%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:36:57 PM UTC 2026
% Result : Unsatisfiable 19.08s 8.03s
% Output : Proof 19.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 9
% Syntax : Number of formulae : 88 ( 68 unt; 0 def)
% Number of atoms : 128 ( 59 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-4 aty)
% Number of variables : 208 ( 19 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,axiom,
quotient(X,Y,divide(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure) ).
fof(f7_nnf,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] : quotient(X,Y,divide(X,Y)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
quotient(X0,X1,divide(X0,X1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(t5,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t17,plain,
quotient(X1,X2,divide(X1,X2)) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f5,axiom,
( X = Y
| ~ less_equal(Y,X)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/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(t9,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t16,plain,
ifeq(less_equal(X1,X2),true,ifeq(less_equal(X2,X1),true,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(f4,axiom,
less_equal(zero,X),
file('/export/starexec/sandbox/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(t1,plain,
less_equal(zero,X1) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t62,plain,
less_equal(zero,X1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t65,plain,
zero = ifeq(less_equal(X1,zero),true,ifeq(true,true,X1,zero),zero),
inference(cp,[status(thm)],[t16,t62]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t469,plain,
zero = ifeq(less_equal(X1,zero),true,X1,zero),
inference(step,[status(thm)],[t65,t13]) ).
cnf(t99,plain,
ifeq(less_equal(X1,zero),true,X1,zero) = zero,
inference(orient,[status(thm)],[t469]) ).
cnf(f1,axiom,
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_equal_quotient) ).
fof(f1_nnf,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( less_equal(X,Y)
| ~ quotient(X,Y,zero) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( less_equal(X0,X1)
| ~ quotient(X0,X1,zero) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t8,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t50,plain,
ifeq(quotient(X1,X2,zero),true,less_equal(X1,X2),true) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(f3,axiom,
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_property) ).
fof(f3_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,V1,Z,V2,V3,V4,V5] :
( less_equal(V4,V5)
| ~ quotient(V1,Z,V5)
| ~ quotient(V3,V2,V4)
| ~ quotient(X,Z,V3)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( less_equal(X6,X7)
| ~ quotient(X2,X3,X7)
| ~ quotient(X5,X4,X6)
| ~ quotient(X0,X3,X5)
| ~ quotient(X1,X3,X4)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t11,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X4,X5),true,ifeq(quotient(X1,X4,X6),true,ifeq(quotient(X6,X5,X7),true,ifeq(quotient(X3,X4,X8),true,less_equal(X7,X8),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t11]) ).
cnf(t27,plain,
true = ifeq(true,true,ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true),true),
inference(cp,[status(thm)],[t26,t17]) ).
cnf(t485,plain,
true = ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true),
inference(step,[status(thm)],[t27,t13]) ).
cnf(t159,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X4,X2,X5),true,ifeq(quotient(X5,X3,X6),true,ifeq(quotient(divide(X4,X1),X2,X7),true,less_equal(X6,X7),true),true),true),true) = true,
inference(orient,[status(thm)],[t485]) ).
cnf(f0,axiom,
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quotient_less_equal) ).
fof(f0_nnf,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] :
( quotient(X,Y,zero)
| ~ less_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( quotient(X0,X1,zero)
| ~ less_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t6,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t54,plain,
ifeq(less_equal(X1,X2),true,quotient(X1,X2,zero),true) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(f2,axiom,
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divisor_existence) ).
fof(f2_nnf,plain,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y,Z] :
( less_equal(Z,X)
| ~ quotient(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( less_equal(X2,X0)
| ~ quotient(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t7,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t44,plain,
ifeq(quotient(X1,X2,X3),true,less_equal(X3,X1),true) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(t45,plain,
true = ifeq(true,true,less_equal(divide(X1,X2),X1),true),
inference(cp,[status(thm)],[t44,t17]) ).
cnf(t462,plain,
true = less_equal(divide(X1,X2),X1),
inference(step,[status(thm)],[t45,t13]) ).
cnf(t78,plain,
less_equal(divide(X1,X2),X1) = true,
inference(orient,[status(thm)],[t462]) ).
cnf(t79,plain,
true = ifeq(true,true,quotient(divide(X1,X2),X1,zero),true),
inference(cp,[status(thm)],[t54,t78]) ).
cnf(t464,plain,
true = quotient(divide(X1,X2),X1,zero),
inference(step,[status(thm)],[t79,t13]) ).
cnf(t86,plain,
quotient(divide(X1,X2),X1,zero) = true,
inference(orient,[status(thm)],[t464]) ).
