%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI044_1 : TPTP v9.3.1. Released v7.5.0.
% 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 : n012.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 08:19:35 AM UTC 2026
% Result : Unsatisfiable 27.51s 6.99s
% Output : Refutation 27.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of formulae : 17 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 132 ( 33 equ; 0 cnn)
% Maximal formula atoms : 33 ( 7 avg)
% Number of connectives : 320 ( 9 ~; 11 |; 61 &; 196 @)
% ( 8 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 75 ( 0 ^; 59 !; 16 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(option_type,type,
option: $tType ).
thf(option_set_type,type,
option_set: $tType ).
thf(subset_decl,type,
subset: option_set > option_set > $o ).
thf(member_decl,type,
member: option > option_set > $o ).
thf(weakly_better_decl,type,
weakly_better: option_set > option_set > $o ).
thf(better_decl,type,
better: option_set > option_set > $o ).
thf(permitted_preference_decl,type,
permitted_preference: option > option > $o ).
thf(required_preference_decl,type,
required_preference: option > option > $o ).
thf(7,axiom,
! [A: option_set,B: option_set,C: option_set] :
( ( ( C @ ( B @ weakly_better ) )
& ( B @ ( A @ weakly_better ) ) )
=> ( C @ ( A @ weakly_better ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_weakly_better_freedom_of_choice) ).
thf(61,plain,
! [A: option_set,B: option_set,C: option_set] :
( ( ( C @ ( B @ weakly_better ) )
& ( B @ ( A @ weakly_better ) ) )
=> ( C @ ( A @ weakly_better ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,axiom,
! [A: option_set,B: option_set] :
( ( B @ ( A @ subset ) )
<=> ! [C: option] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset) ).
thf(9,plain,
! [A: option_set,B: option_set] :
( ( ! [C: option] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: option] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,axiom,
! [A: option_set,B: option_set] :
( ( B @ ( A @ better ) )
<=> ( ~ ( A @ ( B @ weakly_better ) )
& ( B @ ( A @ weakly_better ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',better) ).
thf(17,plain,
! [A: option_set,B: option_set] :
( ( ( ~ ( A @ ( B @ weakly_better ) )
& ( B @ ( A @ weakly_better ) ) )
=> ( B @ ( A @ better ) ) )
& ( ( B @ ( A @ better ) )
=> ( ~ ( A @ ( B @ weakly_better ) )
& ( B @ ( A @ weakly_better ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
! [A: option,B: option,C: option_set,D: option_set] :
( ( ! [E: option] :
( ( D @ ( E @ member ) )
<=> ( E = B ) )
& ! [E: option] :
( ( C @ ( E @ member ) )
<=> ( E = A ) ) )
=> ~ ( D @ ( C @ better ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',parity_of_no_choice_situations) ).
thf(44,plain,
! [A: option,B: option,C: option_set,D: option_set] :
( ( ! [E: option] :
( ( ( E = B )
=> ( D @ ( E @ member ) ) )
& ( ( D @ ( E @ member ) )
=> ( E = B ) ) )
& ! [E: option] :
( ( ( E = A )
=> ( C @ ( E @ member ) ) )
& ( ( C @ ( E @ member ) )
=> ( E = A ) ) ) )
=> ~ ( D @ ( C @ better ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
? [A: option,B: option,C: option,D: option_set,E: option_set,F: option_set,G: option_set] :
( ! [H: option] :
( ( G @ ( H @ member ) )
<=> ( ( H = C )
| ( H = B )
| ( H = A ) ) )
& ! [H: option] :
( ( F @ ( H @ member ) )
<=> ( ( H = B )
| ( H = A ) ) )
& ! [H: option] :
( ( E @ ( H @ member ) )
<=> ( H = C ) )
& ! [H: option] :
( ( D @ ( H @ member ) )
<=> ( H = A ) )
& ( G @ ( C @ member ) )
& ( G @ ( B @ member ) )
& ( G @ ( A @ member ) )
& ( F @ ( B @ member ) )
& ( F @ ( A @ member ) )
& ( E @ ( C @ member ) )
& ( D @ ( A @ member ) )
& ( B @ ( C @ required_preference ) )
& ( A @ ( C @ required_preference ) )
& ( A @ ( B @ permitted_preference ) )
& ( B @ ( A @ permitted_preference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_dominated_diversity) ).
