%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN007-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 01:37:05 PM UTC 2026
% Result : Unsatisfiable 13.60s 7.39s
% Output : Proof 13.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 10
% Syntax : Number of formulae : 103 ( 99 unt; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 17 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-4 aty)
% Number of variables : 91 ( 12 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
sFlat0 = divide(c,b),
introduced(definition) ).
cnf(t47,plain,
divide(c,b) = sFlat0,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sFlat1 = divide(c,a),
introduced(definition) ).
cnf(t55,plain,
divide(c,a) = sFlat1,
inference(orient,[status(thm)],[t9]) ).
cnf(t10,axiom,
sFlat2 = divide(divide(c,b),divide(c,a)),
introduced(definition) ).
cnf(t35,plain,
divide(divide(c,b),divide(c,a)) = sFlat2,
inference(orient,[status(thm)],[t10]) ).
cnf(t1330,plain,
divide(sFlat0,divide(c,a)) = sFlat2,
inference(step,[status(thm)],[t35,t47]) ).
cnf(t54,plain,
divide(sFlat0,divide(c,a)) = sFlat2,
inference(rw,[status(thm)],[t1330]) ).
cnf(t1331,plain,
divide(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t54,t55]) ).
cnf(t105,plain,
divide(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t1331]) ).
cnf(f0,axiom,
divide(divide(X,Y),X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_smaller_than_numerator) ).
fof(f0_nnf,plain,
! [X,Y] : divide(divide(X,Y),X) = zero,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y] : divide(divide(X,Y),X) = zero,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(divide(X0,X1),X0) = zero,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
divide(divide(X1,X2),X1) = zero,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t16,plain,
divide(divide(X1,X2),X1) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(f3,axiom,
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',divide_and_equal) ).
fof(f3_nnf,plain,
! [X,Y] :
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y] :
( X = Y
| divide(Y,X) != zero
| divide(X,Y) != zero ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( X0 = X1
| divide(X1,X0) != zero
| divide(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t6,plain,
ifeq(divide(X1,X2),zero,ifeq(divide(X2,X1),zero,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t12,plain,
ifeq(divide(X1,X2),zero,ifeq(divide(X2,X1),zero,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t6]) ).
cnf(f1,axiom,
divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quotient_property) ).
fof(f1_nnf,plain,
! [X,Z,Y] : divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Z,Y] : divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero,
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
divide(divide(divide(X0,X1),divide(X2,X1)),divide(divide(X0,X2),X1)) = zero,
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t5,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t21,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t5]) ).
cnf(t51,plain,
zero = divide(divide(sFlat0,divide(X1,b)),divide(divide(c,X1),b)),
inference(cp,[status(thm)],[t21,t47]) ).
cnf(t1160,plain,
divide(divide(sFlat0,divide(X1,b)),divide(divide(c,X1),b)) = zero,
inference(orient,[status(thm)],[t51]) ).
cnf(f6,hypothesis,
divide(a,b) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_is_zero) ).
fof(f6_nnf,plain,
divide(a,b) = zero,
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
divide(a,b) = zero,
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t1,plain,
divide(a,b) = zero,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t62,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t1163,plain,
zero = divide(divide(sFlat0,zero),divide(divide(c,a),b)),
inference(cp,[status(thm)],[t1160,t62]) ).
cnf(f2,axiom,
divide(zero,X) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zero_is_smallest) ).
fof(f2_nnf,plain,
! [X] : divide(zero,X) = zero,
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : divide(zero,X) = zero,
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
divide(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t2,plain,
divide(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t43,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t45,plain,
zero = ifeq(divide(X1,zero),zero,ifeq(zero,zero,X1,zero),zero),
inference(cp,[status(thm)],[t12,t43]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t1335,plain,
zero = ifeq(divide(X1,zero),zero,X1,zero),
inference(step,[status(thm)],[t45,t11]) ).
