%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN036-3 : TPTP v9.3.1. Released v1.0.0.
% 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 : n013.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 09:16:32 AM UTC 2026
% Result : Unsatisfiable 3.02s 2.03s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 36
% Syntax : Number of formulae : 73 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 209 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 320 ( 104 ~; 136 |; 0 &; 80 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 20 usr; 15 con; 0-1 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(n2_decl,type,
n2: $o ).
thf(n9_decl,type,
n9: $o ).
thf(n6_decl,type,
n6: $o ).
thf(n10_decl,type,
n10: $o ).
thf(p_decl,type,
p: $i > $o ).
thf(s8_decl,type,
s8: $i ).
thf(n8_decl,type,
n8: $o ).
thf(n7_decl,type,
n7: $o ).
thf(s7_decl,type,
s7: $i ).
thf(n5_decl,type,
n5: $i > $o ).
thf(s6_decl,type,
s6: $i ).
thf(q_decl,type,
q: $i > $o ).
thf(s5_decl,type,
s5: $i > $i ).
thf(s4_decl,type,
s4: $i ).
thf(n4_decl,type,
n4: $o ).
thf(n3_decl,type,
n3: $o ).
thf(s3_decl,type,
s3: $i ).
thf(n1_decl,type,
n1: $i > $o ).
thf(s2_decl,type,
s2: $i ).
thf(s1_decl,type,
s1: $i > $i ).
thf(23,negated_conjecture,
! [A: $i] :
( n2
| ~ ( A @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
thf(69,plain,
! [A: $i] :
( n2
| ~ ( A @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(28,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ p )
| ( A @ p )
| ~ ( A @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
thf(56,plain,
! [B: $i,A: $i] :
( ~ ( B @ p )
| ( A @ p )
| ~ ( A @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(24,negated_conjecture,
( ( s2 @ n1 )
| ~ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
thf(52,plain,
( ( s2 @ n1 )
| ~ n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(34,negated_conjecture,
( n10
| n8
| n7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
thf(61,plain,
( n10
| n8
| n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(32,negated_conjecture,
( ~ n9
| ~ n4
| n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
thf(60,plain,
( ~ n9
| ~ n4
| n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(35,negated_conjecture,
( ~ n10
| n8
| ~ n7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
thf(65,plain,
( ~ n10
| n8
| ~ n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(25,negated_conjecture,
! [A: $i] :
( ( A @ n1 )
| ~ ( A @ s1 @ p )
| ~ ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
thf(53,plain,
! [A: $i] :
( ( A @ n1 )
| ~ ( A @ s1 @ p )
| ~ ( A @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,negated_conjecture,
( ~ n10
| n6
| n9
| ~ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(41,plain,
( ~ n10
| n6
| n9
| ~ n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,negated_conjecture,
( ( s6 @ n5 )
| ~ n6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
thf(39,plain,
( ( s6 @ n5 )
| ~ n6 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,negated_conjecture,
! [A: $i] :
( ( A @ n5 )
| ( A @ s5 @ q )
| ( A @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
thf(66,plain,
! [A: $i] :
( ( A @ n5 )
| ( A @ s5 @ q )
| ( A @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(33,negated_conjecture,
( n10
| ~ n8
| ~ n7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
thf(58,plain,
( n10
| ~ n8
| ~ n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(15,negated_conjecture,
! [A: $i] :
( ( A @ n5 )
| ~ ( A @ s5 @ q )
| ~ ( A @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
thf(51,plain,
! [A: $i] :
( ( A @ n5 )
| ~ ( A @ s5 @ q )
| ~ ( A @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(9,negated_conjecture,
( n8
| ~ ( s8 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(42,plain,
( n8
| ~ ( s8 @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,negated_conjecture,
( n10
| ~ n6
| n9
| ~ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(37,plain,
( n10
| ~ n6
| n9
| ~ n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,negated_conjecture,
( n10
| ~ n6
| ~ n9
| n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(46,plain,
( n10
| ~ n6
| ~ n9
| n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,negated_conjecture,
! [A: $i] :
( n3
| ~ ( A @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
thf(57,plain,
! [A: $i] :
( n3
| ~ ( A @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(10,negated_conjecture,
! [A: $i] :
( ( A @ p )
| ~ n8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(38,plain,
! [A: $i] :
( ( A @ p )
| ~ n8 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(36,negated_conjecture,
( ~ n10
| ~ n8
| n7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
thf(70,plain,
( ~ n10
| ~ n8
| n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,negated_conjecture,
( ( s7 @ p )
| ~ n7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
