%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n017.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 10:28:11 AM UTC 2026
% Result : Unsatisfiable 10.23s 2.03s
% Output : CNFRefutation 10.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 60 unt; 0 typ; 0 def)
% Number of atoms : 156 ( 100 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 534 ( 6 ~; 0 |; 0 &; 528 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 110 ( 0 ^; 110 !; 0 ?; 110 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_axiom,type,
axiom: $i > $i ).
thf(tp_ifeq,type,
ifeq: $i > $i > $i > $i > $i ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_or,type,
or: $i > $i > $i ).
thf(tp_p,type,
p: $i ).
thf(tp_q,type,
q: $i ).
thf(tp_theorem,type,
theorem: $i > $i ).
thf(tp_true,type,
true: $i ).
thf(1,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ X ) @ Y ) ) @ true @ ( theorem @ ( or @ ( not @ X ) @ Z ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_3) ).
thf(2,axiom,
! [Y: $i,X: $i] :
( ( ifeq @ ( theorem @ Y ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ Y ) @ X ) ) @ true @ ( theorem @ X ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
thf(3,axiom,
! [X: $i] :
( ( ifeq @ ( axiom @ X ) @ true @ ( theorem @ X ) @ true )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(8,axiom,
! [A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
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,
( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(13,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(14,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ X ) @ Y ) ) @ true @ ( theorem @ ( or @ ( not @ X ) @ Z ) ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(15,plain,
( ( ! [Y: $i,X: $i] :
( ( ifeq @ ( theorem @ Y ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ Y ) @ X ) ) @ true @ ( theorem @ X ) @ true ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(16,plain,
( ( ! [X: $i] :
( ( ifeq @ ( axiom @ X ) @ true @ ( theorem @ X ) @ true )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] :
( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(21,plain,
( ( ! [A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(23,plain,
( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(24,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[13]) ).
thf(25,plain,
( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(26,plain,
( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(28,plain,
( ( ! [A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(31,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(32,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
= true ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( ifeq @ ( axiom @ X ) @ true @ ( theorem @ X ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(34,plain,
( ( ! [Y: $i,X: $i] :
( ( ifeq @ ( theorem @ Y ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ Y ) @ X ) ) @ true @ ( theorem @ X ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(35,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ Y ) @ Z ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ X ) @ Y ) ) @ true @ ( theorem @ ( or @ ( not @ X ) @ Z ) ) @ true ) @ true )
= true ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(36,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[24]) ).
thf(37,plain,
( ( ( theorem @ ( or @ ( not @ ( not @ p ) ) @ ( or @ ( not @ p ) @ q ) ) )
= true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(38,plain,
! [SV1: $i] :
( ( ! [SY20: $i,SY21: $i] :
( ( ifeq @ SV1 @ SV1 @ SY20 @ SY21 )
= SY20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(39,plain,
! [SV2: $i] :
( ( ( axiom @ ( or @ ( not @ ( or @ SV2 @ SV2 ) ) @ SV2 ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(40,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ( axiom @ ( or @ ( not @ SV3 ) @ ( or @ SY22 @ SV3 ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(41,plain,
! [SV4: $i] :
( ( ! [SY23: $i] :
( ( axiom @ ( or @ ( not @ ( or @ SV4 @ SY23 ) ) @ ( or @ SY23 @ SV4 ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(42,plain,
! [SV5: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ( axiom @ ( or @ ( not @ ( or @ SV5 @ ( or @ SY24 @ SY25 ) ) ) @ ( or @ SY24 @ ( or @ SV5 @ SY25 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(43,plain,
