%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYN618-1 : TPTP v9.3.1. Released v2.5.0.
% 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 : n001.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 09:17:59 AM UTC 2026
% Result : Unsatisfiable 4.47s 2.61s
% Output : Refutation 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 33
% Syntax : Number of formulae : 67 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 145 ( 0 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 512 ( 80 ~; 78 |; 0 &; 354 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 23 usr; 10 con; 0-3 aty)
% Number of variables : 106 ( 0 ^; 106 !; 0 ?; 106 :)
% Comments :
%------------------------------------------------------------------------------
thf(p9_decl,type,
p9: $i > $o ).
thf(c16_decl,type,
c16: $i ).
thf(p10_decl,type,
p10: $i > $i > $o ).
thf(p5_decl,type,
p5: $i > $i > $o ).
thf(p4_decl,type,
p4: $i > $i > $o ).
thf(p2_decl,type,
p2: $i > $i > $o ).
thf(p14_decl,type,
p14: $i > $i > $o ).
thf(p12_decl,type,
p12: $i > $i > $o ).
thf(c19_decl,type,
c19: $i ).
thf(c20_decl,type,
c20: $i ).
thf(p13_decl,type,
p13: $i > $i > $o ).
thf(c23_decl,type,
c23: $i ).
thf(c21_decl,type,
c21: $i ).
thf(c17_decl,type,
c17: $i ).
thf(f3_decl,type,
f3: $i > $i ).
thf(p11_decl,type,
p11: $i > $i > $i > $o ).
thf(c18_decl,type,
c18: $i ).
thf(f8_decl,type,
f8: $i > $i > $i ).
thf(f6_decl,type,
f6: $i > $i ).
thf(f7_decl,type,
f7: $i > $i ).
thf(c22_decl,type,
c22: $i ).
thf(p15_decl,type,
p15: $i > $i > $o ).
thf(c24_decl,type,
c24: $i ).
thf(33,negated_conjecture,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ p11 ) ) )
| ~ ( C @ ( F @ p10 ) )
| ~ ( A @ ( E @ p2 ) )
| ~ ( B @ ( D @ p2 ) )
| ( C @ ( B @ ( A @ p11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_33) ).
thf(56,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ p11 ) ) )
| ~ ( C @ ( F @ p10 ) )
| ~ ( A @ ( E @ p2 ) )
| ~ ( B @ ( D @ p2 ) )
| ( C @ ( B @ ( A @ p11 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f7 @ ( A @ f7 @ p4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_20) ).
thf(52,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f7 @ ( A @ f7 @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(16,negated_conjecture,
c22 @ f7 @ f6 @ ( c23 @ ( c16 @ f3 @ f8 ) @ p5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_16) ).
thf(61,plain,
c22 @ f7 @ f6 @ ( c23 @ ( c16 @ f3 @ f8 ) @ p5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(27,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ p10 ) )
| ~ ( D @ ( C @ p15 ) )
| ~ ( A @ ( C @ p14 ) )
| ( B @ ( A @ p15 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p15_27) ).
thf(60,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ p10 ) )
| ~ ( D @ ( C @ p15 ) )
| ~ ( A @ ( C @ p14 ) )
| ( B @ ( A @ p15 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(6,negated_conjecture,
! [A: $i] : ( A @ ( A @ p14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_6) ).
thf(38,plain,
! [A: $i] : ( A @ ( A @ p14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(30,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_30) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ p5 ) )
| ~ ( C @ ( A @ p2 ) )
| ( D @ ( C @ f8 ) @ ( B @ ( A @ f8 ) @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(29,negated_conjecture,
! [A: $i] :
( ~ ( c18 @ ( c24 @ p15 ) )
| ~ ( A @ ( c19 @ p13 ) )
| ~ ( c21 @ ( A @ p13 ) )
| ( c20 @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_29) ).
thf(53,plain,
! [A: $i] :
( ~ ( c18 @ ( c24 @ p15 ) )
| ~ ( A @ ( c19 @ p13 ) )
| ~ ( c21 @ ( A @ p13 ) )
| ( c20 @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(2,negated_conjecture,
! [A: $i] : ( A @ ( A @ p10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_2) ).
thf(41,plain,
! [A: $i] : ( A @ ( A @ p10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,negated_conjecture,
c23 @ ( c19 @ p13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_9) ).
thf(39,plain,
c23 @ ( c19 @ p13 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f3 @ ( A @ f3 @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_19) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p2 ) )
| ( B @ f3 @ ( A @ f3 @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(10,negated_conjecture,
c21 @ ( c19 @ p13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_10) ).
thf(35,plain,
c21 @ ( c19 @ p13 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(24,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_24) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p2 ) )
| ~ ( A @ ( C @ p2 ) )
| ( B @ ( A @ p2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,negated_conjecture,
c20 @ ( c19 @ p12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_7) ).
thf(43,plain,
c20 @ ( c19 @ p12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,negated_conjecture,
~ ( c22 @ f7 @ f6 @ ( c20 @ ( c16 @ f3 @ f8 ) @ p5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p5_17) ).
thf(58,plain,
~ ( c22 @ f7 @ f6 @ ( c20 @ ( c16 @ f3 @ f8 ) @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,negated_conjecture,
c16 @ f3 @ ( c17 @ p2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_12) ).
