%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% 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 : n011.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 09:45:04 AM UTC 2026
% Result : Unsatisfiable 3.67s 2.50s
% Output : Refutation 4.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 65 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 666 ( 60 ~; 56 |; 0 &; 550 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 74 !; 0 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf('E_decl',type,
'E': $i > $i > $o ).
thf(s_decl,type,
s: $i > $i ).
thf('0_decl',type,
'0': $i ).
thf(f_decl,type,
f: $i > $i ).
thf('LE_decl',type,
'LE': $i > $i > $o ).
thf(iLEQ_decl,type,
iLEQ: $i > $i > $o ).
thf(g_decl,type,
g: $i > $i ).
thf(23,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9_23) ).
thf(69,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_26_17) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(20,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_25_20) ).
thf(65,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_30_13) ).
thf(53,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(26,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11_26) ).
thf(73,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21_11) ).
thf(49,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5_21) ).
thf(66,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(2,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_13_02) ).
thf(35,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10_18) ).
thf(63,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_22_25) ).
thf(72,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(27,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15_27) ).
thf(75,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_12_30) ).
thf(79,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_17_32) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(7,axiom,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6_07) ).
thf(42,plain,
! [A: $i] :
~ ( '0' @ ( A @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_18_04) ).
thf(37,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_16_15) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2_29) ).
thf(78,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(5,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_31_05) ).
thf(38,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_29_24) ).
thf(70,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ 'E' ) )
| ~ ( A @ f @ ( '0' @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(1,axiom,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8_01) ).
thf(33,plain,
! [A: $i] :
( ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) )
| ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_19_09) ).
thf(45,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(19,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4_19) ).
thf(64,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20_08) ).
thf(44,plain,
! [A: $i] : ( A @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7_16) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( '0' @ s @ s @ s @ s @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ s @ s @ s @ s @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ s @ s @ s @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(31,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_24_31) ).
thf(81,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(28,axiom,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_28_28) ).
thf(76,plain,
! [A: $i] :
~ ( A @ g @ f @ ( A @ f @ 'E' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1_06) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( '0' @ ( B @ f @ 'LE' ) )
| ( B @ f @ ( '0' @ 'E' ) )
| ~ ( B @ ( A @ iLEQ ) )
| ~ ( '0' @ s @ ( A @ f @ 'LE' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i] :
~ ( '0' @ ( A @ g @ f @ 'LE' ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_23_14) ).
thf(55,plain,
! [A: $i] :
~ ( '0' @ ( A @ g @ f @ 'LE' ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14_03) ).
thf(36,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_27_12) ).
thf(51,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3_10) ).
thf(47,plain,
! [A: $i] :
( ( A @ g @ f @ ( A @ f @ 'E' ) )
| ~ ( A @ g @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) )
| ~ ( A @ f @ ( '0' @ s @ s @ s @ s @ s @ 'E' ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_0_22) ).
thf(68,plain,
! [A: $i] : ( A @ g @ ( A @ iLEQ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(86,plain,
$false,
inference(e,[status(thm)],[69,61,65,53,73,49,66,35,63,72,75,79,83,42,37,57,78,38,70,33,45,64,44,59,81,76,40,55,36,51,47,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO630-1 : TPTP v9.3.1. Released v7.1.0.
% 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
% 0.13/0.40 % Computer : n011.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 19:40:15 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 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
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/1.20 % [INFO] Parsing done (201ms).
% 1.39/1.21 % [INFO] Running in sequential loop mode.
% 1.99/1.60 % [INFO] eprover registered as external prover.
% 1.99/1.61 % [INFO] Scanning for conjecture ...
% 1.99/1.67 % [INFO] 32 axioms and no conjecture found.
% 2.18/1.76 % [INFO] Problem is propositional (TPTP CNF).
% 2.18/1.77 % [INFO] Type checking passed.
% 2.18/1.77 % [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 ...
% 3.67/2.49 % External prover 'e' found a proof!
% 3.67/2.49 % [INFO] Killing All external provers ...
% 3.67/2.50 % Time passed: 1945ms (effective reasoning time: 1280ms)
% 3.67/2.50 % Axioms used in derivation (32): clause_31_05, clause_23_14, clause_4_19, clause_7_16, clause_3_10, clause_1_06, clause_14_03, clause_16_15, clause_5_21, clause_13_02, clause_29_24, clause_19_09, clause_21_11, clause_28_28, clause_17_32, clause_30_13, clause_9_23, clause_15_27, clause_6_07, clause_26_17, clause_12_30, clause_24_31, clause_25_20, clause_11_26, clause_0_22, clause_10_18, clause_27_12, clause_22_25, clause_18_04, clause_2_29, clause_20_08, clause_8_01
% 3.67/2.50 % No. of inferences in proof: 65
% 3.67/2.50 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1945 ms resp. 1280 ms w/o parsing
% 4.05/2.57 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.05/2.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------