%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG007-1 : 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 : 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 02:38:09 PM UTC 2026
% Result : Unsatisfiable 3.31s 1.19s
% Output : CNFRefutation 3.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 53 unt; 1 def)
% Number of atoms : 236 ( 58 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 77 ( 41 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 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; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 115 ( 0 sgn 115 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : sum(additive_identity,X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity1) ).
fof(f2,axiom,
! [X0] : sum(X0,additive_identity,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',additive_identity2) ).
fof(f6,axiom,
! [X0] : sum(X0,additive_inverse(X0),additive_identity),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',right_inverse) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4,X5] :
( sum(X2,X3,X5)
| ~ sum(X0,X4,X5)
| ~ sum(X1,X3,X4)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',associativity_of_addition2) ).
fof(f9,axiom,
! [X2,X0,X1] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',commutativity_of_addition) ).
fof(f13,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity2) ).
fof(f15,axiom,
! [X2,X3,X0,X1,X6,X4,X5] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/RNG001-0.ax',distributivity4) ).
fof(f18,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f19,negated_conjecture,
~ sum(a,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_plus_a_is_id) ).
tcf(c_68,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_69,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_73,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( sum(X2,X5,X4)
| ~ sum(X1,X5,X3)
| ~ sum(X0,X3,X4)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X5,X1,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X0,X3,X5)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_85,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f18]) ).
tcf(c_86,negated_conjecture,
~ sum(a,a,additive_identity),
inference(cnf_transformation,[],[f19]) ).
tcf(c_95,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(well_definedness,[status(thm)],[c_85]) ).
tcf(c_96,plain,
add(a,a) != additive_identity,
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_97,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_68]) ).
tcf(c_98,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_102,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_73]) ).
tcf(c_105,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( ( add(X2,X5) = X4 )
| ( add(X1,X5) != X3 )
| ( add(X0,X3) != X4 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_75]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X0,X5) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X1,X3) != X5 )
| ( multiply(X0,X3) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_80]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( ( multiply(X5,X1) = X6 )
| ( add(X2,X4) != X6 )
| ( add(X0,X3) != X5 )
| ( multiply(X3,X1) != X4 )
| ( multiply(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_82]) ).
tcf(c_237,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_107]) ).
tcf(c_243,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_105]) ).
tcf(c_245,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_119]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_115]) ).
tcf(c_281,definition,
iPr_def_10 = add(a,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_282,plain,
iPr_def_10 != additive_identity,
inference(demodulation,[status(thm)],[c_96,c_281]) ).
tcf(c_330,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_243,c_237]) ).
tcf(c_331,plain,
additive_inverse(additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_97,c_102]) ).
tcf(c_347,plain,
! [X0: $i] : add(a,add(a,X0)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_281,c_243]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_102,c_243]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_243,c_102]) ).
tcf(c_357,plain,
add(iPr_def_10,additive_inverse(a)) = add(a,additive_identity),
inference(superposition,[status(thm)],[c_102,c_347]) ).
tcf(c_363,plain,
add(iPr_def_10,additive_inverse(a)) = add(additive_identity,a),
inference(theory_normalisation,[status(thm)],[c_357,c_243,c_237]) ).
tcf(c_367,plain,
! [X0: $i] : add(multiply(a,X0),multiply(a,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_281,c_245]) ).
tcf(c_377,plain,
multiply(iPr_def_10,a) = add(a,a),
inference(superposition,[status(thm)],[c_95,c_367]) ).
tcf(c_381,plain,
multiply(iPr_def_10,a) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_377,c_281]) ).
tcf(c_383,plain,
add(iPr_def_10,additive_inverse(a)) = a,
inference(demodulation,[status(thm)],[c_363,c_97]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_350,c_97]) ).
tcf(c_418,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_102,c_412]) ).
tcf(c_419,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_237,c_412]) ).
tcf(c_431,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_418,c_98]) ).
tcf(c_447,plain,
add(a,a) = iPr_def_10,
inference(superposition,[status(thm)],[c_383,c_419]) ).
tcf(c_522,plain,
! [X0: $i] : add(multiply(X0,a),multiply(X0,a)) = multiply(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_447,c_247]) ).
tcf(c_625,plain,
! [X0: $i] : add(a,add(X0,a)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_447,c_330]) ).
