%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 08:22:43 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 17
% Syntax : Number of formulae : 70 ( 11 unt; 0 def)
% Number of atoms : 145 ( 5 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 133 ( 58 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 21 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(not_truthteller_and_liar,axiom,
! [VAR_0] :
( ~ liar(VAR_0)
| ~ truthteller(VAR_0) ),
file('theBenchmark.p',not_truthteller_and_liar) ).
cnf(c_1,plain,
( ~ liar(A)
| ~ truthteller(A) ),
inference(clausify,[status(thm)],[not_truthteller_and_liar]) ).
fof(true_statements_made_by_truthtellers,axiom,
! [VAR_0] :
( truthteller(VAR_0)
| ~ a_truth(statement_by(VAR_0)) ),
file('theBenchmark.p',true_statements_made_by_truthtellers) ).
cnf(c_3,plain,
( truthteller(A)
| ~ a_truth(statement_by(A)) ),
inference(clausify,[status(thm)],[true_statements_made_by_truthtellers]) ).
fof(venusian_female_are_truthtellers,axiom,
! [VAR_0] :
( truthteller(VAR_0)
| ~ female(VAR_0)
| ~ from_venus(VAR_0) ),
file('theBenchmark.p',venusian_female_are_truthtellers) ).
cnf(c_4,plain,
( truthteller(A)
| ~ female(A)
| ~ from_venus(A) ),
inference(clausify,[status(thm)],[venusian_female_are_truthtellers]) ).
cnf(c_9,plain,
( ~ liar(A)
| ~ female(A)
| ~ from_venus(A) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
cnf(c_10,plain,
( ~ liar(A)
| ~ a_truth(statement_by(A)) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
fof(marsian_females_are_liars,axiom,
! [VAR_0] :
( liar(VAR_0)
| ~ female(VAR_0)
| ~ from_mars(VAR_0) ),
file('theBenchmark.p',marsian_females_are_liars) ).
cnf(c_12,plain,
( liar(A)
| ~ female(A)
| ~ from_mars(A) ),
inference(clausify,[status(thm)],[marsian_females_are_liars]) ).
fof(false_statements_made_by_liars,axiom,
! [VAR_0] :
( liar(VAR_0)
| a_truth(statement_by(VAR_0)) ),
file('theBenchmark.p',false_statements_made_by_liars) ).
cnf(c_14,plain,
( liar(A)
| a_truth(statement_by(A)) ),
inference(clausify,[status(thm)],[false_statements_made_by_liars]) ).
cnf(c_16,plain,
( ~ female(A)
| ~ from_venus(A)
| a_truth(statement_by(A)) ),
inference(resolve,[status(thm)],[c_14,c_9]) ).
cnf(c_20,plain,
( ~ a_truth(statement_by(A))
| ~ female(A)
| ~ from_mars(A) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
fof(from_mars_or_venus,axiom,
! [VAR_0] :
( from_venus(VAR_0)
| from_mars(VAR_0) ),
file('theBenchmark.p',from_mars_or_venus) ).
cnf(c_26,plain,
( from_venus(A)
| from_mars(A) ),
inference(clausify,[status(thm)],[from_mars_or_venus]) ).
fof(not_from_mars_and_venus,axiom,
! [VAR_0] :
( ~ from_venus(VAR_0)
| ~ from_mars(VAR_0) ),
file('theBenchmark.p',not_from_mars_and_venus) ).
cnf(c_27,plain,
( ~ from_venus(A)
| ~ from_mars(A) ),
inference(clausify,[status(thm)],[not_from_mars_and_venus]) ).
fof(male_or_female,axiom,
! [VAR_0] :
( female(VAR_0)
| male(VAR_0) ),
file('theBenchmark.p',male_or_female) ).
cnf(c_28,plain,
( female(A)
| male(A) ),
inference(clausify,[status(thm)],[male_or_female]) ).
fof(a_from_mars1,axiom,
( a_truth(a_from_mars)
| ~ from_mars(a) ),
file('theBenchmark.p',a_from_mars1) ).
