%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 12:55:12 PM UTC 2026
% Result : Unsatisfiable 6.15s 6.24s
% Output : Proof 6.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 30 unt; 0 def)
% Number of atoms : 74 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 34 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 59 ( 12 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f6_nnf,plain,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T] :
( class_Ring__and__Field_Opordered__cancel__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f3,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi2,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h1,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi2]) ).
cnf(f5,axiom,
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f5_nnf,plain,
! [T_a,V_b,V_a] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a,V_b,V_a] :
( c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_a,T_a)
| ~ c_lessequals(c_0,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X2,X1,X0),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f1,negated_conjecture,
c_lessequals(c_0,v_h(V_U),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f1_nnf,plain,
! [V_U] : c_lessequals(c_0,v_h(V_U),t_b),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [V_U] : c_lessequals(c_0,v_h(V_U),t_b),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
c_lessequals(c_0,v_h(X0),t_b),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
c_lessequals(c_0,v_h(X0),t_b) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f0,negated_conjecture,
c_lessequals(c_0,v_l(V_U,V_V),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
! [V_U,V_V] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [V_U,V_V] : c_lessequals(c_0,v_l(V_U,V_V),t_b),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
c_lessequals(c_0,v_l(X0,X1),t_b),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
c_lessequals(c_0,v_l(X0,X1),t_b) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h5,plain,
c_lessequals(c_0,c_times(v_l(V0,V1),v_h(V2),t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi4,h1,hi1,hi0]) ).
cnf(f7,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(f7_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( class_OrderedGroup_Olordered__ab__group__abs(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_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h0,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi2]) ).
cnf(f4,axiom,
( c_HOL_Oabs(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f4_nnf,plain,
! [T_a,V_y] :
( c_HOL_Oabs(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_y] :
( c_HOL_Oabs(V_y,T_a) = V_y
| ~ c_lessequals(c_0,V_y,T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_HOL_Oabs(X1,X0) = X1
| ~ c_lessequals(c_0,X1,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,ifeq(c_lessequals(c_0,X1,X0),true,c_HOL_Oabs(X1,X0),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t21,plain,
c_HOL_Oabs(c_times(v_l(X1,X2),v_h(X3),t_b),t_b) = c_times(v_l(X1,X2),v_h(X3),t_b),
inference(hyper_resolution,[status(thm)],[hi3,h0,h5]) ).
cnf(t36,plain,
c_HOL_Oabs(c_times(v_l(X1,X2),v_h(X3),t_b),t_b) = c_times(v_l(X1,X2),v_h(X3),t_b),
inference(orient,[status(thm)],[t21]) ).
cnf(f2,negated_conjecture,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f2_nnf,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),
inference(rw,[status(thm)],[goal_0,t36]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n015.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Fri Sep 25 05:54:32 UTC 2026
% 0.11/5.37 % CPUTime :
% 0.11/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.15/6.24 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.15/6.24 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------