thf(42,plain,
c16 @ f3 @ ( c17 @ p2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1,negated_conjecture,
c16 @ p9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c16_is_p9_1) ).
thf(37,plain,
c16 @ p9,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,negated_conjecture,
c21 @ ( c20 @ p12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_11) ).
thf(46,plain,
c21 @ ( c20 @ p12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(32,negated_conjecture,
! [A: $i] :
( ~ ( c22 @ f7 @ f6 @ ( A @ ( c16 @ f8 ) @ p5 ) )
| ~ ( A @ ( c19 @ p13 ) )
| ~ ( c21 @ ( A @ p13 ) )
| ( c20 @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_32) ).
thf(57,plain,
! [A: $i] :
( ~ ( c22 @ f7 @ f6 @ ( A @ ( c16 @ f8 ) @ p5 ) )
| ~ ( A @ ( c19 @ p13 ) )
| ~ ( c21 @ ( A @ p13 ) )
| ( c20 @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(5,negated_conjecture,
! [A: $i] : ( A @ ( A @ p2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
thf(34,plain,
! [A: $i] : ( A @ ( A @ p2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(18,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f6 @ ( A @ f6 @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_18) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ p4 ) )
| ( B @ f6 @ ( A @ f6 @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_23) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p4 ) )
| ~ ( A @ ( C @ p4 ) )
| ( B @ ( A @ p4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(3,negated_conjecture,
! [A: $i] : ( A @ ( A @ p5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_3) ).
thf(44,plain,
! [A: $i] : ( A @ ( A @ p5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(22,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_22) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(28,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p13 ) )
| ~ ( B @ ( D @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p13 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_28) ).
thf(54,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p13 ) )
| ~ ( B @ ( D @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p13 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,negated_conjecture,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p2 ) )
| ~ ( B @ p9 )
| ( A @ p9 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_15) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ p2 ) )
| ~ ( B @ p9 )
| ( A @ p9 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,negated_conjecture,
! [A: $i] : ( A @ ( A @ p4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_4) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ p4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26,negated_conjecture,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p12_26) ).
thf(63,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ p12 ) )
| ~ ( B @ ( D @ p5 ) )
| ~ ( A @ ( C @ p5 ) )
| ( B @ ( A @ p12 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,negated_conjecture,
c18 @ ( c17 @ ( c16 @ p11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p11_13) ).
thf(40,plain,
c18 @ ( c17 @ ( c16 @ p11 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(21,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p10 ) )
| ~ ( A @ ( C @ p10 ) )
| ( B @ ( A @ p10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_21) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p10 ) )
| ~ ( A @ ( C @ p10 ) )
| ( B @ ( A @ p10 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,negated_conjecture,
c22 @ f7 @ f6 @ ( c20 @ ( c16 @ f8 ) @ p5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_14) ).
thf(36,plain,
c22 @ f7 @ f6 @ ( c20 @ ( c16 @ f8 ) @ p5 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p14 ) )
| ~ ( A @ ( C @ p14 ) )
| ( B @ ( A @ p14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p14_25) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ p14 ) )
| ~ ( A @ ( C @ p14 ) )
| ( B @ ( A @ p14 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(8,negated_conjecture,
c21 @ ( c23 @ p13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13_8) ).
thf(47,plain,
c21 @ ( c23 @ p13 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,negated_conjecture,
! [A: $i] :
( ~ ( c22 @ f7 @ f6 @ ( A @ ( c17 @ f8 ) @ p5 ) )
| ~ ( A @ ( c19 @ p13 ) )
| ~ ( c21 @ ( A @ p13 ) )
| ( c20 @ ( A @ p5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5_31) ).
thf(62,plain,
! [A: $i] :
( ~ ( c22 @ f7 @ f6 @ ( A @ ( c17 @ f8 ) @ p5 ) )
| ~ ( A @ ( c19 @ p13 ) )
| ~ ( c21 @ ( A @ p13 ) )
| ( c20 @ ( A @ p5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(85,plain,
$false,
inference(e,[status(thm)],[56,52,61,60,38,65,53,41,39,66,35,50,43,58,42,37,46,57,34,45,64,44,59,54,49,48,63,40,55,36,51,47,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN618-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.07 % 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
% 0.14/0.41 % Computer : n001.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 18:22:44 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.85/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.21 % [INFO] Parsing done (207ms).
% 1.33/1.23 % [INFO] Running in sequential loop mode.
% 1.94/1.63 % [INFO] eprover registered as external prover.
% 1.94/1.64 % [INFO] Scanning for conjecture ...
% 2.15/1.79 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.34/1.87 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.34/1.87 % [INFO] Problem is propositional (TPTP CNF).
% 2.34/1.88 % [INFO] Type checking passed.
% 2.34/1.88 % [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 ...
% 4.47/2.60 % External prover 'e' found a proof!
% 4.47/2.60 % [INFO] Killing All external provers ...
% 4.47/2.60 % Time passed: 2049ms (effective reasoning time: 1370ms)
% 4.47/2.60 % Axioms used in derivation (0):
% 4.47/2.60 % No. of inferences in proof: 67
% 4.47/2.61 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2049 ms resp. 1370 ms w/o parsing
% 4.47/2.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.47/2.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------