm)],[25726:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(41592,plain,
! [A: $i] :
( ~ $true
| ( A @ ( A @ ( A @ k3 ) ) ) ),
inference(rewrite,[status(thm)],[905,25727]) ).
thf(41593,plain,
! [A: $i] : ( A @ ( A @ ( A @ k3 ) ) ),
inference(simp,[status(thm)],[41592]) ).
thf(278,axiom,
b @ ( d @ q0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(898,plain,
b @ ( d @ q0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(158,axiom,
! [A: $i] :
( ~ ( A @ ( d @ ( e @ m0 ) ) )
| ~ ( A @ ( d @ ( A @ m0 ) ) )
| ( A @ ( A @ ( e @ q1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_107) ).
thf(671,plain,
! [A: $i] :
( ~ ( A @ ( d @ ( e @ m0 ) ) )
| ~ ( A @ ( d @ ( A @ m0 ) ) )
| ( A @ ( A @ ( e @ q1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(672,plain,
! [A: $i] :
( ~ ( A @ ( d @ ( e @ m0 ) ) )
| ~ ( A @ ( d @ ( A @ m0 ) ) )
| ( A @ ( A @ ( e @ q1 ) ) ) ),
inference(cnf,[status(esa)],[671]) ).
thf(181,axiom,
! [B: $i,A: $i] : ( B @ ( d @ ( A @ m0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(716,plain,
! [B: $i,A: $i] : ( B @ ( d @ ( A @ m0 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(26997,plain,
! [A: $i] :
( ~ $true
| ~ $true
| ( A @ ( A @ ( e @ q1 ) ) ) ),
inference(rewrite,[status(thm)],[672,716]) ).
thf(26998,plain,
! [A: $i] : ( A @ ( A @ ( e @ q1 ) ) ),
inference(simp,[status(thm)],[26997]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ q1 ) ) )
| ( A @ ( A @ k2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_129) ).
thf(821,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ q1 ) ) )
| ( A @ ( A @ k2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(822,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ q1 ) ) )
| ( A @ ( A @ k2 ) ) ),
inference(cnf,[status(esa)],[821]) ).
thf(36406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( e @ q1 ) ) )
!= ( B @ ( B @ ( C @ q1 ) ) ) )
| ~ $true
| ( B @ ( B @ k2 ) ) ),
inference(paramod_ordered,[status(thm)],[26998,822]) ).
thf(36407,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( e @ q1 ) ) )
!= ( B @ ( B @ ( C @ q1 ) ) ) )
| ( B @ ( B @ k2 ) ) ),
inference(simp,[status(thm)],[36406]) ).
thf(36408,plain,
! [A: $i] : ( A @ ( A @ k2 ) ),
inference(pattern_uni,[status(thm)],[36407:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( e ))]]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ k3 ) ) )
| ~ ( D @ ( A @ k2 ) )
| ~ ( B @ ( C @ q0 ) )
| ( B @ ( A @ ( A @ k3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_202) ).
thf(876,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ k3 ) ) )
| ~ ( D @ ( A @ k2 ) )
| ~ ( B @ ( C @ q0 ) )
| ( B @ ( A @ ( A @ k3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ k3 ) ) )
| ~ ( D @ ( A @ k2 ) )
| ~ ( B @ ( C @ q0 ) )
| ( B @ ( A @ ( A @ k3 ) ) ) ),
inference(cnf,[status(esa)],[876]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( b @ ( A @ ( A @ k3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(370,plain,
! [A: $i] :
~ ( b @ ( A @ ( A @ k3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(371,plain,
! [A: $i] :
~ ( b @ ( A @ ( A @ k3 ) ) ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(40384,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ k3 ) ) )
!= ( b @ ( F @ ( F @ k3 ) ) ) )
| ~ $true
| ~ ( D @ ( E @ ( B @ k3 ) ) )
| ~ ( D @ ( A @ k2 ) )
| ~ ( B @ ( C @ q0 ) ) ),
inference(paramod_ordered,[status(thm)],[877,371]) ).
thf(40385,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ k3 ) ) )
!= ( b @ ( F @ ( F @ k3 ) ) ) )
| ~ ( D @ ( E @ ( B @ k3 ) ) )
| ~ ( D @ ( A @ k2 ) )
| ~ ( B @ ( C @ q0 ) ) ),
inference(simp,[status(thm)],[40384]) ).