cnf(t126,plain,
ifeq(divide(X1,zero),zero,X1,zero) = zero,
inference(orient,[status(thm)],[t1335]) ).
cnf(t46,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)),
inference(cp,[status(thm)],[t21,t43]) ).
cnf(t760,plain,
divide(divide(divide(X1,X2),zero),divide(divide(X1,zero),X2)) = zero,
inference(orient,[status(thm)],[t46]) ).
cnf(t25,plain,
zero = divide(divide(divide(X1,X1),divide(X2,X1)),zero),
inference(cp,[status(thm)],[t21,t16]) ).
cnf(t143,plain,
divide(divide(divide(X1,X1),divide(X2,X1)),zero) = zero,
inference(orient,[status(thm)],[t25]) ).
cnf(t151,plain,
zero = divide(divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t143,t43]) ).
cnf(t273,plain,
divide(divide(divide(X1,X1),zero),zero) = zero,
inference(orient,[status(thm)],[t151]) ).
cnf(t274,plain,
zero = ifeq(zero,zero,divide(divide(X1,X1),zero),zero),
inference(cp,[status(thm)],[t126,t273]) ).
cnf(t1354,plain,
zero = divide(divide(X1,X1),zero),
inference(step,[status(thm)],[t274,t11]) ).
cnf(t282,plain,
divide(divide(X1,X1),zero) = zero,
inference(orient,[status(thm)],[t1354]) ).
cnf(t283,plain,
zero = ifeq(zero,zero,divide(X1,X1),zero),
inference(cp,[status(thm)],[t126,t282]) ).
cnf(t1355,plain,
zero = divide(X1,X1),
inference(step,[status(thm)],[t283,t11]) ).
cnf(t291,plain,
divide(X1,X1) = zero,
inference(orient,[status(thm)],[t1355]) ).
cnf(t770,plain,
zero = divide(divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t760,t291]) ).
cnf(t1056,plain,
divide(divide(divide(X1,divide(X1,zero)),zero),zero) = zero,
inference(orient,[status(thm)],[t770]) ).
cnf(t1058,plain,
zero = ifeq(zero,zero,divide(divide(X1,divide(X1,zero)),zero),zero),
inference(cp,[status(thm)],[t126,t1056]) ).
cnf(t1421,plain,
zero = divide(divide(X1,divide(X1,zero)),zero),
inference(step,[status(thm)],[t1058,t11]) ).
cnf(t1071,plain,
divide(divide(X1,divide(X1,zero)),zero) = zero,
inference(orient,[status(thm)],[t1421]) ).
cnf(t1073,plain,
zero = ifeq(zero,zero,divide(X1,divide(X1,zero)),zero),
inference(cp,[status(thm)],[t126,t1071]) ).
cnf(t1422,plain,
zero = divide(X1,divide(X1,zero)),
inference(step,[status(thm)],[t1073,t11]) ).
cnf(t1086,plain,
divide(X1,divide(X1,zero)) = zero,
inference(orient,[status(thm)],[t1422]) ).
cnf(t1087,plain,
divide(X1,zero) = ifeq(zero,zero,ifeq(divide(divide(X1,zero),X1),zero,X1,divide(X1,zero)),divide(X1,zero)),
inference(cp,[status(thm)],[t12,t1086]) ).
cnf(t1423,plain,
divide(X1,zero) = ifeq(divide(divide(X1,zero),X1),zero,X1,divide(X1,zero)),
inference(step,[status(thm)],[t1087,t11]) ).
cnf(t1424,plain,
divide(X1,zero) = ifeq(zero,zero,X1,divide(X1,zero)),
inference(step,[status(thm)],[t1423,t16]) ).
cnf(t1425,plain,
divide(X1,zero) = X1,
inference(step,[status(thm)],[t1424,t11]) ).
cnf(t1119,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t1425]) ).
cnf(t1450,plain,
zero = divide(sFlat0,divide(divide(c,a),b)),
inference(step,[status(thm)],[t1163,t1119]) ).
