%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG008-2 : 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 : n018.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 14.07s 2.81s
% Output : CNFRefutation 14.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 51 unt; 1 def)
% Number of atoms : 255 ( 80 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 117 ( 61 ~; 56 |; 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 : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 172 ( 0 sgn 172 !; 0 ?; 137 :)
% 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,
! [X2,X3,X0,X1] :
( X1 = X3
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation1) ).
fof(f19,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation2) ).
fof(f20,axiom,
! [X0] : product(X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_squared_is_x) ).
fof(f21,axiom,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f22,negated_conjecture,
~ product(b,a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_times_a_is_c) ).
tcf(c_71,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_76,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_78,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_79,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X6,X2,X5)
| ~ product(X6,X1,X4)
| ~ product(X6,X0,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f13]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( product(X2,X6,X5)
| ~ product(X1,X6,X4)
| ~ product(X0,X6,X3)
| ~ sum(X3,X4,X5)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ sum(X0,X3,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ~ sum(X3,X1,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_90,plain,
! [X0: $i] : product(X0,X0,X0),
inference(cnf_transformation,[],[f20]) ).
tcf(c_91,plain,
product(a,b,c),
inference(cnf_transformation,[],[f21]) ).
tcf(c_92,negated_conjecture,
~ product(b,a,c),
inference(cnf_transformation,[],[f22]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( add(X0,X3) != X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 = X3 )
| ( add(X3,X1) != X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_89]) ).
tcf(c_105,plain,
! [X0: $i] : multiply(X0,X0) = X0,
inference(well_definedness,[status(thm)],[c_90]) ).
tcf(c_106,plain,
multiply(a,b) = c,
inference(well_definedness,[status(thm)],[c_91]) ).
tcf(c_107,plain,
multiply(b,a) != c,
inference(well_definedness,[status(thm)],[c_92]) ).
tcf(c_108,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_71]) ).
tcf(c_109,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_72]) ).
tcf(c_113,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_76]) ).
tcf(c_116,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_78]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_79]) ).
tcf(c_126,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_83]) ).
tcf(c_130,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_85]) ).
tcf(c_262,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_118]) ).
tcf(c_266,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X2 )
| ( add(X0,X1) != add(X2,X1) ) ),
inference(unflattening,[status(thm)],[c_103]) ).
tcf(c_269,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = X2 )
| ( add(X0,X1) != add(X0,X2) ) ),
inference(unflattening,[status(thm)],[c_101]) ).
tcf(c_276,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_116]) ).
tcf(c_278,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X2,X1)) = multiply(add(X0,X2),X1),
inference(unflattening,[status(thm)],[c_130]) ).
tcf(c_280,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_126]) ).
tcf(c_331,definition,
iPr_def_10 = multiply(b,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_332,plain,
iPr_def_10 != c,
inference(demodulation,[status(thm)],[c_107,c_331]) ).
tcf(c_7385,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_276,c_262]) ).
tcf(c_7570,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_113,c_276]) ).
tcf(c_7622,plain,
! [X0: $i,X1: $i] :
( ( X0 = additive_identity )
| ( add(X0,X1) != X1 ) ),
inference(superposition,[status(thm)],[c_108,c_266]) ).
tcf(c_7624,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( add(X0,additive_inverse(X1)) != additive_identity ) ),
inference(superposition,[status(thm)],[c_113,c_266]) ).
tcf(c_7661,plain,
! [X0: $i,X1: $i] :
( ( X1 = additive_identity )
| ( add(X0,X1) != X0 ) ),
inference(superposition,[status(thm)],[c_109,c_269]) ).
tcf(c_7688,plain,
! [X0: $i,X1: $i] : add(multiply(additive_identity,X0),multiply(X1,X0)) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_108,c_278]) ).
tcf(c_7690,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = multiply(additive_identity,X1),
inference(superposition,[status(thm)],[c_113,c_278]) ).
tcf(c_7698,plain,
! [X0: $i,X1: $i] : add(multiply(X0,add(X0,X1)),multiply(X1,add(X0,X1))) = add(X0,X1),
inference(superposition,[status(thm)],[c_278,c_105]) ).
tcf(c_7702,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_7570,c_108]) ).
tcf(c_7710,plain,
! [X0: $i] : add(X0,additive_identity) = additive_inverse(additive_inverse(X0)),
inference(superposition,[status(thm)],[c_113,c_7702]) ).
tcf(c_7738,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_7710,c_109]) ).
tcf(c_7933,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_108,c_280]) ).
tcf(c_7935,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_113,c_280]) ).
tcf(c_8021,plain,
! [X0: $i] : multiply(additive_identity,X0) = additive_identity,
inference(superposition,[status(thm)],[c_7688,c_7622]) ).
tcf(c_9903,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = additive_identity )
| ( add(X0,add(X1,X2)) != add(X0,X1) ) ),
inference(superposition,[status(thm)],[c_276,c_7661]) ).
tcf(c_13533,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( add(additive_inverse(X0),X1) != additive_identity ) ),
inference(superposition,[status(thm)],[c_262,c_7624]) ).
