%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 12:55:04 PM UTC 2026
% Result : Unsatisfiable 3.63s 0.94s
% Output : Proof 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 75 ( 51 unt; 0 def)
% Number of atoms : 103 ( 63 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 64 ( 36 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-4 aty)
% Number of variables : 82 ( 2 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f8_nnf,plain,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [T] :
( class_Ring__and__Field_Ofield(T)
| ~ class_Ring__and__Field_Oordered__field(T) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Oordered__field(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi6,axiom,
ifeq(class_Ring__and__Field_Oordered__field(X0),true,class_Ring__and__Field_Ofield(X0),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f2,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f2_nnf,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
class_Ring__and__Field_Oordered__field(t_a),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi0,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h0,plain,
class_Ring__and__Field_Ofield(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi0]) ).
cnf(f7,axiom,
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
fof(f7_nnf,plain,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [T] :
( class_OrderedGroup_Osemigroup__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( class_OrderedGroup_Osemigroup__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi5,axiom,
ifeq(class_Ring__and__Field_Ofield(X0),true,class_OrderedGroup_Osemigroup__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h1,plain,
class_OrderedGroup_Osemigroup__mult(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi5,h0]) ).
cnf(f4,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/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
cnf(hi2,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)],[c4]) ).
cnf(t19,plain,
c_times(c_times(X1,X2,t_a),X3,t_a) = c_times(X1,c_times(X2,X3,t_a),t_a),
inference(hyper_resolution,[status(thm)],[hi2,h1]) ).
cnf(t55,plain,
c_times(c_times(X1,X2,t_a),X3,t_a) = c_times(X1,c_times(X2,X3,t_a),t_a),
inference(orient,[status(thm)],[t19]) ).
cnf(t16,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
introduced(definition) ).
cnf(t26,plain,
ifeq(eq(X1,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t16]) ).
cnf(f5,axiom,
( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oright__inverse_0) ).
fof(f5_nnf,plain,
! [T_a,V_a] :
( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [T_a,V_a] :
( c_times(V_a,c_HOL_Oinverse(V_a,T_a),T_a) = c_1
| V_a = c_0
| ~ class_Ring__and__Field_Ofield(T_a) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( c_times(X1,c_HOL_Oinverse(X1,X0),X0) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi3,axiom,
ifeq(class_Ring__and__Field_Ofield(X0),true,or(eq(X1,c_0),eq(c_times(X1,c_HOL_Oinverse(X1,X0),X0),c_1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t18,plain,
or(eq(X1,c_0),eq(c_times(X1,c_HOL_Oinverse(X1,t_a),t_a),c_1)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h0]) ).
cnf(t42,plain,
or(eq(X1,c_0),eq(c_times(X1,c_HOL_Oinverse(X1,t_a),t_a),c_1)) = true,
inference(orient,[status(thm)],[t18]) ).
cnf(f0,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f0_nnf,plain,
v_c != c_0,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
v_c != c_0,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
v_c != c_0,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t5,plain,
eq(v_c,c_0) = false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t58,plain,
eq(v_c,c_0) = false,
inference(orient,[status(thm)],[t5]) ).
cnf(t60,plain,
true = or(false,eq(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),c_1)),
inference(cp,[status(thm)],[t42,t58]) ).
cnf(t8,plain,
or(false,X1) = X1,
introduced(definition) ).
cnf(t30,plain,
or(false,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t74,plain,
true = eq(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),c_1),
inference(step,[status(thm)],[t60,t30]) ).
cnf(t65,plain,
eq(c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),c_1) = true,
inference(orient,[status(thm)],[t74]) ).
cnf(t66,plain,
c_1 = ifeq(true,true,c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),c_1),
inference(cp,[status(thm)],[t26,t65]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t25,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t75,plain,
c_1 = c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a),
inference(step,[status(thm)],[t66,t25]) ).
cnf(t67,plain,
c_times(v_c,c_HOL_Oinverse(v_c,t_a),t_a) = c_1,
inference(orient,[status(thm)],[t75]) ).
cnf(t68,plain,
c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),X1,t_a),t_a) = c_times(c_1,X1,t_a),
inference(cp,[status(thm)],[t55,t67]) ).
cnf(f6,axiom,
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
fof(f6_nnf,plain,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [T] :
( class_OrderedGroup_Omonoid__mult(T)
| ~ class_Ring__and__Field_Ofield(T) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( class_OrderedGroup_Omonoid__mult(X0)
| ~ class_Ring__and__Field_Ofield(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi4,axiom,
ifeq(class_Ring__and__Field_Ofield(X0),true,class_OrderedGroup_Omonoid__mult(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h2,plain,
class_OrderedGroup_Omonoid__mult(t_a) = true,
inference(hyper_resolution,[status(thm)],[hi4,h0]) ).
cnf(f3,axiom,
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f3_nnf,plain,
! [T_a,V_y] :
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [T_a,V_y] :
( c_times(c_1,V_y,T_a) = V_y
| ~ class_OrderedGroup_Omonoid__mult(T_a) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( c_times(c_1,X1,X0) = X1
| ~ class_OrderedGroup_Omonoid__mult(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi1,axiom,
ifeq(class_OrderedGroup_Omonoid__mult(X0),true,c_times(c_1,X1,X0),X1) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t10,plain,
c_times(c_1,X1,t_a) = X1,
inference(hyper_resolution,[status(thm)],[hi1,h2]) ).
cnf(t24,plain,
c_times(c_1,X1,t_a) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t76,plain,
c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),X1,t_a),t_a) = X1,
inference(step,[status(thm)],[t68,t24]) ).
cnf(t71,plain,
c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),X1,t_a),t_a) = X1,
inference(orient,[status(thm)],[t76]) ).
cnf(t4,plain,
eq(X1,X1) = true,
introduced(definition) ).
cnf(t38,plain,
eq(X1,X1) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(f1,negated_conjecture,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1_nnf,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
v_g(v_x) != c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1]) ).
cnf(g0_0,plain,
eq(v_g(v_x),c_times(v_c,c_times(c_HOL_Oinverse(v_c,t_a),v_g(v_x),t_a),t_a)) != false,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
eq(v_g(v_x),v_g(v_x)) != false,
inference(rw,[status(thm)],[g0_0,t71]) ).
cnf(g0_2,plain,
true != false,
inference(rw,[status(thm)],[g0_1,t38]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 05:41:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.63/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.63/0.94 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------