%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 4.48s 1.24s
% Output : Proof 4.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 65 ( 45 unt; 0 def)
% Number of atoms : 97 ( 37 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-4 aty)
% Number of variables : 84 ( 4 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,negated_conjecture,
~ c_lessequals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5_nnf,plain,
! [V_U] : ~ c_lessequals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [V_U] : ~ c_lessequals(v_f(v_x(V_U)),c_times(V_U,c_HOL_Oabs(v_g(v_x(V_U)),t_b),t_b),t_b),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ c_lessequals(v_f(v_x(X0)),c_times(X0,c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t13,plain,
eq(c_lessequals(v_f(v_x(X1)),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),true) = efalse,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t52,plain,
eq(c_lessequals(v_f(v_x(X1)),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),true) = efalse,
inference(orient,[status(thm)],[t13]) ).
cnf(f2,axiom,
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f2_nnf,plain,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,c_HOL_Oabs(c_times(X1,X2,X0),X0),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f8,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f8_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi7,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t12,plain,
c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
inference(hyper_resolution,[status(thm)],[hi2,hi7]) ).
cnf(t43,plain,
c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
inference(orient,[status(thm)],[t12]) ).
cnf(t53,plain,
efalse = eq(c_lessequals(v_f(v_x(c_HOL_Oabs(X1,t_b))),c_HOL_Oabs(c_times(X1,v_g(v_x(c_HOL_Oabs(X1,t_b))),t_b),t_b),t_b),true),
inference(cp,[status(thm)],[t52,t43]) ).
cnf(t177,plain,
eq(c_lessequals(v_f(v_x(c_HOL_Oabs(X1,t_b))),c_HOL_Oabs(c_times(X1,v_g(v_x(c_HOL_Oabs(X1,t_b))),t_b),t_b),t_b),true) = efalse,
inference(orient,[status(thm)],[t53]) ).
cnf(f7,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox2/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,hi7]) ).
cnf(f6,axiom,
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f6_nnf,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T] :
( class_Orderings_Oorder(T)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( class_Orderings_Oorder(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h2,plain,
class_Orderings_Oorder(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi5,h0]) ).
cnf(f1,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/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f1_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)],[f1]) ).
fof(f1_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)],[f1_nnf]) ).
cnf(c1,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)],[f1_sk]) ).
cnf(hi1,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)],[c1]) ).
cnf(f4,negated_conjecture,
c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4_nnf,plain,
! [V_U] : c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [V_U] : c_lessequals(v_f(V_U),c_times(v_c,v_g(V_U),t_b),t_b),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
c_lessequals(v_f(X0),c_times(v_c,v_g(X0),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
c_lessequals(v_f(X0),c_times(v_c,v_g(X0),t_b),t_b) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f3,negated_conjecture,
c_lessequals(c_0,v_f(V_U),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3_nnf,plain,
! [V_U] : c_lessequals(c_0,v_f(V_U),t_b),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [V_U] : c_lessequals(c_0,v_f(V_U),t_b),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
c_lessequals(c_0,v_f(X0),t_b),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
c_lessequals(c_0,v_f(X0),t_b) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h4,plain,
c_lessequals(c_0,c_times(v_c,v_g(V0),t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi1,h2,hi4,hi3]) ).
cnf(f0,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f0_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)],[f0]) ).
fof(f0_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)],[f0_nnf]) ).
cnf(c0,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)],[f0_sk]) ).
cnf(hi0,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)],[c0]) ).
cnf(t11,plain,
c_HOL_Oabs(c_times(v_c,v_g(X1),t_b),t_b) = c_times(v_c,v_g(X1),t_b),
inference(hyper_resolution,[status(thm)],[hi0,h0,h4]) ).
cnf(t44,plain,
c_HOL_Oabs(c_times(v_c,v_g(X1),t_b),t_b) = c_times(v_c,v_g(X1),t_b),
inference(orient,[status(thm)],[t11]) ).
cnf(t184,plain,
efalse = eq(c_lessequals(v_f(v_x(c_HOL_Oabs(v_c,t_b))),c_times(v_c,v_g(v_x(c_HOL_Oabs(v_c,t_b))),t_b),t_b),true),
inference(cp,[status(thm)],[t177,t44]) ).
cnf(t10,plain,
c_lessequals(v_f(X1),c_times(v_c,v_g(X1),t_b),t_b) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t22,plain,
c_lessequals(v_f(X1),c_times(v_c,v_g(X1),t_b),t_b) = true,
inference(orient,[status(thm)],[t10]) ).
cnf(t208,plain,
efalse = eq(true,true),
inference(step,[status(thm)],[t184,t22]) ).
cnf(t3,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t51,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t3]) ).
cnf(t209,plain,
efalse = etrue,
inference(step,[status(thm)],[t208,t51]) ).
cnf(t191,plain,
efalse = etrue,
inference(orient,[status(thm)],[t209]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t191]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA010-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 05:44:35 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.48/1.24 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.48/1.24 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------