%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n008.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 12:55:08 PM UTC 2026
% Result : Unsatisfiable 3.63s 1.08s
% Output : Proof 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 38 unt; 0 def)
% Number of atoms : 74 ( 30 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-4 aty)
% Number of variables : 86 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f1_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(V_a,c_minus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_plus(V_a,V_b,T_a),V_c,T_a)
| ~ class_OrderedGroup_Opordered__ab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_lessequals(X1,c_minus(X3,X2,X0),X0)
| ~ c_lessequals(c_plus(X1,X2,X0),X3,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t9,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t12,plain,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X1),true,ifeq(c_lessequals(c_plus(X2,X3,X1),X4,X1),true,c_lessequals(X2,c_minus(X4,X3,X1),X1),true),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f5,axiom,
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5_nnf,plain,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T] :
( class_OrderedGroup_Opordered__ab__group__add(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f6,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f6_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi5,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t1,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi5]) ).
cnf(t16,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t19,plain,
true = ifeq(true,true,ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true),true),
inference(cp,[status(thm)],[t12,t16]) ).
cnf(t3,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t3]) ).
cnf(t30,plain,
true = ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true),
inference(step,[status(thm)],[t19,t10]) ).
cnf(t24,plain,
ifeq(c_lessequals(c_plus(X1,X2,t_b),X3,t_b),true,c_lessequals(X1,c_minus(X3,X2,t_b),t_b),true) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(h0,plain,
class_OrderedGroup_Opordered__ab__group__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi5]) ).
cnf(f4,axiom,
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4_nnf,plain,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T] :
( class_OrderedGroup_Oab__group__add(T)
| ~ class_OrderedGroup_Opordered__ab__group__add(T) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( class_OrderedGroup_Oab__group__add(X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,class_OrderedGroup_Oab__group__add(X0),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h1,plain,
class_OrderedGroup_Oab__group__add(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0]) ).
cnf(f0,axiom,
( V_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__10_0) ).
fof(f0_nnf,plain,
! [T_a,V_a,V_b] :
( V_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [T_a,V_a,V_b] :
( V_a = c_plus(c_minus(V_a,V_b,T_a),V_b,T_a)
| ~ class_OrderedGroup_Oab__group__add(T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( X1 = c_plus(c_minus(X1,X2,X0),X2,X0)
| ~ class_OrderedGroup_Oab__group__add(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(class_OrderedGroup_Oab__group__add(X0),true,X1,c_plus(c_minus(X1,X2,X0),X2,X0)) = c_plus(c_minus(X1,X2,X0),X2,X0),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t5,plain,
c_plus(c_minus(X1,X2,t_b),X2,t_b) = X1,
inference(hyper_resolution,[status(thm)],[hi0,h1]) ).
cnf(t11,plain,
c_plus(c_minus(X1,X2,t_b),X2,t_b) = X1,
inference(orient,[status(thm)],[t5]) ).
cnf(t25,plain,
true = ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_minus(X1,X3,t_b),c_minus(X2,X3,t_b),t_b),true),
inference(cp,[status(thm)],[t24,t11]) ).
cnf(t26,plain,
ifeq(c_lessequals(X1,X2,t_b),true,c_lessequals(c_minus(X1,X3,t_b),c_minus(X2,X3,t_b),t_b),true) = true,
inference(orient,[status(thm)],[t25]) ).
cnf(f2,negated_conjecture,
c_lessequals(v_k(V_U),v_f(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f2_nnf,plain,
! [V_U] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [V_U] : c_lessequals(v_k(V_U),v_f(V_U),t_b),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
c_lessequals(v_k(X0),v_f(X0),t_b),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t4,plain,
c_lessequals(v_k(X1),v_f(X1),t_b) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t21,plain,
c_lessequals(v_k(X1),v_f(X1),t_b) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t27,plain,
true = ifeq(true,true,c_lessequals(c_minus(v_k(X1),X2,t_b),c_minus(v_f(X1),X2,t_b),t_b),true),
inference(cp,[status(thm)],[t26,t21]) ).
cnf(t31,plain,
true = c_lessequals(c_minus(v_k(X1),X2,t_b),c_minus(v_f(X1),X2,t_b),t_b),
inference(step,[status(thm)],[t27,t10]) ).
cnf(t28,plain,
c_lessequals(c_minus(v_k(X1),X2,t_b),c_minus(v_f(X1),X2,t_b),t_b) = true,
inference(orient,[status(thm)],[t31]) ).
cnf(f3,negated_conjecture,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3_nnf,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t28]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA024-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.41 % Computer : n008.cluster.edu
% 0.18/0.41 % Model : x86_64 x86_64
% 0.18/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.41 % Memory : 8046.5625MB
% 0.18/0.41 % OS : Linux 6.8.0-71-generic
% 0.18/0.41 % CPULimit : 300
% 0.18/0.41 % WCLimit : 300
% 0.18/0.41 % DateTime : Fri Sep 25 05:47:54 UTC 2026
% 0.18/0.41 % CPUTime :
% 0.18/0.41 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.63/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------