cnf(t1451,plain,
zero = divide(sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t1450,t55]) ).
cnf(t1194,plain,
divide(sFlat0,divide(sFlat1,b)) = zero,
inference(orient,[status(thm)],[t1451]) ).
cnf(t1197,plain,
divide(sFlat1,b) = ifeq(zero,zero,ifeq(divide(divide(sFlat1,b),sFlat0),zero,sFlat0,divide(sFlat1,b)),divide(sFlat1,b)),
inference(cp,[status(thm)],[t12,t1194]) ).
cnf(t1452,plain,
divide(sFlat1,b) = ifeq(divide(divide(sFlat1,b),sFlat0),zero,sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t1197,t11]) ).
cnf(t56,plain,
zero = divide(sFlat1,c),
inference(cp,[status(thm)],[t16,t55]) ).
cnf(t97,plain,
divide(sFlat1,c) = zero,
inference(orient,[status(thm)],[t56]) ).
cnf(t104,plain,
zero = divide(divide(divide(sFlat1,X1),divide(c,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t21,t97]) ).
cnf(t1380,plain,
zero = divide(divide(divide(sFlat1,X1),divide(c,X1)),zero),
inference(step,[status(thm)],[t104,t43]) ).
cnf(t466,plain,
divide(divide(divide(sFlat1,X1),divide(c,X1)),zero) = zero,
inference(orient,[status(thm)],[t1380]) ).
cnf(t467,plain,
zero = divide(divide(divide(sFlat1,b),sFlat0),zero),
inference(cp,[status(thm)],[t466,t47]) ).
cnf(t480,plain,
divide(divide(divide(sFlat1,b),sFlat0),zero) = zero,
inference(orient,[status(thm)],[t467]) ).
cnf(t482,plain,
zero = ifeq(zero,zero,divide(divide(sFlat1,b),sFlat0),zero),
inference(cp,[status(thm)],[t126,t480]) ).
cnf(t1381,plain,
zero = divide(divide(sFlat1,b),sFlat0),
inference(step,[status(thm)],[t482,t11]) ).
cnf(t493,plain,
divide(divide(sFlat1,b),sFlat0) = zero,
inference(orient,[status(thm)],[t1381]) ).
cnf(t1453,plain,
divide(sFlat1,b) = ifeq(zero,zero,sFlat0,divide(sFlat1,b)),
inference(step,[status(thm)],[t1452,t493]) ).
cnf(t1454,plain,
divide(sFlat1,b) = sFlat0,
inference(step,[status(thm)],[t1453,t11]) ).
cnf(t1203,plain,
divide(sFlat1,b) = sFlat0,
inference(orient,[status(thm)],[t1454]) ).
cnf(t1204,plain,
zero = divide(sFlat0,sFlat1),
inference(cp,[status(thm)],[t16,t1203]) ).
cnf(t1455,plain,
zero = sFlat2,
inference(step,[status(thm)],[t1204,t105]) ).
cnf(t1218,plain,
zero = sFlat2,
inference(orient,[status(thm)],[t1455]) ).
cnf(f7,negated_conjecture,
divide(divide(c,b),divide(c,a)) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_divide2) ).
fof(f7_nnf,plain,
divide(divide(c,b),divide(c,a)) != zero,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
divide(divide(c,b),divide(c,a)) != zero,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
divide(divide(c,b),divide(c,a)) != zero,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
divide(divide(c,b),divide(c,a)) != zero,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
divide(sFlat0,divide(c,a)) != zero,
inference(rw,[status(thm)],[goal_0,t47]) ).
cnf(g0_1,plain,
divide(sFlat0,sFlat1) != zero,
inference(rw,[status(thm)],[g0_0,t55]) ).
cnf(g0_2,plain,
sFlat2 != zero,
inference(rw,[status(thm)],[g0_1,t105]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t1218]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN007-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.58 % Computer : n003.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Wed Sep 23 16:15:39 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 13.60/7.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.60/7.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------