%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN148-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 09:16:53 AM UTC 2026
% Result : Unsatisfiable 203.71s 119.70s
% Output : Refutation 203.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 8 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 281 ( 61 ~; 48 |; 0 &; 172 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 49 ( 0 ^; 49 !; 0 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(n1_decl,type,
n1: $i > $i > $i > $o ).
thf(c_decl,type,
c: $i ).
thf(d_decl,type,
d: $i ).
thf(p0_decl,type,
p0: $i > $i > $o ).
thf(n0_decl,type,
n0: $i > $i > $o ).
thf(l0_decl,type,
l0: $i > $o ).
thf(s0_decl,type,
s0: $i > $o ).
thf(b_decl,type,
b: $i ).
thf(l1_decl,type,
l1: $i > $i > $o ).
thf(253,axiom,
c @ ( d @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(853,plain,
c @ ( d @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ n0 ) )
| ( A @ ( A @ l1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_002) ).
thf(446,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ n0 ) )
| ( A @ ( A @ l1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(447,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ n0 ) )
| ( A @ ( A @ l1 ) ) ),
inference(cnf,[status(esa)],[446]) ).
thf(4985,plain,
! [B: $i,A: $i] :
( ( ( c @ ( d @ n0 ) )
!= ( A @ ( B @ n0 ) ) )
| ~ $true
| ( A @ ( A @ l1 ) ) ),
inference(paramod_ordered,[status(thm)],[853,447]) ).
thf(4986,plain,
! [B: $i,A: $i] :
( ( ( c @ ( d @ n0 ) )
!= ( A @ ( B @ n0 ) ) )
| ( A @ ( A @ l1 ) ) ),
inference(simp,[status(thm)],[4985]) ).
thf(4987,plain,
c @ ( c @ l1 ),
inference(pattern_uni,[status(thm)],[4986:[bind(A,$thf( c )),bind(B,$thf( d ))]]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ n1 ) ) )
| ~ ( A @ ( C @ l1 ) )
| ~ ( C @ l0 )
| ( B @ ( B @ ( A @ n1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_054) ).
thf(1061,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ n1 ) ) )
| ~ ( A @ ( C @ l1 ) )
| ~ ( C @ l0 )
| ( B @ ( B @ ( A @ n1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(1062,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ n1 ) ) )
| ~ ( A @ ( C @ l1 ) )
| ~ ( C @ l0 )
| ( B @ ( B @ ( A @ n1 ) ) ) ),
inference(cnf,[status(esa)],[1061]) ).
thf(1,negated_conjecture,
~ ( d @ ( d @ ( c @ n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(370,plain,
~ ( d @ ( d @ ( c @ n1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(371,plain,
~ ( d @ ( d @ ( c @ n1 ) ) ),
inference(polarity_switch,[status(thm)],[370]) ).
thf(59469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ n1 ) ) )
!= ( d @ ( d @ ( c @ n1 ) ) ) )
| ~ $true
| ~ ( A @ ( B @ ( A @ n1 ) ) )
| ~ ( A @ ( C @ l1 ) )
| ~ ( C @ l0 ) ),
inference(paramod_ordered,[status(thm)],[1062,371]) ).
thf(59470,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ n1 ) ) )
!= ( d @ ( d @ ( c @ n1 ) ) ) )
| ~ ( A @ ( B @ ( A @ n1 ) ) )
| ~ ( A @ ( C @ l1 ) )
| ~ ( C @ l0 ) ),
inference(simp,[status(thm)],[59469]) ).
thf(59471,plain,
! [A: $i] :
( ~ ( c @ ( d @ ( c @ n1 ) ) )
| ~ ( c @ ( A @ l1 ) )
| ~ ( A @ l0 ) ),
inference(pattern_uni,[status(thm)],[59470:[bind(A,$thf( c )),bind(B,$thf( d ))]]) ).
thf(59642,plain,
! [A: $i] :
( ~ ( c @ ( d @ ( c @ n1 ) ) )
| ~ ( c @ ( A @ l1 ) )
| ~ ( A @ l0 ) ),
inference(simp,[status(thm)],[59471]) ).
thf(263,axiom,
c @ l0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(870,plain,
c @ l0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( b @ p0 ) )
| ~ ( A @ l0 )
| ~ ( b @ s0 )
| ( A @ ( B @ ( A @ n1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_050) ).
