%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA025-2 : 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 : n021.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 0.24s 1.61s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of clauses : 52 ( 17 unt; 4 nHn; 46 RR)
% Number of literals : 113 ( 0 equ; 65 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 78 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,axiom,
( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
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_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_Orderings_Olinorder__not__le_0,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
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_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_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_Ring__and__Field_Oordered__idom_33,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
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(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(i_0_12,negated_conjecture,
~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
cls_conjecture_3,
[final] ).
cnf(i_0_13,axiom,
( c_lessequals(c_Orderings_Omax(X4,X2,X1),X3,X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X3,X1) ),
cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2,
[final] ).
cnf(i_0_14,negated_conjecture,
~ c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
cls_conjecture_2,
[final] ).
cnf(i_0_15,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,
[final] ).
cnf(i_0_16,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
cls_Orderings_Oorder__less__imp__le_0,
[final] ).
cnf(i_0_17,axiom,
( c_less(X2,X3,X1)
| c_lessequals(X3,X2,X1)
| ~ class_Orderings_Olinorder(X1) ),
cls_Orderings_Olinorder__not__le_0,
[final] ).
cnf(i_0_18,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0,
[final] ).
cnf(i_0_19,axiom,
( class_LOrder_Ojoin__semilorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_15,
[final] ).
cnf(i_0_20,axiom,
( class_Orderings_Oorder(X1)
| ~ class_LOrder_Ojoin__semilorder(X1) ),
clsrel_LOrder_Ojoin__semilorder_1,
[final] ).
cnf(i_0_21,axiom,
( class_Orderings_Olinorder(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_33,
[final] ).
cnf(i_0_22,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50,
[final] ).
cnf(i_0_23,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs,
[final] ).
cnf(i_0_24,plain,
class_Orderings_Olinorder(t_b),
inference(scs_inference,[],[i_0_23,i_0_21]) ).
cnf(i_0_25,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_Orderings_Olinorder(X1) ),
inference(rename_variables,[],[i_0_21]) ).
cnf(i_0_26,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(scs_inference,[],[i_0_23,i_0_21,i_0_22]) ).
cnf(i_0_27,plain,
( ~ class_Ring__and__Field_Oordered__idom(X1)
| class_OrderedGroup_Olordered__ab__group__abs(X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_28,plain,
class_LOrder_Ojoin__semilorder(t_b),
inference(scs_inference,[],[i_0_23,i_0_21,i_0_22,i_0_19]) ).
cnf(i_0_29,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| class_LOrder_Ojoin__semilorder(X1) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_30,plain,
class_Orderings_Oorder(t_b),
inference(scs_inference,[],[i_0_23,i_0_21,i_0_22,i_0_19,i_0_20]) ).
cnf(i_0_31,plain,
( ~ class_LOrder_Ojoin__semilorder(X1)
| class_Orderings_Oorder(X1) ),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_32,plain,
~ c_less(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(scs_inference,[],[i_0_12,i_0_23,i_0_21,i_0_22,i_0_19,i_0_20,i_0_16]) ).
cnf(i_0_33,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1)
| c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_34,plain,
c_less(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),t_b),
inference(scs_inference,[],[i_0_12,i_0_23,i_0_21,i_0_22,i_0_19,i_0_20,i_0_16,i_0_17]) ).
cnf(i_0_35,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| c_less(X2,X1,X3) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_36,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(scs_inference,[],[i_0_12,i_0_23,i_0_21,i_0_22,i_0_19,i_0_20,i_0_16,i_0_17,i_0_13]) ).
cnf(i_0_37,plain,
( c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X4,X3) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_38,plain,
( ~ c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),X1,t_b)
| ~ c_lessequals(X1,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b) ),
inference(scs_inference,[],[i_0_12,i_0_23,i_0_21,i_0_22,i_0_19,i_0_20,i_0_16,i_0_17,i_0_13,i_0_18,i_0_15]) ).
cnf(i_0_39,plain,
c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),t_b),
inference(scs_inference,[],[i_0_34,i_0_30,i_0_16]) ).
cnf(i_0_40,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1)
| c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_41,plain,
c_less(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(scs_inference,[],[i_0_14,i_0_34,i_0_24,i_0_30,i_0_16,i_0_17]) ).
cnf(i_0_42,plain,
( c_lessequals(X1,X2,X3)
| ~ class_Orderings_Olinorder(X3)
| c_less(X2,X1,X3) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_43,plain,
( c_lessequals(c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),X1,t_b)
| ~ c_lessequals(c_Orderings_Omax(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),X1,t_b) ),
inference(scs_inference,[],[i_0_14,i_0_34,i_0_24,i_0_30,i_0_16,i_0_17,i_0_15]) ).
cnf(i_0_44,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| c_lessequals(X2,X4,X1)
| ~ c_lessequals(X3,X4,X1) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_45,plain,
c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),c_0,t_b),
inference(scs_inference,[],[i_0_41,i_0_30,i_0_16]) ).
cnf(i_0_46,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1)
| c_lessequals(X2,X3,X1) ),
inference(rename_variables,[],[i_0_16]) ).
cnf(i_0_47,plain,
( c_lessequals(c_minus(v_k(v_x),v_g(v_x),t_b),X1,t_b)
| ~ c_lessequals(c_0,X1,t_b) ),
inference(scs_inference,[],[i_0_45,i_0_30,i_0_15]) ).
cnf(i_0_48,plain,
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X2,X3,X1)
| c_lessequals(X2,X4,X1)
| ~ c_lessequals(X3,X4,X1) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_49,plain,
~ c_lessequals(c_0,c_HOL_Oabs(c_minus(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(scs_inference,[],[i_0_12,i_0_45,i_0_24,i_0_30,i_0_15,i_0_13]) ).
cnf(i_0_50,plain,
( c_lessequals(c_Orderings_Omax(X1,X2,X3),X4,X3)
| ~ class_Orderings_Olinorder(X3)
| ~ c_lessequals(X2,X4,X3)
| ~ c_lessequals(X1,X4,X3) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_51,plain,
$false,
inference(scs_inference,[],[i_0_26,i_0_49,i_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA025-2 : 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
% 0.14/0.32 % Computer : n021.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 10:36:57 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.24/1.61 % Version : CSE_E---1.7
% 0.24/1.61 % Problem : theBenchmark.p
% 0.24/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.24/1.61 % SZS output start CNFRefutation
% See solution above
% 0.24/1.67 % Total time : 1.270s
%------------------------------------------------------------------------------