%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA027-2 : 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 : n002.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 04:09:20 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of clauses : 36 ( 10 unt; 0 nHn; 34 RR)
% Number of literals : 78 ( 2 equ; 48 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
( c_lessequals(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_minus(X3,X4,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( c_plus(c_0,X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( c_lessequals(X2,c_minus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( c_lessequals(X4,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_1,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(c_0_13,axiom,
( c_lessequals(c_plus(X2,X4,X1),X3,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X2,c_minus(X3,X4,X1),X1) ),
cls_OrderedGroup_Ocompare__rls__9_0 ).
cnf(c_0_14,axiom,
( c_plus(c_0,X2,X1) = X2
| ~ class_OrderedGroup_Ocomm__monoid__add(X1) ),
cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0 ).
cnf(c_0_15,axiom,
( c_lessequals(X2,c_minus(X4,X3,X1),X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_plus(X2,X3,X1),X4,X1) ),
cls_OrderedGroup_Ocompare__rls__9_1 ).
cnf(c_0_16,axiom,
( c_lessequals(X4,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X2,X1) ),
cls_Orderings_Oorder__class_Oorder__trans_0 ).
cnf(c_0_17,negated_conjecture,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
cls_conjecture_2 ).
cnf(c_0_18,plain,
( c_lessequals(X1,X2,X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(c_0,c_minus(X2,X1,X3),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_20,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_21,plain,
( c_lessequals(c_0,c_minus(X1,X2,X3),X3)
| ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| ~ c_lessequals(X2,X1,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_22,negated_conjecture,
( c_lessequals(v_g(v_x),X1,t_b)
| ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(v_x),X1,t_b) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
clsrel_LOrder_Ojoin__semilorder_1 ).
cnf(c_0_26,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_15 ).
cnf(c_0_27,negated_conjecture,
( ~ class_Orderings_Oorder(t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_28,plain,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,axiom,
( class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_1 ).
cnf(c_0_30,negated_conjecture,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ class_OrderedGroup_Ocomm__monoid__add(t_b) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_31,axiom,
( class_OrderedGroup_Ocomm__monoid__add(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_23 ).
cnf(c_0_32,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_33,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_34,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA027-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 10:36:16 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.371s
%------------------------------------------------------------------------------