! [SV6: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV6 ) @ SY26 ) ) @ ( or @ ( not @ ( or @ SY27 @ SV6 ) ) @ ( or @ SY27 @ SY26 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(44,plain,
! [SV7: $i] :
( ( ( ifeq @ ( axiom @ SV7 ) @ true @ ( theorem @ SV7 ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(45,plain,
! [SV8: $i] :
( ( ! [SY28: $i] :
( ( ifeq @ ( theorem @ SV8 ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SV8 ) @ SY28 ) ) @ true @ ( theorem @ SY28 ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(46,plain,
! [SV9: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ SV9 ) @ SY29 ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SY30 ) @ SV9 ) ) @ true @ ( theorem @ ( or @ ( not @ SY30 ) @ SY29 ) ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(47,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(48,plain,
! [SV10: $i,SV1: $i] :
( ( ! [SY31: $i] :
( ( ifeq @ SV1 @ SV1 @ SV10 @ SY31 )
= SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(49,plain,
! [SV11: $i,SV3: $i] :
( ( ( axiom @ ( or @ ( not @ SV3 ) @ ( or @ SV11 @ SV3 ) ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(50,plain,
! [SV12: $i,SV4: $i] :
( ( ( axiom @ ( or @ ( not @ ( or @ SV4 @ SV12 ) ) @ ( or @ SV12 @ SV4 ) ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(51,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY32: $i] :
( ( axiom @ ( or @ ( not @ ( or @ SV5 @ ( or @ SV13 @ SY32 ) ) ) @ ( or @ SV13 @ ( or @ SV5 @ SY32 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(52,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY33: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV6 ) @ SV14 ) ) @ ( or @ ( not @ ( or @ SY33 @ SV6 ) ) @ ( or @ SY33 @ SV14 ) ) ) )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(53,plain,
! [SV15: $i,SV8: $i] :
( ( ( ifeq @ ( theorem @ SV8 ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SV8 ) @ SV15 ) ) @ true @ ( theorem @ SV15 ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(54,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY34: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ SV9 ) @ SV16 ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SY34 ) @ SV9 ) ) @ true @ ( theorem @ ( or @ ( not @ SY34 ) @ SV16 ) ) @ true ) @ true )
= true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(55,plain,
! [SV17: $i,SV10: $i,SV1: $i] :
( ( ( ifeq @ SV1 @ SV1 @ SV10 @ SV17 )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(56,plain,
! [SV18: $i,SV13: $i,SV5: $i] :
( ( ( axiom @ ( or @ ( not @ ( or @ SV5 @ ( or @ SV13 @ SV18 ) ) ) @ ( or @ SV13 @ ( or @ SV5 @ SV18 ) ) ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV19: $i,SV14: $i,SV6: $i] :
( ( ( axiom @ ( or @ ( not @ ( or @ ( not @ SV6 ) @ SV14 ) ) @ ( or @ ( not @ ( or @ SV19 @ SV6 ) ) @ ( or @ SV19 @ SV14 ) ) ) )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(58,plain,
! [SV20: $i,SV16: $i,SV9: $i] :
( ( ( ifeq @ ( theorem @ ( or @ ( not @ SV9 ) @ SV16 ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ SV20 ) @ SV9 ) ) @ true @ ( theorem @ ( or @ ( not @ SV20 ) @ SV16 ) ) @ true ) @ true )
= true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(59,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[37,58,57,56,55,53,50,49,47,44,39]) ).
thf(60,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-10 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.07/0.18 % Computer : n017.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 12:07:00 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
% 10.23/2.03
% 10.23/2.03 No.of.Axioms: 10
% 10.23/2.03
% 10.23/2.03 Length.of.Defs: 0
% 10.23/2.03
% 10.23/2.03 Contains.Choice.Funs: false
% 10.23/2.03 ..
% 10.23/2.03
% 10.23/2.03 ********************************
% 10.23/2.03 * All subproblems solved! *
% 10.23/2.03 ********************************
% 10.23/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:59,loop_count:0,foatp_calls:1,translation:fof_full)
% 10.23/2.03
% 10.23/2.03 %**** Beginning of derivation protocol ****
% 10.23/2.03 % SZS output start CNFRefutation
% See solution above
% 10.23/2.03
% 10.23/2.03 %**** End of derivation protocol ****
% 10.23/2.03 %**** no. of clauses in derivation: 60 ****
% 10.23/2.03 %**** clause counter: 59 ****
% 10.23/2.03
% 10.23/2.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:10,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:59,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------