%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : RNG037-1 : 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 : n009.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 02:38:16 PM UTC 2026
% Result : Unsatisfiable 3.27s 1.38s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 69 ( 60 unt; 1 def)
% Number of atoms : 221 ( 58 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 54 ( 30 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 91 ( 0 sgn 91 !; 0 ?; 72 :)
% 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(f18,axiom,
product(a,b,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f19,axiom,
product(a,additive_inverse(b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_inverse_times_b) ).
fof(f20,negated_conjecture,
~ sum(c,d,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_sum_is_additive_identity) ).
tcf(c_69,plain,
! [X0: $i] : sum(additive_identity,X0,X0),
inference(cnf_transformation,[],[f1]) ).
tcf(c_70,plain,
! [X0: $i] : sum(X0,additive_identity,X0),
inference(cnf_transformation,[],[f2]) ).
tcf(c_74,plain,
! [X0: $i] : sum(X0,additive_inverse(X0),additive_identity),
inference(cnf_transformation,[],[f6]) ).
tcf(c_76,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_77,plain,
! [X0: $i,X1: $i,X2: $i] :
( sum(X1,X0,X2)
| ~ sum(X0,X1,X2) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_81,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_86,plain,
product(a,b,d),
inference(cnf_transformation,[],[f18]) ).
tcf(c_87,plain,
product(a,additive_inverse(b),c),
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,negated_conjecture,
~ sum(c,d,additive_identity),
inference(cnf_transformation,[],[f20]) ).
tcf(c_96,plain,
multiply(a,b) = d,
inference(well_definedness,[status(thm)],[c_86]) ).
tcf(c_97,plain,
multiply(a,additive_inverse(b)) = c,
inference(well_definedness,[status(thm)],[c_87]) ).
tcf(c_98,plain,
add(c,d) != additive_identity,
inference(well_definedness,[status(thm)],[c_88]) ).
tcf(c_99,plain,
! [X0: $i] : add(additive_identity,X0) = X0,
inference(well_definedness,[status(thm)],[c_69]) ).
tcf(c_100,plain,
! [X0: $i] : add(X0,additive_identity) = X0,
inference(well_definedness,[status(thm)],[c_70]) ).
tcf(c_104,plain,
! [X0: $i] : add(X0,additive_inverse(X0)) = additive_identity,
inference(well_definedness,[status(thm)],[c_74]) ).
tcf(c_107,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_76]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( add(X1,X0) = X2 )
| ( add(X0,X1) != X2 ) ),
inference(well_definedness,[status(thm)],[c_77]) ).
tcf(c_117,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_81]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : add(X0,X1) = add(X1,X0),
inference(unflattening,[status(thm)],[c_109]) ).
tcf(c_241,plain,
add(d,c) != additive_identity,
inference(demodulation,[status(thm)],[c_98,c_240]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] : add(add(X0,X1),X2) = add(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_107]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i,X2: $i] : add(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,add(X1,X2)),
inference(unflattening,[status(thm)],[c_117]) ).
tcf(c_289,definition,
iPr_def_10 = add(d,c),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_290,plain,
iPr_def_10 != additive_identity,
inference(demodulation,[status(thm)],[c_241,c_289]) ).
tcf(c_346,plain,
! [X0: $i,X1: $i,X2: $i] : add(X0,add(X1,X2)) = add(X1,add(X0,X2)),
inference(superposition,[status(thm)],[c_247,c_240]) ).
tcf(c_347,plain,
additive_inverse(additive_identity) = additive_identity,
inference(superposition,[status(thm)],[c_99,c_104]) ).
tcf(c_364,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = add(additive_identity,X1),
inference(superposition,[status(thm)],[c_104,c_247]) ).
tcf(c_365,plain,
! [X0: $i] : add(d,add(c,X0)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_289,c_247]) ).
tcf(c_367,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(add(X0,X1)))) = additive_identity,
inference(superposition,[status(thm)],[c_247,c_104]) ).
tcf(c_372,plain,
! [X0: $i] : add(d,add(X0,c)) = add(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_240,c_365]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i] : add(X0,add(additive_inverse(X0),X1)) = X1,
inference(demodulation,[status(thm)],[c_364,c_99]) ).
tcf(c_414,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = add(X0,additive_identity),
inference(superposition,[status(thm)],[c_104,c_408]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] : add(X0,add(X1,additive_inverse(X0))) = X1,
inference(superposition,[status(thm)],[c_240,c_408]) ).
tcf(c_424,plain,
add(iPr_def_10,additive_inverse(d)) = c,
inference(superposition,[status(thm)],[c_408,c_372]) ).
tcf(c_427,plain,
! [X0: $i] : additive_inverse(additive_inverse(X0)) = X0,
inference(light_normalisation,[status(thm)],[c_414,c_100]) ).
tcf(c_446,plain,
add(d,c) = iPr_def_10,
inference(superposition,[status(thm)],[c_424,c_415]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i] : add(multiply(X0,additive_identity),multiply(X0,X1)) = multiply(X0,X1),
inference(superposition,[status(thm)],[c_99,c_251]) ).
tcf(c_524,plain,
! [X0: $i,X1: $i] : add(multiply(X0,X1),multiply(X0,additive_inverse(X1))) = multiply(X0,additive_identity),
inference(superposition,[status(thm)],[c_104,c_251]) ).
tcf(c_705,plain,
! [X0: $i] : add(d,add(X0,c)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_446,c_346]) ).
tcf(c_754,plain,
! [X0: $i] : add(d,add(c,X0)) = add(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_240,c_705]) ).
