%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% 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 : n018.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 09:15:16 AM UTC 2026
% Result : Theorem 3.30s 2.29s
% Output : Refutation 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 16 ( 15 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 53 ( 7 ~; 0 |; 0 &; 46 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 ^; 16 !; 3 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
thf(x22_decl,type,
x22: $i > $i > $i ).
thf(proj1S_decl,type,
proj1S: $i > $i ).
thf(s_decl,type,
s: $i > $i ).
thf(z_decl,type,
z: $i ).
thf(x2_decl,type,
x2: $i > $i > $i ).
thf(1,conjecture,
? [A: $i] :
( ( A @ ( A @ x22 ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_007) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ( A @ ( A @ x22 ) )
!= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ? [A: $i] :
( ( A @ ( A @ x22 ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_001) ).
thf(13,plain,
! [A: $i] :
( ( A @ s @ proj1S )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i] :
( z
!= ( A @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_002) ).
thf(16,plain,
! [A: $i] :
( z
!= ( A @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( z @ x2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_003) ).
thf(20,plain,
! [A: $i] :
( ( A @ ( z @ x2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ x22 ) )
= ( A @ ( B @ x22 ) @ ( A @ x2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_006) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ x22 ) )
= ( A @ ( B @ x22 ) @ ( A @ x2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( z @ x22 ) )
= z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_005) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( z @ x22 ) )
= z ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ x2 ) )
= ( A @ ( B @ x2 ) @ s ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_004) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ s @ x2 ) )
= ( A @ ( B @ x2 ) @ s ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[9,13,16,20,29,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWX204+1 : TPTP v9.3.1. Released v9.3.0.
% 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
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sat Sep 26 16:57:51 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.88/0.99 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/1.16 % [INFO] Parsing done (172ms).
% 1.26/1.17 % [INFO] Running in sequential loop mode.
% 1.82/1.59 % [INFO] eprover registered as external prover.
% 2.01/1.60 % [INFO] Scanning for conjecture ...
% 2.01/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.19/1.73 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.19/1.74 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.75 % [INFO] Type checking passed.
% 2.19/1.75 % [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 ...
% 3.30/2.29 % External prover 'e' found a proof!
% 3.30/2.29 % [INFO] Killing All external provers ...
% 3.30/2.29 % Time passed: 1755ms (effective reasoning time: 1108ms)
% 3.30/2.29 % 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)>
% 3.30/2.29 % Axioms used in derivation (6): axiom_002, axiom_006, axiom_005, axiom_001, axiom_004, axiom_003
% 3.30/2.29 % No. of inferences in proof: 16
% 3.30/2.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1755 ms resp. 1108 ms w/o parsing
% 3.59/2.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.59/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------