%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : PUZ032-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Wed Oct 7 10:36:42 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.19s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 69 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 325 ( 86 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 469 ( 74 ~; 84 |; 0 &; 311 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_a_truth,type,
a_truth: $i > $o ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_liar,type,
liar: $i > $i ).
thf(tp_mumble,type,
mumble: $i ).
thf(tp_says,type,
says: $i > $i > $i ).
thf(tp_truthteller,type,
truthteller: $i > $i ).
thf(1,axiom,
! [Statement: $i,Liar: $i] :
( ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_are_told_by_liars) ).
thf(2,axiom,
! [Statement: $i,Truthteller: $i] :
( ~ ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truths_are_told_by_truthtellers) ).
thf(3,axiom,
! [Liar: $i,Statement: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',liars_lie) ).
thf(4,axiom,
! [Truthteller: $i,Statement: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthtellers_tell_truth) ).
thf(5,axiom,
! [X: $i] :
( ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( liar @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_both) ).
thf(6,axiom,
! [X: $i] :
( ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( liar @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
thf(7,axiom,
a_truth @ ( says @ c @ ( liar @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_says_b_is_a_liar) ).
thf(8,axiom,
a_truth @ ( says @ b @ ( says @ a @ ( liar @ a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_says_a_says_hes_a_liar) ).
thf(9,axiom,
a_truth @ ( says @ a @ mumble ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_mumbles) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,negated_conjecture,
~ ( a_truth @ ( truthteller @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_is_a_truthteller) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [Statement: $i,Liar: $i] :
( ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [Statement: $i,Truthteller: $i] :
( ~ ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [Liar: $i,Statement: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [Truthteller: $i,Statement: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [X: $i] :
( ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( a_truth @ ( says @ c @ ( liar @ b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( a_truth @ ( says @ b @ ( says @ a @ ( liar @ a ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( a_truth @ ( says @ a @ mumble ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ~ ( a_truth @ ( truthteller @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ~ ( a_truth @ ( truthteller @ c ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(26,plain,
( ( a_truth @ ( says @ a @ mumble ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(27,plain,
( ( a_truth @ ( says @ b @ ( says @ a @ ( liar @ a ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(28,plain,
( ( a_truth @ ( says @ c @ ( liar @ b ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( a_truth @ ( truthteller @ X ) )
| ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [X: $i] :
( ~ ( a_truth @ ( truthteller @ X ) )
| ~ ( a_truth @ ( liar @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(31,plain,
( ( ! [Truthteller: $i,Statement: $i] :
( ~ ( a_truth @ ( truthteller @ Truthteller ) )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ Statement ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(32,plain,
( ( ! [Liar: $i,Statement: $i] :
( ~ ( a_truth @ ( liar @ Liar ) )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ~ ( a_truth @ Statement ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(33,plain,
( ( ! [Statement: $i,Truthteller: $i] :
( ~ ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Truthteller @ Statement ) )
| ( a_truth @ ( truthteller @ Truthteller ) ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [Statement: $i,Liar: $i] :
( ( a_truth @ Statement )
| ~ ( a_truth @ ( says @ Liar @ Statement ) )
| ( a_truth @ ( liar @ Liar ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(36,plain,
( ( a_truth @ ( truthteller @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(37,plain,
! [SV1: $i] :
( ( ( a_truth @ ( truthteller @ SV1 ) )
| ( a_truth @ ( liar @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(38,plain,
! [SV2: $i] :
( ( ~ ( a_truth @ ( truthteller @ SV2 ) )
| ~ ( a_truth @ ( liar @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(39,plain,
! [SV3: $i] :
( ( ! [SY10: $i] :
( ~ ( a_truth @ ( truthteller @ SV3 ) )
| ~ ( a_truth @ ( says @ SV3 @ SY10 ) )
| ( a_truth @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(40,plain,
! [SV4: $i] :
( ( ! [SY11: $i] :
( ~ ( a_truth @ ( liar @ SV4 ) )
| ~ ( a_truth @ ( says @ SV4 @ SY11 ) )
| ~ ( a_truth @ SY11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV5: $i] :
( ( ! [SY12: $i] :
( ~ ( a_truth @ SV5 )
| ~ ( a_truth @ ( says @ SY12 @ SV5 ) )
| ( a_truth @ ( truthteller @ SY12 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV6: $i] :
( ( ! [SY13: $i] :
( ( a_truth @ SV6 )
| ~ ( a_truth @ ( says @ SY13 @ SV6 ) )
| ( a_truth @ ( liar @ SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV1: $i] :
( ( ( a_truth @ ( truthteller @ SV1 ) )
= $true )
| ( ( a_truth @ ( liar @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(45,plain,
! [SV2: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV2 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( liar @ SV2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(46,plain,
! [SV7: $i,SV3: $i] :
( ( ~ ( a_truth @ ( truthteller @ SV3 ) )
| ~ ( a_truth @ ( says @ SV3 @ SV7 ) )
| ( a_truth @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(47,plain,
! [SV8: $i,SV4: $i] :
( ( ~ ( a_truth @ ( liar @ SV4 ) )
| ~ ( a_truth @ ( says @ SV4 @ SV8 ) )
| ~ ( a_truth @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ( a_truth @ SV5 )
| ~ ( a_truth @ ( says @ SV9 @ SV5 ) )
| ( a_truth @ ( truthteller @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV10: $i,SV6: $i] :
( ( ( a_truth @ SV6 )
| ~ ( a_truth @ ( says @ SV10 @ SV6 ) )
| ( a_truth @ ( liar @ SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV2: $i] :
( ( ( a_truth @ ( truthteller @ SV2 ) )
= $false )
| ( ( ~ ( a_truth @ ( liar @ SV2 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(51,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( a_truth @ ( truthteller @ SV3 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( says @ SV3 @ SV7 ) )
| ( a_truth @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[46]) ).
