%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO691-1.000 : TPTP v9.3.1. Released v7.3.0.
% 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 09:45:13 AM UTC 2026
% Result : Unsatisfiable 3.20s 2.26s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of formulae : 15 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 25 ( 0 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 126 ( 12 ~; 10 |; 0 &; 104 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 34 ( 0 ^; 34 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(seq_decl,type,
seq: $i > $i > $i > $o ).
thf(succ_decl,type,
succ: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(top_decl,type,
top: $i > $i > $o ).
thf(f_decl,type,
f: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(step_decl,type,
step: $i > $i > $o ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( a @ ( B @ f ) @ ( C @ f ) @ f ) @ ( a @ ( C @ f ) @ ( B @ ( A @ f ) @ f ) @ top ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( a @ ( B @ f ) @ ( C @ f ) @ f ) @ ( a @ ( C @ f ) @ ( B @ ( A @ f ) @ f ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_left) ).
thf(13,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ f ) @ ( C @ ( A @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i] : ( A @ ( A @ ( zero @ seq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_sequence_zero) ).
thf(17,plain,
! [A: $i] : ( A @ ( A @ ( zero @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_sequence_succ) ).
thf(18,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ succ @ seq ) ) )
| ~ ( D @ ( C @ step ) )
| ~ ( C @ ( B @ ( A @ seq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ step ) )
| ~ ( B @ ( A @ top ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_top) ).
thf(11,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ step ) )
| ~ ( B @ ( A @ top ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(8,plain,
! [A: $i] :
~ ( A @ ( A @ ( zero @ succ @ succ @ succ @ seq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ f ) @ ( A @ ( C @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rewrite_right) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ f ) @ ( A @ ( C @ f ) @ step ) )
| ~ ( B @ ( A @ step ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[10,13,17,18,11,8,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO691-1.000 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 19:52:13 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 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
% 0.85/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.14 % [INFO] Parsing done (174ms).
% 1.23/1.15 % [INFO] Running in sequential loop mode.
% 1.74/1.56 % [INFO] eprover registered as external prover.
% 1.74/1.57 % [INFO] Scanning for conjecture ...
% 1.93/1.65 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 1.93/1.68 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.06/1.70 % [INFO] Problem is propositional (TPTP CNF).
% 2.06/1.70 % [INFO] Type checking passed.
% 2.06/1.70 % [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 ...
% 3.20/2.26 % External prover 'e' found a proof!
% 3.20/2.26 % [INFO] Killing All external provers ...
% 3.20/2.26 % Time passed: 1745ms (effective reasoning time: 1103ms)
% 3.20/2.26 % Axioms used in derivation (6): rewrite_right, rewrite_top, rule_1, rewrite_sequence_succ, rewrite_sequence_zero, rewrite_left
% 3.20/2.26 % No. of inferences in proof: 15
% 3.20/2.26 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1745 ms resp. 1103 ms w/o parsing
% 3.44/2.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.44/2.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------