tcf(c_667,plain,
! [X0: $i] : add(a,add(a,X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_237,c_625]) ).
tcf(c_757,plain,
! [X0: $i] : add(X0,add(iPr_def_10,additive_inverse(add(a,add(a,X0))))) = additive_identity,
inference(superposition,[status(thm)],[c_667,c_352]) ).
tcf(c_769,plain,
! [X0: $i] : add(X0,add(iPr_def_10,additive_inverse(add(iPr_def_10,X0)))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_757,c_347]) ).
tcf(c_869,plain,
! [X0: $i] : add(iPr_def_10,additive_inverse(add(iPr_def_10,additive_inverse(X0)))) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_769,c_412]) ).
tcf(c_873,plain,
! [X0: $i] : add(iPr_def_10,additive_inverse(add(iPr_def_10,additive_inverse(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_869,c_98]) ).
tcf(c_892,plain,
! [X0: $i] : add(iPr_def_10,additive_inverse(add(iPr_def_10,X0))) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_431,c_873]) ).
tcf(c_979,plain,
multiply(iPr_def_10,iPr_def_10) = add(iPr_def_10,iPr_def_10),
inference(superposition,[status(thm)],[c_381,c_522]) ).
tcf(c_995,plain,
add(iPr_def_10,iPr_def_10) = iPr_def_10,
inference(demodulation,[status(thm)],[c_979,c_95]) ).
tcf(c_1002,plain,
add(iPr_def_10,additive_inverse(iPr_def_10)) = additive_inverse(iPr_def_10),
inference(superposition,[status(thm)],[c_995,c_892]) ).
tcf(c_1009,plain,
additive_inverse(iPr_def_10) = additive_identity,
inference(demodulation,[status(thm)],[c_1002,c_102]) ).
tcf(c_1013,plain,
additive_inverse(additive_identity) = iPr_def_10,
inference(superposition,[status(thm)],[c_1009,c_431]) ).
tcf(c_1018,plain,
additive_identity = iPr_def_10,
inference(demodulation,[status(thm)],[c_331,c_1013]) ).
tcf(c_1025,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_282,c_1018]) ).
tcf(c_1026,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_1025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 07:42:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.42 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
% 0.11/0.43
% 0.11/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.43
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 3.31/1.19 % SZS status Started for theBenchmark.p
% 3.31/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.31/1.19
% 3.31/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.31/1.19
% 3.31/1.19 % ------ iProver source info
% 3.31/1.19
% 3.31/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.31/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.31/1.19 % git: non_committed_changes: false
% 3.31/1.19
% 3.31/1.19 % ------ Parsing...% successful
% 3.31/1.19
% 3.31/1.19
% 3.31/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.31/1.19
% 3.31/1.19 % ------ Preprocessing... sup_sim: 15 sf_s rm: 0 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 3.31/1.19
% 3.31/1.19 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.31/1.19 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.31/1.19
% 3.31/1.19 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.31/1.19 % ------ Proving...
% 3.31/1.19 % ------ Problem Properties
% 3.31/1.19
% 3.31/1.19 %
% 3.31/1.19 % clauses 11
% 3.31/1.19 % conjectures 0
% 3.31/1.19 % EPR 1
% 3.31/1.19 % Horn 11
% 3.31/1.19 % unary 11
% 3.31/1.19 % binary 0
% 3.31/1.19 % lits 11
% 3.31/1.19 % lits eq 11
% 3.31/1.19 % fd_pure 0
% 3.31/1.19 % fd_pseudo 0
% 3.31/1.19 % fd_cond 0
% 3.31/1.19 % fd_pseudo_cond 0
% 3.31/1.19 % AC symbols 1
% 3.31/1.19
% 3.31/1.19 % ------ Schedule UEQ
% 3.31/1.19
% 3.31/1.19 % ------ Option_UEQ Time Limit: 10.
% 3.31/1.19
% 3.31/1.19
% 3.31/1.19 % ------
% 3.31/1.19 % Current options:
% 3.31/1.19 % ------
% 3.31/1.19
% 3.31/1.19
% 3.31/1.19 %
% 3.31/1.19
% 3.31/1.19 % ------ Proving...
% 3.31/1.19 %
% 3.31/1.19
% 3.31/1.19 % SZS status Unsatisfiable for theBenchmark.p
% 3.31/1.19
% 3.31/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.31/1.19
%------------------------------------------------------------------------------