%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL096-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 10:27:58 AM UTC 2026
% Result : Unsatisfiable 32.44s 5.63s
% Output : CNFRefutation 32.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 148 ( 43 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 535 ( 19 ~; 18 |; 0 &; 498 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 5 con; 0-2 aty)
% Number of variables : 126 ( 0 ^; 126 !; 0 ?; 126 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_equivalent,type,
equivalent: $i > $i > $i ).
thf(tp_is_a_theorem,type,
is_a_theorem: $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i,Z: $i,U: $i,V: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ Z ) @ U ) @ ( equivalent @ ( equivalent @ ( equivalent @ X @ V ) @ Z ) @ ( equivalent @ ( equivalent @ Y @ V ) @ U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_4) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i,U: $i,V: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ U ) @ ( equivalent @ ( equivalent @ Y @ Z ) @ U ) ) @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_3) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i,U: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ ( equivalent @ Y @ Z ) ) @ U ) @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lg_2) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equivalent @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
thf(5,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(6,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[5]) ).
thf(7,negated_conjecture,
~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lg_1) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ Z ) @ U ) @ ( equivalent @ ( equivalent @ ( equivalent @ X @ V ) @ Z ) @ ( equivalent @ ( equivalent @ Y @ V ) @ U ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(10,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ U ) @ ( equivalent @ ( equivalent @ Y @ Z ) @ U ) ) @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(11,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ ( equivalent @ Y @ Z ) ) @ U ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equivalent @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( ~ ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equivalent @ X @ Y ) )
| ~ ( is_a_theorem @ X )
| ( is_a_theorem @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ ( equivalent @ Y @ Z ) ) @ U ) @ U ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ ( equivalent @ X @ Z ) ) @ U ) @ ( equivalent @ ( equivalent @ Y @ Z ) @ U ) ) @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i,Z: $i,U: $i,V: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ X @ Y ) @ Z ) @ U ) @ ( equivalent @ ( equivalent @ ( equivalent @ X @ V ) @ Z ) @ ( equivalent @ ( equivalent @ Y @ V ) @ U ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ a @ ( equivalent @ ( equivalent @ b @ b ) @ a ) ) @ c ) @ c ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[15]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY16: $i] :
( ~ ( is_a_theorem @ ( equivalent @ SV1 @ SY16 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SY16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY17: $i,SY18: $i,SY19: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV2 @ SY17 ) @ ( equivalent @ SV2 @ SY18 ) ) @ ( equivalent @ SY17 @ SY18 ) ) @ SY19 ) @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
! [SV3: $i] :
( ( ! [SY20: $i,SY21: $i,SY22: $i,SY23: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SY20 ) @ ( equivalent @ SV3 @ SY21 ) ) @ SY22 ) @ ( equivalent @ ( equivalent @ SY20 @ SY21 ) @ SY22 ) ) @ SY23 ) @ SY23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV4: $i] :
( ( ! [SY24: $i,SY25: $i,SY26: $i,SY27: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SY24 ) @ SY25 ) @ SY26 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SY27 ) @ SY25 ) @ ( equivalent @ ( equivalent @ SY24 @ SY27 ) @ SY26 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: $i,SV1: $i] :
( ( ~ ( is_a_theorem @ ( equivalent @ SV1 @ SV5 ) )
| ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( ! [SY28: $i,SY29: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV2 @ SV6 ) @ ( equivalent @ SV2 @ SY28 ) ) @ ( equivalent @ SV6 @ SY28 ) ) @ SY29 ) @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV7: $i,SV3: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV7 ) @ ( equivalent @ SV3 @ SY30 ) ) @ SY31 ) @ ( equivalent @ ( equivalent @ SV7 @ SY30 ) @ SY31 ) ) @ SY32 ) @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV8: $i,SV4: $i] :