thf(40386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( b @ k3 ) ) )
| ~ ( C @ ( A @ k2 ) )
| ~ ( b @ ( B @ q0 ) ) ),
inference(pattern_uni,[status(thm)],[40385:[bind(A,$thf( A )),bind(B,$thf( b )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( E )),bind(F,$thf( A ))]]) ).
thf(40396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( b @ k3 ) ) )
| ~ ( C @ ( A @ k2 ) )
| ~ ( b @ ( B @ q0 ) ) ),
inference(simp,[status(thm)],[40386]) ).
thf(40444,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2 ) )
!= ( D @ ( B @ k2 ) ) )
| ~ ( D @ ( E @ ( b @ k3 ) ) )
| ~ $true
| ~ ( b @ ( C @ q0 ) ) ),
inference(paramod_ordered,[status(thm)],[36408,40396]) ).
thf(40445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ k2 ) )
!= ( D @ ( B @ k2 ) ) )
| ~ ( D @ ( E @ ( b @ k3 ) ) )
| ~ ( b @ ( C @ q0 ) ) ),
inference(simp,[status(thm)],[40444]) ).
thf(40446,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( b @ k3 ) ) )
| ~ ( b @ ( B @ q0 ) ) ),
inference(pattern_uni,[status(thm)],[40445:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( A ))]]) ).
thf(40465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( b @ k3 ) ) )
| ~ ( b @ ( B @ q0 ) ) ),
inference(simp,[status(thm)],[40446]) ).
thf(40479,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( d @ q0 ) )
!= ( b @ ( B @ q0 ) ) )
| ~ ( A @ ( C @ ( b @ k3 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[898,40465]) ).
thf(40480,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( d @ q0 ) )
!= ( b @ ( B @ q0 ) ) )
| ~ ( A @ ( C @ ( b @ k3 ) ) ) ),
inference(simp,[status(thm)],[40479]) ).
thf(40481,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( b @ k3 ) ) ),
inference(pattern_uni,[status(thm)],[40480:[bind(A,$thf( A )),bind(B,$thf( d ))]]) ).
thf(40502,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( b @ k3 ) ) ),
inference(simp,[status(thm)],[40481]) ).
thf(41596,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ k3 ) ) )
!= ( B @ ( C @ ( b @ k3 ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[41593,40502]) ).
thf(41597,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ k3 ) ) )
!= ( B @ ( C @ ( b @ k3 ) ) ) ),
inference(simp,[status(thm)],[41596]) ).
thf(41598,plain,
$false,
inference(pattern_uni,[status(thm)],[41597:[bind(A,$thf( b )),bind(B,$thf( b )),bind(C,$thf( b ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN114-1 : TPTP v9.3.1. Released v1.1.0.
% 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
% 0.24/5.53 % Computer : n008.cluster.edu
% 0.24/5.53 % Model : x86_64 x86_64
% 0.24/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/5.53 % Memory : 8046.5625MB
% 0.24/5.53 % OS : Linux 6.8.0-71-generic
% 0.24/5.53 % CPULimit : 300
% 0.24/5.53 % WCLimit : 300
% 0.24/5.53 % DateTime : Sat Sep 26 17:13:15 UTC 2026
% 0.24/5.54 % CPUTime :
% 0.24/5.54 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
% 1.32/6.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.39/6.86 % [INFO] Parsing done (457ms).
% 2.39/6.87 % [INFO] Running in sequential loop mode.
% 3.16/7.15 % [INFO] eprover registered as external prover.
% 3.47/7.16 % [INFO] Scanning for conjecture ...
% 3.63/7.29 % [INFO] Found a conjecture (or negated_conjecture) and 368 axioms. Running axiom selection ...
% 4.32/7.45 % [INFO] Axiom selection finished. Selected 368 axioms (removed 0 axioms).
% 5.30/7.66 % [INFO] Problem is propositional (TPTP CNF).
% 5.30/7.67 % [INFO] Type checking passed.
% 5.30/7.68 % [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 ...
% 186.90/94.76 % [INFO] Killing All external provers ...
% 186.90/94.77 % Time passed: 89015ms (effective reasoning time: 87891ms)
% 186.90/94.77 % Axioms used in derivation (9): rule_085, axiom_19, rule_210, rule_129, rule_137, rule_107, rule_202, axiom_29, axiom_14
% 186.90/94.77 % No. of inferences in proof: 55
% 186.90/94.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 89015 ms resp. 87891 ms w/o parsing
% 187.24/94.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 187.24/94.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------