cnf(t177,plain,
true = ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X2,X4),true,ifeq(quotient(X4,X3,X5),true,ifeq(true,true,less_equal(X5,zero),true),true),true),true),
inference(cp,[status(thm)],[t159,t86]) ).
cnf(t505,plain,
true = ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X2,X4),true,ifeq(quotient(X4,X3,X5),true,less_equal(X5,zero),true),true),true),
inference(step,[status(thm)],[t177,t13]) ).
cnf(t394,plain,
ifeq(quotient(X1,X2,X3),true,ifeq(quotient(X2,X2,X4),true,ifeq(quotient(X4,X3,X5),true,less_equal(X5,zero),true),true),true) = true,
inference(orient,[status(thm)],[t505]) ).
cnf(t397,plain,
true = ifeq(true,true,ifeq(quotient(X1,X1,X2),true,ifeq(quotient(X2,zero,X3),true,less_equal(X3,zero),true),true),true),
inference(cp,[status(thm)],[t394,t86]) ).
cnf(t508,plain,
true = ifeq(quotient(X1,X1,X2),true,ifeq(quotient(X2,zero,X3),true,less_equal(X3,zero),true),true),
inference(step,[status(thm)],[t397,t13]) ).
cnf(t405,plain,
ifeq(quotient(X1,X1,X2),true,ifeq(quotient(X2,zero,X3),true,less_equal(X3,zero),true),true) = true,
inference(orient,[status(thm)],[t508]) ).
cnf(t406,plain,
true = ifeq(true,true,ifeq(quotient(divide(X1,X1),zero,X2),true,less_equal(X2,zero),true),true),
inference(cp,[status(thm)],[t405,t17]) ).
cnf(t509,plain,
true = ifeq(quotient(divide(X1,X1),zero,X2),true,less_equal(X2,zero),true),
inference(step,[status(thm)],[t406,t13]) ).
cnf(t408,plain,
ifeq(quotient(divide(X1,X1),zero,X2),true,less_equal(X2,zero),true) = true,
inference(orient,[status(thm)],[t509]) ).
cnf(t409,plain,
true = ifeq(true,true,less_equal(divide(divide(X1,X1),zero),zero),true),
inference(cp,[status(thm)],[t408,t17]) ).
cnf(t510,plain,
true = less_equal(divide(divide(X1,X1),zero),zero),
inference(step,[status(thm)],[t409,t13]) ).
cnf(t410,plain,
less_equal(divide(divide(X1,X1),zero),zero) = true,
inference(orient,[status(thm)],[t510]) ).
cnf(t411,plain,
zero = ifeq(true,true,divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t99,t410]) ).
cnf(t511,plain,
zero = divide(divide(X1,X1),zero),
inference(step,[status(thm)],[t411,t13]) ).
cnf(t416,plain,
divide(divide(X1,X1),zero) = zero,
inference(orient,[status(thm)],[t511]) ).
cnf(t417,plain,
true = quotient(divide(X1,X1),zero,zero),
inference(cp,[status(thm)],[t17,t416]) ).
cnf(t421,plain,
quotient(divide(X1,X1),zero,zero) = true,
inference(orient,[status(thm)],[t417]) ).
cnf(t423,plain,
true = ifeq(true,true,less_equal(divide(X1,X1),zero),true),
inference(cp,[status(thm)],[t50,t421]) ).
cnf(t512,plain,
true = less_equal(divide(X1,X1),zero),
inference(step,[status(thm)],[t423,t13]) ).
cnf(t433,plain,
less_equal(divide(X1,X1),zero) = true,
inference(orient,[status(thm)],[t512]) ).
cnf(t434,plain,
zero = ifeq(true,true,divide(X1,X1),zero),
inference(cp,[status(thm)],[t99,t433]) ).
cnf(t513,plain,
zero = divide(X1,X1),
inference(step,[status(thm)],[t434,t13]) ).
cnf(t438,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t513]) ).
cnf(t439,plain,
true = quotient(X1,X1,zero),
inference(cp,[status(thm)],[t17,t438]) ).
cnf(t445,plain,
quotient(X1,X1,zero) = true,
inference(orient,[status(thm)],[t439]) ).
cnf(f11,negated_conjecture,
~ quotient(x,x,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_x_divide_x_is_zero) ).
fof(f11_nnf,plain,
~ quotient(x,x,zero),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ quotient(x,x,zero),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ quotient(x,x,zero),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(goal_0,negated_conjecture,
quotient(x,x,zero) != true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t445]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n005.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 16:08:38 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.08/8.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.08/8.03 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------