%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HEN006-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:37:03 PM UTC 2026
% Result : Unsatisfiable 5.67s 1.27s
% Output : Proof 5.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 46 unt; 0 def)
% Number of atoms : 46 ( 45 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 11 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t23,plain,
divide(divide(divide(X1,X2),divide(X3,X2)),divide(divide(X1,X3),X2)) = zero,
inference(orient,[status(thm)],[t6]) ).
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(t28,plain,
zero = divide(divide(divide(X1,X2),zero),divide(divide(X1,divide(X2,X3)),X2)),
inference(cp,[status(thm)],[t23,t16]) ).
cnf(f5,axiom,
divide(X,zero) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_divide_zero_is_x) ).
fof(f5_nnf,plain,
! [X] : divide(X,zero) = X,
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : divide(X,zero) = X,
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
divide(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t1,plain,
divide(X1,zero) = X1,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t8,plain,
divide(X1,zero) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t106,plain,
zero = divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)),
inference(step,[status(thm)],[t28,t8]) ).
cnf(t77,plain,
divide(divide(X1,X2),divide(divide(X1,divide(X2,X3)),X2)) = zero,
inference(orient,[status(thm)],[t106]) ).
cnf(f6,hypothesis,
divide(divide(a,b),d) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_divide_b_divide_d_is_zero) ).
fof(f6_nnf,plain,
divide(divide(a,b),d) = zero,
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
divide(divide(a,b),d) = zero,
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t4,plain,
divide(divide(a,b),d) = zero,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t40,plain,
divide(divide(a,b),d) = zero,
inference(orient,[status(thm)],[t4]) ).
cnf(t46,plain,
zero = divide(divide(divide(a,d),divide(b,d)),zero),
inference(cp,[status(thm)],[t23,t40]) ).
cnf(t100,plain,
zero = divide(divide(a,d),divide(b,d)),
inference(step,[status(thm)],[t46,t8]) ).
cnf(t59,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(orient,[status(thm)],[t100]) ).
cnf(t79,plain,
zero = divide(divide(divide(a,d),b),divide(zero,b)),
inference(cp,[status(thm)],[t77,t59]) ).
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(t48,plain,
divide(zero,X1) = zero,
inference(orient,[status(thm)],[t2]) ).
cnf(t107,plain,
zero = divide(divide(divide(a,d),b),zero),
inference(step,[status(thm)],[t79,t48]) ).
cnf(t108,plain,
zero = divide(divide(a,d),b),
inference(step,[status(thm)],[t107,t8]) ).
cnf(t88,plain,
divide(divide(a,d),b) = zero,
inference(orient,[status(thm)],[t108]) ).
cnf(f7,negated_conjecture,
divide(divide(a,d),b) != zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_divide1) ).
fof(f7_nnf,plain,
divide(divide(a,d),b) != zero,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
divide(divide(a,d),b) != zero,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
divide(divide(a,d),b) != zero,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
divide(divide(a,d),b) != zero,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
zero != zero,
inference(rw,[status(thm)],[goal_0,t88]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HEN006-5 : 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 : n019.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 16:12:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.67/1.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.67/1.27 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------