%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 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 : n001.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 10:09:32 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.22s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 282 ( 119 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 311 ( 52 ~; 64 |; 0 &; 195 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 77 ( 0 ^; 77 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_1,type,
c_1: $i ).
thf(tp_c_HOL_Oabs,type,
c_HOL_Oabs: $i > $i > $i ).
thf(tp_c_HOL_Oinverse,type,
c_HOL_Oinverse: $i > $i > $i ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_times,type,
c_times: $i > $i > $i > $i ).
thf(tp_class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
thf(tp_class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
thf(tp_class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
thf(tp_class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
thf(tp_t_a,type,
t_a: $i ).
thf(tp_v_c,type,
v_c: $i ).
thf(1,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oorder @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
thf(2,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
thf(3,axiom,
! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ofield @ T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
thf(4,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_a = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= c_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
thf(5,axiom,
! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
thf(6,axiom,
! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( ( c_HOL_Oabs @ V_a @ T_a )
!= c_0 )
| ( V_a = c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
thf(7,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(8,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,negated_conjecture,
class_Ring__and__Field_Oordered__field @ t_a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
thf(10,negated_conjecture,
! [V_U: $i] :
~ ( c_lessequals @ c_1 @ ( c_times @ V_U @ ( c_HOL_Oabs @ v_c @ t_a ) @ t_a ) @ t_a ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(11,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(12,plain,
$false = $false,
inference(unfold_def,[status(thm)],[8]) ).
thf(13,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(14,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(15,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ofield @ T ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ( V_a = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= c_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(17,plain,
( ( ! [T_a: $i,V_x: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(18,plain,
( ( ! [T_a: $i,V_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ( ( c_HOL_Oabs @ V_a @ T_a )
!= c_0 )
| ( V_a = c_0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(19,plain,
( ( class_Ring__and__Field_Oordered__field @ t_a )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(20,plain,
( ( ! [V_U: $i] :
~ ( c_lessequals @ c_1 @ ( c_times @ V_U @ ( c_HOL_Oabs @ v_c @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(21,plain,
( ( v_c != c_0 )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(22,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ! [V_a: $i] :
( ( V_a = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= c_1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(24,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(25,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ! [V_a: $i] :
( ( ( c_HOL_Oabs @ V_a @ T_a )
!= c_0 )
| ( V_a = c_0 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(26,plain,
( ( v_c != c_0 )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(27,plain,
( ( v_c != c_0 )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(28,plain,
( ( ! [V_U: $i] :
~ ( c_lessequals @ c_1 @ ( c_times @ V_U @ ( c_HOL_Oabs @ v_c @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(29,plain,
( ( class_Ring__and__Field_Oordered__field @ t_a )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(30,plain,
( ( ! [T_a: $i] :
( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ T_a )
| ! [V_a: $i] :
( ( ( c_HOL_Oabs @ V_a @ T_a )
!= c_0 )
| ( V_a = c_0 ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(31,plain,
( ( ! [T_a: $i] :
( ~ ( class_Orderings_Oorder @ T_a )
| ! [V_x: $i] : ( c_lessequals @ V_x @ V_x @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(32,plain,
( ( ! [T_a: $i] :
( ~ ( class_Ring__and__Field_Ofield @ T_a )
| ! [V_a: $i] :
( ( V_a = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ V_a @ T_a ) @ V_a @ T_a )
= c_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(33,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Ring__and__Field_Ofield @ T ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(34,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_OrderedGroup_Olordered__ab__group__abs @ T ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(35,plain,
( ( ! [T: $i] :
( ~ ( class_Ring__and__Field_Oordered__field @ T )
| ( class_Orderings_Oorder @ T ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(36,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[22]) ).
