%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN005-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 01:37:01 PM UTC 2026
% Result : Unsatisfiable 4.63s 1.12s
% Output : Proof 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 51 ( 47 unt; 0 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 48 ( 6 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t7,plain,
ifeq(divide(X1,X2),zero,ifeq(divide(X2,X1),zero,X1,X2),X2) = X2,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t9,plain,
ifeq(divide(X1,X2),zero,ifeq(divide(X2,X1),zero,X1,X2),X2) = X2,
inference(orient,[status(thm)],[t7]) ).
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(t3,plain,
divide(zero,X1) = zero,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t32,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t3]) ).
cnf(t34,plain,
zero = ifeq(divide(X1,zero),zero,ifeq(zero,zero,X1,zero),zero),
inference(cp,[status(thm)],[t9,t32]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t166,plain,
zero = ifeq(divide(X1,zero),zero,X1,zero),
inference(step,[status(thm)],[t34,t8]) ).
cnf(t49,plain,
ifeq(divide(X1,zero),zero,X1,zero) = zero,
inference(orient,[status(thm)],[t166]) ).
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(t6,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t18,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t6]) ).
cnf(f5,hypothesis,
divide(a,b) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_is_zero) ).
fof(f5_nnf,plain,
divide(a,b) = zero,
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
divide(a,b) = zero,
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(t1,plain,
divide(a,b) = zero,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t41,plain,
divide(a,b) = zero,
inference(orient,[status(thm)],[t1]) ).
cnf(t45,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),divide(zero,X1)),
inference(cp,[status(thm)],[t18,t41]) ).
cnf(t179,plain,
zero = divide(divide(divide(a,X1),divide(b,X1)),zero),
inference(step,[status(thm)],[t45,t32]) ).
cnf(t134,plain,
divide(divide(divide(a,X1),divide(b,X1)),zero) = zero,
inference(orient,[status(thm)],[t179]) ).
cnf(f6,hypothesis,
divide(b,c) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_divide_c_is_zero) ).
fof(f6_nnf,plain,
divide(b,c) = zero,
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
divide(b,c) = zero,
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t2,plain,
divide(b,c) = zero,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t36,plain,
divide(b,c) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t135,plain,
zero = divide(divide(divide(a,c),zero),zero),
inference(cp,[status(thm)],[t134,t36]) ).
cnf(t143,plain,
divide(divide(divide(a,c),zero),zero) = zero,
inference(orient,[status(thm)],[t135]) ).
cnf(t144,plain,
zero = ifeq(zero,zero,divide(divide(a,c),zero),zero),
inference(cp,[status(thm)],[t49,t143]) ).
cnf(t180,plain,
zero = divide(divide(a,c),zero),
inference(step,[status(thm)],[t144,t8]) ).
cnf(t150,plain,
divide(divide(a,c),zero) = zero,
inference(orient,[status(thm)],[t180]) ).
cnf(t151,plain,
zero = ifeq(zero,zero,divide(a,c),zero),
inference(cp,[status(thm)],[t49,t150]) ).
cnf(t181,plain,
zero = divide(a,c),
inference(step,[status(thm)],[t151,t8]) ).
cnf(t158,plain,
divide(a,c) = zero,
inference(orient,[status(thm)],[t181]) ).
cnf(f7,negated_conjecture,
divide(a,c) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_transitivity_of_divide_to_zero) ).
fof(f7_nnf,plain,
divide(a,c) != zero,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
divide(a,c) != zero,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
divide(a,c) != zero,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
divide(a,c) != zero,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t158]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HEN005-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Wed Sep 23 16:13:49 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.63/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.63/1.12 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------