%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : BOO011-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 12:59:35 PM UTC 2026
% Result : Unsatisfiable 5.65s 1.26s
% Output : Proof 5.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 34 unt; 0 def)
% Number of atoms : 46 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 48 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t23,axiom,
sFlat0 = inverse(additive_identity),
introduced(definition) ).
cnf(t291,plain,
inverse(additive_identity) = sFlat0,
inference(orient,[status(thm)],[t23]) ).
cnf(f20,axiom,
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',addition_is_well_defined) ).
fof(f20_nnf,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X,Y,U,V] :
( U = V
| ~ sum(X,Y,V)
| ~ sum(X,Y,U) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( X2 = X3
| ~ sum(X0,X1,X3)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t14,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t25,plain,
ifeq(sum(X1,X2,X3),true,ifeq(sum(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t14]) ).
cnf(f5,axiom,
sum(X,additive_identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity2) ).
fof(f5_nnf,plain,
! [X] : sum(X,additive_identity,X),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] : sum(X,additive_identity,X),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
sum(X0,additive_identity,X0),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t2,plain,
sum(X1,additive_identity,X1) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t74,plain,
sum(X1,additive_identity,X1) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t77,plain,
X1 = ifeq(true,true,ifeq(sum(X2,additive_identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t25,t74]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t24,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t458,plain,
X1 = ifeq(sum(X2,additive_identity,X1),true,X2,X1),
inference(step,[status(thm)],[t77,t24]) ).
cnf(t438,plain,
ifeq(sum(X1,additive_identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t458]) ).
cnf(f16,axiom,
sum(inverse(X),X,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_inverse1) ).
fof(f16_nnf,plain,
! [X] : sum(inverse(X),X,multiplicative_identity),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X] : sum(inverse(X),X,multiplicative_identity),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
sum(inverse(X0),X0,multiplicative_identity),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(t8,plain,
sum(inverse(X1),X1,multiplicative_identity) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t147,plain,
sum(inverse(X1),X1,multiplicative_identity) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t294,plain,
true = sum(sFlat0,additive_identity,multiplicative_identity),
inference(cp,[status(thm)],[t147,t291]) ).
cnf(t344,plain,
sum(sFlat0,additive_identity,multiplicative_identity) = true,
inference(orient,[status(thm)],[t294]) ).
cnf(t441,plain,
multiplicative_identity = ifeq(true,true,sFlat0,multiplicative_identity),
inference(cp,[status(thm)],[t438,t344]) ).
cnf(t459,plain,
multiplicative_identity = sFlat0,
inference(step,[status(thm)],[t441,t24]) ).
cnf(t451,plain,
multiplicative_identity = sFlat0,
inference(orient,[status(thm)],[t459]) ).
cnf(f22,negated_conjecture,
inverse(additive_identity) != multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
fof(f22_nnf,plain,
inverse(additive_identity) != multiplicative_identity,
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
inverse(additive_identity) != multiplicative_identity,
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
inverse(additive_identity) != multiplicative_identity,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(additive_identity) != multiplicative_identity,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
sFlat0 != multiplicative_identity,
inference(rw,[status(thm)],[goal_0,t291]) ).
cnf(g0_1,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_0,t451]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 06:29:32 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.65/1.26 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.65/1.26 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------