%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWX233-1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 11:02:37 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 144 ( 93 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 134 ( 7 ~; 0 |; 0 &; 127 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 ^; 42 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_aux,type,
aux: $i > $i > $i ).
thf(tp_bfalse,type,
bfalse: $i ).
thf(tp_btrue,type,
btrue: $i ).
thf(tp_cons,type,
cons: $i > $i > $i ).
thf(tp_eq,type,
eq: $i > $i > $i ).
thf(tp_f,type,
f: $i > $i ).
thf(tp_g,type,
g: $i > $i ).
thf(tp_h,type,
h: $i > $i ).
thf(tp_nil,type,
nil: $i ).
thf(tp_prop1,type,
prop1: $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( eq @ X @ X )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_011) ).
thf(2,axiom,
( ( eq @ btrue @ bfalse )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_010) ).
thf(3,axiom,
( ( eq @ bfalse @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_009) ).
thf(4,axiom,
! [X: $i] :
( ( prop1 @ X )
= ( eq @ ( f @ X ) @ bfalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_008) ).
thf(5,axiom,
! [Y: $i,Z: $i] :
( ( f @ ( cons @ Y @ Z ) )
= ( aux @ Z @ ( f @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_007) ).
thf(6,axiom,
( ( f @ nil )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_006) ).
thf(7,axiom,
( ( g @ bfalse )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_005) ).
thf(8,axiom,
( ( g @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_004) ).
thf(9,axiom,
! [Y: $i,Xs: $i] :
( ( h @ ( cons @ Y @ Xs ) )
= Xs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_003) ).
thf(10,axiom,
( ( h @ nil )
= nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_002) ).
thf(11,axiom,
! [Z: $i] :
( ( aux @ Z @ bfalse )
= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_001) ).
thf(12,axiom,
! [Z: $i] :
( ( aux @ Z @ btrue )
= bfalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
! [X: $i] :
( ( eq @ ( prop1 @ X ) @ bfalse )
!= btrue ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ( eq @ btrue @ bfalse )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ( eq @ bfalse @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( prop1 @ X )
= ( eq @ ( f @ X ) @ bfalse ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [Y: $i,Z: $i] :
( ( f @ ( cons @ Y @ Z ) )
= ( aux @ Z @ ( f @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ( f @ nil )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ( g @ bfalse )
= btrue )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ( g @ btrue )
= bfalse )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [Y: $i,Xs: $i] :
( ( h @ ( cons @ Y @ Xs ) )
= Xs ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ( h @ nil )
= nil )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [Z: $i] :
( ( aux @ Z @ bfalse )
= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [Z: $i] :
( ( aux @ Z @ btrue )
= bfalse ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( eq @ ( prop1 @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i] :
( ( eq @ ( prop1 @ X ) @ bfalse )
!= btrue ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(32,plain,
( ( ! [Z: $i] :
( ( aux @ Z @ btrue )
= bfalse ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(33,plain,
( ( ! [Z: $i] :
( ( aux @ Z @ bfalse )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(34,plain,
( ( ( h @ nil )
= nil )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(35,plain,
( ( ! [Y: $i,Xs: $i] :
( ( h @ ( cons @ Y @ Xs ) )
= Xs ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(36,plain,
( ( ( g @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ( g @ bfalse )
= btrue )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(38,plain,
( ( ( f @ nil )
= btrue )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(39,plain,
( ( ! [Y: $i,Z: $i] :
( ( f @ ( cons @ Y @ Z ) )
= ( aux @ Z @ ( f @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( prop1 @ X )
= ( eq @ ( f @ X ) @ bfalse ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(41,plain,
( ( ( eq @ bfalse @ btrue )
= bfalse )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(42,plain,
( ( ( eq @ btrue @ bfalse )
= bfalse )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( eq @ X @ X )
= btrue ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(44,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[30]) ).
thf(45,plain,
( ( ! [SX0: $i] :
( ( eq @ ( prop1 @ SX0 ) @ bfalse )
!= btrue ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(46,plain,
! [SV1: $i] :
( ( ( aux @ SV1 @ btrue )
= bfalse )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(47,plain,
! [SV2: $i] :
( ( ( aux @ SV2 @ bfalse )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(48,plain,
! [SV3: $i] :
( ( ! [SY9: $i] :
( ( h @ ( cons @ SV3 @ SY9 ) )
= SY9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(49,plain,
! [SV4: $i] :
( ( ! [SY10: $i] :
( ( f @ ( cons @ SV4 @ SY10 ) )
= ( aux @ SY10 @ ( f @ SY10 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(50,plain,
! [SV5: $i] :
( ( ( prop1 @ SV5 )
= ( eq @ ( f @ SV5 ) @ bfalse ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(51,plain,
! [SV6: $i] :
( ( ( eq @ SV6 @ SV6 )
= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(52,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV7: $i] :
( ( ( eq @ ( prop1 @ SV7 ) @ bfalse )
!= btrue )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV8: $i,SV3: $i] :
( ( ( h @ ( cons @ SV3 @ SV8 ) )
= SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV9: $i,SV4: $i] :
( ( ( f @ ( cons @ SV4 @ SV9 ) )
= ( aux @ SV9 @ ( f @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV7: $i] :
( ( ( eq @ ( prop1 @ SV7 ) @ bfalse )
= btrue )
= $false ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,56,55,54,52,51,50,47,46,42,41,38,37,36]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX233-1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n003.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 17:16:39 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 13
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 0
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 58 ****
% 0.07/0.23 %**** clause counter: 57 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:13,ps:3,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------