thf(45,plain,
( ( s7 @ p )
| ~ n7 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,negated_conjecture,
( ~ n10
| ~ n6
| n9
| n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(64,plain,
( ~ n10
| ~ n6
| n9
| n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(2,negated_conjecture,
( n10
| n6
| ~ n9
| ~ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(44,plain,
( n10
| n6
| ~ n9
| ~ n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,negated_conjecture,
! [B: $i,A: $i] :
( ( B @ q )
| ~ ( A @ q )
| ~ ( A @ n5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( B @ q )
| ~ ( A @ q )
| ~ ( A @ n5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(30,negated_conjecture,
( n9
| n4
| n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
thf(71,plain,
( n9
| n4
| n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(20,negated_conjecture,
! [A: $i] :
( ( A @ q )
| ~ n4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
thf(54,plain,
! [A: $i] :
( ( A @ q )
| ~ n4 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(8,negated_conjecture,
( ~ n10
| n6
| ~ n9
| n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(49,plain,
( ~ n10
| n6
| ~ n9
| n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,negated_conjecture,
! [A: $i] :
( n7
| ~ ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(48,plain,
! [A: $i] :
( n7
| ~ ( A @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(27,negated_conjecture,
! [B: $i,A: $i] :
( ( B @ p )
| ~ ( A @ p )
| ~ ( A @ n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ p )
| ~ ( A @ p )
| ~ ( A @ n1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,negated_conjecture,
( n10
| n6
| n9
| n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(50,plain,
( n10
| n6
| n9
| n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,negated_conjecture,
( ~ n9
| n4
| ~ n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
thf(67,plain,
( ~ n9
| n4
| ~ n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,negated_conjecture,
( n4
| ~ ( s4 @ q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
thf(72,plain,
( n4
| ~ ( s4 @ q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(13,negated_conjecture,
! [A: $i] :
( n6
| ~ ( A @ n5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
thf(43,plain,
! [A: $i] :
( n6
| ~ ( A @ n5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(1,negated_conjecture,
( ~ n10
| ~ n6
| ~ n9
| ~ n2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(40,plain,
( ~ n10
| ~ n6
| ~ n9
| ~ n2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(29,negated_conjecture,
( n9
| ~ n4
| ~ n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
thf(55,plain,
( n9
| ~ n4
| ~ n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ q )
| ( A @ q )
| ~ ( A @ n5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
thf(47,plain,
! [B: $i,A: $i] :
( ~ ( B @ q )
| ( A @ q )
| ~ ( A @ n5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(26,negated_conjecture,
! [A: $i] :
( ( A @ n1 )
| ( A @ s1 @ p )
| ( A @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_26) ).
thf(68,plain,
! [A: $i] :
( ( A @ n1 )
| ( A @ s1 @ p )
| ( A @ p ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(22,negated_conjecture,
( ( s3 @ q )
| ~ n3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
thf(62,plain,
( ( s3 @ q )
| ~ n3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(112,plain,
$false,
inference(e,[status(thm)],[69,56,52,61,60,65,53,41,39,66,58,51,42,37,46,57,38,70,45,64,44,59,71,54,49,48,63,50,67,72,43,40,55,47,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN036-3 : TPTP v9.3.1. Released v1.0.0.
% 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
% 0.12/0.39 % Computer : n013.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 17:04:10 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.85/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.18 % [INFO] Parsing done (202ms).
% 1.42/1.20 % [INFO] Running in sequential loop mode.
% 1.88/1.56 % [INFO] eprover registered as external prover.
% 1.88/1.56 % [INFO] Scanning for conjecture ...
% 2.10/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.10/1.66 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.10/1.66 % [INFO] Problem is propositional (TPTP CNF).
% 2.10/1.66 % [INFO] Type checking passed.
% 2.10/1.66 % [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 ...
% 3.02/2.02 % External prover 'e' found a proof!
% 3.02/2.03 % [INFO] Killing All external provers ...
% 3.02/2.03 % Time passed: 1494ms (effective reasoning time: 822ms)
% 3.02/2.03 % Axioms used in derivation (0):
% 3.02/2.03 % No. of inferences in proof: 73
% 3.02/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1494 ms resp. 822 ms w/o parsing
% 3.60/2.06 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.60/2.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------