thf(887,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( b @ p0 ) )
| ~ ( A @ l0 )
| ~ ( b @ s0 )
| ( A @ ( B @ ( A @ n1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(888,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( b @ p0 ) )
| ~ ( A @ l0 )
| ~ ( b @ s0 )
| ( A @ ( B @ ( A @ n1 ) ) ) ),
inference(cnf,[status(esa)],[887]) ).
thf(60,axiom,
! [A: $i] : ( A @ ( b @ p0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(483,plain,
! [A: $i] : ( A @ ( b @ p0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(46,axiom,
b @ s0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(456,plain,
b @ s0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(43049,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( A @ l0 )
| ~ $true
| ( A @ ( B @ ( A @ n1 ) ) ) ),
inference(rewrite,[status(thm)],[888,483,456]) ).
thf(43050,plain,
! [B: $i,A: $i] :
( ~ ( A @ l0 )
| ( A @ ( B @ ( A @ n1 ) ) ) ),
inference(simp,[status(thm)],[43049]) ).
thf(43054,plain,
! [B: $i,A: $i] :
( ( ( c @ l0 )
!= ( A @ l0 ) )
| ~ $true
| ( A @ ( B @ ( A @ n1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[870,43050]) ).
thf(43055,plain,
! [B: $i,A: $i] :
( ( ( c @ l0 )
!= ( A @ l0 ) )
| ( A @ ( B @ ( A @ n1 ) ) ) ),
inference(simp,[status(thm)],[43054]) ).
thf(43056,plain,
! [A: $i] : ( c @ ( A @ ( c @ n1 ) ) ),
inference(pattern_uni,[status(thm)],[43055:[bind(A,$thf( c ))]]) ).
thf(43081,plain,
! [A: $i] : ( c @ ( A @ ( c @ n1 ) ) ),
inference(simp,[status(thm)],[43056]) ).
thf(59672,plain,
! [A: $i] :
( ~ $true
| ~ ( c @ ( A @ l1 ) )
| ~ ( A @ l0 ) ),
inference(rewrite,[status(thm)],[59642,43081]) ).
thf(59673,plain,
! [A: $i] :
( ~ ( c @ ( A @ l1 ) )
| ~ ( A @ l0 ) ),
inference(simp,[status(thm)],[59672]) ).
thf(59694,plain,
! [A: $i] :
( ( ( c @ ( c @ l1 ) )
!= ( c @ ( A @ l1 ) ) )
| ~ $true
| ~ ( A @ l0 ) ),
inference(paramod_ordered,[status(thm)],[4987,59673]) ).
thf(59695,plain,
! [A: $i] :
( ( ( c @ ( c @ l1 ) )
!= ( c @ ( A @ l1 ) ) )
| ~ ( A @ l0 ) ),
inference(simp,[status(thm)],[59694]) ).
thf(59696,plain,
~ ( c @ l0 ),
inference(pattern_uni,[status(thm)],[59695:[bind(A,$thf( c ))]]) ).
thf(59707,plain,
~ $true,
inference(rewrite,[status(thm)],[59696,870]) ).
thf(59708,plain,
$false,
inference(simp,[status(thm)],[59707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN148-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.40 % Computer : n018.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 17:17:51 UTC 2026
% 0.15/0.40 % CPUTime :
% 0.15/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.49/1.29 % [INFO] Parsing done (306ms).
% 1.98/1.31 % [INFO] Running in sequential loop mode.
% 2.50/1.69 % [INFO] eprover registered as external prover.
% 2.69/1.70 % [INFO] Scanning for conjecture ...
% 2.94/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 368 axioms. Running axiom selection ...
% 3.17/1.99 % [INFO] Axiom selection finished. Selected 368 axioms (removed 0 axioms).
% 4.11/2.19 % [INFO] Problem is propositional (TPTP CNF).
% 4.27/2.20 % [INFO] Type checking passed.
% 4.27/2.21 % [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 ...
% 203.61/119.70 % [INFO] Killing All external provers ...
% 203.71/119.70 % Time passed: 119148ms (effective reasoning time: 118387ms)
% 203.71/119.70 % Axioms used in derivation (7): axiom_26, axiom_24, rule_002, rule_054, axiom_5, axiom_14, rule_050
% 203.71/119.70 % No. of inferences in proof: 40
% 203.71/119.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 119148 ms resp. 118387 ms w/o parsing
% 203.71/119.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 203.71/119.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------