%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n012.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 02:39:44 PM UTC 2026
% Result : Unsatisfiable 2.20s 1.06s
% Output : CNFRefutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 18 unt; 0 def)
% Number of atoms : 32 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 21 ( 12 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : add(X0,X1) = add(X1,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',commutativity_of_add) ).
fof(f2,axiom,
! [X2,X0,X1] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',associativity_of_add) ).
fof(f3,axiom,
! [X0,X1] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/ROB001-0.ax',robbins_axiom) ).
fof(f8,axiom,
negate(add(d,e)) = negate(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condition) ).
fof(f9,axiom,
positive_integer(k),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_positive) ).
fof(f10,axiom,
! [X2,X0,X1] :
( negate(add(X0,multiply(X2,add(X1,negate(add(X1,negate(X0))))))) = negate(X0)
| ~ positive_integer(X2)
| negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_3_6) ).
fof(f11,plain,
! [X2,X0,X1] :
( negate(X0) = negate(add(X0,multiply(X2,add(X1,negate(add(X1,negate(X0)))))))
| ~ positive_integer(X2)
| negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_result) ).
fof(f13,plain,
negate(e) != negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))),
inference(reorient_equations,[],[f12]) ).
tcf(c_60,plain,
negate(add(d,e)) = negate(e),
inference(cnf_transformation,[],[f8]) ).
tcf(c_61,negated_conjecture,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) != negate(e),
inference(cnf_transformation,[],[f13]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( negate(add(X0,multiply(X2,add(X1,negate(add(X1,negate(X0))))))) = negate(X0) )
| ~ positive_integer(X2)
| ( negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : negate(add(negate(add(X0,X1)),negate(add(X0,negate(X1))))) = X0,
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
positive_integer(k),
inference(cnf_transformation,[],[f9]) ).
tcf(c_71,plain,
negate(add(e,d)) = negate(e),
inference(theory_normalisation,[status(thm)],[c_60,c_62,c_63]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( negate(add(X0,multiply(X2,add(X1,negate(add(X1,negate(X0))))))) = negate(X0) )
| ( X2 != k )
| ( negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_64]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( negate(add(X0,multiply(k,add(X1,negate(add(X1,negate(X0))))))) = negate(X0) )
| ( negate(add(negate(X0),negate(add(X1,negate(X0))))) != X1 ) ),
inference(unflattening,[status(thm)],[c_100]) ).
tcf(c_183,plain,
! [X0: $i,X1: $i] : negate(add(negate(add(X0,X1)),negate(add(X1,negate(X0))))) = X1,
inference(superposition,[status(thm)],[c_63,c_65]) ).
tcf(c_219,plain,
negate(add(negate(e),negate(add(d,negate(e))))) = d,
inference(superposition,[status(thm)],[c_71,c_183]) ).
tcf(c_376,plain,
negate(add(e,multiply(k,add(d,negate(add(d,negate(e))))))) = negate(e),
inference(superposition,[status(thm)],[c_219,c_101]) ).
tcf(c_383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_376,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ROB016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 08:26:50 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.33
% 0.03/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.33
% 0.03/0.33 % Detected problem language: tptp
% 0.06/0.33 % Proving...
% 2.20/1.06 % SZS status Started for theBenchmark.p
% 2.20/1.06 % SZS status Unsatisfiable for theBenchmark.p
% 2.20/1.06
% 2.20/1.06 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.20/1.06
% 2.20/1.06 % ------ iProver source info
% 2.20/1.06
% 2.20/1.06 % git: date: 2026-07-19 20:42:38 +0200
% 2.20/1.06 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.20/1.06 % git: non_committed_changes: false
% 2.20/1.06
% 2.20/1.06 % ------ Parsing...% successful
% 2.20/1.06
% 2.20/1.06
% 2.20/1.06 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.20/1.06
% 2.20/1.06 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.20/1.06
% 2.20/1.06 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.20/1.06
% 2.20/1.06 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 2.20/1.06 % ------ Proving...
% 2.20/1.06 % ------ Problem Properties
% 2.20/1.06
% 2.20/1.06 %
% 2.20/1.06 % clauses 6
% 2.20/1.06 % conjectures 1
% 2.20/1.06 % EPR 0
% 2.20/1.06 % Horn 6
% 2.20/1.06 % unary 5
% 2.20/1.06 % binary 1
% 2.20/1.06 % lits 7
% 2.20/1.06 % lits eq 7
% 2.20/1.06 % fd_pure 0
% 2.20/1.06 % fd_pseudo 0
% 2.20/1.06 % fd_cond 0
% 2.20/1.06 % fd_pseudo_cond 0
% 2.20/1.06 % AC symbols 1
% 2.20/1.06
% 2.20/1.06 % ------ Schedule dynamic 5 is on
% 2.20/1.06
% 2.20/1.06 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.20/1.06
% 2.20/1.06
% 2.20/1.06 % ------
% 2.20/1.06 % Current options:
% 2.20/1.06 % ------
% 2.20/1.06
% 2.20/1.06
% 2.20/1.06 %
% 2.20/1.06
% 2.20/1.06 % ------ Proving...
% 2.20/1.06 %
% 2.20/1.06
% 2.20/1.06 % SZS status Unsatisfiable for theBenchmark.p
% 2.20/1.06
% 2.20/1.06 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.20/1.06
% 2.20/1.06
%------------------------------------------------------------------------------