tcf(c_13575,plain,
! [X0: $i] : multiply(X0,additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_7933,c_7622]) ).
tcf(c_15664,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(additive_inverse(X0),X1)) = additive_identity,
inference(demodulation,[status(thm)],[c_7690,c_8021]) ).
tcf(c_15665,plain,
! [X0: $i] : add(X0,multiply(additive_inverse(X0),X0)) = additive_identity,
inference(superposition,[status(thm)],[c_105,c_15664]) ).
tcf(c_19013,plain,
! [X0: $i] : multiply(additive_inverse(additive_inverse(X0)),additive_inverse(X0)) = X0,
inference(superposition,[status(thm)],[c_15665,c_13533]) ).
tcf(c_19017,plain,
! [X0: $i] : multiply(X0,additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_19013,c_7738]) ).
tcf(c_21879,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_7935,c_13575]) ).
tcf(c_21912,plain,
! [X0: $i] : add(multiply(X0,X0),X0) = additive_identity,
inference(superposition,[status(thm)],[c_19017,c_21879]) ).
tcf(c_21936,plain,
! [X0: $i] : add(X0,multiply(X0,X0)) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_21912,c_276,c_262]) ).
tcf(c_21937,plain,
! [X0: $i] : add(X0,X0) = additive_identity,
inference(light_normalisation,[status(thm)],[c_21936,c_105]) ).
tcf(c_23652,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( add(X0,X1) != additive_identity ) ),
inference(superposition,[status(thm)],[c_21937,c_269]) ).
tcf(c_26067,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,add(multiply(X0,X1),multiply(X1,X0)))) = add(X0,X1),
inference(demodulation,[status(thm)],[c_7698,c_105,c_262,c_276,c_280,c_7385]) ).
tcf(c_26153,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X1,X0)) = additive_identity,
inference(superposition,[status(thm)],[c_26067,c_9903]) ).
tcf(c_29094,plain,
! [X0: $i,X1: $i] : multiply(X0,X1) = multiply(X1,X0),
inference(superposition,[status(thm)],[c_26153,c_23652]) ).
tcf(c_29171,plain,
multiply(a,b) = iPr_def_10,
inference(demodulation,[status(thm)],[c_331,c_29094]) ).
tcf(c_29176,plain,
c = iPr_def_10,
inference(demodulation,[status(thm)],[c_106,c_29171]) ).
tcf(c_29181,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_332,c_29176]) ).
tcf(c_29182,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_29181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG008-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.38 % Computer : n018.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Thu Sep 24 07:45:18 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.42 Running first-order theorem proving
% 0.09/0.42 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
% 0.09/0.43
% 0.09/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.43
% 0.09/0.43 % Detected problem language: tptp
% 0.09/0.45 % Proving...
% 14.07/2.81 % SZS status Started for theBenchmark.p
% 14.07/2.81 % SZS status Unsatisfiable for theBenchmark.p
% 14.07/2.81
% 14.07/2.81 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 14.07/2.81
% 14.07/2.81 % ------ iProver source info
% 14.07/2.81
% 14.07/2.81 % git: date: 2026-07-19 20:42:38 +0200
% 14.07/2.81 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 14.07/2.81 % git: non_committed_changes: false
% 14.07/2.81
% 14.07/2.81 % ------ Parsing...% successful
% 14.07/2.81
% 14.07/2.81
% 14.07/2.81 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 14.07/2.81
% 14.07/2.81 % ------ Preprocessing... sup_sim: 17 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 %
% 14.07/2.81
% 14.07/2.81 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 14.07/2.81
% 14.07/2.81 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 14.07/2.81 % ------ Proving...
% 14.07/2.81 % ------ Problem Properties
% 14.07/2.81
% 14.07/2.81 %
% 14.07/2.81 % clauses 14
% 14.07/2.81 % conjectures 0
% 14.07/2.81 % EPR 1
% 14.07/2.81 % Horn 14
% 14.07/2.81 % unary 12
% 14.07/2.81 % binary 2
% 14.07/2.81 % lits 16
% 14.07/2.81 % lits eq 16
% 14.07/2.81 % fd_pure 0
% 14.07/2.81 % fd_pseudo 0
% 14.07/2.81 % fd_cond 0
% 14.07/2.81 % fd_pseudo_cond 2
% 14.07/2.81 % AC symbols 1
% 14.07/2.81
% 14.07/2.81 % ------ Schedule dynamic 5 is on
% 14.07/2.81
% 14.07/2.81 % ------ no conjectures: strip conj schedule
% 14.07/2.81
% 14.07/2.81 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 14.07/2.81
% 14.07/2.81
% 14.07/2.81 % ------
% 14.07/2.81 % Current options:
% 14.07/2.81 % ------
% 14.07/2.81
% 14.07/2.81
% 14.07/2.81 %
% 14.07/2.81
% 14.07/2.81 % ------ Proving...
% 14.07/2.81 %
% 14.07/2.81
% 14.07/2.81 % SZS status Unsatisfiable for theBenchmark.p
% 14.07/2.81
% 14.07/2.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 14.07/2.81
% 14.07/2.81
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