%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA032-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 5.13s 1.17s
% Output : Proof 5.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 70 ( 38 unt; 0 def)
% Number of atoms : 110 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 90 ( 50 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-4 aty)
% Number of variables : 98 ( 4 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f6_nnf,plain,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Oab__semigroup__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f10,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f10_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(hi9,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h3,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi9]) ).
cnf(f2,axiom,
( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
fof(f2_nnf,plain,
! [T_a,V_a,V_b] :
( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [T_a,V_a,V_b] :
( c_times(V_a,V_b,T_a) = c_times(V_b,V_a,T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( c_times(X1,X2,X0) = c_times(X2,X1,X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
ifeq(class_OrderedGroup_Oab__semigroup__mult(X0),true,c_times(X1,X2,X0),c_times(X2,X1,X0)) = c_times(X2,X1,X0),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t7,plain,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(hyper_resolution,[status(thm)],[hi2,h3]) ).
cnf(t43,plain,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(orient,[status(thm)],[t7]) ).
cnf(f7,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f7_nnf,plain,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( class_OrderedGroup_Osemigroup__mult(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_Osemigroup__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h2,plain,
class_OrderedGroup_Osemigroup__mult(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi9]) ).
cnf(f1,axiom,
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
fof(f1_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_times(c_times(V_a,V_b,T_a),V_c,T_a) = c_times(V_a,c_times(V_b,V_c,T_a),T_a)
| ~ class_OrderedGroup_Osemigroup__mult(T_a) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(class_OrderedGroup_Osemigroup__mult(X0),true,c_times(c_times(X1,X2,X0),X3,X0),c_times(X1,c_times(X2,X3,X0),X0)) = c_times(X1,c_times(X2,X3,X0),X0),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t14,plain,
c_times(c_times(X1,X2,t_b),X3,t_b) = c_times(X1,c_times(X2,X3,t_b),t_b),
inference(hyper_resolution,[status(thm)],[hi1,h2]) ).
cnf(t51,plain,
c_times(c_times(X1,X2,t_b),X3,t_b) = c_times(X1,c_times(X2,X3,t_b),t_b),
inference(orient,[status(thm)],[t14]) ).
cnf(f9,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f9_nnf,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [T] :
( class_OrderedGroup_Olordered__ab__group__abs(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h0,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi9]) ).
cnf(f0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f0_nnf,plain,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [T_a,V_a] :
( c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a)
| ~ class_OrderedGroup_Olordered__ab__group__abs(T_a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),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,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
c_lessequals(c_0,c_HOL_Oabs(V0,t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi0,h0]) ).
cnf(f8,axiom,
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f8_nnf,plain,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T] :
( class_Ring__and__Field_Opordered__semiring(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( class_Ring__and__Field_Opordered__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h1,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi9]) ).
cnf(f3,axiom,
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring_h57e6052f6a1e05b1) ).
fof(f3_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_lessequals(c_times(V_c,V_a,T_a),c_times(V_c,V_b,T_a),T_a)
| ~ c_lessequals(c_0,V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ class_Ring__and__Field_Opordered__semiring(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0)
| ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(class_Ring__and__Field_Opordered__semiring(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(c_0,X3,X0),true,c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f4,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f4_nnf,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t17,plain,
c_lessequals(c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_HOL_Oabs(X1,t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(hyper_resolution,[status(thm)],[hi3,h1,hi4,h4]) ).
cnf(t61,plain,
c_lessequals(c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_HOL_Oabs(X1,t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(f5,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f5_nnf,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(goal_0,negated_conjecture,
c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(g0_0,plain,
c_lessequals(c_times(c_HOL_Oabs(v_b(v_x),t_b),c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) != true,
inference(rw,[status(thm)],[goal_0,t43]) ).
cnf(g0_1,plain,
c_lessequals(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) != true,
inference(rw,[status(thm)],[g0_0,t43]) ).
cnf(g0_2,plain,
c_lessequals(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(c_HOL_Oabs(v_g(v_x),t_b),v_c,t_b),t_b),t_b) != true,
inference(rw,[status(thm)],[g0_1,t51]) ).
cnf(g0_3,plain,
c_lessequals(c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != true,
inference(rw,[status(thm)],[g0_2,t43]) ).
cnf(g0_4,plain,
true != true,
inference(rw,[status(thm)],[g0_3,t61]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA032-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.34 % Computer : n018.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Fri Sep 25 05:51:04 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.13/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.13/1.17 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------