thf(52,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( a_truth @ ( liar @ SV4 ) ) )
= $true )
| ( ( ~ ( a_truth @ ( says @ SV4 @ SV8 ) )
| ~ ( a_truth @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( a_truth @ SV5 ) )
= $true )
| ( ( ~ ( a_truth @ ( says @ SV9 @ SV5 ) )
| ( a_truth @ ( truthteller @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV10: $i,SV6: $i] :
( ( ( a_truth @ SV6 )
= $true )
| ( ( ~ ( a_truth @ ( says @ SV10 @ SV6 ) )
| ( a_truth @ ( liar @ SV10 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(55,plain,
! [SV2: $i] :
( ( ( a_truth @ ( liar @ SV2 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(56,plain,
! [SV7: $i,SV3: $i] :
( ( ( a_truth @ ( truthteller @ SV3 ) )
= $false )
| ( ( ~ ( a_truth @ ( says @ SV3 @ SV7 ) )
| ( a_truth @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV8: $i,SV4: $i] :
( ( ( a_truth @ ( liar @ SV4 ) )
= $false )
| ( ( ~ ( a_truth @ ( says @ SV4 @ SV8 ) )
| ~ ( a_truth @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV9: $i,SV5: $i] :
( ( ( a_truth @ SV5 )
= $false )
| ( ( ~ ( a_truth @ ( says @ SV9 @ SV5 ) )
| ( a_truth @ ( truthteller @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(59,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( a_truth @ ( says @ SV10 @ SV6 ) ) )
= $true )
| ( ( a_truth @ ( liar @ SV10 ) )
= $true )
| ( ( a_truth @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV7: $i,SV3: $i] :
( ( ( ~ ( a_truth @ ( says @ SV3 @ SV7 ) ) )
= $true )
| ( ( a_truth @ SV7 )
= $true )
| ( ( a_truth @ ( truthteller @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(61,plain,
! [SV8: $i,SV4: $i] :
( ( ( ~ ( a_truth @ ( says @ SV4 @ SV8 ) ) )
= $true )
| ( ( ~ ( a_truth @ SV8 ) )
= $true )
| ( ( a_truth @ ( liar @ SV4 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(62,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ( a_truth @ ( says @ SV9 @ SV5 ) ) )
= $true )
| ( ( a_truth @ ( truthteller @ SV9 ) )
= $true )
| ( ( a_truth @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(63,plain,
! [SV6: $i,SV10: $i] :
( ( ( a_truth @ ( says @ SV10 @ SV6 ) )
= $false )
| ( ( a_truth @ ( liar @ SV10 ) )
= $true )
| ( ( a_truth @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(64,plain,
! [SV7: $i,SV3: $i] :
( ( ( a_truth @ ( says @ SV3 @ SV7 ) )
= $false )
| ( ( a_truth @ SV7 )
= $true )
| ( ( a_truth @ ( truthteller @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(65,plain,
! [SV8: $i,SV4: $i] :
( ( ( a_truth @ ( says @ SV4 @ SV8 ) )
= $false )
| ( ( ~ ( a_truth @ SV8 ) )
= $true )
| ( ( a_truth @ ( liar @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV5: $i,SV9: $i] :
( ( ( a_truth @ ( says @ SV9 @ SV5 ) )
= $false )
| ( ( a_truth @ ( truthteller @ SV9 ) )
= $true )
| ( ( a_truth @ SV5 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV4: $i,SV8: $i] :
( ( ( a_truth @ SV8 )
= $false )
| ( ( a_truth @ ( says @ SV4 @ SV8 ) )
= $false )
| ( ( a_truth @ ( liar @ SV4 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(68,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,67,66,64,63,55,44,43,36,28,27]) ).
thf(69,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ032-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.16 % Computer : n026.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Oct 6 14:00:02 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19
% 0.09/0.19 No.of.Axioms: 10
% 0.09/0.19
% 0.09/0.19 Length.of.Defs: 0
% 0.09/0.19
% 0.09/0.19 Contains.Choice.Funs: false
% 0.09/0.19 .
% 0.09/0.19
% 0.09/0.19 ********************************
% 0.09/0.19 * All subproblems solved! *
% 0.09/0.19 ********************************
% 0.09/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:68,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.19
% 0.09/0.19 %**** Beginning of derivation protocol ****
% 0.09/0.19 % SZS output start CNFRefutation
% See solution above
% 0.09/0.19
% 0.09/0.19 %**** End of derivation protocol ****
% 0.09/0.19 %**** no. of clauses in derivation: 69 ****
% 0.09/0.19 %**** clause counter: 68 ****
% 0.09/0.19
% 0.09/0.19 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:10,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:68,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------