%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM001-1 : 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 : n004.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 02:23:12 PM UTC 2026
% Result : Unsatisfiable 1.21s 1.29s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 20 unt; 4 def)
% Number of atoms : 59 ( 4 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 19 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',transitivity) ).
fof(f3,axiom,
! [X0,X1] : equalish(add(X0,X1),add(X1,X0)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',commutativity_of_addition) ).
fof(f4,axiom,
! [X2,X0,X1] : equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM002-0.ax',associativity_of_addition) ).
fof(f13,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equation) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(X0,X2)
| ~ equalish(X1,X2)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : equalish(add(X0,X1),add(X1,X0)),
inference(cnf_transformation,[],[f3]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : equalish(add(X0,add(X1,X2)),add(add(X0,X1),X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,negated_conjecture,
~ equalish(add(add(a,b),c),add(a,add(b,c))),
inference(cnf_transformation,[],[f13]) ).
tcf(c_128,definition,
iPr_def_10 = add(a,b),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_129,definition,
iPr_def_11 = add(iPr_def_10,c),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_130,definition,
iPr_def_12 = add(b,c),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_131,definition,
iPr_def_13 = add(a,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_132,negated_conjecture,
~ equalish(iPr_def_11,iPr_def_13),
inference(demodulation,[status(thm)],[c_74,c_130,c_131,c_128,c_129]) ).
tcf(c_307,plain,
equalish(iPr_def_11,add(c,iPr_def_10)),
inference(superposition,[status(thm)],[c_129,c_64]) ).
tcf(c_312,plain,
equalish(add(iPr_def_12,a),iPr_def_13),
inference(superposition,[status(thm)],[c_131,c_64]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] :
( equalish(add(X1,X0),X2)
| ~ equalish(add(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_64,c_63]) ).
tcf(c_347,plain,
! [X0: $i] : equalish(add(b,add(c,X0)),add(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_130,c_65]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( equalish(add(X0,add(X1,X2)),X3)
| ~ equalish(add(add(X0,X1),X2),X3) ),
inference(superposition,[status(thm)],[c_65,c_63]) ).
tcf(c_375,plain,
! [X0: $i] :
( equalish(iPr_def_11,X0)
| ~ equalish(add(c,iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_307,c_63]) ).
tcf(c_937,plain,
! [X0: $i] : equalish(add(add(c,X0),b),add(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_347,c_325]) ).
tcf(c_2365,plain,
! [X0: $i] : equalish(add(c,add(X0,b)),add(iPr_def_12,X0)),
inference(superposition,[status(thm)],[c_937,c_350]) ).
tcf(c_3130,plain,
equalish(add(c,iPr_def_10),add(iPr_def_12,a)),
inference(superposition,[status(thm)],[c_128,c_2365]) ).
tcf(c_3182,plain,
equalish(iPr_def_11,add(iPr_def_12,a)),
inference(superposition,[status(thm)],[c_3130,c_375]) ).
tcf(c_3192,plain,
! [X0: $i] :
( equalish(iPr_def_11,X0)
| ~ equalish(add(iPr_def_12,a),X0) ),
inference(superposition,[status(thm)],[c_3182,c_63]) ).
tcf(c_3630,plain,
equalish(iPr_def_11,iPr_def_13),
inference(superposition,[status(thm)],[c_312,c_3192]) ).
tcf(c_3638,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3630,c_132]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 02:37:37 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 1.21/1.29 % SZS status Started for theBenchmark.p
% 1.21/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.21/1.29
% 1.21/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.21/1.29
% 1.21/1.29 % ------ iProver source info
% 1.21/1.29
% 1.21/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.21/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.21/1.29 % git: non_committed_changes: false
% 1.21/1.29
% 1.21/1.29 % ------ Parsing...% successful
% 1.21/1.29
% 1.21/1.29
% 1.21/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.21/1.29
% 1.21/1.29 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.21/1.29
% 1.21/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.21/1.29
% 1.21/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.21/1.29 % ------ Proving...
% 1.21/1.29 % ------ Problem Properties
% 1.21/1.29
% 1.21/1.29 %
% 1.21/1.29 % clauses 17
% 1.21/1.29 % conjectures 1
% 1.21/1.29 % EPR 3
% 1.21/1.29 % Horn 17
% 1.21/1.29 % unary 12
% 1.21/1.29 % binary 0
% 1.21/1.29 % lits 27
% 1.21/1.29 % lits eq 4
% 1.21/1.29 % fd_pure 0
% 1.21/1.29 % fd_pseudo 0
% 1.21/1.29 % fd_cond 0
% 1.21/1.29 % fd_pseudo_cond 0
% 1.21/1.29 % AC symbols 0
% 1.21/1.29
% 1.21/1.29 % ------ Schedule dynamic 5 is on
% 1.21/1.29
% 1.21/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.21/1.29
% 1.21/1.29
% 1.21/1.29 % ------
% 1.21/1.29 % Current options:
% 1.21/1.29 % ------
% 1.21/1.29
% 1.21/1.29
% 1.21/1.29 %
% 1.21/1.29
% 1.21/1.29 % ------ Proving...
% 1.21/1.29 %
% 1.21/1.29
% 1.21/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 1.21/1.29
% 1.21/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.21/1.29
% 1.21/1.29
%------------------------------------------------------------------------------