%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 12:55:10 PM UTC 2026
% Result : Unsatisfiable 24.88s 3.75s
% Output : CNFRefutation 24.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 31 ( 31 unt; 0 nHn; 18 RR)
% Number of literals : 31 ( 30 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 26 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(hi12,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi9,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h1,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi9]) ).
cnf(hi13,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h0,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi9]) ).
cnf(hi4,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h5,plain,
c_lessequals(c_0,c_HOL_Oabs(V0,t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0]) ).
cnf(hi10,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h4,plain,
class_Orderings_Oorder(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi10,h0]) ).
cnf(hi3,axiom,
ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi5,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h6,plain,
c_lessequals(c_0,v_c,t_b) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi5,h4]) ).
cnf(hi11,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h2,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi9]) ).
cnf(hi2,axiom,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h12,plain,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(V0,t_b),t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi2,h2,h6,h5]) ).
cnf(hi1,axiom,
ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi6,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi7,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t36,plain,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi1,h12,h5,hi6,hi7,h1]) ).
cnf(hi0,axiom,
ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t15,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)],[hi0,hi9]) ).
cnf(t259,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)],[t15]) ).
cnf(t324,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(step,[status(thm)],[t36,t259]) ).
cnf(t42,axiom,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t258,plain,
c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(orient,[status(thm)],[t42]) ).
cnf(t325,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(step,[status(thm)],[t324,t258]) ).
cnf(t292,plain,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(orient,[status(thm)],[t325]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t292]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.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 05:51:39 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.88/3.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.88/3.75 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------