tcf(c_796,plain,
! [X0: $i] : add(X0,add(iPr_def_10,additive_inverse(add(d,add(c,X0))))) = additive_identity,
inference(superposition,[status(thm)],[c_754,c_367]) ).
tcf(c_808,plain,
! [X0: $i] : add(X0,add(iPr_def_10,additive_inverse(add(iPr_def_10,X0)))) = additive_identity,
inference(light_normalisation,[status(thm)],[c_796,c_365]) ).
tcf(c_846,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_808,c_408]) ).
tcf(c_852,plain,
! [X0: $i] : add(iPr_def_10,additive_inverse(add(iPr_def_10,additive_inverse(X0)))) = X0,
inference(light_normalisation,[status(thm)],[c_846,c_100]) ).
tcf(c_877,plain,
! [X0: $i] : add(iPr_def_10,additive_inverse(add(iPr_def_10,X0))) = additive_inverse(X0),
inference(superposition,[status(thm)],[c_427,c_852]) ).
tcf(c_978,plain,
add(multiply(a,additive_identity),c) = c,
inference(superposition,[status(thm)],[c_97,c_522]) ).
tcf(c_992,plain,
add(c,multiply(a,additive_identity)) = c,
inference(theory_normalisation,[status(thm)],[c_978,c_247,c_240]) ).
tcf(c_1009,plain,
add(iPr_def_10,multiply(a,additive_identity)) = add(d,c),
inference(superposition,[status(thm)],[c_992,c_365]) ).
tcf(c_1010,plain,
add(iPr_def_10,multiply(a,additive_identity)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_1009,c_446]) ).
tcf(c_1028,plain,
additive_inverse(multiply(a,additive_identity)) = add(iPr_def_10,additive_inverse(iPr_def_10)),
inference(superposition,[status(thm)],[c_1010,c_877]) ).
tcf(c_1035,plain,
additive_inverse(multiply(a,additive_identity)) = additive_identity,
inference(demodulation,[status(thm)],[c_1028,c_104]) ).
tcf(c_1037,plain,
multiply(a,additive_identity) = additive_inverse(additive_identity),
inference(superposition,[status(thm)],[c_1035,c_427]) ).
tcf(c_1040,plain,
multiply(a,additive_identity) = additive_identity,
inference(light_normalisation,[status(thm)],[c_1037,c_347]) ).
tcf(c_2363,plain,
add(multiply(a,b),c) = multiply(a,additive_identity),
inference(superposition,[status(thm)],[c_97,c_524]) ).
tcf(c_2387,plain,
add(c,multiply(a,b)) = multiply(a,additive_identity),
inference(theory_normalisation,[status(thm)],[c_2363,c_247,c_240]) ).
tcf(c_2388,plain,
add(c,d) = additive_identity,
inference(light_normalisation,[status(thm)],[c_2387,c_96,c_1040]) ).
tcf(c_2389,plain,
add(d,c) = additive_identity,
inference(theory_normalisation,[status(thm)],[c_2388,c_247,c_240]) ).
tcf(c_2390,plain,
additive_identity = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_2389,c_446]) ).
tcf(c_2433,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_290,c_2390]) ).
tcf(c_2434,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_2433]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 07:55:14 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 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
% 0.14/0.44
% 0.14/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.44
% 0.14/0.45 % Detected problem language: tptp
% 0.14/0.47 % Proving...
% 3.27/1.38 % SZS status Started for theBenchmark.p
% 3.27/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 3.27/1.38
% 3.27/1.38 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.27/1.38
% 3.27/1.38 % ------ iProver source info
% 3.27/1.38
% 3.27/1.38 % git: date: 2026-07-19 20:42:38 +0200
% 3.27/1.38 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.27/1.38 % git: non_committed_changes: false
% 3.27/1.38
% 3.27/1.38 % ------ Parsing...% successful
% 3.27/1.38
% 3.27/1.38
% 3.27/1.38 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.27/1.38
% 3.27/1.38 % ------ Preprocessing... sup_sim: 16 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 %
% 3.27/1.38
% 3.27/1.38 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 3.27/1.38 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.27/1.38
% 3.27/1.38 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 3.27/1.38 % ------ Proving...
% 3.27/1.38 % ------ Problem Properties
% 3.27/1.38
% 3.27/1.38 %
% 3.27/1.38 % clauses 12
% 3.27/1.38 % conjectures 0
% 3.27/1.38 % EPR 1
% 3.27/1.38 % Horn 12
% 3.27/1.38 % unary 12
% 3.27/1.38 % binary 0
% 3.27/1.38 % lits 12
% 3.27/1.38 % lits eq 12
% 3.27/1.38 % fd_pure 0
% 3.27/1.38 % fd_pseudo 0
% 3.27/1.38 % fd_cond 0
% 3.27/1.38 % fd_pseudo_cond 0
% 3.27/1.38 % AC symbols 1
% 3.27/1.38
% 3.27/1.38 % ------ Schedule UEQ
% 3.27/1.38
% 3.27/1.38 % ------ Option_UEQ Time Limit: 10.
% 3.27/1.38
% 3.27/1.38
% 3.27/1.38 % ------
% 3.27/1.38 % Current options:
% 3.27/1.38 % ------
% 3.27/1.38
% 3.27/1.38
% 3.27/1.38 %
% 3.27/1.38
% 3.27/1.38 % ------ Proving...
% 3.27/1.38 %
% 3.27/1.38
% 3.27/1.38 % SZS status Unsatisfiable for theBenchmark.p
% 3.27/1.38
% 3.27/1.38 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.27/1.38
% 3.27/1.38
%------------------------------------------------------------------------------