%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : 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 09:16:33 AM UTC 2026
% Result : Unsatisfiable 4.61s 2.66s
% Output : Refutation 4.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 27
% Syntax : Number of formulae : 55 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 163 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 738 ( 90 ~; 108 |; 0 &; 540 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 168 ( 0 ^; 168 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
thf(p_decl,type,
p: $i > $i > $o ).
thf(f1_decl,type,
f1: $i > $i > $i ).
thf(s_decl,type,
s: $i > $i > $o ).
thf(q_decl,type,
q: $i > $i > $o ).
thf(27,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ s ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_27) ).
thf(52,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ s ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(26,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ f1 ) @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_26) ).
thf(53,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ f1 ) @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f1 ) @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f1 ) @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(9,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ f1 ) @ ( C @ q ) )
| ~ ( B @ ( B @ q ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ f1 ) @ ( C @ q ) )
| ~ ( B @ ( B @ q ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(7,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ s ) )
| ~ ( B @ ( B @ q ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_18) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ s ) )
| ~ ( B @ ( B @ q ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(2,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f1 ) @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f1 ) @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(19,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ f1 ) @ ( C @ q ) )
| ~ ( C @ ( B @ f1 ) @ ( B @ s ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_19) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ f1 ) @ ( C @ q ) )
| ~ ( C @ ( B @ f1 ) @ ( B @ s ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ s ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ f1 ) @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ f1 ) @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ f1 ) @ q ) )
| ~ ( B @ ( B @ q ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_17) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ f1 ) @ q ) )
| ~ ( B @ ( B @ q ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f1 ) @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ f1 ) @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ~ ( B @ ( A @ f1 ) @ ( A @ s ) )
| ( B @ ( A @ f1 ) @ ( B @ ( A @ f1 ) @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(21,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ s ) )
| ~ ( C @ ( B @ f1 ) @ ( B @ s ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_21) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ s ) )
| ~ ( C @ ( B @ f1 ) @ ( B @ s ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ f1 ) @ q ) )
| ( A @ ( C @ ( B @ f1 ) @ s ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_23) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ f1 ) @ q ) )
| ( A @ ( C @ ( B @ f1 ) @ s ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(24,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ s ) )
| ( A @ ( C @ ( B @ f1 ) @ s ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_24) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ s ) )
| ( A @ ( C @ ( B @ f1 ) @ s ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(25,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ f1 ) @ ( D @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_25) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ f1 ) @ ( D @ q ) )
| ~ ( C @ ( C @ q ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(20,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ f1 ) @ q ) )
| ~ ( C @ ( B @ f1 ) @ ( B @ s ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ f1 ) @ q ) )
| ~ ( C @ ( B @ f1 ) @ ( B @ s ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ f1 ) @ ( B @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(14,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ f1 ) @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ~ ( A @ ( A @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ f1 ) @ q ) )
| ( C @ ( B @ ( A @ f1 ) @ s ) )
| ~ ( A @ ( A @ p ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ f1 ) @ ( C @ q ) )
| ( A @ ( C @ ( B @ f1 ) @ s ) )
| ( B @ ( A @ s ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_22) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ f1 ) @ ( C @ q ) )
| ( A @ ( C @ ( B @ f1 ) @ s ) )
| ( B @ ( A @ s ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(86,plain,
$false,
inference(e,[status(thm)],[52,53,41,44,39,35,48,43,40,47,42,37,46,29,33,28,38,45,32,34,54,49,50,31,36,30,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN039-1 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.15/0.41 % Computer : n018.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 17:07:51 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.86/1.01 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.39/1.21 % [INFO] Parsing done (196ms).
% 1.39/1.22 % [INFO] Running in sequential loop mode.
% 2.13/1.63 % [INFO] eprover registered as external prover.
% 2.13/1.64 % [INFO] Scanning for conjecture ...
% 2.33/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.53/1.88 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.53/1.88 % [INFO] Problem is propositional (TPTP CNF).
% 2.53/1.88 % [INFO] Type checking passed.
% 2.53/1.89 % [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 ...
% 4.61/2.66 % External prover 'e' found a proof!
% 4.61/2.66 % [INFO] Killing All external provers ...
% 4.61/2.66 % Time passed: 2097ms (effective reasoning time: 1430ms)
% 4.61/2.66 % Axioms used in derivation (0):
% 4.61/2.66 % No. of inferences in proof: 55
% 4.61/2.66 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2097 ms resp. 1430 ms w/o parsing
% 4.79/2.72 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.79/2.73 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------