%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN085+1 : TPTP v9.3.1. Released v7.3.0.
% 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 : n012.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 08:18:42 AM UTC 2026
% Result : Theorem 8.40s 2.52s
% Output : Refutation 8.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 169 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 563 ( 88 ~; 67 |; 62 &; 346 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 5 usr; 1 con; 0-3 aty)
% Number of variables : 149 ( 0 ^; 109 !; 40 ?; 149 :)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $o ).
thf(r3_decl,type,
r3: $i > $i > $i > $o ).
thf(r2_decl,type,
r2: $i > $i > $o ).
thf(id_decl,type,
id: $i > $i > $o ).
thf(r4_decl,type,
r4: $i > $i > $i > $o ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
thf(52,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) )
| ! [C: $i] :
( ~ ( A @ ( B @ ( C @ r3 ) ) )
| ~ ( C @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidzero) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) )
| ! [C: $i] :
( ~ ( A @ ( B @ ( C @ r3 ) ) )
| ~ ( C @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
| ! [B: $i] :
( ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) )
| ! [C: $i] :
( ~ ( A @ ( B @ ( C @ r3 ) ) )
| ~ ( C @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(17,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(97,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
thf(59,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(14,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
thf(86,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(103,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
thf(80,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(43,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
thf(36,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(68,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(46,plain,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( A @ id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(93,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(29,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(61,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
thf(74,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2090,plain,
$false,
inference(e,[status(thm)],[52,21,97,109,59,86,103,80,95,43,36,68,46,93,57,29,61,116,74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN085+1 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % 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
% 0.06/0.31 % Computer : n012.cluster.edu
% 0.06/0.31 % Model : x86_64 x86_64
% 0.06/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.31 % Memory : 8046.5625MB
% 0.06/0.31 % OS : Linux 6.8.0-71-generic
% 0.06/0.31 % CPULimit : 300
% 0.06/0.31 % WCLimit : 300
% 0.06/0.31 % DateTime : Sat Sep 26 04:32:05 UTC 2026
% 0.06/0.32 % CPUTime :
% 0.06/0.32 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
% 0.39/0.61 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.71 % [INFO] Parsing done (103ms).
% 0.68/0.72 % [INFO] Running in sequential loop mode.
% 1.05/0.90 % [INFO] eprover registered as external prover.
% 1.05/0.91 % [INFO] Scanning for conjecture ...
% 1.05/0.95 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 1.05/0.99 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.28/1.02 % [INFO] Problem is first-order (TPTP FOF).
% 1.28/1.02 % [INFO] Type checking passed.
% 1.28/1.02 % [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 ...
% 8.40/2.52 % External prover 'e' found a proof!
% 8.40/2.52 % [INFO] Killing All external provers ...
% 8.40/2.52 % Time passed: 2128ms (effective reasoning time: 1797ms)
% 8.40/2.52 % Solved by 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)>
% 8.40/2.52 % Axioms used in derivation (18): axiom_7, axiom_10, axiom_1a, axiom_4a, axiom_2, axiom_6, axiom_3, axiom_7a, axiom_8, axiom_6a, axiom_5, axiom_3a, axiom_11, axiom_9, axiom_4, axiom_1, axiom_2a, axiom_5a
% 8.40/2.52 % No. of inferences in proof: 40
% 8.40/2.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2128 ms resp. 1797 ms w/o parsing
% 8.40/2.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.40/2.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------