cnf(c_34,plain,
( a_truth(a_from_mars)
| ~ from_mars(a) ),
inference(clausify,[status(thm)],[a_from_mars1]) ).
fof(a_from_mars2,axiom,
( ~ a_truth(a_from_mars)
| from_mars(a) ),
file('theBenchmark.p',a_from_mars2) ).
cnf(c_35,plain,
( ~ a_truth(a_from_mars)
| from_mars(a) ),
inference(clausify,[status(thm)],[a_from_mars2]) ).
fof(a_from_mars3,axiom,
( ~ a_truth(statement_by(b))
| ~ a_truth(a_from_mars) ),
file('theBenchmark.p',a_from_mars3) ).
cnf(c_36,plain,
( ~ a_truth(statement_by(b))
| ~ a_truth(a_from_mars) ),
inference(clausify,[status(thm)],[a_from_mars3]) ).
fof(a_states,axiom,
statement_by(a) = a_from_mars,
file('theBenchmark.p',a_states) ).
cnf(c_37,plain,
statement_by(a) = a_from_mars,
inference(clausify,[status(thm)],[a_states]) ).
cnf(c_38,plain,
a_from_mars = statement_by(a),
inference(copy,[status(thm)],[c_37]) ).
fof(b_states,axiom,
statement_by(b) = a_has_lied,
file('theBenchmark.p',b_states) ).
cnf(c_39,plain,
statement_by(b) = a_has_lied,
inference(clausify,[status(thm)],[b_states]) ).
fof(truth_of_bs_statement,axiom,
( a_truth(statement_by(b))
| a_truth(a_from_mars) ),
file('theBenchmark.p',truth_of_bs_statement) ).
cnf(c_40,plain,
( a_truth(statement_by(b))
| a_truth(a_from_mars) ),
inference(clausify,[status(thm)],[truth_of_bs_statement]) ).
cnf(c_145,plain,
( a_truth(statement_by(b))
| a_truth(statement_by(a)) ),
inference(paramod,[status(thm)],[c_38,c_40]) ).
cnf(c_41,plain,
( a_truth(a_has_lied)
| a_truth(statement_by(a)) ),
inference(paramod,[status(thm)],[c_39,c_145]) ).
fof(different_sex2,axiom,
( female(b)
| ~ male(a) ),
file('theBenchmark.p',different_sex2) ).
cnf(c_43,plain,
( female(b)
| ~ male(a) ),
inference(clausify,[status(thm)],[different_sex2]) ).
fof(one_from_mars,axiom,
( from_mars(a)
| from_mars(b) ),
file('theBenchmark.p',one_from_mars) ).
cnf(c_44,plain,
( from_mars(a)
| from_mars(b) ),
inference(clausify,[status(thm)],[one_from_mars]) ).
fof(one_from_venus,axiom,
( from_venus(b)
| from_venus(a) ),
file('theBenchmark.p',one_from_venus) ).
cnf(c_45,plain,
( from_venus(b)
| from_venus(a) ),
inference(clausify,[status(thm)],[one_from_venus]) ).
cnf(c_146,plain,
( ~ a_truth(statement_by(b))
| ~ a_truth(statement_by(a)) ),
inference(paramod,[status(thm)],[c_38,c_36]) ).
cnf(c_46,plain,
( ~ a_truth(a_has_lied)
| ~ a_truth(statement_by(a)) ),
inference(paramod,[status(thm)],[c_39,c_146]) ).
cnf(c_47,plain,
( ~ a_truth(statement_by(a))
| from_mars(a) ),
inference(paramod,[status(thm)],[c_38,c_35]) ).
cnf(c_48,plain,
( a_truth(statement_by(a))
| ~ from_mars(a) ),
inference(paramod,[status(thm)],[c_38,c_34]) ).
cnf(c_53,plain,
( ~ female(A)
| a_truth(statement_by(A))
| from_mars(A) ),
inference(resolve,[status(thm)],[c_26,c_16]) ).
