%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG018+1 : TPTP v9.3.1. Released v2.7.0.
% 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 : n004.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 06:45:54 AM UTC 2026
% Result : Theorem 2.98s 1.62s
% Output : Refutation 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 67 ( 16 equ; 0 cnn)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 188 ( 7 ~; 0 |; 16 &; 126 @)
% ( 0 <=>; 39 =>; 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 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 36 !; 4 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(sorti1_decl,type,
sorti1: $i > $o ).
thf(sorti2_decl,type,
sorti2: $i > $o ).
thf(h_decl,type,
h: $i > $i ).
thf(j_decl,type,
j: $i > $i ).
thf(op1_decl,type,
op1: $i > $i > $i ).
thf(op2_decl,type,
op2: $i > $i > $i ).
thf(3,axiom,
! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( B @ ( A @ op1 ) @ sorti1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
thf(24,plain,
! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( B @ ( A @ op1 ) @ sorti1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( ( ! [A: $i] :
( ( A @ sorti2 )
=> ( A @ j @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( A @ h @ sorti2 ) ) )
=> ~ ( ! [A: $i] :
( ( A @ sorti1 )
=> ( ( A @ h @ j )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( A @ j @ h )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
thf(2,negated_conjecture,
~ ( ( ! [A: $i] :
( ( A @ sorti2 )
=> ( A @ j @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( A @ h @ sorti2 ) ) )
=> ~ ( ! [A: $i] :
( ( A @ sorti1 )
=> ( ( A @ h @ j )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( A @ j @ h )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ( ( ! [A: $i] :
( ( A @ sorti2 )
=> ( A @ j @ sorti1 ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ( A @ h @ sorti2 ) ) )
=> ~ ( ! [A: $i] :
( ( A @ sorti1 )
=> ( ( A @ h @ j )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ( ( A @ j @ h )
= A ) )
& ! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( A @ op2 ) @ j )
= ( B @ j @ ( A @ j @ op1 ) ) ) ) )
& ! [A: $i] :
( ( A @ sorti1 )
=> ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( A @ op1 ) @ h )
= ( B @ h @ ( A @ h @ op2 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( B @ ( A @ op2 ) @ sorti2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
thf(26,plain,
! [A: $i] :
( ( A @ sorti2 )
=> ! [B: $i] :
( ( B @ sorti2 )
=> ( B @ ( A @ op2 ) @ sorti2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
? [A: $i] :
( ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( B @ op1 ) )
= A ) )
& ( A @ sorti1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
thf(28,plain,
? [A: $i] :
( ! [B: $i] :
( ( B @ sorti1 )
=> ( ( B @ ( B @ op1 ) )
= A ) )
& ( A @ sorti1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(6,axiom,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( B @ op2 ) )
= A ) )
& ( A @ sorti2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
thf(33,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ( B @ sorti2 )
=> ( ( B @ ( B @ op2 ) )
= A ) )
& ( A @ sorti2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,plain,
$false,
inference(e,[status(thm)],[24,7,26,28,33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG018+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.07 % 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
% 0.14/0.39 % Computer : n004.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 20:58:52 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.60/0.69 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.72/0.79 % [INFO] Parsing done (91ms).
% 0.72/0.79 % [INFO] Running in sequential loop mode.
% 1.16/0.98 % [INFO] eprover registered as external prover.
% 1.16/0.98 % [INFO] Scanning for conjecture ...
% 1.45/1.03 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 1.45/1.06 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 1.45/1.06 % [INFO] Problem is first-order (TPTP FOF).
% 1.45/1.07 % [INFO] Type checking passed.
% 1.45/1.07 % [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 ...
% 2.98/1.61 % External prover 'e' found a proof!
% 2.98/1.61 % [INFO] Killing All external provers ...
% 2.98/1.61 % Time passed: 1120ms (effective reasoning time: 816ms)
% 2.98/1.61 % 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)>
% 2.98/1.61 % Axioms used in derivation (4): ax1, ax2, ax3, ax4
% 2.98/1.61 % No. of inferences in proof: 12
% 2.98/1.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1120 ms resp. 816 ms w/o parsing
% 2.98/1.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.98/1.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------