thf(37,plain,
( ( v_c = c_0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(38,plain,
! [SV1: $i] :
( ( ~ ( c_lessequals @ c_1 @ ( c_times @ SV1 @ ( c_HOL_Oabs @ v_c @ t_a ) @ t_a ) @ t_a ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(39,plain,
! [SV2: $i] :
( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV2 )
| ! [SY10: $i] :
( ( ( c_HOL_Oabs @ SY10 @ SV2 )
!= c_0 )
| ( SY10 = c_0 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(40,plain,
! [SV3: $i] :
( ( ~ ( class_Orderings_Oorder @ SV3 )
| ! [SY11: $i] : ( c_lessequals @ SY11 @ SY11 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(41,plain,
! [SV4: $i] :
( ( ~ ( class_Ring__and__Field_Ofield @ SV4 )
| ! [SY12: $i] :
( ( SY12 = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ SY12 @ SV4 ) @ SY12 @ SV4 )
= c_1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(42,plain,
! [SV5: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV5 )
| ( class_Ring__and__Field_Ofield @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(43,plain,
! [SV6: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV6 )
| ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(44,plain,
! [SV7: $i] :
( ( ~ ( class_Ring__and__Field_Oordered__field @ SV7 )
| ( class_Orderings_Oorder @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(45,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(46,plain,
! [SV1: $i] :
( ( c_lessequals @ c_1 @ ( c_times @ SV1 @ ( c_HOL_Oabs @ v_c @ t_a ) @ t_a ) @ t_a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(47,plain,
! [SV2: $i] :
( ( ( ~ ( class_OrderedGroup_Olordered__ab__group__abs @ SV2 ) )
= $true )
| ( ( ! [SY10: $i] :
( ( ( c_HOL_Oabs @ SY10 @ SV2 )
!= c_0 )
| ( SY10 = c_0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(48,plain,
! [SV3: $i] :
( ( ( ~ ( class_Orderings_Oorder @ SV3 ) )
= $true )
| ( ( ! [SY11: $i] : ( c_lessequals @ SY11 @ SY11 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(49,plain,
! [SV4: $i] :
( ( ( ~ ( class_Ring__and__Field_Ofield @ SV4 ) )
= $true )
| ( ( ! [SY12: $i] :
( ( SY12 = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ SY12 @ SV4 ) @ SY12 @ SV4 )
= c_1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(50,plain,
! [SV5: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV5 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(51,plain,
! [SV6: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV6 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(52,plain,
! [SV7: $i] :
( ( ( ~ ( class_Ring__and__Field_Oordered__field @ SV7 ) )
= $true )
| ( ( class_Orderings_Oorder @ SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(53,plain,
! [SV2: $i] :
( ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV2 )
= $false )
| ( ( ! [SY10: $i] :
( ( ( c_HOL_Oabs @ SY10 @ SV2 )
!= c_0 )
| ( SY10 = c_0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV3: $i] :
( ( ( class_Orderings_Oorder @ SV3 )
= $false )
| ( ( ! [SY11: $i] : ( c_lessequals @ SY11 @ SY11 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV4: $i] :
( ( ( class_Ring__and__Field_Ofield @ SV4 )
= $false )
| ( ( ! [SY12: $i] :
( ( SY12 = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ SY12 @ SV4 ) @ SY12 @ SV4 )
= c_1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV5: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV5 )
= $false )
| ( ( class_Ring__and__Field_Ofield @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV6: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV6 )
= $false )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV6 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV7: $i] :
( ( ( class_Ring__and__Field_Oordered__field @ SV7 )
= $false )
| ( ( class_Orderings_Oorder @ SV7 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( ( c_HOL_Oabs @ SV8 @ SV2 )
!= c_0 )
| ( SV8 = c_0 ) )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV3: $i,SV9: $i] :
( ( ( c_lessequals @ SV9 @ SV9 @ SV3 )
= $true )
| ( ( class_Orderings_Oorder @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(61,plain,
! [SV4: $i,SV10: $i] :
( ( ( ( SV10 = c_0 )
| ( ( c_times @ ( c_HOL_Oinverse @ SV10 @ SV4 ) @ SV10 @ SV4 )
= c_1 ) )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(62,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( c_HOL_Oabs @ SV8 @ SV2 )
!= c_0 )
= $true )
| ( ( SV8 = c_0 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV4: $i,SV10: $i] :
( ( ( SV10 = c_0 )
= $true )
| ( ( ( c_times @ ( c_HOL_Oinverse @ SV10 @ SV4 ) @ SV10 @ SV4 )
= c_1 )
= $true )
| ( ( class_Ring__and__Field_Ofield @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(64,plain,
! [SV2: $i,SV8: $i] :
( ( ( ( c_HOL_Oabs @ SV8 @ SV2 )
= c_0 )
= $false )
| ( ( SV8 = c_0 )
= $true )
| ( ( class_OrderedGroup_Olordered__ab__group__abs @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(65,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[29,64,63,60,58,57,56,46,45,37]) ).
thf(66,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 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
% 0.10/0.17 % Computer : n001.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 18:22:54 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.22
% 0.10/0.22 No.of.Axioms: 9
% 0.10/0.22
% 0.10/0.22 Length.of.Defs: 0
% 0.10/0.22
% 0.10/0.22 Contains.Choice.Funs: false
% 0.10/0.22 .
% 0.10/0.22
% 0.10/0.22 ********************************
% 0.10/0.22 * All subproblems solved! *
% 0.10/0.22 ********************************
% 0.10/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:65,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.10/0.22
% 0.10/0.22 %**** Beginning of derivation protocol ****
% 0.10/0.22 % SZS output start CNFRefutation
% See solution above
% 0.10/0.22
% 0.10/0.22 %**** End of derivation protocol ****
% 0.10/0.22 %**** no. of clauses in derivation: 66 ****
% 0.10/0.22 %**** clause counter: 65 ****
% 0.10/0.22
% 0.10/0.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:9,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:65,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------