%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 01:37:10 PM UTC 2026
% Result : Unsatisfiable 7.16s 1.43s
% Output : CNFRefutation 7.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 24 ( 24 unt; 0 nHn; 13 RR)
% Number of literals : 24 ( 23 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 31 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(hi3,axiom,
ifeq(quotient(V3,V2,V4),true,ifeq(quotient(V1,Z,V5),true,ifeq(quotient(Y,Z,V2),true,ifeq(quotient(X,Z,V3),true,ifeq(quotient(X,Y,V1),true,less_equal(V4,V5),true),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi12,axiom,
quotient(X,zero,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi7,axiom,
quotient(X,Y,divide(X,Y)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi11,axiom,
quotient(X,X,zero) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi17,axiom,
quotient(identity,a,idQa) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h123,plain,
less_equal(idQa,divide(idQa,a)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi12,hi7,hi11,hi17,hi17]) ).
cnf(hi1,axiom,
ifeq(quotient(X,Y,zero),true,less_equal(X,Y),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h0,plain,
less_equal(V0,V0) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi11]) ).
cnf(hi14,axiom,
ifeq(quotient(X,Z,W2),true,ifeq(quotient(X,Y,W1),true,ifeq(less_equal(W1,Z),true,less_equal(W2,Y),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi18,axiom,
quotient(identity,idQa,idQ_idQa) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h1,plain,
less_equal(idQ_idQa,a) = true,
inference(hyper_resolution,[status(thm)],[hi14,hi18,hi17,h0]) ).
cnf(hi15,axiom,
ifeq(quotient(Z,Y,W1),true,ifeq(quotient(Z,X,W2),true,ifeq(less_equal(X,Y),true,less_equal(W1,W2),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(hi19,axiom,
quotient(idQa,idQ_idQa,idQa_Q__idQ_idQa) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h41,plain,
less_equal(divide(idQa,a),idQa_Q__idQ_idQa) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi7,hi19,h1]) ).
cnf(hi13,axiom,
ifeq(less_equal(Y,Z),true,ifeq(less_equal(X,Y),true,less_equal(X,Z),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h302,plain,
less_equal(idQa,idQa_Q__idQ_idQa) = true,
inference(hyper_resolution,[status(thm)],[hi13,h41,h123]) ).
cnf(hi4,axiom,
less_equal(zero,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(h3,plain,
less_equal(idQa_Q__idQ_idQa,idQa) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi19,hi12,hi4]) ).
cnf(hi5,axiom,
ifeq2(less_equal(Y,X),true,ifeq2(less_equal(X,Y),true,X,Y),Y) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t0,plain,
idQa_Q__idQ_idQa = idQa,
inference(hyper_resolution,[status(thm)],[hi5,h3,h302]) ).
cnf(t1607,plain,
idQa = idQa_Q__idQ_idQa,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
idQa_Q__idQ_idQa != idQa,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
idQa_Q__idQ_idQa != idQa_Q__idQ_idQa,
inference(rw,[status(thm)],[goal_0,t1607]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN010-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 16:15:41 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.16/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.16/1.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------