%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 2.31s 0.78s
% Output : Proof 2.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 32 unt; 0 def)
% Number of atoms : 64 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 48 ( 32 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 69 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,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(f5_nnf,plain,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T] :
( class_OrderedGroup_Oab__semigroup__mult(T)
| ~ class_Ring__and__Field_Oordered__idom(T) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( class_OrderedGroup_Oab__semigroup__mult(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Oab__semigroup__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f1,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f1_nnf,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi0,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h0,plain,
class_OrderedGroup_Oab__semigroup__mult(t_b) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi0]) ).
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(hi1,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(t3,plain,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(hyper_resolution,[status(thm)],[hi1,h0]) ).
cnf(t12,plain,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(orient,[status(thm)],[t3]) ).
cnf(f3,axiom,
( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__3_0) ).
fof(f3_nnf,plain,
! [T_a,V_a,V_b,V_c] :
( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_a,V_b,V_c] :
( c_times(V_a,c_times(V_b,V_c,T_a),T_a) = c_times(V_b,c_times(V_a,V_c,T_a),T_a)
| ~ class_OrderedGroup_Oab__semigroup__mult(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_times(X1,c_times(X2,X3,X0),X0) = c_times(X2,c_times(X1,X3,X0),X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(class_OrderedGroup_Oab__semigroup__mult(X0),true,c_times(X1,c_times(X2,X3,X0),X0),c_times(X2,c_times(X1,X3,X0),X0)) = c_times(X2,c_times(X1,X3,X0),X0),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t5,plain,
c_times(X1,c_times(X2,X3,t_b),t_b) = c_times(X2,c_times(X1,X3,t_b),t_b),
inference(hyper_resolution,[status(thm)],[hi2,h0]) ).
cnf(t20,plain,
c_times(X1,c_times(X2,X3,t_b),t_b) = c_times(X2,c_times(X1,X3,t_b),t_b),
inference(orient,[status(thm)],[t5]) ).
cnf(f4,axiom,
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f4_nnf,plain,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [T_a,V_a,V_b] :
( c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a) = c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a)
| ~ class_Ring__and__Field_Oordered__idom(T_a) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X0),true,c_HOL_Oabs(c_times(X1,X2,X0),X0),c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0)) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t6,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)],[hi3,hi0]) ).
cnf(t34,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)],[t6]) ).
cnf(f0,negated_conjecture,
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) != 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),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f0_nnf,plain,
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) != 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),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
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) != 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),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
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) != 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),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
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(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,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_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[goal_0,t12]) ).
cnf(g0_1,plain,
c_times(c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_0,t12]) ).
cnf(g0_2,plain,
c_times(c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),v_c,t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_1,t12]) ).
cnf(g0_3,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),v_c,t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_2,t20]) ).
cnf(g0_4,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_c,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_3,t12]) ).
cnf(g0_5,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_g(v_x),t_b),v_ca,t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_4,t12]) ).
cnf(g0_6,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_c,v_ca,t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_5,t20]) ).
cnf(g0_7,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(c_HOL_Oabs(v_g(v_x),t_b),c_times(v_ca,v_c,t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_6,t12]) ).
cnf(g0_8,plain,
c_times(c_HOL_Oabs(v_f(v_x),t_b),c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_7,t12]) ).
cnf(g0_9,plain,
c_times(c_times(v_ca,v_c,t_b),c_times(c_HOL_Oabs(v_f(v_x),t_b),c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_8,t20]) ).
cnf(g0_10,plain,
c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) != c_times(c_times(v_ca,v_c,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),
inference(rw,[status(thm)],[g0_9,t34]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 25 05:49:06 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.31/0.78 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.31/0.78 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------