( ( ! [SY33: $i,SY34: $i,SY35: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV8 ) @ SY33 ) @ SY34 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SY35 ) @ SY33 ) @ ( equivalent @ ( equivalent @ SV8 @ SY35 ) @ SY34 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ ( equivalent @ SV1 @ SV5 ) ) )
= $true )
| ( ( ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV5 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV9: $i,SV6: $i,SV2: $i] :
( ( ! [SY36: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV2 @ SV6 ) @ ( equivalent @ SV2 @ SV9 ) ) @ ( equivalent @ SV6 @ SV9 ) ) @ SY36 ) @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV10: $i,SV7: $i,SV3: $i] :
( ( ! [SY37: $i,SY38: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV7 ) @ ( equivalent @ SV3 @ SV10 ) ) @ SY37 ) @ ( equivalent @ ( equivalent @ SV7 @ SV10 ) @ SY37 ) ) @ SY38 ) @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV11: $i,SV8: $i,SV4: $i] :
( ( ! [SY39: $i,SY40: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV8 ) @ SV11 ) @ SY39 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SY40 ) @ SV11 ) @ ( equivalent @ ( equivalent @ SV8 @ SY40 ) @ SY39 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV5: $i,SV1: $i] :
( ( ( is_a_theorem @ ( equivalent @ SV1 @ SV5 ) )
= $false )
| ( ( ~ ( is_a_theorem @ SV1 )
| ( is_a_theorem @ SV5 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV12: $i,SV9: $i,SV6: $i,SV2: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV2 @ SV6 ) @ ( equivalent @ SV2 @ SV9 ) ) @ ( equivalent @ SV6 @ SV9 ) ) @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV13: $i,SV10: $i,SV7: $i,SV3: $i] :
( ( ! [SY41: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV7 ) @ ( equivalent @ SV3 @ SV10 ) ) @ SV13 ) @ ( equivalent @ ( equivalent @ SV7 @ SV10 ) @ SV13 ) ) @ SY41 ) @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV14: $i,SV11: $i,SV8: $i,SV4: $i] :
( ( ! [SY42: $i] : ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV8 ) @ SV11 ) @ SV14 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SY42 ) @ SV11 ) @ ( equivalent @ ( equivalent @ SV8 @ SY42 ) @ SV14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV5: $i,SV1: $i] :
( ( ( ~ ( is_a_theorem @ SV1 ) )
= $true )
| ( ( is_a_theorem @ SV5 )
= $true )
| ( ( is_a_theorem @ ( equivalent @ SV1 @ SV5 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV15: $i,SV13: $i,SV10: $i,SV7: $i,SV3: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV3 @ SV7 ) @ ( equivalent @ SV3 @ SV10 ) ) @ SV13 ) @ ( equivalent @ ( equivalent @ SV7 @ SV10 ) @ SV13 ) ) @ SV15 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV16: $i,SV14: $i,SV11: $i,SV8: $i,SV4: $i] :
( ( is_a_theorem @ ( equivalent @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV8 ) @ SV11 ) @ SV14 ) @ ( equivalent @ ( equivalent @ ( equivalent @ SV4 @ SV16 ) @ SV11 ) @ ( equivalent @ ( equivalent @ SV8 @ SV16 ) @ SV14 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV5: $i,SV1: $i] :
( ( ( is_a_theorem @ SV1 )
= $false )
| ( ( is_a_theorem @ SV5 )
= $true )
| ( ( is_a_theorem @ ( equivalent @ SV1 @ SV5 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[21,42,41,40,36,26]) ).
thf(44,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL096-1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n013.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 12:08:44 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
% 32.44/5.63
% 32.44/5.63 No.of.Axioms: 5
% 32.44/5.63
% 32.44/5.63 Length.of.Defs: 0
% 32.44/5.63
% 32.44/5.63 Contains.Choice.Funs: false
% 32.44/5.63 .
% 32.44/5.63
% 32.44/5.63 ********************************
% 32.44/5.63 * All subproblems solved! *
% 32.44/5.63 ********************************
% 32.44/5.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 32.44/5.63
% 32.44/5.63 %**** Beginning of derivation protocol ****
% 32.44/5.63 % SZS output start CNFRefutation
% See solution above
% 32.44/5.63
% 32.44/5.63 %**** End of derivation protocol ****
% 32.44/5.63 %**** no. of clauses in derivation: 44 ****
% 32.44/5.63 %**** clause counter: 43 ****
% 32.44/5.63
% 32.44/5.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:43,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------