%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA015-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:09:17 PM UTC 2026
% Result : Unsatisfiable 1.39s 1.77s
% Output : CNFRefutation 1.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 34 ( 8 unt; 0 nHn; 26 RR)
% Number of literals : 75 ( 4 equ; 50 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 48 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X1)),t_a),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_0,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_g(X1),t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_46,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_46) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_47,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_47) ).
cnf(c_0_12,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(X1)),t_a),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),
cls_conjecture_2 ).
cnf(c_0_13,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0 ).
cnf(c_0_14,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_0,X4,X1) ),
cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 ).
cnf(c_0_15,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_Ring__and__Field_Oabs__mult_0 ).
cnf(c_0_16,negated_conjecture,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ c_lessequals(c_HOL_Oabs(c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x(c_times(X1,X2,t_a))),t_a),t_a),c_times(X1,c_times(X2,c_HOL_Oabs(v_f(v_x(c_times(X1,X2,t_a))),t_a),t_a),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( c_lessequals(c_HOL_Oabs(c_times(X1,X2,X3),X3),c_times(c_HOL_Oabs(X1,X3),X4,X3),X3)
| ~ class_Ring__and__Field_Opordered__semiring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,X3),X3)
| ~ c_lessequals(c_HOL_Oabs(X2,X3),X4,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_g(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X1,t_a))),t_a),c_times(X1,c_HOL_Oabs(v_f(v_x(c_times(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),X1,t_a))),t_a),t_a),t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_g(X1),t_a),c_times(v_d,c_HOL_Oabs(v_f(X1),t_a),t_a),t_a),
cls_conjecture_1 ).
cnf(c_0_20,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ c_lessequals(c_0,c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_22,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_a)
| ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_46 ).
cnf(c_0_24,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
tfree_tcs ).
cnf(c_0_25,negated_conjecture,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_26,axiom,
( class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_34 ).
cnf(c_0_27,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
clsrel_Ring__and__Field_Ofield_21 ).
cnf(c_0_28,axiom,
( class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_0 ).
cnf(c_0_29,negated_conjecture,
( ~ class_OrderedGroup_Osemigroup__mult(t_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24])]) ).
cnf(c_0_30,plain,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24])]) ).
cnf(c_0_32,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_47 ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA015-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n019.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:35:14 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.39/1.77 % Version : CSE_E---1.7
% 1.39/1.77 % Problem : theBenchmark.p
% 1.39/1.77 % SZS status Unsatisfiable for theBenchmark.p
% 1.39/1.77 % SZS output start CNFRefutation
% See solution above
% 1.39/1.77 % Total time : 1.371s
%------------------------------------------------------------------------------