%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN584-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n003.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 09:17:54 AM UTC 2026
% Result : Unsatisfiable 6.59s 3.62s
% Output : Refutation 6.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 51 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 572 ( 66 ~; 62 |; 0 &; 444 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 21 usr; 7 con; 0-2 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(p12_decl,type,
p12: $i > $i > $o ).
thf(p6_decl,type,
p6: $i > $i > $o ).
thf(p5_decl,type,
p5: $i > $i > $o ).
thf(p3_decl,type,
p3: $i > $i > $o ).
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(f11_decl,type,
f11: $i > $i ).
thf(f4_decl,type,
f4: $i > $i ).
thf(f10_decl,type,
f10: $i > $i ).
thf(p16_decl,type,
p16: $i > $i > $o ).
thf(p15_decl,type,
p15: $i > $i > $o ).
thf(f13_decl,type,
f13: $i > $i > $i ).
thf(f8_decl,type,
f8: $i > $i > $i ).
thf(f9_decl,type,
f9: $i > $i > $i ).
thf(f7_decl,type,
f7: $i > $i > $i ).
thf(f14_decl,type,
f14: $i > $i > $i ).
thf(c22_decl,type,
c22: $i ).
thf(c18_decl,type,
c18: $i ).
thf(c19_decl,type,
c19: $i ).
thf(c20_decl,type,
c20: $i ).
thf(c21_decl,type,
c21: $i ).
thf(c17_decl,type,
c17: $i ).
thf(18,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f9 ) @ ( B @ ( A @ f9 ) @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_18) ).
thf(41,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f9 ) @ ( B @ ( A @ f9 ) @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,negated_conjecture,
! [A: $i] :
( ~ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( A @ p15 ) )
| ~ ( A @ ( c22 @ p16 ) )
| ~ ( c17 @ ( A @ p16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p16_24) ).
thf(49,plain,
! [A: $i] :
( ~ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( A @ p15 ) )
| ~ ( A @ ( c22 @ p16 ) )
| ~ ( c17 @ ( A @ p16 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_7) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f4 @ ( A @ f4 @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_2) ).
thf(35,plain,
! [A: $i] : ( A @ ( A @ p6 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ p12 ) )
| ~ ( B @ ( D @ p3 ) )
| ~ ( D @ ( C @ p15 ) )
| ( B @ ( A @ p15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_15) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ p12 ) )
| ~ ( B @ ( D @ p3 ) )
| ~ ( D @ ( C @ p15 ) )
| ( B @ ( A @ p15 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_11) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,negated_conjecture,
! [A: $i] : ( A @ ( A @ p3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_4) ).
thf(47,plain,
! [A: $i] : ( A @ ( A @ p3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p12 ) )
| ~ ( C @ ( A @ p12 ) )
| ( D @ ( C @ f13 ) @ ( B @ ( A @ f13 ) @ p12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_16) ).
thf(42,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p12 ) )
| ~ ( C @ ( A @ p12 ) )
| ( D @ ( C @ f13 ) @ ( B @ ( A @ f13 ) @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(22,negated_conjecture,
c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( c17 @ p15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_22) ).
thf(37,plain,
c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( c17 @ p15 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(19,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p6 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f7 ) @ ( B @ ( A @ f7 ) @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_19) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p6 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f7 ) @ ( B @ ( A @ f7 ) @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(20,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ p2 ) )
| ~ ( D @ ( B @ p12 ) )
| ( D @ ( C @ f14 ) @ ( B @ ( A @ f14 ) @ p12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_20) ).
thf(29,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ p2 ) )
| ~ ( D @ ( B @ p12 ) )
| ( D @ ( C @ f14 ) @ ( B @ ( A @ f14 ) @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p12 ) )
| ~ ( A @ ( C @ p12 ) )
| ( B @ ( A @ p12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_9) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p12 ) )
| ~ ( A @ ( C @ p12 ) )
| ( B @ ( A @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ p12 ) )
| ~ ( C @ ( D @ p16 ) )
| ~ ( B @ ( C @ p12 ) )
| ( B @ ( A @ p16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p16_14) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ p12 ) )
| ~ ( C @ ( D @ p16 ) )
| ~ ( B @ ( C @ p12 ) )
| ( B @ ( A @ p16 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3_12) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p3 ) )
| ~ ( A @ ( C @ p3 ) )
| ( B @ ( A @ p3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f10 @ ( A @ f10 @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_8) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f10 @ ( A @ f10 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(21,negated_conjecture,
c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( c22 @ p15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p15_21) ).
thf(32,plain,
c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( c22 @ p15 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_13) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(23,negated_conjecture,
c22 @ ( c17 @ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f14 ) @ ( c17 @ f13 ) @ p12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_23) ).
thf(44,plain,
c22 @ ( c17 @ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f14 ) @ ( c17 @ f13 ) @ p12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p6 ) )
| ~ ( A @ ( C @ p6 ) )
| ( B @ ( A @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_10) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p6 ) )
| ~ ( A @ ( C @ p6 ) )
| ( B @ ( A @ p6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(25,negated_conjecture,
~ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( c17 @ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f14 ) @ ( c17 @ f13 ) @ p15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_p15_25) ).
thf(50,plain,
~ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f4 @ ( c17 @ ( c20 @ f11 @ f10 @ ( c21 @ f9 ) @ ( c20 @ f11 @ f10 @ ( c19 @ f9 ) @ f8 ) @ ( c18 @ f7 ) @ f14 ) @ ( c17 @ f13 ) @ p15 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f11 @ ( A @ f11 @ p5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_6) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p5 ) )
| ( B @ f11 @ ( A @ f11 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(3,negated_conjecture,
! [A: $i] : ( A @ ( A @ p5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p5_3) ).
thf(40,plain,
! [A: $i] : ( A @ ( A @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2_5) ).
thf(26,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6_17) ).
thf(36,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p5 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,negated_conjecture,
! [A: $i] : ( A @ ( A @ p12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p12_1) ).
thf(30,plain,
! [A: $i] : ( A @ ( A @ p12 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(68,plain,
$false,
inference(e,[status(thm)],[41,49,39,35,48,43,47,42,37,46,29,33,28,38,45,32,34,44,27,50,31,40,26,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN584-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.13 % 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
% 0.23/0.50 % Computer : n003.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sat Sep 26 18:16:39 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.44/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.62 % [INFO] Parsing done (280ms).
% 1.99/1.64 % [INFO] Running in sequential loop mode.
% 3.11/2.23 % [INFO] eprover registered as external prover.
% 3.11/2.25 % [INFO] Scanning for conjecture ...
% 3.49/2.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.70/2.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.70/2.59 % [INFO] Problem is propositional (TPTP CNF).
% 3.90/2.60 % [INFO] Type checking passed.
% 3.90/2.60 % [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 ...
% 6.59/3.61 % External prover 'e' found a proof!
% 6.59/3.61 % [INFO] Killing All external provers ...
% 6.59/3.61 % Time passed: 2911ms (effective reasoning time: 1962ms)
% 6.59/3.62 % Axioms used in derivation (0):
% 6.59/3.62 % No. of inferences in proof: 51
% 6.59/3.62 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2911 ms resp. 1962 ms w/o parsing
% 6.83/3.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.83/3.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------