cnf(c_67,plain,
( ~ female(a)
| ~ from_mars(a)
| a_truth(a_has_lied) ),
inference(resolve,[status(thm)],[c_41,c_20]) ).
cnf(c_73,plain,
( female(a)
| female(b) ),
inference(resolve,[status(thm)],[c_43,c_28]) ).
cnf(c_147,plain,
( ~ a_truth(statement_by(b))
| ~ female(b)
| from_mars(a) ),
inference(resolve,[status(thm)],[c_44,c_20]) ).
cnf(c_77,plain,
( ~ a_truth(a_has_lied)
| ~ female(b)
| from_mars(a) ),
inference(paramod,[status(thm)],[c_39,c_147]) ).
cnf(c_79,plain,
( ~ from_mars(b)
| from_venus(a) ),
inference(resolve,[status(thm)],[c_45,c_27]) ).
cnf(c_84,plain,
( a_truth(a_has_lied)
| from_mars(a) ),
inference(resolve,[status(thm)],[c_47,c_41]) ).
cnf(c_97,plain,
( ~ from_venus(a)
| a_truth(a_has_lied) ),
inference(resolve,[status(thm)],[c_84,c_27]) ).
cnf(c_148,plain,
( female(a)
| a_truth(statement_by(b))
| from_mars(b) ),
inference(resolve,[status(thm)],[c_53,c_73]) ).
cnf(c_100,plain,
( female(a)
| a_truth(a_has_lied)
| from_mars(b) ),
inference(paramod,[status(thm)],[c_39,c_148]) ).
cnf(c_149,plain,
( a_truth(a_has_lied)
| ~ female(a)
| a_truth(a_has_lied) ),
inference(resolve,[status(thm)],[c_67,c_84]) ).
cnf(c_105,plain,
( ~ female(a)
| a_truth(a_has_lied) ),
inference(copy,[status(thm)],[c_149]) ).
cnf(c_106,plain,
( female(a)
| ~ a_truth(a_has_lied)
| from_mars(a) ),
inference(resolve,[status(thm)],[c_77,c_73]) ).
cnf(c_150,plain,
( a_truth(a_has_lied)
| a_truth(a_has_lied)
| from_mars(b) ),
inference(resolve,[status(thm)],[c_100,c_105]) ).
cnf(c_111,plain,
( a_truth(a_has_lied)
| from_mars(b) ),
inference(copy,[status(thm)],[c_150]) ).
cnf(c_112,plain,
( from_venus(a)
| a_truth(a_has_lied) ),
inference(resolve,[status(thm)],[c_111,c_79]) ).
cnf(c_151,plain,
( a_truth(a_has_lied)
| a_truth(a_has_lied) ),
inference(resolve,[status(thm)],[c_112,c_97]) ).
cnf(c_116,plain,
a_truth(a_has_lied),
inference(copy,[status(thm)],[c_151]) ).
cnf(c_119,plain,
( female(a)
| from_mars(a) ),
inference(resolve,[status(thm)],[c_116,c_106]) ).
cnf(c_128,plain,
~ a_truth(statement_by(a)),
inference(resolve,[status(thm)],[c_116,c_46]) ).
cnf(c_129,plain,
~ from_mars(a),
inference(resolve,[status(thm)],[c_128,c_48]) ).
cnf(c_131,plain,
female(a),
inference(resolve,[status(thm)],[c_129,c_119]) ).
cnf(c_152,plain,
( a_truth(statement_by(a))
| from_mars(a) ),
inference(resolve,[status(thm)],[c_131,c_53]) ).
cnf(c_153,plain,
a_truth(statement_by(a)),
inference(resolve,[status(thm)],[c_129,c_152]) ).
cnf(c_144,plain,
$false,
inference(resolve,[status(thm)],[c_128,c_153]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:03:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3399270 was started by sandbox on n009,
% 0.09/0.36 % Sat Sep 26 05:03:30 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.13/0.38 % Length of proof is 44.
% 0.13/0.38 % Level of proof is 11.
% 0.13/0.38 % Maximum clause weight is 17.000.
% 0.13/0.38 % Given clauses 74.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------