%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 01:37:02 PM UTC 2026
% Result : Unsatisfiable 4.53s 1.14s
% Output : Proof 4.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 9
% Syntax : Number of formulae : 117 ( 105 unt; 0 def)
% Number of atoms : 133 ( 97 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 150 ( 21 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f1,axiom,
( less_equal(X,Y)
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal2) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| divide(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t9,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t85,plain,
ifeq(divide(X1,X2),zero,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t9]) ).
cnf(f0,axiom,
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_less_equal1) ).
fof(f0_nnf,plain,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( divide(X,Y) = zero
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( divide(X0,X1) = zero
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(less_equal(X0,X1),true,divide(X0,X1),zero) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f3,axiom,
less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Z,Y] : less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
less_equal(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t11,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi3]) ).
cnf(t20,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t11]) ).
cnf(f2,axiom,
less_equal(divide(X,Y),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f2_nnf,plain,
! [X,Y] : less_equal(divide(X,Y),X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : less_equal(divide(X,Y),X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
less_equal(divide(X0,X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
less_equal(divide(X0,X1),X0) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t4,plain,
divide(divide(X1,X2),X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi2]) ).
cnf(t17,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t23,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)),
inference(cp,[status(thm)],[t20,t17]) ).
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_equal_and_equal) ).
fof(f5_nnf,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X0 = X1
| ~ less_equal(X1,X0)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t12,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t15,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f4_nnf,plain,
! [X] : less_equal(zero,X),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] : less_equal(zero,X),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
less_equal(zero,X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t3,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t82,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t84,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t15,t82]) ).
cnf(t6,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(t317,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t84,t14]) ).
cnf(t89,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t317]) ).
cnf(hi4,axiom,
less_equal(zero,X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t1,plain,
divide(zero,X1) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi4]) ).
cnf(t38,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t39,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(cp,[status(thm)],[t20,t38]) ).
cnf(t181,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)) = zero,
inference(orient,[status(thm)],[t39]) ).
cnf(t24,plain,
zero = divide(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(cp,[status(thm)],[t20,t17]) ).
cnf(t90,plain,
divide(divide(divide(X1,X1),divide(X2,X1)),zero) = zero,
inference(orient,[status(thm)],[t24]) ).
cnf(t91,plain,
zero = divide(divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t90,t38]) ).
cnf(t103,plain,
divide(divide(divide(X1,X1),zero),zero) = zero,
inference(orient,[status(thm)],[t91]) ).
cnf(t104,plain,
true = ifeq(zero,zero,less_equal(divide(divide(X1,X1),zero),zero),true),
inference(cp,[status(thm)],[t85,t103]) ).
cnf(t318,plain,
true = less_equal(divide(divide(X1,X1),zero),zero),
inference(step,[status(thm)],[t104,t14]) ).
cnf(t110,plain,
less_equal(divide(divide(X1,X1),zero),zero) = true,
inference(orient,[status(thm)],[t318]) ).
cnf(t111,plain,
zero = ifeq(true,true,divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t89,t110]) ).
cnf(t319,plain,
zero = divide(divide(X1,X1),zero),
inference(step,[status(thm)],[t111,t14]) ).
cnf(t115,plain,
divide(divide(X1,X1),zero) = zero,
inference(orient,[status(thm)],[t319]) ).
cnf(t116,plain,
true = ifeq(zero,zero,less_equal(divide(X1,X1),zero),true),
inference(cp,[status(thm)],[t85,t115]) ).
cnf(t320,plain,
true = less_equal(divide(X1,X1),zero),
inference(step,[status(thm)],[t116,t14]) ).
cnf(t123,plain,
less_equal(divide(X1,X1),zero) = true,
inference(orient,[status(thm)],[t320]) ).
cnf(t124,plain,
zero = ifeq(true,true,divide(X1,X1),zero),
inference(cp,[status(thm)],[t89,t123]) ).
cnf(t321,plain,
zero = divide(X1,X1),
inference(step,[status(thm)],[t124,t14]) ).
cnf(t128,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t321]) ).
cnf(t183,plain,
zero = divide(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t181,t128]) ).
cnf(t201,plain,
divide(divide(divide(X1,divide(X1,zero)),zero),zero) = zero,
inference(orient,[status(thm)],[t183]) ).
cnf(t202,plain,
true = ifeq(zero,zero,less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),true),
inference(cp,[status(thm)],[t85,t201]) ).
cnf(t334,plain,
true = less_equal(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(step,[status(thm)],[t202,t14]) ).
cnf(t244,plain,
less_equal(divide(divide(X1,divide(X1,zero)),zero),zero) = true,
inference(orient,[status(thm)],[t334]) ).
cnf(t245,plain,
zero = ifeq(true,true,divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t89,t244]) ).
