%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : ALG434-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n010.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 12:52:32 PM UTC 2026
% Result : Unsatisfiable 9.83s 1.90s
% Output : Proof 9.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 52 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 30 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-4 aty)
% Number of variables : 36 ( 7 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f374,negated_conjecture,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f374_nnf,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(nnf_transformation,[status(thm)],[f374]) ).
fof(f374_sk,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(skolemisation,[status(esa)],[f374_nnf]) ).
cnf(c374,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(esa)],[f374_sk]) ).
cnf(t50,plain,
ifeq(c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c374]) ).
cnf(f366,axiom,
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dvd__smult_0) ).
fof(f366_nnf,plain,
! [T_a,V_p,V_a,V_q] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(nnf_transformation,[status(thm)],[f366]) ).
fof(f366_sk,plain,
! [T_a,V_p,V_a,V_q] :
( ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_a) ),
inference(skolemisation,[status(esa)],[f366_nnf]) ).
cnf(c366,plain,
( ~ c_Ring__and__Field_Odvd__class_Odvd(X1,X3,tc_Polynomial_Opoly(X0))
| c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X2,X3,X0),tc_Polynomial_Opoly(X0))
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[status(esa)],[f366_sk]) ).
cnf(hi364,axiom,
ifeq(class_Ring__and__Field_Ocomm__semiring__1(X0),true,ifeq(c_Ring__and__Field_Odvd__class_Odvd(X1,X2,tc_Polynomial_Opoly(X0)),true,c_Ring__and__Field_Odvd__class_Odvd(X1,c_Polynomial_Osmult(X3,X2,X0),tc_Polynomial_Opoly(X0)),true),true) = true,
inference(equality_encoding,[status(esa)],[c366]) ).
cnf(f382,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f382_nnf,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(nnf_transformation,[status(thm)],[f382]) ).
cnf(c382,plain,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[status(esa)],[f382_nnf]) ).
cnf(hi379,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) = true,
inference(equality_encoding,[status(esa)],[c382]) ).
cnf(f373,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f373_nnf,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(nnf_transformation,[status(thm)],[f373]) ).
cnf(c373,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)),
inference(cnf_transformation,[status(esa)],[f373_nnf]) ).
cnf(hi371,axiom,
c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = true,
inference(equality_encoding,[status(esa)],[c373]) ).
cnf(t21,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(X1,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = true,
inference(hyper_resolution,[status(thm)],[hi364,hi379,hi371]) ).
cnf(t227,plain,
c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(X1,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) = true,
inference(orient,[status(thm)],[t21]) ).
cnf(t252,plain,
ifeq(true,true,false,true) = true,
inference(step,[status(thm)],[t50,t227]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t97,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t253,plain,
false = true,
inference(step,[status(thm)],[t252,t97]) ).
cnf(t241,plain,
false = true,
inference(orient,[status(thm)],[t253]) ).
cnf(f26,axiom,
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).
fof(f26_nnf,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [T_a] :
( c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( c_HOL_Oone__class_Oone(X0) != c_HOL_Ozero__class_Ozero(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(f222,axiom,
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f222_nnf,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(nnf_transformation,[status(thm)],[f222]) ).
fof(f222_sk,plain,
! [T_a] :
( c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a)
| ~ class_Ring__and__Field_Ozero__neq__one(T_a) ),
inference(skolemisation,[status(esa)],[f222_nnf]) ).
cnf(c222,plain,
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
inference(cnf_transformation,[status(esa)],[f222_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c26,c222,c374]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t241]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG434-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 05:38:43 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.83/1.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.83/1.90 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------