%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 : Fri Sep 25 12:55:03 PM UTC 2026
% Result : Unsatisfiable 4.02s 1.08s
% Output : Proof 4.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 80 ( 27 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 38 ~; 35 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f5_nnf,plain,
! [T_a,V_a] :
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a,V_a] :
( c_times(c_HOL_Oinverse(V_a,T_a),V_a,T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_times(c_HOL_Oinverse(X1,X0),X1,X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f6,axiom,
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f6_nnf,plain,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(f2,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f2_nnf,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p9,plain,
class_Ring__and__Field_Ofield(t_a),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(p14,plain,
( c_times(c_HOL_Oinverse(X0,t_a),X0,t_a) = c_1
| X0 = c_0 ),
inference(resolution,[status(thm)],[c5,p9]) ).
cnf(f1,negated_conjecture,
~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
! [V_U] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_U] : ~ c_lessequals(c_1,c_times(V_U,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_lessequals(c_1,c_times(X0,c_HOL_Oabs(v_c,t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p15,plain,
( ~ c_lessequals(c_1,c_1,t_a)
| c_HOL_Oabs(v_c,t_a) = c_0 ),
inference(superposition,[status(thm)],[p14,c1]) ).
cnf(f8,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f8_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p12,plain,
class_Orderings_Oorder(t_a),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(f4,axiom,
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f4_nnf,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_x] :
( c_lessequals(V_x,V_x,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(X1,X1,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p13,plain,
c_lessequals(X0,X0,t_a),
inference(resolution,[status(thm)],[p12,c4]) ).
cnf(p16,plain,
c_HOL_Oabs(v_c,t_a) = c_0,
inference(resolution,[status(thm)],[p15,p13]) ).
cnf(f7,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f7_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p10,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(f3,axiom,
( V_a = c_0
| c_HOL_Oabs(V_a,T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f3_nnf,plain,
! [T_a,V_a] :
( V_a = c_0
| c_HOL_Oabs(V_a,T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_a] :
( V_a = c_0
| c_HOL_Oabs(V_a,T_a) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X1 = c_0
| c_HOL_Oabs(X1,X0) != c_0
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p11,plain,
( X0 = c_0
| c_HOL_Oabs(X0,t_a) != c_0 ),
inference(resolution,[status(thm)],[p10,c3]) ).
cnf(p18,plain,
v_c = c_0,
inference(resolution,[status(thm)],[p16,p11]) ).
cnf(f0,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
v_c != c_0,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
v_c != c_0,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
v_c != c_0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p19,plain,
$false,
inference(resolution,[status(thm)],[p18,c0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 05:44:50 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.02/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.02/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------