%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN563-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n007.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 09:17:51 AM UTC 2026
% Result : Unsatisfiable 3.80s 1.87s
% Output : Refutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 20
% Syntax : Number of formulae : 41 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 41 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 352 ( 2 ~; 0 |; 0 &; 350 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(p2_decl,type,
p2: $i > $i > $i ).
thf(true_decl,type,
true: $i ).
thf(p6_decl,type,
p6: $i > $i > $i ).
thf(f4_decl,type,
f4: $i > $i ).
thf(c7_decl,type,
c7: $i ).
thf(c8_decl,type,
c8: $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(p5_decl,type,
p5: $i > $i > $i ).
thf(f3_decl,type,
f3: $i > $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(17,negated_conjecture,
( ( b @ ( a @ ( true @ ( c8 @ f4 @ f3 @ ( c7 @ f4 @ p6 ) @ ifeq ) ) ) )
= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p6_5) ).
thf(29,plain,
( ( b @ ( a @ ( true @ ( c8 @ f4 @ f3 @ ( c7 @ f4 @ p6 ) @ ifeq ) ) ) )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ p2 ) @ ( true @ ( C @ ( A @ p2 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_13) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ p2 ) @ ( true @ ( C @ ( A @ p2 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ( true @ ( A @ f3 @ ( c7 @ p6 ) @ ( true @ ( A @ ( c7 @ p6 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_9) ).
thf(31,plain,
! [A: $i] :
( ( true @ ( A @ f3 @ ( c7 @ p6 ) @ ( true @ ( A @ ( c7 @ p6 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ p2 ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( A @ p2 ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(4,negated_conjecture,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ p6 ) @ ( true @ ( B @ ( A @ p5 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_6) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ p6 ) @ ( true @ ( B @ ( A @ p5 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,negated_conjecture,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ p5 ) @ ( true @ ( B @ ( A @ f4 @ p6 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_8) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ p5 ) @ ( true @ ( B @ ( A @ f4 @ p6 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,negated_conjecture,
! [A: $i] :
( ( A @ f4 @ f3 @ ( A @ f3 @ f3 @ p5 ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_7) ).
thf(21,plain,
! [A: $i] :
( ( A @ f4 @ f3 @ ( A @ f3 @ f3 @ p5 ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,negated_conjecture,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
thf(33,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ p6 ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_2) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ p6 ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( D @ ( B @ p5 ) @ ( true @ ( C @ ( A @ p5 ) @ ifeq2 ) ) ) @ ( true @ ( D @ ( C @ p2 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_17) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( D @ ( B @ p5 ) @ ( true @ ( C @ ( A @ p5 ) @ ifeq2 ) ) ) @ ( true @ ( D @ ( C @ p2 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(3,negated_conjecture,
( ( c8 @ f4 @ ( c7 @ f4 @ p2 ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
thf(32,plain,
( ( c8 @ f4 @ ( c7 @ f4 @ p2 ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,negated_conjecture,
( ( b @ ( a @ ( true @ ( c8 @ ( c7 @ f4 @ p6 ) @ ifeq ) ) ) )
= b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p6_3) ).
thf(34,plain,
( ( b @ ( a @ ( true @ ( c8 @ ( c7 @ f4 @ p6 ) @ ifeq ) ) ) )
= b ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,negated_conjecture,
! [B: $i,A: $i] :
( ( true @ ( B @ f4 @ ( A @ f4 @ p2 ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ f4 @ ( A @ f4 @ p2 ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( A @ p5 ) @ ( true @ ( C @ ( B @ p5 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p6 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_15) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( C @ ( A @ p5 ) @ ( true @ ( C @ ( B @ p5 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p6 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ( true @ ( B @ f3 @ ( A @ f3 @ p2 ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_11) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ f3 @ ( A @ f3 @ p2 ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( D @ p6 ) @ ( true @ ( A @ ( C @ p6 ) @ ifeq2 ) ) ) @ ( true @ ( D @ ( C @ p2 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_16) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( D @ p6 ) @ ( true @ ( A @ ( C @ p6 ) @ ifeq2 ) ) ) @ ( true @ ( D @ ( C @ p2 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p2 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ f4 @ p6 ) @ ( true @ ( B @ ( A @ p5 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_10) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ f4 @ p6 ) @ ( true @ ( B @ ( A @ p5 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ p6 ) @ ( true @ ( A @ ( C @ p6 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p6 ) @ ifeq2 ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6_14) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ p6 ) @ ( true @ ( A @ ( C @ p6 ) @ ifeq2 ) ) ) @ ( true @ ( B @ ( A @ p6 ) @ ifeq2 ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(143,plain,
$false,
inference(e,[status(thm)],[29,60,35,31,58,24,37,25,21,33,28,38,32,34,22,27,26,23,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN563-10 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.16/0.41 % Computer : n007.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 18:11:54 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.68/0.73 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.91/0.83 % [INFO] Parsing done (104ms).
% 0.91/0.84 % [INFO] Running in sequential loop mode.
% 1.39/1.04 % [INFO] eprover registered as external prover.
% 1.39/1.05 % [INFO] Scanning for conjecture ...
% 1.39/1.13 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.66/1.17 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 1.66/1.17 % [INFO] Problem is propositional (TPTP CNF).
% 1.66/1.18 % [INFO] Type checking passed.
% 1.66/1.18 % [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 ...
% 3.80/1.87 % External prover 'e' found a proof!
% 3.80/1.87 % [INFO] Killing All external provers ...
% 3.80/1.87 % Time passed: 1366ms (effective reasoning time: 1029ms)
% 3.80/1.87 % Axioms used in derivation (2): ifeq_axiom_001, ifeq_axiom
% 3.80/1.87 % No. of inferences in proof: 41
% 3.80/1.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1366 ms resp. 1029 ms w/o parsing
% 4.45/1.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.45/1.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------