%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : ALG069-10 : 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 : n016.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 06:46:03 AM UTC 2026
% Result : Unsatisfiable 3.72s 7.59s
% Output : Refutation 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 14
% Syntax : Number of formulae : 29 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 29 ( 28 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 266 ( 2 ~; 0 |; 0 &; 264 @)
% ( 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 : 14 ( 12 usr; 3 con; 0-4 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(sorti1_decl,type,
sorti1: $i > $i ).
thf(true_decl,type,
true: $i ).
thf(sorti2_decl,type,
sorti2: $i > $i ).
thf(h_decl,type,
h: $i > $i ).
thf(ifeq2_decl,type,
ifeq2: $i > $i > $i > $i > $i ).
thf(op2_decl,type,
op2: $i > $i > $i ).
thf(op1_decl,type,
op1: $i > $i > $i ).
thf(j_decl,type,
j: $i > $i ).
thf(sK2_ax3_V_decl,type,
sK2_ax3_V: $i > $i ).
thf(tuple_decl,type,
tuple: $i > $i > $i ).
thf(sK1_ax4_U_decl,type,
sK1_ax4_U: $i ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ op2 ) @ sorti2 @ ( true @ ( B @ sorti2 @ ifeq ) ) ) @ ( true @ ( A @ sorti2 @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ op2 ) @ sorti2 @ ( true @ ( B @ sorti2 @ ifeq ) ) ) @ ( true @ ( A @ sorti2 @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ j @ h @ ( true @ ( A @ sorti2 @ ifeq2 ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_5) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ j @ h @ ( true @ ( A @ sorti2 @ ifeq2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq2 ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ sorti2 @ ( A @ ( A @ op2 ) @ tuple ) )
!= ( true @ ( sK1_ax4_U @ tuple ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4_1) ).
thf(39,plain,
! [A: $i] :
( ( A @ sorti2 @ ( A @ ( A @ op2 ) @ tuple ) )
!= ( true @ ( sK1_ax4_U @ tuple ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,axiom,
! [A: $i] :
( ( true @ ( A @ sK2_ax3_V @ sorti1 @ ( true @ ( A @ sorti1 @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3_1) ).
thf(35,plain,
! [A: $i] :
( ( true @ ( A @ sK2_ax3_V @ sorti1 @ ( true @ ( A @ sorti1 @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
( ( A @ ( B @ op1 ) @ h @ ( A @ ( B @ op1 ) @ h @ ( A @ h @ ( B @ h @ op2 ) @ ( true @ ( B @ sorti1 @ ifeq2 ) ) ) @ ( true @ ( A @ sorti1 @ ifeq2 ) ) ) )
= ( A @ ( B @ op1 ) @ h ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_1) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ op1 ) @ h @ ( A @ ( B @ op1 ) @ h @ ( A @ h @ ( B @ h @ op2 ) @ ( true @ ( B @ sorti1 @ ifeq2 ) ) ) @ ( true @ ( A @ sorti1 @ ifeq2 ) ) ) )
= ( A @ ( B @ op1 ) @ h ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,negated_conjecture,
! [A: $i] :
( ( A @ ( A @ h @ j @ ( true @ ( A @ sorti1 @ ifeq2 ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_2) ).
thf(19,plain,
! [A: $i] :
( ( A @ ( A @ h @ j @ ( true @ ( A @ sorti1 @ ifeq2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,negated_conjecture,
! [B: $i,A: $i] :
( ( A @ ( B @ op2 ) @ j @ ( A @ ( B @ op2 ) @ j @ ( A @ j @ ( B @ j @ op1 ) @ ( true @ ( B @ sorti2 @ ifeq2 ) ) ) @ ( true @ ( A @ sorti2 @ ifeq2 ) ) ) )
= ( A @ ( B @ op2 ) @ j ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_4) ).
thf(15,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ op2 ) @ j @ ( A @ ( B @ op2 ) @ j @ ( A @ j @ ( B @ j @ op1 ) @ ( true @ ( B @ sorti2 @ ifeq2 ) ) ) @ ( true @ ( A @ sorti2 @ ifeq2 ) ) ) )
= ( A @ ( B @ op2 ) @ j ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
( ( sK1_ax4_U @ sorti2 )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
thf(42,plain,
( ( sK1_ax4_U @ sorti2 )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( A @ sK2_ax3_V @ ( A @ sK2_ax3_V @ op1 ) @ ( true @ ( A @ sorti1 @ ifeq2 ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( A @ sK2_ax3_V @ ( A @ sK2_ax3_V @ op1 ) @ ( true @ ( A @ sorti1 @ ifeq2 ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ( true @ ( A @ j @ sorti1 @ ( true @ ( A @ sorti2 @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1_3) ).
thf(20,plain,
! [A: $i] :
( ( true @ ( A @ j @ sorti1 @ ( true @ ( A @ sorti2 @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ( true @ ( A @ h @ sorti2 @ ( true @ ( A @ sorti1 @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
thf(16,plain,
! [A: $i] :
( ( true @ ( A @ h @ sorti2 @ ( true @ ( A @ sorti1 @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ op1 ) @ sorti1 @ ( true @ ( B @ sorti1 @ ifeq ) ) ) @ ( true @ ( A @ sorti1 @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ op1 ) @ sorti1 @ ( true @ ( B @ sorti1 @ ifeq ) ) ) @ ( true @ ( A @ sorti1 @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,plain,
$false,
inference(e,[status(thm)],[33,17,27,39,35,18,19,15,42,37,20,29,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG069-10 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.17/5.53 % Computer : n016.cluster.edu
% 0.17/5.53 % Model : x86_64 x86_64
% 0.17/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/5.53 % Memory : 8046.5625MB
% 0.17/5.53 % OS : Linux 6.8.0-71-generic
% 0.17/5.53 % CPULimit : 300
% 0.17/5.53 % WCLimit : 300
% 0.17/5.53 % DateTime : Sat Sep 26 21:10:22 UTC 2026
% 0.17/5.53 % CPUTime :
% 0.17/5.53 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
% 0.89/6.12 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/6.31 % [INFO] Parsing done (191ms).
% 1.37/6.33 % [INFO] Running in sequential loop mode.
% 1.96/6.74 % [INFO] eprover registered as external prover.
% 1.96/6.75 % [INFO] Scanning for conjecture ...
% 2.16/6.86 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 2.33/6.92 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 2.33/6.93 % [INFO] Problem is propositional (TPTP CNF).
% 2.33/6.93 % [INFO] Type checking passed.
% 2.33/6.94 % [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 ...
% 3.72/7.59 % External prover 'e' found a proof!
% 3.72/7.59 % [INFO] Killing All external provers ...
% 3.72/7.59 % Time passed: 1912ms (effective reasoning time: 1252ms)
% 3.72/7.59 % Axioms used in derivation (8): ax3_1, ax4, ifeq_axiom_001, ifeq_axiom, ax1, ax3, ax2, ax4_1
% 3.72/7.59 % No. of inferences in proof: 29
% 3.72/7.59 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 1912 ms resp. 1252 ms w/o parsing
% 4.04/7.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.04/7.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------