thf(63,plain,
? [A: option,B: option,C: option,D: option_set,E: option_set,F: option_set,G: option_set] :
( ! [H: option] :
( ( ( ( H = C )
| ( H = B )
| ( H = A ) )
=> ( G @ ( H @ member ) ) )
& ( ( G @ ( H @ member ) )
=> ( ( H = C )
| ( H = B )
| ( H = A ) ) ) )
& ! [H: option] :
( ( ( ( H = B )
| ( H = A ) )
=> ( F @ ( H @ member ) ) )
& ( ( F @ ( H @ member ) )
=> ( ( H = B )
| ( H = A ) ) ) )
& ! [H: option] :
( ( ( H = C )
=> ( E @ ( H @ member ) ) )
& ( ( E @ ( H @ member ) )
=> ( H = C ) ) )
& ! [H: option] :
( ( ( H = A )
=> ( D @ ( H @ member ) ) )
& ( ( D @ ( H @ member ) )
=> ( H = A ) ) )
& ( G @ ( C @ member ) )
& ( G @ ( B @ member ) )
& ( G @ ( A @ member ) )
& ( F @ ( B @ member ) )
& ( F @ ( A @ member ) )
& ( E @ ( C @ member ) )
& ( D @ ( A @ member ) )
& ( B @ ( C @ required_preference ) )
& ( A @ ( C @ required_preference ) )
& ( A @ ( B @ permitted_preference ) )
& ( B @ ( A @ permitted_preference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
! [A: option_set,B: option_set] :
( ( B @ ( A @ subset ) )
=> ( A @ ( B @ weakly_better ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',harmlessness_of_expansions) ).
thf(42,plain,
! [A: option_set,B: option_set] :
( ( B @ ( A @ subset ) )
=> ( A @ ( B @ weakly_better ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: option,B: option,C: option_set,D: option_set] :
( ( ! [E: option] :
( ( D @ ( E @ member ) )
=> ( E = A ) )
& ! [E: option] :
( ( C @ ( E @ member ) )
=> ( ( E = B )
| ( E = A ) ) )
& ( D @ ( A @ member ) )
& ( C @ ( B @ member ) )
& ( C @ ( A @ member ) )
& ( A @ ( B @ permitted_preference ) )
& ( B @ ( A @ permitted_preference ) ) )
=> ( D @ ( C @ better ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',value_of_rational_diversity) ).
thf(24,plain,
! [A: option,B: option,C: option_set,D: option_set] :
( ( ! [E: option] :
( ( D @ ( E @ member ) )
=> ( E = A ) )
& ! [E: option] :
( ( C @ ( E @ member ) )
=> ( ( E = B )
| ( E = A ) ) )
& ( D @ ( A @ member ) )
& ( C @ ( B @ member ) )
& ( C @ ( A @ member ) )
& ( A @ ( B @ permitted_preference ) )
& ( B @ ( A @ permitted_preference ) ) )
=> ( D @ ( C @ better ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: option_set,B: option_set] :
( ( ? [C: option] :
( ! [D: option] :
( ( ~ ( A @ ( D @ member ) )
& ( B @ ( D @ member ) ) )
=> ( D @ ( C @ required_preference ) ) )
& ( A @ ( C @ member ) ) )
& ( B @ ( A @ subset ) ) )
=> ~ ( A @ ( B @ better ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insignificance_of_dominated_options) ).
thf(37,plain,
! [A: option_set,B: option_set] :
( ( ? [C: option] :
( ! [D: option] :
( ( ~ ( A @ ( D @ member ) )
& ( B @ ( D @ member ) ) )
=> ( D @ ( C @ required_preference ) ) )
& ( A @ ( C @ member ) ) )
& ( B @ ( A @ subset ) ) )
=> ~ ( A @ ( B @ better ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(26907,plain,
$false,
inference(e,[status(thm)],[61,9,17,44,63,42,24,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PHI044_1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % 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
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sat Sep 26 04:41:20 UTC 2026
% 0.05/0.31 % CPUTime :
% 0.05/0.31 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
% 0.39/0.59 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.52/0.69 % [INFO] Parsing done (90ms).
% 0.52/0.69 % [INFO] Running in sequential loop mode.
% 0.88/0.87 % [INFO] eprover registered as external prover.
% 0.88/0.87 % [INFO] Scanning for conjecture ...
% 1.06/0.90 % [INFO] 8 axioms and no conjecture found.
% 1.06/0.95 % [INFO] Problem is typed first-order (TPTP TFF).
% 1.06/0.95 % [INFO] Type checking passed.
% 1.06/0.95 % [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 ...
% 27.51/6.99 % External prover 'e' found a proof!
% 27.51/6.99 % [INFO] Killing All external provers ...
% 27.51/6.99 % Time passed: 6602ms (effective reasoning time: 6296ms)
% 27.51/6.99 % Axioms used in derivation (8): harmlessness_of_expansions, existence_of_dominated_diversity, insignificance_of_dominated_options, subset, value_of_rational_diversity, transitivity_of_weakly_better_freedom_of_choice, better, parity_of_no_choice_situations
% 27.51/6.99 % No. of inferences in proof: 17
% 27.51/6.99 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6602 ms resp. 6296 ms w/o parsing
% 27.51/7.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.51/7.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------