%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 02:18:30 PM UTC 2026
% Result : Unsatisfiable 0.16s 6.02s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 40 unt; 0 def)
% Number of atoms : 76 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 120 ( 0 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( equalish(C,subtract(B,D))
| ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution1) ).
fof(f10_nnf,plain,
! [A,B,C,D] :
( equalish(C,subtract(B,D))
| ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C,D] :
( equalish(C,subtract(B,D))
| ~ equalish(C,subtract(A,D))
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( equalish(X2,subtract(X1,X3))
| ~ equalish(X2,subtract(X0,X3))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(equalish(X0,X1),true,ifeq(equalish(X2,subtract(X0,X3)),true,equalish(X2,subtract(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f2,axiom,
equalish(add(A,B),add(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
fof(f2_nnf,plain,
! [A,B] : equalish(add(A,B),add(B,A)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : equalish(add(A,B),add(B,A)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
equalish(add(X0,X1),add(X1,X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
equalish(add(X0,X1),add(X1,X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f0,axiom,
equalish(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f0_nnf,plain,
! [A] : equalish(A,A),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : equalish(A,A),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
equalish(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
equalish(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h3,plain,
equalish(subtract(add(V0,V1),V2),subtract(add(V1,V0),V2)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi2,hi0]) ).
cnf(f1,axiom,
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f1_nnf,plain,
! [A,B,C] :
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( equalish(A,C)
| ~ equalish(B,C)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(equalish(X0,X1),true,ifeq(equalish(X1,X2),true,equalish(X0,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f4,axiom,
equalish(subtract(add(A,B),B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction1) ).
fof(f4_nnf,plain,
! [A,B] : equalish(subtract(add(A,B),B),A),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] : equalish(subtract(add(A,B),B),A),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
equalish(subtract(add(X0,X1),X1),X0),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
equalish(subtract(add(X0,X1),X1),X0) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h211,plain,
equalish(subtract(add(V0,V1),V0),V1) = true,
inference(hyper_resolution,[status(thm)],[hi1,h3,hi4]) ).
cnf(f11,axiom,
( equalish(C,subtract(D,B))
| ~ equalish(C,subtract(D,A))
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution2) ).
fof(f11_nnf,plain,
! [A,B,C,D] :
( equalish(C,subtract(D,B))
| ~ equalish(C,subtract(D,A))
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C,D] :
( equalish(C,subtract(D,B))
| ~ equalish(C,subtract(D,A))
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( equalish(X2,subtract(X3,X1))
| ~ equalish(X2,subtract(X3,X0))
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,axiom,
ifeq(equalish(X0,X1),true,ifeq(equalish(X2,subtract(X3,X0)),true,equalish(X2,subtract(X3,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f3,axiom,
equalish(add(A,add(B,C)),add(add(A,B),C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition) ).
fof(f3_nnf,plain,
! [A,B,C] : equalish(add(A,add(B,C)),add(add(A,B),C)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] : equalish(add(A,add(B,C)),add(add(A,B),C)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f5,axiom,
equalish(A,subtract(add(A,B),B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction2) ).
fof(f5_nnf,plain,
! [A,B] : equalish(A,subtract(add(A,B),B)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] : equalish(A,subtract(add(A,B),B)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
equalish(X0,subtract(add(X0,X1),X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
equalish(X0,subtract(add(X0,X1),X1)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h47,plain,
equalish(V0,subtract(add(V0,add(V1,add(V2,V3))),add(add(V1,V2),V3))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi3,hi5]) ).
cnf(t170,plain,
equalish(add(add(X1,X2),X3),add(X1,add(X2,X3))) = true,
inference(hyper_resolution,[status(thm)],[hi1,h47,h211]) ).
cnf(t407,plain,
equalish(add(add(X1,X2),X3),add(X1,add(X2,X3))) = true,
inference(orient,[status(thm)],[t170]) ).
cnf(f12,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
fof(f12_nnf,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
equalish(add(add(a,b),c),add(a,add(b,c))) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t407]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/5.38 % Computer : n006.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 02:37:34 UTC 2026
% 0.12/5.38 % CPUTime :
% 0.12/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/6.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/6.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------