cnf(t335,plain,
zero = divide(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t245,t14]) ).
cnf(t249,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(orient,[status(thm)],[t335]) ).
cnf(t250,plain,
true = ifeq(zero,zero,less_equal(divide(X1,divide(X1,zero)),zero),true),
inference(cp,[status(thm)],[t85,t249]) ).
cnf(t336,plain,
true = less_equal(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t250,t14]) ).
cnf(t258,plain,
less_equal(divide(X1,divide(X1,zero)),zero) = true,
inference(orient,[status(thm)],[t336]) ).
cnf(t259,plain,
zero = ifeq(true,true,divide(X1,divide(X1,zero)),zero),
inference(cp,[status(thm)],[t89,t258]) ).
cnf(t337,plain,
zero = divide(X1,divide(X1,zero)),
inference(step,[status(thm)],[t259,t14]) ).
cnf(t263,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t337]) ).
cnf(t264,plain,
true = ifeq(zero,zero,less_equal(X1,divide(X1,zero)),true),
inference(cp,[status(thm)],[t85,t263]) ).
cnf(t338,plain,
true = less_equal(X1,divide(X1,zero)),
inference(step,[status(thm)],[t264,t14]) ).
cnf(t273,plain,
less_equal(X1,divide(X1,zero)) = true,
inference(orient,[status(thm)],[t338]) ).
cnf(t274,plain,
divide(X1,zero) = ifeq(true,true,ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),divide(X1,zero)),
inference(cp,[status(thm)],[t15,t273]) ).
cnf(t339,plain,
divide(X1,zero) = ifeq(less_equal(divide(X1,zero),X1),true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t274,t14]) ).
cnf(t7,plain,
less_equal(divide(X1,X2),X1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t49,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t340,plain,
divide(X1,zero) = ifeq(true,true,X1,divide(X1,zero)),
inference(step,[status(thm)],[t339,t49]) ).
cnf(t341,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t340,t14]) ).
cnf(t276,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t341]) ).
cnf(t344,plain,
zero = divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(step,[status(thm)],[t23,t276]) ).
cnf(t288,plain,
divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(orient,[status(thm)],[t344]) ).
cnf(t13,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t57,plain,
less_equal(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = true,
inference(orient,[status(thm)],[t13]) ).
cnf(f7,hypothesis,
less_equal(divide(a,b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_LE_d) ).
fof(f7_nnf,plain,
less_equal(divide(a,b),d),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
less_equal(divide(a,b),d),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,axiom,
less_equal(divide(a,b),d) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t5,plain,
divide(divide(a,b),d) = zero,
inference(hyper_resolution,[status(thm)],[hi0,hi7]) ).
cnf(t32,plain,
divide(divide(a,b),d) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t70,plain,
true = less_equal(divide(divide(a,d),divide(b,d)),zero),
inference(cp,[status(thm)],[t57,t32]) ).
cnf(t145,plain,
less_equal(divide(divide(a,d),divide(b,d)),zero) = true,
inference(orient,[status(thm)],[t70]) ).
cnf(t146,plain,
zero = ifeq(true,true,divide(divide(a,d),divide(b,d)),zero),
inference(cp,[status(thm)],[t89,t145]) ).
cnf(t323,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(step,[status(thm)],[t146,t14]) ).
cnf(t150,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(orient,[status(thm)],[t323]) ).
cnf(t289,plain,
zero = divide(divide(divide(a,d),b),divide(zero,b)),
inference(cp,[status(thm)],[t288,t150]) ).
cnf(t345,plain,
zero = divide(divide(divide(a,d),b),zero),
inference(step,[status(thm)],[t289,t38]) ).
cnf(t346,plain,
zero = divide(divide(a,d),b),
inference(step,[status(thm)],[t345,t276]) ).
cnf(t302,plain,
divide(divide(a,d),b) = zero,
inference(orient,[status(thm)],[t346]) ).
cnf(t303,plain,
true = ifeq(zero,zero,less_equal(divide(a,d),b),true),
inference(cp,[status(thm)],[t85,t302]) ).
cnf(t347,plain,
true = less_equal(divide(a,d),b),
inference(step,[status(thm)],[t303,t14]) ).
cnf(t311,plain,
less_equal(divide(a,d),b) = true,
inference(orient,[status(thm)],[t347]) ).
cnf(f8,negated_conjecture,
~ less_equal(divide(a,d),b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_divide_d_LE_b) ).
fof(f8_nnf,plain,
~ less_equal(divide(a,d),b),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ less_equal(divide(a,d),b),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ less_equal(divide(a,d),b),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
less_equal(divide(a,d),b) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t311]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 16:12:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.53/1.14 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.53/1.14 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------