%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 12:55:11 PM UTC 2026
% Result : Unsatisfiable 0.14s 10.90s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 31 unt; 0 def)
% Number of atoms : 103 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 86 ( 4 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f9_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f2,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f2_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
class_Ring__and__Field_Oordered__idom(t_a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi1,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_a) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h0,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi1]) ).
cnf(f4,axiom,
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f4_nnf,plain,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3,plain,
c_lessequals(c_0,c_HOL_Oabs(V0,t_a),t_a) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0]) ).
cnf(f3,axiom,
( c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__self_0) ).
fof(f3_nnf,plain,
! [T_a,V_a] :
( c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_a] :
( c_lessequals(V_a,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(X1,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(X1,c_HOL_Oabs(X1,X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h4,plain,
c_lessequals(V0,c_HOL_Oabs(V0,t_a),t_a) = true,
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(f7,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f7_nnf,plain,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h2,plain,
class_Ring__and__Field_Opordered__semiring(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi1]) ).
cnf(f6,axiom,
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring_hcd82f89c512673aa) ).
fof(f6_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(class_Ring__and__Field_Opordered__semiring(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(c_0,X3,X0),true,c_lessequals(c_times(X1,X3,X0),c_times(X2,X3,X0),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h11,plain,
c_lessequals(c_times(V0,c_HOL_Oabs(V1,t_a),t_a),c_times(c_HOL_Oabs(V0,t_a),c_HOL_Oabs(V1,t_a),t_a),t_a) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2,h4,h3]) ).
cnf(f8,axiom,
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f8_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( class_Orderings_Oorder(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h1,plain,
class_Orderings_Oorder(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1]) ).
cnf(f5,axiom,
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f5_nnf,plain,
! [T_a,V_y,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a,V_y,V_z,V_x] :
( c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ class_Orderings_Oorder(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(X3,X2,X0)
| ~ c_lessequals(X3,X1,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X3,X1,X0),true,c_lessequals(X3,X2,X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
! [V_U] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_U] : c_lessequals(c_HOL_Oabs(v_h(V_U),t_a),c_times(v_c,c_HOL_Oabs(v_f(V_U),t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_h(X0),t_a),c_times(v_c,c_HOL_Oabs(v_f(X0),t_a),t_a),t_a) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t25,plain,
c_lessequals(c_HOL_Oabs(v_h(X1),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(X1),t_a),t_a),t_a) = true,
inference(hyper_resolution,[status(thm)],[hi4,h1,h11,hi0]) ).
cnf(t112,plain,
c_lessequals(c_HOL_Oabs(v_h(X1),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(X1),t_a),t_a),t_a) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f1,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1_nnf,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_h(v_x),t_a),c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x),t_a),t_a),t_a) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t112]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.37 % Computer : n004.cluster.edu
% 0.11/10.37 % Model : x86_64 x86_64
% 0.11/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.37 % Memory : 8046.5625MB
% 0.11/10.37 % OS : Linux 6.8.0-71-generic
% 0.11/10.37 % CPULimit : 300
% 0.11/10.37 % WCLimit : 300
% 0.11/10.37 % DateTime : Fri Sep 25 05:50:36 UTC 2026
% 0.11/10.37 % CPUTime :
% 0.11/10.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/10.90 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.90 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------